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      1 /* ------------------------------------------------------------------ */
      2 /* Decimal Number arithmetic module                                   */
      3 /* ------------------------------------------------------------------ */
      4 /* Copyright (c) IBM Corporation, 2000-2010.  All rights reserved.    */
      5 /*                                                                    */
      6 /* This software is made available under the terms of the             */
      7 /* ICU License -- ICU 1.8.1 and later.                                */
      8 /*                                                                    */
      9 /* The description and User's Guide ("The decNumber C Library") for   */
     10 /* this software is called decNumber.pdf.  This document is           */
     11 /* available, together with arithmetic and format specifications,     */
     12 /* testcases, and Web links, on the General Decimal Arithmetic page.  */
     13 /*                                                                    */
     14 /* Please send comments, suggestions, and corrections to the author:  */
     15 /*   mfc (at) uk.ibm.com                                                   */
     16 /*   Mike Cowlishaw, IBM Fellow                                       */
     17 /*   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         */
     18 /* ------------------------------------------------------------------ */
     19 
     20 /* Modified version, for use from within ICU.
     21  *    Renamed public functions, to avoid an unwanted export of the
     22  *    standard names from the ICU library.
     23  *
     24  *    Use ICU's uprv_malloc() and uprv_free()
     25  *
     26  *    Revert comment syntax to plain C
     27  *
     28  *    Remove a few compiler warnings.
     29  */
     30 
     31 /* This module comprises the routines for arbitrary-precision General */
     32 /* Decimal Arithmetic as defined in the specification which may be    */
     33 /* found on the General Decimal Arithmetic pages.  It implements both */
     34 /* the full ('extended') arithmetic and the simpler ('subset')        */
     35 /* arithmetic.                                                        */
     36 /*                                                                    */
     37 /* Usage notes:                                                       */
     38 /*                                                                    */
     39 /* 1. This code is ANSI C89 except:                                   */
     40 /*                                                                    */
     41 /*    a) C99 line comments (double forward slash) are used.  (Most C  */
     42 /*       compilers accept these.  If yours does not, a simple script  */
     43 /*       can be used to convert them to ANSI C comments.)             */
     44 /*                                                                    */
     45 /*    b) Types from C99 stdint.h are used.  If you do not have this   */
     46 /*       header file, see the User's Guide section of the decNumber   */
     47 /*       documentation; this lists the necessary definitions.         */
     48 /*                                                                    */
     49 /*    c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and       */
     50 /*       uint64_t types may be used.  To avoid these, set DECUSE64=0  */
     51 /*       and DECDPUN<=4 (see documentation).                          */
     52 /*                                                                    */
     53 /*    The code also conforms to C99 restrictions; in particular,      */
     54 /*    strict aliasing rules are observed.                             */
     55 /*                                                                    */
     56 /* 2. The decNumber format which this library uses is optimized for   */
     57 /*    efficient processing of relatively short numbers; in particular */
     58 /*    it allows the use of fixed sized structures and minimizes copy  */
     59 /*    and move operations.  It does, however, support arbitrary       */
     60 /*    precision (up to 999,999,999 digits) and arbitrary exponent     */
     61 /*    range (Emax in the range 0 through 999,999,999 and Emin in the  */
     62 /*    range -999,999,999 through 0).  Mathematical functions (for     */
     63 /*    example decNumberExp) as identified below are restricted more   */
     64 /*    tightly: digits, emax, and -emin in the context must be <=      */
     65 /*    DEC_MAX_MATH (999999), and their operand(s) must be within      */
     66 /*    these bounds.                                                   */
     67 /*                                                                    */
     68 /* 3. Logical functions are further restricted; their operands must   */
     69 /*    be finite, positive, have an exponent of zero, and all digits   */
     70 /*    must be either 0 or 1.  The result will only contain digits     */
     71 /*    which are 0 or 1 (and will have exponent=0 and a sign of 0).    */
     72 /*                                                                    */
     73 /* 4. Operands to operator functions are never modified unless they   */
     74 /*    are also specified to be the result number (which is always     */
     75 /*    permitted).  Other than that case, operands must not overlap.   */
     76 /*                                                                    */
     77 /* 5. Error handling: the type of the error is ORed into the status   */
     78 /*    flags in the current context (decContext structure).  The       */
     79 /*    SIGFPE signal is then raised if the corresponding trap-enabler  */
     80 /*    flag in the decContext is set (is 1).                           */
     81 /*                                                                    */
     82 /*    It is the responsibility of the caller to clear the status      */
     83 /*    flags as required.                                              */
     84 /*                                                                    */
     85 /*    The result of any routine which returns a number will always    */
     86 /*    be a valid number (which may be a special value, such as an     */
     87 /*    Infinity or NaN).                                               */
     88 /*                                                                    */
     89 /* 6. The decNumber format is not an exchangeable concrete            */
     90 /*    representation as it comprises fields which may be machine-     */
     91 /*    dependent (packed or unpacked, or special length, for example). */
     92 /*    Canonical conversions to and from strings are provided; other   */
     93 /*    conversions are available in separate modules.                  */
     94 /*                                                                    */
     95 /* 7. Normally, input operands are assumed to be valid.  Set DECCHECK */
     96 /*    to 1 for extended operand checking (including NULL operands).   */
     97 /*    Results are undefined if a badly-formed structure (or a NULL    */
     98 /*    pointer to a structure) is provided, though with DECCHECK       */
     99 /*    enabled the operator routines are protected against exceptions. */
    100 /*    (Except if the result pointer is NULL, which is unrecoverable.) */
    101 /*                                                                    */
    102 /*    However, the routines will never cause exceptions if they are   */
    103 /*    given well-formed operands, even if the value of the operands   */
    104 /*    is inappropriate for the operation and DECCHECK is not set.     */
    105 /*    (Except for SIGFPE, as and where documented.)                   */
    106 /*                                                                    */
    107 /* 8. Subset arithmetic is available only if DECSUBSET is set to 1.   */
    108 /* ------------------------------------------------------------------ */
    109 /* Implementation notes for maintenance of this module:               */
    110 /*                                                                    */
    111 /* 1. Storage leak protection:  Routines which use malloc are not     */
    112 /*    permitted to use return for fastpath or error exits (i.e.,      */
    113 /*    they follow strict structured programming conventions).         */
    114 /*    Instead they have a do{}while(0); construct surrounding the     */
    115 /*    code which is protected -- break may be used to exit this.      */
    116 /*    Other routines can safely use the return statement inline.      */
    117 /*                                                                    */
    118 /*    Storage leak accounting can be enabled using DECALLOC.          */
    119 /*                                                                    */
    120 /* 2. All loops use the for(;;) construct.  Any do construct does     */
    121 /*    not loop; it is for allocation protection as just described.    */
    122 /*                                                                    */
    123 /* 3. Setting status in the context must always be the very last      */
    124 /*    action in a routine, as non-0 status may raise a trap and hence */
    125 /*    the call to set status may not return (if the handler uses long */
    126 /*    jump).  Therefore all cleanup must be done first.  In general,  */
    127 /*    to achieve this status is accumulated and is only applied just  */
    128 /*    before return by calling decContextSetStatus (via decStatus).   */
    129 /*                                                                    */
    130 /*    Routines which allocate storage cannot, in general, use the     */
    131 /*    'top level' routines which could cause a non-returning          */
    132 /*    transfer of control.  The decXxxxOp routines are safe (do not   */
    133 /*    call decStatus even if traps are set in the context) and should */
    134 /*    be used instead (they are also a little faster).                */
    135 /*                                                                    */
    136 /* 4. Exponent checking is minimized by allowing the exponent to      */
    137 /*    grow outside its limits during calculations, provided that      */
    138 /*    the decFinalize function is called later.  Multiplication and   */
    139 /*    division, and intermediate calculations in exponentiation,      */
    140 /*    require more careful checks because of the risk of 31-bit       */
    141 /*    overflow (the most negative valid exponent is -1999999997, for  */
    142 /*    a 999999999-digit number with adjusted exponent of -999999999). */
    143 /*                                                                    */
    144 /* 5. Rounding is deferred until finalization of results, with any    */
    145 /*    'off to the right' data being represented as a single digit     */
    146 /*    residue (in the range -1 through 9).  This avoids any double-   */
    147 /*    rounding when more than one shortening takes place (for         */
    148 /*    example, when a result is subnormal).                           */
    149 /*                                                                    */
    150 /* 6. The digits count is allowed to rise to a multiple of DECDPUN    */
    151 /*    during many operations, so whole Units are handled and exact    */
    152 /*    accounting of digits is not needed.  The correct digits value   */
    153 /*    is found by decGetDigits, which accounts for leading zeros.     */
    154 /*    This must be called before any rounding if the number of digits */
    155 /*    is not known exactly.                                           */
    156 /*                                                                    */
    157 /* 7. The multiply-by-reciprocal 'trick' is used for partitioning     */
    158 /*    numbers up to four digits, using appropriate constants.  This   */
    159 /*    is not useful for longer numbers because overflow of 32 bits    */
    160 /*    would lead to 4 multiplies, which is almost as expensive as     */
    161 /*    a divide (unless a floating-point or 64-bit multiply is         */
    162 /*    assumed to be available).                                       */
    163 /*                                                                    */
    164 /* 8. Unusual abbreviations that may be used in the commentary:       */
    165 /*      lhs -- left hand side (operand, of an operation)              */
    166 /*      lsd -- least significant digit (of coefficient)               */
    167 /*      lsu -- least significant Unit (of coefficient)                */
    168 /*      msd -- most significant digit (of coefficient)                */
    169 /*      msi -- most significant item (in an array)                    */
    170 /*      msu -- most significant Unit (of coefficient)                 */
    171 /*      rhs -- right hand side (operand, of an operation)             */
    172 /*      +ve -- positive                                               */
    173 /*      -ve -- negative                                               */
    174 /*      **  -- raise to the power                                     */
    175 /* ------------------------------------------------------------------ */
    176 
    177 #include <stdlib.h>                /* for malloc, free, etc.  */
    178 #include <cmemory.h>               /* for uprv_malloc, etc., in ICU */
    179 /*  #include <stdio.h>   */        /* for printf [if needed]  */
    180 #include <string.h>                /* for strcpy  */
    181 #include <ctype.h>                 /* for lower  */
    182 #include "decNumber.h"             /* base number library  */
    183 #include "decNumberLocal.h"        /* decNumber local types, etc.  */
    184 
    185 /* Constants */
    186 /* Public lookup table used by the D2U macro  */
    187 const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
    188 
    189 #define DECVERB     1              /* set to 1 for verbose DECCHECK  */
    190 #define powers      DECPOWERS      /* old internal name  */
    191 
    192 /* Local constants  */
    193 #define DIVIDE      0x80           /* Divide operators  */
    194 #define REMAINDER   0x40           /* ..  */
    195 #define DIVIDEINT   0x20           /* ..  */
    196 #define REMNEAR     0x10           /* ..  */
    197 #define COMPARE     0x01           /* Compare operators  */
    198 #define COMPMAX     0x02           /* ..  */
    199 #define COMPMIN     0x03           /* ..  */
    200 #define COMPTOTAL   0x04           /* ..  */
    201 #define COMPNAN     0x05           /* .. [NaN processing]  */
    202 #define COMPSIG     0x06           /* .. [signaling COMPARE]  */
    203 #define COMPMAXMAG  0x07           /* ..  */
    204 #define COMPMINMAG  0x08           /* ..  */
    205 
    206 #define DEC_sNaN     0x40000000    /* local status: sNaN signal  */
    207 #define BADINT  (Int)0x80000000    /* most-negative Int; error indicator  */
    208 /* Next two indicate an integer >= 10**6, and its parity (bottom bit)  */
    209 #define BIGEVEN (Int)0x80000002
    210 #define BIGODD  (Int)0x80000003
    211 
    212 static Unit uarrone[1]={1};   /* Unit array of 1, used for incrementing  */
    213 
    214 /* Granularity-dependent code */
    215 #if DECDPUN<=4
    216   #define eInt  Int           /* extended integer  */
    217   #define ueInt uInt          /* unsigned extended integer  */
    218   /* Constant multipliers for divide-by-power-of five using reciprocal  */
    219   /* multiply, after removing powers of 2 by shifting, and final shift  */
    220   /* of 17 [we only need up to **4]  */
    221   static const uInt multies[]={131073, 26215, 5243, 1049, 210};
    222   /* QUOT10 -- macro to return the quotient of unit u divided by 10**n  */
    223   #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
    224 #else
    225   /* For DECDPUN>4 non-ANSI-89 64-bit types are needed.  */
    226   #if !DECUSE64
    227     #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
    228   #endif
    229   #define eInt  Long          /* extended integer  */
    230   #define ueInt uLong         /* unsigned extended integer  */
    231 #endif
    232 
    233 /* Local routines */
    234 static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
    235                               decContext *, uByte, uInt *);
    236 static Flag        decBiStr(const char *, const char *, const char *);
    237 static uInt        decCheckMath(const decNumber *, decContext *, uInt *);
    238 static void        decApplyRound(decNumber *, decContext *, Int, uInt *);
    239 static Int         decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
    240 static decNumber * decCompareOp(decNumber *, const decNumber *,
    241                               const decNumber *, decContext *,
    242                               Flag, uInt *);
    243 static void        decCopyFit(decNumber *, const decNumber *, decContext *,
    244                               Int *, uInt *);
    245 static decNumber * decDecap(decNumber *, Int);
    246 static decNumber * decDivideOp(decNumber *, const decNumber *,
    247                               const decNumber *, decContext *, Flag, uInt *);
    248 static decNumber * decExpOp(decNumber *, const decNumber *,
    249                               decContext *, uInt *);
    250 static void        decFinalize(decNumber *, decContext *, Int *, uInt *);
    251 static Int         decGetDigits(Unit *, Int);
    252 static Int         decGetInt(const decNumber *);
    253 static decNumber * decLnOp(decNumber *, const decNumber *,
    254                               decContext *, uInt *);
    255 static decNumber * decMultiplyOp(decNumber *, const decNumber *,
    256                               const decNumber *, decContext *,
    257                               uInt *);
    258 static decNumber * decNaNs(decNumber *, const decNumber *,
    259                               const decNumber *, decContext *, uInt *);
    260 static decNumber * decQuantizeOp(decNumber *, const decNumber *,
    261                               const decNumber *, decContext *, Flag,
    262                               uInt *);
    263 static void        decReverse(Unit *, Unit *);
    264 static void        decSetCoeff(decNumber *, decContext *, const Unit *,
    265                               Int, Int *, uInt *);
    266 static void        decSetMaxValue(decNumber *, decContext *);
    267 static void        decSetOverflow(decNumber *, decContext *, uInt *);
    268 static void        decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
    269 static Int         decShiftToLeast(Unit *, Int, Int);
    270 static Int         decShiftToMost(Unit *, Int, Int);
    271 static void        decStatus(decNumber *, uInt, decContext *);
    272 static void        decToString(const decNumber *, char[], Flag);
    273 static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
    274 static Int         decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
    275                               Unit *, Int);
    276 static Int         decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
    277 
    278 #if !DECSUBSET
    279 /* decFinish == decFinalize when no subset arithmetic needed */
    280 #define decFinish(a,b,c,d) decFinalize(a,b,c,d)
    281 #else
    282 static void        decFinish(decNumber *, decContext *, Int *, uInt *);
    283 static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
    284 #endif
    285 
    286 /* Local macros */
    287 /* masked special-values bits  */
    288 #define SPECIALARG  (rhs->bits & DECSPECIAL)
    289 #define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
    290 
    291 /* For use in ICU */
    292 #define malloc(a) uprv_malloc(a)
    293 #define free(a) uprv_free(a)
    294 
    295 /* Diagnostic macros, etc. */
    296 #if DECALLOC
    297 /* Handle malloc/free accounting.  If enabled, our accountable routines  */
    298 /* are used; otherwise the code just goes straight to the system malloc  */
    299 /* and free routines.  */
    300 #define malloc(a) decMalloc(a)
    301 #define free(a) decFree(a)
    302 #define DECFENCE 0x5a              /* corruption detector  */
    303 /* 'Our' malloc and free:  */
    304 static void *decMalloc(size_t);
    305 static void  decFree(void *);
    306 uInt decAllocBytes=0;              /* count of bytes allocated  */
    307 /* Note that DECALLOC code only checks for storage buffer overflow.  */
    308 /* To check for memory leaks, the decAllocBytes variable must be  */
    309 /* checked to be 0 at appropriate times (e.g., after the test  */
    310 /* harness completes a set of tests).  This checking may be unreliable  */
    311 /* if the testing is done in a multi-thread environment.  */
    312 #endif
    313 
    314 #if DECCHECK
    315 /* Optional checking routines.  Enabling these means that decNumber  */
    316 /* and decContext operands to operator routines are checked for  */
    317 /* correctness.  This roughly doubles the execution time of the  */
    318 /* fastest routines (and adds 600+ bytes), so should not normally be  */
    319 /* used in 'production'.  */
    320 /* decCheckInexact is used to check that inexact results have a full  */
    321 /* complement of digits (where appropriate -- this is not the case  */
    322 /* for Quantize, for example)  */
    323 #define DECUNRESU ((decNumber *)(void *)0xffffffff)
    324 #define DECUNUSED ((const decNumber *)(void *)0xffffffff)
    325 #define DECUNCONT ((decContext *)(void *)(0xffffffff))
    326 static Flag decCheckOperands(decNumber *, const decNumber *,
    327                              const decNumber *, decContext *);
    328 static Flag decCheckNumber(const decNumber *);
    329 static void decCheckInexact(const decNumber *, decContext *);
    330 #endif
    331 
    332 #if DECTRACE || DECCHECK
    333 /* Optional trace/debugging routines (may or may not be used)  */
    334 void decNumberShow(const decNumber *);  /* displays the components of a number  */
    335 static void decDumpAr(char, const Unit *, Int);
    336 #endif
    337 
    338 /* ================================================================== */
    339 /* Conversions                                                        */
    340 /* ================================================================== */
    341 
    342 /* ------------------------------------------------------------------ */
    343 /* from-int32 -- conversion from Int or uInt                          */
    344 /*                                                                    */
    345 /*  dn is the decNumber to receive the integer                        */
    346 /*  in or uin is the integer to be converted                          */
    347 /*  returns dn                                                        */
    348 /*                                                                    */
    349 /* No error is possible.                                              */
    350 /* ------------------------------------------------------------------ */
    351 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromInt32(decNumber *dn, Int in) {
    352   uInt unsig;
    353   if (in>=0) unsig=in;
    354    else {                               /* negative (possibly BADINT)  */
    355     if (in==BADINT) unsig=(uInt)1073741824*2; /* special case  */
    356      else unsig=-in;                    /* invert  */
    357     }
    358   /* in is now positive  */
    359   uprv_decNumberFromUInt32(dn, unsig);
    360   if (in<0) dn->bits=DECNEG;            /* sign needed  */
    361   return dn;
    362   } /* decNumberFromInt32  */
    363 
    364 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromUInt32(decNumber *dn, uInt uin) {
    365   Unit *up;                             /* work pointer  */
    366   uprv_decNumberZero(dn);                    /* clean  */
    367   if (uin==0) return dn;                /* [or decGetDigits bad call]  */
    368   for (up=dn->lsu; uin>0; up++) {
    369     *up=(Unit)(uin%(DECDPUNMAX+1));
    370     uin=uin/(DECDPUNMAX+1);
    371     }
    372   dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
    373   return dn;
    374   } /* decNumberFromUInt32  */
    375 
    376 /* ------------------------------------------------------------------ */
    377 /* to-int32 -- conversion to Int or uInt                              */
    378 /*                                                                    */
    379 /*  dn is the decNumber to convert                                    */
    380 /*  set is the context for reporting errors                           */
    381 /*  returns the converted decNumber, or 0 if Invalid is set           */
    382 /*                                                                    */
    383 /* Invalid is set if the decNumber does not have exponent==0 or if    */
    384 /* it is a NaN, Infinite, or out-of-range.                            */
    385 /* ------------------------------------------------------------------ */
    386 U_CAPI Int U_EXPORT2 uprv_decNumberToInt32(const decNumber *dn, decContext *set) {
    387   #if DECCHECK
    388   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
    389   #endif
    390 
    391   /* special or too many digits, or bad exponent  */
    392   if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad  */
    393    else { /* is a finite integer with 10 or fewer digits  */
    394     Int d;                         /* work  */
    395     const Unit *up;                /* ..  */
    396     uInt hi=0, lo;                 /* ..  */
    397     up=dn->lsu;                    /* -> lsu  */
    398     lo=*up;                        /* get 1 to 9 digits  */
    399     #if DECDPUN>1                  /* split to higher  */
    400       hi=lo/10;
    401       lo=lo%10;
    402     #endif
    403     up++;
    404     /* collect remaining Units, if any, into hi  */
    405     for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
    406     /* now low has the lsd, hi the remainder  */
    407     if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range?  */
    408       /* most-negative is a reprieve  */
    409       if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
    410       /* bad -- drop through  */
    411       }
    412      else { /* in-range always  */
    413       Int i=X10(hi)+lo;
    414       if (dn->bits&DECNEG) return -i;
    415       return i;
    416       }
    417     } /* integer  */
    418   uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return]  */
    419   return 0;
    420   } /* decNumberToInt32  */
    421 
    422 U_CAPI uInt U_EXPORT2 uprv_decNumberToUInt32(const decNumber *dn, decContext *set) {
    423   #if DECCHECK
    424   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
    425   #endif
    426   /* special or too many digits, or bad exponent, or negative (<0)  */
    427   if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
    428     || (dn->bits&DECNEG && !ISZERO(dn)));                   /* bad  */
    429    else { /* is a finite integer with 10 or fewer digits  */
    430     Int d;                         /* work  */
    431     const Unit *up;                /* ..  */
    432     uInt hi=0, lo;                 /* ..  */
    433     up=dn->lsu;                    /* -> lsu  */
    434     lo=*up;                        /* get 1 to 9 digits  */
    435     #if DECDPUN>1                  /* split to higher  */
    436       hi=lo/10;
    437       lo=lo%10;
    438     #endif
    439     up++;
    440     /* collect remaining Units, if any, into hi  */
    441     for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
    442 
    443     /* now low has the lsd, hi the remainder  */
    444     if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible  */
    445      else return X10(hi)+lo;
    446     } /* integer  */
    447   uprv_decContextSetStatus(set, DEC_Invalid_operation); /* [may not return]  */
    448   return 0;
    449   } /* decNumberToUInt32  */
    450 
    451 /* ------------------------------------------------------------------ */
    452 /* to-scientific-string -- conversion to numeric string               */
    453 /* to-engineering-string -- conversion to numeric string              */
    454 /*                                                                    */
    455 /*   decNumberToString(dn, string);                                   */
    456 /*   decNumberToEngString(dn, string);                                */
    457 /*                                                                    */
    458 /*  dn is the decNumber to convert                                    */
    459 /*  string is the string where the result will be laid out            */
    460 /*                                                                    */
    461 /*  string must be at least dn->digits+14 characters long             */
    462 /*                                                                    */
    463 /*  No error is possible, and no status can be set.                   */
    464 /* ------------------------------------------------------------------ */
    465 U_CAPI char * U_EXPORT2 uprv_decNumberToString(const decNumber *dn, char *string){
    466   decToString(dn, string, 0);
    467   return string;
    468   } /* DecNumberToString  */
    469 
    470 U_CAPI char * U_EXPORT2 uprv_decNumberToEngString(const decNumber *dn, char *string){
    471   decToString(dn, string, 1);
    472   return string;
    473   } /* DecNumberToEngString  */
    474 
    475 /* ------------------------------------------------------------------ */
    476 /* to-number -- conversion from numeric string                        */
    477 /*                                                                    */
    478 /* decNumberFromString -- convert string to decNumber                 */
    479 /*   dn        -- the number structure to fill                        */
    480 /*   chars[]   -- the string to convert ('\0' terminated)             */
    481 /*   set       -- the context used for processing any error,          */
    482 /*                determining the maximum precision available         */
    483 /*                (set.digits), determining the maximum and minimum   */
    484 /*                exponent (set.emax and set.emin), determining if    */
    485 /*                extended values are allowed, and checking the       */
    486 /*                rounding mode if overflow occurs or rounding is     */
    487 /*                needed.                                             */
    488 /*                                                                    */
    489 /* The length of the coefficient and the size of the exponent are     */
    490 /* checked by this routine, so the correct error (Underflow or        */
    491 /* Overflow) can be reported or rounding applied, as necessary.       */
    492 /*                                                                    */
    493 /* If bad syntax is detected, the result will be a quiet NaN.         */
    494 /* ------------------------------------------------------------------ */
    495 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFromString(decNumber *dn, const char chars[],
    496                                 decContext *set) {
    497   Int   exponent=0;                /* working exponent [assume 0]  */
    498   uByte bits=0;                    /* working flags [assume +ve]  */
    499   Unit  *res;                      /* where result will be built  */
    500   Unit  resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary  */
    501                                    /* [+9 allows for ln() constants]  */
    502   Unit  *allocres=NULL;            /* -> allocated result, iff allocated  */
    503   Int   d=0;                       /* count of digits found in decimal part  */
    504   const char *dotchar=NULL;        /* where dot was found  */
    505   const char *cfirst=chars;        /* -> first character of decimal part  */
    506   const char *last=NULL;           /* -> last digit of decimal part  */
    507   const char *c;                   /* work  */
    508   Unit  *up;                       /* ..  */
    509   #if DECDPUN>1
    510   Int   cut, out;                  /* ..  */
    511   #endif
    512   Int   residue;                   /* rounding residue  */
    513   uInt  status=0;                  /* error code  */
    514 
    515   #if DECCHECK
    516   if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
    517     return uprv_decNumberZero(dn);
    518   #endif
    519 
    520   do {                             /* status & malloc protection  */
    521     for (c=chars;; c++) {          /* -> input character  */
    522       if (*c>='0' && *c<='9') {    /* test for Arabic digit  */
    523         last=c;
    524         d++;                       /* count of real digits  */
    525         continue;                  /* still in decimal part  */
    526         }
    527       if (*c=='.' && dotchar==NULL) { /* first '.'  */
    528         dotchar=c;                 /* record offset into decimal part  */
    529         if (c==cfirst) cfirst++;   /* first digit must follow  */
    530         continue;}
    531       if (c==chars) {              /* first in string...  */
    532         if (*c=='-') {             /* valid - sign  */
    533           cfirst++;
    534           bits=DECNEG;
    535           continue;}
    536         if (*c=='+') {             /* valid + sign  */
    537           cfirst++;
    538           continue;}
    539         }
    540       /* *c is not a digit, or a valid +, -, or '.'  */
    541       break;
    542       } /* c  */
    543 
    544     if (last==NULL) {              /* no digits yet  */
    545       status=DEC_Conversion_syntax;/* assume the worst  */
    546       if (*c=='\0') break;         /* and no more to come...  */
    547       #if DECSUBSET
    548       /* if subset then infinities and NaNs are not allowed  */
    549       if (!set->extended) break;   /* hopeless  */
    550       #endif
    551       /* Infinities and NaNs are possible, here  */
    552       if (dotchar!=NULL) break;    /* .. unless had a dot  */
    553       uprv_decNumberZero(dn);           /* be optimistic  */
    554       if (decBiStr(c, "infinity", "INFINITY")
    555        || decBiStr(c, "inf", "INF")) {
    556         dn->bits=bits | DECINF;
    557         status=0;                  /* is OK  */
    558         break; /* all done  */
    559         }
    560       /* a NaN expected  */
    561       /* 2003.09.10 NaNs are now permitted to have a sign  */
    562       dn->bits=bits | DECNAN;      /* assume simple NaN  */
    563       if (*c=='s' || *c=='S') {    /* looks like an sNaN  */
    564         c++;
    565         dn->bits=bits | DECSNAN;
    566         }
    567       if (*c!='n' && *c!='N') break;    /* check caseless "NaN"  */
    568       c++;
    569       if (*c!='a' && *c!='A') break;    /* ..  */
    570       c++;
    571       if (*c!='n' && *c!='N') break;    /* ..  */
    572       c++;
    573       /* now either nothing, or nnnn payload, expected  */
    574       /* -> start of integer and skip leading 0s [including plain 0]  */
    575       for (cfirst=c; *cfirst=='0';) cfirst++;
    576       if (*cfirst=='\0') {         /* "NaN" or "sNaN", maybe with all 0s  */
    577         status=0;                  /* it's good  */
    578         break;                     /* ..  */
    579         }
    580       /* something other than 0s; setup last and d as usual [no dots]  */
    581       for (c=cfirst;; c++, d++) {
    582         if (*c<'0' || *c>'9') break; /* test for Arabic digit  */
    583         last=c;
    584         }
    585       if (*c!='\0') break;         /* not all digits  */
    586       if (d>set->digits-1) {
    587         /* [NB: payload in a decNumber can be full length unless  */
    588         /* clamped, in which case can only be digits-1]  */
    589         if (set->clamp) break;
    590         if (d>set->digits) break;
    591         } /* too many digits?  */
    592       /* good; drop through to convert the integer to coefficient  */
    593       status=0;                    /* syntax is OK  */
    594       bits=dn->bits;               /* for copy-back  */
    595       } /* last==NULL  */
    596 
    597      else if (*c!='\0') {          /* more to process...  */
    598       /* had some digits; exponent is only valid sequence now  */
    599       Flag nege;                   /* 1=negative exponent  */
    600       const char *firstexp;        /* -> first significant exponent digit  */
    601       status=DEC_Conversion_syntax;/* assume the worst  */
    602       if (*c!='e' && *c!='E') break;
    603       /* Found 'e' or 'E' -- now process explicit exponent */
    604       /* 1998.07.11: sign no longer required  */
    605       nege=0;
    606       c++;                         /* to (possible) sign  */
    607       if (*c=='-') {nege=1; c++;}
    608        else if (*c=='+') c++;
    609       if (*c=='\0') break;
    610 
    611       for (; *c=='0' && *(c+1)!='\0';) c++;  /* strip insignificant zeros  */
    612       firstexp=c;                            /* save exponent digit place  */
    613       for (; ;c++) {
    614         if (*c<'0' || *c>'9') break;         /* not a digit  */
    615         exponent=X10(exponent)+(Int)*c-(Int)'0';
    616         } /* c  */
    617       /* if not now on a '\0', *c must not be a digit  */
    618       if (*c!='\0') break;
    619 
    620       /* (this next test must be after the syntax checks)  */
    621       /* if it was too long the exponent may have wrapped, so check  */
    622       /* carefully and set it to a certain overflow if wrap possible  */
    623       if (c>=firstexp+9+1) {
    624         if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
    625         /* [up to 1999999999 is OK, for example 1E-1000000998]  */
    626         }
    627       if (nege) exponent=-exponent;     /* was negative  */
    628       status=0;                         /* is OK  */
    629       } /* stuff after digits  */
    630 
    631     /* Here when whole string has been inspected; syntax is good  */
    632     /* cfirst->first digit (never dot), last->last digit (ditto)  */
    633 
    634     /* strip leading zeros/dot [leave final 0 if all 0's]  */
    635     if (*cfirst=='0') {                 /* [cfirst has stepped over .]  */
    636       for (c=cfirst; c<last; c++, cfirst++) {
    637         if (*c=='.') continue;          /* ignore dots  */
    638         if (*c!='0') break;             /* non-zero found  */
    639         d--;                            /* 0 stripped  */
    640         } /* c  */
    641       #if DECSUBSET
    642       /* make a rapid exit for easy zeros if !extended  */
    643       if (*cfirst=='0' && !set->extended) {
    644         uprv_decNumberZero(dn);              /* clean result  */
    645         break;                          /* [could be return]  */
    646         }
    647       #endif
    648       } /* at least one leading 0  */
    649 
    650     /* Handle decimal point...  */
    651     if (dotchar!=NULL && dotchar<last)  /* non-trailing '.' found?  */
    652       exponent-=(last-dotchar);         /* adjust exponent  */
    653     /* [we can now ignore the .]  */
    654 
    655     /* OK, the digits string is good.  Assemble in the decNumber, or in  */
    656     /* a temporary units array if rounding is needed  */
    657     if (d<=set->digits) res=dn->lsu;    /* fits into supplied decNumber  */
    658      else {                             /* rounding needed  */
    659       Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed  */
    660       res=resbuff;                      /* assume use local buffer  */
    661       if (needbytes>(Int)sizeof(resbuff)) { /* too big for local  */
    662         allocres=(Unit *)malloc(needbytes);
    663         if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
    664         res=allocres;
    665         }
    666       }
    667     /* res now -> number lsu, buffer, or allocated storage for Unit array  */
    668 
    669     /* Place the coefficient into the selected Unit array  */
    670     /* [this is often 70% of the cost of this function when DECDPUN>1]  */
    671     #if DECDPUN>1
    672     out=0;                         /* accumulator  */
    673     up=res+D2U(d)-1;               /* -> msu  */
    674     cut=d-(up-res)*DECDPUN;        /* digits in top unit  */
    675     for (c=cfirst;; c++) {         /* along the digits  */
    676       if (*c=='.') continue;       /* ignore '.' [don't decrement cut]  */
    677       out=X10(out)+(Int)*c-(Int)'0';
    678       if (c==last) break;          /* done [never get to trailing '.']  */
    679       cut--;
    680       if (cut>0) continue;         /* more for this unit  */
    681       *up=(Unit)out;               /* write unit  */
    682       up--;                        /* prepare for unit below..  */
    683       cut=DECDPUN;                 /* ..  */
    684       out=0;                       /* ..  */
    685       } /* c  */
    686     *up=(Unit)out;                 /* write lsu  */
    687 
    688     #else
    689     /* DECDPUN==1  */
    690     up=res;                        /* -> lsu  */
    691     for (c=last; c>=cfirst; c--) { /* over each character, from least  */
    692       if (*c=='.') continue;       /* ignore . [don't step up]  */
    693       *up=(Unit)((Int)*c-(Int)'0');
    694       up++;
    695       } /* c  */
    696     #endif
    697 
    698     dn->bits=bits;
    699     dn->exponent=exponent;
    700     dn->digits=d;
    701 
    702     /* if not in number (too long) shorten into the number  */
    703     if (d>set->digits) {
    704       residue=0;
    705       decSetCoeff(dn, set, res, d, &residue, &status);
    706       /* always check for overflow or subnormal and round as needed  */
    707       decFinalize(dn, set, &residue, &status);
    708       }
    709      else { /* no rounding, but may still have overflow or subnormal  */
    710       /* [these tests are just for performance; finalize repeats them]  */
    711       if ((dn->exponent-1<set->emin-dn->digits)
    712        || (dn->exponent-1>set->emax-set->digits)) {
    713         residue=0;
    714         decFinalize(dn, set, &residue, &status);
    715         }
    716       }
    717     /* decNumberShow(dn);  */
    718     } while(0);                         /* [for break]  */
    719 
    720   if (allocres!=NULL) free(allocres);   /* drop any storage used  */
    721   if (status!=0) decStatus(dn, status, set);
    722   return dn;
    723   } /* decNumberFromString */
    724 
    725 /* ================================================================== */
    726 /* Operators                                                          */
    727 /* ================================================================== */
    728 
    729 /* ------------------------------------------------------------------ */
    730 /* decNumberAbs -- absolute value operator                            */
    731 /*                                                                    */
    732 /*   This computes C = abs(A)                                         */
    733 /*                                                                    */
    734 /*   res is C, the result.  C may be A                                */
    735 /*   rhs is A                                                         */
    736 /*   set is the context                                               */
    737 /*                                                                    */
    738 /* See also decNumberCopyAbs for a quiet bitwise version of this.     */
    739 /* C must have space for set->digits digits.                          */
    740 /* ------------------------------------------------------------------ */
    741 /* This has the same effect as decNumberPlus unless A is negative,    */
    742 /* in which case it has the same effect as decNumberMinus.            */
    743 /* ------------------------------------------------------------------ */
    744 U_CAPI decNumber * U_EXPORT2 uprv_decNumberAbs(decNumber *res, const decNumber *rhs,
    745                          decContext *set) {
    746   decNumber dzero;                      /* for 0  */
    747   uInt status=0;                        /* accumulator  */
    748 
    749   #if DECCHECK
    750   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
    751   #endif
    752 
    753   uprv_decNumberZero(&dzero);                /* set 0  */
    754   dzero.exponent=rhs->exponent;         /* [no coefficient expansion]  */
    755   decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
    756   if (status!=0) decStatus(res, status, set);
    757   #if DECCHECK
    758   decCheckInexact(res, set);
    759   #endif
    760   return res;
    761   } /* decNumberAbs  */
    762 
    763 /* ------------------------------------------------------------------ */
    764 /* decNumberAdd -- add two Numbers                                    */
    765 /*                                                                    */
    766 /*   This computes C = A + B                                          */
    767 /*                                                                    */
    768 /*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
    769 /*   lhs is A                                                         */
    770 /*   rhs is B                                                         */
    771 /*   set is the context                                               */
    772 /*                                                                    */
    773 /* C must have space for set->digits digits.                          */
    774 /* ------------------------------------------------------------------ */
    775 /* This just calls the routine shared with Subtract                   */
    776 U_CAPI decNumber * U_EXPORT2 uprv_decNumberAdd(decNumber *res, const decNumber *lhs,
    777                          const decNumber *rhs, decContext *set) {
    778   uInt status=0;                        /* accumulator  */
    779   decAddOp(res, lhs, rhs, set, 0, &status);
    780   if (status!=0) decStatus(res, status, set);
    781   #if DECCHECK
    782   decCheckInexact(res, set);
    783   #endif
    784   return res;
    785   } /* decNumberAdd  */
    786 
    787 /* ------------------------------------------------------------------ */
    788 /* decNumberAnd -- AND two Numbers, digitwise                         */
    789 /*                                                                    */
    790 /*   This computes C = A & B                                          */
    791 /*                                                                    */
    792 /*   res is C, the result.  C may be A and/or B (e.g., X=X&X)         */
    793 /*   lhs is A                                                         */
    794 /*   rhs is B                                                         */
    795 /*   set is the context (used for result length and error report)     */
    796 /*                                                                    */
    797 /* C must have space for set->digits digits.                          */
    798 /*                                                                    */
    799 /* Logical function restrictions apply (see above); a NaN is          */
    800 /* returned with Invalid_operation if a restriction is violated.      */
    801 /* ------------------------------------------------------------------ */
    802 U_CAPI decNumber * U_EXPORT2 uprv_decNumberAnd(decNumber *res, const decNumber *lhs,
    803                          const decNumber *rhs, decContext *set) {
    804   const Unit *ua, *ub;                  /* -> operands  */
    805   const Unit *msua, *msub;              /* -> operand msus  */
    806   Unit *uc,  *msuc;                     /* -> result and its msu  */
    807   Int   msudigs;                        /* digits in res msu  */
    808   #if DECCHECK
    809   if (decCheckOperands(res, lhs, rhs, set)) return res;
    810   #endif
    811 
    812   if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
    813    || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
    814     decStatus(res, DEC_Invalid_operation, set);
    815     return res;
    816     }
    817 
    818   /* operands are valid  */
    819   ua=lhs->lsu;                          /* bottom-up  */
    820   ub=rhs->lsu;                          /* ..  */
    821   uc=res->lsu;                          /* ..  */
    822   msua=ua+D2U(lhs->digits)-1;           /* -> msu of lhs  */
    823   msub=ub+D2U(rhs->digits)-1;           /* -> msu of rhs  */
    824   msuc=uc+D2U(set->digits)-1;           /* -> msu of result  */
    825   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder]  */
    826   for (; uc<=msuc; ua++, ub++, uc++) {  /* Unit loop  */
    827     Unit a, b;                          /* extract units  */
    828     if (ua>msua) a=0;
    829      else a=*ua;
    830     if (ub>msub) b=0;
    831      else b=*ub;
    832     *uc=0;                              /* can now write back  */
    833     if (a|b) {                          /* maybe 1 bits to examine  */
    834       Int i, j;
    835       *uc=0;                            /* can now write back  */
    836       /* This loop could be unrolled and/or use BIN2BCD tables  */
    837       for (i=0; i<DECDPUN; i++) {
    838         if (a&b&1) *uc=*uc+(Unit)powers[i];  /* effect AND  */
    839         j=a%10;
    840         a=a/10;
    841         j|=b%10;
    842         b=b/10;
    843         if (j>1) {
    844           decStatus(res, DEC_Invalid_operation, set);
    845           return res;
    846           }
    847         if (uc==msuc && i==msudigs-1) break; /* just did final digit  */
    848         } /* each digit  */
    849       } /* both OK  */
    850     } /* each unit  */
    851   /* [here uc-1 is the msu of the result]  */
    852   res->digits=decGetDigits(res->lsu, uc-res->lsu);
    853   res->exponent=0;                      /* integer  */
    854   res->bits=0;                          /* sign=0  */
    855   return res;  /* [no status to set]  */
    856   } /* decNumberAnd  */
    857 
    858 /* ------------------------------------------------------------------ */
    859 /* decNumberCompare -- compare two Numbers                            */
    860 /*                                                                    */
    861 /*   This computes C = A ? B                                          */
    862 /*                                                                    */
    863 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
    864 /*   lhs is A                                                         */
    865 /*   rhs is B                                                         */
    866 /*   set is the context                                               */
    867 /*                                                                    */
    868 /* C must have space for one digit (or NaN).                          */
    869 /* ------------------------------------------------------------------ */
    870 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompare(decNumber *res, const decNumber *lhs,
    871                              const decNumber *rhs, decContext *set) {
    872   uInt status=0;                        /* accumulator  */
    873   decCompareOp(res, lhs, rhs, set, COMPARE, &status);
    874   if (status!=0) decStatus(res, status, set);
    875   return res;
    876   } /* decNumberCompare  */
    877 
    878 /* ------------------------------------------------------------------ */
    879 /* decNumberCompareSignal -- compare, signalling on all NaNs          */
    880 /*                                                                    */
    881 /*   This computes C = A ? B                                          */
    882 /*                                                                    */
    883 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
    884 /*   lhs is A                                                         */
    885 /*   rhs is B                                                         */
    886 /*   set is the context                                               */
    887 /*                                                                    */
    888 /* C must have space for one digit (or NaN).                          */
    889 /* ------------------------------------------------------------------ */
    890 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareSignal(decNumber *res, const decNumber *lhs,
    891                                    const decNumber *rhs, decContext *set) {
    892   uInt status=0;                        /* accumulator  */
    893   decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
    894   if (status!=0) decStatus(res, status, set);
    895   return res;
    896   } /* decNumberCompareSignal  */
    897 
    898 /* ------------------------------------------------------------------ */
    899 /* decNumberCompareTotal -- compare two Numbers, using total ordering */
    900 /*                                                                    */
    901 /*   This computes C = A ? B, under total ordering                    */
    902 /*                                                                    */
    903 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
    904 /*   lhs is A                                                         */
    905 /*   rhs is B                                                         */
    906 /*   set is the context                                               */
    907 /*                                                                    */
    908 /* C must have space for one digit; the result will always be one of  */
    909 /* -1, 0, or 1.                                                       */
    910 /* ------------------------------------------------------------------ */
    911 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotal(decNumber *res, const decNumber *lhs,
    912                                   const decNumber *rhs, decContext *set) {
    913   uInt status=0;                        /* accumulator  */
    914   decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
    915   if (status!=0) decStatus(res, status, set);
    916   return res;
    917   } /* decNumberCompareTotal  */
    918 
    919 /* ------------------------------------------------------------------ */
    920 /* decNumberCompareTotalMag -- compare, total ordering of magnitudes  */
    921 /*                                                                    */
    922 /*   This computes C = |A| ? |B|, under total ordering                */
    923 /*                                                                    */
    924 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
    925 /*   lhs is A                                                         */
    926 /*   rhs is B                                                         */
    927 /*   set is the context                                               */
    928 /*                                                                    */
    929 /* C must have space for one digit; the result will always be one of  */
    930 /* -1, 0, or 1.                                                       */
    931 /* ------------------------------------------------------------------ */
    932 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
    933                                      const decNumber *rhs, decContext *set) {
    934   uInt status=0;                   /* accumulator  */
    935   uInt needbytes;                  /* for space calculations  */
    936   decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0  */
    937   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated  */
    938   decNumber bufb[D2N(DECBUFFER+1)];
    939   decNumber *allocbufb=NULL;       /* -> allocated bufb, iff allocated  */
    940   decNumber *a, *b;                /* temporary pointers  */
    941 
    942   #if DECCHECK
    943   if (decCheckOperands(res, lhs, rhs, set)) return res;
    944   #endif
    945 
    946   do {                                  /* protect allocated storage  */
    947     /* if either is negative, take a copy and absolute  */
    948     if (decNumberIsNegative(lhs)) {     /* lhs<0  */
    949       a=bufa;
    950       needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
    951       if (needbytes>sizeof(bufa)) {     /* need malloc space  */
    952         allocbufa=(decNumber *)malloc(needbytes);
    953         if (allocbufa==NULL) {          /* hopeless -- abandon  */
    954           status|=DEC_Insufficient_storage;
    955           break;}
    956         a=allocbufa;                    /* use the allocated space  */
    957         }
    958       uprv_decNumberCopy(a, lhs);            /* copy content  */
    959       a->bits&=~DECNEG;                 /* .. and clear the sign  */
    960       lhs=a;                            /* use copy from here on  */
    961       }
    962     if (decNumberIsNegative(rhs)) {     /* rhs<0  */
    963       b=bufb;
    964       needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
    965       if (needbytes>sizeof(bufb)) {     /* need malloc space  */
    966         allocbufb=(decNumber *)malloc(needbytes);
    967         if (allocbufb==NULL) {          /* hopeless -- abandon  */
    968           status|=DEC_Insufficient_storage;
    969           break;}
    970         b=allocbufb;                    /* use the allocated space  */
    971         }
    972       uprv_decNumberCopy(b, rhs);            /* copy content  */
    973       b->bits&=~DECNEG;                 /* .. and clear the sign  */
    974       rhs=b;                            /* use copy from here on  */
    975       }
    976     decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
    977     } while(0);                         /* end protected  */
    978 
    979   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used  */
    980   if (allocbufb!=NULL) free(allocbufb); /* ..  */
    981   if (status!=0) decStatus(res, status, set);
    982   return res;
    983   } /* decNumberCompareTotalMag  */
    984 
    985 /* ------------------------------------------------------------------ */
    986 /* decNumberDivide -- divide one number by another                    */
    987 /*                                                                    */
    988 /*   This computes C = A / B                                          */
    989 /*                                                                    */
    990 /*   res is C, the result.  C may be A and/or B (e.g., X=X/X)         */
    991 /*   lhs is A                                                         */
    992 /*   rhs is B                                                         */
    993 /*   set is the context                                               */
    994 /*                                                                    */
    995 /* C must have space for set->digits digits.                          */
    996 /* ------------------------------------------------------------------ */
    997 U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivide(decNumber *res, const decNumber *lhs,
    998                             const decNumber *rhs, decContext *set) {
    999   uInt status=0;                        /* accumulator  */
   1000   decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
   1001   if (status!=0) decStatus(res, status, set);
   1002   #if DECCHECK
   1003   decCheckInexact(res, set);
   1004   #endif
   1005   return res;
   1006   } /* decNumberDivide  */
   1007 
   1008 /* ------------------------------------------------------------------ */
   1009 /* decNumberDivideInteger -- divide and return integer quotient       */
   1010 /*                                                                    */
   1011 /*   This computes C = A # B, where # is the integer divide operator  */
   1012 /*                                                                    */
   1013 /*   res is C, the result.  C may be A and/or B (e.g., X=X#X)         */
   1014 /*   lhs is A                                                         */
   1015 /*   rhs is B                                                         */
   1016 /*   set is the context                                               */
   1017 /*                                                                    */
   1018 /* C must have space for set->digits digits.                          */
   1019 /* ------------------------------------------------------------------ */
   1020 U_CAPI decNumber * U_EXPORT2 uprv_decNumberDivideInteger(decNumber *res, const decNumber *lhs,
   1021                                    const decNumber *rhs, decContext *set) {
   1022   uInt status=0;                        /* accumulator  */
   1023   decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
   1024   if (status!=0) decStatus(res, status, set);
   1025   return res;
   1026   } /* decNumberDivideInteger  */
   1027 
   1028 /* ------------------------------------------------------------------ */
   1029 /* decNumberExp -- exponentiation                                     */
   1030 /*                                                                    */
   1031 /*   This computes C = exp(A)                                         */
   1032 /*                                                                    */
   1033 /*   res is C, the result.  C may be A                                */
   1034 /*   rhs is A                                                         */
   1035 /*   set is the context; note that rounding mode has no effect        */
   1036 /*                                                                    */
   1037 /* C must have space for set->digits digits.                          */
   1038 /*                                                                    */
   1039 /* Mathematical function restrictions apply (see above); a NaN is     */
   1040 /* returned with Invalid_operation if a restriction is violated.      */
   1041 /*                                                                    */
   1042 /* Finite results will always be full precision and Inexact, except   */
   1043 /* when A is a zero or -Infinity (giving 1 or 0 respectively).        */
   1044 /*                                                                    */
   1045 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
   1046 /* almost always be correctly rounded, but may be up to 1 ulp in      */
   1047 /* error in rare cases.                                               */
   1048 /* ------------------------------------------------------------------ */
   1049 /* This is a wrapper for decExpOp which can handle the slightly wider */
   1050 /* (double) range needed by Ln (which has to be able to calculate     */
   1051 /* exp(-a) where a can be the tiniest number (Ntiny).                 */
   1052 /* ------------------------------------------------------------------ */
   1053 U_CAPI decNumber * U_EXPORT2 uprv_decNumberExp(decNumber *res, const decNumber *rhs,
   1054                          decContext *set) {
   1055   uInt status=0;                        /* accumulator  */
   1056   #if DECSUBSET
   1057   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated  */
   1058   #endif
   1059 
   1060   #if DECCHECK
   1061   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1062   #endif
   1063 
   1064   /* Check restrictions; these restrictions ensure that if h=8 (see  */
   1065   /* decExpOp) then the result will either overflow or underflow to 0.  */
   1066   /* Other math functions restrict the input range, too, for inverses.  */
   1067   /* If not violated then carry out the operation.  */
   1068   if (!decCheckMath(rhs, set, &status)) do { /* protect allocation  */
   1069     #if DECSUBSET
   1070     if (!set->extended) {
   1071       /* reduce operand and set lostDigits status, as needed  */
   1072       if (rhs->digits>set->digits) {
   1073         allocrhs=decRoundOperand(rhs, set, &status);
   1074         if (allocrhs==NULL) break;
   1075         rhs=allocrhs;
   1076         }
   1077       }
   1078     #endif
   1079     decExpOp(res, rhs, set, &status);
   1080     } while(0);                         /* end protected  */
   1081 
   1082   #if DECSUBSET
   1083   if (allocrhs !=NULL) free(allocrhs);  /* drop any storage used  */
   1084   #endif
   1085   /* apply significant status  */
   1086   if (status!=0) decStatus(res, status, set);
   1087   #if DECCHECK
   1088   decCheckInexact(res, set);
   1089   #endif
   1090   return res;
   1091   } /* decNumberExp  */
   1092 
   1093 /* ------------------------------------------------------------------ */
   1094 /* decNumberFMA -- fused multiply add                                 */
   1095 /*                                                                    */
   1096 /*   This computes D = (A * B) + C with only one rounding             */
   1097 /*                                                                    */
   1098 /*   res is D, the result.  D may be A or B or C (e.g., X=FMA(X,X,X)) */
   1099 /*   lhs is A                                                         */
   1100 /*   rhs is B                                                         */
   1101 /*   fhs is C [far hand side]                                         */
   1102 /*   set is the context                                               */
   1103 /*                                                                    */
   1104 /* Mathematical function restrictions apply (see above); a NaN is     */
   1105 /* returned with Invalid_operation if a restriction is violated.      */
   1106 /*                                                                    */
   1107 /* C must have space for set->digits digits.                          */
   1108 /* ------------------------------------------------------------------ */
   1109 U_CAPI decNumber * U_EXPORT2 uprv_decNumberFMA(decNumber *res, const decNumber *lhs,
   1110                          const decNumber *rhs, const decNumber *fhs,
   1111                          decContext *set) {
   1112   uInt status=0;                   /* accumulator  */
   1113   decContext dcmul;                /* context for the multiplication  */
   1114   uInt needbytes;                  /* for space calculations  */
   1115   decNumber bufa[D2N(DECBUFFER*2+1)];
   1116   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated  */
   1117   decNumber *acc;                  /* accumulator pointer  */
   1118   decNumber dzero;                 /* work  */
   1119 
   1120   #if DECCHECK
   1121   if (decCheckOperands(res, lhs, rhs, set)) return res;
   1122   if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
   1123   #endif
   1124 
   1125   do {                                  /* protect allocated storage  */
   1126     #if DECSUBSET
   1127     if (!set->extended) {               /* [undefined if subset]  */
   1128       status|=DEC_Invalid_operation;
   1129       break;}
   1130     #endif
   1131     /* Check math restrictions [these ensure no overflow or underflow]  */
   1132     if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
   1133      || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
   1134      || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
   1135     /* set up context for multiply  */
   1136     dcmul=*set;
   1137     dcmul.digits=lhs->digits+rhs->digits; /* just enough  */
   1138     /* [The above may be an over-estimate for subset arithmetic, but that's OK]  */
   1139     dcmul.emax=DEC_MAX_EMAX;            /* effectively unbounded ..  */
   1140     dcmul.emin=DEC_MIN_EMIN;            /* [thanks to Math restrictions]  */
   1141     /* set up decNumber space to receive the result of the multiply  */
   1142     acc=bufa;                           /* may fit  */
   1143     needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
   1144     if (needbytes>sizeof(bufa)) {       /* need malloc space  */
   1145       allocbufa=(decNumber *)malloc(needbytes);
   1146       if (allocbufa==NULL) {            /* hopeless -- abandon  */
   1147         status|=DEC_Insufficient_storage;
   1148         break;}
   1149       acc=allocbufa;                    /* use the allocated space  */
   1150       }
   1151     /* multiply with extended range and necessary precision  */
   1152     /*printf("emin=%ld\n", dcmul.emin);  */
   1153     decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
   1154     /* Only Invalid operation (from sNaN or Inf * 0) is possible in  */
   1155     /* status; if either is seen than ignore fhs (in case it is  */
   1156     /* another sNaN) and set acc to NaN unless we had an sNaN  */
   1157     /* [decMultiplyOp leaves that to caller]  */
   1158     /* Note sNaN has to go through addOp to shorten payload if  */
   1159     /* necessary  */
   1160     if ((status&DEC_Invalid_operation)!=0) {
   1161       if (!(status&DEC_sNaN)) {         /* but be true invalid  */
   1162         uprv_decNumberZero(res);             /* acc not yet set  */
   1163         res->bits=DECNAN;
   1164         break;
   1165         }
   1166       uprv_decNumberZero(&dzero);            /* make 0 (any non-NaN would do)  */
   1167       fhs=&dzero;                       /* use that  */
   1168       }
   1169     #if DECCHECK
   1170      else { /* multiply was OK  */
   1171       if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
   1172       }
   1173     #endif
   1174     /* add the third operand and result -> res, and all is done  */
   1175     decAddOp(res, acc, fhs, set, 0, &status);
   1176     } while(0);                         /* end protected  */
   1177 
   1178   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used  */
   1179   if (status!=0) decStatus(res, status, set);
   1180   #if DECCHECK
   1181   decCheckInexact(res, set);
   1182   #endif
   1183   return res;
   1184   } /* decNumberFMA  */
   1185 
   1186 /* ------------------------------------------------------------------ */
   1187 /* decNumberInvert -- invert a Number, digitwise                      */
   1188 /*                                                                    */
   1189 /*   This computes C = ~A                                             */
   1190 /*                                                                    */
   1191 /*   res is C, the result.  C may be A (e.g., X=~X)                   */
   1192 /*   rhs is A                                                         */
   1193 /*   set is the context (used for result length and error report)     */
   1194 /*                                                                    */
   1195 /* C must have space for set->digits digits.                          */
   1196 /*                                                                    */
   1197 /* Logical function restrictions apply (see above); a NaN is          */
   1198 /* returned with Invalid_operation if a restriction is violated.      */
   1199 /* ------------------------------------------------------------------ */
   1200 U_CAPI decNumber * U_EXPORT2 uprv_decNumberInvert(decNumber *res, const decNumber *rhs,
   1201                             decContext *set) {
   1202   const Unit *ua, *msua;                /* -> operand and its msu  */
   1203   Unit  *uc, *msuc;                     /* -> result and its msu  */
   1204   Int   msudigs;                        /* digits in res msu  */
   1205   #if DECCHECK
   1206   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1207   #endif
   1208 
   1209   if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
   1210     decStatus(res, DEC_Invalid_operation, set);
   1211     return res;
   1212     }
   1213   /* operand is valid  */
   1214   ua=rhs->lsu;                          /* bottom-up  */
   1215   uc=res->lsu;                          /* ..  */
   1216   msua=ua+D2U(rhs->digits)-1;           /* -> msu of rhs  */
   1217   msuc=uc+D2U(set->digits)-1;           /* -> msu of result  */
   1218   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder]  */
   1219   for (; uc<=msuc; ua++, uc++) {        /* Unit loop  */
   1220     Unit a;                             /* extract unit  */
   1221     Int  i, j;                          /* work  */
   1222     if (ua>msua) a=0;
   1223      else a=*ua;
   1224     *uc=0;                              /* can now write back  */
   1225     /* always need to examine all bits in rhs  */
   1226     /* This loop could be unrolled and/or use BIN2BCD tables  */
   1227     for (i=0; i<DECDPUN; i++) {
   1228       if ((~a)&1) *uc=*uc+(Unit)powers[i];   /* effect INVERT  */
   1229       j=a%10;
   1230       a=a/10;
   1231       if (j>1) {
   1232         decStatus(res, DEC_Invalid_operation, set);
   1233         return res;
   1234         }
   1235       if (uc==msuc && i==msudigs-1) break;   /* just did final digit  */
   1236       } /* each digit  */
   1237     } /* each unit  */
   1238   /* [here uc-1 is the msu of the result]  */
   1239   res->digits=decGetDigits(res->lsu, uc-res->lsu);
   1240   res->exponent=0;                      /* integer  */
   1241   res->bits=0;                          /* sign=0  */
   1242   return res;  /* [no status to set]  */
   1243   } /* decNumberInvert  */
   1244 
   1245 /* ------------------------------------------------------------------ */
   1246 /* decNumberLn -- natural logarithm                                   */
   1247 /*                                                                    */
   1248 /*   This computes C = ln(A)                                          */
   1249 /*                                                                    */
   1250 /*   res is C, the result.  C may be A                                */
   1251 /*   rhs is A                                                         */
   1252 /*   set is the context; note that rounding mode has no effect        */
   1253 /*                                                                    */
   1254 /* C must have space for set->digits digits.                          */
   1255 /*                                                                    */
   1256 /* Notable cases:                                                     */
   1257 /*   A<0 -> Invalid                                                   */
   1258 /*   A=0 -> -Infinity (Exact)                                         */
   1259 /*   A=+Infinity -> +Infinity (Exact)                                 */
   1260 /*   A=1 exactly -> 0 (Exact)                                         */
   1261 /*                                                                    */
   1262 /* Mathematical function restrictions apply (see above); a NaN is     */
   1263 /* returned with Invalid_operation if a restriction is violated.      */
   1264 /*                                                                    */
   1265 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
   1266 /* almost always be correctly rounded, but may be up to 1 ulp in      */
   1267 /* error in rare cases.                                               */
   1268 /* ------------------------------------------------------------------ */
   1269 /* This is a wrapper for decLnOp which can handle the slightly wider  */
   1270 /* (+11) range needed by Ln, Log10, etc. (which may have to be able   */
   1271 /* to calculate at p+e+2).                                            */
   1272 /* ------------------------------------------------------------------ */
   1273 U_CAPI decNumber * U_EXPORT2 uprv_decNumberLn(decNumber *res, const decNumber *rhs,
   1274                         decContext *set) {
   1275   uInt status=0;                   /* accumulator  */
   1276   #if DECSUBSET
   1277   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated  */
   1278   #endif
   1279 
   1280   #if DECCHECK
   1281   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1282   #endif
   1283 
   1284   /* Check restrictions; this is a math function; if not violated  */
   1285   /* then carry out the operation.  */
   1286   if (!decCheckMath(rhs, set, &status)) do { /* protect allocation  */
   1287     #if DECSUBSET
   1288     if (!set->extended) {
   1289       /* reduce operand and set lostDigits status, as needed  */
   1290       if (rhs->digits>set->digits) {
   1291         allocrhs=decRoundOperand(rhs, set, &status);
   1292         if (allocrhs==NULL) break;
   1293         rhs=allocrhs;
   1294         }
   1295       /* special check in subset for rhs=0  */
   1296       if (ISZERO(rhs)) {                /* +/- zeros -> error  */
   1297         status|=DEC_Invalid_operation;
   1298         break;}
   1299       } /* extended=0  */
   1300     #endif
   1301     decLnOp(res, rhs, set, &status);
   1302     } while(0);                         /* end protected  */
   1303 
   1304   #if DECSUBSET
   1305   if (allocrhs !=NULL) free(allocrhs);  /* drop any storage used  */
   1306   #endif
   1307   /* apply significant status  */
   1308   if (status!=0) decStatus(res, status, set);
   1309   #if DECCHECK
   1310   decCheckInexact(res, set);
   1311   #endif
   1312   return res;
   1313   } /* decNumberLn  */
   1314 
   1315 /* ------------------------------------------------------------------ */
   1316 /* decNumberLogB - get adjusted exponent, by 754 rules                */
   1317 /*                                                                    */
   1318 /*   This computes C = adjustedexponent(A)                            */
   1319 /*                                                                    */
   1320 /*   res is C, the result.  C may be A                                */
   1321 /*   rhs is A                                                         */
   1322 /*   set is the context, used only for digits and status              */
   1323 /*                                                                    */
   1324 /* C must have space for 10 digits (A might have 10**9 digits and     */
   1325 /* an exponent of +999999999, or one digit and an exponent of         */
   1326 /* -1999999999).                                                      */
   1327 /*                                                                    */
   1328 /* This returns the adjusted exponent of A after (in theory) padding  */
   1329 /* with zeros on the right to set->digits digits while keeping the    */
   1330 /* same value.  The exponent is not limited by emin/emax.             */
   1331 /*                                                                    */
   1332 /* Notable cases:                                                     */
   1333 /*   A<0 -> Use |A|                                                   */
   1334 /*   A=0 -> -Infinity (Division by zero)                              */
   1335 /*   A=Infinite -> +Infinity (Exact)                                  */
   1336 /*   A=1 exactly -> 0 (Exact)                                         */
   1337 /*   NaNs are propagated as usual                                     */
   1338 /* ------------------------------------------------------------------ */
   1339 U_CAPI decNumber * U_EXPORT2 uprv_decNumberLogB(decNumber *res, const decNumber *rhs,
   1340                           decContext *set) {
   1341   uInt status=0;                   /* accumulator  */
   1342 
   1343   #if DECCHECK
   1344   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1345   #endif
   1346 
   1347   /* NaNs as usual; Infinities return +Infinity; 0->oops  */
   1348   if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
   1349    else if (decNumberIsInfinite(rhs)) uprv_decNumberCopyAbs(res, rhs);
   1350    else if (decNumberIsZero(rhs)) {
   1351     uprv_decNumberZero(res);                 /* prepare for Infinity  */
   1352     res->bits=DECNEG|DECINF;            /* -Infinity  */
   1353     status|=DEC_Division_by_zero;       /* as per 754  */
   1354     }
   1355    else { /* finite non-zero  */
   1356     Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent  */
   1357     uprv_decNumberFromInt32(res, ae);        /* lay it out  */
   1358     }
   1359 
   1360   if (status!=0) decStatus(res, status, set);
   1361   return res;
   1362   } /* decNumberLogB  */
   1363 
   1364 /* ------------------------------------------------------------------ */
   1365 /* decNumberLog10 -- logarithm in base 10                             */
   1366 /*                                                                    */
   1367 /*   This computes C = log10(A)                                       */
   1368 /*                                                                    */
   1369 /*   res is C, the result.  C may be A                                */
   1370 /*   rhs is A                                                         */
   1371 /*   set is the context; note that rounding mode has no effect        */
   1372 /*                                                                    */
   1373 /* C must have space for set->digits digits.                          */
   1374 /*                                                                    */
   1375 /* Notable cases:                                                     */
   1376 /*   A<0 -> Invalid                                                   */
   1377 /*   A=0 -> -Infinity (Exact)                                         */
   1378 /*   A=+Infinity -> +Infinity (Exact)                                 */
   1379 /*   A=10**n (if n is an integer) -> n (Exact)                        */
   1380 /*                                                                    */
   1381 /* Mathematical function restrictions apply (see above); a NaN is     */
   1382 /* returned with Invalid_operation if a restriction is violated.      */
   1383 /*                                                                    */
   1384 /* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will    */
   1385 /* almost always be correctly rounded, but may be up to 1 ulp in      */
   1386 /* error in rare cases.                                               */
   1387 /* ------------------------------------------------------------------ */
   1388 /* This calculates ln(A)/ln(10) using appropriate precision.  For     */
   1389 /* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the      */
   1390 /* requested digits and t is the number of digits in the exponent     */
   1391 /* (maximum 6).  For ln(10) it is p + 3; this is often handled by the */
   1392 /* fastpath in decLnOp.  The final division is done to the requested  */
   1393 /* precision.                                                         */
   1394 /* ------------------------------------------------------------------ */
   1395 U_CAPI decNumber * U_EXPORT2 uprv_decNumberLog10(decNumber *res, const decNumber *rhs,
   1396                           decContext *set) {
   1397   uInt status=0, ignore=0;         /* status accumulators  */
   1398   uInt needbytes;                  /* for space calculations  */
   1399   Int p;                           /* working precision  */
   1400   Int t;                           /* digits in exponent of A  */
   1401 
   1402   /* buffers for a and b working decimals  */
   1403   /* (adjustment calculator, same size)  */
   1404   decNumber bufa[D2N(DECBUFFER+2)];
   1405   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated  */
   1406   decNumber *a=bufa;               /* temporary a  */
   1407   decNumber bufb[D2N(DECBUFFER+2)];
   1408   decNumber *allocbufb=NULL;       /* -> allocated bufb, iff allocated  */
   1409   decNumber *b=bufb;               /* temporary b  */
   1410   decNumber bufw[D2N(10)];         /* working 2-10 digit number  */
   1411   decNumber *w=bufw;               /* ..  */
   1412   #if DECSUBSET
   1413   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated  */
   1414   #endif
   1415 
   1416   decContext aset;                 /* working context  */
   1417 
   1418   #if DECCHECK
   1419   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1420   #endif
   1421 
   1422   /* Check restrictions; this is a math function; if not violated  */
   1423   /* then carry out the operation.  */
   1424   if (!decCheckMath(rhs, set, &status)) do { /* protect malloc  */
   1425     #if DECSUBSET
   1426     if (!set->extended) {
   1427       /* reduce operand and set lostDigits status, as needed  */
   1428       if (rhs->digits>set->digits) {
   1429         allocrhs=decRoundOperand(rhs, set, &status);
   1430         if (allocrhs==NULL) break;
   1431         rhs=allocrhs;
   1432         }
   1433       /* special check in subset for rhs=0  */
   1434       if (ISZERO(rhs)) {                /* +/- zeros -> error  */
   1435         status|=DEC_Invalid_operation;
   1436         break;}
   1437       } /* extended=0  */
   1438     #endif
   1439 
   1440     uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context  */
   1441 
   1442     /* handle exact powers of 10; only check if +ve finite  */
   1443     if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
   1444       Int residue=0;               /* (no residue)  */
   1445       uInt copystat=0;             /* clean status  */
   1446 
   1447       /* round to a single digit...  */
   1448       aset.digits=1;
   1449       decCopyFit(w, rhs, &aset, &residue, &copystat); /* copy & shorten  */
   1450       /* if exact and the digit is 1, rhs is a power of 10  */
   1451       if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
   1452         /* the exponent, conveniently, is the power of 10; making  */
   1453         /* this the result needs a little care as it might not fit,  */
   1454         /* so first convert it into the working number, and then move  */
   1455         /* to res  */
   1456         uprv_decNumberFromInt32(w, w->exponent);
   1457         residue=0;
   1458         decCopyFit(res, w, set, &residue, &status); /* copy & round  */
   1459         decFinish(res, set, &residue, &status);     /* cleanup/set flags  */
   1460         break;
   1461         } /* not a power of 10  */
   1462       } /* not a candidate for exact  */
   1463 
   1464     /* simplify the information-content calculation to use 'total  */
   1465     /* number of digits in a, including exponent' as compared to the  */
   1466     /* requested digits, as increasing this will only rarely cost an  */
   1467     /* iteration in ln(a) anyway  */
   1468     t=6;                                /* it can never be >6  */
   1469 
   1470     /* allocate space when needed...  */
   1471     p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
   1472     needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
   1473     if (needbytes>sizeof(bufa)) {       /* need malloc space  */
   1474       allocbufa=(decNumber *)malloc(needbytes);
   1475       if (allocbufa==NULL) {            /* hopeless -- abandon  */
   1476         status|=DEC_Insufficient_storage;
   1477         break;}
   1478       a=allocbufa;                      /* use the allocated space  */
   1479       }
   1480     aset.digits=p;                      /* as calculated  */
   1481     aset.emax=DEC_MAX_MATH;             /* usual bounds  */
   1482     aset.emin=-DEC_MAX_MATH;            /* ..  */
   1483     aset.clamp=0;                       /* and no concrete format  */
   1484     decLnOp(a, rhs, &aset, &status);    /* a=ln(rhs)  */
   1485 
   1486     /* skip the division if the result so far is infinite, NaN, or  */
   1487     /* zero, or there was an error; note NaN from sNaN needs copy  */
   1488     if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
   1489     if (a->bits&DECSPECIAL || ISZERO(a)) {
   1490       uprv_decNumberCopy(res, a);            /* [will fit]  */
   1491       break;}
   1492 
   1493     /* for ln(10) an extra 3 digits of precision are needed  */
   1494     p=set->digits+3;
   1495     needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
   1496     if (needbytes>sizeof(bufb)) {       /* need malloc space  */
   1497       allocbufb=(decNumber *)malloc(needbytes);
   1498       if (allocbufb==NULL) {            /* hopeless -- abandon  */
   1499         status|=DEC_Insufficient_storage;
   1500         break;}
   1501       b=allocbufb;                      /* use the allocated space  */
   1502       }
   1503     uprv_decNumberZero(w);                   /* set up 10...  */
   1504     #if DECDPUN==1
   1505     w->lsu[1]=1; w->lsu[0]=0;           /* ..  */
   1506     #else
   1507     w->lsu[0]=10;                       /* ..  */
   1508     #endif
   1509     w->digits=2;                        /* ..  */
   1510 
   1511     aset.digits=p;
   1512     decLnOp(b, w, &aset, &ignore);      /* b=ln(10)  */
   1513 
   1514     aset.digits=set->digits;            /* for final divide  */
   1515     decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result  */
   1516     } while(0);                         /* [for break]  */
   1517 
   1518   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used  */
   1519   if (allocbufb!=NULL) free(allocbufb); /* ..  */
   1520   #if DECSUBSET
   1521   if (allocrhs !=NULL) free(allocrhs);  /* ..  */
   1522   #endif
   1523   /* apply significant status  */
   1524   if (status!=0) decStatus(res, status, set);
   1525   #if DECCHECK
   1526   decCheckInexact(res, set);
   1527   #endif
   1528   return res;
   1529   } /* decNumberLog10  */
   1530 
   1531 /* ------------------------------------------------------------------ */
   1532 /* decNumberMax -- compare two Numbers and return the maximum         */
   1533 /*                                                                    */
   1534 /*   This computes C = A ? B, returning the maximum by 754 rules      */
   1535 /*                                                                    */
   1536 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
   1537 /*   lhs is A                                                         */
   1538 /*   rhs is B                                                         */
   1539 /*   set is the context                                               */
   1540 /*                                                                    */
   1541 /* C must have space for set->digits digits.                          */
   1542 /* ------------------------------------------------------------------ */
   1543 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMax(decNumber *res, const decNumber *lhs,
   1544                          const decNumber *rhs, decContext *set) {
   1545   uInt status=0;                        /* accumulator  */
   1546   decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
   1547   if (status!=0) decStatus(res, status, set);
   1548   #if DECCHECK
   1549   decCheckInexact(res, set);
   1550   #endif
   1551   return res;
   1552   } /* decNumberMax  */
   1553 
   1554 /* ------------------------------------------------------------------ */
   1555 /* decNumberMaxMag -- compare and return the maximum by magnitude     */
   1556 /*                                                                    */
   1557 /*   This computes C = A ? B, returning the maximum by 754 rules      */
   1558 /*                                                                    */
   1559 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
   1560 /*   lhs is A                                                         */
   1561 /*   rhs is B                                                         */
   1562 /*   set is the context                                               */
   1563 /*                                                                    */
   1564 /* C must have space for set->digits digits.                          */
   1565 /* ------------------------------------------------------------------ */
   1566 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMaxMag(decNumber *res, const decNumber *lhs,
   1567                          const decNumber *rhs, decContext *set) {
   1568   uInt status=0;                        /* accumulator  */
   1569   decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
   1570   if (status!=0) decStatus(res, status, set);
   1571   #if DECCHECK
   1572   decCheckInexact(res, set);
   1573   #endif
   1574   return res;
   1575   } /* decNumberMaxMag  */
   1576 
   1577 /* ------------------------------------------------------------------ */
   1578 /* decNumberMin -- compare two Numbers and return the minimum         */
   1579 /*                                                                    */
   1580 /*   This computes C = A ? B, returning the minimum by 754 rules      */
   1581 /*                                                                    */
   1582 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
   1583 /*   lhs is A                                                         */
   1584 /*   rhs is B                                                         */
   1585 /*   set is the context                                               */
   1586 /*                                                                    */
   1587 /* C must have space for set->digits digits.                          */
   1588 /* ------------------------------------------------------------------ */
   1589 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMin(decNumber *res, const decNumber *lhs,
   1590                          const decNumber *rhs, decContext *set) {
   1591   uInt status=0;                        /* accumulator  */
   1592   decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
   1593   if (status!=0) decStatus(res, status, set);
   1594   #if DECCHECK
   1595   decCheckInexact(res, set);
   1596   #endif
   1597   return res;
   1598   } /* decNumberMin  */
   1599 
   1600 /* ------------------------------------------------------------------ */
   1601 /* decNumberMinMag -- compare and return the minimum by magnitude     */
   1602 /*                                                                    */
   1603 /*   This computes C = A ? B, returning the minimum by 754 rules      */
   1604 /*                                                                    */
   1605 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
   1606 /*   lhs is A                                                         */
   1607 /*   rhs is B                                                         */
   1608 /*   set is the context                                               */
   1609 /*                                                                    */
   1610 /* C must have space for set->digits digits.                          */
   1611 /* ------------------------------------------------------------------ */
   1612 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinMag(decNumber *res, const decNumber *lhs,
   1613                          const decNumber *rhs, decContext *set) {
   1614   uInt status=0;                        /* accumulator  */
   1615   decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
   1616   if (status!=0) decStatus(res, status, set);
   1617   #if DECCHECK
   1618   decCheckInexact(res, set);
   1619   #endif
   1620   return res;
   1621   } /* decNumberMinMag  */
   1622 
   1623 /* ------------------------------------------------------------------ */
   1624 /* decNumberMinus -- prefix minus operator                            */
   1625 /*                                                                    */
   1626 /*   This computes C = 0 - A                                          */
   1627 /*                                                                    */
   1628 /*   res is C, the result.  C may be A                                */
   1629 /*   rhs is A                                                         */
   1630 /*   set is the context                                               */
   1631 /*                                                                    */
   1632 /* See also decNumberCopyNegate for a quiet bitwise version of this.  */
   1633 /* C must have space for set->digits digits.                          */
   1634 /* ------------------------------------------------------------------ */
   1635 /* Simply use AddOp for the subtract, which will do the necessary.    */
   1636 /* ------------------------------------------------------------------ */
   1637 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMinus(decNumber *res, const decNumber *rhs,
   1638                            decContext *set) {
   1639   decNumber dzero;
   1640   uInt status=0;                        /* accumulator  */
   1641 
   1642   #if DECCHECK
   1643   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1644   #endif
   1645 
   1646   uprv_decNumberZero(&dzero);                /* make 0  */
   1647   dzero.exponent=rhs->exponent;         /* [no coefficient expansion]  */
   1648   decAddOp(res, &dzero, rhs, set, DECNEG, &status);
   1649   if (status!=0) decStatus(res, status, set);
   1650   #if DECCHECK
   1651   decCheckInexact(res, set);
   1652   #endif
   1653   return res;
   1654   } /* decNumberMinus  */
   1655 
   1656 /* ------------------------------------------------------------------ */
   1657 /* decNumberNextMinus -- next towards -Infinity                       */
   1658 /*                                                                    */
   1659 /*   This computes C = A - infinitesimal, rounded towards -Infinity   */
   1660 /*                                                                    */
   1661 /*   res is C, the result.  C may be A                                */
   1662 /*   rhs is A                                                         */
   1663 /*   set is the context                                               */
   1664 /*                                                                    */
   1665 /* This is a generalization of 754 NextDown.                          */
   1666 /* ------------------------------------------------------------------ */
   1667 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextMinus(decNumber *res, const decNumber *rhs,
   1668                                decContext *set) {
   1669   decNumber dtiny;                           /* constant  */
   1670   decContext workset=*set;                   /* work  */
   1671   uInt status=0;                             /* accumulator  */
   1672   #if DECCHECK
   1673   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1674   #endif
   1675 
   1676   /* +Infinity is the special case  */
   1677   if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
   1678     decSetMaxValue(res, set);                /* is +ve  */
   1679     /* there is no status to set  */
   1680     return res;
   1681     }
   1682   uprv_decNumberZero(&dtiny);                     /* start with 0  */
   1683   dtiny.lsu[0]=1;                            /* make number that is ..  */
   1684   dtiny.exponent=DEC_MIN_EMIN-1;             /* .. smaller than tiniest  */
   1685   workset.round=DEC_ROUND_FLOOR;
   1686   decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
   1687   status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please  */
   1688   if (status!=0) decStatus(res, status, set);
   1689   return res;
   1690   } /* decNumberNextMinus  */
   1691 
   1692 /* ------------------------------------------------------------------ */
   1693 /* decNumberNextPlus -- next towards +Infinity                        */
   1694 /*                                                                    */
   1695 /*   This computes C = A + infinitesimal, rounded towards +Infinity   */
   1696 /*                                                                    */
   1697 /*   res is C, the result.  C may be A                                */
   1698 /*   rhs is A                                                         */
   1699 /*   set is the context                                               */
   1700 /*                                                                    */
   1701 /* This is a generalization of 754 NextUp.                            */
   1702 /* ------------------------------------------------------------------ */
   1703 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextPlus(decNumber *res, const decNumber *rhs,
   1704                               decContext *set) {
   1705   decNumber dtiny;                           /* constant  */
   1706   decContext workset=*set;                   /* work  */
   1707   uInt status=0;                             /* accumulator  */
   1708   #if DECCHECK
   1709   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1710   #endif
   1711 
   1712   /* -Infinity is the special case  */
   1713   if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
   1714     decSetMaxValue(res, set);
   1715     res->bits=DECNEG;                        /* negative  */
   1716     /* there is no status to set  */
   1717     return res;
   1718     }
   1719   uprv_decNumberZero(&dtiny);                     /* start with 0  */
   1720   dtiny.lsu[0]=1;                            /* make number that is ..  */
   1721   dtiny.exponent=DEC_MIN_EMIN-1;             /* .. smaller than tiniest  */
   1722   workset.round=DEC_ROUND_CEILING;
   1723   decAddOp(res, rhs, &dtiny, &workset, 0, &status);
   1724   status&=DEC_Invalid_operation|DEC_sNaN;    /* only sNaN Invalid please  */
   1725   if (status!=0) decStatus(res, status, set);
   1726   return res;
   1727   } /* decNumberNextPlus  */
   1728 
   1729 /* ------------------------------------------------------------------ */
   1730 /* decNumberNextToward -- next towards rhs                            */
   1731 /*                                                                    */
   1732 /*   This computes C = A +/- infinitesimal, rounded towards           */
   1733 /*   +/-Infinity in the direction of B, as per 754-1985 nextafter     */
   1734 /*   modified during revision but dropped from 754-2008.              */
   1735 /*                                                                    */
   1736 /*   res is C, the result.  C may be A or B.                          */
   1737 /*   lhs is A                                                         */
   1738 /*   rhs is B                                                         */
   1739 /*   set is the context                                               */
   1740 /*                                                                    */
   1741 /* This is a generalization of 754-1985 NextAfter.                    */
   1742 /* ------------------------------------------------------------------ */
   1743 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNextToward(decNumber *res, const decNumber *lhs,
   1744                                 const decNumber *rhs, decContext *set) {
   1745   decNumber dtiny;                           /* constant  */
   1746   decContext workset=*set;                   /* work  */
   1747   Int result;                                /* ..  */
   1748   uInt status=0;                             /* accumulator  */
   1749   #if DECCHECK
   1750   if (decCheckOperands(res, lhs, rhs, set)) return res;
   1751   #endif
   1752 
   1753   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
   1754     decNaNs(res, lhs, rhs, set, &status);
   1755     }
   1756    else { /* Is numeric, so no chance of sNaN Invalid, etc.  */
   1757     result=decCompare(lhs, rhs, 0);     /* sign matters  */
   1758     if (result==BADINT) status|=DEC_Insufficient_storage; /* rare  */
   1759      else { /* valid compare  */
   1760       if (result==0) uprv_decNumberCopySign(res, lhs, rhs); /* easy  */
   1761        else { /* differ: need NextPlus or NextMinus  */
   1762         uByte sub;                      /* add or subtract  */
   1763         if (result<0) {                 /* lhs<rhs, do nextplus  */
   1764           /* -Infinity is the special case  */
   1765           if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
   1766             decSetMaxValue(res, set);
   1767             res->bits=DECNEG;           /* negative  */
   1768             return res;                 /* there is no status to set  */
   1769             }
   1770           workset.round=DEC_ROUND_CEILING;
   1771           sub=0;                        /* add, please  */
   1772           } /* plus  */
   1773          else {                         /* lhs>rhs, do nextminus  */
   1774           /* +Infinity is the special case  */
   1775           if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
   1776             decSetMaxValue(res, set);
   1777             return res;                 /* there is no status to set  */
   1778             }
   1779           workset.round=DEC_ROUND_FLOOR;
   1780           sub=DECNEG;                   /* subtract, please  */
   1781           } /* minus  */
   1782         uprv_decNumberZero(&dtiny);          /* start with 0  */
   1783         dtiny.lsu[0]=1;                 /* make number that is ..  */
   1784         dtiny.exponent=DEC_MIN_EMIN-1;  /* .. smaller than tiniest  */
   1785         decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or -  */
   1786         /* turn off exceptions if the result is a normal number  */
   1787         /* (including Nmin), otherwise let all status through  */
   1788         if (uprv_decNumberIsNormal(res, set)) status=0;
   1789         } /* unequal  */
   1790       } /* compare OK  */
   1791     } /* numeric  */
   1792   if (status!=0) decStatus(res, status, set);
   1793   return res;
   1794   } /* decNumberNextToward  */
   1795 
   1796 /* ------------------------------------------------------------------ */
   1797 /* decNumberOr -- OR two Numbers, digitwise                           */
   1798 /*                                                                    */
   1799 /*   This computes C = A | B                                          */
   1800 /*                                                                    */
   1801 /*   res is C, the result.  C may be A and/or B (e.g., X=X|X)         */
   1802 /*   lhs is A                                                         */
   1803 /*   rhs is B                                                         */
   1804 /*   set is the context (used for result length and error report)     */
   1805 /*                                                                    */
   1806 /* C must have space for set->digits digits.                          */
   1807 /*                                                                    */
   1808 /* Logical function restrictions apply (see above); a NaN is          */
   1809 /* returned with Invalid_operation if a restriction is violated.      */
   1810 /* ------------------------------------------------------------------ */
   1811 U_CAPI decNumber * U_EXPORT2 uprv_decNumberOr(decNumber *res, const decNumber *lhs,
   1812                         const decNumber *rhs, decContext *set) {
   1813   const Unit *ua, *ub;                  /* -> operands  */
   1814   const Unit *msua, *msub;              /* -> operand msus  */
   1815   Unit  *uc, *msuc;                     /* -> result and its msu  */
   1816   Int   msudigs;                        /* digits in res msu  */
   1817   #if DECCHECK
   1818   if (decCheckOperands(res, lhs, rhs, set)) return res;
   1819   #endif
   1820 
   1821   if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   1822    || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
   1823     decStatus(res, DEC_Invalid_operation, set);
   1824     return res;
   1825     }
   1826   /* operands are valid  */
   1827   ua=lhs->lsu;                          /* bottom-up  */
   1828   ub=rhs->lsu;                          /* ..  */
   1829   uc=res->lsu;                          /* ..  */
   1830   msua=ua+D2U(lhs->digits)-1;           /* -> msu of lhs  */
   1831   msub=ub+D2U(rhs->digits)-1;           /* -> msu of rhs  */
   1832   msuc=uc+D2U(set->digits)-1;           /* -> msu of result  */
   1833   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder]  */
   1834   for (; uc<=msuc; ua++, ub++, uc++) {  /* Unit loop  */
   1835     Unit a, b;                          /* extract units  */
   1836     if (ua>msua) a=0;
   1837      else a=*ua;
   1838     if (ub>msub) b=0;
   1839      else b=*ub;
   1840     *uc=0;                              /* can now write back  */
   1841     if (a|b) {                          /* maybe 1 bits to examine  */
   1842       Int i, j;
   1843       /* This loop could be unrolled and/or use BIN2BCD tables  */
   1844       for (i=0; i<DECDPUN; i++) {
   1845         if ((a|b)&1) *uc=*uc+(Unit)powers[i];     /* effect OR  */
   1846         j=a%10;
   1847         a=a/10;
   1848         j|=b%10;
   1849         b=b/10;
   1850         if (j>1) {
   1851           decStatus(res, DEC_Invalid_operation, set);
   1852           return res;
   1853           }
   1854         if (uc==msuc && i==msudigs-1) break;      /* just did final digit  */
   1855         } /* each digit  */
   1856       } /* non-zero  */
   1857     } /* each unit  */
   1858   /* [here uc-1 is the msu of the result]  */
   1859   res->digits=decGetDigits(res->lsu, uc-res->lsu);
   1860   res->exponent=0;                      /* integer  */
   1861   res->bits=0;                          /* sign=0  */
   1862   return res;  /* [no status to set]  */
   1863   } /* decNumberOr  */
   1864 
   1865 /* ------------------------------------------------------------------ */
   1866 /* decNumberPlus -- prefix plus operator                              */
   1867 /*                                                                    */
   1868 /*   This computes C = 0 + A                                          */
   1869 /*                                                                    */
   1870 /*   res is C, the result.  C may be A                                */
   1871 /*   rhs is A                                                         */
   1872 /*   set is the context                                               */
   1873 /*                                                                    */
   1874 /* See also decNumberCopy for a quiet bitwise version of this.        */
   1875 /* C must have space for set->digits digits.                          */
   1876 /* ------------------------------------------------------------------ */
   1877 /* This simply uses AddOp; Add will take fast path after preparing A. */
   1878 /* Performance is a concern here, as this routine is often used to    */
   1879 /* check operands and apply rounding and overflow/underflow testing.  */
   1880 /* ------------------------------------------------------------------ */
   1881 U_CAPI decNumber * U_EXPORT2 uprv_decNumberPlus(decNumber *res, const decNumber *rhs,
   1882                           decContext *set) {
   1883   decNumber dzero;
   1884   uInt status=0;                        /* accumulator  */
   1885   #if DECCHECK
   1886   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   1887   #endif
   1888 
   1889   uprv_decNumberZero(&dzero);                /* make 0  */
   1890   dzero.exponent=rhs->exponent;         /* [no coefficient expansion]  */
   1891   decAddOp(res, &dzero, rhs, set, 0, &status);
   1892   if (status!=0) decStatus(res, status, set);
   1893   #if DECCHECK
   1894   decCheckInexact(res, set);
   1895   #endif
   1896   return res;
   1897   } /* decNumberPlus  */
   1898 
   1899 /* ------------------------------------------------------------------ */
   1900 /* decNumberMultiply -- multiply two Numbers                          */
   1901 /*                                                                    */
   1902 /*   This computes C = A x B                                          */
   1903 /*                                                                    */
   1904 /*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
   1905 /*   lhs is A                                                         */
   1906 /*   rhs is B                                                         */
   1907 /*   set is the context                                               */
   1908 /*                                                                    */
   1909 /* C must have space for set->digits digits.                          */
   1910 /* ------------------------------------------------------------------ */
   1911 U_CAPI decNumber * U_EXPORT2 uprv_decNumberMultiply(decNumber *res, const decNumber *lhs,
   1912                               const decNumber *rhs, decContext *set) {
   1913   uInt status=0;                   /* accumulator  */
   1914   decMultiplyOp(res, lhs, rhs, set, &status);
   1915   if (status!=0) decStatus(res, status, set);
   1916   #if DECCHECK
   1917   decCheckInexact(res, set);
   1918   #endif
   1919   return res;
   1920   } /* decNumberMultiply  */
   1921 
   1922 /* ------------------------------------------------------------------ */
   1923 /* decNumberPower -- raise a number to a power                        */
   1924 /*                                                                    */
   1925 /*   This computes C = A ** B                                         */
   1926 /*                                                                    */
   1927 /*   res is C, the result.  C may be A and/or B (e.g., X=X**X)        */
   1928 /*   lhs is A                                                         */
   1929 /*   rhs is B                                                         */
   1930 /*   set is the context                                               */
   1931 /*                                                                    */
   1932 /* C must have space for set->digits digits.                          */
   1933 /*                                                                    */
   1934 /* Mathematical function restrictions apply (see above); a NaN is     */
   1935 /* returned with Invalid_operation if a restriction is violated.      */
   1936 /*                                                                    */
   1937 /* However, if 1999999997<=B<=999999999 and B is an integer then the  */
   1938 /* restrictions on A and the context are relaxed to the usual bounds, */
   1939 /* for compatibility with the earlier (integer power only) version    */
   1940 /* of this function.                                                  */
   1941 /*                                                                    */
   1942 /* When B is an integer, the result may be exact, even if rounded.    */
   1943 /*                                                                    */
   1944 /* The final result is rounded according to the context; it will      */
   1945 /* almost always be correctly rounded, but may be up to 1 ulp in      */
   1946 /* error in rare cases.                                               */
   1947 /* ------------------------------------------------------------------ */
   1948 U_CAPI decNumber * U_EXPORT2 uprv_decNumberPower(decNumber *res, const decNumber *lhs,
   1949                            const decNumber *rhs, decContext *set) {
   1950   #if DECSUBSET
   1951   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated  */
   1952   decNumber *allocrhs=NULL;        /* .., rhs  */
   1953   #endif
   1954   decNumber *allocdac=NULL;        /* -> allocated acc buffer, iff used  */
   1955   decNumber *allocinv=NULL;        /* -> allocated 1/x buffer, iff used  */
   1956   Int   reqdigits=set->digits;     /* requested DIGITS  */
   1957   Int   n;                         /* rhs in binary  */
   1958   Flag  rhsint=0;                  /* 1 if rhs is an integer  */
   1959   Flag  useint=0;                  /* 1 if can use integer calculation  */
   1960   Flag  isoddint=0;                /* 1 if rhs is an integer and odd  */
   1961   Int   i;                         /* work  */
   1962   #if DECSUBSET
   1963   Int   dropped;                   /* ..  */
   1964   #endif
   1965   uInt  needbytes;                 /* buffer size needed  */
   1966   Flag  seenbit;                   /* seen a bit while powering  */
   1967   Int   residue=0;                 /* rounding residue  */
   1968   uInt  status=0;                  /* accumulators  */
   1969   uByte bits=0;                    /* result sign if errors  */
   1970   decContext aset;                 /* working context  */
   1971   decNumber dnOne;                 /* work value 1...  */
   1972   /* local accumulator buffer [a decNumber, with digits+elength+1 digits]  */
   1973   decNumber dacbuff[D2N(DECBUFFER+9)];
   1974   decNumber *dac=dacbuff;          /* -> result accumulator  */
   1975   /* same again for possible 1/lhs calculation  */
   1976   decNumber invbuff[D2N(DECBUFFER+9)];
   1977 
   1978   #if DECCHECK
   1979   if (decCheckOperands(res, lhs, rhs, set)) return res;
   1980   #endif
   1981 
   1982   do {                             /* protect allocated storage  */
   1983     #if DECSUBSET
   1984     if (!set->extended) { /* reduce operands and set status, as needed  */
   1985       if (lhs->digits>reqdigits) {
   1986         alloclhs=decRoundOperand(lhs, set, &status);
   1987         if (alloclhs==NULL) break;
   1988         lhs=alloclhs;
   1989         }
   1990       if (rhs->digits>reqdigits) {
   1991         allocrhs=decRoundOperand(rhs, set, &status);
   1992         if (allocrhs==NULL) break;
   1993         rhs=allocrhs;
   1994         }
   1995       }
   1996     #endif
   1997     /* [following code does not require input rounding]  */
   1998 
   1999     /* handle NaNs and rhs Infinity (lhs infinity is harder)  */
   2000     if (SPECIALARGS) {
   2001       if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs  */
   2002         decNaNs(res, lhs, rhs, set, &status);
   2003         break;}
   2004       if (decNumberIsInfinite(rhs)) {   /* rhs Infinity  */
   2005         Flag rhsneg=rhs->bits&DECNEG;   /* save rhs sign  */
   2006         if (decNumberIsNegative(lhs)    /* lhs<0  */
   2007          && !decNumberIsZero(lhs))      /* ..  */
   2008           status|=DEC_Invalid_operation;
   2009          else {                         /* lhs >=0  */
   2010           uprv_decNumberZero(&dnOne);        /* set up 1  */
   2011           dnOne.lsu[0]=1;
   2012           uprv_decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1  */
   2013           uprv_decNumberZero(res);           /* prepare for 0/1/Infinity  */
   2014           if (decNumberIsNegative(dac)) {    /* lhs<1  */
   2015             if (rhsneg) res->bits|=DECINF;   /* +Infinity [else is +0]  */
   2016             }
   2017            else if (dac->lsu[0]==0) {        /* lhs=1  */
   2018             /* 1**Infinity is inexact, so return fully-padded 1.0000  */
   2019             Int shift=set->digits-1;
   2020             *res->lsu=1;                     /* was 0, make int 1  */
   2021             res->digits=decShiftToMost(res->lsu, 1, shift);
   2022             res->exponent=-shift;            /* make 1.0000...  */
   2023             status|=DEC_Inexact|DEC_Rounded; /* deemed inexact  */
   2024             }
   2025            else {                            /* lhs>1  */
   2026             if (!rhsneg) res->bits|=DECINF;  /* +Infinity [else is +0]  */
   2027             }
   2028           } /* lhs>=0  */
   2029         break;}
   2030       /* [lhs infinity drops through]  */
   2031       } /* specials  */
   2032 
   2033     /* Original rhs may be an integer that fits and is in range  */
   2034     n=decGetInt(rhs);
   2035     if (n!=BADINT) {                    /* it is an integer  */
   2036       rhsint=1;                         /* record the fact for 1**n  */
   2037       isoddint=(Flag)n&1;               /* [works even if big]  */
   2038       if (n!=BIGEVEN && n!=BIGODD)      /* can use integer path?  */
   2039         useint=1;                       /* looks good  */
   2040       }
   2041 
   2042     if (decNumberIsNegative(lhs)        /* -x ..  */
   2043       && isoddint) bits=DECNEG;         /* .. to an odd power  */
   2044 
   2045     /* handle LHS infinity  */
   2046     if (decNumberIsInfinite(lhs)) {     /* [NaNs already handled]  */
   2047       uByte rbits=rhs->bits;            /* save  */
   2048       uprv_decNumberZero(res);               /* prepare  */
   2049       if (n==0) *res->lsu=1;            /* [-]Inf**0 => 1  */
   2050        else {
   2051         /* -Inf**nonint -> error  */
   2052         if (!rhsint && decNumberIsNegative(lhs)) {
   2053           status|=DEC_Invalid_operation;     /* -Inf**nonint is error  */
   2054           break;}
   2055         if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n  */
   2056         /* [otherwise will be 0 or -0]  */
   2057         res->bits=bits;
   2058         }
   2059       break;}
   2060 
   2061     /* similarly handle LHS zero  */
   2062     if (decNumberIsZero(lhs)) {
   2063       if (n==0) {                            /* 0**0 => Error  */
   2064         #if DECSUBSET
   2065         if (!set->extended) {                /* [unless subset]  */
   2066           uprv_decNumberZero(res);
   2067           *res->lsu=1;                       /* return 1  */
   2068           break;}
   2069         #endif
   2070         status|=DEC_Invalid_operation;
   2071         }
   2072        else {                                /* 0**x  */
   2073         uByte rbits=rhs->bits;               /* save  */
   2074         if (rbits & DECNEG) {                /* was a 0**(-n)  */
   2075           #if DECSUBSET
   2076           if (!set->extended) {              /* [bad if subset]  */
   2077             status|=DEC_Invalid_operation;
   2078             break;}
   2079           #endif
   2080           bits|=DECINF;
   2081           }
   2082         uprv_decNumberZero(res);                  /* prepare  */
   2083         /* [otherwise will be 0 or -0]  */
   2084         res->bits=bits;
   2085         }
   2086       break;}
   2087 
   2088     /* here both lhs and rhs are finite; rhs==0 is handled in the  */
   2089     /* integer path.  Next handle the non-integer cases  */
   2090     if (!useint) {                      /* non-integral rhs  */
   2091       /* any -ve lhs is bad, as is either operand or context out of  */
   2092       /* bounds  */
   2093       if (decNumberIsNegative(lhs)) {
   2094         status|=DEC_Invalid_operation;
   2095         break;}
   2096       if (decCheckMath(lhs, set, &status)
   2097        || decCheckMath(rhs, set, &status)) break; /* variable status  */
   2098 
   2099       uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context  */
   2100       aset.emax=DEC_MAX_MATH;           /* usual bounds  */
   2101       aset.emin=-DEC_MAX_MATH;          /* ..  */
   2102       aset.clamp=0;                     /* and no concrete format  */
   2103 
   2104       /* calculate the result using exp(ln(lhs)*rhs), which can  */
   2105       /* all be done into the accumulator, dac.  The precision needed  */
   2106       /* is enough to contain the full information in the lhs (which  */
   2107       /* is the total digits, including exponent), or the requested  */
   2108       /* precision, if larger, + 4; 6 is used for the exponent  */
   2109       /* maximum length, and this is also used when it is shorter  */
   2110       /* than the requested digits as it greatly reduces the >0.5 ulp  */
   2111       /* cases at little cost (because Ln doubles digits each  */
   2112       /* iteration so a few extra digits rarely causes an extra  */
   2113       /* iteration)  */
   2114       aset.digits=MAXI(lhs->digits, set->digits)+6+4;
   2115       } /* non-integer rhs  */
   2116 
   2117      else { /* rhs is in-range integer  */
   2118       if (n==0) {                       /* x**0 = 1  */
   2119         /* (0**0 was handled above)  */
   2120         uprv_decNumberZero(res);             /* result=1  */
   2121         *res->lsu=1;                    /* ..  */
   2122         break;}
   2123       /* rhs is a non-zero integer  */
   2124       if (n<0) n=-n;                    /* use abs(n)  */
   2125 
   2126       aset=*set;                        /* clone the context  */
   2127       aset.round=DEC_ROUND_HALF_EVEN;   /* internally use balanced  */
   2128       /* calculate the working DIGITS  */
   2129       aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
   2130       #if DECSUBSET
   2131       if (!set->extended) aset.digits--;     /* use classic precision  */
   2132       #endif
   2133       /* it's an error if this is more than can be handled  */
   2134       if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
   2135       } /* integer path  */
   2136 
   2137     /* aset.digits is the count of digits for the accumulator needed  */
   2138     /* if accumulator is too long for local storage, then allocate  */
   2139     needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
   2140     /* [needbytes also used below if 1/lhs needed]  */
   2141     if (needbytes>sizeof(dacbuff)) {
   2142       allocdac=(decNumber *)malloc(needbytes);
   2143       if (allocdac==NULL) {   /* hopeless -- abandon  */
   2144         status|=DEC_Insufficient_storage;
   2145         break;}
   2146       dac=allocdac;           /* use the allocated space  */
   2147       }
   2148     /* here, aset is set up and accumulator is ready for use  */
   2149 
   2150     if (!useint) {                           /* non-integral rhs  */
   2151       /* x ** y; special-case x=1 here as it will otherwise always  */
   2152       /* reduce to integer 1; decLnOp has a fastpath which detects  */
   2153       /* the case of x=1  */
   2154       decLnOp(dac, lhs, &aset, &status);     /* dac=ln(lhs)  */
   2155       /* [no error possible, as lhs 0 already handled]  */
   2156       if (ISZERO(dac)) {                     /* x==1, 1.0, etc.  */
   2157         /* need to return fully-padded 1.0000 etc., but rhsint->1  */
   2158         *dac->lsu=1;                         /* was 0, make int 1  */
   2159         if (!rhsint) {                       /* add padding  */
   2160           Int shift=set->digits-1;
   2161           dac->digits=decShiftToMost(dac->lsu, 1, shift);
   2162           dac->exponent=-shift;              /* make 1.0000...  */
   2163           status|=DEC_Inexact|DEC_Rounded;   /* deemed inexact  */
   2164           }
   2165         }
   2166        else {
   2167         decMultiplyOp(dac, dac, rhs, &aset, &status);  /* dac=dac*rhs  */
   2168         decExpOp(dac, dac, &aset, &status);            /* dac=exp(dac)  */
   2169         }
   2170       /* and drop through for final rounding  */
   2171       } /* non-integer rhs  */
   2172 
   2173      else {                             /* carry on with integer  */
   2174       uprv_decNumberZero(dac);               /* acc=1  */
   2175       *dac->lsu=1;                      /* ..  */
   2176 
   2177       /* if a negative power the constant 1 is needed, and if not subset  */
   2178       /* invert the lhs now rather than inverting the result later  */
   2179       if (decNumberIsNegative(rhs)) {   /* was a **-n [hence digits>0]  */
   2180         decNumber *inv=invbuff;         /* asssume use fixed buffer  */
   2181         uprv_decNumberCopy(&dnOne, dac);     /* dnOne=1;  [needed now or later]  */
   2182         #if DECSUBSET
   2183         if (set->extended) {            /* need to calculate 1/lhs  */
   2184         #endif
   2185           /* divide lhs into 1, putting result in dac [dac=1/dac]  */
   2186           decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
   2187           /* now locate or allocate space for the inverted lhs  */
   2188           if (needbytes>sizeof(invbuff)) {
   2189             allocinv=(decNumber *)malloc(needbytes);
   2190             if (allocinv==NULL) {       /* hopeless -- abandon  */
   2191               status|=DEC_Insufficient_storage;
   2192               break;}
   2193             inv=allocinv;               /* use the allocated space  */
   2194             }
   2195           /* [inv now points to big-enough buffer or allocated storage]  */
   2196           uprv_decNumberCopy(inv, dac);      /* copy the 1/lhs  */
   2197           uprv_decNumberCopy(dac, &dnOne);   /* restore acc=1  */
   2198           lhs=inv;                      /* .. and go forward with new lhs  */
   2199         #if DECSUBSET
   2200           }
   2201         #endif
   2202         }
   2203 
   2204       /* Raise-to-the-power loop...  */
   2205       seenbit=0;                   /* set once a 1-bit is encountered  */
   2206       for (i=1;;i++){              /* for each bit [top bit ignored]  */
   2207         /* abandon if had overflow or terminal underflow  */
   2208         if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting?  */
   2209           if (status&DEC_Overflow || ISZERO(dac)) break;
   2210           }
   2211         /* [the following two lines revealed an optimizer bug in a C++  */
   2212         /* compiler, with symptom: 5**3 -> 25, when n=n+n was used]  */
   2213         n=n<<1;                    /* move next bit to testable position  */
   2214         if (n<0) {                 /* top bit is set  */
   2215           seenbit=1;               /* OK, significant bit seen  */
   2216           decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x  */
   2217           }
   2218         if (i==31) break;          /* that was the last bit  */
   2219         if (!seenbit) continue;    /* no need to square 1  */
   2220         decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square]  */
   2221         } /*i*/ /* 32 bits  */
   2222 
   2223       /* complete internal overflow or underflow processing  */
   2224       if (status & (DEC_Overflow|DEC_Underflow)) {
   2225         #if DECSUBSET
   2226         /* If subset, and power was negative, reverse the kind of -erflow  */
   2227         /* [1/x not yet done]  */
   2228         if (!set->extended && decNumberIsNegative(rhs)) {
   2229           if (status & DEC_Overflow)
   2230             status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
   2231            else { /* trickier -- Underflow may or may not be set  */
   2232             status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both]  */
   2233             status|=DEC_Overflow;
   2234             }
   2235           }
   2236         #endif
   2237         dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign  */
   2238         /* round subnormals [to set.digits rather than aset.digits]  */
   2239         /* or set overflow result similarly as required  */
   2240         decFinalize(dac, set, &residue, &status);
   2241         uprv_decNumberCopy(res, dac);   /* copy to result (is now OK length)  */
   2242         break;
   2243         }
   2244 
   2245       #if DECSUBSET
   2246       if (!set->extended &&                  /* subset math  */
   2247           decNumberIsNegative(rhs)) {        /* was a **-n [hence digits>0]  */
   2248         /* so divide result into 1 [dac=1/dac]  */
   2249         decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
   2250         }
   2251       #endif
   2252       } /* rhs integer path  */
   2253 
   2254     /* reduce result to the requested length and copy to result  */
   2255     decCopyFit(res, dac, set, &residue, &status);
   2256     decFinish(res, set, &residue, &status);  /* final cleanup  */
   2257     #if DECSUBSET
   2258     if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros  */
   2259     #endif
   2260     } while(0);                         /* end protected  */
   2261 
   2262   if (allocdac!=NULL) free(allocdac);   /* drop any storage used  */
   2263   if (allocinv!=NULL) free(allocinv);   /* ..  */
   2264   #if DECSUBSET
   2265   if (alloclhs!=NULL) free(alloclhs);   /* ..  */
   2266   if (allocrhs!=NULL) free(allocrhs);   /* ..  */
   2267   #endif
   2268   if (status!=0) decStatus(res, status, set);
   2269   #if DECCHECK
   2270   decCheckInexact(res, set);
   2271   #endif
   2272   return res;
   2273   } /* decNumberPower  */
   2274 
   2275 /* ------------------------------------------------------------------ */
   2276 /* decNumberQuantize -- force exponent to requested value             */
   2277 /*                                                                    */
   2278 /*   This computes C = op(A, B), where op adjusts the coefficient     */
   2279 /*   of C (by rounding or shifting) such that the exponent (-scale)   */
   2280 /*   of C has exponent of B.  The numerical value of C will equal A,  */
   2281 /*   except for the effects of any rounding that occurred.            */
   2282 /*                                                                    */
   2283 /*   res is C, the result.  C may be A or B                           */
   2284 /*   lhs is A, the number to adjust                                   */
   2285 /*   rhs is B, the number with exponent to match                      */
   2286 /*   set is the context                                               */
   2287 /*                                                                    */
   2288 /* C must have space for set->digits digits.                          */
   2289 /*                                                                    */
   2290 /* Unless there is an error or the result is infinite, the exponent   */
   2291 /* after the operation is guaranteed to be equal to that of B.        */
   2292 /* ------------------------------------------------------------------ */
   2293 U_CAPI decNumber * U_EXPORT2 uprv_decNumberQuantize(decNumber *res, const decNumber *lhs,
   2294                               const decNumber *rhs, decContext *set) {
   2295   uInt status=0;                        /* accumulator  */
   2296   decQuantizeOp(res, lhs, rhs, set, 1, &status);
   2297   if (status!=0) decStatus(res, status, set);
   2298   return res;
   2299   } /* decNumberQuantize  */
   2300 
   2301 /* ------------------------------------------------------------------ */
   2302 /* decNumberReduce -- remove trailing zeros                           */
   2303 /*                                                                    */
   2304 /*   This computes C = 0 + A, and normalizes the result               */
   2305 /*                                                                    */
   2306 /*   res is C, the result.  C may be A                                */
   2307 /*   rhs is A                                                         */
   2308 /*   set is the context                                               */
   2309 /*                                                                    */
   2310 /* C must have space for set->digits digits.                          */
   2311 /* ------------------------------------------------------------------ */
   2312 /* Previously known as Normalize  */
   2313 U_CAPI decNumber * U_EXPORT2 uprv_decNumberNormalize(decNumber *res, const decNumber *rhs,
   2314                                decContext *set) {
   2315   return uprv_decNumberReduce(res, rhs, set);
   2316   } /* decNumberNormalize  */
   2317 
   2318 U_CAPI decNumber * U_EXPORT2 uprv_decNumberReduce(decNumber *res, const decNumber *rhs,
   2319                             decContext *set) {
   2320   #if DECSUBSET
   2321   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated  */
   2322   #endif
   2323   uInt status=0;                   /* as usual  */
   2324   Int  residue=0;                  /* as usual  */
   2325   Int  dropped;                    /* work  */
   2326 
   2327   #if DECCHECK
   2328   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   2329   #endif
   2330 
   2331   do {                             /* protect allocated storage  */
   2332     #if DECSUBSET
   2333     if (!set->extended) {
   2334       /* reduce operand and set lostDigits status, as needed  */
   2335       if (rhs->digits>set->digits) {
   2336         allocrhs=decRoundOperand(rhs, set, &status);
   2337         if (allocrhs==NULL) break;
   2338         rhs=allocrhs;
   2339         }
   2340       }
   2341     #endif
   2342     /* [following code does not require input rounding]  */
   2343 
   2344     /* Infinities copy through; NaNs need usual treatment  */
   2345     if (decNumberIsNaN(rhs)) {
   2346       decNaNs(res, rhs, NULL, set, &status);
   2347       break;
   2348       }
   2349 
   2350     /* reduce result to the requested length and copy to result  */
   2351     decCopyFit(res, rhs, set, &residue, &status); /* copy & round  */
   2352     decFinish(res, set, &residue, &status);       /* cleanup/set flags  */
   2353     decTrim(res, set, 1, 0, &dropped);            /* normalize in place  */
   2354                                                   /* [may clamp]  */
   2355     } while(0);                              /* end protected  */
   2356 
   2357   #if DECSUBSET
   2358   if (allocrhs !=NULL) free(allocrhs);       /* ..  */
   2359   #endif
   2360   if (status!=0) decStatus(res, status, set);/* then report status  */
   2361   return res;
   2362   } /* decNumberReduce  */
   2363 
   2364 /* ------------------------------------------------------------------ */
   2365 /* decNumberRescale -- force exponent to requested value              */
   2366 /*                                                                    */
   2367 /*   This computes C = op(A, B), where op adjusts the coefficient     */
   2368 /*   of C (by rounding or shifting) such that the exponent (-scale)   */
   2369 /*   of C has the value B.  The numerical value of C will equal A,    */
   2370 /*   except for the effects of any rounding that occurred.            */
   2371 /*                                                                    */
   2372 /*   res is C, the result.  C may be A or B                           */
   2373 /*   lhs is A, the number to adjust                                   */
   2374 /*   rhs is B, the requested exponent                                 */
   2375 /*   set is the context                                               */
   2376 /*                                                                    */
   2377 /* C must have space for set->digits digits.                          */
   2378 /*                                                                    */
   2379 /* Unless there is an error or the result is infinite, the exponent   */
   2380 /* after the operation is guaranteed to be equal to B.                */
   2381 /* ------------------------------------------------------------------ */
   2382 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRescale(decNumber *res, const decNumber *lhs,
   2383                              const decNumber *rhs, decContext *set) {
   2384   uInt status=0;                        /* accumulator  */
   2385   decQuantizeOp(res, lhs, rhs, set, 0, &status);
   2386   if (status!=0) decStatus(res, status, set);
   2387   return res;
   2388   } /* decNumberRescale  */
   2389 
   2390 /* ------------------------------------------------------------------ */
   2391 /* decNumberRemainder -- divide and return remainder                  */
   2392 /*                                                                    */
   2393 /*   This computes C = A % B                                          */
   2394 /*                                                                    */
   2395 /*   res is C, the result.  C may be A and/or B (e.g., X=X%X)         */
   2396 /*   lhs is A                                                         */
   2397 /*   rhs is B                                                         */
   2398 /*   set is the context                                               */
   2399 /*                                                                    */
   2400 /* C must have space for set->digits digits.                          */
   2401 /* ------------------------------------------------------------------ */
   2402 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainder(decNumber *res, const decNumber *lhs,
   2403                                const decNumber *rhs, decContext *set) {
   2404   uInt status=0;                        /* accumulator  */
   2405   decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
   2406   if (status!=0) decStatus(res, status, set);
   2407   #if DECCHECK
   2408   decCheckInexact(res, set);
   2409   #endif
   2410   return res;
   2411   } /* decNumberRemainder  */
   2412 
   2413 /* ------------------------------------------------------------------ */
   2414 /* decNumberRemainderNear -- divide and return remainder from nearest */
   2415 /*                                                                    */
   2416 /*   This computes C = A % B, where % is the IEEE remainder operator  */
   2417 /*                                                                    */
   2418 /*   res is C, the result.  C may be A and/or B (e.g., X=X%X)         */
   2419 /*   lhs is A                                                         */
   2420 /*   rhs is B                                                         */
   2421 /*   set is the context                                               */
   2422 /*                                                                    */
   2423 /* C must have space for set->digits digits.                          */
   2424 /* ------------------------------------------------------------------ */
   2425 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRemainderNear(decNumber *res, const decNumber *lhs,
   2426                                    const decNumber *rhs, decContext *set) {
   2427   uInt status=0;                        /* accumulator  */
   2428   decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
   2429   if (status!=0) decStatus(res, status, set);
   2430   #if DECCHECK
   2431   decCheckInexact(res, set);
   2432   #endif
   2433   return res;
   2434   } /* decNumberRemainderNear  */
   2435 
   2436 /* ------------------------------------------------------------------ */
   2437 /* decNumberRotate -- rotate the coefficient of a Number left/right   */
   2438 /*                                                                    */
   2439 /*   This computes C = A rot B  (in base ten and rotating set->digits */
   2440 /*   digits).                                                         */
   2441 /*                                                                    */
   2442 /*   res is C, the result.  C may be A and/or B (e.g., X=XrotX)       */
   2443 /*   lhs is A                                                         */
   2444 /*   rhs is B, the number of digits to rotate (-ve to right)          */
   2445 /*   set is the context                                               */
   2446 /*                                                                    */
   2447 /* The digits of the coefficient of A are rotated to the left (if B   */
   2448 /* is positive) or to the right (if B is negative) without adjusting  */
   2449 /* the exponent or the sign of A.  If lhs->digits is less than        */
   2450 /* set->digits the coefficient is padded with zeros on the left       */
   2451 /* before the rotate.  Any leading zeros in the result are removed    */
   2452 /* as usual.                                                          */
   2453 /*                                                                    */
   2454 /* B must be an integer (q=0) and in the range -set->digits through   */
   2455 /* +set->digits.                                                      */
   2456 /* C must have space for set->digits digits.                          */
   2457 /* NaNs are propagated as usual.  Infinities are unaffected (but      */
   2458 /* B must be valid).  No status is set unless B is invalid or an      */
   2459 /* operand is an sNaN.                                                */
   2460 /* ------------------------------------------------------------------ */
   2461 U_CAPI decNumber * U_EXPORT2 uprv_decNumberRotate(decNumber *res, const decNumber *lhs,
   2462                            const decNumber *rhs, decContext *set) {
   2463   uInt status=0;              /* accumulator  */
   2464   Int  rotate;                /* rhs as an Int  */
   2465 
   2466   #if DECCHECK
   2467   if (decCheckOperands(res, lhs, rhs, set)) return res;
   2468   #endif
   2469 
   2470   /* NaNs propagate as normal  */
   2471   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
   2472     decNaNs(res, lhs, rhs, set, &status);
   2473    /* rhs must be an integer  */
   2474    else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
   2475     status=DEC_Invalid_operation;
   2476    else { /* both numeric, rhs is an integer  */
   2477     rotate=decGetInt(rhs);                   /* [cannot fail]  */
   2478     if (rotate==BADINT                       /* something bad ..  */
   2479      || rotate==BIGODD || rotate==BIGEVEN    /* .. very big ..  */
   2480      || abs(rotate)>set->digits)             /* .. or out of range  */
   2481       status=DEC_Invalid_operation;
   2482      else {                                  /* rhs is OK  */
   2483       uprv_decNumberCopy(res, lhs);
   2484       /* convert -ve rotate to equivalent positive rotation  */
   2485       if (rotate<0) rotate=set->digits+rotate;
   2486       if (rotate!=0 && rotate!=set->digits   /* zero or full rotation  */
   2487        && !decNumberIsInfinite(res)) {       /* lhs was infinite  */
   2488         /* left-rotate to do; 0 < rotate < set->digits  */
   2489         uInt units, shift;                   /* work  */
   2490         uInt msudigits;                      /* digits in result msu  */
   2491         Unit *msu=res->lsu+D2U(res->digits)-1;    /* current msu  */
   2492         Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu  */
   2493         for (msu++; msu<=msumax; msu++) *msu=0;   /* ensure high units=0  */
   2494         res->digits=set->digits;                  /* now full-length  */
   2495         msudigits=MSUDIGITS(res->digits);         /* actual digits in msu  */
   2496 
   2497         /* rotation here is done in-place, in three steps  */
   2498         /* 1. shift all to least up to one unit to unit-align final  */
   2499         /*    lsd [any digits shifted out are rotated to the left,  */
   2500         /*    abutted to the original msd (which may require split)]  */
   2501         /*  */
   2502         /*    [if there are no whole units left to rotate, the  */
   2503         /*    rotation is now complete]  */
   2504         /*  */
   2505         /* 2. shift to least, from below the split point only, so that  */
   2506         /*    the final msd is in the right place in its Unit [any  */
   2507         /*    digits shifted out will fit exactly in the current msu,  */
   2508         /*    left aligned, no split required]  */
   2509         /*  */
   2510         /* 3. rotate all the units by reversing left part, right  */
   2511         /*    part, and then whole  */
   2512         /*  */
   2513         /* example: rotate right 8 digits (2 units + 2), DECDPUN=3.  */
   2514         /*  */
   2515         /*   start: 00a bcd efg hij klm npq  */
   2516         /*  */
   2517         /*      1a  000 0ab cde fgh|ijk lmn [pq saved]  */
   2518         /*      1b  00p qab cde fgh|ijk lmn  */
   2519         /*  */
   2520         /*      2a  00p qab cde fgh|00i jkl [mn saved]  */
   2521         /*      2b  mnp qab cde fgh|00i jkl  */
   2522         /*  */
   2523         /*      3a  fgh cde qab mnp|00i jkl  */
   2524         /*      3b  fgh cde qab mnp|jkl 00i  */
   2525         /*      3c  00i jkl mnp qab cde fgh  */
   2526 
   2527         /* Step 1: amount to shift is the partial right-rotate count  */
   2528         rotate=set->digits-rotate;      /* make it right-rotate  */
   2529         units=rotate/DECDPUN;           /* whole units to rotate  */
   2530         shift=rotate%DECDPUN;           /* left-over digits count  */
   2531         if (shift>0) {                  /* not an exact number of units  */
   2532           uInt save=res->lsu[0]%powers[shift];    /* save low digit(s)  */
   2533           decShiftToLeast(res->lsu, D2U(res->digits), shift);
   2534           if (shift>msudigits) {        /* msumax-1 needs >0 digits  */
   2535             uInt rem=save%powers[shift-msudigits];/* split save  */
   2536             *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert  */
   2537             *(msumax-1)=*(msumax-1)
   2538                        +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* ..  */
   2539             }
   2540            else { /* all fits in msumax  */
   2541             *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1]  */
   2542             }
   2543           } /* digits shift needed  */
   2544 
   2545         /* If whole units to rotate...  */
   2546         if (units>0) {                  /* some to do  */
   2547           /* Step 2: the units to touch are the whole ones in rotate,  */
   2548           /*   if any, and the shift is DECDPUN-msudigits (which may be  */
   2549           /*   0, again)  */
   2550           shift=DECDPUN-msudigits;
   2551           if (shift>0) {                /* not an exact number of units  */
   2552             uInt save=res->lsu[0]%powers[shift];  /* save low digit(s)  */
   2553             decShiftToLeast(res->lsu, units, shift);
   2554             *msumax=*msumax+(Unit)(save*powers[msudigits]);
   2555             } /* partial shift needed  */
   2556 
   2557           /* Step 3: rotate the units array using triple reverse  */
   2558           /* (reversing is easy and fast)  */
   2559           decReverse(res->lsu+units, msumax);     /* left part  */
   2560           decReverse(res->lsu, res->lsu+units-1); /* right part  */
   2561           decReverse(res->lsu, msumax);           /* whole  */
   2562           } /* whole units to rotate  */
   2563         /* the rotation may have left an undetermined number of zeros  */
   2564         /* on the left, so true length needs to be calculated  */
   2565         res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
   2566         } /* rotate needed  */
   2567       } /* rhs OK  */
   2568     } /* numerics  */
   2569   if (status!=0) decStatus(res, status, set);
   2570   return res;
   2571   } /* decNumberRotate  */
   2572 
   2573 /* ------------------------------------------------------------------ */
   2574 /* decNumberSameQuantum -- test for equal exponents                   */
   2575 /*                                                                    */
   2576 /*   res is the result number, which will contain either 0 or 1       */
   2577 /*   lhs is a number to test                                          */
   2578 /*   rhs is the second (usually a pattern)                            */
   2579 /*                                                                    */
   2580 /* No errors are possible and no context is needed.                   */
   2581 /* ------------------------------------------------------------------ */
   2582 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSameQuantum(decNumber *res, const decNumber *lhs,
   2583                                  const decNumber *rhs) {
   2584   Unit ret=0;                      /* return value  */
   2585 
   2586   #if DECCHECK
   2587   if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
   2588   #endif
   2589 
   2590   if (SPECIALARGS) {
   2591     if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
   2592      else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
   2593      /* [anything else with a special gives 0]  */
   2594     }
   2595    else if (lhs->exponent==rhs->exponent) ret=1;
   2596 
   2597   uprv_decNumberZero(res);              /* OK to overwrite an operand now  */
   2598   *res->lsu=ret;
   2599   return res;
   2600   } /* decNumberSameQuantum  */
   2601 
   2602 /* ------------------------------------------------------------------ */
   2603 /* decNumberScaleB -- multiply by a power of 10                       */
   2604 /*                                                                    */
   2605 /* This computes C = A x 10**B where B is an integer (q=0) with       */
   2606 /* maximum magnitude 2*(emax+digits)                                  */
   2607 /*                                                                    */
   2608 /*   res is C, the result.  C may be A or B                           */
   2609 /*   lhs is A, the number to adjust                                   */
   2610 /*   rhs is B, the requested power of ten to use                      */
   2611 /*   set is the context                                               */
   2612 /*                                                                    */
   2613 /* C must have space for set->digits digits.                          */
   2614 /*                                                                    */
   2615 /* The result may underflow or overflow.                              */
   2616 /* ------------------------------------------------------------------ */
   2617 U_CAPI decNumber * U_EXPORT2 uprv_decNumberScaleB(decNumber *res, const decNumber *lhs,
   2618                             const decNumber *rhs, decContext *set) {
   2619   Int  reqexp;                /* requested exponent change [B]  */
   2620   uInt status=0;              /* accumulator  */
   2621   Int  residue;               /* work  */
   2622 
   2623   #if DECCHECK
   2624   if (decCheckOperands(res, lhs, rhs, set)) return res;
   2625   #endif
   2626 
   2627   /* Handle special values except lhs infinite  */
   2628   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
   2629     decNaNs(res, lhs, rhs, set, &status);
   2630     /* rhs must be an integer  */
   2631    else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
   2632     status=DEC_Invalid_operation;
   2633    else {
   2634     /* lhs is a number; rhs is a finite with q==0  */
   2635     reqexp=decGetInt(rhs);                   /* [cannot fail]  */
   2636     if (reqexp==BADINT                       /* something bad ..  */
   2637      || reqexp==BIGODD || reqexp==BIGEVEN    /* .. very big ..  */
   2638      || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range  */
   2639       status=DEC_Invalid_operation;
   2640      else {                                  /* rhs is OK  */
   2641       uprv_decNumberCopy(res, lhs);               /* all done if infinite lhs  */
   2642       if (!decNumberIsInfinite(res)) {       /* prepare to scale  */
   2643         res->exponent+=reqexp;               /* adjust the exponent  */
   2644         residue=0;
   2645         decFinalize(res, set, &residue, &status); /* .. and check  */
   2646         } /* finite LHS  */
   2647       } /* rhs OK  */
   2648     } /* rhs finite  */
   2649   if (status!=0) decStatus(res, status, set);
   2650   return res;
   2651   } /* decNumberScaleB  */
   2652 
   2653 /* ------------------------------------------------------------------ */
   2654 /* decNumberShift -- shift the coefficient of a Number left or right  */
   2655 /*                                                                    */
   2656 /*   This computes C = A << B or C = A >> -B  (in base ten).          */
   2657 /*                                                                    */
   2658 /*   res is C, the result.  C may be A and/or B (e.g., X=X<<X)        */
   2659 /*   lhs is A                                                         */
   2660 /*   rhs is B, the number of digits to shift (-ve to right)           */
   2661 /*   set is the context                                               */
   2662 /*                                                                    */
   2663 /* The digits of the coefficient of A are shifted to the left (if B   */
   2664 /* is positive) or to the right (if B is negative) without adjusting  */
   2665 /* the exponent or the sign of A.                                     */
   2666 /*                                                                    */
   2667 /* B must be an integer (q=0) and in the range -set->digits through   */
   2668 /* +set->digits.                                                      */
   2669 /* C must have space for set->digits digits.                          */
   2670 /* NaNs are propagated as usual.  Infinities are unaffected (but      */
   2671 /* B must be valid).  No status is set unless B is invalid or an      */
   2672 /* operand is an sNaN.                                                */
   2673 /* ------------------------------------------------------------------ */
   2674 U_CAPI decNumber * U_EXPORT2 uprv_decNumberShift(decNumber *res, const decNumber *lhs,
   2675                            const decNumber *rhs, decContext *set) {
   2676   uInt status=0;              /* accumulator  */
   2677   Int  shift;                 /* rhs as an Int  */
   2678 
   2679   #if DECCHECK
   2680   if (decCheckOperands(res, lhs, rhs, set)) return res;
   2681   #endif
   2682 
   2683   /* NaNs propagate as normal  */
   2684   if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
   2685     decNaNs(res, lhs, rhs, set, &status);
   2686    /* rhs must be an integer  */
   2687    else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
   2688     status=DEC_Invalid_operation;
   2689    else { /* both numeric, rhs is an integer  */
   2690     shift=decGetInt(rhs);                    /* [cannot fail]  */
   2691     if (shift==BADINT                        /* something bad ..  */
   2692      || shift==BIGODD || shift==BIGEVEN      /* .. very big ..  */
   2693      || abs(shift)>set->digits)              /* .. or out of range  */
   2694       status=DEC_Invalid_operation;
   2695      else {                                  /* rhs is OK  */
   2696       uprv_decNumberCopy(res, lhs);
   2697       if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do  */
   2698         if (shift>0) {                       /* to left  */
   2699           if (shift==set->digits) {          /* removing all  */
   2700             *res->lsu=0;                     /* so place 0  */
   2701             res->digits=1;                   /* ..  */
   2702             }
   2703            else {                            /*  */
   2704             /* first remove leading digits if necessary  */
   2705             if (res->digits+shift>set->digits) {
   2706               decDecap(res, res->digits+shift-set->digits);
   2707               /* that updated res->digits; may have gone to 1 (for a  */
   2708               /* single digit or for zero  */
   2709               }
   2710             if (res->digits>1 || *res->lsu)  /* if non-zero..  */
   2711               res->digits=decShiftToMost(res->lsu, res->digits, shift);
   2712             } /* partial left  */
   2713           } /* left  */
   2714          else { /* to right  */
   2715           if (-shift>=res->digits) {         /* discarding all  */
   2716             *res->lsu=0;                     /* so place 0  */
   2717             res->digits=1;                   /* ..  */
   2718             }
   2719            else {
   2720             decShiftToLeast(res->lsu, D2U(res->digits), -shift);
   2721             res->digits-=(-shift);
   2722             }
   2723           } /* to right  */
   2724         } /* non-0 non-Inf shift  */
   2725       } /* rhs OK  */
   2726     } /* numerics  */
   2727   if (status!=0) decStatus(res, status, set);
   2728   return res;
   2729   } /* decNumberShift  */
   2730 
   2731 /* ------------------------------------------------------------------ */
   2732 /* decNumberSquareRoot -- square root operator                        */
   2733 /*                                                                    */
   2734 /*   This computes C = squareroot(A)                                  */
   2735 /*                                                                    */
   2736 /*   res is C, the result.  C may be A                                */
   2737 /*   rhs is A                                                         */
   2738 /*   set is the context; note that rounding mode has no effect        */
   2739 /*                                                                    */
   2740 /* C must have space for set->digits digits.                          */
   2741 /* ------------------------------------------------------------------ */
   2742 /* This uses the following varying-precision algorithm in:            */
   2743 /*                                                                    */
   2744 /*   Properly Rounded Variable Precision Square Root, T. E. Hull and  */
   2745 /*   A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
   2746 /*   pp229-237, ACM, September 1985.                                  */
   2747 /*                                                                    */
   2748 /* The square-root is calculated using Newton's method, after which   */
   2749 /* a check is made to ensure the result is correctly rounded.         */
   2750 /*                                                                    */
   2751 /* % [Reformatted original Numerical Turing source code follows.]     */
   2752 /* function sqrt(x : real) : real                                     */
   2753 /* % sqrt(x) returns the properly rounded approximation to the square */
   2754 /* % root of x, in the precision of the calling environment, or it    */
   2755 /* % fails if x < 0.                                                  */
   2756 /* % t e hull and a abrham, august, 1984                              */
   2757 /* if x <= 0 then                                                     */
   2758 /*   if x < 0 then                                                    */
   2759 /*     assert false                                                   */
   2760 /*   else                                                             */
   2761 /*     result 0                                                       */
   2762 /*   end if                                                           */
   2763 /* end if                                                             */
   2764 /* var f := setexp(x, 0)  % fraction part of x   [0.1 <= x < 1]       */
   2765 /* var e := getexp(x)     % exponent part of x                        */
   2766 /* var approx : real                                                  */
   2767 /* if e mod 2 = 0  then                                               */
   2768 /*   approx := .259 + .819 * f   % approx to root of f                */
   2769 /* else                                                               */
   2770 /*   f := f/l0                   % adjustments                        */
   2771 /*   e := e + 1                  %   for odd                          */
   2772 /*   approx := .0819 + 2.59 * f  %   exponent                         */
   2773 /* end if                                                             */
   2774 /*                                                                    */
   2775 /* var p:= 3                                                          */
   2776 /* const maxp := currentprecision + 2                                 */
   2777 /* loop                                                               */
   2778 /*   p := min(2*p - 2, maxp)     % p = 4,6,10, . . . , maxp           */
   2779 /*   precision p                                                      */
   2780 /*   approx := .5 * (approx + f/approx)                               */
   2781 /*   exit when p = maxp                                               */
   2782 /* end loop                                                           */
   2783 /*                                                                    */
   2784 /* % approx is now within 1 ulp of the properly rounded square root   */
   2785 /* % of f; to ensure proper rounding, compare squares of (approx -    */
   2786 /* % l/2 ulp) and (approx + l/2 ulp) with f.                          */
   2787 /* p := currentprecision                                              */
   2788 /* begin                                                              */
   2789 /*   precision p + 2                                                  */
   2790 /*   const approxsubhalf := approx - setexp(.5, -p)                   */
   2791 /*   if mulru(approxsubhalf, approxsubhalf) > f then                  */
   2792 /*     approx := approx - setexp(.l, -p + 1)                          */
   2793 /*   else                                                             */
   2794 /*     const approxaddhalf := approx + setexp(.5, -p)                 */
   2795 /*     if mulrd(approxaddhalf, approxaddhalf) < f then                */
   2796 /*       approx := approx + setexp(.l, -p + 1)                        */
   2797 /*     end if                                                         */
   2798 /*   end if                                                           */
   2799 /* end                                                                */
   2800 /* result setexp(approx, e div 2)  % fix exponent                     */
   2801 /* end sqrt                                                           */
   2802 /* ------------------------------------------------------------------ */
   2803 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSquareRoot(decNumber *res, const decNumber *rhs,
   2804                                 decContext *set) {
   2805   decContext workset, approxset;   /* work contexts  */
   2806   decNumber dzero;                 /* used for constant zero  */
   2807   Int  maxp;                       /* largest working precision  */
   2808   Int  workp;                      /* working precision  */
   2809   Int  residue=0;                  /* rounding residue  */
   2810   uInt status=0, ignore=0;         /* status accumulators  */
   2811   uInt rstatus;                    /* ..  */
   2812   Int  exp;                        /* working exponent  */
   2813   Int  ideal;                      /* ideal (preferred) exponent  */
   2814   Int  needbytes;                  /* work  */
   2815   Int  dropped;                    /* ..  */
   2816 
   2817   #if DECSUBSET
   2818   decNumber *allocrhs=NULL;        /* non-NULL if rounded rhs allocated  */
   2819   #endif
   2820   /* buffer for f [needs +1 in case DECBUFFER 0]  */
   2821   decNumber buff[D2N(DECBUFFER+1)];
   2822   /* buffer for a [needs +2 to match likely maxp]  */
   2823   decNumber bufa[D2N(DECBUFFER+2)];
   2824   /* buffer for temporary, b [must be same size as a]  */
   2825   decNumber bufb[D2N(DECBUFFER+2)];
   2826   decNumber *allocbuff=NULL;       /* -> allocated buff, iff allocated  */
   2827   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated  */
   2828   decNumber *allocbufb=NULL;       /* -> allocated bufb, iff allocated  */
   2829   decNumber *f=buff;               /* reduced fraction  */
   2830   decNumber *a=bufa;               /* approximation to result  */
   2831   decNumber *b=bufb;               /* intermediate result  */
   2832   /* buffer for temporary variable, up to 3 digits  */
   2833   decNumber buft[D2N(3)];
   2834   decNumber *t=buft;               /* up-to-3-digit constant or work  */
   2835 
   2836   #if DECCHECK
   2837   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   2838   #endif
   2839 
   2840   do {                             /* protect allocated storage  */
   2841     #if DECSUBSET
   2842     if (!set->extended) {
   2843       /* reduce operand and set lostDigits status, as needed  */
   2844       if (rhs->digits>set->digits) {
   2845         allocrhs=decRoundOperand(rhs, set, &status);
   2846         if (allocrhs==NULL) break;
   2847         /* [Note: 'f' allocation below could reuse this buffer if  */
   2848         /* used, but as this is rare they are kept separate for clarity.]  */
   2849         rhs=allocrhs;
   2850         }
   2851       }
   2852     #endif
   2853     /* [following code does not require input rounding]  */
   2854 
   2855     /* handle infinities and NaNs  */
   2856     if (SPECIALARG) {
   2857       if (decNumberIsInfinite(rhs)) {         /* an infinity  */
   2858         if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
   2859          else uprv_decNumberCopy(res, rhs);        /* +Infinity  */
   2860         }
   2861        else decNaNs(res, rhs, NULL, set, &status); /* a NaN  */
   2862       break;
   2863       }
   2864 
   2865     /* calculate the ideal (preferred) exponent [floor(exp/2)]  */
   2866     /* [It would be nicer to write: ideal=rhs->exponent>>1, but this  */
   2867     /* generates a compiler warning.  Generated code is the same.]  */
   2868     ideal=(rhs->exponent&~1)/2;         /* target  */
   2869 
   2870     /* handle zeros  */
   2871     if (ISZERO(rhs)) {
   2872       uprv_decNumberCopy(res, rhs);          /* could be 0 or -0  */
   2873       res->exponent=ideal;              /* use the ideal [safe]  */
   2874       /* use decFinish to clamp any out-of-range exponent, etc.  */
   2875       decFinish(res, set, &residue, &status);
   2876       break;
   2877       }
   2878 
   2879     /* any other -x is an oops  */
   2880     if (decNumberIsNegative(rhs)) {
   2881       status|=DEC_Invalid_operation;
   2882       break;
   2883       }
   2884 
   2885     /* space is needed for three working variables  */
   2886     /*   f -- the same precision as the RHS, reduced to 0.01->0.99...  */
   2887     /*   a -- Hull's approximation -- precision, when assigned, is  */
   2888     /*        currentprecision+1 or the input argument precision,  */
   2889     /*        whichever is larger (+2 for use as temporary)  */
   2890     /*   b -- intermediate temporary result (same size as a)  */
   2891     /* if any is too long for local storage, then allocate  */
   2892     workp=MAXI(set->digits+1, rhs->digits);  /* actual rounding precision  */
   2893     workp=MAXI(workp, 7);                    /* at least 7 for low cases  */
   2894     maxp=workp+2;                            /* largest working precision  */
   2895 
   2896     needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
   2897     if (needbytes>(Int)sizeof(buff)) {
   2898       allocbuff=(decNumber *)malloc(needbytes);
   2899       if (allocbuff==NULL) {  /* hopeless -- abandon  */
   2900         status|=DEC_Insufficient_storage;
   2901         break;}
   2902       f=allocbuff;            /* use the allocated space  */
   2903       }
   2904     /* a and b both need to be able to hold a maxp-length number  */
   2905     needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
   2906     if (needbytes>(Int)sizeof(bufa)) {            /* [same applies to b]  */
   2907       allocbufa=(decNumber *)malloc(needbytes);
   2908       allocbufb=(decNumber *)malloc(needbytes);
   2909       if (allocbufa==NULL || allocbufb==NULL) {   /* hopeless  */
   2910         status|=DEC_Insufficient_storage;
   2911         break;}
   2912       a=allocbufa;            /* use the allocated spaces  */
   2913       b=allocbufb;            /* ..  */
   2914       }
   2915 
   2916     /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1  */
   2917     uprv_decNumberCopy(f, rhs);
   2918     exp=f->exponent+f->digits;               /* adjusted to Hull rules  */
   2919     f->exponent=-(f->digits);                /* to range  */
   2920 
   2921     /* set up working context  */
   2922     uprv_decContextDefault(&workset, DEC_INIT_DECIMAL64);
   2923     workset.emax=DEC_MAX_EMAX;
   2924     workset.emin=DEC_MIN_EMIN;
   2925 
   2926     /* [Until further notice, no error is possible and status bits  */
   2927     /* (Rounded, etc.) should be ignored, not accumulated.]  */
   2928 
   2929     /* Calculate initial approximation, and allow for odd exponent  */
   2930     workset.digits=workp;                    /* p for initial calculation  */
   2931     t->bits=0; t->digits=3;
   2932     a->bits=0; a->digits=3;
   2933     if ((exp & 1)==0) {                      /* even exponent  */
   2934       /* Set t=0.259, a=0.819  */
   2935       t->exponent=-3;
   2936       a->exponent=-3;
   2937       #if DECDPUN>=3
   2938         t->lsu[0]=259;
   2939         a->lsu[0]=819;
   2940       #elif DECDPUN==2
   2941         t->lsu[0]=59; t->lsu[1]=2;
   2942         a->lsu[0]=19; a->lsu[1]=8;
   2943       #else
   2944         t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
   2945         a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
   2946       #endif
   2947       }
   2948      else {                                  /* odd exponent  */
   2949       /* Set t=0.0819, a=2.59  */
   2950       f->exponent--;                         /* f=f/10  */
   2951       exp++;                                 /* e=e+1  */
   2952       t->exponent=-4;
   2953       a->exponent=-2;
   2954       #if DECDPUN>=3
   2955         t->lsu[0]=819;
   2956         a->lsu[0]=259;
   2957       #elif DECDPUN==2
   2958         t->lsu[0]=19; t->lsu[1]=8;
   2959         a->lsu[0]=59; a->lsu[1]=2;
   2960       #else
   2961         t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
   2962         a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
   2963       #endif
   2964       }
   2965 
   2966     decMultiplyOp(a, a, f, &workset, &ignore);    /* a=a*f  */
   2967     decAddOp(a, a, t, &workset, 0, &ignore);      /* ..+t  */
   2968     /* [a is now the initial approximation for sqrt(f), calculated with  */
   2969     /* currentprecision, which is also a's precision.]  */
   2970 
   2971     /* the main calculation loop  */
   2972     uprv_decNumberZero(&dzero);                   /* make 0  */
   2973     uprv_decNumberZero(t);                        /* set t = 0.5  */
   2974     t->lsu[0]=5;                             /* ..  */
   2975     t->exponent=-1;                          /* ..  */
   2976     workset.digits=3;                        /* initial p  */
   2977     for (; workset.digits<maxp;) {
   2978       /* set p to min(2*p - 2, maxp)  [hence 3; or: 4, 6, 10, ... , maxp]  */
   2979       workset.digits=MINI(workset.digits*2-2, maxp);
   2980       /* a = 0.5 * (a + f/a)  */
   2981       /* [calculated at p then rounded to currentprecision]  */
   2982       decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a  */
   2983       decAddOp(b, b, a, &workset, 0, &ignore);         /* b=b+a  */
   2984       decMultiplyOp(a, b, t, &workset, &ignore);       /* a=b*0.5  */
   2985       } /* loop  */
   2986 
   2987     /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits  */
   2988     /* now reduce to length, etc.; this needs to be done with a  */
   2989     /* having the correct exponent so as to handle subnormals  */
   2990     /* correctly  */
   2991     approxset=*set;                          /* get emin, emax, etc.  */
   2992     approxset.round=DEC_ROUND_HALF_EVEN;
   2993     a->exponent+=exp/2;                      /* set correct exponent  */
   2994     rstatus=0;                               /* clear status  */
   2995     residue=0;                               /* .. and accumulator  */
   2996     decCopyFit(a, a, &approxset, &residue, &rstatus);  /* reduce (if needed)  */
   2997     decFinish(a, &approxset, &residue, &rstatus);      /* clean and finalize  */
   2998 
   2999     /* Overflow was possible if the input exponent was out-of-range,  */
   3000     /* in which case quit  */
   3001     if (rstatus&DEC_Overflow) {
   3002       status=rstatus;                        /* use the status as-is  */
   3003       uprv_decNumberCopy(res, a);                 /* copy to result  */
   3004       break;
   3005       }
   3006 
   3007     /* Preserve status except Inexact/Rounded  */
   3008     status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
   3009 
   3010     /* Carry out the Hull correction  */
   3011     a->exponent-=exp/2;                      /* back to 0.1->1  */
   3012 
   3013     /* a is now at final precision and within 1 ulp of the properly  */
   3014     /* rounded square root of f; to ensure proper rounding, compare  */
   3015     /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f.  */
   3016     /* Here workset.digits=maxp and t=0.5, and a->digits determines  */
   3017     /* the ulp  */
   3018     workset.digits--;                             /* maxp-1 is OK now  */
   3019     t->exponent=-a->digits-1;                     /* make 0.5 ulp  */
   3020     decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp  */
   3021     workset.round=DEC_ROUND_UP;
   3022     decMultiplyOp(b, b, b, &workset, &ignore);    /* b = mulru(b, b)  */
   3023     decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed  */
   3024     if (decNumberIsNegative(b)) {                 /* f < b [i.e., b > f]  */
   3025       /* this is the more common adjustment, though both are rare  */
   3026       t->exponent++;                              /* make 1.0 ulp  */
   3027       t->lsu[0]=1;                                /* ..  */
   3028       decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp  */
   3029       /* assign to approx [round to length]  */
   3030       approxset.emin-=exp/2;                      /* adjust to match a  */
   3031       approxset.emax-=exp/2;
   3032       decAddOp(a, &dzero, a, &approxset, 0, &ignore);
   3033       }
   3034      else {
   3035       decAddOp(b, a, t, &workset, 0, &ignore);    /* b = a + 0.5 ulp  */
   3036       workset.round=DEC_ROUND_DOWN;
   3037       decMultiplyOp(b, b, b, &workset, &ignore);  /* b = mulrd(b, b)  */
   3038       decCompareOp(b, b, f, &workset, COMPARE, &ignore);   /* b ? f  */
   3039       if (decNumberIsNegative(b)) {               /* b < f  */
   3040         t->exponent++;                            /* make 1.0 ulp  */
   3041         t->lsu[0]=1;                              /* ..  */
   3042         decAddOp(a, a, t, &workset, 0, &ignore);  /* a = a + 1 ulp  */
   3043         /* assign to approx [round to length]  */
   3044         approxset.emin-=exp/2;                    /* adjust to match a  */
   3045         approxset.emax-=exp/2;
   3046         decAddOp(a, &dzero, a, &approxset, 0, &ignore);
   3047         }
   3048       }
   3049     /* [no errors are possible in the above, and rounding/inexact during  */
   3050     /* estimation are irrelevant, so status was not accumulated]  */
   3051 
   3052     /* Here, 0.1 <= a < 1  (still), so adjust back  */
   3053     a->exponent+=exp/2;                      /* set correct exponent  */
   3054 
   3055     /* count droppable zeros [after any subnormal rounding] by  */
   3056     /* trimming a copy  */
   3057     uprv_decNumberCopy(b, a);
   3058     decTrim(b, set, 1, 1, &dropped);         /* [drops trailing zeros]  */
   3059 
   3060     /* Set Inexact and Rounded.  The answer can only be exact if  */
   3061     /* it is short enough so that squaring it could fit in workp  */
   3062     /* digits, so this is the only (relatively rare) condition that  */
   3063     /* a careful check is needed  */
   3064     if (b->digits*2-1 > workp) {             /* cannot fit  */
   3065       status|=DEC_Inexact|DEC_Rounded;
   3066       }
   3067      else {                                  /* could be exact/unrounded  */
   3068       uInt mstatus=0;                        /* local status  */
   3069       decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply  */
   3070       if (mstatus&DEC_Overflow) {            /* result just won't fit  */
   3071         status|=DEC_Inexact|DEC_Rounded;
   3072         }
   3073        else {                                /* plausible  */
   3074         decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs  */
   3075         if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal  */
   3076          else {                              /* is Exact  */
   3077           /* here, dropped is the count of trailing zeros in 'a'  */
   3078           /* use closest exponent to ideal...  */
   3079           Int todrop=ideal-a->exponent;      /* most that can be dropped  */
   3080           if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s  */
   3081            else {                            /* unrounded  */
   3082             /* there are some to drop, but emax may not allow all  */
   3083             Int maxexp=set->emax-set->digits+1;
   3084             Int maxdrop=maxexp-a->exponent;
   3085             if (todrop>maxdrop && set->clamp) { /* apply clamping  */
   3086               todrop=maxdrop;
   3087               status|=DEC_Clamped;
   3088               }
   3089             if (dropped<todrop) {            /* clamp to those available  */
   3090               todrop=dropped;
   3091               status|=DEC_Clamped;
   3092               }
   3093             if (todrop>0) {                  /* have some to drop  */
   3094               decShiftToLeast(a->lsu, D2U(a->digits), todrop);
   3095               a->exponent+=todrop;           /* maintain numerical value  */
   3096               a->digits-=todrop;             /* new length  */
   3097               }
   3098             }
   3099           }
   3100         }
   3101       }
   3102 
   3103     /* double-check Underflow, as perhaps the result could not have  */
   3104     /* been subnormal (initial argument too big), or it is now Exact  */
   3105     if (status&DEC_Underflow) {
   3106       Int ae=rhs->exponent+rhs->digits-1;    /* adjusted exponent  */
   3107       /* check if truly subnormal  */
   3108       #if DECEXTFLAG                         /* DEC_Subnormal too  */
   3109         if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
   3110       #else
   3111         if (ae>=set->emin*2) status&=~DEC_Underflow;
   3112       #endif
   3113       /* check if truly inexact  */
   3114       if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
   3115       }
   3116 
   3117     uprv_decNumberCopy(res, a);                   /* a is now the result  */
   3118     } while(0);                              /* end protected  */
   3119 
   3120   if (allocbuff!=NULL) free(allocbuff);      /* drop any storage used  */
   3121   if (allocbufa!=NULL) free(allocbufa);      /* ..  */
   3122   if (allocbufb!=NULL) free(allocbufb);      /* ..  */
   3123   #if DECSUBSET
   3124   if (allocrhs !=NULL) free(allocrhs);       /* ..  */
   3125   #endif
   3126   if (status!=0) decStatus(res, status, set);/* then report status  */
   3127   #if DECCHECK
   3128   decCheckInexact(res, set);
   3129   #endif
   3130   return res;
   3131   } /* decNumberSquareRoot  */
   3132 
   3133 /* ------------------------------------------------------------------ */
   3134 /* decNumberSubtract -- subtract two Numbers                          */
   3135 /*                                                                    */
   3136 /*   This computes C = A - B                                          */
   3137 /*                                                                    */
   3138 /*   res is C, the result.  C may be A and/or B (e.g., X=X-X)         */
   3139 /*   lhs is A                                                         */
   3140 /*   rhs is B                                                         */
   3141 /*   set is the context                                               */
   3142 /*                                                                    */
   3143 /* C must have space for set->digits digits.                          */
   3144 /* ------------------------------------------------------------------ */
   3145 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSubtract(decNumber *res, const decNumber *lhs,
   3146                               const decNumber *rhs, decContext *set) {
   3147   uInt status=0;                        /* accumulator  */
   3148 
   3149   decAddOp(res, lhs, rhs, set, DECNEG, &status);
   3150   if (status!=0) decStatus(res, status, set);
   3151   #if DECCHECK
   3152   decCheckInexact(res, set);
   3153   #endif
   3154   return res;
   3155   } /* decNumberSubtract  */
   3156 
   3157 /* ------------------------------------------------------------------ */
   3158 /* decNumberToIntegralExact -- round-to-integral-value with InExact   */
   3159 /* decNumberToIntegralValue -- round-to-integral-value                */
   3160 /*                                                                    */
   3161 /*   res is the result                                                */
   3162 /*   rhs is input number                                              */
   3163 /*   set is the context                                               */
   3164 /*                                                                    */
   3165 /* res must have space for any value of rhs.                          */
   3166 /*                                                                    */
   3167 /* This implements the IEEE special operators and therefore treats    */
   3168 /* special values as valid.  For finite numbers it returns            */
   3169 /* rescale(rhs, 0) if rhs->exponent is <0.                            */
   3170 /* Otherwise the result is rhs (so no error is possible, except for   */
   3171 /* sNaN).                                                             */
   3172 /*                                                                    */
   3173 /* The context is used for rounding mode and status after sNaN, but   */
   3174 /* the digits setting is ignored.  The Exact version will signal      */
   3175 /* Inexact if the result differs numerically from rhs; the other      */
   3176 /* never signals Inexact.                                             */
   3177 /* ------------------------------------------------------------------ */
   3178 U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
   3179                                      decContext *set) {
   3180   decNumber dn;
   3181   decContext workset;              /* working context  */
   3182   uInt status=0;                   /* accumulator  */
   3183 
   3184   #if DECCHECK
   3185   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   3186   #endif
   3187 
   3188   /* handle infinities and NaNs  */
   3189   if (SPECIALARG) {
   3190     if (decNumberIsInfinite(rhs)) uprv_decNumberCopy(res, rhs); /* an Infinity  */
   3191      else decNaNs(res, rhs, NULL, set, &status); /* a NaN  */
   3192     }
   3193    else { /* finite  */
   3194     /* have a finite number; no error possible (res must be big enough)  */
   3195     if (rhs->exponent>=0) return uprv_decNumberCopy(res, rhs);
   3196     /* that was easy, but if negative exponent there is work to do...  */
   3197     workset=*set;                  /* clone rounding, etc.  */
   3198     workset.digits=rhs->digits;    /* no length rounding  */
   3199     workset.traps=0;               /* no traps  */
   3200     uprv_decNumberZero(&dn);            /* make a number with exponent 0  */
   3201     uprv_decNumberQuantize(res, rhs, &dn, &workset);
   3202     status|=workset.status;
   3203     }
   3204   if (status!=0) decStatus(res, status, set);
   3205   return res;
   3206   } /* decNumberToIntegralExact  */
   3207 
   3208 U_CAPI decNumber * U_EXPORT2 uprv_decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
   3209                                      decContext *set) {
   3210   decContext workset=*set;         /* working context  */
   3211   workset.traps=0;                 /* no traps  */
   3212   uprv_decNumberToIntegralExact(res, rhs, &workset);
   3213   /* this never affects set, except for sNaNs; NaN will have been set  */
   3214   /* or propagated already, so no need to call decStatus  */
   3215   set->status|=workset.status&DEC_Invalid_operation;
   3216   return res;
   3217   } /* decNumberToIntegralValue  */
   3218 
   3219 /* ------------------------------------------------------------------ */
   3220 /* decNumberXor -- XOR two Numbers, digitwise                         */
   3221 /*                                                                    */
   3222 /*   This computes C = A ^ B                                          */
   3223 /*                                                                    */
   3224 /*   res is C, the result.  C may be A and/or B (e.g., X=X^X)         */
   3225 /*   lhs is A                                                         */
   3226 /*   rhs is B                                                         */
   3227 /*   set is the context (used for result length and error report)     */
   3228 /*                                                                    */
   3229 /* C must have space for set->digits digits.                          */
   3230 /*                                                                    */
   3231 /* Logical function restrictions apply (see above); a NaN is          */
   3232 /* returned with Invalid_operation if a restriction is violated.      */
   3233 /* ------------------------------------------------------------------ */
   3234 U_CAPI decNumber * U_EXPORT2 uprv_decNumberXor(decNumber *res, const decNumber *lhs,
   3235                          const decNumber *rhs, decContext *set) {
   3236   const Unit *ua, *ub;                  /* -> operands  */
   3237   const Unit *msua, *msub;              /* -> operand msus  */
   3238   Unit  *uc, *msuc;                     /* -> result and its msu  */
   3239   Int   msudigs;                        /* digits in res msu  */
   3240   #if DECCHECK
   3241   if (decCheckOperands(res, lhs, rhs, set)) return res;
   3242   #endif
   3243 
   3244   if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
   3245    || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
   3246     decStatus(res, DEC_Invalid_operation, set);
   3247     return res;
   3248     }
   3249   /* operands are valid  */
   3250   ua=lhs->lsu;                          /* bottom-up  */
   3251   ub=rhs->lsu;                          /* ..  */
   3252   uc=res->lsu;                          /* ..  */
   3253   msua=ua+D2U(lhs->digits)-1;           /* -> msu of lhs  */
   3254   msub=ub+D2U(rhs->digits)-1;           /* -> msu of rhs  */
   3255   msuc=uc+D2U(set->digits)-1;           /* -> msu of result  */
   3256   msudigs=MSUDIGITS(set->digits);       /* [faster than remainder]  */
   3257   for (; uc<=msuc; ua++, ub++, uc++) {  /* Unit loop  */
   3258     Unit a, b;                          /* extract units  */
   3259     if (ua>msua) a=0;
   3260      else a=*ua;
   3261     if (ub>msub) b=0;
   3262      else b=*ub;
   3263     *uc=0;                              /* can now write back  */
   3264     if (a|b) {                          /* maybe 1 bits to examine  */
   3265       Int i, j;
   3266       /* This loop could be unrolled and/or use BIN2BCD tables  */
   3267       for (i=0; i<DECDPUN; i++) {
   3268         if ((a^b)&1) *uc=*uc+(Unit)powers[i];     /* effect XOR  */
   3269         j=a%10;
   3270         a=a/10;
   3271         j|=b%10;
   3272         b=b/10;
   3273         if (j>1) {
   3274           decStatus(res, DEC_Invalid_operation, set);
   3275           return res;
   3276           }
   3277         if (uc==msuc && i==msudigs-1) break;      /* just did final digit  */
   3278         } /* each digit  */
   3279       } /* non-zero  */
   3280     } /* each unit  */
   3281   /* [here uc-1 is the msu of the result]  */
   3282   res->digits=decGetDigits(res->lsu, uc-res->lsu);
   3283   res->exponent=0;                      /* integer  */
   3284   res->bits=0;                          /* sign=0  */
   3285   return res;  /* [no status to set]  */
   3286   } /* decNumberXor  */
   3287 
   3288 
   3289 /* ================================================================== */
   3290 /* Utility routines                                                   */
   3291 /* ================================================================== */
   3292 
   3293 /* ------------------------------------------------------------------ */
   3294 /* decNumberClass -- return the decClass of a decNumber               */
   3295 /*   dn -- the decNumber to test                                      */
   3296 /*   set -- the context to use for Emin                               */
   3297 /*   returns the decClass enum                                        */
   3298 /* ------------------------------------------------------------------ */
   3299 enum decClass uprv_decNumberClass(const decNumber *dn, decContext *set) {
   3300   if (decNumberIsSpecial(dn)) {
   3301     if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
   3302     if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
   3303     /* must be an infinity  */
   3304     if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
   3305     return DEC_CLASS_POS_INF;
   3306     }
   3307   /* is finite  */
   3308   if (uprv_decNumberIsNormal(dn, set)) { /* most common  */
   3309     if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
   3310     return DEC_CLASS_POS_NORMAL;
   3311     }
   3312   /* is subnormal or zero  */
   3313   if (decNumberIsZero(dn)) {    /* most common  */
   3314     if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
   3315     return DEC_CLASS_POS_ZERO;
   3316     }
   3317   if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
   3318   return DEC_CLASS_POS_SUBNORMAL;
   3319   } /* decNumberClass  */
   3320 
   3321 /* ------------------------------------------------------------------ */
   3322 /* decNumberClassToString -- convert decClass to a string             */
   3323 /*                                                                    */
   3324 /*  eclass is a valid decClass                                        */
   3325 /*  returns a constant string describing the class (max 13+1 chars)   */
   3326 /* ------------------------------------------------------------------ */
   3327 const char *uprv_decNumberClassToString(enum decClass eclass) {
   3328   if (eclass==DEC_CLASS_POS_NORMAL)    return DEC_ClassString_PN;
   3329   if (eclass==DEC_CLASS_NEG_NORMAL)    return DEC_ClassString_NN;
   3330   if (eclass==DEC_CLASS_POS_ZERO)      return DEC_ClassString_PZ;
   3331   if (eclass==DEC_CLASS_NEG_ZERO)      return DEC_ClassString_NZ;
   3332   if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
   3333   if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
   3334   if (eclass==DEC_CLASS_POS_INF)       return DEC_ClassString_PI;
   3335   if (eclass==DEC_CLASS_NEG_INF)       return DEC_ClassString_NI;
   3336   if (eclass==DEC_CLASS_QNAN)          return DEC_ClassString_QN;
   3337   if (eclass==DEC_CLASS_SNAN)          return DEC_ClassString_SN;
   3338   return DEC_ClassString_UN;           /* Unknown  */
   3339   } /* decNumberClassToString  */
   3340 
   3341 /* ------------------------------------------------------------------ */
   3342 /* decNumberCopy -- copy a number                                     */
   3343 /*                                                                    */
   3344 /*   dest is the target decNumber                                     */
   3345 /*   src  is the source decNumber                                     */
   3346 /*   returns dest                                                     */
   3347 /*                                                                    */
   3348 /* (dest==src is allowed and is a no-op)                              */
   3349 /* All fields are updated as required.  This is a utility operation,  */
   3350 /* so special values are unchanged and no error is possible.          */
   3351 /* ------------------------------------------------------------------ */
   3352 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopy(decNumber *dest, const decNumber *src) {
   3353 
   3354   #if DECCHECK
   3355   if (src==NULL) return uprv_decNumberZero(dest);
   3356   #endif
   3357 
   3358   if (dest==src) return dest;                /* no copy required  */
   3359 
   3360   /* Use explicit assignments here as structure assignment could copy  */
   3361   /* more than just the lsu (for small DECDPUN).  This would not affect  */
   3362   /* the value of the results, but could disturb test harness spill  */
   3363   /* checking.  */
   3364   dest->bits=src->bits;
   3365   dest->exponent=src->exponent;
   3366   dest->digits=src->digits;
   3367   dest->lsu[0]=src->lsu[0];
   3368   if (src->digits>DECDPUN) {                 /* more Units to come  */
   3369     const Unit *smsup, *s;                   /* work  */
   3370     Unit  *d;                                /* ..  */
   3371     /* memcpy for the remaining Units would be safe as they cannot  */
   3372     /* overlap.  However, this explicit loop is faster in short cases.  */
   3373     d=dest->lsu+1;                           /* -> first destination  */
   3374     smsup=src->lsu+D2U(src->digits);         /* -> source msu+1  */
   3375     for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
   3376     }
   3377   return dest;
   3378   } /* decNumberCopy  */
   3379 
   3380 /* ------------------------------------------------------------------ */
   3381 /* decNumberCopyAbs -- quiet absolute value operator                  */
   3382 /*                                                                    */
   3383 /*   This sets C = abs(A)                                             */
   3384 /*                                                                    */
   3385 /*   res is C, the result.  C may be A                                */
   3386 /*   rhs is A                                                         */
   3387 /*                                                                    */
   3388 /* C must have space for set->digits digits.                          */
   3389 /* No exception or error can occur; this is a quiet bitwise operation.*/
   3390 /* See also decNumberAbs for a checking version of this.              */
   3391 /* ------------------------------------------------------------------ */
   3392 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
   3393   #if DECCHECK
   3394   if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
   3395   #endif
   3396   uprv_decNumberCopy(res, rhs);
   3397   res->bits&=~DECNEG;                   /* turn off sign  */
   3398   return res;
   3399   } /* decNumberCopyAbs  */
   3400 
   3401 /* ------------------------------------------------------------------ */
   3402 /* decNumberCopyNegate -- quiet negate value operator                 */
   3403 /*                                                                    */
   3404 /*   This sets C = negate(A)                                          */
   3405 /*                                                                    */
   3406 /*   res is C, the result.  C may be A                                */
   3407 /*   rhs is A                                                         */
   3408 /*                                                                    */
   3409 /* C must have space for set->digits digits.                          */
   3410 /* No exception or error can occur; this is a quiet bitwise operation.*/
   3411 /* See also decNumberMinus for a checking version of this.            */
   3412 /* ------------------------------------------------------------------ */
   3413 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
   3414   #if DECCHECK
   3415   if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
   3416   #endif
   3417   uprv_decNumberCopy(res, rhs);
   3418   res->bits^=DECNEG;                    /* invert the sign  */
   3419   return res;
   3420   } /* decNumberCopyNegate  */
   3421 
   3422 /* ------------------------------------------------------------------ */
   3423 /* decNumberCopySign -- quiet copy and set sign operator              */
   3424 /*                                                                    */
   3425 /*   This sets C = A with the sign of B                               */
   3426 /*                                                                    */
   3427 /*   res is C, the result.  C may be A                                */
   3428 /*   lhs is A                                                         */
   3429 /*   rhs is B                                                         */
   3430 /*                                                                    */
   3431 /* C must have space for set->digits digits.                          */
   3432 /* No exception or error can occur; this is a quiet bitwise operation.*/
   3433 /* ------------------------------------------------------------------ */
   3434 U_CAPI decNumber * U_EXPORT2 uprv_decNumberCopySign(decNumber *res, const decNumber *lhs,
   3435                               const decNumber *rhs) {
   3436   uByte sign;                           /* rhs sign  */
   3437   #if DECCHECK
   3438   if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
   3439   #endif
   3440   sign=rhs->bits & DECNEG;              /* save sign bit  */
   3441   uprv_decNumberCopy(res, lhs);
   3442   res->bits&=~DECNEG;                   /* clear the sign  */
   3443   res->bits|=sign;                      /* set from rhs  */
   3444   return res;
   3445   } /* decNumberCopySign  */
   3446 
   3447 /* ------------------------------------------------------------------ */
   3448 /* decNumberGetBCD -- get the coefficient in BCD8                     */
   3449 /*   dn is the source decNumber                                       */
   3450 /*   bcd is the uInt array that will receive dn->digits BCD bytes,    */
   3451 /*     most-significant at offset 0                                   */
   3452 /*   returns bcd                                                      */
   3453 /*                                                                    */
   3454 /* bcd must have at least dn->digits bytes.  No error is possible; if */
   3455 /* dn is a NaN or Infinite, digits must be 1 and the coefficient 0.   */
   3456 /* ------------------------------------------------------------------ */
   3457 U_CAPI uByte * U_EXPORT2 uprv_decNumberGetBCD(const decNumber *dn, uByte *bcd) {
   3458   uByte *ub=bcd+dn->digits-1;      /* -> lsd  */
   3459   const Unit *up=dn->lsu;          /* Unit pointer, -> lsu  */
   3460 
   3461   #if DECDPUN==1                   /* trivial simple copy  */
   3462     for (; ub>=bcd; ub--, up++) *ub=*up;
   3463   #else                            /* chopping needed  */
   3464     uInt u=*up;                    /* work  */
   3465     uInt cut=DECDPUN;              /* downcounter through unit  */
   3466     for (; ub>=bcd; ub--) {
   3467       *ub=(uByte)(u%10);           /* [*6554 trick inhibits, here]  */
   3468       u=u/10;
   3469       cut--;
   3470       if (cut>0) continue;         /* more in this unit  */
   3471       up++;
   3472       u=*up;
   3473       cut=DECDPUN;
   3474       }
   3475   #endif
   3476   return bcd;
   3477   } /* decNumberGetBCD  */
   3478 
   3479 /* ------------------------------------------------------------------ */
   3480 /* decNumberSetBCD -- set (replace) the coefficient from BCD8         */
   3481 /*   dn is the target decNumber                                       */
   3482 /*   bcd is the uInt array that will source n BCD bytes, most-        */
   3483 /*     significant at offset 0                                        */
   3484 /*   n is the number of digits in the source BCD array (bcd)          */
   3485 /*   returns dn                                                       */
   3486 /*                                                                    */
   3487 /* dn must have space for at least n digits.  No error is possible;   */
   3488 /* if dn is a NaN, or Infinite, or is to become a zero, n must be 1   */
   3489 /* and bcd[0] zero.                                                   */
   3490 /* ------------------------------------------------------------------ */
   3491 U_CAPI decNumber * U_EXPORT2 uprv_decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
   3492   Unit *up=dn->lsu+D2U(dn->digits)-1;   /* -> msu [target pointer]  */
   3493   const uByte *ub=bcd;                  /* -> source msd  */
   3494 
   3495   #if DECDPUN==1                        /* trivial simple copy  */
   3496     for (; ub<bcd+n; ub++, up--) *up=*ub;
   3497   #else                                 /* some assembly needed  */
   3498     /* calculate how many digits in msu, and hence first cut  */
   3499     Int cut=MSUDIGITS(n);               /* [faster than remainder]  */
   3500     for (;up>=dn->lsu; up--) {          /* each Unit from msu  */
   3501       *up=0;                            /* will take <=DECDPUN digits  */
   3502       for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
   3503       cut=DECDPUN;                      /* next Unit has all digits  */
   3504       }
   3505   #endif
   3506   dn->digits=n;                         /* set digit count  */
   3507   return dn;
   3508   } /* decNumberSetBCD  */
   3509 
   3510 /* ------------------------------------------------------------------ */
   3511 /* decNumberIsNormal -- test normality of a decNumber                 */
   3512 /*   dn is the decNumber to test                                      */
   3513 /*   set is the context to use for Emin                               */
   3514 /*   returns 1 if |dn| is finite and >=Nmin, 0 otherwise              */
   3515 /* ------------------------------------------------------------------ */
   3516 Int uprv_decNumberIsNormal(const decNumber *dn, decContext *set) {
   3517   Int ae;                               /* adjusted exponent  */
   3518   #if DECCHECK
   3519   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
   3520   #endif
   3521 
   3522   if (decNumberIsSpecial(dn)) return 0; /* not finite  */
   3523   if (decNumberIsZero(dn)) return 0;    /* not non-zero  */
   3524 
   3525   ae=dn->exponent+dn->digits-1;         /* adjusted exponent  */
   3526   if (ae<set->emin) return 0;           /* is subnormal  */
   3527   return 1;
   3528   } /* decNumberIsNormal  */
   3529 
   3530 /* ------------------------------------------------------------------ */
   3531 /* decNumberIsSubnormal -- test subnormality of a decNumber           */
   3532 /*   dn is the decNumber to test                                      */
   3533 /*   set is the context to use for Emin                               */
   3534 /*   returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise    */
   3535 /* ------------------------------------------------------------------ */
   3536 Int uprv_decNumberIsSubnormal(const decNumber *dn, decContext *set) {
   3537   Int ae;                               /* adjusted exponent  */
   3538   #if DECCHECK
   3539   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
   3540   #endif
   3541 
   3542   if (decNumberIsSpecial(dn)) return 0; /* not finite  */
   3543   if (decNumberIsZero(dn)) return 0;    /* not non-zero  */
   3544 
   3545   ae=dn->exponent+dn->digits-1;         /* adjusted exponent  */
   3546   if (ae<set->emin) return 1;           /* is subnormal  */
   3547   return 0;
   3548   } /* decNumberIsSubnormal  */
   3549 
   3550 /* ------------------------------------------------------------------ */
   3551 /* decNumberTrim -- remove insignificant zeros                        */
   3552 /*                                                                    */
   3553 /*   dn is the number to trim                                         */
   3554 /*   returns dn                                                       */
   3555 /*                                                                    */
   3556 /* All fields are updated as required.  This is a utility operation,  */
   3557 /* so special values are unchanged and no error is possible.  The     */
   3558 /* zeros are removed unconditionally.                                 */
   3559 /* ------------------------------------------------------------------ */
   3560 U_CAPI decNumber * U_EXPORT2 uprv_decNumberTrim(decNumber *dn) {
   3561   Int  dropped;                    /* work  */
   3562   decContext set;                  /* ..  */
   3563   #if DECCHECK
   3564   if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
   3565   #endif
   3566   uprv_decContextDefault(&set, DEC_INIT_BASE);    /* clamp=0  */
   3567   return decTrim(dn, &set, 0, 1, &dropped);
   3568   } /* decNumberTrim  */
   3569 
   3570 /* ------------------------------------------------------------------ */
   3571 /* decNumberVersion -- return the name and version of this module     */
   3572 /*                                                                    */
   3573 /* No error is possible.                                              */
   3574 /* ------------------------------------------------------------------ */
   3575 const char * uprv_decNumberVersion(void) {
   3576   return DECVERSION;
   3577   } /* decNumberVersion  */
   3578 
   3579 /* ------------------------------------------------------------------ */
   3580 /* decNumberZero -- set a number to 0                                 */
   3581 /*                                                                    */
   3582 /*   dn is the number to set, with space for one digit                */
   3583 /*   returns dn                                                       */
   3584 /*                                                                    */
   3585 /* No error is possible.                                              */
   3586 /* ------------------------------------------------------------------ */
   3587 /* Memset is not used as it is much slower in some environments.  */
   3588 U_CAPI decNumber * U_EXPORT2 uprv_decNumberZero(decNumber *dn) {
   3589 
   3590   #if DECCHECK
   3591   if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
   3592   #endif
   3593 
   3594   dn->bits=0;
   3595   dn->exponent=0;
   3596   dn->digits=1;
   3597   dn->lsu[0]=0;
   3598   return dn;
   3599   } /* decNumberZero  */
   3600 
   3601 /* ================================================================== */
   3602 /* Local routines                                                     */
   3603 /* ================================================================== */
   3604 
   3605 /* ------------------------------------------------------------------ */
   3606 /* decToString -- lay out a number into a string                      */
   3607 /*                                                                    */
   3608 /*   dn     is the number to lay out                                  */
   3609 /*   string is where to lay out the number                            */
   3610 /*   eng    is 1 if Engineering, 0 if Scientific                      */
   3611 /*                                                                    */
   3612 /* string must be at least dn->digits+14 characters long              */
   3613 /* No error is possible.                                              */
   3614 /*                                                                    */
   3615 /* Note that this routine can generate a -0 or 0.000.  These are      */
   3616 /* never generated in subset to-number or arithmetic, but can occur   */
   3617 /* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234).              */
   3618 /* ------------------------------------------------------------------ */
   3619 /* If DECCHECK is enabled the string "?" is returned if a number is  */
   3620 /* invalid.  */
   3621 static void decToString(const decNumber *dn, char *string, Flag eng) {
   3622   Int exp=dn->exponent;       /* local copy  */
   3623   Int e;                      /* E-part value  */
   3624   Int pre;                    /* digits before the '.'  */
   3625   Int cut;                    /* for counting digits in a Unit  */
   3626   char *c=string;             /* work [output pointer]  */
   3627   const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer]  */
   3628   uInt u, pow;                /* work  */
   3629 
   3630   #if DECCHECK
   3631   if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
   3632     strcpy(string, "?");
   3633     return;}
   3634   #endif
   3635 
   3636   if (decNumberIsNegative(dn)) {   /* Negatives get a minus  */
   3637     *c='-';
   3638     c++;
   3639     }
   3640   if (dn->bits&DECSPECIAL) {       /* Is a special value  */
   3641     if (decNumberIsInfinite(dn)) {
   3642       strcpy(c,   "Inf");
   3643       strcpy(c+3, "inity");
   3644       return;}
   3645     /* a NaN  */
   3646     if (dn->bits&DECSNAN) {        /* signalling NaN  */
   3647       *c='s';
   3648       c++;
   3649       }
   3650     strcpy(c, "NaN");
   3651     c+=3;                          /* step past  */
   3652     /* if not a clean non-zero coefficient, that's all there is in a  */
   3653     /* NaN string  */
   3654     if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
   3655     /* [drop through to add integer]  */
   3656     }
   3657 
   3658   /* calculate how many digits in msu, and hence first cut  */
   3659   cut=MSUDIGITS(dn->digits);       /* [faster than remainder]  */
   3660   cut--;                           /* power of ten for digit  */
   3661 
   3662   if (exp==0) {                    /* simple integer [common fastpath]  */
   3663     for (;up>=dn->lsu; up--) {     /* each Unit from msu  */
   3664       u=*up;                       /* contains DECDPUN digits to lay out  */
   3665       for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
   3666       cut=DECDPUN-1;               /* next Unit has all digits  */
   3667       }
   3668     *c='\0';                       /* terminate the string  */
   3669     return;}
   3670 
   3671   /* non-0 exponent -- assume plain form */
   3672   pre=dn->digits+exp;              /* digits before '.'  */
   3673   e=0;                             /* no E  */
   3674   if ((exp>0) || (pre<-5)) {       /* need exponential form  */
   3675     e=exp+dn->digits-1;            /* calculate E value  */
   3676     pre=1;                         /* assume one digit before '.'  */
   3677     if (eng && (e!=0)) {           /* engineering: may need to adjust  */
   3678       Int adj;                     /* adjustment  */
   3679       /* The C remainder operator is undefined for negative numbers, so  */
   3680       /* a positive remainder calculation must be used here  */
   3681       if (e<0) {
   3682         adj=(-e)%3;
   3683         if (adj!=0) adj=3-adj;
   3684         }
   3685        else { /* e>0  */
   3686         adj=e%3;
   3687         }
   3688       e=e-adj;
   3689       /* if dealing with zero still produce an exponent which is a  */
   3690       /* multiple of three, as expected, but there will only be the  */
   3691       /* one zero before the E, still.  Otherwise note the padding.  */
   3692       if (!ISZERO(dn)) pre+=adj;
   3693        else {  /* is zero  */
   3694         if (adj!=0) {              /* 0.00Esnn needed  */
   3695           e=e+3;
   3696           pre=-(2-adj);
   3697           }
   3698         } /* zero  */
   3699       } /* eng  */
   3700     } /* need exponent  */
   3701 
   3702   /* lay out the digits of the coefficient, adding 0s and . as needed */
   3703   u=*up;
   3704   if (pre>0) {                     /* xxx.xxx or xx00 (engineering) form  */
   3705     Int n=pre;
   3706     for (; pre>0; pre--, c++, cut--) {
   3707       if (cut<0) {                 /* need new Unit  */
   3708         if (up==dn->lsu) break;    /* out of input digits (pre>digits)  */
   3709         up--;
   3710         cut=DECDPUN-1;
   3711         u=*up;
   3712         }
   3713       TODIGIT(u, cut, c, pow);
   3714       }
   3715     if (n<dn->digits) {            /* more to come, after '.'  */
   3716       *c='.'; c++;
   3717       for (;; c++, cut--) {
   3718         if (cut<0) {               /* need new Unit  */
   3719           if (up==dn->lsu) break;  /* out of input digits  */
   3720           up--;
   3721           cut=DECDPUN-1;
   3722           u=*up;
   3723           }
   3724         TODIGIT(u, cut, c, pow);
   3725         }
   3726       }
   3727      else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed  */
   3728     }
   3729    else {                          /* 0.xxx or 0.000xxx form  */
   3730     *c='0'; c++;
   3731     *c='.'; c++;
   3732     for (; pre<0; pre++, c++) *c='0';   /* add any 0's after '.'  */
   3733     for (; ; c++, cut--) {
   3734       if (cut<0) {                 /* need new Unit  */
   3735         if (up==dn->lsu) break;    /* out of input digits  */
   3736         up--;
   3737         cut=DECDPUN-1;
   3738         u=*up;
   3739         }
   3740       TODIGIT(u, cut, c, pow);
   3741       }
   3742     }
   3743 
   3744   /* Finally add the E-part, if needed.  It will never be 0, has a
   3745      base maximum and minimum of +999999999 through -999999999, but
   3746      could range down to -1999999998 for anormal numbers */
   3747   if (e!=0) {
   3748     Flag had=0;               /* 1=had non-zero  */
   3749     *c='E'; c++;
   3750     *c='+'; c++;              /* assume positive  */
   3751     u=e;                      /* ..  */
   3752     if (e<0) {
   3753       *(c-1)='-';             /* oops, need -  */
   3754       u=-e;                   /* uInt, please  */
   3755       }
   3756     /* lay out the exponent [_itoa or equivalent is not ANSI C]  */
   3757     for (cut=9; cut>=0; cut--) {
   3758       TODIGIT(u, cut, c, pow);
   3759       if (*c=='0' && !had) continue;    /* skip leading zeros  */
   3760       had=1;                            /* had non-0  */
   3761       c++;                              /* step for next  */
   3762       } /* cut  */
   3763     }
   3764   *c='\0';          /* terminate the string (all paths)  */
   3765   return;
   3766   } /* decToString  */
   3767 
   3768 /* ------------------------------------------------------------------ */
   3769 /* decAddOp -- add/subtract operation                                 */
   3770 /*                                                                    */
   3771 /*   This computes C = A + B                                          */
   3772 /*                                                                    */
   3773 /*   res is C, the result.  C may be A and/or B (e.g., X=X+X)         */
   3774 /*   lhs is A                                                         */
   3775 /*   rhs is B                                                         */
   3776 /*   set is the context                                               */
   3777 /*   negate is DECNEG if rhs should be negated, or 0 otherwise        */
   3778 /*   status accumulates status for the caller                         */
   3779 /*                                                                    */
   3780 /* C must have space for set->digits digits.                          */
   3781 /* Inexact in status must be 0 for correct Exact zero sign in result  */
   3782 /* ------------------------------------------------------------------ */
   3783 /* If possible, the coefficient is calculated directly into C.        */
   3784 /* However, if:                                                       */
   3785 /*   -- a digits+1 calculation is needed because the numbers are      */
   3786 /*      unaligned and span more than set->digits digits               */
   3787 /*   -- a carry to digits+1 digits looks possible                     */
   3788 /*   -- C is the same as A or B, and the result would destructively   */
   3789 /*      overlap the A or B coefficient                                */
   3790 /* then the result must be calculated into a temporary buffer.  In    */
   3791 /* this case a local (stack) buffer is used if possible, and only if  */
   3792 /* too long for that does malloc become the final resort.             */
   3793 /*                                                                    */
   3794 /* Misalignment is handled as follows:                                */
   3795 /*   Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp.    */
   3796 /*   BPad: Apply the padding by a combination of shifting (whole      */
   3797 /*         units) and multiplication (part units).                    */
   3798 /*                                                                    */
   3799 /* Addition, especially x=x+1, is speed-critical.                     */
   3800 /* The static buffer is larger than might be expected to allow for    */
   3801 /* calls from higher-level funtions (notable exp).                    */
   3802 /* ------------------------------------------------------------------ */
   3803 static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
   3804                             const decNumber *rhs, decContext *set,
   3805                             uByte negate, uInt *status) {
   3806   #if DECSUBSET
   3807   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated  */
   3808   decNumber *allocrhs=NULL;        /* .., rhs  */
   3809   #endif
   3810   Int   rhsshift;                  /* working shift (in Units)  */
   3811   Int   maxdigits;                 /* longest logical length  */
   3812   Int   mult;                      /* multiplier  */
   3813   Int   residue;                   /* rounding accumulator  */
   3814   uByte bits;                      /* result bits  */
   3815   Flag  diffsign;                  /* non-0 if arguments have different sign  */
   3816   Unit  *acc;                      /* accumulator for result  */
   3817   Unit  accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many  */
   3818                                    /* allocations when called from  */
   3819                                    /* other operations, notable exp]  */
   3820   Unit  *allocacc=NULL;            /* -> allocated acc buffer, iff allocated  */
   3821   Int   reqdigits=set->digits;     /* local copy; requested DIGITS  */
   3822   Int   padding;                   /* work  */
   3823 
   3824   #if DECCHECK
   3825   if (decCheckOperands(res, lhs, rhs, set)) return res;
   3826   #endif
   3827 
   3828   do {                             /* protect allocated storage  */
   3829     #if DECSUBSET
   3830     if (!set->extended) {
   3831       /* reduce operands and set lostDigits status, as needed  */
   3832       if (lhs->digits>reqdigits) {
   3833         alloclhs=decRoundOperand(lhs, set, status);
   3834         if (alloclhs==NULL) break;
   3835         lhs=alloclhs;
   3836         }
   3837       if (rhs->digits>reqdigits) {
   3838         allocrhs=decRoundOperand(rhs, set, status);
   3839         if (allocrhs==NULL) break;
   3840         rhs=allocrhs;
   3841         }
   3842       }
   3843     #endif
   3844     /* [following code does not require input rounding]  */
   3845 
   3846     /* note whether signs differ [used all paths]  */
   3847     diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
   3848 
   3849     /* handle infinities and NaNs  */
   3850     if (SPECIALARGS) {                  /* a special bit set  */
   3851       if (SPECIALARGS & (DECSNAN | DECNAN))  /* a NaN  */
   3852         decNaNs(res, lhs, rhs, set, status);
   3853        else { /* one or two infinities  */
   3854         if (decNumberIsInfinite(lhs)) { /* LHS is infinity  */
   3855           /* two infinities with different signs is invalid  */
   3856           if (decNumberIsInfinite(rhs) && diffsign) {
   3857             *status|=DEC_Invalid_operation;
   3858             break;
   3859             }
   3860           bits=lhs->bits & DECNEG;      /* get sign from LHS  */
   3861           }
   3862          else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity  */
   3863         bits|=DECINF;
   3864         uprv_decNumberZero(res);
   3865         res->bits=bits;                 /* set +/- infinity  */
   3866         } /* an infinity  */
   3867       break;
   3868       }
   3869 
   3870     /* Quick exit for add 0s; return the non-0, modified as need be  */
   3871     if (ISZERO(lhs)) {
   3872       Int adjust;                       /* work  */
   3873       Int lexp=lhs->exponent;           /* save in case LHS==RES  */
   3874       bits=lhs->bits;                   /* ..  */
   3875       residue=0;                        /* clear accumulator  */
   3876       decCopyFit(res, rhs, set, &residue, status); /* copy (as needed)  */
   3877       res->bits^=negate;                /* flip if rhs was negated  */
   3878       #if DECSUBSET
   3879       if (set->extended) {              /* exponents on zeros count  */
   3880       #endif
   3881         /* exponent will be the lower of the two  */
   3882         adjust=lexp-res->exponent;      /* adjustment needed [if -ve]  */
   3883         if (ISZERO(res)) {              /* both 0: special IEEE 754 rules  */
   3884           if (adjust<0) res->exponent=lexp;  /* set exponent  */
   3885           /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0  */
   3886           if (diffsign) {
   3887             if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
   3888              else res->bits=DECNEG;     /* preserve 0 sign  */
   3889             }
   3890           }
   3891          else { /* non-0 res  */
   3892           if (adjust<0) {     /* 0-padding needed  */
   3893             if ((res->digits-adjust)>set->digits) {
   3894               adjust=res->digits-set->digits;     /* to fit exactly  */
   3895               *status|=DEC_Rounded;               /* [but exact]  */
   3896               }
   3897             res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
   3898             res->exponent+=adjust;                /* set the exponent.  */
   3899             }
   3900           } /* non-0 res  */
   3901       #if DECSUBSET
   3902         } /* extended  */
   3903       #endif
   3904       decFinish(res, set, &residue, status);      /* clean and finalize  */
   3905       break;}
   3906 
   3907     if (ISZERO(rhs)) {                  /* [lhs is non-zero]  */
   3908       Int adjust;                       /* work  */
   3909       Int rexp=rhs->exponent;           /* save in case RHS==RES  */
   3910       bits=rhs->bits;                   /* be clean  */
   3911       residue=0;                        /* clear accumulator  */
   3912       decCopyFit(res, lhs, set, &residue, status); /* copy (as needed)  */
   3913       #if DECSUBSET
   3914       if (set->extended) {              /* exponents on zeros count  */
   3915       #endif
   3916         /* exponent will be the lower of the two  */
   3917         /* [0-0 case handled above]  */
   3918         adjust=rexp-res->exponent;      /* adjustment needed [if -ve]  */
   3919         if (adjust<0) {     /* 0-padding needed  */
   3920           if ((res->digits-adjust)>set->digits) {
   3921             adjust=res->digits-set->digits;     /* to fit exactly  */
   3922             *status|=DEC_Rounded;               /* [but exact]  */
   3923             }
   3924           res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
   3925           res->exponent+=adjust;                /* set the exponent.  */
   3926           }
   3927       #if DECSUBSET
   3928         } /* extended  */
   3929       #endif
   3930       decFinish(res, set, &residue, status);      /* clean and finalize  */
   3931       break;}
   3932 
   3933     /* [NB: both fastpath and mainpath code below assume these cases  */
   3934     /* (notably 0-0) have already been handled]  */
   3935 
   3936     /* calculate the padding needed to align the operands  */
   3937     padding=rhs->exponent-lhs->exponent;
   3938 
   3939     /* Fastpath cases where the numbers are aligned and normal, the RHS  */
   3940     /* is all in one unit, no operand rounding is needed, and no carry,  */
   3941     /* lengthening, or borrow is needed  */
   3942     if (padding==0
   3943         && rhs->digits<=DECDPUN
   3944         && rhs->exponent>=set->emin     /* [some normals drop through]  */
   3945         && rhs->exponent<=set->emax-set->digits+1 /* [could clamp]  */
   3946         && rhs->digits<=reqdigits
   3947         && lhs->digits<=reqdigits) {
   3948       Int partial=*lhs->lsu;
   3949       if (!diffsign) {                  /* adding  */
   3950         partial+=*rhs->lsu;
   3951         if ((partial<=DECDPUNMAX)       /* result fits in unit  */
   3952          && (lhs->digits>=DECDPUN ||    /* .. and no digits-count change  */
   3953              partial<(Int)powers[lhs->digits])) { /* ..  */
   3954           if (res!=lhs) uprv_decNumberCopy(res, lhs);  /* not in place  */
   3955           *res->lsu=(Unit)partial;      /* [copy could have overwritten RHS]  */
   3956           break;
   3957           }
   3958         /* else drop out for careful add  */
   3959         }
   3960        else {                           /* signs differ  */
   3961         partial-=*rhs->lsu;
   3962         if (partial>0) { /* no borrow needed, and non-0 result  */
   3963           if (res!=lhs) uprv_decNumberCopy(res, lhs);  /* not in place  */
   3964           *res->lsu=(Unit)partial;
   3965           /* this could have reduced digits [but result>0]  */
   3966           res->digits=decGetDigits(res->lsu, D2U(res->digits));
   3967           break;
   3968           }
   3969         /* else drop out for careful subtract  */
   3970         }
   3971       }
   3972 
   3973     /* Now align (pad) the lhs or rhs so they can be added or  */
   3974     /* subtracted, as necessary.  If one number is much larger than  */
   3975     /* the other (that is, if in plain form there is a least one  */
   3976     /* digit between the lowest digit of one and the highest of the  */
   3977     /* other) padding with up to DIGITS-1 trailing zeros may be  */
   3978     /* needed; then apply rounding (as exotic rounding modes may be  */
   3979     /* affected by the residue).  */
   3980     rhsshift=0;               /* rhs shift to left (padding) in Units  */
   3981     bits=lhs->bits;           /* assume sign is that of LHS  */
   3982     mult=1;                   /* likely multiplier  */
   3983 
   3984     /* [if padding==0 the operands are aligned; no padding is needed]  */
   3985     if (padding!=0) {
   3986       /* some padding needed; always pad the RHS, as any required  */
   3987       /* padding can then be effected by a simple combination of  */
   3988       /* shifts and a multiply  */
   3989       Flag swapped=0;
   3990       if (padding<0) {                  /* LHS needs the padding  */
   3991         const decNumber *t;
   3992         padding=-padding;               /* will be +ve  */
   3993         bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS  */
   3994         t=lhs; lhs=rhs; rhs=t;
   3995         swapped=1;
   3996         }
   3997 
   3998       /* If, after pad, rhs would be longer than lhs by digits+1 or  */
   3999       /* more then lhs cannot affect the answer, except as a residue,  */
   4000       /* so only need to pad up to a length of DIGITS+1.  */
   4001       if (rhs->digits+padding > lhs->digits+reqdigits+1) {
   4002         /* The RHS is sufficient  */
   4003         /* for residue use the relative sign indication...  */
   4004         Int shift=reqdigits-rhs->digits;     /* left shift needed  */
   4005         residue=1;                           /* residue for rounding  */
   4006         if (diffsign) residue=-residue;      /* signs differ  */
   4007         /* copy, shortening if necessary  */
   4008         decCopyFit(res, rhs, set, &residue, status);
   4009         /* if it was already shorter, then need to pad with zeros  */
   4010         if (shift>0) {
   4011           res->digits=decShiftToMost(res->lsu, res->digits, shift);
   4012           res->exponent-=shift;              /* adjust the exponent.  */
   4013           }
   4014         /* flip the result sign if unswapped and rhs was negated  */
   4015         if (!swapped) res->bits^=negate;
   4016         decFinish(res, set, &residue, status);    /* done  */
   4017         break;}
   4018 
   4019       /* LHS digits may affect result  */
   4020       rhsshift=D2U(padding+1)-1;        /* this much by Unit shift ..  */
   4021       mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication  */
   4022       } /* padding needed  */
   4023 
   4024     if (diffsign) mult=-mult;           /* signs differ  */
   4025 
   4026     /* determine the longer operand  */
   4027     maxdigits=rhs->digits+padding;      /* virtual length of RHS  */
   4028     if (lhs->digits>maxdigits) maxdigits=lhs->digits;
   4029 
   4030     /* Decide on the result buffer to use; if possible place directly  */
   4031     /* into result.  */
   4032     acc=res->lsu;                       /* assume add direct to result  */
   4033     /* If destructive overlap, or the number is too long, or a carry or  */
   4034     /* borrow to DIGITS+1 might be possible, a buffer must be used.  */
   4035     /* [Might be worth more sophisticated tests when maxdigits==reqdigits]  */
   4036     if ((maxdigits>=reqdigits)          /* is, or could be, too large  */
   4037      || (res==rhs && rhsshift>0)) {     /* destructive overlap  */
   4038       /* buffer needed, choose it; units for maxdigits digits will be  */
   4039       /* needed, +1 Unit for carry or borrow  */
   4040       Int need=D2U(maxdigits)+1;
   4041       acc=accbuff;                      /* assume use local buffer  */
   4042       if (need*sizeof(Unit)>sizeof(accbuff)) {
   4043         /* printf("malloc add %ld %ld\n", need, sizeof(accbuff));  */
   4044         allocacc=(Unit *)malloc(need*sizeof(Unit));
   4045         if (allocacc==NULL) {           /* hopeless -- abandon  */
   4046           *status|=DEC_Insufficient_storage;
   4047           break;}
   4048         acc=allocacc;
   4049         }
   4050       }
   4051 
   4052     res->bits=(uByte)(bits&DECNEG);     /* it's now safe to overwrite..  */
   4053     res->exponent=lhs->exponent;        /* .. operands (even if aliased)  */
   4054 
   4055     #if DECTRACE
   4056       decDumpAr('A', lhs->lsu, D2U(lhs->digits));
   4057       decDumpAr('B', rhs->lsu, D2U(rhs->digits));
   4058       printf("  :h: %ld %ld\n", rhsshift, mult);
   4059     #endif
   4060 
   4061     /* add [A+B*m] or subtract [A+B*(-m)]  */
   4062     res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
   4063                               rhs->lsu, D2U(rhs->digits),
   4064                               rhsshift, acc, mult)
   4065                *DECDPUN;           /* [units -> digits]  */
   4066     if (res->digits<0) {           /* borrowed...  */
   4067       res->digits=-res->digits;
   4068       res->bits^=DECNEG;           /* flip the sign  */
   4069       }
   4070     #if DECTRACE
   4071       decDumpAr('+', acc, D2U(res->digits));
   4072     #endif
   4073 
   4074     /* If a buffer was used the result must be copied back, possibly  */
   4075     /* shortening.  (If no buffer was used then the result must have  */
   4076     /* fit, so can't need rounding and residue must be 0.)  */
   4077     residue=0;                     /* clear accumulator  */
   4078     if (acc!=res->lsu) {
   4079       #if DECSUBSET
   4080       if (set->extended) {         /* round from first significant digit  */
   4081       #endif
   4082         /* remove leading zeros that were added due to rounding up to  */
   4083         /* integral Units -- before the test for rounding.  */
   4084         if (res->digits>reqdigits)
   4085           res->digits=decGetDigits(acc, D2U(res->digits));
   4086         decSetCoeff(res, set, acc, res->digits, &residue, status);
   4087       #if DECSUBSET
   4088         }
   4089        else { /* subset arithmetic rounds from original significant digit  */
   4090         /* May have an underestimate.  This only occurs when both  */
   4091         /* numbers fit in DECDPUN digits and are padding with a  */
   4092         /* negative multiple (-10, -100...) and the top digit(s) become  */
   4093         /* 0.  (This only matters when using X3.274 rules where the  */
   4094         /* leading zero could be included in the rounding.)  */
   4095         if (res->digits<maxdigits) {
   4096           *(acc+D2U(res->digits))=0; /* ensure leading 0 is there  */
   4097           res->digits=maxdigits;
   4098           }
   4099          else {
   4100           /* remove leading zeros that added due to rounding up to  */
   4101           /* integral Units (but only those in excess of the original  */
   4102           /* maxdigits length, unless extended) before test for rounding.  */
   4103           if (res->digits>reqdigits) {
   4104             res->digits=decGetDigits(acc, D2U(res->digits));
   4105             if (res->digits<maxdigits) res->digits=maxdigits;
   4106             }
   4107           }
   4108         decSetCoeff(res, set, acc, res->digits, &residue, status);
   4109         /* Now apply rounding if needed before removing leading zeros.  */
   4110         /* This is safe because subnormals are not a possibility  */
   4111         if (residue!=0) {
   4112           decApplyRound(res, set, residue, status);
   4113           residue=0;                 /* did what needed to be done  */
   4114           }
   4115         } /* subset  */
   4116       #endif
   4117       } /* used buffer  */
   4118 
   4119     /* strip leading zeros [these were left on in case of subset subtract]  */
   4120     res->digits=decGetDigits(res->lsu, D2U(res->digits));
   4121 
   4122     /* apply checks and rounding  */
   4123     decFinish(res, set, &residue, status);
   4124 
   4125     /* "When the sum of two operands with opposite signs is exactly  */
   4126     /* zero, the sign of that sum shall be '+' in all rounding modes  */
   4127     /* except round toward -Infinity, in which mode that sign shall be  */
   4128     /* '-'."  [Subset zeros also never have '-', set by decFinish.]  */
   4129     if (ISZERO(res) && diffsign
   4130      #if DECSUBSET
   4131      && set->extended
   4132      #endif
   4133      && (*status&DEC_Inexact)==0) {
   4134       if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG;   /* sign -  */
   4135                                   else res->bits&=~DECNEG;  /* sign +  */
   4136       }
   4137     } while(0);                              /* end protected  */
   4138 
   4139   if (allocacc!=NULL) free(allocacc);        /* drop any storage used  */
   4140   #if DECSUBSET
   4141   if (allocrhs!=NULL) free(allocrhs);        /* ..  */
   4142   if (alloclhs!=NULL) free(alloclhs);        /* ..  */
   4143   #endif
   4144   return res;
   4145   } /* decAddOp  */
   4146 
   4147 /* ------------------------------------------------------------------ */
   4148 /* decDivideOp -- division operation                                  */
   4149 /*                                                                    */
   4150 /*  This routine performs the calculations for all four division      */
   4151 /*  operators (divide, divideInteger, remainder, remainderNear).      */
   4152 /*                                                                    */
   4153 /*  C=A op B                                                          */
   4154 /*                                                                    */
   4155 /*   res is C, the result.  C may be A and/or B (e.g., X=X/X)         */
   4156 /*   lhs is A                                                         */
   4157 /*   rhs is B                                                         */
   4158 /*   set is the context                                               */
   4159 /*   op  is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively.    */
   4160 /*   status is the usual accumulator                                  */
   4161 /*                                                                    */
   4162 /* C must have space for set->digits digits.                          */
   4163 /*                                                                    */
   4164 /* ------------------------------------------------------------------ */
   4165 /*   The underlying algorithm of this routine is the same as in the   */
   4166 /*   1981 S/370 implementation, that is, non-restoring long division  */
   4167 /*   with bi-unit (rather than bi-digit) estimation for each unit     */
   4168 /*   multiplier.  In this pseudocode overview, complications for the  */
   4169 /*   Remainder operators and division residues for exact rounding are */
   4170 /*   omitted for clarity.                                             */
   4171 /*                                                                    */
   4172 /*     Prepare operands and handle special values                     */
   4173 /*     Test for x/0 and then 0/x                                      */
   4174 /*     Exp =Exp1 - Exp2                                               */
   4175 /*     Exp =Exp +len(var1) -len(var2)                                 */
   4176 /*     Sign=Sign1 * Sign2                                             */
   4177 /*     Pad accumulator (Var1) to double-length with 0's (pad1)        */
   4178 /*     Pad Var2 to same length as Var1                                */
   4179 /*     msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round  */
   4180 /*     have=0                                                         */
   4181 /*     Do until (have=digits+1 OR residue=0)                          */
   4182 /*       if exp<0 then if integer divide/residue then leave           */
   4183 /*       this_unit=0                                                  */
   4184 /*       Do forever                                                   */
   4185 /*          compare numbers                                           */
   4186 /*          if <0 then leave inner_loop                               */
   4187 /*          if =0 then (* quick exit without subtract *) do           */
   4188 /*             this_unit=this_unit+1; output this_unit                */
   4189 /*             leave outer_loop; end                                  */
   4190 /*          Compare lengths of numbers (mantissae):                   */
   4191 /*          If same then tops2=msu2pair -- {units 1&2 of var2}        */
   4192 /*                  else tops2=msu2plus -- {0, unit 1 of var2}        */
   4193 /*          tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
   4194 /*          mult=tops1/tops2  -- Good and safe guess at divisor       */
   4195 /*          if mult=0 then mult=1                                     */
   4196 /*          this_unit=this_unit+mult                                  */
   4197 /*          subtract                                                  */
   4198 /*          end inner_loop                                            */
   4199 /*        if have\=0 | this_unit\=0 then do                           */
   4200 /*          output this_unit                                          */
   4201 /*          have=have+1; end                                          */
   4202 /*        var2=var2/10                                                */
   4203 /*        exp=exp-1                                                   */
   4204 /*        end outer_loop                                              */
   4205 /*     exp=exp+1   -- set the proper exponent                         */
   4206 /*     if have=0 then generate answer=0                               */
   4207 /*     Return (Result is defined by Var1)                             */
   4208 /*                                                                    */
   4209 /* ------------------------------------------------------------------ */
   4210 /* Two working buffers are needed during the division; one (digits+   */
   4211 /* 1) to accumulate the result, and the other (up to 2*digits+1) for  */
   4212 /* long subtractions.  These are acc and var1 respectively.           */
   4213 /* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
   4214 /* The static buffers may be larger than might be expected to allow   */
   4215 /* for calls from higher-level funtions (notable exp).                */
   4216 /* ------------------------------------------------------------------ */
   4217 static decNumber * decDivideOp(decNumber *res,
   4218                                const decNumber *lhs, const decNumber *rhs,
   4219                                decContext *set, Flag op, uInt *status) {
   4220   #if DECSUBSET
   4221   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated  */
   4222   decNumber *allocrhs=NULL;        /* .., rhs  */
   4223   #endif
   4224   Unit  accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer  */
   4225   Unit  *acc=accbuff;              /* -> accumulator array for result  */
   4226   Unit  *allocacc=NULL;            /* -> allocated buffer, iff allocated  */
   4227   Unit  *accnext;                  /* -> where next digit will go  */
   4228   Int   acclength;                 /* length of acc needed [Units]  */
   4229   Int   accunits;                  /* count of units accumulated  */
   4230   Int   accdigits;                 /* count of digits accumulated  */
   4231 
   4232   Unit  varbuff[SD2U(DECBUFFER*2+DECDPUN)];  /* buffer for var1  */
   4233   Unit  *var1=varbuff;             /* -> var1 array for long subtraction  */
   4234   Unit  *varalloc=NULL;            /* -> allocated buffer, iff used  */
   4235   Unit  *msu1;                     /* -> msu of var1  */
   4236 
   4237   const Unit *var2;                /* -> var2 array  */
   4238   const Unit *msu2;                /* -> msu of var2  */
   4239   Int   msu2plus;                  /* msu2 plus one [does not vary]  */
   4240   eInt  msu2pair;                  /* msu2 pair plus one [does not vary]  */
   4241 
   4242   Int   var1units, var2units;      /* actual lengths  */
   4243   Int   var2ulen;                  /* logical length (units)  */
   4244   Int   var1initpad=0;             /* var1 initial padding (digits)  */
   4245   Int   maxdigits;                 /* longest LHS or required acc length  */
   4246   Int   mult;                      /* multiplier for subtraction  */
   4247   Unit  thisunit;                  /* current unit being accumulated  */
   4248   Int   residue;                   /* for rounding  */
   4249   Int   reqdigits=set->digits;     /* requested DIGITS  */
   4250   Int   exponent;                  /* working exponent  */
   4251   Int   maxexponent=0;             /* DIVIDE maximum exponent if unrounded  */
   4252   uByte bits;                      /* working sign  */
   4253   Unit  *target;                   /* work  */
   4254   const Unit *source;              /* ..  */
   4255   uInt  const *pow;                /* ..  */
   4256   Int   shift, cut;                /* ..  */
   4257   #if DECSUBSET
   4258   Int   dropped;                   /* work  */
   4259   #endif
   4260 
   4261   #if DECCHECK
   4262   if (decCheckOperands(res, lhs, rhs, set)) return res;
   4263   #endif
   4264 
   4265   do {                             /* protect allocated storage  */
   4266     #if DECSUBSET
   4267     if (!set->extended) {
   4268       /* reduce operands and set lostDigits status, as needed  */
   4269       if (lhs->digits>reqdigits) {
   4270         alloclhs=decRoundOperand(lhs, set, status);
   4271         if (alloclhs==NULL) break;
   4272         lhs=alloclhs;
   4273         }
   4274       if (rhs->digits>reqdigits) {
   4275         allocrhs=decRoundOperand(rhs, set, status);
   4276         if (allocrhs==NULL) break;
   4277         rhs=allocrhs;
   4278         }
   4279       }
   4280     #endif
   4281     /* [following code does not require input rounding]  */
   4282 
   4283     bits=(lhs->bits^rhs->bits)&DECNEG;  /* assumed sign for divisions  */
   4284 
   4285     /* handle infinities and NaNs  */
   4286     if (SPECIALARGS) {                  /* a special bit set  */
   4287       if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs  */
   4288         decNaNs(res, lhs, rhs, set, status);
   4289         break;
   4290         }
   4291       /* one or two infinities  */
   4292       if (decNumberIsInfinite(lhs)) {   /* LHS (dividend) is infinite  */
   4293         if (decNumberIsInfinite(rhs) || /* two infinities are invalid ..  */
   4294             op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity  */
   4295           *status|=DEC_Invalid_operation;
   4296           break;
   4297           }
   4298         /* [Note that infinity/0 raises no exceptions]  */
   4299         uprv_decNumberZero(res);
   4300         res->bits=bits|DECINF;          /* set +/- infinity  */
   4301         break;
   4302         }
   4303        else {                           /* RHS (divisor) is infinite  */
   4304         residue=0;
   4305         if (op&(REMAINDER|REMNEAR)) {
   4306           /* result is [finished clone of] lhs  */
   4307           decCopyFit(res, lhs, set, &residue, status);
   4308           }
   4309          else {  /* a division  */
   4310           uprv_decNumberZero(res);
   4311           res->bits=bits;               /* set +/- zero  */
   4312           /* for DIVIDEINT the exponent is always 0.  For DIVIDE, result  */
   4313           /* is a 0 with infinitely negative exponent, clamped to minimum  */
   4314           if (op&DIVIDE) {
   4315             res->exponent=set->emin-set->digits+1;
   4316             *status|=DEC_Clamped;
   4317             }
   4318           }
   4319         decFinish(res, set, &residue, status);
   4320         break;
   4321         }
   4322       }
   4323 
   4324     /* handle 0 rhs (x/0)  */
   4325     if (ISZERO(rhs)) {                  /* x/0 is always exceptional  */
   4326       if (ISZERO(lhs)) {
   4327         uprv_decNumberZero(res);             /* [after lhs test]  */
   4328         *status|=DEC_Division_undefined;/* 0/0 will become NaN  */
   4329         }
   4330        else {
   4331         uprv_decNumberZero(res);
   4332         if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
   4333          else {
   4334           *status|=DEC_Division_by_zero; /* x/0  */
   4335           res->bits=bits|DECINF;         /* .. is +/- Infinity  */
   4336           }
   4337         }
   4338       break;}
   4339 
   4340     /* handle 0 lhs (0/x)  */
   4341     if (ISZERO(lhs)) {                  /* 0/x [x!=0]  */
   4342       #if DECSUBSET
   4343       if (!set->extended) uprv_decNumberZero(res);
   4344        else {
   4345       #endif
   4346         if (op&DIVIDE) {
   4347           residue=0;
   4348           exponent=lhs->exponent-rhs->exponent; /* ideal exponent  */
   4349           uprv_decNumberCopy(res, lhs);      /* [zeros always fit]  */
   4350           res->bits=bits;               /* sign as computed  */
   4351           res->exponent=exponent;       /* exponent, too  */
   4352           decFinalize(res, set, &residue, status);   /* check exponent  */
   4353           }
   4354          else if (op&DIVIDEINT) {
   4355           uprv_decNumberZero(res);           /* integer 0  */
   4356           res->bits=bits;               /* sign as computed  */
   4357           }
   4358          else {                         /* a remainder  */
   4359           exponent=rhs->exponent;       /* [save in case overwrite]  */
   4360           uprv_decNumberCopy(res, lhs);      /* [zeros always fit]  */
   4361           if (exponent<res->exponent) res->exponent=exponent; /* use lower  */
   4362           }
   4363       #if DECSUBSET
   4364         }
   4365       #endif
   4366       break;}
   4367 
   4368     /* Precalculate exponent.  This starts off adjusted (and hence fits  */
   4369     /* in 31 bits) and becomes the usual unadjusted exponent as the  */
   4370     /* division proceeds.  The order of evaluation is important, here,  */
   4371     /* to avoid wrap.  */
   4372     exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
   4373 
   4374     /* If the working exponent is -ve, then some quick exits are  */
   4375     /* possible because the quotient is known to be <1  */
   4376     /* [for REMNEAR, it needs to be < -1, as -0.5 could need work]  */
   4377     if (exponent<0 && !(op==DIVIDE)) {
   4378       if (op&DIVIDEINT) {
   4379         uprv_decNumberZero(res);                  /* integer part is 0  */
   4380         #if DECSUBSET
   4381         if (set->extended)
   4382         #endif
   4383           res->bits=bits;                    /* set +/- zero  */
   4384         break;}
   4385       /* fastpath remainders so long as the lhs has the smaller  */
   4386       /* (or equal) exponent  */
   4387       if (lhs->exponent<=rhs->exponent) {
   4388         if (op&REMAINDER || exponent<-1) {
   4389           /* It is REMAINDER or safe REMNEAR; result is [finished  */
   4390           /* clone of] lhs  (r = x - 0*y)  */
   4391           residue=0;
   4392           decCopyFit(res, lhs, set, &residue, status);
   4393           decFinish(res, set, &residue, status);
   4394           break;
   4395           }
   4396         /* [unsafe REMNEAR drops through]  */
   4397         }
   4398       } /* fastpaths  */
   4399 
   4400     /* Long (slow) division is needed; roll up the sleeves... */
   4401 
   4402     /* The accumulator will hold the quotient of the division.  */
   4403     /* If it needs to be too long for stack storage, then allocate.  */
   4404     acclength=D2U(reqdigits+DECDPUN);   /* in Units  */
   4405     if (acclength*sizeof(Unit)>sizeof(accbuff)) {
   4406       /* printf("malloc dvacc %ld units\n", acclength);  */
   4407       allocacc=(Unit *)malloc(acclength*sizeof(Unit));
   4408       if (allocacc==NULL) {             /* hopeless -- abandon  */
   4409         *status|=DEC_Insufficient_storage;
   4410         break;}
   4411       acc=allocacc;                     /* use the allocated space  */
   4412       }
   4413 
   4414     /* var1 is the padded LHS ready for subtractions.  */
   4415     /* If it needs to be too long for stack storage, then allocate.  */
   4416     /* The maximum units needed for var1 (long subtraction) is:  */
   4417     /* Enough for  */
   4418     /*     (rhs->digits+reqdigits-1) -- to allow full slide to right  */
   4419     /* or  (lhs->digits)             -- to allow for long lhs  */
   4420     /* whichever is larger  */
   4421     /*   +1                -- for rounding of slide to right  */
   4422     /*   +1                -- for leading 0s  */
   4423     /*   +1                -- for pre-adjust if a remainder or DIVIDEINT  */
   4424     /* [Note: unused units do not participate in decUnitAddSub data]  */
   4425     maxdigits=rhs->digits+reqdigits-1;
   4426     if (lhs->digits>maxdigits) maxdigits=lhs->digits;
   4427     var1units=D2U(maxdigits)+2;
   4428     /* allocate a guard unit above msu1 for REMAINDERNEAR  */
   4429     if (!(op&DIVIDE)) var1units++;
   4430     if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
   4431       /* printf("malloc dvvar %ld units\n", var1units+1);  */
   4432       varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
   4433       if (varalloc==NULL) {             /* hopeless -- abandon  */
   4434         *status|=DEC_Insufficient_storage;
   4435         break;}
   4436       var1=varalloc;                    /* use the allocated space  */
   4437       }
   4438 
   4439     /* Extend the lhs and rhs to full long subtraction length.  The lhs  */
   4440     /* is truly extended into the var1 buffer, with 0 padding, so a  */
   4441     /* subtract in place is always possible.  The rhs (var2) has  */
   4442     /* virtual padding (implemented by decUnitAddSub).  */
   4443     /* One guard unit was allocated above msu1 for rem=rem+rem in  */
   4444     /* REMAINDERNEAR.  */
   4445     msu1=var1+var1units-1;              /* msu of var1  */
   4446     source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array  */
   4447     for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
   4448     for (; target>=var1; target--) *target=0;
   4449 
   4450     /* rhs (var2) is left-aligned with var1 at the start  */
   4451     var2ulen=var1units;                 /* rhs logical length (units)  */
   4452     var2units=D2U(rhs->digits);         /* rhs actual length (units)  */
   4453     var2=rhs->lsu;                      /* -> rhs array  */
   4454     msu2=var2+var2units-1;              /* -> msu of var2 [never changes]  */
   4455     /* now set up the variables which will be used for estimating the  */
   4456     /* multiplication factor.  If these variables are not exact, add  */
   4457     /* 1 to make sure that the multiplier is never overestimated.  */
   4458     msu2plus=*msu2;                     /* it's value ..  */
   4459     if (var2units>1) msu2plus++;        /* .. +1 if any more  */
   4460     msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair ..  */
   4461     if (var2units>1) {                  /* .. [else treat 2nd as 0]  */
   4462       msu2pair+=*(msu2-1);              /* ..  */
   4463       if (var2units>2) msu2pair++;      /* .. +1 if any more  */
   4464       }
   4465 
   4466     /* The calculation is working in units, which may have leading zeros,  */
   4467     /* but the exponent was calculated on the assumption that they are  */
   4468     /* both left-aligned.  Adjust the exponent to compensate: add the  */
   4469     /* number of leading zeros in var1 msu and subtract those in var2 msu.  */
   4470     /* [This is actually done by counting the digits and negating, as  */
   4471     /* lead1=DECDPUN-digits1, and similarly for lead2.]  */
   4472     for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
   4473     for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
   4474 
   4475     /* Now, if doing an integer divide or remainder, ensure that  */
   4476     /* the result will be Unit-aligned.  To do this, shift the var1  */
   4477     /* accumulator towards least if need be.  (It's much easier to  */
   4478     /* do this now than to reassemble the residue afterwards, if  */
   4479     /* doing a remainder.)  Also ensure the exponent is not negative.  */
   4480     if (!(op&DIVIDE)) {
   4481       Unit *u;                          /* work  */
   4482       /* save the initial 'false' padding of var1, in digits  */
   4483       var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
   4484       /* Determine the shift to do.  */
   4485       if (exponent<0) cut=-exponent;
   4486        else cut=DECDPUN-exponent%DECDPUN;
   4487       decShiftToLeast(var1, var1units, cut);
   4488       exponent+=cut;                    /* maintain numerical value  */
   4489       var1initpad-=cut;                 /* .. and reduce padding  */
   4490       /* clean any most-significant units which were just emptied  */
   4491       for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
   4492       } /* align  */
   4493      else { /* is DIVIDE  */
   4494       maxexponent=lhs->exponent-rhs->exponent;    /* save  */
   4495       /* optimization: if the first iteration will just produce 0,  */
   4496       /* preadjust to skip it [valid for DIVIDE only]  */
   4497       if (*msu1<*msu2) {
   4498         var2ulen--;                     /* shift down  */
   4499         exponent-=DECDPUN;              /* update the exponent  */
   4500         }
   4501       }
   4502 
   4503     /* ---- start the long-division loops ------------------------------  */
   4504     accunits=0;                         /* no units accumulated yet  */
   4505     accdigits=0;                        /* .. or digits  */
   4506     accnext=acc+acclength-1;            /* -> msu of acc [NB: allows digits+1]  */
   4507     for (;;) {                          /* outer forever loop  */
   4508       thisunit=0;                       /* current unit assumed 0  */
   4509       /* find the next unit  */
   4510       for (;;) {                        /* inner forever loop  */
   4511         /* strip leading zero units [from either pre-adjust or from  */
   4512         /* subtract last time around].  Leave at least one unit.  */
   4513         for (; *msu1==0 && msu1>var1; msu1--) var1units--;
   4514 
   4515         if (var1units<var2ulen) break;       /* var1 too low for subtract  */
   4516         if (var1units==var2ulen) {           /* unit-by-unit compare needed  */
   4517           /* compare the two numbers, from msu  */
   4518           const Unit *pv1, *pv2;
   4519           Unit v2;                           /* units to compare  */
   4520           pv2=msu2;                          /* -> msu  */
   4521           for (pv1=msu1; ; pv1--, pv2--) {
   4522             /* v1=*pv1 -- always OK  */
   4523             v2=0;                            /* assume in padding  */
   4524             if (pv2>=var2) v2=*pv2;          /* in range  */
   4525             if (*pv1!=v2) break;             /* no longer the same  */
   4526             if (pv1==var1) break;            /* done; leave pv1 as is  */
   4527             }
   4528           /* here when all inspected or a difference seen  */
   4529           if (*pv1<v2) break;                /* var1 too low to subtract  */
   4530           if (*pv1==v2) {                    /* var1 == var2  */
   4531             /* reach here if var1 and var2 are identical; subtraction  */
   4532             /* would increase digit by one, and the residue will be 0 so  */
   4533             /* the calculation is done; leave the loop with residue=0.  */
   4534             thisunit++;                      /* as though subtracted  */
   4535             *var1=0;                         /* set var1 to 0  */
   4536             var1units=1;                     /* ..  */
   4537             break;  /* from inner  */
   4538             } /* var1 == var2  */
   4539           /* *pv1>v2.  Prepare for real subtraction; the lengths are equal  */
   4540           /* Estimate the multiplier (there's always a msu1-1)...  */
   4541           /* Bring in two units of var2 to provide a good estimate.  */
   4542           mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
   4543           } /* lengths the same  */
   4544          else { /* var1units > var2ulen, so subtraction is safe  */
   4545           /* The var2 msu is one unit towards the lsu of the var1 msu,  */
   4546           /* so only one unit for var2 can be used.  */
   4547           mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
   4548           }
   4549         if (mult==0) mult=1;                 /* must always be at least 1  */
   4550         /* subtraction needed; var1 is > var2  */
   4551         thisunit=(Unit)(thisunit+mult);      /* accumulate  */
   4552         /* subtract var1-var2, into var1; only the overlap needs  */
   4553         /* processing, as this is an in-place calculation  */
   4554         shift=var2ulen-var2units;
   4555         #if DECTRACE
   4556           decDumpAr('1', &var1[shift], var1units-shift);
   4557           decDumpAr('2', var2, var2units);
   4558           printf("m=%ld\n", -mult);
   4559         #endif
   4560         decUnitAddSub(&var1[shift], var1units-shift,
   4561                       var2, var2units, 0,
   4562                       &var1[shift], -mult);
   4563         #if DECTRACE
   4564           decDumpAr('#', &var1[shift], var1units-shift);
   4565         #endif
   4566         /* var1 now probably has leading zeros; these are removed at the  */
   4567         /* top of the inner loop.  */
   4568         } /* inner loop  */
   4569 
   4570       /* The next unit has been calculated in full; unless it's a  */
   4571       /* leading zero, add to acc  */
   4572       if (accunits!=0 || thisunit!=0) {      /* is first or non-zero  */
   4573         *accnext=thisunit;                   /* store in accumulator  */
   4574         /* account exactly for the new digits  */
   4575         if (accunits==0) {
   4576           accdigits++;                       /* at least one  */
   4577           for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
   4578           }
   4579          else accdigits+=DECDPUN;
   4580         accunits++;                          /* update count  */
   4581         accnext--;                           /* ready for next  */
   4582         if (accdigits>reqdigits) break;      /* have enough digits  */
   4583         }
   4584 
   4585       /* if the residue is zero, the operation is done (unless divide  */
   4586       /* or divideInteger and still not enough digits yet)  */
   4587       if (*var1==0 && var1units==1) {        /* residue is 0  */
   4588         if (op&(REMAINDER|REMNEAR)) break;
   4589         if ((op&DIVIDE) && (exponent<=maxexponent)) break;
   4590         /* [drop through if divideInteger]  */
   4591         }
   4592       /* also done enough if calculating remainder or integer  */
   4593       /* divide and just did the last ('units') unit  */
   4594       if (exponent==0 && !(op&DIVIDE)) break;
   4595 
   4596       /* to get here, var1 is less than var2, so divide var2 by the per-  */
   4597       /* Unit power of ten and go for the next digit  */
   4598       var2ulen--;                            /* shift down  */
   4599       exponent-=DECDPUN;                     /* update the exponent  */
   4600       } /* outer loop  */
   4601 
   4602     /* ---- division is complete ---------------------------------------  */
   4603     /* here: acc      has at least reqdigits+1 of good results (or fewer  */
   4604     /*                if early stop), starting at accnext+1 (its lsu)  */
   4605     /*       var1     has any residue at the stopping point  */
   4606     /*       accunits is the number of digits collected in acc  */
   4607     if (accunits==0) {             /* acc is 0  */
   4608       accunits=1;                  /* show have a unit ..  */
   4609       accdigits=1;                 /* ..  */
   4610       *accnext=0;                  /* .. whose value is 0  */
   4611       }
   4612      else accnext++;               /* back to last placed  */
   4613     /* accnext now -> lowest unit of result  */
   4614 
   4615     residue=0;                     /* assume no residue  */
   4616     if (op&DIVIDE) {
   4617       /* record the presence of any residue, for rounding  */
   4618       if (*var1!=0 || var1units>1) residue=1;
   4619        else { /* no residue  */
   4620         /* Had an exact division; clean up spurious trailing 0s.  */
   4621         /* There will be at most DECDPUN-1, from the final multiply,  */
   4622         /* and then only if the result is non-0 (and even) and the  */
   4623         /* exponent is 'loose'.  */
   4624         #if DECDPUN>1
   4625         Unit lsu=*accnext;
   4626         if (!(lsu&0x01) && (lsu!=0)) {
   4627           /* count the trailing zeros  */
   4628           Int drop=0;
   4629           for (;; drop++) {    /* [will terminate because lsu!=0]  */
   4630             if (exponent>=maxexponent) break;     /* don't chop real 0s  */
   4631             #if DECDPUN<=4
   4632               if ((lsu-QUOT10(lsu, drop+1)
   4633                   *powers[drop+1])!=0) break;     /* found non-0 digit  */
   4634             #else
   4635               if (lsu%powers[drop+1]!=0) break;   /* found non-0 digit  */
   4636             #endif
   4637             exponent++;
   4638             }
   4639           if (drop>0) {
   4640             accunits=decShiftToLeast(accnext, accunits, drop);
   4641             accdigits=decGetDigits(accnext, accunits);
   4642             accunits=D2U(accdigits);
   4643             /* [exponent was adjusted in the loop]  */
   4644             }
   4645           } /* neither odd nor 0  */
   4646         #endif
   4647         } /* exact divide  */
   4648       } /* divide  */
   4649      else /* op!=DIVIDE */ {
   4650       /* check for coefficient overflow  */
   4651       if (accdigits+exponent>reqdigits) {
   4652         *status|=DEC_Division_impossible;
   4653         break;
   4654         }
   4655       if (op & (REMAINDER|REMNEAR)) {
   4656         /* [Here, the exponent will be 0, because var1 was adjusted  */
   4657         /* appropriately.]  */
   4658         Int postshift;                       /* work  */
   4659         Flag wasodd=0;                       /* integer was odd  */
   4660         Unit *quotlsu;                       /* for save  */
   4661         Int  quotdigits;                     /* ..  */
   4662 
   4663         bits=lhs->bits;                      /* remainder sign is always as lhs  */
   4664 
   4665         /* Fastpath when residue is truly 0 is worthwhile [and  */
   4666         /* simplifies the code below]  */
   4667         if (*var1==0 && var1units==1) {      /* residue is 0  */
   4668           Int exp=lhs->exponent;             /* save min(exponents)  */
   4669           if (rhs->exponent<exp) exp=rhs->exponent;
   4670           uprv_decNumberZero(res);                /* 0 coefficient  */
   4671           #if DECSUBSET
   4672           if (set->extended)
   4673           #endif
   4674           res->exponent=exp;                 /* .. with proper exponent  */
   4675           res->bits=(uByte)(bits&DECNEG);          /* [cleaned]  */
   4676           decFinish(res, set, &residue, status);   /* might clamp  */
   4677           break;
   4678           }
   4679         /* note if the quotient was odd  */
   4680         if (*accnext & 0x01) wasodd=1;       /* acc is odd  */
   4681         quotlsu=accnext;                     /* save in case need to reinspect  */
   4682         quotdigits=accdigits;                /* ..  */
   4683 
   4684         /* treat the residue, in var1, as the value to return, via acc  */
   4685         /* calculate the unused zero digits.  This is the smaller of:  */
   4686         /*   var1 initial padding (saved above)  */
   4687         /*   var2 residual padding, which happens to be given by:  */
   4688         postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
   4689         /* [the 'exponent' term accounts for the shifts during divide]  */
   4690         if (var1initpad<postshift) postshift=var1initpad;
   4691 
   4692         /* shift var1 the requested amount, and adjust its digits  */
   4693         var1units=decShiftToLeast(var1, var1units, postshift);
   4694         accnext=var1;
   4695         accdigits=decGetDigits(var1, var1units);
   4696         accunits=D2U(accdigits);
   4697 
   4698         exponent=lhs->exponent;         /* exponent is smaller of lhs & rhs  */
   4699         if (rhs->exponent<exponent) exponent=rhs->exponent;
   4700 
   4701         /* Now correct the result if doing remainderNear; if it  */
   4702         /* (looking just at coefficients) is > rhs/2, or == rhs/2 and  */
   4703         /* the integer was odd then the result should be rem-rhs.  */
   4704         if (op&REMNEAR) {
   4705           Int compare, tarunits;        /* work  */
   4706           Unit *up;                     /* ..  */
   4707           /* calculate remainder*2 into the var1 buffer (which has  */
   4708           /* 'headroom' of an extra unit and hence enough space)  */
   4709           /* [a dedicated 'double' loop would be faster, here]  */
   4710           tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
   4711                                  0, accnext, 1);
   4712           /* decDumpAr('r', accnext, tarunits);  */
   4713 
   4714           /* Here, accnext (var1) holds tarunits Units with twice the  */
   4715           /* remainder's coefficient, which must now be compared to the  */
   4716           /* RHS.  The remainder's exponent may be smaller than the RHS's.  */
   4717           compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
   4718                                  rhs->exponent-exponent);
   4719           if (compare==BADINT) {             /* deep trouble  */
   4720             *status|=DEC_Insufficient_storage;
   4721             break;}
   4722 
   4723           /* now restore the remainder by dividing by two; the lsu  */
   4724           /* is known to be even.  */
   4725           for (up=accnext; up<accnext+tarunits; up++) {
   4726             Int half;              /* half to add to lower unit  */
   4727             half=*up & 0x01;
   4728             *up/=2;                /* [shift]  */
   4729             if (!half) continue;
   4730             *(up-1)+=(DECDPUNMAX+1)/2;
   4731             }
   4732           /* [accunits still describes the original remainder length]  */
   4733 
   4734           if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed  */
   4735             Int exp, expunits, exprem;       /* work  */
   4736             /* This is effectively causing round-up of the quotient,  */
   4737             /* so if it was the rare case where it was full and all  */
   4738             /* nines, it would overflow and hence division-impossible  */
   4739             /* should be raised  */
   4740             Flag allnines=0;                 /* 1 if quotient all nines  */
   4741             if (quotdigits==reqdigits) {     /* could be borderline  */
   4742               for (up=quotlsu; ; up++) {
   4743                 if (quotdigits>DECDPUN) {
   4744                   if (*up!=DECDPUNMAX) break;/* non-nines  */
   4745                   }
   4746                  else {                      /* this is the last Unit  */
   4747                   if (*up==powers[quotdigits]-1) allnines=1;
   4748                   break;
   4749                   }
   4750                 quotdigits-=DECDPUN;         /* checked those digits  */
   4751                 } /* up  */
   4752               } /* borderline check  */
   4753             if (allnines) {
   4754               *status|=DEC_Division_impossible;
   4755               break;}
   4756 
   4757             /* rem-rhs is needed; the sign will invert.  Again, var1  */
   4758             /* can safely be used for the working Units array.  */
   4759             exp=rhs->exponent-exponent;      /* RHS padding needed  */
   4760             /* Calculate units and remainder from exponent.  */
   4761             expunits=exp/DECDPUN;
   4762             exprem=exp%DECDPUN;
   4763             /* subtract [A+B*(-m)]; the result will always be negative  */
   4764             accunits=-decUnitAddSub(accnext, accunits,
   4765                                     rhs->lsu, D2U(rhs->digits),
   4766                                     expunits, accnext, -(Int)powers[exprem]);
   4767             accdigits=decGetDigits(accnext, accunits); /* count digits exactly  */
   4768             accunits=D2U(accdigits);    /* and recalculate the units for copy  */
   4769             /* [exponent is as for original remainder]  */
   4770             bits^=DECNEG;               /* flip the sign  */
   4771             }
   4772           } /* REMNEAR  */
   4773         } /* REMAINDER or REMNEAR  */
   4774       } /* not DIVIDE  */
   4775 
   4776     /* Set exponent and bits  */
   4777     res->exponent=exponent;
   4778     res->bits=(uByte)(bits&DECNEG);          /* [cleaned]  */
   4779 
   4780     /* Now the coefficient.  */
   4781     decSetCoeff(res, set, accnext, accdigits, &residue, status);
   4782 
   4783     decFinish(res, set, &residue, status);   /* final cleanup  */
   4784 
   4785     #if DECSUBSET
   4786     /* If a divide then strip trailing zeros if subset [after round]  */
   4787     if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
   4788     #endif
   4789     } while(0);                              /* end protected  */
   4790 
   4791   if (varalloc!=NULL) free(varalloc);   /* drop any storage used  */
   4792   if (allocacc!=NULL) free(allocacc);   /* ..  */
   4793   #if DECSUBSET
   4794   if (allocrhs!=NULL) free(allocrhs);   /* ..  */
   4795   if (alloclhs!=NULL) free(alloclhs);   /* ..  */
   4796   #endif
   4797   return res;
   4798   } /* decDivideOp  */
   4799 
   4800 /* ------------------------------------------------------------------ */
   4801 /* decMultiplyOp -- multiplication operation                          */
   4802 /*                                                                    */
   4803 /*  This routine performs the multiplication C=A x B.                 */
   4804 /*                                                                    */
   4805 /*   res is C, the result.  C may be A and/or B (e.g., X=X*X)         */
   4806 /*   lhs is A                                                         */
   4807 /*   rhs is B                                                         */
   4808 /*   set is the context                                               */
   4809 /*   status is the usual accumulator                                  */
   4810 /*                                                                    */
   4811 /* C must have space for set->digits digits.                          */
   4812 /*                                                                    */
   4813 /* ------------------------------------------------------------------ */
   4814 /* 'Classic' multiplication is used rather than Karatsuba, as the     */
   4815 /* latter would give only a minor improvement for the short numbers   */
   4816 /* expected to be handled most (and uses much more memory).           */
   4817 /*                                                                    */
   4818 /* There are two major paths here: the general-purpose ('old code')   */
   4819 /* path which handles all DECDPUN values, and a fastpath version      */
   4820 /* which is used if 64-bit ints are available, DECDPUN<=4, and more   */
   4821 /* than two calls to decUnitAddSub would be made.                     */
   4822 /*                                                                    */
   4823 /* The fastpath version lumps units together into 8-digit or 9-digit  */
   4824 /* chunks, and also uses a lazy carry strategy to minimise expensive  */
   4825 /* 64-bit divisions.  The chunks are then broken apart again into     */
   4826 /* units for continuing processing.  Despite this overhead, the       */
   4827 /* fastpath can speed up some 16-digit operations by 10x (and much    */
   4828 /* more for higher-precision calculations).                           */
   4829 /*                                                                    */
   4830 /* A buffer always has to be used for the accumulator; in the         */
   4831 /* fastpath, buffers are also always needed for the chunked copies of */
   4832 /* of the operand coefficients.                                       */
   4833 /* Static buffers are larger than needed just for multiply, to allow  */
   4834 /* for calls from other operations (notably exp).                     */
   4835 /* ------------------------------------------------------------------ */
   4836 #define FASTMUL (DECUSE64 && DECDPUN<5)
   4837 static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
   4838                                  const decNumber *rhs, decContext *set,
   4839                                  uInt *status) {
   4840   Int    accunits;                 /* Units of accumulator in use  */
   4841   Int    exponent;                 /* work  */
   4842   Int    residue=0;                /* rounding residue  */
   4843   uByte  bits;                     /* result sign  */
   4844   Unit  *acc;                      /* -> accumulator Unit array  */
   4845   Int    needbytes;                /* size calculator  */
   4846   void  *allocacc=NULL;            /* -> allocated accumulator, iff allocated  */
   4847   Unit  accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0,  */
   4848                                    /* *4 for calls from other operations)  */
   4849   const Unit *mer, *mermsup;       /* work  */
   4850   Int   madlength;                 /* Units in multiplicand  */
   4851   Int   shift;                     /* Units to shift multiplicand by  */
   4852 
   4853   #if FASTMUL
   4854     /* if DECDPUN is 1 or 3 work in base 10**9, otherwise  */
   4855     /* (DECDPUN is 2 or 4) then work in base 10**8  */
   4856     #if DECDPUN & 1                /* odd  */
   4857       #define FASTBASE 1000000000  /* base  */
   4858       #define FASTDIGS          9  /* digits in base  */
   4859       #define FASTLAZY         18  /* carry resolution point [1->18]  */
   4860     #else
   4861       #define FASTBASE  100000000
   4862       #define FASTDIGS          8
   4863       #define FASTLAZY       1844  /* carry resolution point [1->1844]  */
   4864     #endif
   4865     /* three buffers are used, two for chunked copies of the operands  */
   4866     /* (base 10**8 or base 10**9) and one base 2**64 accumulator with  */
   4867     /* lazy carry evaluation  */
   4868     uInt   zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0)  */
   4869     uInt  *zlhi=zlhibuff;                 /* -> lhs array  */
   4870     uInt  *alloclhi=NULL;                 /* -> allocated buffer, iff allocated  */
   4871     uInt   zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0)  */
   4872     uInt  *zrhi=zrhibuff;                 /* -> rhs array  */
   4873     uInt  *allocrhi=NULL;                 /* -> allocated buffer, iff allocated  */
   4874     uLong  zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0)  */
   4875     /* [allocacc is shared for both paths, as only one will run]  */
   4876     uLong *zacc=zaccbuff;          /* -> accumulator array for exact result  */
   4877     #if DECDPUN==1
   4878     Int    zoff;                   /* accumulator offset  */
   4879     #endif
   4880     uInt  *lip, *rip;              /* item pointers  */
   4881     uInt  *lmsi, *rmsi;            /* most significant items  */
   4882     Int    ilhs, irhs, iacc;       /* item counts in the arrays  */
   4883     Int    lazy;                   /* lazy carry counter  */
   4884     uLong  lcarry;                 /* uLong carry  */
   4885     uInt   carry;                  /* carry (NB not uLong)  */
   4886     Int    count;                  /* work  */
   4887     const  Unit *cup;              /* ..  */
   4888     Unit  *up;                     /* ..  */
   4889     uLong *lp;                     /* ..  */
   4890     Int    p;                      /* ..  */
   4891   #endif
   4892 
   4893   #if DECSUBSET
   4894     decNumber *alloclhs=NULL;      /* -> allocated buffer, iff allocated  */
   4895     decNumber *allocrhs=NULL;      /* -> allocated buffer, iff allocated  */
   4896   #endif
   4897 
   4898   #if DECCHECK
   4899   if (decCheckOperands(res, lhs, rhs, set)) return res;
   4900   #endif
   4901 
   4902   /* precalculate result sign  */
   4903   bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
   4904 
   4905   /* handle infinities and NaNs  */
   4906   if (SPECIALARGS) {               /* a special bit set  */
   4907     if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs  */
   4908       decNaNs(res, lhs, rhs, set, status);
   4909       return res;}
   4910     /* one or two infinities; Infinity * 0 is invalid  */
   4911     if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
   4912       ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
   4913       *status|=DEC_Invalid_operation;
   4914       return res;}
   4915     uprv_decNumberZero(res);
   4916     res->bits=bits|DECINF;         /* infinity  */
   4917     return res;}
   4918 
   4919   /* For best speed, as in DMSRCN [the original Rexx numerics  */
   4920   /* module], use the shorter number as the multiplier (rhs) and  */
   4921   /* the longer as the multiplicand (lhs) to minimise the number of  */
   4922   /* adds (partial products)  */
   4923   if (lhs->digits<rhs->digits) {   /* swap...  */
   4924     const decNumber *hold=lhs;
   4925     lhs=rhs;
   4926     rhs=hold;
   4927     }
   4928 
   4929   do {                             /* protect allocated storage  */
   4930     #if DECSUBSET
   4931     if (!set->extended) {
   4932       /* reduce operands and set lostDigits status, as needed  */
   4933       if (lhs->digits>set->digits) {
   4934         alloclhs=decRoundOperand(lhs, set, status);
   4935         if (alloclhs==NULL) break;
   4936         lhs=alloclhs;
   4937         }
   4938       if (rhs->digits>set->digits) {
   4939         allocrhs=decRoundOperand(rhs, set, status);
   4940         if (allocrhs==NULL) break;
   4941         rhs=allocrhs;
   4942         }
   4943       }
   4944     #endif
   4945     /* [following code does not require input rounding]  */
   4946 
   4947     #if FASTMUL                    /* fastpath can be used  */
   4948     /* use the fast path if there are enough digits in the shorter  */
   4949     /* operand to make the setup and takedown worthwhile  */
   4950     #define NEEDTWO (DECDPUN*2)    /* within two decUnitAddSub calls  */
   4951     if (rhs->digits>NEEDTWO) {     /* use fastpath...  */
   4952       /* calculate the number of elements in each array  */
   4953       ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling]  */
   4954       irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* ..  */
   4955       iacc=ilhs+irhs;
   4956 
   4957       /* allocate buffers if required, as usual  */
   4958       needbytes=ilhs*sizeof(uInt);
   4959       if (needbytes>(Int)sizeof(zlhibuff)) {
   4960         alloclhi=(uInt *)malloc(needbytes);
   4961         zlhi=alloclhi;}
   4962       needbytes=irhs*sizeof(uInt);
   4963       if (needbytes>(Int)sizeof(zrhibuff)) {
   4964         allocrhi=(uInt *)malloc(needbytes);
   4965         zrhi=allocrhi;}
   4966 
   4967       /* Allocating the accumulator space needs a special case when  */
   4968       /* DECDPUN=1 because when converting the accumulator to Units  */
   4969       /* after the multiplication each 8-byte item becomes 9 1-byte  */
   4970       /* units.  Therefore iacc extra bytes are needed at the front  */
   4971       /* (rounded up to a multiple of 8 bytes), and the uLong  */
   4972       /* accumulator starts offset the appropriate number of units  */
   4973       /* to the right to avoid overwrite during the unchunking.  */
   4974       needbytes=iacc*sizeof(uLong);
   4975       #if DECDPUN==1
   4976       zoff=(iacc+7)/8;        /* items to offset by  */
   4977       needbytes+=zoff*8;
   4978       #endif
   4979       if (needbytes>(Int)sizeof(zaccbuff)) {
   4980         allocacc=(uLong *)malloc(needbytes);
   4981         zacc=(uLong *)allocacc;}
   4982       if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
   4983         *status|=DEC_Insufficient_storage;
   4984         break;}
   4985 
   4986       acc=(Unit *)zacc;       /* -> target Unit array  */
   4987       #if DECDPUN==1
   4988       zacc+=zoff;             /* start uLong accumulator to right  */
   4989       #endif
   4990 
   4991       /* assemble the chunked copies of the left and right sides  */
   4992       for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
   4993         for (p=0, *lip=0; p<FASTDIGS && count>0;
   4994              p+=DECDPUN, cup++, count-=DECDPUN)
   4995           *lip+=*cup*powers[p];
   4996       lmsi=lip-1;     /* save -> msi  */
   4997       for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
   4998         for (p=0, *rip=0; p<FASTDIGS && count>0;
   4999              p+=DECDPUN, cup++, count-=DECDPUN)
   5000           *rip+=*cup*powers[p];
   5001       rmsi=rip-1;     /* save -> msi  */
   5002 
   5003       /* zero the accumulator  */
   5004       for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
   5005 
   5006       /* Start the multiplication */
   5007       /* Resolving carries can dominate the cost of accumulating the  */
   5008       /* partial products, so this is only done when necessary.  */
   5009       /* Each uLong item in the accumulator can hold values up to  */
   5010       /* 2**64-1, and each partial product can be as large as  */
   5011       /* (10**FASTDIGS-1)**2.  When FASTDIGS=9, this can be added to  */
   5012       /* itself 18.4 times in a uLong without overflowing, so during  */
   5013       /* the main calculation resolution is carried out every 18th  */
   5014       /* add -- every 162 digits.  Similarly, when FASTDIGS=8, the  */
   5015       /* partial products can be added to themselves 1844.6 times in  */
   5016       /* a uLong without overflowing, so intermediate carry  */
   5017       /* resolution occurs only every 14752 digits.  Hence for common  */
   5018       /* short numbers usually only the one final carry resolution  */
   5019       /* occurs.  */
   5020       /* (The count is set via FASTLAZY to simplify experiments to  */
   5021       /* measure the value of this approach: a 35% improvement on a  */
   5022       /* [34x34] multiply.)  */
   5023       lazy=FASTLAZY;                         /* carry delay count  */
   5024       for (rip=zrhi; rip<=rmsi; rip++) {     /* over each item in rhs  */
   5025         lp=zacc+(rip-zrhi);                  /* where to add the lhs  */
   5026         for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs  */
   5027           *lp+=(uLong)(*lip)*(*rip);         /* [this should in-line]  */
   5028           } /* lip loop  */
   5029         lazy--;
   5030         if (lazy>0 && rip!=rmsi) continue;
   5031         lazy=FASTLAZY;                       /* reset delay count  */
   5032         /* spin up the accumulator resolving overflows  */
   5033         for (lp=zacc; lp<zacc+iacc; lp++) {
   5034           if (*lp<FASTBASE) continue;        /* it fits  */
   5035           lcarry=*lp/FASTBASE;               /* top part [slow divide]  */
   5036           /* lcarry can exceed 2**32-1, so check again; this check  */
   5037           /* and occasional extra divide (slow) is well worth it, as  */
   5038           /* it allows FASTLAZY to be increased to 18 rather than 4  */
   5039           /* in the FASTDIGS=9 case  */
   5040           if (lcarry<FASTBASE) carry=(uInt)lcarry;  /* [usual]  */
   5041            else { /* two-place carry [fairly rare]  */
   5042             uInt carry2=(uInt)(lcarry/FASTBASE);    /* top top part  */
   5043             *(lp+2)+=carry2;                        /* add to item+2  */
   5044             *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow]  */
   5045             carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline]  */
   5046             }
   5047           *(lp+1)+=carry;                    /* add to item above [inline]  */
   5048           *lp-=((uLong)FASTBASE*carry);      /* [inline]  */
   5049           } /* carry resolution  */
   5050         } /* rip loop  */
   5051 
   5052       /* The multiplication is complete; time to convert back into  */
   5053       /* units.  This can be done in-place in the accumulator and in  */
   5054       /* 32-bit operations, because carries were resolved after the  */
   5055       /* final add.  This needs N-1 divides and multiplies for  */
   5056       /* each item in the accumulator (which will become up to N  */
   5057       /* units, where 2<=N<=9).  */
   5058       for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
   5059         uInt item=(uInt)*lp;                 /* decapitate to uInt  */
   5060         for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
   5061           uInt part=item/(DECDPUNMAX+1);
   5062           *up=(Unit)(item-(part*(DECDPUNMAX+1)));
   5063           item=part;
   5064           } /* p  */
   5065         *up=(Unit)item; up++;                /* [final needs no division]  */
   5066         } /* lp  */
   5067       accunits=up-acc;                       /* count of units  */
   5068       }
   5069      else { /* here to use units directly, without chunking ['old code']  */
   5070     #endif
   5071 
   5072       /* if accumulator will be too long for local storage, then allocate  */
   5073       acc=accbuff;                 /* -> assume buffer for accumulator  */
   5074       needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
   5075       if (needbytes>(Int)sizeof(accbuff)) {
   5076         allocacc=(Unit *)malloc(needbytes);
   5077         if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
   5078         acc=(Unit *)allocacc;                /* use the allocated space  */
   5079         }
   5080 
   5081       /* Now the main long multiplication loop */
   5082       /* Unlike the equivalent in the IBM Java implementation, there  */
   5083       /* is no advantage in calculating from msu to lsu.  So, do it  */
   5084       /* by the book, as it were.  */
   5085       /* Each iteration calculates ACC=ACC+MULTAND*MULT  */
   5086       accunits=1;                  /* accumulator starts at '0'  */
   5087       *acc=0;                      /* .. (lsu=0)  */
   5088       shift=0;                     /* no multiplicand shift at first  */
   5089       madlength=D2U(lhs->digits);  /* this won't change  */
   5090       mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier  */
   5091 
   5092       for (mer=rhs->lsu; mer<mermsup; mer++) {
   5093         /* Here, *mer is the next Unit in the multiplier to use  */
   5094         /* If non-zero [optimization] add it...  */
   5095         if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
   5096                                             lhs->lsu, madlength, 0,
   5097                                             &acc[shift], *mer)
   5098                                             + shift;
   5099          else { /* extend acc with a 0; it will be used shortly  */
   5100           *(acc+accunits)=0;       /* [this avoids length of <=0 later]  */
   5101           accunits++;
   5102           }
   5103         /* multiply multiplicand by 10**DECDPUN for next Unit to left  */
   5104         shift++;                   /* add this for 'logical length'  */
   5105         } /* n  */
   5106     #if FASTMUL
   5107       } /* unchunked units  */
   5108     #endif
   5109     /* common end-path  */
   5110     #if DECTRACE
   5111       decDumpAr('*', acc, accunits);         /* Show exact result  */
   5112     #endif
   5113 
   5114     /* acc now contains the exact result of the multiplication,  */
   5115     /* possibly with a leading zero unit; build the decNumber from  */
   5116     /* it, noting if any residue  */
   5117     res->bits=bits;                          /* set sign  */
   5118     res->digits=decGetDigits(acc, accunits); /* count digits exactly  */
   5119 
   5120     /* There can be a 31-bit wrap in calculating the exponent.  */
   5121     /* This can only happen if both input exponents are negative and  */
   5122     /* both their magnitudes are large.  If there was a wrap, set a  */
   5123     /* safe very negative exponent, from which decFinalize() will  */
   5124     /* raise a hard underflow shortly.  */
   5125     exponent=lhs->exponent+rhs->exponent;    /* calculate exponent  */
   5126     if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
   5127       exponent=-2*DECNUMMAXE;                /* force underflow  */
   5128     res->exponent=exponent;                  /* OK to overwrite now  */
   5129 
   5130 
   5131     /* Set the coefficient.  If any rounding, residue records  */
   5132     decSetCoeff(res, set, acc, res->digits, &residue, status);
   5133     decFinish(res, set, &residue, status);   /* final cleanup  */
   5134     } while(0);                         /* end protected  */
   5135 
   5136   if (allocacc!=NULL) free(allocacc);   /* drop any storage used  */
   5137   #if DECSUBSET
   5138   if (allocrhs!=NULL) free(allocrhs);   /* ..  */
   5139   if (alloclhs!=NULL) free(alloclhs);   /* ..  */
   5140   #endif
   5141   #if FASTMUL
   5142   if (allocrhi!=NULL) free(allocrhi);   /* ..  */
   5143   if (alloclhi!=NULL) free(alloclhi);   /* ..  */
   5144   #endif
   5145   return res;
   5146   } /* decMultiplyOp  */
   5147 
   5148 /* ------------------------------------------------------------------ */
   5149 /* decExpOp -- effect exponentiation                                  */
   5150 /*                                                                    */
   5151 /*   This computes C = exp(A)                                         */
   5152 /*                                                                    */
   5153 /*   res is C, the result.  C may be A                                */
   5154 /*   rhs is A                                                         */
   5155 /*   set is the context; note that rounding mode has no effect        */
   5156 /*                                                                    */
   5157 /* C must have space for set->digits digits. status is updated but    */
   5158 /* not set.                                                           */
   5159 /*                                                                    */
   5160 /* Restrictions:                                                      */
   5161 /*                                                                    */
   5162 /*   digits, emax, and -emin in the context must be less than         */
   5163 /*   2*DEC_MAX_MATH (1999998), and the rhs must be within these       */
   5164 /*   bounds or a zero.  This is an internal routine, so these         */
   5165 /*   restrictions are contractual and not enforced.                   */
   5166 /*                                                                    */
   5167 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
   5168 /* almost always be correctly rounded, but may be up to 1 ulp in      */
   5169 /* error in rare cases.                                               */
   5170 /*                                                                    */
   5171 /* Finite results will always be full precision and Inexact, except   */
   5172 /* when A is a zero or -Infinity (giving 1 or 0 respectively).        */
   5173 /* ------------------------------------------------------------------ */
   5174 /* This approach used here is similar to the algorithm described in   */
   5175 /*                                                                    */
   5176 /*   Variable Precision Exponential Function, T. E. Hull and          */
   5177 /*   A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
   5178 /*   pp79-91, ACM, June 1986.                                         */
   5179 /*                                                                    */
   5180 /* with the main difference being that the iterations in the series   */
   5181 /* evaluation are terminated dynamically (which does not require the  */
   5182 /* extra variable-precision variables which are expensive in this     */
   5183 /* context).                                                          */
   5184 /*                                                                    */
   5185 /* The error analysis in Hull & Abrham's paper applies except for the */
   5186 /* round-off error accumulation during the series evaluation.  This   */
   5187 /* code does not precalculate the number of iterations and so cannot  */
   5188 /* use Horner's scheme.  Instead, the accumulation is done at double- */
   5189 /* precision, which ensures that the additions of the terms are exact */
   5190 /* and do not accumulate round-off (and any round-off errors in the   */
   5191 /* terms themselves move 'to the right' faster than they can          */
   5192 /* accumulate).  This code also extends the calculation by allowing,  */
   5193 /* in the spirit of other decNumber operators, the input to be more   */
   5194 /* precise than the result (the precision used is based on the more   */
   5195 /* precise of the input or requested result).                         */
   5196 /*                                                                    */
   5197 /* Implementation notes:                                              */
   5198 /*                                                                    */
   5199 /* 1. This is separated out as decExpOp so it can be called from      */
   5200 /*    other Mathematical functions (notably Ln) with a wider range    */
   5201 /*    than normal.  In particular, it can handle the slightly wider   */
   5202 /*    (double) range needed by Ln (which has to be able to calculate  */
   5203 /*    exp(-x) where x can be the tiniest number (Ntiny).              */
   5204 /*                                                                    */
   5205 /* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop         */
   5206 /*    iterations by appoximately a third with additional (although    */
   5207 /*    diminishing) returns as the range is reduced to even smaller    */
   5208 /*    fractions.  However, h (the power of 10 used to correct the     */
   5209 /*    result at the end, see below) must be kept <=8 as otherwise     */
   5210 /*    the final result cannot be computed.  Hence the leverage is a   */
   5211 /*    sliding value (8-h), where potentially the range is reduced     */
   5212 /*    more for smaller values.                                        */
   5213 /*                                                                    */
   5214 /*    The leverage that can be applied in this way is severely        */
   5215 /*    limited by the cost of the raise-to-the power at the end,       */
   5216 /*    which dominates when the number of iterations is small (less    */
   5217 /*    than ten) or when rhs is short.  As an example, the adjustment  */
   5218 /*    x**10,000,000 needs 31 multiplications, all but one full-width. */
   5219 /*                                                                    */
   5220 /* 3. The restrictions (especially precision) could be raised with    */
   5221 /*    care, but the full decNumber range seems very hard within the   */
   5222 /*    32-bit limits.                                                  */
   5223 /*                                                                    */
   5224 /* 4. The working precisions for the static buffers are twice the     */
   5225 /*    obvious size to allow for calls from decNumberPower.            */
   5226 /* ------------------------------------------------------------------ */
   5227 decNumber * decExpOp(decNumber *res, const decNumber *rhs,
   5228                          decContext *set, uInt *status) {
   5229   uInt ignore=0;                   /* working status  */
   5230   Int h;                           /* adjusted exponent for 0.xxxx  */
   5231   Int p;                           /* working precision  */
   5232   Int residue;                     /* rounding residue  */
   5233   uInt needbytes;                  /* for space calculations  */
   5234   const decNumber *x=rhs;          /* (may point to safe copy later)  */
   5235   decContext aset, tset, dset;     /* working contexts  */
   5236   Int comp;                        /* work  */
   5237 
   5238   /* the argument is often copied to normalize it, so (unusually) it  */
   5239   /* is treated like other buffers, using DECBUFFER, +1 in case  */
   5240   /* DECBUFFER is 0  */
   5241   decNumber bufr[D2N(DECBUFFER*2+1)];
   5242   decNumber *allocrhs=NULL;        /* non-NULL if rhs buffer allocated  */
   5243 
   5244   /* the working precision will be no more than set->digits+8+1  */
   5245   /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER  */
   5246   /* is 0 (and twice that for the accumulator)  */
   5247 
   5248   /* buffer for t, term (working precision plus)  */
   5249   decNumber buft[D2N(DECBUFFER*2+9+1)];
   5250   decNumber *allocbuft=NULL;       /* -> allocated buft, iff allocated  */
   5251   decNumber *t=buft;               /* term  */
   5252   /* buffer for a, accumulator (working precision * 2), at least 9  */
   5253   decNumber bufa[D2N(DECBUFFER*4+18+1)];
   5254   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated  */
   5255   decNumber *a=bufa;               /* accumulator  */
   5256   /* decNumber for the divisor term; this needs at most 9 digits  */
   5257   /* and so can be fixed size [16 so can use standard context]  */
   5258   decNumber bufd[D2N(16)];
   5259   decNumber *d=bufd;               /* divisor  */
   5260   decNumber numone;                /* constant 1  */
   5261 
   5262   #if DECCHECK
   5263   Int iterations=0;                /* for later sanity check  */
   5264   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   5265   #endif
   5266 
   5267   do {                                  /* protect allocated storage  */
   5268     if (SPECIALARG) {                   /* handle infinities and NaNs  */
   5269       if (decNumberIsInfinite(rhs)) {   /* an infinity  */
   5270         if (decNumberIsNegative(rhs))   /* -Infinity -> +0  */
   5271           uprv_decNumberZero(res);
   5272          else uprv_decNumberCopy(res, rhs);  /* +Infinity -> self  */
   5273         }
   5274        else decNaNs(res, rhs, NULL, set, status); /* a NaN  */
   5275       break;}
   5276 
   5277     if (ISZERO(rhs)) {                  /* zeros -> exact 1  */
   5278       uprv_decNumberZero(res);               /* make clean 1  */
   5279       *res->lsu=1;                      /* ..  */
   5280       break;}                           /* [no status to set]  */
   5281 
   5282     /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path  */
   5283     /* positive and negative tiny cases which will result in inexact  */
   5284     /* 1.  This also allows the later add-accumulate to always be  */
   5285     /* exact (because its length will never be more than twice the  */
   5286     /* working precision).  */
   5287     /* The comparator (tiny) needs just one digit, so use the  */
   5288     /* decNumber d for it (reused as the divisor, etc., below); its  */
   5289     /* exponent is such that if x is positive it will have  */
   5290     /* set->digits-1 zeros between the decimal point and the digit,  */
   5291     /* which is 4, and if x is negative one more zero there as the  */
   5292     /* more precise result will be of the form 0.9999999 rather than  */
   5293     /* 1.0000001.  Hence, tiny will be 0.0000004  if digits=7 and x>0  */
   5294     /* or 0.00000004 if digits=7 and x<0.  If RHS not larger than  */
   5295     /* this then the result will be 1.000000  */
   5296     uprv_decNumberZero(d);                   /* clean  */
   5297     *d->lsu=4;                          /* set 4 ..  */
   5298     d->exponent=-set->digits;           /* * 10**(-d)  */
   5299     if (decNumberIsNegative(rhs)) d->exponent--;  /* negative case  */
   5300     comp=decCompare(d, rhs, 1);         /* signless compare  */
   5301     if (comp==BADINT) {
   5302       *status|=DEC_Insufficient_storage;
   5303       break;}
   5304     if (comp>=0) {                      /* rhs < d  */
   5305       Int shift=set->digits-1;
   5306       uprv_decNumberZero(res);               /* set 1  */
   5307       *res->lsu=1;                      /* ..  */
   5308       res->digits=decShiftToMost(res->lsu, 1, shift);
   5309       res->exponent=-shift;                  /* make 1.0000...  */
   5310       *status|=DEC_Inexact | DEC_Rounded;    /* .. inexactly  */
   5311       break;} /* tiny  */
   5312 
   5313     /* set up the context to be used for calculating a, as this is  */
   5314     /* used on both paths below  */
   5315     uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64);
   5316     /* accumulator bounds are as requested (could underflow)  */
   5317     aset.emax=set->emax;                /* usual bounds  */
   5318     aset.emin=set->emin;                /* ..  */
   5319     aset.clamp=0;                       /* and no concrete format  */
   5320 
   5321     /* calculate the adjusted (Hull & Abrham) exponent (where the  */
   5322     /* decimal point is just to the left of the coefficient msd)  */
   5323     h=rhs->exponent+rhs->digits;
   5324     /* if h>8 then 10**h cannot be calculated safely; however, when  */
   5325     /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at  */
   5326     /* least 6.59E+4342944, so (due to the restriction on Emax/Emin)  */
   5327     /* overflow (or underflow to 0) is guaranteed -- so this case can  */
   5328     /* be handled by simply forcing the appropriate excess  */
   5329     if (h>8) {                          /* overflow/underflow  */
   5330       /* set up here so Power call below will over or underflow to  */
   5331       /* zero; set accumulator to either 2 or 0.02  */
   5332       /* [stack buffer for a is always big enough for this]  */
   5333       uprv_decNumberZero(a);
   5334       *a->lsu=2;                        /* not 1 but < exp(1)  */
   5335       if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02  */
   5336       h=8;                              /* clamp so 10**h computable  */
   5337       p=9;                              /* set a working precision  */
   5338       }
   5339      else {                             /* h<=8  */
   5340       Int maxlever=(rhs->digits>8?1:0);
   5341       /* [could/should increase this for precisions >40 or so, too]  */
   5342 
   5343       /* if h is 8, cannot normalize to a lower upper limit because  */
   5344       /* the final result will not be computable (see notes above),  */
   5345       /* but leverage can be applied whenever h is less than 8.  */
   5346       /* Apply as much as possible, up to a MAXLEVER digits, which  */
   5347       /* sets the tradeoff against the cost of the later a**(10**h).  */
   5348       /* As h is increased, the working precision below also  */
   5349       /* increases to compensate for the "constant digits at the  */
   5350       /* front" effect.  */
   5351       Int lever=MINI(8-h, maxlever);    /* leverage attainable  */
   5352       Int use=-rhs->digits-lever;       /* exponent to use for RHS  */
   5353       h+=lever;                         /* apply leverage selected  */
   5354       if (h<0) {                        /* clamp  */
   5355         use+=h;                         /* [may end up subnormal]  */
   5356         h=0;
   5357         }
   5358       /* Take a copy of RHS if it needs normalization (true whenever x>=1)  */
   5359       if (rhs->exponent!=use) {
   5360         decNumber *newrhs=bufr;         /* assume will fit on stack  */
   5361         needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
   5362         if (needbytes>sizeof(bufr)) {   /* need malloc space  */
   5363           allocrhs=(decNumber *)malloc(needbytes);
   5364           if (allocrhs==NULL) {         /* hopeless -- abandon  */
   5365             *status|=DEC_Insufficient_storage;
   5366             break;}
   5367           newrhs=allocrhs;              /* use the allocated space  */
   5368           }
   5369         uprv_decNumberCopy(newrhs, rhs);     /* copy to safe space  */
   5370         newrhs->exponent=use;           /* normalize; now <1  */
   5371         x=newrhs;                       /* ready for use  */
   5372         /* decNumberShow(x);  */
   5373         }
   5374 
   5375       /* Now use the usual power series to evaluate exp(x).  The  */
   5376       /* series starts as 1 + x + x^2/2 ... so prime ready for the  */
   5377       /* third term by setting the term variable t=x, the accumulator  */
   5378       /* a=1, and the divisor d=2.  */
   5379 
   5380       /* First determine the working precision.  From Hull & Abrham  */
   5381       /* this is set->digits+h+2.  However, if x is 'over-precise' we  */
   5382       /* need to allow for all its digits to potentially participate  */
   5383       /* (consider an x where all the excess digits are 9s) so in  */
   5384       /* this case use x->digits+h+2  */
   5385       p=MAXI(x->digits, set->digits)+h+2;    /* [h<=8]  */
   5386 
   5387       /* a and t are variable precision, and depend on p, so space  */
   5388       /* must be allocated for them if necessary  */
   5389 
   5390       /* the accumulator needs to be able to hold 2p digits so that  */
   5391       /* the additions on the second and subsequent iterations are  */
   5392       /* sufficiently exact.  */
   5393       needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
   5394       if (needbytes>sizeof(bufa)) {     /* need malloc space  */
   5395         allocbufa=(decNumber *)malloc(needbytes);
   5396         if (allocbufa==NULL) {          /* hopeless -- abandon  */
   5397           *status|=DEC_Insufficient_storage;
   5398           break;}
   5399         a=allocbufa;                    /* use the allocated space  */
   5400         }
   5401       /* the term needs to be able to hold p digits (which is  */
   5402       /* guaranteed to be larger than x->digits, so the initial copy  */
   5403       /* is safe); it may also be used for the raise-to-power  */
   5404       /* calculation below, which needs an extra two digits  */
   5405       needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
   5406       if (needbytes>sizeof(buft)) {     /* need malloc space  */
   5407         allocbuft=(decNumber *)malloc(needbytes);
   5408         if (allocbuft==NULL) {          /* hopeless -- abandon  */
   5409           *status|=DEC_Insufficient_storage;
   5410           break;}
   5411         t=allocbuft;                    /* use the allocated space  */
   5412         }
   5413 
   5414       uprv_decNumberCopy(t, x);              /* term=x  */
   5415       uprv_decNumberZero(a); *a->lsu=1;      /* accumulator=1  */
   5416       uprv_decNumberZero(d); *d->lsu=2;      /* divisor=2  */
   5417       uprv_decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment  */
   5418 
   5419       /* set up the contexts for calculating a, t, and d  */
   5420       uprv_decContextDefault(&tset, DEC_INIT_DECIMAL64);
   5421       dset=tset;
   5422       /* accumulator bounds are set above, set precision now  */
   5423       aset.digits=p*2;                  /* double  */
   5424       /* term bounds avoid any underflow or overflow  */
   5425       tset.digits=p;
   5426       tset.emin=DEC_MIN_EMIN;           /* [emax is plenty]  */
   5427       /* [dset.digits=16, etc., are sufficient]  */
   5428 
   5429       /* finally ready to roll  */
   5430       for (;;) {
   5431         #if DECCHECK
   5432         iterations++;
   5433         #endif
   5434         /* only the status from the accumulation is interesting  */
   5435         /* [but it should remain unchanged after first add]  */
   5436         decAddOp(a, a, t, &aset, 0, status);           /* a=a+t  */
   5437         decMultiplyOp(t, t, x, &tset, &ignore);        /* t=t*x  */
   5438         decDivideOp(t, t, d, &tset, DIVIDE, &ignore);  /* t=t/d  */
   5439         /* the iteration ends when the term cannot affect the result,  */
   5440         /* if rounded to p digits, which is when its value is smaller  */
   5441         /* than the accumulator by p+1 digits.  There must also be  */
   5442         /* full precision in a.  */
   5443         if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
   5444             && (a->digits>=p)) break;
   5445         decAddOp(d, d, &numone, &dset, 0, &ignore);    /* d=d+1  */
   5446         } /* iterate  */
   5447 
   5448       #if DECCHECK
   5449       /* just a sanity check; comment out test to show always  */
   5450       if (iterations>p+3)
   5451         printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
   5452                (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
   5453       #endif
   5454       } /* h<=8  */
   5455 
   5456     /* apply postconditioning: a=a**(10**h) -- this is calculated  */
   5457     /* at a slightly higher precision than Hull & Abrham suggest  */
   5458     if (h>0) {
   5459       Int seenbit=0;               /* set once a 1-bit is seen  */
   5460       Int i;                       /* counter  */
   5461       Int n=powers[h];             /* always positive  */
   5462       aset.digits=p+2;             /* sufficient precision  */
   5463       /* avoid the overhead and many extra digits of decNumberPower  */
   5464       /* as all that is needed is the short 'multipliers' loop; here  */
   5465       /* accumulate the answer into t  */
   5466       uprv_decNumberZero(t); *t->lsu=1; /* acc=1  */
   5467       for (i=1;;i++){              /* for each bit [top bit ignored]  */
   5468         /* abandon if have had overflow or terminal underflow  */
   5469         if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting?  */
   5470           if (*status&DEC_Overflow || ISZERO(t)) break;}
   5471         n=n<<1;                    /* move next bit to testable position  */
   5472         if (n<0) {                 /* top bit is set  */
   5473           seenbit=1;               /* OK, have a significant bit  */
   5474           decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x  */
   5475           }
   5476         if (i==31) break;          /* that was the last bit  */
   5477         if (!seenbit) continue;    /* no need to square 1  */
   5478         decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square]  */
   5479         } /*i*/ /* 32 bits  */
   5480       /* decNumberShow(t);  */
   5481       a=t;                         /* and carry on using t instead of a  */
   5482       }
   5483 
   5484     /* Copy and round the result to res  */
   5485     residue=1;                          /* indicate dirt to right ..  */
   5486     if (ISZERO(a)) residue=0;           /* .. unless underflowed to 0  */
   5487     aset.digits=set->digits;            /* [use default rounding]  */
   5488     decCopyFit(res, a, &aset, &residue, status); /* copy & shorten  */
   5489     decFinish(res, set, &residue, status);       /* cleanup/set flags  */
   5490     } while(0);                         /* end protected  */
   5491 
   5492   if (allocrhs !=NULL) free(allocrhs);  /* drop any storage used  */
   5493   if (allocbufa!=NULL) free(allocbufa); /* ..  */
   5494   if (allocbuft!=NULL) free(allocbuft); /* ..  */
   5495   /* [status is handled by caller]  */
   5496   return res;
   5497   } /* decExpOp  */
   5498 
   5499 /* ------------------------------------------------------------------ */
   5500 /* Initial-estimate natural logarithm table                           */
   5501 /*                                                                    */
   5502 /*   LNnn -- 90-entry 16-bit table for values from .10 through .99.   */
   5503 /*           The result is a 4-digit encode of the coefficient (c=the */
   5504 /*           top 14 bits encoding 0-9999) and a 2-digit encode of the */
   5505 /*           exponent (e=the bottom 2 bits encoding 0-3)              */
   5506 /*                                                                    */
   5507 /*           The resulting value is given by:                         */
   5508 /*                                                                    */
   5509 /*             v = -c * 10**(-e-3)                                    */
   5510 /*                                                                    */
   5511 /*           where e and c are extracted from entry k = LNnn[x-10]    */
   5512 /*           where x is truncated (NB) into the range 10 through 99,  */
   5513 /*           and then c = k>>2 and e = k&3.                           */
   5514 /* ------------------------------------------------------------------ */
   5515 const uShort LNnn[90]={9016,  8652,  8316,  8008,  7724,  7456,  7208,
   5516   6972,  6748,  6540,  6340,  6148,  5968,  5792,  5628,  5464,  5312,
   5517   5164,  5020,  4884,  4748,  4620,  4496,  4376,  4256,  4144,  4032,
   5518  39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
   5519  29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
   5520  22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
   5521  15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
   5522  10197,  9685,  9177,  8677,  8185,  7697,  7213,  6737,  6269,  5801,
   5523   5341,  4889,  4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
   5524  10130,  6046, 20055};
   5525 
   5526 /* ------------------------------------------------------------------ */
   5527 /* decLnOp -- effect natural logarithm                                */
   5528 /*                                                                    */
   5529 /*   This computes C = ln(A)                                          */
   5530 /*                                                                    */
   5531 /*   res is C, the result.  C may be A                                */
   5532 /*   rhs is A                                                         */
   5533 /*   set is the context; note that rounding mode has no effect        */
   5534 /*                                                                    */
   5535 /* C must have space for set->digits digits.                          */
   5536 /*                                                                    */
   5537 /* Notable cases:                                                     */
   5538 /*   A<0 -> Invalid                                                   */
   5539 /*   A=0 -> -Infinity (Exact)                                         */
   5540 /*   A=+Infinity -> +Infinity (Exact)                                 */
   5541 /*   A=1 exactly -> 0 (Exact)                                         */
   5542 /*                                                                    */
   5543 /* Restrictions (as for Exp):                                         */
   5544 /*                                                                    */
   5545 /*   digits, emax, and -emin in the context must be less than         */
   5546 /*   DEC_MAX_MATH+11 (1000010), and the rhs must be within these      */
   5547 /*   bounds or a zero.  This is an internal routine, so these         */
   5548 /*   restrictions are contractual and not enforced.                   */
   5549 /*                                                                    */
   5550 /* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will      */
   5551 /* almost always be correctly rounded, but may be up to 1 ulp in      */
   5552 /* error in rare cases.                                               */
   5553 /* ------------------------------------------------------------------ */
   5554 /* The result is calculated using Newton's method, with each          */
   5555 /* iteration calculating a' = a + x * exp(-a) - 1.  See, for example, */
   5556 /* Epperson 1989.                                                     */
   5557 /*                                                                    */
   5558 /* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
   5559 /* This has to be calculated at the sum of the precision of x and the */
   5560 /* working precision.                                                 */
   5561 /*                                                                    */
   5562 /* Implementation notes:                                              */
   5563 /*                                                                    */
   5564 /* 1. This is separated out as decLnOp so it can be called from       */
   5565 /*    other Mathematical functions (e.g., Log 10) with a wider range  */
   5566 /*    than normal.  In particular, it can handle the slightly wider   */
   5567 /*    (+9+2) range needed by a power function.                        */
   5568 /*                                                                    */
   5569 /* 2. The speed of this function is about 10x slower than exp, as     */
   5570 /*    it typically needs 4-6 iterations for short numbers, and the    */
   5571 /*    extra precision needed adds a squaring effect, twice.           */
   5572 /*                                                                    */
   5573 /* 3. Fastpaths are included for ln(10) and ln(2), up to length 40,   */
   5574 /*    as these are common requests.  ln(10) is used by log10(x).      */
   5575 /*                                                                    */
   5576 /* 4. An iteration might be saved by widening the LNnn table, and     */
   5577 /*    would certainly save at least one if it were made ten times     */
   5578 /*    bigger, too (for truncated fractions 0.100 through 0.999).      */
   5579 /*    However, for most practical evaluations, at least four or five  */
   5580 /*    iterations will be neede -- so this would only speed up by      */
   5581 /*    20-25% and that probably does not justify increasing the table  */
   5582 /*    size.                                                           */
   5583 /*                                                                    */
   5584 /* 5. The static buffers are larger than might be expected to allow   */
   5585 /*    for calls from decNumberPower.                                  */
   5586 /* ------------------------------------------------------------------ */
   5587 decNumber * decLnOp(decNumber *res, const decNumber *rhs,
   5588                     decContext *set, uInt *status) {
   5589   uInt ignore=0;                   /* working status accumulator  */
   5590   uInt needbytes;                  /* for space calculations  */
   5591   Int residue;                     /* rounding residue  */
   5592   Int r;                           /* rhs=f*10**r [see below]  */
   5593   Int p;                           /* working precision  */
   5594   Int pp;                          /* precision for iteration  */
   5595   Int t;                           /* work  */
   5596 
   5597   /* buffers for a (accumulator, typically precision+2) and b  */
   5598   /* (adjustment calculator, same size)  */
   5599   decNumber bufa[D2N(DECBUFFER+12)];
   5600   decNumber *allocbufa=NULL;       /* -> allocated bufa, iff allocated  */
   5601   decNumber *a=bufa;               /* accumulator/work  */
   5602   decNumber bufb[D2N(DECBUFFER*2+2)];
   5603   decNumber *allocbufb=NULL;       /* -> allocated bufa, iff allocated  */
   5604   decNumber *b=bufb;               /* adjustment/work  */
   5605 
   5606   decNumber  numone;               /* constant 1  */
   5607   decNumber  cmp;                  /* work  */
   5608   decContext aset, bset;           /* working contexts  */
   5609 
   5610   #if DECCHECK
   5611   Int iterations=0;                /* for later sanity check  */
   5612   if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
   5613   #endif
   5614 
   5615   do {                                  /* protect allocated storage  */
   5616     if (SPECIALARG) {                   /* handle infinities and NaNs  */
   5617       if (decNumberIsInfinite(rhs)) {   /* an infinity  */
   5618         if (decNumberIsNegative(rhs))   /* -Infinity -> error  */
   5619           *status|=DEC_Invalid_operation;
   5620          else uprv_decNumberCopy(res, rhs);  /* +Infinity -> self  */
   5621         }
   5622        else decNaNs(res, rhs, NULL, set, status); /* a NaN  */
   5623       break;}
   5624 
   5625     if (ISZERO(rhs)) {                  /* +/- zeros -> -Infinity  */
   5626       uprv_decNumberZero(res);               /* make clean  */
   5627       res->bits=DECINF|DECNEG;          /* set - infinity  */
   5628       break;}                           /* [no status to set]  */
   5629 
   5630     /* Non-zero negatives are bad...  */
   5631     if (decNumberIsNegative(rhs)) {     /* -x -> error  */
   5632       *status|=DEC_Invalid_operation;
   5633       break;}
   5634 
   5635     /* Here, rhs is positive, finite, and in range  */
   5636 
   5637     /* lookaside fastpath code for ln(2) and ln(10) at common lengths  */
   5638     if (rhs->exponent==0 && set->digits<=40) {
   5639       #if DECDPUN==1
   5640       if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10)  */
   5641       #else
   5642       if (rhs->lsu[0]==10 && rhs->digits==2) {                  /* ln(10)  */
   5643       #endif
   5644         aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
   5645         #define LN10 "2.302585092994045684017991454684364207601"
   5646         uprv_decNumberFromString(res, LN10, &aset);
   5647         *status|=(DEC_Inexact | DEC_Rounded); /* is inexact  */
   5648         break;}
   5649       if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2)  */
   5650         aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
   5651         #define LN2 "0.6931471805599453094172321214581765680755"
   5652         uprv_decNumberFromString(res, LN2, &aset);
   5653         *status|=(DEC_Inexact | DEC_Rounded);
   5654         break;}
   5655       } /* integer and short  */
   5656 
   5657     /* Determine the working precision.  This is normally the  */
   5658     /* requested precision + 2, with a minimum of 9.  However, if  */
   5659     /* the rhs is 'over-precise' then allow for all its digits to  */
   5660     /* potentially participate (consider an rhs where all the excess  */
   5661     /* digits are 9s) so in this case use rhs->digits+2.  */
   5662     p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
   5663 
   5664     /* Allocate space for the accumulator and the high-precision  */
   5665     /* adjustment calculator, if necessary.  The accumulator must  */
   5666     /* be able to hold p digits, and the adjustment up to  */
   5667     /* rhs->digits+p digits.  They are also made big enough for 16  */
   5668     /* digits so that they can be used for calculating the initial  */
   5669     /* estimate.  */
   5670     needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
   5671     if (needbytes>sizeof(bufa)) {     /* need malloc space  */
   5672       allocbufa=(decNumber *)malloc(needbytes);
   5673       if (allocbufa==NULL) {          /* hopeless -- abandon  */
   5674         *status|=DEC_Insufficient_storage;
   5675         break;}
   5676       a=allocbufa;                    /* use the allocated space  */
   5677       }
   5678     pp=p+rhs->digits;
   5679     needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
   5680     if (needbytes>sizeof(bufb)) {     /* need malloc space  */
   5681       allocbufb=(decNumber *)malloc(needbytes);
   5682       if (allocbufb==NULL) {          /* hopeless -- abandon  */
   5683         *status|=DEC_Insufficient_storage;
   5684         break;}
   5685       b=allocbufb;                    /* use the allocated space  */
   5686       }
   5687 
   5688     /* Prepare an initial estimate in acc. Calculate this by  */
   5689     /* considering the coefficient of x to be a normalized fraction,  */
   5690     /* f, with the decimal point at far left and multiplied by  */
   5691     /* 10**r.  Then, rhs=f*10**r and 0.1<=f<1, and  */
   5692     /*   ln(x) = ln(f) + ln(10)*r  */
   5693     /* Get the initial estimate for ln(f) from a small lookup  */
   5694     /* table (see above) indexed by the first two digits of f,  */
   5695     /* truncated.  */
   5696 
   5697     uprv_decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended  */
   5698     r=rhs->exponent+rhs->digits;        /* 'normalised' exponent  */
   5699     uprv_decNumberFromInt32(a, r);           /* a=r  */
   5700     uprv_decNumberFromInt32(b, 2302585);     /* b=ln(10) (2.302585)  */
   5701     b->exponent=-6;                     /*  ..  */
   5702     decMultiplyOp(a, a, b, &aset, &ignore);  /* a=a*b  */
   5703     /* now get top two digits of rhs into b by simple truncate and  */
   5704     /* force to integer  */
   5705     residue=0;                          /* (no residue)  */
   5706     aset.digits=2; aset.round=DEC_ROUND_DOWN;
   5707     decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten  */
   5708     b->exponent=0;                      /* make integer  */
   5709     t=decGetInt(b);                     /* [cannot fail]  */
   5710     if (t<10) t=X10(t);                 /* adjust single-digit b  */
   5711     t=LNnn[t-10];                       /* look up ln(b)  */
   5712     uprv_decNumberFromInt32(b, t>>2);        /* b=ln(b) coefficient  */
   5713     b->exponent=-(t&3)-3;               /* set exponent  */
   5714     b->bits=DECNEG;                     /* ln(0.10)->ln(0.99) always -ve  */
   5715     aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore  */
   5716     decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b  */
   5717     /* the initial estimate is now in a, with up to 4 digits correct.  */
   5718     /* When rhs is at or near Nmax the estimate will be low, so we  */
   5719     /* will approach it from below, avoiding overflow when calling exp.  */
   5720 
   5721     uprv_decNumberZero(&numone); *numone.lsu=1;   /* constant 1 for adjustment  */
   5722 
   5723     /* accumulator bounds are as requested (could underflow, but  */
   5724     /* cannot overflow)  */
   5725     aset.emax=set->emax;
   5726     aset.emin=set->emin;
   5727     aset.clamp=0;                       /* no concrete format  */
   5728     /* set up a context to be used for the multiply and subtract  */
   5729     bset=aset;
   5730     bset.emax=DEC_MAX_MATH*2;           /* use double bounds for the  */
   5731     bset.emin=-DEC_MAX_MATH*2;          /* adjustment calculation  */
   5732                                         /* [see decExpOp call below]  */
   5733     /* for each iteration double the number of digits to calculate,  */
   5734     /* up to a maximum of p  */
   5735     pp=9;                               /* initial precision  */
   5736     /* [initially 9 as then the sequence starts 7+2, 16+2, and  */
   5737     /* 34+2, which is ideal for standard-sized numbers]  */
   5738     aset.digits=pp;                     /* working context  */
   5739     bset.digits=pp+rhs->digits;         /* wider context  */
   5740     for (;;) {                          /* iterate  */
   5741       #if DECCHECK
   5742       iterations++;
   5743       if (iterations>24) break;         /* consider 9 * 2**24  */
   5744       #endif
   5745       /* calculate the adjustment (exp(-a)*x-1) into b.  This is a  */
   5746       /* catastrophic subtraction but it really is the difference  */
   5747       /* from 1 that is of interest.  */
   5748       /* Use the internal entry point to Exp as it allows the double  */
   5749       /* range for calculating exp(-a) when a is the tiniest subnormal.  */
   5750       a->bits^=DECNEG;                  /* make -a  */
   5751       decExpOp(b, a, &bset, &ignore);   /* b=exp(-a)  */
   5752       a->bits^=DECNEG;                  /* restore sign of a  */
   5753       /* now multiply by rhs and subtract 1, at the wider precision  */
   5754       decMultiplyOp(b, b, rhs, &bset, &ignore);        /* b=b*rhs  */
   5755       decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1  */
   5756 
   5757       /* the iteration ends when the adjustment cannot affect the  */
   5758       /* result by >=0.5 ulp (at the requested digits), which  */
   5759       /* is when its value is smaller than the accumulator by  */
   5760       /* set->digits+1 digits (or it is zero) -- this is a looser  */
   5761       /* requirement than for Exp because all that happens to the  */
   5762       /* accumulator after this is the final rounding (but note that  */
   5763       /* there must also be full precision in a, or a=0).  */
   5764 
   5765       if (decNumberIsZero(b) ||
   5766           (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
   5767         if (a->digits==p) break;
   5768         if (decNumberIsZero(a)) {
   5769           decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ?  */
   5770           if (cmp.lsu[0]==0) a->exponent=0;            /* yes, exact 0  */
   5771            else *status|=(DEC_Inexact | DEC_Rounded);  /* no, inexact  */
   5772           break;
   5773           }
   5774         /* force padding if adjustment has gone to 0 before full length  */
   5775         if (decNumberIsZero(b)) b->exponent=a->exponent-p;
   5776         }
   5777 
   5778       /* not done yet ...  */
   5779       decAddOp(a, a, b, &aset, 0, &ignore);  /* a=a+b for next estimate  */
   5780       if (pp==p) continue;                   /* precision is at maximum  */
   5781       /* lengthen the next calculation  */
   5782       pp=pp*2;                               /* double precision  */
   5783       if (pp>p) pp=p;                        /* clamp to maximum  */
   5784       aset.digits=pp;                        /* working context  */
   5785       bset.digits=pp+rhs->digits;            /* wider context  */
   5786       } /* Newton's iteration  */
   5787 
   5788     #if DECCHECK
   5789     /* just a sanity check; remove the test to show always  */
   5790     if (iterations>24)
   5791       printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
   5792             (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
   5793     #endif
   5794 
   5795     /* Copy and round the result to res  */
   5796     residue=1;                          /* indicate dirt to right  */
   5797     if (ISZERO(a)) residue=0;           /* .. unless underflowed to 0  */
   5798     aset.digits=set->digits;            /* [use default rounding]  */
   5799     decCopyFit(res, a, &aset, &residue, status); /* copy & shorten  */
   5800     decFinish(res, set, &residue, status);       /* cleanup/set flags  */
   5801     } while(0);                         /* end protected  */
   5802 
   5803   if (allocbufa!=NULL) free(allocbufa); /* drop any storage used  */
   5804   if (allocbufb!=NULL) free(allocbufb); /* ..  */
   5805   /* [status is handled by caller]  */
   5806   return res;
   5807   } /* decLnOp  */
   5808 
   5809 /* ------------------------------------------------------------------ */
   5810 /* decQuantizeOp  -- force exponent to requested value                */
   5811 /*                                                                    */
   5812 /*   This computes C = op(A, B), where op adjusts the coefficient     */
   5813 /*   of C (by rounding or shifting) such that the exponent (-scale)   */
   5814 /*   of C has the value B or matches the exponent of B.               */
   5815 /*   The numerical value of C will equal A, except for the effects of */
   5816 /*   any rounding that occurred.                                      */
   5817 /*                                                                    */
   5818 /*   res is C, the result.  C may be A or B                           */
   5819 /*   lhs is A, the number to adjust                                   */
   5820 /*   rhs is B, the requested exponent                                 */
   5821 /*   set is the context                                               */
   5822 /*   quant is 1 for quantize or 0 for rescale                         */
   5823 /*   status is the status accumulator (this can be called without     */
   5824 /*          risk of control loss)                                     */
   5825 /*                                                                    */
   5826 /* C must have space for set->digits digits.                          */
   5827 /*                                                                    */
   5828 /* Unless there is an error or the result is infinite, the exponent   */
   5829 /* after the operation is guaranteed to be that requested.            */
   5830 /* ------------------------------------------------------------------ */
   5831 static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
   5832                                  const decNumber *rhs, decContext *set,
   5833                                  Flag quant, uInt *status) {
   5834   #if DECSUBSET
   5835   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated  */
   5836   decNumber *allocrhs=NULL;        /* .., rhs  */
   5837   #endif
   5838   const decNumber *inrhs=rhs;      /* save original rhs  */
   5839   Int   reqdigits=set->digits;     /* requested DIGITS  */
   5840   Int   reqexp;                    /* requested exponent [-scale]  */
   5841   Int   residue=0;                 /* rounding residue  */
   5842   Int   etiny=set->emin-(reqdigits-1);
   5843 
   5844   #if DECCHECK
   5845   if (decCheckOperands(res, lhs, rhs, set)) return res;
   5846   #endif
   5847 
   5848   do {                             /* protect allocated storage  */
   5849     #if DECSUBSET
   5850     if (!set->extended) {
   5851       /* reduce operands and set lostDigits status, as needed  */
   5852       if (lhs->digits>reqdigits) {
   5853         alloclhs=decRoundOperand(lhs, set, status);
   5854         if (alloclhs==NULL) break;
   5855         lhs=alloclhs;
   5856         }
   5857       if (rhs->digits>reqdigits) { /* [this only checks lostDigits]  */
   5858         allocrhs=decRoundOperand(rhs, set, status);
   5859         if (allocrhs==NULL) break;
   5860         rhs=allocrhs;
   5861         }
   5862       }
   5863     #endif
   5864     /* [following code does not require input rounding]  */
   5865 
   5866     /* Handle special values  */
   5867     if (SPECIALARGS) {
   5868       /* NaNs get usual processing  */
   5869       if (SPECIALARGS & (DECSNAN | DECNAN))
   5870         decNaNs(res, lhs, rhs, set, status);
   5871       /* one infinity but not both is bad  */
   5872       else if ((lhs->bits ^ rhs->bits) & DECINF)
   5873         *status|=DEC_Invalid_operation;
   5874       /* both infinity: return lhs  */
   5875       else uprv_decNumberCopy(res, lhs);          /* [nop if in place]  */
   5876       break;
   5877       }
   5878 
   5879     /* set requested exponent  */
   5880     if (quant) reqexp=inrhs->exponent;  /* quantize -- match exponents  */
   5881      else {                             /* rescale -- use value of rhs  */
   5882       /* Original rhs must be an integer that fits and is in range,  */
   5883       /* which could be from -1999999997 to +999999999, thanks to  */
   5884       /* subnormals  */
   5885       reqexp=decGetInt(inrhs);               /* [cannot fail]  */
   5886       }
   5887 
   5888     #if DECSUBSET
   5889     if (!set->extended) etiny=set->emin;     /* no subnormals  */
   5890     #endif
   5891 
   5892     if (reqexp==BADINT                       /* bad (rescale only) or ..  */
   5893      || reqexp==BIGODD || reqexp==BIGEVEN    /* very big (ditto) or ..  */
   5894      || (reqexp<etiny)                       /* < lowest  */
   5895      || (reqexp>set->emax)) {                /* > emax  */
   5896       *status|=DEC_Invalid_operation;
   5897       break;}
   5898 
   5899     /* the RHS has been processed, so it can be overwritten now if necessary  */
   5900     if (ISZERO(lhs)) {                       /* zero coefficient unchanged  */
   5901       uprv_decNumberCopy(res, lhs);               /* [nop if in place]  */
   5902       res->exponent=reqexp;                  /* .. just set exponent  */
   5903       #if DECSUBSET
   5904       if (!set->extended) res->bits=0;       /* subset specification; no -0  */
   5905       #endif
   5906       }
   5907      else {                                  /* non-zero lhs  */
   5908       Int adjust=reqexp-lhs->exponent;       /* digit adjustment needed  */
   5909       /* if adjusted coefficient will definitely not fit, give up now  */
   5910       if ((lhs->digits-adjust)>reqdigits) {
   5911         *status|=DEC_Invalid_operation;
   5912         break;
   5913         }
   5914 
   5915       if (adjust>0) {                        /* increasing exponent  */
   5916         /* this will decrease the length of the coefficient by adjust  */
   5917         /* digits, and must round as it does so  */
   5918         decContext workset;                  /* work  */
   5919         workset=*set;                        /* clone rounding, etc.  */
   5920         workset.digits=lhs->digits-adjust;   /* set requested length  */
   5921         /* [note that the latter can be <1, here]  */
   5922         decCopyFit(res, lhs, &workset, &residue, status); /* fit to result  */
   5923         decApplyRound(res, &workset, residue, status);    /* .. and round  */
   5924         residue=0;                                        /* [used]  */
   5925         /* If just rounded a 999s case, exponent will be off by one;  */
   5926         /* adjust back (after checking space), if so.  */
   5927         if (res->exponent>reqexp) {
   5928           /* re-check needed, e.g., for quantize(0.9999, 0.001) under  */
   5929           /* set->digits==3  */
   5930           if (res->digits==reqdigits) {      /* cannot shift by 1  */
   5931             *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these]  */
   5932             *status|=DEC_Invalid_operation;
   5933             break;
   5934             }
   5935           res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift  */
   5936           res->exponent--;                   /* (re)adjust the exponent.  */
   5937           }
   5938         #if DECSUBSET
   5939         if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0  */
   5940         #endif
   5941         } /* increase  */
   5942        else /* adjust<=0 */ {                /* decreasing or = exponent  */
   5943         /* this will increase the length of the coefficient by -adjust  */
   5944         /* digits, by adding zero or more trailing zeros; this is  */
   5945         /* already checked for fit, above  */
   5946         uprv_decNumberCopy(res, lhs);             /* [it will fit]  */
   5947         /* if padding needed (adjust<0), add it now...  */
   5948         if (adjust<0) {
   5949           res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
   5950           res->exponent+=adjust;             /* adjust the exponent  */
   5951           }
   5952         } /* decrease  */
   5953       } /* non-zero  */
   5954 
   5955     /* Check for overflow [do not use Finalize in this case, as an  */
   5956     /* overflow here is a "don't fit" situation]  */
   5957     if (res->exponent>set->emax-res->digits+1) {  /* too big  */
   5958       *status|=DEC_Invalid_operation;
   5959       break;
   5960       }
   5961      else {
   5962       decFinalize(res, set, &residue, status);    /* set subnormal flags  */
   5963       *status&=~DEC_Underflow;          /* suppress Underflow [as per 754]  */
   5964       }
   5965     } while(0);                         /* end protected  */
   5966 
   5967   #if DECSUBSET
   5968   if (allocrhs!=NULL) free(allocrhs);   /* drop any storage used  */
   5969   if (alloclhs!=NULL) free(alloclhs);   /* ..  */
   5970   #endif
   5971   return res;
   5972   } /* decQuantizeOp  */
   5973 
   5974 /* ------------------------------------------------------------------ */
   5975 /* decCompareOp -- compare, min, or max two Numbers                   */
   5976 /*                                                                    */
   5977 /*   This computes C = A ? B and carries out one of four operations:  */
   5978 /*     COMPARE    -- returns the signum (as a number) giving the      */
   5979 /*                   result of a comparison unless one or both        */
   5980 /*                   operands is a NaN (in which case a NaN results)  */
   5981 /*     COMPSIG    -- as COMPARE except that a quiet NaN raises        */
   5982 /*                   Invalid operation.                               */
   5983 /*     COMPMAX    -- returns the larger of the operands, using the    */
   5984 /*                   754 maxnum operation                             */
   5985 /*     COMPMAXMAG -- ditto, comparing absolute values                 */
   5986 /*     COMPMIN    -- the 754 minnum operation                         */
   5987 /*     COMPMINMAG -- ditto, comparing absolute values                 */
   5988 /*     COMTOTAL   -- returns the signum (as a number) giving the      */
   5989 /*                   result of a comparison using 754 total ordering  */
   5990 /*                                                                    */
   5991 /*   res is C, the result.  C may be A and/or B (e.g., X=X?X)         */
   5992 /*   lhs is A                                                         */
   5993 /*   rhs is B                                                         */
   5994 /*   set is the context                                               */
   5995 /*   op  is the operation flag                                        */
   5996 /*   status is the usual accumulator                                  */
   5997 /*                                                                    */
   5998 /* C must have space for one digit for COMPARE or set->digits for     */
   5999 /* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG.                       */
   6000 /* ------------------------------------------------------------------ */
   6001 /* The emphasis here is on speed for common cases, and avoiding       */
   6002 /* coefficient comparison if possible.                                */
   6003 /* ------------------------------------------------------------------ */
   6004 static decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
   6005                          const decNumber *rhs, decContext *set,
   6006                          Flag op, uInt *status) {
   6007   #if DECSUBSET
   6008   decNumber *alloclhs=NULL;        /* non-NULL if rounded lhs allocated  */
   6009   decNumber *allocrhs=NULL;        /* .., rhs  */
   6010   #endif
   6011   Int   result=0;                  /* default result value  */
   6012   uByte merged;                    /* work  */
   6013 
   6014   #if DECCHECK
   6015   if (decCheckOperands(res, lhs, rhs, set)) return res;
   6016   #endif
   6017 
   6018   do {                             /* protect allocated storage  */
   6019     #if DECSUBSET
   6020     if (!set->extended) {
   6021       /* reduce operands and set lostDigits status, as needed  */
   6022       if (lhs->digits>set->digits) {
   6023         alloclhs=decRoundOperand(lhs, set, status);
   6024         if (alloclhs==NULL) {result=BADINT; break;}
   6025         lhs=alloclhs;
   6026         }
   6027       if (rhs->digits>set->digits) {
   6028         allocrhs=decRoundOperand(rhs, set, status);
   6029         if (allocrhs==NULL) {result=BADINT; break;}
   6030         rhs=allocrhs;
   6031         }
   6032       }
   6033     #endif
   6034     /* [following code does not require input rounding]  */
   6035 
   6036     /* If total ordering then handle differing signs 'up front'  */
   6037     if (op==COMPTOTAL) {                /* total ordering  */
   6038       if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
   6039         result=-1;
   6040         break;
   6041         }
   6042       if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
   6043         result=+1;
   6044         break;
   6045         }
   6046       }
   6047 
   6048     /* handle NaNs specially; let infinities drop through  */
   6049     /* This assumes sNaN (even just one) leads to NaN.  */
   6050     merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
   6051     if (merged) {                       /* a NaN bit set  */
   6052       if (op==COMPARE);                 /* result will be NaN  */
   6053        else if (op==COMPSIG)            /* treat qNaN as sNaN  */
   6054         *status|=DEC_Invalid_operation | DEC_sNaN;
   6055        else if (op==COMPTOTAL) {        /* total ordering, always finite  */
   6056         /* signs are known to be the same; compute the ordering here  */
   6057         /* as if the signs are both positive, then invert for negatives  */
   6058         if (!decNumberIsNaN(lhs)) result=-1;
   6059          else if (!decNumberIsNaN(rhs)) result=+1;
   6060          /* here if both NaNs  */
   6061          else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
   6062          else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
   6063          else { /* both NaN or both sNaN  */
   6064           /* now it just depends on the payload  */
   6065           result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
   6066                                 rhs->lsu, D2U(rhs->digits), 0);
   6067           /* [Error not possible, as these are 'aligned']  */
   6068           } /* both same NaNs  */
   6069         if (decNumberIsNegative(lhs)) result=-result;
   6070         break;
   6071         } /* total order  */
   6072 
   6073        else if (merged & DECSNAN);           /* sNaN -> qNaN  */
   6074        else { /* here if MIN or MAX and one or two quiet NaNs  */
   6075         /* min or max -- 754 rules ignore single NaN  */
   6076         if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
   6077           /* just one NaN; force choice to be the non-NaN operand  */
   6078           op=COMPMAX;
   6079           if (lhs->bits & DECNAN) result=-1; /* pick rhs  */
   6080                              else result=+1; /* pick lhs  */
   6081           break;
   6082           }
   6083         } /* max or min  */
   6084       op=COMPNAN;                            /* use special path  */
   6085       decNaNs(res, lhs, rhs, set, status);   /* propagate NaN  */
   6086       break;
   6087       }
   6088     /* have numbers  */
   6089     if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
   6090      else result=decCompare(lhs, rhs, 0);    /* sign matters  */
   6091     } while(0);                              /* end protected  */
   6092 
   6093   if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare  */
   6094    else {
   6095     if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum  */
   6096       if (op==COMPTOTAL && result==0) {
   6097         /* operands are numerically equal or same NaN (and same sign,  */
   6098         /* tested first); if identical, leave result 0  */
   6099         if (lhs->exponent!=rhs->exponent) {
   6100           if (lhs->exponent<rhs->exponent) result=-1;
   6101            else result=+1;
   6102           if (decNumberIsNegative(lhs)) result=-result;
   6103           } /* lexp!=rexp  */
   6104         } /* total-order by exponent  */
   6105       uprv_decNumberZero(res);               /* [always a valid result]  */
   6106       if (result!=0) {                  /* must be -1 or +1  */
   6107         *res->lsu=1;
   6108         if (result<0) res->bits=DECNEG;
   6109         }
   6110       }
   6111      else if (op==COMPNAN);             /* special, drop through  */
   6112      else {                             /* MAX or MIN, non-NaN result  */
   6113       Int residue=0;                    /* rounding accumulator  */
   6114       /* choose the operand for the result  */
   6115       const decNumber *choice;
   6116       if (result==0) { /* operands are numerically equal  */
   6117         /* choose according to sign then exponent (see 754)  */
   6118         uByte slhs=(lhs->bits & DECNEG);
   6119         uByte srhs=(rhs->bits & DECNEG);
   6120         #if DECSUBSET
   6121         if (!set->extended) {           /* subset: force left-hand  */
   6122           op=COMPMAX;
   6123           result=+1;
   6124           }
   6125         else
   6126         #endif
   6127         if (slhs!=srhs) {          /* signs differ  */
   6128           if (slhs) result=-1;     /* rhs is max  */
   6129                else result=+1;     /* lhs is max  */
   6130           }
   6131          else if (slhs && srhs) {  /* both negative  */
   6132           if (lhs->exponent<rhs->exponent) result=+1;
   6133                                       else result=-1;
   6134           /* [if equal, use lhs, technically identical]  */
   6135           }
   6136          else {                    /* both positive  */
   6137           if (lhs->exponent>rhs->exponent) result=+1;
   6138                                       else result=-1;
   6139           /* [ditto]  */
   6140           }
   6141         } /* numerically equal  */
   6142       /* here result will be non-0; reverse if looking for MIN  */
   6143       if (op==COMPMIN || op==COMPMINMAG) result=-result;
   6144       choice=(result>0 ? lhs : rhs);    /* choose  */
   6145       /* copy chosen to result, rounding if need be  */
   6146       decCopyFit(res, choice, set, &residue, status);
   6147       decFinish(res, set, &residue, status);
   6148       }
   6149     }
   6150   #if DECSUBSET
   6151   if (allocrhs!=NULL) free(allocrhs);   /* free any storage used  */
   6152   if (alloclhs!=NULL) free(alloclhs);   /* ..  */
   6153   #endif
   6154   return res;
   6155   } /* decCompareOp  */
   6156 
   6157 /* ------------------------------------------------------------------ */
   6158 /* decCompare -- compare two decNumbers by numerical value            */
   6159 /*                                                                    */
   6160 /*  This routine compares A ? B without altering them.                */
   6161 /*                                                                    */
   6162 /*  Arg1 is A, a decNumber which is not a NaN                         */
   6163 /*  Arg2 is B, a decNumber which is not a NaN                         */
   6164 /*  Arg3 is 1 for a sign-independent compare, 0 otherwise             */
   6165 /*                                                                    */
   6166 /*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
   6167 /*  (the only possible failure is an allocation error)                */
   6168 /* ------------------------------------------------------------------ */
   6169 static Int decCompare(const decNumber *lhs, const decNumber *rhs,
   6170                       Flag abs_c) {
   6171   Int   result;                    /* result value  */
   6172   Int   sigr;                      /* rhs signum  */
   6173   Int   compare;                   /* work  */
   6174 
   6175   result=1;                                  /* assume signum(lhs)  */
   6176   if (ISZERO(lhs)) result=0;
   6177   if (abs_c) {
   6178     if (ISZERO(rhs)) return result;          /* LHS wins or both 0  */
   6179     /* RHS is non-zero  */
   6180     if (result==0) return -1;                /* LHS is 0; RHS wins  */
   6181     /* [here, both non-zero, result=1]  */
   6182     }
   6183    else {                                    /* signs matter  */
   6184     if (result && decNumberIsNegative(lhs)) result=-1;
   6185     sigr=1;                                  /* compute signum(rhs)  */
   6186     if (ISZERO(rhs)) sigr=0;
   6187      else if (decNumberIsNegative(rhs)) sigr=-1;
   6188     if (result > sigr) return +1;            /* L > R, return 1  */
   6189     if (result < sigr) return -1;            /* L < R, return -1  */
   6190     if (result==0) return 0;                   /* both 0  */
   6191     }
   6192 
   6193   /* signums are the same; both are non-zero  */
   6194   if ((lhs->bits | rhs->bits) & DECINF) {    /* one or more infinities  */
   6195     if (decNumberIsInfinite(rhs)) {
   6196       if (decNumberIsInfinite(lhs)) result=0;/* both infinite  */
   6197        else result=-result;                  /* only rhs infinite  */
   6198       }
   6199     return result;
   6200     }
   6201   /* must compare the coefficients, allowing for exponents  */
   6202   if (lhs->exponent>rhs->exponent) {         /* LHS exponent larger  */
   6203     /* swap sides, and sign  */
   6204     const decNumber *temp=lhs;
   6205     lhs=rhs;
   6206     rhs=temp;
   6207     result=-result;
   6208     }
   6209   compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
   6210                          rhs->lsu, D2U(rhs->digits),
   6211                          rhs->exponent-lhs->exponent);
   6212   if (compare!=BADINT) compare*=result;      /* comparison succeeded  */
   6213   return compare;
   6214   } /* decCompare  */
   6215 
   6216 /* ------------------------------------------------------------------ */
   6217 /* decUnitCompare -- compare two >=0 integers in Unit arrays          */
   6218 /*                                                                    */
   6219 /*  This routine compares A ? B*10**E where A and B are unit arrays   */
   6220 /*  A is a plain integer                                              */
   6221 /*  B has an exponent of E (which must be non-negative)               */
   6222 /*                                                                    */
   6223 /*  Arg1 is A first Unit (lsu)                                        */
   6224 /*  Arg2 is A length in Units                                         */
   6225 /*  Arg3 is B first Unit (lsu)                                        */
   6226 /*  Arg4 is B length in Units                                         */
   6227 /*  Arg5 is E (0 if the units are aligned)                            */
   6228 /*                                                                    */
   6229 /*  returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure   */
   6230 /*  (the only possible failure is an allocation error, which can      */
   6231 /*  only occur if E!=0)                                               */
   6232 /* ------------------------------------------------------------------ */
   6233 static Int decUnitCompare(const Unit *a, Int alength,
   6234                           const Unit *b, Int blength, Int exp) {
   6235   Unit  *acc;                      /* accumulator for result  */
   6236   Unit  accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer  */
   6237   Unit  *allocacc=NULL;            /* -> allocated acc buffer, iff allocated  */
   6238   Int   accunits, need;            /* units in use or needed for acc  */
   6239   const Unit *l, *r, *u;           /* work  */
   6240   Int   expunits, exprem, result;  /* ..  */
   6241 
   6242   if (exp==0) {                    /* aligned; fastpath  */
   6243     if (alength>blength) return 1;
   6244     if (alength<blength) return -1;
   6245     /* same number of units in both -- need unit-by-unit compare  */
   6246     l=a+alength-1;
   6247     r=b+alength-1;
   6248     for (;l>=a; l--, r--) {
   6249       if (*l>*r) return 1;
   6250       if (*l<*r) return -1;
   6251       }
   6252     return 0;                      /* all units match  */
   6253     } /* aligned  */
   6254 
   6255   /* Unaligned.  If one is >1 unit longer than the other, padded  */
   6256   /* approximately, then can return easily  */
   6257   if (alength>blength+(Int)D2U(exp)) return 1;
   6258   if (alength+1<blength+(Int)D2U(exp)) return -1;
   6259 
   6260   /* Need to do a real subtract.  For this, a result buffer is needed  */
   6261   /* even though only the sign is of interest.  Its length needs  */
   6262   /* to be the larger of alength and padded blength, +2  */
   6263   need=blength+D2U(exp);                /* maximum real length of B  */
   6264   if (need<alength) need=alength;
   6265   need+=2;
   6266   acc=accbuff;                          /* assume use local buffer  */
   6267   if (need*sizeof(Unit)>sizeof(accbuff)) {
   6268     allocacc=(Unit *)malloc(need*sizeof(Unit));
   6269     if (allocacc==NULL) return BADINT;  /* hopeless -- abandon  */
   6270     acc=allocacc;
   6271     }
   6272   /* Calculate units and remainder from exponent.  */
   6273   expunits=exp/DECDPUN;
   6274   exprem=exp%DECDPUN;
   6275   /* subtract [A+B*(-m)]  */
   6276   accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
   6277                          -(Int)powers[exprem]);
   6278   /* [UnitAddSub result may have leading zeros, even on zero]  */
   6279   if (accunits<0) result=-1;            /* negative result  */
   6280    else {                               /* non-negative result  */
   6281     /* check units of the result before freeing any storage  */
   6282     for (u=acc; u<acc+accunits-1 && *u==0;) u++;
   6283     result=(*u==0 ? 0 : +1);
   6284     }
   6285   /* clean up and return the result  */
   6286   if (allocacc!=NULL) free(allocacc);   /* drop any storage used  */
   6287   return result;
   6288   } /* decUnitCompare  */
   6289 
   6290 /* ------------------------------------------------------------------ */
   6291 /* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays   */
   6292 /*                                                                    */
   6293 /*  This routine performs the calculation:                            */
   6294 /*                                                                    */
   6295 /*  C=A+(B*M)                                                         */
   6296 /*                                                                    */
   6297 /*  Where M is in the range -DECDPUNMAX through +DECDPUNMAX.          */
   6298 /*                                                                    */
   6299 /*  A may be shorter or longer than B.                                */
   6300 /*                                                                    */
   6301 /*  Leading zeros are not removed after a calculation.  The result is */
   6302 /*  either the same length as the longer of A and B (adding any       */
   6303 /*  shift), or one Unit longer than that (if a Unit carry occurred).  */
   6304 /*                                                                    */
   6305 /*  A and B content are not altered unless C is also A or B.          */
   6306 /*  C may be the same array as A or B, but only if no zero padding is */
   6307 /*  requested (that is, C may be B only if bshift==0).                */
   6308 /*  C is filled from the lsu; only those units necessary to complete  */
   6309 /*  the calculation are referenced.                                   */
   6310 /*                                                                    */
   6311 /*  Arg1 is A first Unit (lsu)                                        */
   6312 /*  Arg2 is A length in Units                                         */
   6313 /*  Arg3 is B first Unit (lsu)                                        */
   6314 /*  Arg4 is B length in Units                                         */
   6315 /*  Arg5 is B shift in Units  (>=0; pads with 0 units if positive)    */
   6316 /*  Arg6 is C first Unit (lsu)                                        */
   6317 /*  Arg7 is M, the multiplier                                         */
   6318 /*                                                                    */
   6319 /*  returns the count of Units written to C, which will be non-zero   */
   6320 /*  and negated if the result is negative.  That is, the sign of the  */
   6321 /*  returned Int is the sign of the result (positive for zero) and    */
   6322 /*  the absolute value of the Int is the count of Units.              */
   6323 /*                                                                    */
   6324 /*  It is the caller's responsibility to make sure that C size is     */
   6325 /*  safe, allowing space if necessary for a one-Unit carry.           */
   6326 /*                                                                    */
   6327 /*  This routine is severely performance-critical; *any* change here  */
   6328 /*  must be measured (timed) to assure no performance degradation.    */
   6329 /*  In particular, trickery here tends to be counter-productive, as   */
   6330 /*  increased complexity of code hurts register optimizations on      */
   6331 /*  register-poor architectures.  Avoiding divisions is nearly        */
   6332 /*  always a Good Idea, however.                                      */
   6333 /*                                                                    */
   6334 /* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark  */
   6335 /* (IBM Warwick, UK) for some of the ideas used in this routine.      */
   6336 /* ------------------------------------------------------------------ */
   6337 static Int decUnitAddSub(const Unit *a, Int alength,
   6338                          const Unit *b, Int blength, Int bshift,
   6339                          Unit *c, Int m) {
   6340   const Unit *alsu=a;              /* A lsu [need to remember it]  */
   6341   Unit *clsu=c;                    /* C ditto  */
   6342   Unit *minC;                      /* low water mark for C  */
   6343   Unit *maxC;                      /* high water mark for C  */
   6344   eInt carry=0;                    /* carry integer (could be Long)  */
   6345   Int  add;                        /* work  */
   6346   #if DECDPUN<=4                   /* myriadal, millenary, etc.  */
   6347   Int  est;                        /* estimated quotient  */
   6348   #endif
   6349 
   6350   #if DECTRACE
   6351   if (alength<1 || blength<1)
   6352     printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
   6353   #endif
   6354 
   6355   maxC=c+alength;                  /* A is usually the longer  */
   6356   minC=c+blength;                  /* .. and B the shorter  */
   6357   if (bshift!=0) {                 /* B is shifted; low As copy across  */
   6358     minC+=bshift;
   6359     /* if in place [common], skip copy unless there's a gap [rare]  */
   6360     if (a==c && bshift<=alength) {
   6361       c+=bshift;
   6362       a+=bshift;
   6363       }
   6364      else for (; c<clsu+bshift; a++, c++) {  /* copy needed  */
   6365       if (a<alsu+alength) *c=*a;
   6366        else *c=0;
   6367       }
   6368     }
   6369   if (minC>maxC) { /* swap  */
   6370     Unit *hold=minC;
   6371     minC=maxC;
   6372     maxC=hold;
   6373     }
   6374 
   6375   /* For speed, do the addition as two loops; the first where both A  */
   6376   /* and B contribute, and the second (if necessary) where only one or  */
   6377   /* other of the numbers contribute.  */
   6378   /* Carry handling is the same (i.e., duplicated) in each case.  */
   6379   for (; c<minC; c++) {
   6380     carry+=*a;
   6381     a++;
   6382     carry+=((eInt)*b)*m;                /* [special-casing m=1/-1  */
   6383     b++;                                /* here is not a win]  */
   6384     /* here carry is new Unit of digits; it could be +ve or -ve  */
   6385     if ((ueInt)carry<=DECDPUNMAX) {     /* fastpath 0-DECDPUNMAX  */
   6386       *c=(Unit)carry;
   6387       carry=0;
   6388       continue;
   6389       }
   6390     #if DECDPUN==4                           /* use divide-by-multiply  */
   6391       if (carry>=0) {
   6392         est=(((ueInt)carry>>11)*53687)>>18;
   6393         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder  */
   6394         carry=est;                           /* likely quotient [89%]  */
   6395         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct  */
   6396         carry++;
   6397         *c-=DECDPUNMAX+1;
   6398         continue;
   6399         }
   6400       /* negative case  */
   6401       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6402       est=(((ueInt)carry>>11)*53687)>>18;
   6403       *c=(Unit)(carry-est*(DECDPUNMAX+1));
   6404       carry=est-(DECDPUNMAX+1);              /* correctly negative  */
   6405       if (*c<DECDPUNMAX+1) continue;         /* was OK  */
   6406       carry++;
   6407       *c-=DECDPUNMAX+1;
   6408     #elif DECDPUN==3
   6409       if (carry>=0) {
   6410         est=(((ueInt)carry>>3)*16777)>>21;
   6411         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder  */
   6412         carry=est;                           /* likely quotient [99%]  */
   6413         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct  */
   6414         carry++;
   6415         *c-=DECDPUNMAX+1;
   6416         continue;
   6417         }
   6418       /* negative case  */
   6419       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6420       est=(((ueInt)carry>>3)*16777)>>21;
   6421       *c=(Unit)(carry-est*(DECDPUNMAX+1));
   6422       carry=est-(DECDPUNMAX+1);              /* correctly negative  */
   6423       if (*c<DECDPUNMAX+1) continue;         /* was OK  */
   6424       carry++;
   6425       *c-=DECDPUNMAX+1;
   6426     #elif DECDPUN<=2
   6427       /* Can use QUOT10 as carry <= 4 digits  */
   6428       if (carry>=0) {
   6429         est=QUOT10(carry, DECDPUN);
   6430         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder  */
   6431         carry=est;                           /* quotient  */
   6432         continue;
   6433         }
   6434       /* negative case  */
   6435       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6436       est=QUOT10(carry, DECDPUN);
   6437       *c=(Unit)(carry-est*(DECDPUNMAX+1));
   6438       carry=est-(DECDPUNMAX+1);              /* correctly negative  */
   6439     #else
   6440       /* remainder operator is undefined if negative, so must test  */
   6441       if ((ueInt)carry<(DECDPUNMAX+1)*2) {   /* fastpath carry +1  */
   6442         *c=(Unit)(carry-(DECDPUNMAX+1));     /* [helps additions]  */
   6443         carry=1;
   6444         continue;
   6445         }
   6446       if (carry>=0) {
   6447         *c=(Unit)(carry%(DECDPUNMAX+1));
   6448         carry=carry/(DECDPUNMAX+1);
   6449         continue;
   6450         }
   6451       /* negative case  */
   6452       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6453       *c=(Unit)(carry%(DECDPUNMAX+1));
   6454       carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
   6455     #endif
   6456     } /* c  */
   6457 
   6458   /* now may have one or other to complete  */
   6459   /* [pretest to avoid loop setup/shutdown]  */
   6460   if (c<maxC) for (; c<maxC; c++) {
   6461     if (a<alsu+alength) {               /* still in A  */
   6462       carry+=*a;
   6463       a++;
   6464       }
   6465      else {                             /* inside B  */
   6466       carry+=((eInt)*b)*m;
   6467       b++;
   6468       }
   6469     /* here carry is new Unit of digits; it could be +ve or -ve and  */
   6470     /* magnitude up to DECDPUNMAX squared  */
   6471     if ((ueInt)carry<=DECDPUNMAX) {     /* fastpath 0-DECDPUNMAX  */
   6472       *c=(Unit)carry;
   6473       carry=0;
   6474       continue;
   6475       }
   6476     /* result for this unit is negative or >DECDPUNMAX  */
   6477     #if DECDPUN==4                           /* use divide-by-multiply  */
   6478       if (carry>=0) {
   6479         est=(((ueInt)carry>>11)*53687)>>18;
   6480         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder  */
   6481         carry=est;                           /* likely quotient [79.7%]  */
   6482         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct  */
   6483         carry++;
   6484         *c-=DECDPUNMAX+1;
   6485         continue;
   6486         }
   6487       /* negative case  */
   6488       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6489       est=(((ueInt)carry>>11)*53687)>>18;
   6490       *c=(Unit)(carry-est*(DECDPUNMAX+1));
   6491       carry=est-(DECDPUNMAX+1);              /* correctly negative  */
   6492       if (*c<DECDPUNMAX+1) continue;         /* was OK  */
   6493       carry++;
   6494       *c-=DECDPUNMAX+1;
   6495     #elif DECDPUN==3
   6496       if (carry>=0) {
   6497         est=(((ueInt)carry>>3)*16777)>>21;
   6498         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder  */
   6499         carry=est;                           /* likely quotient [99%]  */
   6500         if (*c<DECDPUNMAX+1) continue;       /* estimate was correct  */
   6501         carry++;
   6502         *c-=DECDPUNMAX+1;
   6503         continue;
   6504         }
   6505       /* negative case  */
   6506       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6507       est=(((ueInt)carry>>3)*16777)>>21;
   6508       *c=(Unit)(carry-est*(DECDPUNMAX+1));
   6509       carry=est-(DECDPUNMAX+1);              /* correctly negative  */
   6510       if (*c<DECDPUNMAX+1) continue;         /* was OK  */
   6511       carry++;
   6512       *c-=DECDPUNMAX+1;
   6513     #elif DECDPUN<=2
   6514       if (carry>=0) {
   6515         est=QUOT10(carry, DECDPUN);
   6516         *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder  */
   6517         carry=est;                           /* quotient  */
   6518         continue;
   6519         }
   6520       /* negative case  */
   6521       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6522       est=QUOT10(carry, DECDPUN);
   6523       *c=(Unit)(carry-est*(DECDPUNMAX+1));
   6524       carry=est-(DECDPUNMAX+1);              /* correctly negative  */
   6525     #else
   6526       if ((ueInt)carry<(DECDPUNMAX+1)*2){    /* fastpath carry 1  */
   6527         *c=(Unit)(carry-(DECDPUNMAX+1));
   6528         carry=1;
   6529         continue;
   6530         }
   6531       /* remainder operator is undefined if negative, so must test  */
   6532       if (carry>=0) {
   6533         *c=(Unit)(carry%(DECDPUNMAX+1));
   6534         carry=carry/(DECDPUNMAX+1);
   6535         continue;
   6536         }
   6537       /* negative case  */
   6538       carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive  */
   6539       *c=(Unit)(carry%(DECDPUNMAX+1));
   6540       carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
   6541     #endif
   6542     } /* c  */
   6543 
   6544   /* OK, all A and B processed; might still have carry or borrow  */
   6545   /* return number of Units in the result, negated if a borrow  */
   6546   if (carry==0) return c-clsu;     /* no carry, so no more to do  */
   6547   if (carry>0) {                   /* positive carry  */
   6548     *c=(Unit)carry;                /* place as new unit  */
   6549     c++;                           /* ..  */
   6550     return c-clsu;
   6551     }
   6552   /* -ve carry: it's a borrow; complement needed  */
   6553   add=1;                           /* temporary carry...  */
   6554   for (c=clsu; c<maxC; c++) {
   6555     add=DECDPUNMAX+add-*c;
   6556     if (add<=DECDPUNMAX) {
   6557       *c=(Unit)add;
   6558       add=0;
   6559       }
   6560      else {
   6561       *c=0;
   6562       add=1;
   6563       }
   6564     }
   6565   /* add an extra unit iff it would be non-zero  */
   6566   #if DECTRACE
   6567     printf("UAS borrow: add %ld, carry %ld\n", add, carry);
   6568   #endif
   6569   if ((add-carry-1)!=0) {
   6570     *c=(Unit)(add-carry-1);
   6571     c++;                      /* interesting, include it  */
   6572     }
   6573   return clsu-c;              /* -ve result indicates borrowed  */
   6574   } /* decUnitAddSub  */
   6575 
   6576 /* ------------------------------------------------------------------ */
   6577 /* decTrim -- trim trailing zeros or normalize                        */
   6578 /*                                                                    */
   6579 /*   dn is the number to trim or normalize                            */
   6580 /*   set is the context to use to check for clamp                     */
   6581 /*   all is 1 to remove all trailing zeros, 0 for just fraction ones  */
   6582 /*   noclamp is 1 to unconditional (unclamped) trim                   */
   6583 /*   dropped returns the number of discarded trailing zeros           */
   6584 /*   returns dn                                                       */
   6585 /*                                                                    */
   6586 /* If clamp is set in the context then the number of zeros trimmed    */
   6587 /* may be limited if the exponent is high.                            */
   6588 /* All fields are updated as required.  This is a utility operation,  */
   6589 /* so special values are unchanged and no error is possible.          */
   6590 /* ------------------------------------------------------------------ */
   6591 static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
   6592                            Flag noclamp, Int *dropped) {
   6593   Int   d, exp;                    /* work  */
   6594   uInt  cut;                       /* ..  */
   6595   Unit  *up;                       /* -> current Unit  */
   6596 
   6597   #if DECCHECK
   6598   if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
   6599   #endif
   6600 
   6601   *dropped=0;                           /* assume no zeros dropped  */
   6602   if ((dn->bits & DECSPECIAL)           /* fast exit if special ..  */
   6603     || (*dn->lsu & 0x01)) return dn;    /* .. or odd  */
   6604   if (ISZERO(dn)) {                     /* .. or 0  */
   6605     dn->exponent=0;                     /* (sign is preserved)  */
   6606     return dn;
   6607     }
   6608 
   6609   /* have a finite number which is even  */
   6610   exp=dn->exponent;
   6611   cut=1;                           /* digit (1-DECDPUN) in Unit  */
   6612   up=dn->lsu;                      /* -> current Unit  */
   6613   for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit]  */
   6614     /* slice by powers  */
   6615     #if DECDPUN<=4
   6616       uInt quot=QUOT10(*up, cut);
   6617       if ((*up-quot*powers[cut])!=0) break;  /* found non-0 digit  */
   6618     #else
   6619       if (*up%powers[cut]!=0) break;         /* found non-0 digit  */
   6620     #endif
   6621     /* have a trailing 0  */
   6622     if (!all) {                    /* trimming  */
   6623       /* [if exp>0 then all trailing 0s are significant for trim]  */
   6624       if (exp<=0) {                /* if digit might be significant  */
   6625         if (exp==0) break;         /* then quit  */
   6626         exp++;                     /* next digit might be significant  */
   6627         }
   6628       }
   6629     cut++;                         /* next power  */
   6630     if (cut>DECDPUN) {             /* need new Unit  */
   6631       up++;
   6632       cut=1;
   6633       }
   6634     } /* d  */
   6635   if (d==0) return dn;             /* none to drop  */
   6636 
   6637   /* may need to limit drop if clamping  */
   6638   if (set->clamp && !noclamp) {
   6639     Int maxd=set->emax-set->digits+1-dn->exponent;
   6640     if (maxd<=0) return dn;        /* nothing possible  */
   6641     if (d>maxd) d=maxd;
   6642     }
   6643 
   6644   /* effect the drop  */
   6645   decShiftToLeast(dn->lsu, D2U(dn->digits), d);
   6646   dn->exponent+=d;                 /* maintain numerical value  */
   6647   dn->digits-=d;                   /* new length  */
   6648   *dropped=d;                      /* report the count  */
   6649   return dn;
   6650   } /* decTrim  */
   6651 
   6652 /* ------------------------------------------------------------------ */
   6653 /* decReverse -- reverse a Unit array in place                        */
   6654 /*                                                                    */
   6655 /*   ulo    is the start of the array                                 */
   6656 /*   uhi    is the end of the array (highest Unit to include)         */
   6657 /*                                                                    */
   6658 /* The units ulo through uhi are reversed in place (if the number     */
   6659 /* of units is odd, the middle one is untouched).  Note that the      */
   6660 /* digit(s) in each unit are unaffected.                              */
   6661 /* ------------------------------------------------------------------ */
   6662 static void decReverse(Unit *ulo, Unit *uhi) {
   6663   Unit temp;
   6664   for (; ulo<uhi; ulo++, uhi--) {
   6665     temp=*ulo;
   6666     *ulo=*uhi;
   6667     *uhi=temp;
   6668     }
   6669   return;
   6670   } /* decReverse  */
   6671 
   6672 /* ------------------------------------------------------------------ */
   6673 /* decShiftToMost -- shift digits in array towards most significant   */
   6674 /*                                                                    */
   6675 /*   uar    is the array                                              */
   6676 /*   digits is the count of digits in use in the array                */
   6677 /*   shift  is the number of zeros to pad with (least significant);   */
   6678 /*     it must be zero or positive                                    */
   6679 /*                                                                    */
   6680 /*   returns the new length of the integer in the array, in digits    */
   6681 /*                                                                    */
   6682 /* No overflow is permitted (that is, the uar array must be known to  */
   6683 /* be large enough to hold the result, after shifting).               */
   6684 /* ------------------------------------------------------------------ */
   6685 static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
   6686   Unit  *target, *source, *first;  /* work  */
   6687   Int   cut;                       /* odd 0's to add  */
   6688   uInt  next;                      /* work  */
   6689 
   6690   if (shift==0) return digits;     /* [fastpath] nothing to do  */
   6691   if ((digits+shift)<=DECDPUN) {   /* [fastpath] single-unit case  */
   6692     *uar=(Unit)(*uar*powers[shift]);
   6693     return digits+shift;
   6694     }
   6695 
   6696   next=0;                          /* all paths  */
   6697   source=uar+D2U(digits)-1;        /* where msu comes from  */
   6698   target=source+D2U(shift);        /* where upper part of first cut goes  */
   6699   cut=DECDPUN-MSUDIGITS(shift);    /* where to slice  */
   6700   if (cut==0) {                    /* unit-boundary case  */
   6701     for (; source>=uar; source--, target--) *target=*source;
   6702     }
   6703    else {
   6704     first=uar+D2U(digits+shift)-1; /* where msu of source will end up  */
   6705     for (; source>=uar; source--, target--) {
   6706       /* split the source Unit and accumulate remainder for next  */
   6707       #if DECDPUN<=4
   6708         uInt quot=QUOT10(*source, cut);
   6709         uInt rem=*source-quot*powers[cut];
   6710         next+=quot;
   6711       #else
   6712         uInt rem=*source%powers[cut];
   6713         next+=*source/powers[cut];
   6714       #endif
   6715       if (target<=first) *target=(Unit)next;   /* write to target iff valid  */
   6716       next=rem*powers[DECDPUN-cut];            /* save remainder for next Unit  */
   6717       }
   6718     } /* shift-move  */
   6719 
   6720   /* propagate any partial unit to one below and clear the rest  */
   6721   for (; target>=uar; target--) {
   6722     *target=(Unit)next;
   6723     next=0;
   6724     }
   6725   return digits+shift;
   6726   } /* decShiftToMost  */
   6727 
   6728 /* ------------------------------------------------------------------ */
   6729 /* decShiftToLeast -- shift digits in array towards least significant */
   6730 /*                                                                    */
   6731 /*   uar   is the array                                               */
   6732 /*   units is length of the array, in units                           */
   6733 /*   shift is the number of digits to remove from the lsu end; it     */
   6734 /*     must be zero or positive and <= than units*DECDPUN.            */
   6735 /*                                                                    */
   6736 /*   returns the new length of the integer in the array, in units     */
   6737 /*                                                                    */
   6738 /* Removed digits are discarded (lost).  Units not required to hold   */
   6739 /* the final result are unchanged.                                    */
   6740 /* ------------------------------------------------------------------ */
   6741 static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
   6742   Unit  *target, *up;              /* work  */
   6743   Int   cut, count;                /* work  */
   6744   Int   quot, rem;                 /* for division  */
   6745 
   6746   if (shift==0) return units;      /* [fastpath] nothing to do  */
   6747   if (shift==units*DECDPUN) {      /* [fastpath] little to do  */
   6748     *uar=0;                        /* all digits cleared gives zero  */
   6749     return 1;                      /* leaves just the one  */
   6750     }
   6751 
   6752   target=uar;                      /* both paths  */
   6753   cut=MSUDIGITS(shift);
   6754   if (cut==DECDPUN) {              /* unit-boundary case; easy  */
   6755     up=uar+D2U(shift);
   6756     for (; up<uar+units; target++, up++) *target=*up;
   6757     return target-uar;
   6758     }
   6759 
   6760   /* messier  */
   6761   up=uar+D2U(shift-cut);           /* source; correct to whole Units  */
   6762   count=units*DECDPUN-shift;       /* the maximum new length  */
   6763   #if DECDPUN<=4
   6764     quot=QUOT10(*up, cut);
   6765   #else
   6766     quot=*up/powers[cut];
   6767   #endif
   6768   for (; ; target++) {
   6769     *target=(Unit)quot;
   6770     count-=(DECDPUN-cut);
   6771     if (count<=0) break;
   6772     up++;
   6773     quot=*up;
   6774     #if DECDPUN<=4
   6775       quot=QUOT10(quot, cut);
   6776       rem=*up-quot*powers[cut];
   6777     #else
   6778       rem=quot%powers[cut];
   6779       quot=quot/powers[cut];
   6780     #endif
   6781     *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
   6782     count-=cut;
   6783     if (count<=0) break;
   6784     }
   6785   return target-uar+1;
   6786   } /* decShiftToLeast  */
   6787 
   6788 #if DECSUBSET
   6789 /* ------------------------------------------------------------------ */
   6790 /* decRoundOperand -- round an operand  [used for subset only]        */
   6791 /*                                                                    */
   6792 /*   dn is the number to round (dn->digits is > set->digits)          */
   6793 /*   set is the relevant context                                      */
   6794 /*   status is the status accumulator                                 */
   6795 /*                                                                    */
   6796 /*   returns an allocated decNumber with the rounded result.          */
   6797 /*                                                                    */
   6798 /* lostDigits and other status may be set by this.                    */
   6799 /*                                                                    */
   6800 /* Since the input is an operand, it must not be modified.            */
   6801 /* Instead, return an allocated decNumber, rounded as required.       */
   6802 /* It is the caller's responsibility to free the allocated storage.   */
   6803 /*                                                                    */
   6804 /* If no storage is available then the result cannot be used, so NULL */
   6805 /* is returned.                                                       */
   6806 /* ------------------------------------------------------------------ */
   6807 static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
   6808                                   uInt *status) {
   6809   decNumber *res;                       /* result structure  */
   6810   uInt newstatus=0;                     /* status from round  */
   6811   Int  residue=0;                       /* rounding accumulator  */
   6812 
   6813   /* Allocate storage for the returned decNumber, big enough for the  */
   6814   /* length specified by the context  */
   6815   res=(decNumber *)malloc(sizeof(decNumber)
   6816                           +(D2U(set->digits)-1)*sizeof(Unit));
   6817   if (res==NULL) {
   6818     *status|=DEC_Insufficient_storage;
   6819     return NULL;
   6820     }
   6821   decCopyFit(res, dn, set, &residue, &newstatus);
   6822   decApplyRound(res, set, residue, &newstatus);
   6823 
   6824   /* If that set Inexact then "lost digits" is raised...  */
   6825   if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
   6826   *status|=newstatus;
   6827   return res;
   6828   } /* decRoundOperand  */
   6829 #endif
   6830 
   6831 /* ------------------------------------------------------------------ */
   6832 /* decCopyFit -- copy a number, truncating the coefficient if needed  */
   6833 /*                                                                    */
   6834 /*   dest is the target decNumber                                     */
   6835 /*   src  is the source decNumber                                     */
   6836 /*   set is the context [used for length (digits) and rounding mode]  */
   6837 /*   residue is the residue accumulator                               */
   6838 /*   status contains the current status to be updated                 */
   6839 /*                                                                    */
   6840 /* (dest==src is allowed and will be a no-op if fits)                 */
   6841 /* All fields are updated as required.                                */
   6842 /* ------------------------------------------------------------------ */
   6843 static void decCopyFit(decNumber *dest, const decNumber *src,
   6844                        decContext *set, Int *residue, uInt *status) {
   6845   dest->bits=src->bits;
   6846   dest->exponent=src->exponent;
   6847   decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
   6848   } /* decCopyFit  */
   6849 
   6850 /* ------------------------------------------------------------------ */
   6851 /* decSetCoeff -- set the coefficient of a number                     */
   6852 /*                                                                    */
   6853 /*   dn    is the number whose coefficient array is to be set.        */
   6854 /*         It must have space for set->digits digits                  */
   6855 /*   set   is the context [for size]                                  */
   6856 /*   lsu   -> lsu of the source coefficient [may be dn->lsu]          */
   6857 /*   len   is digits in the source coefficient [may be dn->digits]    */
   6858 /*   residue is the residue accumulator.  This has values as in       */
   6859 /*         decApplyRound, and will be unchanged unless the            */
   6860 /*         target size is less than len.  In this case, the           */
   6861 /*         coefficient is truncated and the residue is updated to     */
   6862 /*         reflect the previous residue and the dropped digits.       */
   6863 /*   status is the status accumulator, as usual                       */
   6864 /*                                                                    */
   6865 /* The coefficient may already be in the number, or it can be an      */
   6866 /* external intermediate array.  If it is in the number, lsu must ==  */
   6867 /* dn->lsu and len must == dn->digits.                                */
   6868 /*                                                                    */
   6869 /* Note that the coefficient length (len) may be < set->digits, and   */
   6870 /* in this case this merely copies the coefficient (or is a no-op     */
   6871 /* if dn->lsu==lsu).                                                  */
   6872 /*                                                                    */
   6873 /* Note also that (only internally, from decQuantizeOp and            */
   6874 /* decSetSubnormal) the value of set->digits may be less than one,    */
   6875 /* indicating a round to left.  This routine handles that case        */
   6876 /* correctly; caller ensures space.                                   */
   6877 /*                                                                    */
   6878 /* dn->digits, dn->lsu (and as required), and dn->exponent are        */
   6879 /* updated as necessary.   dn->bits (sign) is unchanged.              */
   6880 /*                                                                    */
   6881 /* DEC_Rounded status is set if any digits are discarded.             */
   6882 /* DEC_Inexact status is set if any non-zero digits are discarded, or */
   6883 /*                       incoming residue was non-0 (implies rounded) */
   6884 /* ------------------------------------------------------------------ */
   6885 /* mapping array: maps 0-9 to canonical residues, so that a residue  */
   6886 /* can be adjusted in the range [-1, +1] and achieve correct rounding  */
   6887 /*                             0  1  2  3  4  5  6  7  8  9  */
   6888 static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
   6889 static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
   6890                         Int len, Int *residue, uInt *status) {
   6891   Int   discard;              /* number of digits to discard  */
   6892   uInt  cut;                  /* cut point in Unit  */
   6893   const Unit *up;             /* work  */
   6894   Unit  *target;              /* ..  */
   6895   Int   count;                /* ..  */
   6896   #if DECDPUN<=4
   6897   uInt  temp;                 /* ..  */
   6898   #endif
   6899 
   6900   discard=len-set->digits;    /* digits to discard  */
   6901   if (discard<=0) {           /* no digits are being discarded  */
   6902     if (dn->lsu!=lsu) {       /* copy needed  */
   6903       /* copy the coefficient array to the result number; no shift needed  */
   6904       count=len;              /* avoids D2U  */
   6905       up=lsu;
   6906       for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
   6907         *target=*up;
   6908       dn->digits=len;         /* set the new length  */
   6909       }
   6910     /* dn->exponent and residue are unchanged, record any inexactitude  */
   6911     if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
   6912     return;
   6913     }
   6914 
   6915   /* some digits must be discarded ...  */
   6916   dn->exponent+=discard;      /* maintain numerical value  */
   6917   *status|=DEC_Rounded;       /* accumulate Rounded status  */
   6918   if (*residue>1) *residue=1; /* previous residue now to right, so reduce  */
   6919 
   6920   if (discard>len) {          /* everything, +1, is being discarded  */
   6921     /* guard digit is 0  */
   6922     /* residue is all the number [NB could be all 0s]  */
   6923     if (*residue<=0) {        /* not already positive  */
   6924       count=len;              /* avoids D2U  */
   6925       for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0  */
   6926         *residue=1;
   6927         break;                /* no need to check any others  */
   6928         }
   6929       }
   6930     if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude  */
   6931     *dn->lsu=0;               /* coefficient will now be 0  */
   6932     dn->digits=1;             /* ..  */
   6933     return;
   6934     } /* total discard  */
   6935 
   6936   /* partial discard [most common case]  */
   6937   /* here, at least the first (most significant) discarded digit exists  */
   6938 
   6939   /* spin up the number, noting residue during the spin, until get to  */
   6940   /* the Unit with the first discarded digit.  When reach it, extract  */
   6941   /* it and remember its position  */
   6942   count=0;
   6943   for (up=lsu;; up++) {
   6944     count+=DECDPUN;
   6945     if (count>=discard) break; /* full ones all checked  */
   6946     if (*up!=0) *residue=1;
   6947     } /* up  */
   6948 
   6949   /* here up -> Unit with first discarded digit  */
   6950   cut=discard-(count-DECDPUN)-1;
   6951   if (cut==DECDPUN-1) {       /* unit-boundary case (fast)  */
   6952     Unit half=(Unit)powers[DECDPUN]>>1;
   6953     /* set residue directly  */
   6954     if (*up>=half) {
   6955       if (*up>half) *residue=7;
   6956       else *residue+=5;       /* add sticky bit  */
   6957       }
   6958      else { /* <half  */
   6959       if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit]  */
   6960       }
   6961     if (set->digits<=0) {     /* special for Quantize/Subnormal :-(  */
   6962       *dn->lsu=0;             /* .. result is 0  */
   6963       dn->digits=1;           /* ..  */
   6964       }
   6965      else {                   /* shift to least  */
   6966       count=set->digits;      /* now digits to end up with  */
   6967       dn->digits=count;       /* set the new length  */
   6968       up++;                   /* move to next  */
   6969       /* on unit boundary, so shift-down copy loop is simple  */
   6970       for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
   6971         *target=*up;
   6972       }
   6973     } /* unit-boundary case  */
   6974 
   6975    else { /* discard digit is in low digit(s), and not top digit  */
   6976     uInt  discard1;                /* first discarded digit  */
   6977     uInt  quot, rem;               /* for divisions  */
   6978     if (cut==0) quot=*up;          /* is at bottom of unit  */
   6979      else /* cut>0 */ {            /* it's not at bottom of unit  */
   6980       #if DECDPUN<=4
   6981         quot=QUOT10(*up, cut);
   6982         rem=*up-quot*powers[cut];
   6983       #else
   6984         rem=*up%powers[cut];
   6985         quot=*up/powers[cut];
   6986       #endif
   6987       if (rem!=0) *residue=1;
   6988       }
   6989     /* discard digit is now at bottom of quot  */
   6990     #if DECDPUN<=4
   6991       temp=(quot*6554)>>16;        /* fast /10  */
   6992       /* Vowels algorithm here not a win (9 instructions)  */
   6993       discard1=quot-X10(temp);
   6994       quot=temp;
   6995     #else
   6996       discard1=quot%10;
   6997       quot=quot/10;
   6998     #endif
   6999     /* here, discard1 is the guard digit, and residue is everything  */
   7000     /* else [use mapping array to accumulate residue safely]  */
   7001     *residue+=resmap[discard1];
   7002     cut++;                         /* update cut  */
   7003     /* here: up -> Unit of the array with bottom digit  */
   7004     /*       cut is the division point for each Unit  */
   7005     /*       quot holds the uncut high-order digits for the current unit  */
   7006     if (set->digits<=0) {          /* special for Quantize/Subnormal :-(  */
   7007       *dn->lsu=0;                  /* .. result is 0  */
   7008       dn->digits=1;                /* ..  */
   7009       }
   7010      else {                        /* shift to least needed  */
   7011       count=set->digits;           /* now digits to end up with  */
   7012       dn->digits=count;            /* set the new length  */
   7013       /* shift-copy the coefficient array to the result number  */
   7014       for (target=dn->lsu; ; target++) {
   7015         *target=(Unit)quot;
   7016         count-=(DECDPUN-cut);
   7017         if (count<=0) break;
   7018         up++;
   7019         quot=*up;
   7020         #if DECDPUN<=4
   7021           quot=QUOT10(quot, cut);
   7022           rem=*up-quot*powers[cut];
   7023         #else
   7024           rem=quot%powers[cut];
   7025           quot=quot/powers[cut];
   7026         #endif
   7027         *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
   7028         count-=cut;
   7029         if (count<=0) break;
   7030         } /* shift-copy loop  */
   7031       } /* shift to least  */
   7032     } /* not unit boundary  */
   7033 
   7034   if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude  */
   7035   return;
   7036   } /* decSetCoeff  */
   7037 
   7038 /* ------------------------------------------------------------------ */
   7039 /* decApplyRound -- apply pending rounding to a number                */
   7040 /*                                                                    */
   7041 /*   dn    is the number, with space for set->digits digits           */
   7042 /*   set   is the context [for size and rounding mode]                */
   7043 /*   residue indicates pending rounding, being any accumulated        */
   7044 /*         guard and sticky information.  It may be:                  */
   7045 /*         6-9: rounding digit is >5                                  */
   7046 /*         5:   rounding digit is exactly half-way                    */
   7047 /*         1-4: rounding digit is <5 and >0                           */
   7048 /*         0:   the coefficient is exact                              */
   7049 /*        -1:   as 1, but the hidden digits are subtractive, that     */
   7050 /*              is, of the opposite sign to dn.  In this case the     */
   7051 /*              coefficient must be non-0.  This case occurs when     */
   7052 /*              subtracting a small number (which can be reduced to   */
   7053 /*              a sticky bit); see decAddOp.                          */
   7054 /*   status is the status accumulator, as usual                       */
   7055 /*                                                                    */
   7056 /* This routine applies rounding while keeping the length of the      */
   7057 /* coefficient constant.  The exponent and status are unchanged       */
   7058 /* except if:                                                         */
   7059 /*                                                                    */
   7060 /*   -- the coefficient was increased and is all nines (in which      */
   7061 /*      case Overflow could occur, and is handled directly here so    */
   7062 /*      the caller does not need to re-test for overflow)             */
   7063 /*                                                                    */
   7064 /*   -- the coefficient was decreased and becomes all nines (in which */
   7065 /*      case Underflow could occur, and is also handled directly).    */
   7066 /*                                                                    */
   7067 /* All fields in dn are updated as required.                          */
   7068 /*                                                                    */
   7069 /* ------------------------------------------------------------------ */
   7070 static void decApplyRound(decNumber *dn, decContext *set, Int residue,
   7071                           uInt *status) {
   7072   Int  bump;                  /* 1 if coefficient needs to be incremented  */
   7073                               /* -1 if coefficient needs to be decremented  */
   7074 
   7075   if (residue==0) return;     /* nothing to apply  */
   7076 
   7077   bump=0;                     /* assume a smooth ride  */
   7078 
   7079   /* now decide whether, and how, to round, depending on mode  */
   7080   switch (set->round) {
   7081     case DEC_ROUND_05UP: {    /* round zero or five up (for reround)  */
   7082       /* This is the same as DEC_ROUND_DOWN unless there is a  */
   7083       /* positive residue and the lsd of dn is 0 or 5, in which case  */
   7084       /* it is bumped; when residue is <0, the number is therefore  */
   7085       /* bumped down unless the final digit was 1 or 6 (in which  */
   7086       /* case it is bumped down and then up -- a no-op)  */
   7087       Int lsd5=*dn->lsu%5;     /* get lsd and quintate  */
   7088       if (residue<0 && lsd5!=1) bump=-1;
   7089        else if (residue>0 && lsd5==0) bump=1;
   7090       /* [bump==1 could be applied directly; use common path for clarity]  */
   7091       break;} /* r-05  */
   7092 
   7093     case DEC_ROUND_DOWN: {
   7094       /* no change, except if negative residue  */
   7095       if (residue<0) bump=-1;
   7096       break;} /* r-d  */
   7097 
   7098     case DEC_ROUND_HALF_DOWN: {
   7099       if (residue>5) bump=1;
   7100       break;} /* r-h-d  */
   7101 
   7102     case DEC_ROUND_HALF_EVEN: {
   7103       if (residue>5) bump=1;            /* >0.5 goes up  */
   7104        else if (residue==5) {           /* exactly 0.5000...  */
   7105         /* 0.5 goes up iff [new] lsd is odd  */
   7106         if (*dn->lsu & 0x01) bump=1;
   7107         }
   7108       break;} /* r-h-e  */
   7109 
   7110     case DEC_ROUND_HALF_UP: {
   7111       if (residue>=5) bump=1;
   7112       break;} /* r-h-u  */
   7113 
   7114     case DEC_ROUND_UP: {
   7115       if (residue>0) bump=1;
   7116       break;} /* r-u  */
   7117 
   7118     case DEC_ROUND_CEILING: {
   7119       /* same as _UP for positive numbers, and as _DOWN for negatives  */
   7120       /* [negative residue cannot occur on 0]  */
   7121       if (decNumberIsNegative(dn)) {
   7122         if (residue<0) bump=-1;
   7123         }
   7124        else {
   7125         if (residue>0) bump=1;
   7126         }
   7127       break;} /* r-c  */
   7128 
   7129     case DEC_ROUND_FLOOR: {
   7130       /* same as _UP for negative numbers, and as _DOWN for positive  */
   7131       /* [negative residue cannot occur on 0]  */
   7132       if (!decNumberIsNegative(dn)) {
   7133         if (residue<0) bump=-1;
   7134         }
   7135        else {
   7136         if (residue>0) bump=1;
   7137         }
   7138       break;} /* r-f  */
   7139 
   7140     default: {      /* e.g., DEC_ROUND_MAX  */
   7141       *status|=DEC_Invalid_context;
   7142       #if DECTRACE || (DECCHECK && DECVERB)
   7143       printf("Unknown rounding mode: %d\n", set->round);
   7144       #endif
   7145       break;}
   7146     } /* switch  */
   7147 
   7148   /* now bump the number, up or down, if need be  */
   7149   if (bump==0) return;                       /* no action required  */
   7150 
   7151   /* Simply use decUnitAddSub unless bumping up and the number is  */
   7152   /* all nines.  In this special case set to 100... explicitly  */
   7153   /* and adjust the exponent by one (as otherwise could overflow  */
   7154   /* the array)  */
   7155   /* Similarly handle all-nines result if bumping down.  */
   7156   if (bump>0) {
   7157     Unit *up;                                /* work  */
   7158     uInt count=dn->digits;                   /* digits to be checked  */
   7159     for (up=dn->lsu; ; up++) {
   7160       if (count<=DECDPUN) {
   7161         /* this is the last Unit (the msu)  */
   7162         if (*up!=powers[count]-1) break;     /* not still 9s  */
   7163         /* here if it, too, is all nines  */
   7164         *up=(Unit)powers[count-1];           /* here 999 -> 100 etc.  */
   7165         for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0  */
   7166         dn->exponent++;                      /* and bump exponent  */
   7167         /* [which, very rarely, could cause Overflow...]  */
   7168         if ((dn->exponent+dn->digits)>set->emax+1) {
   7169           decSetOverflow(dn, set, status);
   7170           }
   7171         return;                              /* done  */
   7172         }
   7173       /* a full unit to check, with more to come  */
   7174       if (*up!=DECDPUNMAX) break;            /* not still 9s  */
   7175       count-=DECDPUN;
   7176       } /* up  */
   7177     } /* bump>0  */
   7178    else {                                    /* -1  */
   7179     /* here checking for a pre-bump of 1000... (leading 1, all  */
   7180     /* other digits zero)  */
   7181     Unit *up, *sup;                          /* work  */
   7182     uInt count=dn->digits;                   /* digits to be checked  */
   7183     for (up=dn->lsu; ; up++) {
   7184       if (count<=DECDPUN) {
   7185         /* this is the last Unit (the msu)  */
   7186         if (*up!=powers[count-1]) break;     /* not 100..  */
   7187         /* here if have the 1000... case  */
   7188         sup=up;                              /* save msu pointer  */
   7189         *up=(Unit)powers[count]-1;           /* here 100 in msu -> 999  */
   7190         /* others all to all-nines, too  */
   7191         for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
   7192         dn->exponent--;                      /* and bump exponent  */
   7193 
   7194         /* iff the number was at the subnormal boundary (exponent=etiny)  */
   7195         /* then the exponent is now out of range, so it will in fact get  */
   7196         /* clamped to etiny and the final 9 dropped.  */
   7197         /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin,  */
   7198         /*        dn->exponent, set->digits);  */
   7199         if (dn->exponent+1==set->emin-set->digits+1) {
   7200           if (count==1 && dn->digits==1) *sup=0;  /* here 9 -> 0[.9]  */
   7201            else {
   7202             *sup=(Unit)powers[count-1]-1;    /* here 999.. in msu -> 99..  */
   7203             dn->digits--;
   7204             }
   7205           dn->exponent++;
   7206           *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
   7207           }
   7208         return;                              /* done  */
   7209         }
   7210 
   7211       /* a full unit to check, with more to come  */
   7212       if (*up!=0) break;                     /* not still 0s  */
   7213       count-=DECDPUN;
   7214       } /* up  */
   7215 
   7216     } /* bump<0  */
   7217 
   7218   /* Actual bump needed.  Do it.  */
   7219   decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
   7220   } /* decApplyRound  */
   7221 
   7222 #if DECSUBSET
   7223 /* ------------------------------------------------------------------ */
   7224 /* decFinish -- finish processing a number                            */
   7225 /*                                                                    */
   7226 /*   dn is the number                                                 */
   7227 /*   set is the context                                               */
   7228 /*   residue is the rounding accumulator (as in decApplyRound)        */
   7229 /*   status is the accumulator                                        */
   7230 /*                                                                    */
   7231 /* This finishes off the current number by:                           */
   7232 /*    1. If not extended:                                             */
   7233 /*       a. Converting a zero result to clean '0'                     */
   7234 /*       b. Reducing positive exponents to 0, if would fit in digits  */
   7235 /*    2. Checking for overflow and subnormals (always)                */
   7236 /* Note this is just Finalize when no subset arithmetic.              */
   7237 /* All fields are updated as required.                                */
   7238 /* ------------------------------------------------------------------ */
   7239 static void decFinish(decNumber *dn, decContext *set, Int *residue,
   7240                       uInt *status) {
   7241   if (!set->extended) {
   7242     if ISZERO(dn) {                /* value is zero  */
   7243       dn->exponent=0;              /* clean exponent ..  */
   7244       dn->bits=0;                  /* .. and sign  */
   7245       return;                      /* no error possible  */
   7246       }
   7247     if (dn->exponent>=0) {         /* non-negative exponent  */
   7248       /* >0; reduce to integer if possible  */
   7249       if (set->digits >= (dn->exponent+dn->digits)) {
   7250         dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
   7251         dn->exponent=0;
   7252         }
   7253       }
   7254     } /* !extended  */
   7255 
   7256   decFinalize(dn, set, residue, status);
   7257   } /* decFinish  */
   7258 #endif
   7259 
   7260 /* ------------------------------------------------------------------ */
   7261 /* decFinalize -- final check, clamp, and round of a number           */
   7262 /*                                                                    */
   7263 /*   dn is the number                                                 */
   7264 /*   set is the context                                               */
   7265 /*   residue is the rounding accumulator (as in decApplyRound)        */
   7266 /*   status is the status accumulator                                 */
   7267 /*                                                                    */
   7268 /* This finishes off the current number by checking for subnormal     */
   7269 /* results, applying any pending rounding, checking for overflow,     */
   7270 /* and applying any clamping.                                         */
   7271 /* Underflow and overflow conditions are raised as appropriate.       */
   7272 /* All fields are updated as required.                                */
   7273 /* ------------------------------------------------------------------ */
   7274 static void decFinalize(decNumber *dn, decContext *set, Int *residue,
   7275                         uInt *status) {
   7276   Int shift;                            /* shift needed if clamping  */
   7277   Int tinyexp=set->emin-dn->digits+1;   /* precalculate subnormal boundary  */
   7278 
   7279   /* Must be careful, here, when checking the exponent as the  */
   7280   /* adjusted exponent could overflow 31 bits [because it may already  */
   7281   /* be up to twice the expected].  */
   7282 
   7283   /* First test for subnormal.  This must be done before any final  */
   7284   /* round as the result could be rounded to Nmin or 0.  */
   7285   if (dn->exponent<=tinyexp) {          /* prefilter  */
   7286     Int comp;
   7287     decNumber nmin;
   7288     /* A very nasty case here is dn == Nmin and residue<0  */
   7289     if (dn->exponent<tinyexp) {
   7290       /* Go handle subnormals; this will apply round if needed.  */
   7291       decSetSubnormal(dn, set, residue, status);
   7292       return;
   7293       }
   7294     /* Equals case: only subnormal if dn=Nmin and negative residue  */
   7295     uprv_decNumberZero(&nmin);
   7296     nmin.lsu[0]=1;
   7297     nmin.exponent=set->emin;
   7298     comp=decCompare(dn, &nmin, 1);                /* (signless compare)  */
   7299     if (comp==BADINT) {                           /* oops  */
   7300       *status|=DEC_Insufficient_storage;          /* abandon...  */
   7301       return;
   7302       }
   7303     if (*residue<0 && comp==0) {                  /* neg residue and dn==Nmin  */
   7304       decApplyRound(dn, set, *residue, status);   /* might force down  */
   7305       decSetSubnormal(dn, set, residue, status);
   7306       return;
   7307       }
   7308     }
   7309 
   7310   /* now apply any pending round (this could raise overflow).  */
   7311   if (*residue!=0) decApplyRound(dn, set, *residue, status);
   7312 
   7313   /* Check for overflow [redundant in the 'rare' case] or clamp  */
   7314   if (dn->exponent<=set->emax-set->digits+1) return;   /* neither needed  */
   7315 
   7316 
   7317   /* here when might have an overflow or clamp to do  */
   7318   if (dn->exponent>set->emax-dn->digits+1) {           /* too big  */
   7319     decSetOverflow(dn, set, status);
   7320     return;
   7321     }
   7322   /* here when the result is normal but in clamp range  */
   7323   if (!set->clamp) return;
   7324 
   7325   /* here when need to apply the IEEE exponent clamp (fold-down)  */
   7326   shift=dn->exponent-(set->emax-set->digits+1);
   7327 
   7328   /* shift coefficient (if non-zero)  */
   7329   if (!ISZERO(dn)) {
   7330     dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
   7331     }
   7332   dn->exponent-=shift;   /* adjust the exponent to match  */
   7333   *status|=DEC_Clamped;  /* and record the dirty deed  */
   7334   return;
   7335   } /* decFinalize  */
   7336 
   7337 /* ------------------------------------------------------------------ */
   7338 /* decSetOverflow -- set number to proper overflow value              */
   7339 /*                                                                    */
   7340 /*   dn is the number (used for sign [only] and result)               */
   7341 /*   set is the context [used for the rounding mode, etc.]            */
   7342 /*   status contains the current status to be updated                 */
   7343 /*                                                                    */
   7344 /* This sets the sign of a number and sets its value to either        */
   7345 /* Infinity or the maximum finite value, depending on the sign of     */
   7346 /* dn and the rounding mode, following IEEE 754 rules.                */
   7347 /* ------------------------------------------------------------------ */
   7348 static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
   7349   Flag needmax=0;                  /* result is maximum finite value  */
   7350   uByte sign=dn->bits&DECNEG;      /* clean and save sign bit  */
   7351 
   7352   if (ISZERO(dn)) {                /* zero does not overflow magnitude  */
   7353     Int emax=set->emax;                      /* limit value  */
   7354     if (set->clamp) emax-=set->digits-1;     /* lower if clamping  */
   7355     if (dn->exponent>emax) {                 /* clamp required  */
   7356       dn->exponent=emax;
   7357       *status|=DEC_Clamped;
   7358       }
   7359     return;
   7360     }
   7361 
   7362   uprv_decNumberZero(dn);
   7363   switch (set->round) {
   7364     case DEC_ROUND_DOWN: {
   7365       needmax=1;                   /* never Infinity  */
   7366       break;} /* r-d  */
   7367     case DEC_ROUND_05UP: {
   7368       needmax=1;                   /* never Infinity  */
   7369       break;} /* r-05  */
   7370     case DEC_ROUND_CEILING: {
   7371       if (sign) needmax=1;         /* Infinity if non-negative  */
   7372       break;} /* r-c  */
   7373     case DEC_ROUND_FLOOR: {
   7374       if (!sign) needmax=1;        /* Infinity if negative  */
   7375       break;} /* r-f  */
   7376     default: break;                /* Infinity in all other cases  */
   7377     }
   7378   if (needmax) {
   7379     decSetMaxValue(dn, set);
   7380     dn->bits=sign;                 /* set sign  */
   7381     }
   7382    else dn->bits=sign|DECINF;      /* Value is +/-Infinity  */
   7383   *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
   7384   } /* decSetOverflow  */
   7385 
   7386 /* ------------------------------------------------------------------ */
   7387 /* decSetMaxValue -- set number to +Nmax (maximum normal value)       */
   7388 /*                                                                    */
   7389 /*   dn is the number to set                                          */
   7390 /*   set is the context [used for digits and emax]                    */
   7391 /*                                                                    */
   7392 /* This sets the number to the maximum positive value.                */
   7393 /* ------------------------------------------------------------------ */
   7394 static void decSetMaxValue(decNumber *dn, decContext *set) {
   7395   Unit *up;                        /* work  */
   7396   Int count=set->digits;           /* nines to add  */
   7397   dn->digits=count;
   7398   /* fill in all nines to set maximum value  */
   7399   for (up=dn->lsu; ; up++) {
   7400     if (count>DECDPUN) *up=DECDPUNMAX;  /* unit full o'nines  */
   7401      else {                             /* this is the msu  */
   7402       *up=(Unit)(powers[count]-1);
   7403       break;
   7404       }
   7405     count-=DECDPUN;                /* filled those digits  */
   7406     } /* up  */
   7407   dn->bits=0;                      /* + sign  */
   7408   dn->exponent=set->emax-set->digits+1;
   7409   } /* decSetMaxValue  */
   7410 
   7411 /* ------------------------------------------------------------------ */
   7412 /* decSetSubnormal -- process value whose exponent is <Emin           */
   7413 /*                                                                    */
   7414 /*   dn is the number (used as input as well as output; it may have   */
   7415 /*         an allowed subnormal value, which may need to be rounded)  */
   7416 /*   set is the context [used for the rounding mode]                  */
   7417 /*   residue is any pending residue                                   */
   7418 /*   status contains the current status to be updated                 */
   7419 /*                                                                    */
   7420 /* If subset mode, set result to zero and set Underflow flags.        */
   7421 /*                                                                    */
   7422 /* Value may be zero with a low exponent; this does not set Subnormal */
   7423 /* but the exponent will be clamped to Etiny.                         */
   7424 /*                                                                    */
   7425 /* Otherwise ensure exponent is not out of range, and round as        */
   7426 /* necessary.  Underflow is set if the result is Inexact.             */
   7427 /* ------------------------------------------------------------------ */
   7428 static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
   7429                             uInt *status) {
   7430   decContext workset;         /* work  */
   7431   Int        etiny, adjust;   /* ..  */
   7432 
   7433   #if DECSUBSET
   7434   /* simple set to zero and 'hard underflow' for subset  */
   7435   if (!set->extended) {
   7436     uprv_decNumberZero(dn);
   7437     /* always full overflow  */
   7438     *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
   7439     return;
   7440     }
   7441   #endif
   7442 
   7443   /* Full arithmetic -- allow subnormals, rounded to minimum exponent  */
   7444   /* (Etiny) if needed  */
   7445   etiny=set->emin-(set->digits-1);      /* smallest allowed exponent  */
   7446 
   7447   if ISZERO(dn) {                       /* value is zero  */
   7448     /* residue can never be non-zero here  */
   7449     #if DECCHECK
   7450       if (*residue!=0) {
   7451         printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
   7452         *status|=DEC_Invalid_operation;
   7453         }
   7454     #endif
   7455     if (dn->exponent<etiny) {           /* clamp required  */
   7456       dn->exponent=etiny;
   7457       *status|=DEC_Clamped;
   7458       }
   7459     return;
   7460     }
   7461 
   7462   *status|=DEC_Subnormal;               /* have a non-zero subnormal  */
   7463   adjust=etiny-dn->exponent;            /* calculate digits to remove  */
   7464   if (adjust<=0) {                      /* not out of range; unrounded  */
   7465     /* residue can never be non-zero here, except in the Nmin-residue  */
   7466     /* case (which is a subnormal result), so can take fast-path here  */
   7467     /* it may already be inexact (from setting the coefficient)  */
   7468     if (*status&DEC_Inexact) *status|=DEC_Underflow;
   7469     return;
   7470     }
   7471 
   7472   /* adjust>0, so need to rescale the result so exponent becomes Etiny  */
   7473   /* [this code is similar to that in rescale]  */
   7474   workset=*set;                         /* clone rounding, etc.  */
   7475   workset.digits=dn->digits-adjust;     /* set requested length  */
   7476   workset.emin-=adjust;                 /* and adjust emin to match  */
   7477   /* [note that the latter can be <1, here, similar to Rescale case]  */
   7478   decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
   7479   decApplyRound(dn, &workset, *residue, status);
   7480 
   7481   /* Use 754 default rule: Underflow is set iff Inexact  */
   7482   /* [independent of whether trapped]  */
   7483   if (*status&DEC_Inexact) *status|=DEC_Underflow;
   7484 
   7485   /* if rounded up a 999s case, exponent will be off by one; adjust  */
   7486   /* back if so [it will fit, because it was shortened earlier]  */
   7487   if (dn->exponent>etiny) {
   7488     dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
   7489     dn->exponent--;                     /* (re)adjust the exponent.  */
   7490     }
   7491 
   7492   /* if rounded to zero, it is by definition clamped...  */
   7493   if (ISZERO(dn)) *status|=DEC_Clamped;
   7494   } /* decSetSubnormal  */
   7495 
   7496 /* ------------------------------------------------------------------ */
   7497 /* decCheckMath - check entry conditions for a math function          */
   7498 /*                                                                    */
   7499 /*   This checks the context and the operand                          */
   7500 /*                                                                    */
   7501 /*   rhs is the operand to check                                      */
   7502 /*   set is the context to check                                      */
   7503 /*   status is unchanged if both are good                             */
   7504 /*                                                                    */
   7505 /* returns non-zero if status is changed, 0 otherwise                 */
   7506 /*                                                                    */
   7507 /* Restrictions enforced:                                             */
   7508 /*                                                                    */
   7509 /*   digits, emax, and -emin in the context must be less than         */
   7510 /*   DEC_MAX_MATH (999999), and A must be within these bounds if      */
   7511 /*   non-zero.  Invalid_operation is set in the status if a           */
   7512 /*   restriction is violated.                                         */
   7513 /* ------------------------------------------------------------------ */
   7514 static uInt decCheckMath(const decNumber *rhs, decContext *set,
   7515                          uInt *status) {
   7516   uInt save=*status;                         /* record  */
   7517   if (set->digits>DEC_MAX_MATH
   7518    || set->emax>DEC_MAX_MATH
   7519    || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
   7520    else if ((rhs->digits>DEC_MAX_MATH
   7521      || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
   7522      || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
   7523      && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
   7524   return (*status!=save);
   7525   } /* decCheckMath  */
   7526 
   7527 /* ------------------------------------------------------------------ */
   7528 /* decGetInt -- get integer from a number                             */
   7529 /*                                                                    */
   7530 /*   dn is the number [which will not be altered]                     */
   7531 /*                                                                    */
   7532 /*   returns one of:                                                  */
   7533 /*     BADINT if there is a non-zero fraction                         */
   7534 /*     the converted integer                                          */
   7535 /*     BIGEVEN if the integer is even and magnitude > 2*10**9         */
   7536 /*     BIGODD  if the integer is odd  and magnitude > 2*10**9         */
   7537 /*                                                                    */
   7538 /* This checks and gets a whole number from the input decNumber.      */
   7539 /* The sign can be determined from dn by the caller when BIGEVEN or   */
   7540 /* BIGODD is returned.                                                */
   7541 /* ------------------------------------------------------------------ */
   7542 static Int decGetInt(const decNumber *dn) {
   7543   Int  theInt;                          /* result accumulator  */
   7544   const Unit *up;                       /* work  */
   7545   Int  got;                             /* digits (real or not) processed  */
   7546   Int  ilength=dn->digits+dn->exponent; /* integral length  */
   7547   Flag neg=decNumberIsNegative(dn);     /* 1 if -ve  */
   7548 
   7549   /* The number must be an integer that fits in 10 digits  */
   7550   /* Assert, here, that 10 is enough for any rescale Etiny  */
   7551   #if DEC_MAX_EMAX > 999999999
   7552     #error GetInt may need updating [for Emax]
   7553   #endif
   7554   #if DEC_MIN_EMIN < -999999999
   7555     #error GetInt may need updating [for Emin]
   7556   #endif
   7557   if (ISZERO(dn)) return 0;             /* zeros are OK, with any exponent  */
   7558 
   7559   up=dn->lsu;                           /* ready for lsu  */
   7560   theInt=0;                             /* ready to accumulate  */
   7561   if (dn->exponent>=0) {                /* relatively easy  */
   7562     /* no fractional part [usual]; allow for positive exponent  */
   7563     got=dn->exponent;
   7564     }
   7565    else { /* -ve exponent; some fractional part to check and discard  */
   7566     Int count=-dn->exponent;            /* digits to discard  */
   7567     /* spin up whole units until reach the Unit with the unit digit  */
   7568     for (; count>=DECDPUN; up++) {
   7569       if (*up!=0) return BADINT;        /* non-zero Unit to discard  */
   7570       count-=DECDPUN;
   7571       }
   7572     if (count==0) got=0;                /* [a multiple of DECDPUN]  */
   7573      else {                             /* [not multiple of DECDPUN]  */
   7574       Int rem;                          /* work  */
   7575       /* slice off fraction digits and check for non-zero  */
   7576       #if DECDPUN<=4
   7577         theInt=QUOT10(*up, count);
   7578         rem=*up-theInt*powers[count];
   7579       #else
   7580         rem=*up%powers[count];          /* slice off discards  */
   7581         theInt=*up/powers[count];
   7582       #endif
   7583       if (rem!=0) return BADINT;        /* non-zero fraction  */
   7584       /* it looks good  */
   7585       got=DECDPUN-count;                /* number of digits so far  */
   7586       up++;                             /* ready for next  */
   7587       }
   7588     }
   7589   /* now it's known there's no fractional part  */
   7590 
   7591   /* tricky code now, to accumulate up to 9.3 digits  */
   7592   if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there  */
   7593 
   7594   if (ilength<11) {
   7595     Int save=theInt;
   7596     /* collect any remaining unit(s)  */
   7597     for (; got<ilength; up++) {
   7598       theInt+=*up*powers[got];
   7599       got+=DECDPUN;
   7600       }
   7601     if (ilength==10) {                  /* need to check for wrap  */
   7602       if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
   7603          /* [that test also disallows the BADINT result case]  */
   7604        else if (neg && theInt>1999999997) ilength=11;
   7605        else if (!neg && theInt>999999999) ilength=11;
   7606       if (ilength==11) theInt=save;     /* restore correct low bit  */
   7607       }
   7608     }
   7609 
   7610   if (ilength>10) {                     /* too big  */
   7611     if (theInt&1) return BIGODD;        /* bottom bit 1  */
   7612     return BIGEVEN;                     /* bottom bit 0  */
   7613     }
   7614 
   7615   if (neg) theInt=-theInt;              /* apply sign  */
   7616   return theInt;
   7617   } /* decGetInt  */
   7618 
   7619 /* ------------------------------------------------------------------ */
   7620 /* decDecap -- decapitate the coefficient of a number                 */
   7621 /*                                                                    */
   7622 /*   dn   is the number to be decapitated                             */
   7623 /*   drop is the number of digits to be removed from the left of dn;  */
   7624 /*     this must be <= dn->digits (if equal, the coefficient is       */
   7625 /*     set to 0)                                                      */
   7626 /*                                                                    */
   7627 /* Returns dn; dn->digits will be <= the initial digits less drop     */
   7628 /* (after removing drop digits there may be leading zero digits       */
   7629 /* which will also be removed).  Only dn->lsu and dn->digits change.  */
   7630 /* ------------------------------------------------------------------ */
   7631 static decNumber *decDecap(decNumber *dn, Int drop) {
   7632   Unit *msu;                            /* -> target cut point  */
   7633   Int cut;                              /* work  */
   7634   if (drop>=dn->digits) {               /* losing the whole thing  */
   7635     #if DECCHECK
   7636     if (drop>dn->digits)
   7637       printf("decDecap called with drop>digits [%ld>%ld]\n",
   7638              (LI)drop, (LI)dn->digits);
   7639     #endif
   7640     dn->lsu[0]=0;
   7641     dn->digits=1;
   7642     return dn;
   7643     }
   7644   msu=dn->lsu+D2U(dn->digits-drop)-1;   /* -> likely msu  */
   7645   cut=MSUDIGITS(dn->digits-drop);       /* digits to be in use in msu  */
   7646   if (cut!=DECDPUN) *msu%=powers[cut];  /* clear left digits  */
   7647   /* that may have left leading zero digits, so do a proper count...  */
   7648   dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
   7649   return dn;
   7650   } /* decDecap  */
   7651 
   7652 /* ------------------------------------------------------------------ */
   7653 /* decBiStr -- compare string with pairwise options                   */
   7654 /*                                                                    */
   7655 /*   targ is the string to compare                                    */
   7656 /*   str1 is one of the strings to compare against (length may be 0)  */
   7657 /*   str2 is the other; it must be the same length as str1            */
   7658 /*                                                                    */
   7659 /*   returns 1 if strings compare equal, (that is, it is the same     */
   7660 /*   length as str1 and str2, and each character of targ is in either */
   7661 /*   str1 or str2 in the corresponding position), or 0 otherwise      */
   7662 /*                                                                    */
   7663 /* This is used for generic caseless compare, including the awkward   */
   7664 /* case of the Turkish dotted and dotless Is.  Use as (for example):  */
   7665 /*   if (decBiStr(test, "mike", "MIKE")) ...                          */
   7666 /* ------------------------------------------------------------------ */
   7667 static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
   7668   for (;;targ++, str1++, str2++) {
   7669     if (*targ!=*str1 && *targ!=*str2) return 0;
   7670     /* *targ has a match in one (or both, if terminator)  */
   7671     if (*targ=='\0') break;
   7672     } /* forever  */
   7673   return 1;
   7674   } /* decBiStr  */
   7675 
   7676 /* ------------------------------------------------------------------ */
   7677 /* decNaNs -- handle NaN operand or operands                          */
   7678 /*                                                                    */
   7679 /*   res     is the result number                                     */
   7680 /*   lhs     is the first operand                                     */
   7681 /*   rhs     is the second operand, or NULL if none                   */
   7682 /*   context is used to limit payload length                          */
   7683 /*   status  contains the current status                              */
   7684 /*   returns res in case convenient                                   */
   7685 /*                                                                    */
   7686 /* Called when one or both operands is a NaN, and propagates the      */
   7687 /* appropriate result to res.  When an sNaN is found, it is changed   */
   7688 /* to a qNaN and Invalid operation is set.                            */
   7689 /* ------------------------------------------------------------------ */
   7690 static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
   7691                            const decNumber *rhs, decContext *set,
   7692                            uInt *status) {
   7693   /* This decision tree ends up with LHS being the source pointer,  */
   7694   /* and status updated if need be  */
   7695   if (lhs->bits & DECSNAN)
   7696     *status|=DEC_Invalid_operation | DEC_sNaN;
   7697    else if (rhs==NULL);
   7698    else if (rhs->bits & DECSNAN) {
   7699     lhs=rhs;
   7700     *status|=DEC_Invalid_operation | DEC_sNaN;
   7701     }
   7702    else if (lhs->bits & DECNAN);
   7703    else lhs=rhs;
   7704 
   7705   /* propagate the payload  */
   7706   if (lhs->digits<=set->digits) uprv_decNumberCopy(res, lhs); /* easy  */
   7707    else { /* too long  */
   7708     const Unit *ul;
   7709     Unit *ur, *uresp1;
   7710     /* copy safe number of units, then decapitate  */
   7711     res->bits=lhs->bits;                /* need sign etc.  */
   7712     uresp1=res->lsu+D2U(set->digits);
   7713     for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
   7714     res->digits=D2U(set->digits)*DECDPUN;
   7715     /* maybe still too long  */
   7716     if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
   7717     }
   7718 
   7719   res->bits&=~DECSNAN;        /* convert any sNaN to NaN, while  */
   7720   res->bits|=DECNAN;          /* .. preserving sign  */
   7721   res->exponent=0;            /* clean exponent  */
   7722                               /* [coefficient was copied/decapitated]  */
   7723   return res;
   7724   } /* decNaNs  */
   7725 
   7726 /* ------------------------------------------------------------------ */
   7727 /* decStatus -- apply non-zero status                                 */
   7728 /*                                                                    */
   7729 /*   dn     is the number to set if error                             */
   7730 /*   status contains the current status (not yet in context)          */
   7731 /*   set    is the context                                            */
   7732 /*                                                                    */
   7733 /* If the status is an error status, the number is set to a NaN,      */
   7734 /* unless the error was an overflow, divide-by-zero, or underflow,    */
   7735 /* in which case the number will have already been set.               */
   7736 /*                                                                    */
   7737 /* The context status is then updated with the new status.  Note that */
   7738 /* this may raise a signal, so control may never return from this     */
   7739 /* routine (hence resources must be recovered before it is called).   */
   7740 /* ------------------------------------------------------------------ */
   7741 static void decStatus(decNumber *dn, uInt status, decContext *set) {
   7742   if (status & DEC_NaNs) {              /* error status -> NaN  */
   7743     /* if cause was an sNaN, clear and propagate [NaN is already set up]  */
   7744     if (status & DEC_sNaN) status&=~DEC_sNaN;
   7745      else {
   7746       uprv_decNumberZero(dn);                /* other error: clean throughout  */
   7747       dn->bits=DECNAN;                  /* and make a quiet NaN  */
   7748       }
   7749     }
   7750   uprv_decContextSetStatus(set, status);     /* [may not return]  */
   7751   return;
   7752   } /* decStatus  */
   7753 
   7754 /* ------------------------------------------------------------------ */
   7755 /* decGetDigits -- count digits in a Units array                      */
   7756 /*                                                                    */
   7757 /*   uar is the Unit array holding the number (this is often an       */
   7758 /*          accumulator of some sort)                                 */
   7759 /*   len is the length of the array in units [>=1]                    */
   7760 /*                                                                    */
   7761 /*   returns the number of (significant) digits in the array          */
   7762 /*                                                                    */
   7763 /* All leading zeros are excluded, except the last if the array has   */
   7764 /* only zero Units.                                                   */
   7765 /* ------------------------------------------------------------------ */
   7766 /* This may be called twice during some operations.  */
   7767 static Int decGetDigits(Unit *uar, Int len) {
   7768   Unit *up=uar+(len-1);            /* -> msu  */
   7769   Int  digits=(len-1)*DECDPUN+1;   /* possible digits excluding msu  */
   7770   #if DECDPUN>4
   7771   uInt const *pow;                 /* work  */
   7772   #endif
   7773                                    /* (at least 1 in final msu)  */
   7774   #if DECCHECK
   7775   if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
   7776   #endif
   7777 
   7778   for (; up>=uar; up--) {
   7779     if (*up==0) {                  /* unit is all 0s  */
   7780       if (digits==1) break;        /* a zero has one digit  */
   7781       digits-=DECDPUN;             /* adjust for 0 unit  */
   7782       continue;}
   7783     /* found the first (most significant) non-zero Unit  */
   7784     #if DECDPUN>1                  /* not done yet  */
   7785     if (*up<10) break;             /* is 1-9  */
   7786     digits++;
   7787     #if DECDPUN>2                  /* not done yet  */
   7788     if (*up<100) break;            /* is 10-99  */
   7789     digits++;
   7790     #if DECDPUN>3                  /* not done yet  */
   7791     if (*up<1000) break;           /* is 100-999  */
   7792     digits++;
   7793     #if DECDPUN>4                  /* count the rest ...  */
   7794     for (pow=&powers[4]; *up>=*pow; pow++) digits++;
   7795     #endif
   7796     #endif
   7797     #endif
   7798     #endif
   7799     break;
   7800     } /* up  */
   7801   return digits;
   7802   } /* decGetDigits  */
   7803 
   7804 #if DECTRACE | DECCHECK
   7805 /* ------------------------------------------------------------------ */
   7806 /* decNumberShow -- display a number [debug aid]                      */
   7807 /*   dn is the number to show                                         */
   7808 /*                                                                    */
   7809 /* Shows: sign, exponent, coefficient (msu first), digits             */
   7810 /*    or: sign, special-value                                         */
   7811 /* ------------------------------------------------------------------ */
   7812 /* this is public so other modules can use it  */
   7813 void uprv_decNumberShow(const decNumber *dn) {
   7814   const Unit *up;                  /* work  */
   7815   uInt u, d;                       /* ..  */
   7816   Int cut;                         /* ..  */
   7817   char isign='+';                  /* main sign  */
   7818   if (dn==NULL) {
   7819     printf("NULL\n");
   7820     return;}
   7821   if (decNumberIsNegative(dn)) isign='-';
   7822   printf(" >> %c ", isign);
   7823   if (dn->bits&DECSPECIAL) {       /* Is a special value  */
   7824     if (decNumberIsInfinite(dn)) printf("Infinity");
   7825      else {                                  /* a NaN  */
   7826       if (dn->bits&DECSNAN) printf("sNaN");  /* signalling NaN  */
   7827        else printf("NaN");
   7828       }
   7829     /* if coefficient and exponent are 0, no more to do  */
   7830     if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
   7831       printf("\n");
   7832       return;}
   7833     /* drop through to report other information  */
   7834     printf(" ");
   7835     }
   7836 
   7837   /* now carefully display the coefficient  */
   7838   up=dn->lsu+D2U(dn->digits)-1;         /* msu  */
   7839   printf("%ld", (LI)*up);
   7840   for (up=up-1; up>=dn->lsu; up--) {
   7841     u=*up;
   7842     printf(":");
   7843     for (cut=DECDPUN-1; cut>=0; cut--) {
   7844       d=u/powers[cut];
   7845       u-=d*powers[cut];
   7846       printf("%ld", (LI)d);
   7847       } /* cut  */
   7848     } /* up  */
   7849   if (dn->exponent!=0) {
   7850     char esign='+';
   7851     if (dn->exponent<0) esign='-';
   7852     printf(" E%c%ld", esign, (LI)abs(dn->exponent));
   7853     }
   7854   printf(" [%ld]\n", (LI)dn->digits);
   7855   } /* decNumberShow  */
   7856 #endif
   7857 
   7858 #if DECTRACE || DECCHECK
   7859 /* ------------------------------------------------------------------ */
   7860 /* decDumpAr -- display a unit array [debug/check aid]                */
   7861 /*   name is a single-character tag name                              */
   7862 /*   ar   is the array to display                                     */
   7863 /*   len  is the length of the array in Units                         */
   7864 /* ------------------------------------------------------------------ */
   7865 static void decDumpAr(char name, const Unit *ar, Int len) {
   7866   Int i;
   7867   const char *spec;
   7868   #if DECDPUN==9
   7869     spec="%09d ";
   7870   #elif DECDPUN==8
   7871     spec="%08d ";
   7872   #elif DECDPUN==7
   7873     spec="%07d ";
   7874   #elif DECDPUN==6
   7875     spec="%06d ";
   7876   #elif DECDPUN==5
   7877     spec="%05d ";
   7878   #elif DECDPUN==4
   7879     spec="%04d ";
   7880   #elif DECDPUN==3
   7881     spec="%03d ";
   7882   #elif DECDPUN==2
   7883     spec="%02d ";
   7884   #else
   7885     spec="%d ";
   7886   #endif
   7887   printf("  :%c: ", name);
   7888   for (i=len-1; i>=0; i--) {
   7889     if (i==len-1) printf("%ld ", (LI)ar[i]);
   7890      else printf(spec, ar[i]);
   7891     }
   7892   printf("\n");
   7893   return;}
   7894 #endif
   7895 
   7896 #if DECCHECK
   7897 /* ------------------------------------------------------------------ */
   7898 /* decCheckOperands -- check operand(s) to a routine                  */
   7899 /*   res is the result structure (not checked; it will be set to      */
   7900 /*          quiet NaN if error found (and it is not NULL))            */
   7901 /*   lhs is the first operand (may be DECUNRESU)                      */
   7902 /*   rhs is the second (may be DECUNUSED)                             */
   7903 /*   set is the context (may be DECUNCONT)                            */
   7904 /*   returns 0 if both operands, and the context are clean, or 1      */
   7905 /*     otherwise (in which case the context will show an error,       */
   7906 /*     unless NULL).  Note that res is not cleaned; caller should     */
   7907 /*     handle this so res=NULL case is safe.                          */
   7908 /* The caller is expected to abandon immediately if 1 is returned.    */
   7909 /* ------------------------------------------------------------------ */
   7910 static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
   7911                              const decNumber *rhs, decContext *set) {
   7912   Flag bad=0;
   7913   if (set==NULL) {                 /* oops; hopeless  */
   7914     #if DECTRACE || DECVERB
   7915     printf("Reference to context is NULL.\n");
   7916     #endif
   7917     bad=1;
   7918     return 1;}
   7919    else if (set!=DECUNCONT
   7920      && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
   7921     bad=1;
   7922     #if DECTRACE || DECVERB
   7923     printf("Bad context [digits=%ld round=%ld].\n",
   7924            (LI)set->digits, (LI)set->round);
   7925     #endif
   7926     }
   7927    else {
   7928     if (res==NULL) {
   7929       bad=1;
   7930       #if DECTRACE
   7931       /* this one not DECVERB as standard tests include NULL  */
   7932       printf("Reference to result is NULL.\n");
   7933       #endif
   7934       }
   7935     if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
   7936     if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
   7937     }
   7938   if (bad) {
   7939     if (set!=DECUNCONT) uprv_decContextSetStatus(set, DEC_Invalid_operation);
   7940     if (res!=DECUNRESU && res!=NULL) {
   7941       uprv_decNumberZero(res);
   7942       res->bits=DECNAN;       /* qNaN  */
   7943       }
   7944     }
   7945   return bad;
   7946   } /* decCheckOperands  */
   7947 
   7948 /* ------------------------------------------------------------------ */
   7949 /* decCheckNumber -- check a number                                   */
   7950 /*   dn is the number to check                                        */
   7951 /*   returns 0 if the number is clean, or 1 otherwise                 */
   7952 /*                                                                    */
   7953 /* The number is considered valid if it could be a result from some   */
   7954 /* operation in some valid context.                                   */
   7955 /* ------------------------------------------------------------------ */
   7956 static Flag decCheckNumber(const decNumber *dn) {
   7957   const Unit *up;             /* work  */
   7958   uInt maxuint;               /* ..  */
   7959   Int ae, d, digits;          /* ..  */
   7960   Int emin, emax;             /* ..  */
   7961 
   7962   if (dn==NULL) {             /* hopeless  */
   7963     #if DECTRACE
   7964     /* this one not DECVERB as standard tests include NULL  */
   7965     printf("Reference to decNumber is NULL.\n");
   7966     #endif
   7967     return 1;}
   7968 
   7969   /* check special values  */
   7970   if (dn->bits & DECSPECIAL) {
   7971     if (dn->exponent!=0) {
   7972       #if DECTRACE || DECVERB
   7973       printf("Exponent %ld (not 0) for a special value [%02x].\n",
   7974              (LI)dn->exponent, dn->bits);
   7975       #endif
   7976       return 1;}
   7977 
   7978     /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only  */
   7979     if (decNumberIsInfinite(dn)) {
   7980       if (dn->digits!=1) {
   7981         #if DECTRACE || DECVERB
   7982         printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
   7983         #endif
   7984         return 1;}
   7985       if (*dn->lsu!=0) {
   7986         #if DECTRACE || DECVERB
   7987         printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
   7988         #endif
   7989         decDumpAr('I', dn->lsu, D2U(dn->digits));
   7990         return 1;}
   7991       } /* Inf  */
   7992     /* 2002.12.26: negative NaNs can now appear through proposed IEEE  */
   7993     /*             concrete formats (decimal64, etc.).  */
   7994     return 0;
   7995     }
   7996 
   7997   /* check the coefficient  */
   7998   if (dn->digits<1 || dn->digits>DECNUMMAXP) {
   7999     #if DECTRACE || DECVERB
   8000     printf("Digits %ld in number.\n", (LI)dn->digits);
   8001     #endif
   8002     return 1;}
   8003 
   8004   d=dn->digits;
   8005 
   8006   for (up=dn->lsu; d>0; up++) {
   8007     if (d>DECDPUN) maxuint=DECDPUNMAX;
   8008      else {                   /* reached the msu  */
   8009       maxuint=powers[d]-1;
   8010       if (dn->digits>1 && *up<powers[d-1]) {
   8011         #if DECTRACE || DECVERB
   8012         printf("Leading 0 in number.\n");
   8013         uprv_decNumberShow(dn);
   8014         #endif
   8015         return 1;}
   8016       }
   8017     if (*up>maxuint) {
   8018       #if DECTRACE || DECVERB
   8019       printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
   8020               (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
   8021       #endif
   8022       return 1;}
   8023     d-=DECDPUN;
   8024     }
   8025 
   8026   /* check the exponent.  Note that input operands can have exponents  */
   8027   /* which are out of the set->emin/set->emax and set->digits range  */
   8028   /* (just as they can have more digits than set->digits).  */
   8029   ae=dn->exponent+dn->digits-1;    /* adjusted exponent  */
   8030   emax=DECNUMMAXE;
   8031   emin=DECNUMMINE;
   8032   digits=DECNUMMAXP;
   8033   if (ae<emin-(digits-1)) {
   8034     #if DECTRACE || DECVERB
   8035     printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
   8036     uprv_decNumberShow(dn);
   8037     #endif
   8038     return 1;}
   8039   if (ae>+emax) {
   8040     #if DECTRACE || DECVERB
   8041     printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
   8042     uprv_decNumberShow(dn);
   8043     #endif
   8044     return 1;}
   8045 
   8046   return 0;              /* it's OK  */
   8047   } /* decCheckNumber  */
   8048 
   8049 /* ------------------------------------------------------------------ */
   8050 /* decCheckInexact -- check a normal finite inexact result has digits */
   8051 /*   dn is the number to check                                        */
   8052 /*   set is the context (for status and precision)                    */
   8053 /*   sets Invalid operation, etc., if some digits are missing         */
   8054 /* [this check is not made for DECSUBSET compilation or when          */
   8055 /* subnormal is not set]                                              */
   8056 /* ------------------------------------------------------------------ */
   8057 static void decCheckInexact(const decNumber *dn, decContext *set) {
   8058   #if !DECSUBSET && DECEXTFLAG
   8059     if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
   8060      && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
   8061       #if DECTRACE || DECVERB
   8062       printf("Insufficient digits [%ld] on normal Inexact result.\n",
   8063              (LI)dn->digits);
   8064       uprv_decNumberShow(dn);
   8065       #endif
   8066       uprv_decContextSetStatus(set, DEC_Invalid_operation);
   8067       }
   8068   #else
   8069     /* next is a noop for quiet compiler  */
   8070     if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
   8071   #endif
   8072   return;
   8073   } /* decCheckInexact  */
   8074 #endif
   8075 
   8076 #if DECALLOC
   8077 #undef malloc
   8078 #undef free
   8079 /* ------------------------------------------------------------------ */
   8080 /* decMalloc -- accountable allocation routine                        */
   8081 /*   n is the number of bytes to allocate                             */
   8082 /*                                                                    */
   8083 /* Semantics is the same as the stdlib malloc routine, but bytes      */
   8084 /* allocated are accounted for globally, and corruption fences are    */
   8085 /* added before and after the 'actual' storage.                       */
   8086 /* ------------------------------------------------------------------ */
   8087 /* This routine allocates storage with an extra twelve bytes; 8 are   */
   8088 /* at the start and hold:                                             */
   8089 /*   0-3 the original length requested                                */
   8090 /*   4-7 buffer corruption detection fence (DECFENCE, x4)             */
   8091 /* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
   8092 /* ------------------------------------------------------------------ */
   8093 static void *decMalloc(size_t n) {
   8094   uInt  size=n+12;                 /* true size  */
   8095   void  *alloc;                    /* -> allocated storage  */
   8096   uByte *b, *b0;                   /* work  */
   8097   uInt  uiwork;                    /* for macros  */
   8098 
   8099   alloc=malloc(size);              /* -> allocated storage  */
   8100   if (alloc==NULL) return NULL;    /* out of strorage  */
   8101   b0=(uByte *)alloc;               /* as bytes  */
   8102   decAllocBytes+=n;                /* account for storage  */
   8103   UBFROMUI(alloc, n);              /* save n  */
   8104   /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n);  */
   8105   for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
   8106   for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
   8107   return b0+8;                     /* -> play area  */
   8108   } /* decMalloc  */
   8109 
   8110 /* ------------------------------------------------------------------ */
   8111 /* decFree -- accountable free routine                                */
   8112 /*   alloc is the storage to free                                     */
   8113 /*                                                                    */
   8114 /* Semantics is the same as the stdlib malloc routine, except that    */
   8115 /* the global storage accounting is updated and the fences are        */
   8116 /* checked to ensure that no routine has written 'out of bounds'.     */
   8117 /* ------------------------------------------------------------------ */
   8118 /* This routine first checks that the fences have not been corrupted. */
   8119 /* It then frees the storage using the 'truw' storage address (that   */
   8120 /* is, offset by 8).                                                  */
   8121 /* ------------------------------------------------------------------ */
   8122 static void decFree(void *alloc) {
   8123   uInt  n;                         /* original length  */
   8124   uByte *b, *b0;                   /* work  */
   8125   uInt  uiwork;                    /* for macros  */
   8126 
   8127   if (alloc==NULL) return;         /* allowed; it's a nop  */
   8128   b0=(uByte *)alloc;               /* as bytes  */
   8129   b0-=8;                           /* -> true start of storage  */
   8130   n=UBTOUI(b0);                    /* lift length  */
   8131   for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
   8132     printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
   8133            b-b0-8, (LI)b0);
   8134   for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
   8135     printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
   8136            b-b0-8, (LI)b0, (LI)n);
   8137   free(b0);                        /* drop the storage  */
   8138   decAllocBytes-=n;                /* account for storage  */
   8139   /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n);  */
   8140   } /* decFree  */
   8141 #define malloc(a) decMalloc(a)
   8142 #define free(a) decFree(a)
   8143 #endif
   8144