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      1 // Copyright (C) 2016 and later: Unicode, Inc. and others.
      2 // License & terms of use: http://www.unicode.org/copyright.html
      3 /* ------------------------------------------------------------------ */
      4 /* decNumber package local type, tuning, and macro definitions        */
      5 /* ------------------------------------------------------------------ */
      6 /* Copyright (c) IBM Corporation, 2000-2016.   All rights reserved.   */
      7 /*                                                                    */
      8 /* This software is made available under the terms of the             */
      9 /* ICU License -- ICU 1.8.1 and later.                                */
     10 /*                                                                    */
     11 /* The description and User's Guide ("The decNumber C Library") for   */
     12 /* this software is called decNumber.pdf.  This document is           */
     13 /* available, together with arithmetic and format specifications,     */
     14 /* testcases, and Web links, on the General Decimal Arithmetic page.  */
     15 /*                                                                    */
     16 /* Please send comments, suggestions, and corrections to the author:  */
     17 /*   mfc (at) uk.ibm.com                                                   */
     18 /*   Mike Cowlishaw, IBM Fellow                                       */
     19 /*   IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK         */
     20 /* ------------------------------------------------------------------ */
     21 /* This header file is included by all modules in the decNumber       */
     22 /* library, and contains local type definitions, tuning parameters,   */
     23 /* etc.  It should not need to be used by application programs.       */
     24 /* decNumber.h or one of decDouble (etc.) must be included first.     */
     25 /* ------------------------------------------------------------------ */
     26 
     27 #if !defined(DECNUMBERLOC)
     28   #define DECNUMBERLOC
     29   #define DECVERSION    "decNumber 3.61" /* Package Version [16 max.] */
     30   #define DECNLAUTHOR   "Mike Cowlishaw"              /* Who to blame */
     31 
     32   #include <stdlib.h>         /* for abs                              */
     33   #include <string.h>         /* for memset, strcpy                   */
     34   #include "decContext.h"
     35 
     36   /* Conditional code flag -- set this to match hardware platform     */
     37   #if !defined(DECLITEND)
     38   #define DECLITEND 1         /* 1=little-endian, 0=big-endian        */
     39   #endif
     40 
     41   /* Conditional code flag -- set this to 1 for best performance      */
     42   #if !defined(DECUSE64)
     43   #define DECUSE64  1         /* 1=use int64s, 0=int32 & smaller only */
     44   #endif
     45 
     46   /* Conditional check flags -- set these to 0 for best performance   */
     47   #if !defined(DECCHECK)
     48   #define DECCHECK  0         /* 1 to enable robust checking          */
     49   #endif
     50   #if !defined(DECALLOC)
     51   #define DECALLOC  0         /* 1 to enable memory accounting        */
     52   #endif
     53   #if !defined(DECTRACE)
     54   #define DECTRACE  0         /* 1 to trace certain internals, etc.   */
     55   #endif
     56 
     57   /* Tuning parameter for decNumber (arbitrary precision) module      */
     58   #if !defined(DECBUFFER)
     59   #define DECBUFFER 36        /* Size basis for local buffers.  This  */
     60                               /* should be a common maximum precision */
     61                               /* rounded up to a multiple of 4; must  */
     62                               /* be zero or positive.                 */
     63   #endif
     64 
     65   /* ---------------------------------------------------------------- */
     66   /* Definitions for all modules (general-purpose)                    */
     67   /* ---------------------------------------------------------------- */
     68 
     69   /* Local names for common types -- for safety, decNumber modules do */
     70   /* not use int or long directly.                                    */
     71   #define Flag   uint8_t
     72   #define Byte   int8_t
     73   #define uByte  uint8_t
     74   #define Short  int16_t
     75   #define uShort uint16_t
     76   #define Int    int32_t
     77   #define uInt   uint32_t
     78   #define Unit   decNumberUnit
     79   #if DECUSE64
     80   #define Long   int64_t
     81   #define uLong  uint64_t
     82   #endif
     83 
     84   /* Development-use definitions                                      */
     85   typedef long int LI;        /* for printf arguments only            */
     86   #define DECNOINT  0         /* 1 to check no internal use of 'int'  */
     87                               /*   or stdint types                    */
     88   #if DECNOINT
     89     /* if these interfere with your C includes, do not set DECNOINT   */
     90     #define int     ?         /* enable to ensure that plain C 'int'  */
     91     #define long    ??        /* .. or 'long' types are not used      */
     92   #endif
     93 
     94   /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts      */
     95   /* (that is, sets w to be the high-order word of the 64-bit result; */
     96   /* the low-order word is simply u*v.)                               */
     97   /* This version is derived from Knuth via Hacker's Delight;         */
     98   /* it seems to optimize better than some others tried               */
     99   #define LONGMUL32HI(w, u, v) {             \
    100     uInt u0, u1, v0, v1, w0, w1, w2, t;      \
    101     u0=u & 0xffff; u1=u>>16;                 \
    102     v0=v & 0xffff; v1=v>>16;                 \
    103     w0=u0*v0;                                \
    104     t=u1*v0 + (w0>>16);                      \
    105     w1=t & 0xffff; w2=t>>16;                 \
    106     w1=u0*v1 + w1;                           \
    107     (w)=u1*v1 + w2 + (w1>>16);}
    108 
    109   /* ROUNDUP -- round an integer up to a multiple of n                */
    110   #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n)
    111   #define ROUNDUP4(i)   (((i)+3)&~3)    /* special for n=4            */
    112 
    113   /* ROUNDDOWN -- round an integer down to a multiple of n            */
    114   #define ROUNDDOWN(i, n) (((i)/n)*n)
    115   #define ROUNDDOWN4(i)   ((i)&~3)      /* special for n=4            */
    116 
    117   /* References to multi-byte sequences under different sizes; these  */
    118   /* require locally declared variables, but do not violate strict    */
    119   /* aliasing or alignment (as did the UINTAT simple cast to uInt).   */
    120   /* Variables needed are uswork, uiwork, etc. [so do not use at same */
    121   /* level in an expression, e.g., UBTOUI(x)==UBTOUI(y) may fail].    */
    122 
    123   /* Return a uInt, etc., from bytes starting at a char* or uByte*    */
    124   #define UBTOUS(b)  (memcpy((void *)&uswork, b, 2), uswork)
    125   #define UBTOUI(b)  (memcpy((void *)&uiwork, b, 4), uiwork)
    126 
    127   /* Store a uInt, etc., into bytes starting at a char* or uByte*.    */
    128   /* Returns i, evaluated, for convenience; has to use uiwork because */
    129   /* i may be an expression.                                          */
    130   #define UBFROMUS(b, i)  (uswork=(i), memcpy(b, (void *)&uswork, 2), uswork)
    131   #define UBFROMUI(b, i)  (uiwork=(i), memcpy(b, (void *)&uiwork, 4), uiwork)
    132 
    133   /* X10 and X100 -- multiply integer i by 10 or 100                  */
    134   /* [shifts are usually faster than multiply; could be conditional]  */
    135   #define X10(i)  (((i)<<1)+((i)<<3))
    136   #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6))
    137 
    138   /* MAXI and MINI -- general max & min (not in ANSI) for integers    */
    139   #define MAXI(x,y) ((x)<(y)?(y):(x))
    140   #define MINI(x,y) ((x)>(y)?(y):(x))
    141 
    142   /* Useful constants                                                 */
    143   #define BILLION      1000000000            /* 10**9                 */
    144   /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC       */
    145   #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0')
    146 
    147 
    148   /* ---------------------------------------------------------------- */
    149   /* Definitions for arbitary-precision modules (only valid after     */
    150   /* decNumber.h has been included)                                   */
    151   /* ---------------------------------------------------------------- */
    152 
    153   /* Limits and constants                                             */
    154   #define DECNUMMAXP 999999999  /* maximum precision code can handle  */
    155   #define DECNUMMAXE 999999999  /* maximum adjusted exponent ditto    */
    156   #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto    */
    157   #if (DECNUMMAXP != DEC_MAX_DIGITS)
    158     #error Maximum digits mismatch
    159   #endif
    160   #if (DECNUMMAXE != DEC_MAX_EMAX)
    161     #error Maximum exponent mismatch
    162   #endif
    163   #if (DECNUMMINE != DEC_MIN_EMIN)
    164     #error Minimum exponent mismatch
    165   #endif
    166 
    167   /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN       */
    168   /* digits, and D2UTABLE -- the initializer for the D2U table        */
    169   #if   DECDPUN==1
    170     #define DECDPUNMAX 9
    171     #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,  \
    172                       18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \
    173                       33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \
    174                       48,49}
    175   #elif DECDPUN==2
    176     #define DECDPUNMAX 99
    177     #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,  \
    178                       11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \
    179                       18,19,19,20,20,21,21,22,22,23,23,24,24,25}
    180   #elif DECDPUN==3
    181     #define DECDPUNMAX 999
    182     #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,  \
    183                       8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \
    184                       13,14,14,14,15,15,15,16,16,16,17}
    185   #elif DECDPUN==4
    186     #define DECDPUNMAX 9999
    187     #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,  \
    188                       6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \
    189                       11,11,11,12,12,12,12,13}
    190   #elif DECDPUN==5
    191     #define DECDPUNMAX 99999
    192     #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,  \
    193                       5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,  \
    194                       9,9,10,10,10,10}
    195   #elif DECDPUN==6
    196     #define DECDPUNMAX 999999
    197     #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,  \
    198                       4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8,  \
    199                       8,8,8,8,8,9}
    200   #elif DECDPUN==7
    201     #define DECDPUNMAX 9999999
    202     #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,  \
    203                       4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,  \
    204                       7,7,7,7,7,7}
    205   #elif DECDPUN==8
    206     #define DECDPUNMAX 99999999
    207     #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,  \
    208                       3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,  \
    209                       6,6,6,6,6,7}
    210   #elif DECDPUN==9
    211     #define DECDPUNMAX 999999999
    212     #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,  \
    213                       3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,  \
    214                       5,5,6,6,6,6}
    215   #elif defined(DECDPUN)
    216     #error DECDPUN must be in the range 1-9
    217   #endif
    218 
    219   /* ----- Shared data (in decNumber.c) ----- */
    220   /* Public lookup table used by the D2U macro (see below)            */
    221   #define DECMAXD2U 49
    222   /*extern const uByte d2utable[DECMAXD2U+1];*/
    223 
    224   /* ----- Macros ----- */
    225   /* ISZERO -- return true if decNumber dn is a zero                  */
    226   /* [performance-critical in some situations]                        */
    227   #define ISZERO(dn) decNumberIsZero(dn)     /* now just a local name */
    228 
    229   /* D2U -- return the number of Units needed to hold d digits        */
    230   /* (runtime version, with table lookaside for small d)              */
    231   #if DECDPUN==8
    232     #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3))
    233   #elif DECDPUN==4
    234     #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2))
    235   #else
    236     #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN)
    237   #endif
    238   /* SD2U -- static D2U macro (for compile-time calculation)          */
    239   #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN)
    240 
    241   /* MSUDIGITS -- returns digits in msu, from digits, calculated      */
    242   /* using D2U                                                        */
    243   #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN)
    244 
    245   /* D2N -- return the number of decNumber structs that would be      */
    246   /* needed to contain that number of digits (and the initial         */
    247   /* decNumber struct) safely.  Note that one Unit is included in the */
    248   /* initial structure.  Used for allocating space that is aligned on */
    249   /* a decNumber struct boundary. */
    250   #define D2N(d) \
    251     ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber))
    252 
    253   /* TODIGIT -- macro to remove the leading digit from the unsigned   */
    254   /* integer u at column cut (counting from the right, LSD=0) and     */
    255   /* place it as an ASCII character into the character pointed to by  */
    256   /* c.  Note that cut must be <= 9, and the maximum value for u is   */
    257   /* 2,000,000,000 (as is needed for negative exponents of            */
    258   /* subnormals).  The unsigned integer pow is used as a temporary    */
    259   /* variable. */
    260   #define TODIGIT(u, cut, c, pow) {       \
    261     *(c)='0';                             \
    262     pow=DECPOWERS[cut]*2;                 \
    263     if ((u)>pow) {                        \
    264       pow*=4;                             \
    265       if ((u)>=pow) {(u)-=pow; *(c)+=8;}  \
    266       pow/=2;                             \
    267       if ((u)>=pow) {(u)-=pow; *(c)+=4;}  \
    268       pow/=2;                             \
    269       }                                   \
    270     if ((u)>=pow) {(u)-=pow; *(c)+=2;}    \
    271     pow/=2;                               \
    272     if ((u)>=pow) {(u)-=pow; *(c)+=1;}    \
    273     }
    274 
    275   /* ---------------------------------------------------------------- */
    276   /* Definitions for fixed-precision modules (only valid after        */
    277   /* decSingle.h, decDouble.h, or decQuad.h has been included)        */
    278   /* ---------------------------------------------------------------- */
    279 
    280   /* bcdnum -- a structure describing a format-independent finite     */
    281   /* number, whose coefficient is a string of bcd8 uBytes             */
    282   typedef struct {
    283     uByte   *msd;             /* -> most significant digit            */
    284     uByte   *lsd;             /* -> least ditto                       */
    285     uInt     sign;            /* 0=positive, DECFLOAT_Sign=negative   */
    286     Int      exponent;        /* Unadjusted signed exponent (q), or   */
    287                               /* DECFLOAT_NaN etc. for a special      */
    288     } bcdnum;
    289 
    290   /* Test if exponent or bcdnum exponent must be a special, etc.      */
    291   #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp)
    292   #define EXPISINF(exp) (exp==DECFLOAT_Inf)
    293   #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN)
    294   #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent))
    295 
    296   /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian  */
    297   /* (array) notation (the 0 word or byte contains the sign bit),     */
    298   /* automatically adjusting for endianness; similarly address a word */
    299   /* in the next-wider format (decFloatWider, or dfw)                 */
    300   #define DECWORDS  (DECBYTES/4)
    301   #define DECWWORDS (DECWBYTES/4)
    302   #if DECLITEND
    303     #define DFBYTE(df, off)   ((df)->bytes[DECBYTES-1-(off)])
    304     #define DFWORD(df, off)   ((df)->words[DECWORDS-1-(off)])
    305     #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)])
    306   #else
    307     #define DFBYTE(df, off)   ((df)->bytes[off])
    308     #define DFWORD(df, off)   ((df)->words[off])
    309     #define DFWWORD(dfw, off) ((dfw)->words[off])
    310   #endif
    311 
    312   /* Tests for sign or specials, directly on DECFLOATs                */
    313   #define DFISSIGNED(df)   (DFWORD(df, 0)&0x80000000)
    314   #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000)
    315   #define DFISINF(df)     ((DFWORD(df, 0)&0x7c000000)==0x78000000)
    316   #define DFISNAN(df)     ((DFWORD(df, 0)&0x7c000000)==0x7c000000)
    317   #define DFISQNAN(df)    ((DFWORD(df, 0)&0x7e000000)==0x7c000000)
    318   #define DFISSNAN(df)    ((DFWORD(df, 0)&0x7e000000)==0x7e000000)
    319 
    320   /* Shared lookup tables                                             */
    321   extern const uInt   DECCOMBMSD[64];   /* Combination field -> MSD   */
    322   extern const uInt   DECCOMBFROM[48];  /* exp+msd -> Combination     */
    323 
    324   /* Private generic (utility) routine                                */
    325   #if DECCHECK || DECTRACE
    326     extern void decShowNum(const bcdnum *, const char *);
    327   #endif
    328 
    329   /* Format-dependent macros and constants                            */
    330   #if defined(DECPMAX)
    331 
    332     /* Useful constants                                               */
    333     #define DECPMAX9  (ROUNDUP(DECPMAX, 9)/9)  /* 'Pmax' in 10**9s    */
    334     /* Top words for a zero                                           */
    335     #define SINGLEZERO   0x22500000
    336     #define DOUBLEZERO   0x22380000
    337     #define QUADZERO     0x22080000
    338     /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */
    339 
    340     /* Format-dependent common tests:                                 */
    341     /*   DFISZERO   -- test for (any) zero                            */
    342     /*   DFISCCZERO -- test for coefficient continuation being zero   */
    343     /*   DFISCC01   -- test for coefficient contains only 0s and 1s   */
    344     /*   DFISINT    -- test for finite and exponent q=0               */
    345     /*   DFISUINT01 -- test for sign=0, finite, exponent q=0, and     */
    346     /*                 MSD=0 or 1                                     */
    347     /*   ZEROWORD is also defined here.                               */
    348     /* In DFISZERO the first test checks the least-significant word   */
    349     /* (most likely to be non-zero); the penultimate tests MSD and    */
    350     /* DPDs in the signword, and the final test excludes specials and */
    351     /* MSD>7.  DFISINT similarly has to allow for the two forms of    */
    352     /* MSD codes.  DFISUINT01 only has to allow for one form of MSD   */
    353     /* code.                                                          */
    354     #if DECPMAX==7
    355       #define ZEROWORD SINGLEZERO
    356       /* [test macros not needed except for Zero]                     */
    357       #define DFISZERO(df)  ((DFWORD(df, 0)&0x1c0fffff)==0         \
    358                           && (DFWORD(df, 0)&0x60000000)!=0x60000000)
    359     #elif DECPMAX==16
    360       #define ZEROWORD DOUBLEZERO
    361       #define DFISZERO(df)  ((DFWORD(df, 1)==0                     \
    362                           && (DFWORD(df, 0)&0x1c03ffff)==0         \
    363                           && (DFWORD(df, 0)&0x60000000)!=0x60000000))
    364       #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000  \
    365                          ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000)
    366       #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000)
    367       #define DFISCCZERO(df) (DFWORD(df, 1)==0                     \
    368                           && (DFWORD(df, 0)&0x0003ffff)==0)
    369       #define DFISCC01(df)  ((DFWORD(df, 0)&~0xfffc9124)==0        \
    370                           && (DFWORD(df, 1)&~0x49124491)==0)
    371     #elif DECPMAX==34
    372       #define ZEROWORD QUADZERO
    373       #define DFISZERO(df)  ((DFWORD(df, 3)==0                     \
    374                           &&  DFWORD(df, 2)==0                     \
    375                           &&  DFWORD(df, 1)==0                     \
    376                           && (DFWORD(df, 0)&0x1c003fff)==0         \
    377                           && (DFWORD(df, 0)&0x60000000)!=0x60000000))
    378       #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000  \
    379                          ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000)
    380       #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000)
    381       #define DFISCCZERO(df) (DFWORD(df, 3)==0                     \
    382                           &&  DFWORD(df, 2)==0                     \
    383                           &&  DFWORD(df, 1)==0                     \
    384                           && (DFWORD(df, 0)&0x00003fff)==0)
    385 
    386       #define DFISCC01(df)   ((DFWORD(df, 0)&~0xffffc912)==0       \
    387                           &&  (DFWORD(df, 1)&~0x44912449)==0       \
    388                           &&  (DFWORD(df, 2)&~0x12449124)==0       \
    389                           &&  (DFWORD(df, 3)&~0x49124491)==0)
    390     #endif
    391 
    392     /* Macros to test if a certain 10 bits of a uInt or pair of uInts */
    393     /* are a canonical declet [higher or lower bits are ignored].     */
    394     /* declet is at offset 0 (from the right) in a uInt:              */
    395     #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e)
    396     /* declet is at offset k (a multiple of 2) in a uInt:             */
    397     #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0            \
    398       || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))
    399     /* declet is at offset k (a multiple of 2) in a pair of uInts:    */
    400     /* [the top 2 bits will always be in the more-significant uInt]   */
    401     #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0     \
    402       || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k)))                  \
    403       || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))
    404 
    405     /* Macro to test whether a full-length (length DECPMAX) BCD8      */
    406     /* coefficient, starting at uByte u, is all zeros                 */
    407     /* Test just the LSWord first, then the remainder as a sequence   */
    408     /* of tests in order to avoid same-level use of UBTOUI            */
    409     #if DECPMAX==7
    410       #define ISCOEFFZERO(u) (                                      \
    411            UBTOUI((u)+DECPMAX-4)==0                                 \
    412         && UBTOUS((u)+DECPMAX-6)==0                                 \
    413         && *(u)==0)
    414     #elif DECPMAX==16
    415       #define ISCOEFFZERO(u) (                                      \
    416            UBTOUI((u)+DECPMAX-4)==0                                 \
    417         && UBTOUI((u)+DECPMAX-8)==0                                 \
    418         && UBTOUI((u)+DECPMAX-12)==0                                \
    419         && UBTOUI(u)==0)
    420     #elif DECPMAX==34
    421       #define ISCOEFFZERO(u) (                                      \
    422            UBTOUI((u)+DECPMAX-4)==0                                 \
    423         && UBTOUI((u)+DECPMAX-8)==0                                 \
    424         && UBTOUI((u)+DECPMAX-12)==0                                \
    425         && UBTOUI((u)+DECPMAX-16)==0                                \
    426         && UBTOUI((u)+DECPMAX-20)==0                                \
    427         && UBTOUI((u)+DECPMAX-24)==0                                \
    428         && UBTOUI((u)+DECPMAX-28)==0                                \
    429         && UBTOUI((u)+DECPMAX-32)==0                                \
    430         && UBTOUS(u)==0)
    431     #endif
    432 
    433     /* Macros and masks for the exponent continuation field and MSD   */
    434     /* Get the exponent continuation from a decFloat *df as an Int    */
    435     #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL)))
    436     /* Ditto, from the next-wider format                              */
    437     #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL)))
    438     /* Get the biased exponent similarly                              */
    439     #define GETEXP(df)  ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df)))
    440     /* Get the unbiased exponent similarly                            */
    441     #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS)
    442     /* Get the MSD similarly (as uInt)                                */
    443     #define GETMSD(df)   (DECCOMBMSD[DFWORD((df), 0)>>26])
    444 
    445     /* Compile-time computes of the exponent continuation field masks */
    446     /* full exponent continuation field:                              */
    447     #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))
    448     /* same, not including its first digit (the qNaN/sNaN selector):  */
    449     #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))
    450 
    451     /* Macros to decode the coefficient in a finite decFloat *df into */
    452     /* a BCD string (uByte *bcdin) of length DECPMAX uBytes.          */
    453 
    454     /* In-line sequence to convert least significant 10 bits of uInt  */
    455     /* dpd to three BCD8 digits starting at uByte u.  Note that an    */
    456     /* extra byte is written to the right of the three digits because */
    457     /* four bytes are moved at a time for speed; the alternative      */
    458     /* macro moves exactly three bytes (usually slower).              */
    459     #define dpd2bcd8(u, dpd)  memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4)
    460     #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3)
    461 
    462     /* Decode the declets.  After extracting each one, it is decoded  */
    463     /* to BCD8 using a table lookup (also used for variable-length    */
    464     /* decode).  Each DPD decode is 3 bytes BCD8 plus a one-byte      */
    465     /* length which is not used, here).  Fixed-length 4-byte moves    */
    466     /* are fast, however, almost everywhere, and so are used except   */
    467     /* for the final three bytes (to avoid overrun).  The code below  */
    468     /* is 36 instructions for Doubles and about 70 for Quads, even    */
    469     /* on IA32.                                                       */
    470 
    471     /* Two macros are defined for each format:                        */
    472     /*   GETCOEFF extracts the coefficient of the current format      */
    473     /*   GETWCOEFF extracts the coefficient of the next-wider format. */
    474     /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */
    475 
    476     #if DECPMAX==7
    477     #define GETCOEFF(df, bcd) {                          \
    478       uInt sourhi=DFWORD(df, 0);                         \
    479       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
    480       dpd2bcd8(bcd+1, sourhi>>10);                       \
    481       dpd2bcd83(bcd+4, sourhi);}
    482     #define GETWCOEFF(df, bcd) {                         \
    483       uInt sourhi=DFWWORD(df, 0);                        \
    484       uInt sourlo=DFWWORD(df, 1);                        \
    485       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
    486       dpd2bcd8(bcd+1, sourhi>>8);                        \
    487       dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30));       \
    488       dpd2bcd8(bcd+7, sourlo>>20);                       \
    489       dpd2bcd8(bcd+10, sourlo>>10);                      \
    490       dpd2bcd83(bcd+13, sourlo);}
    491 
    492     #elif DECPMAX==16
    493     #define GETCOEFF(df, bcd) {                          \
    494       uInt sourhi=DFWORD(df, 0);                         \
    495       uInt sourlo=DFWORD(df, 1);                         \
    496       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
    497       dpd2bcd8(bcd+1, sourhi>>8);                        \
    498       dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30));       \
    499       dpd2bcd8(bcd+7, sourlo>>20);                       \
    500       dpd2bcd8(bcd+10, sourlo>>10);                      \
    501       dpd2bcd83(bcd+13, sourlo);}
    502     #define GETWCOEFF(df, bcd) {                         \
    503       uInt sourhi=DFWWORD(df, 0);                        \
    504       uInt sourmh=DFWWORD(df, 1);                        \
    505       uInt sourml=DFWWORD(df, 2);                        \
    506       uInt sourlo=DFWWORD(df, 3);                        \
    507       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
    508       dpd2bcd8(bcd+1, sourhi>>4);                        \
    509       dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26));     \
    510       dpd2bcd8(bcd+7, sourmh>>16);                       \
    511       dpd2bcd8(bcd+10, sourmh>>6);                       \
    512       dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28));    \
    513       dpd2bcd8(bcd+16, sourml>>18);                      \
    514       dpd2bcd8(bcd+19, sourml>>8);                       \
    515       dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30));    \
    516       dpd2bcd8(bcd+25, sourlo>>20);                      \
    517       dpd2bcd8(bcd+28, sourlo>>10);                      \
    518       dpd2bcd83(bcd+31, sourlo);}
    519 
    520     #elif DECPMAX==34
    521     #define GETCOEFF(df, bcd) {                          \
    522       uInt sourhi=DFWORD(df, 0);                         \
    523       uInt sourmh=DFWORD(df, 1);                         \
    524       uInt sourml=DFWORD(df, 2);                         \
    525       uInt sourlo=DFWORD(df, 3);                         \
    526       *(bcd)=(uByte)DECCOMBMSD[sourhi>>26];              \
    527       dpd2bcd8(bcd+1, sourhi>>4);                        \
    528       dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26));     \
    529       dpd2bcd8(bcd+7, sourmh>>16);                       \
    530       dpd2bcd8(bcd+10, sourmh>>6);                       \
    531       dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28));    \
    532       dpd2bcd8(bcd+16, sourml>>18);                      \
    533       dpd2bcd8(bcd+19, sourml>>8);                       \
    534       dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30));    \
    535       dpd2bcd8(bcd+25, sourlo>>20);                      \
    536       dpd2bcd8(bcd+28, sourlo>>10);                      \
    537       dpd2bcd83(bcd+31, sourlo);}
    538 
    539       #define GETWCOEFF(df, bcd) {??} /* [should never be used]       */
    540     #endif
    541 
    542     /* Macros to decode the coefficient in a finite decFloat *df into */
    543     /* a base-billion uInt array, with the least-significant          */
    544     /* 0-999999999 'digit' at offset 0.                               */
    545 
    546     /* Decode the declets.  After extracting each one, it is decoded  */
    547     /* to binary using a table lookup.  Three tables are used; one    */
    548     /* the usual DPD to binary, the other two pre-multiplied by 1000  */
    549     /* and 1000000 to avoid multiplication during decode.  These      */
    550     /* tables can also be used for multiplying up the MSD as the DPD  */
    551     /* code for 0 through 9 is the identity.                          */
    552     #define DPD2BIN0 DPD2BIN         /* for prettier code             */
    553 
    554     #if DECPMAX==7
    555     #define GETCOEFFBILL(df, buf) {                           \
    556       uInt sourhi=DFWORD(df, 0);                              \
    557       (buf)[0]=DPD2BIN0[sourhi&0x3ff]                         \
    558               +DPD2BINK[(sourhi>>10)&0x3ff]                   \
    559               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
    560 
    561     #elif DECPMAX==16
    562     #define GETCOEFFBILL(df, buf) {                           \
    563       uInt sourhi, sourlo;                                    \
    564       sourlo=DFWORD(df, 1);                                   \
    565       (buf)[0]=DPD2BIN0[sourlo&0x3ff]                         \
    566               +DPD2BINK[(sourlo>>10)&0x3ff]                   \
    567               +DPD2BINM[(sourlo>>20)&0x3ff];                  \
    568       sourhi=DFWORD(df, 0);                                   \
    569       (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff]   \
    570               +DPD2BINK[(sourhi>>8)&0x3ff]                    \
    571               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
    572 
    573     #elif DECPMAX==34
    574     #define GETCOEFFBILL(df, buf) {                           \
    575       uInt sourhi, sourmh, sourml, sourlo;                    \
    576       sourlo=DFWORD(df, 3);                                   \
    577       (buf)[0]=DPD2BIN0[sourlo&0x3ff]                         \
    578               +DPD2BINK[(sourlo>>10)&0x3ff]                   \
    579               +DPD2BINM[(sourlo>>20)&0x3ff];                  \
    580       sourml=DFWORD(df, 2);                                   \
    581       (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff]   \
    582               +DPD2BINK[(sourml>>8)&0x3ff]                    \
    583               +DPD2BINM[(sourml>>18)&0x3ff];                  \
    584       sourmh=DFWORD(df, 1);                                   \
    585       (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff]   \
    586               +DPD2BINK[(sourmh>>6)&0x3ff]                    \
    587               +DPD2BINM[(sourmh>>16)&0x3ff];                  \
    588       sourhi=DFWORD(df, 0);                                   \
    589       (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff]   \
    590               +DPD2BINK[(sourhi>>4)&0x3ff]                    \
    591               +DPD2BINM[DECCOMBMSD[sourhi>>26]];}
    592 
    593     #endif
    594 
    595     /* Macros to decode the coefficient in a finite decFloat *df into */
    596     /* a base-thousand uInt array (of size DECLETS+1, to allow for    */
    597     /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/
    598 
    599     /* Decode the declets.  After extracting each one, it is decoded  */
    600     /* to binary using a table lookup.                                */
    601     #if DECPMAX==7
    602     #define GETCOEFFTHOU(df, buf) {                           \
    603       uInt sourhi=DFWORD(df, 0);                              \
    604       (buf)[0]=DPD2BIN[sourhi&0x3ff];                         \
    605       (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff];                   \
    606       (buf)[2]=DECCOMBMSD[sourhi>>26];}
    607 
    608     #elif DECPMAX==16
    609     #define GETCOEFFTHOU(df, buf) {                           \
    610       uInt sourhi, sourlo;                                    \
    611       sourlo=DFWORD(df, 1);                                   \
    612       (buf)[0]=DPD2BIN[sourlo&0x3ff];                         \
    613       (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff];                   \
    614       (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff];                   \
    615       sourhi=DFWORD(df, 0);                                   \
    616       (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff];   \
    617       (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff];                    \
    618       (buf)[5]=DECCOMBMSD[sourhi>>26];}
    619 
    620     #elif DECPMAX==34
    621     #define GETCOEFFTHOU(df, buf) {                           \
    622       uInt sourhi, sourmh, sourml, sourlo;                    \
    623       sourlo=DFWORD(df, 3);                                   \
    624       (buf)[0]=DPD2BIN[sourlo&0x3ff];                         \
    625       (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff];                   \
    626       (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff];                   \
    627       sourml=DFWORD(df, 2);                                   \
    628       (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff];   \
    629       (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff];                    \
    630       (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff];                   \
    631       sourmh=DFWORD(df, 1);                                   \
    632       (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff];   \
    633       (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff];                    \
    634       (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff];                   \
    635       sourhi=DFWORD(df, 0);                                   \
    636       (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff];   \
    637       (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff];                   \
    638       (buf)[11]=DECCOMBMSD[sourhi>>26];}
    639     #endif
    640 
    641 
    642     /* Macros to decode the coefficient in a finite decFloat *df and  */
    643     /* add to a base-thousand uInt array (as for GETCOEFFTHOU).       */
    644     /* After the addition then most significant 'digit' in the array  */
    645     /* might have a value larger then 10 (with a maximum of 19).      */
    646     #if DECPMAX==7
    647     #define ADDCOEFFTHOU(df, buf) {                           \
    648       uInt sourhi=DFWORD(df, 0);                              \
    649       (buf)[0]+=DPD2BIN[sourhi&0x3ff];                        \
    650       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
    651       (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff];                  \
    652       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
    653       (buf)[2]+=DECCOMBMSD[sourhi>>26];}
    654 
    655     #elif DECPMAX==16
    656     #define ADDCOEFFTHOU(df, buf) {                           \
    657       uInt sourhi, sourlo;                                    \
    658       sourlo=DFWORD(df, 1);                                   \
    659       (buf)[0]+=DPD2BIN[sourlo&0x3ff];                        \
    660       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
    661       (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff];                  \
    662       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
    663       (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff];                  \
    664       if (buf[2]>999) {buf[2]-=1000; buf[3]++;}               \
    665       sourhi=DFWORD(df, 0);                                   \
    666       (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff];  \
    667       if (buf[3]>999) {buf[3]-=1000; buf[4]++;}               \
    668       (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff];                   \
    669       if (buf[4]>999) {buf[4]-=1000; buf[5]++;}               \
    670       (buf)[5]+=DECCOMBMSD[sourhi>>26];}
    671 
    672     #elif DECPMAX==34
    673     #define ADDCOEFFTHOU(df, buf) {                           \
    674       uInt sourhi, sourmh, sourml, sourlo;                    \
    675       sourlo=DFWORD(df, 3);                                   \
    676       (buf)[0]+=DPD2BIN[sourlo&0x3ff];                        \
    677       if (buf[0]>999) {buf[0]-=1000; buf[1]++;}               \
    678       (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff];                  \
    679       if (buf[1]>999) {buf[1]-=1000; buf[2]++;}               \
    680       (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff];                  \
    681       if (buf[2]>999) {buf[2]-=1000; buf[3]++;}               \
    682       sourml=DFWORD(df, 2);                                   \
    683       (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff];  \
    684       if (buf[3]>999) {buf[3]-=1000; buf[4]++;}               \
    685       (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff];                   \
    686       if (buf[4]>999) {buf[4]-=1000; buf[5]++;}               \
    687       (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff];                  \
    688       if (buf[5]>999) {buf[5]-=1000; buf[6]++;}               \
    689       sourmh=DFWORD(df, 1);                                   \
    690       (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff];  \
    691       if (buf[6]>999) {buf[6]-=1000; buf[7]++;}               \
    692       (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff];                   \
    693       if (buf[7]>999) {buf[7]-=1000; buf[8]++;}               \
    694       (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff];                  \
    695       if (buf[8]>999) {buf[8]-=1000; buf[9]++;}               \
    696       sourhi=DFWORD(df, 0);                                   \
    697       (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff];  \
    698       if (buf[9]>999) {buf[9]-=1000; buf[10]++;}              \
    699       (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff];                  \
    700       if (buf[10]>999) {buf[10]-=1000; buf[11]++;}            \
    701       (buf)[11]+=DECCOMBMSD[sourhi>>26];}
    702     #endif
    703 
    704 
    705     /* Set a decFloat to the maximum positive finite number (Nmax)    */
    706     #if DECPMAX==7
    707     #define DFSETNMAX(df)            \
    708       {DFWORD(df, 0)=0x77f3fcff;}
    709     #elif DECPMAX==16
    710     #define DFSETNMAX(df)            \
    711       {DFWORD(df, 0)=0x77fcff3f;     \
    712        DFWORD(df, 1)=0xcff3fcff;}
    713     #elif DECPMAX==34
    714     #define DFSETNMAX(df)            \
    715       {DFWORD(df, 0)=0x77ffcff3;     \
    716        DFWORD(df, 1)=0xfcff3fcf;     \
    717        DFWORD(df, 2)=0xf3fcff3f;     \
    718        DFWORD(df, 3)=0xcff3fcff;}
    719     #endif
    720 
    721   /* [end of format-dependent macros and constants]                   */
    722   #endif
    723 
    724 #else
    725   #error decNumberLocal included more than once
    726 #endif
    727