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      1 //===-- lib/truncdfsf2.c - double -> single conversion ------------*- C -*-===//
      2 //
      3 //                     The LLVM Compiler Infrastructure
      4 //
      5 // This file is dual licensed under the MIT and the University of Illinois Open
      6 // Source Licenses. See LICENSE.TXT for details.
      7 //
      8 //===----------------------------------------------------------------------===//
      9 //
     10 // This file implements a fairly generic conversion from a wider to a narrower
     11 // IEEE-754 floating-point type in the default (round to nearest, ties to even)
     12 // rounding mode.  The constants and types defined following the includes below
     13 // parameterize the conversion.
     14 //
     15 // This routine can be trivially adapted to support conversions to
     16 // half-precision or from quad-precision. It does not support types that don't
     17 // use the usual IEEE-754 interchange formats; specifically, some work would be
     18 // needed to adapt it to (for example) the Intel 80-bit format or PowerPC
     19 // double-double format.
     20 //
     21 // Note please, however, that this implementation is only intended to support
     22 // *narrowing* operations; if you need to convert to a *wider* floating-point
     23 // type (e.g. float -> double), then this routine will not do what you want it
     24 // to.
     25 //
     26 // It also requires that integer types at least as large as both formats
     27 // are available on the target platform; this may pose a problem when trying
     28 // to add support for quad on some 32-bit systems, for example.
     29 //
     30 // Finally, the following assumptions are made:
     31 //
     32 // 1. floating-point types and integer types have the same endianness on the
     33 //    target platform
     34 //
     35 // 2. quiet NaNs, if supported, are indicated by the leading bit of the
     36 //    significand field being set
     37 //
     38 //===----------------------------------------------------------------------===//
     39 
     40 #include "int_lib.h"
     41 
     42 typedef double src_t;
     43 typedef uint64_t src_rep_t;
     44 #define SRC_REP_C UINT64_C
     45 static const int srcSigBits = 52;
     46 
     47 typedef float dst_t;
     48 typedef uint32_t dst_rep_t;
     49 #define DST_REP_C UINT32_C
     50 static const int dstSigBits = 23;
     51 
     52 // End of specialization parameters.  Two helper routines for conversion to and
     53 // from the representation of floating-point data as integer values follow.
     54 
     55 static inline src_rep_t srcToRep(src_t x) {
     56     const union { src_t f; src_rep_t i; } rep = {.f = x};
     57     return rep.i;
     58 }
     59 
     60 static inline dst_t dstFromRep(dst_rep_t x) {
     61     const union { dst_t f; dst_rep_t i; } rep = {.i = x};
     62     return rep.f;
     63 }
     64 
     65 // End helper routines.  Conversion implementation follows.
     66 
     67 ARM_EABI_FNALIAS(d2f, truncdfsf2)
     68 
     69 COMPILER_RT_ABI dst_t
     70 __truncdfsf2(src_t a) {
     71 
     72     // Various constants whose values follow from the type parameters.
     73     // Any reasonable optimizer will fold and propagate all of these.
     74     const int srcBits = sizeof(src_t)*CHAR_BIT;
     75     const int srcExpBits = srcBits - srcSigBits - 1;
     76     const int srcInfExp = (1 << srcExpBits) - 1;
     77     const int srcExpBias = srcInfExp >> 1;
     78 
     79     const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits;
     80     const src_rep_t significandMask = srcMinNormal - 1;
     81     const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits;
     82     const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits);
     83     const src_rep_t srcAbsMask = srcSignMask - 1;
     84     const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1;
     85     const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1);
     86 
     87     const int dstBits = sizeof(dst_t)*CHAR_BIT;
     88     const int dstExpBits = dstBits - dstSigBits - 1;
     89     const int dstInfExp = (1 << dstExpBits) - 1;
     90     const int dstExpBias = dstInfExp >> 1;
     91 
     92     const int underflowExponent = srcExpBias + 1 - dstExpBias;
     93     const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;
     94     const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits;
     95     const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits;
     96 
     97     const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1);
     98     const dst_rep_t dstNaNCode = dstQNaN - 1;
     99 
    100     // Break a into a sign and representation of the absolute value
    101     const src_rep_t aRep = srcToRep(a);
    102     const src_rep_t aAbs = aRep & srcAbsMask;
    103     const src_rep_t sign = aRep & srcSignMask;
    104     dst_rep_t absResult;
    105 
    106     if (aAbs - underflow < aAbs - overflow) {
    107         // The exponent of a is within the range of normal numbers in the
    108         // destination format.  We can convert by simply right-shifting with
    109         // rounding and adjusting the exponent.
    110         absResult = aAbs >> (srcSigBits - dstSigBits);
    111         absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits;
    112 
    113         const src_rep_t roundBits = aAbs & roundMask;
    114 
    115         // Round to nearest
    116         if (roundBits > halfway)
    117             absResult++;
    118 
    119         // Ties to even
    120         else if (roundBits == halfway)
    121             absResult += absResult & 1;
    122     }
    123 
    124     else if (aAbs > srcInfinity) {
    125         // a is NaN.
    126         // Conjure the result by beginning with infinity, setting the qNaN
    127         // bit and inserting the (truncated) trailing NaN field.
    128         absResult = (dst_rep_t)dstInfExp << dstSigBits;
    129         absResult |= dstQNaN;
    130         absResult |= aAbs & dstNaNCode;
    131     }
    132 
    133     else if (aAbs > overflow) {
    134         // a overflows to infinity.
    135         absResult = (dst_rep_t)dstInfExp << dstSigBits;
    136     }
    137 
    138     else {
    139         // a underflows on conversion to the destination type or is an exact
    140         // zero.  The result may be a denormal or zero.  Extract the exponent
    141         // to get the shift amount for the denormalization.
    142         const int aExp = aAbs >> srcSigBits;
    143         const int shift = srcExpBias - dstExpBias - aExp + 1;
    144 
    145         const src_rep_t significand = (aRep & significandMask) | srcMinNormal;
    146 
    147         // Right shift by the denormalization amount with sticky.
    148         if (shift > srcSigBits) {
    149             absResult = 0;
    150         } else {
    151             const bool sticky = significand << (srcBits - shift);
    152             src_rep_t denormalizedSignificand = significand >> shift | sticky;
    153             absResult = denormalizedSignificand >> (srcSigBits - dstSigBits);
    154             const src_rep_t roundBits = denormalizedSignificand & roundMask;
    155             // Round to nearest
    156             if (roundBits > halfway)
    157                 absResult++;
    158             // Ties to even
    159             else if (roundBits == halfway)
    160                 absResult += absResult & 1;
    161         }
    162     }
    163 
    164     // Apply the signbit to (dst_t)abs(a).
    165     const dst_rep_t result = absResult | sign >> (srcBits - dstBits);
    166     return dstFromRep(result);
    167 
    168 }
    169