lib/truncdfsf2.c

   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 }