1//= lib/fp_trunc_impl.inc - high precision -> low precision conversion *-*-===// 2// 3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4// See https://llvm.org/LICENSE.txt for license information. 5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6// 7//===----------------------------------------------------------------------===// 8// 9// This file implements a fairly generic conversion from a wider to a narrower 10// IEEE-754 floating-point type in the default (round to nearest, ties to even) 11// rounding mode. The constants and types defined following the includes below 12// parameterize the conversion. 13// 14// This routine can be trivially adapted to support conversions to 15// half-precision or from quad-precision. It does not support types that don't 16// use the usual IEEE-754 interchange formats; specifically, some work would be 17// needed to adapt it to (for example) the Intel 80-bit format or PowerPC 18// double-double format. 19// 20// Note please, however, that this implementation is only intended to support 21// *narrowing* operations; if you need to convert to a *wider* floating-point 22// type (e.g. float -> double), then this routine will not do what you want it 23// to. 24// 25// It also requires that integer types at least as large as both formats 26// are available on the target platform; this may pose a problem when trying 27// to add support for quad on some 32-bit systems, for example. 28// 29// Finally, the following assumptions are made: 30// 31// 1. Floating-point types and integer types have the same endianness on the 32// target platform. 33// 34// 2. Quiet NaNs, if supported, are indicated by the leading bit of the 35// significand field being set. 36// 37//===----------------------------------------------------------------------===// 38 39#include "fp_trunc.h" 40 41static __inline dst_t __truncXfYf2__(src_t a) { 42 // Various constants whose values follow from the type parameters. 43 // Any reasonable optimizer will fold and propagate all of these. 44 const int srcBits = sizeof(src_t) * CHAR_BIT; 45 const int srcExpBits = srcBits - srcSigBits - 1; 46 const int srcInfExp = (1 << srcExpBits) - 1; 47 const int srcExpBias = srcInfExp >> 1; 48 49 const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigBits; 50 const src_rep_t srcSignificandMask = srcMinNormal - 1; 51 const src_rep_t srcInfinity = (src_rep_t)srcInfExp << srcSigBits; 52 const src_rep_t srcSignMask = SRC_REP_C(1) << (srcSigBits + srcExpBits); 53 const src_rep_t srcAbsMask = srcSignMask - 1; 54 const src_rep_t roundMask = (SRC_REP_C(1) << (srcSigBits - dstSigBits)) - 1; 55 const src_rep_t halfway = SRC_REP_C(1) << (srcSigBits - dstSigBits - 1); 56 const src_rep_t srcQNaN = SRC_REP_C(1) << (srcSigBits - 1); 57 const src_rep_t srcNaNCode = srcQNaN - 1; 58 59 const int dstBits = sizeof(dst_t) * CHAR_BIT; 60 const int dstExpBits = dstBits - dstSigBits - 1; 61 const int dstInfExp = (1 << dstExpBits) - 1; 62 const int dstExpBias = dstInfExp >> 1; 63 64 const int underflowExponent = srcExpBias + 1 - dstExpBias; 65 const int overflowExponent = srcExpBias + dstInfExp - dstExpBias; 66 const src_rep_t underflow = (src_rep_t)underflowExponent << srcSigBits; 67 const src_rep_t overflow = (src_rep_t)overflowExponent << srcSigBits; 68 69 const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigBits - 1); 70 const dst_rep_t dstNaNCode = dstQNaN - 1; 71 72 // Break a into a sign and representation of the absolute value. 73 const src_rep_t aRep = srcToRep(a); 74 const src_rep_t aAbs = aRep & srcAbsMask; 75 const src_rep_t sign = aRep & srcSignMask; 76 dst_rep_t absResult; 77 78 if (aAbs - underflow < aAbs - overflow) { 79 // The exponent of a is within the range of normal numbers in the 80 // destination format. We can convert by simply right-shifting with 81 // rounding and adjusting the exponent. 82 absResult = aAbs >> (srcSigBits - dstSigBits); 83 absResult -= (dst_rep_t)(srcExpBias - dstExpBias) << dstSigBits; 84 85 const src_rep_t roundBits = aAbs & roundMask; 86 // Round to nearest. 87 if (roundBits > halfway) 88 absResult++; 89 // Tie to even. 90 else if (roundBits == halfway) 91 absResult += absResult & 1; 92 } else if (aAbs > srcInfinity) { 93 // a is NaN. 94 // Conjure the result by beginning with infinity, setting the qNaN 95 // bit and inserting the (truncated) trailing NaN field. 96 absResult = (dst_rep_t)dstInfExp << dstSigBits; 97 absResult |= dstQNaN; 98 absResult |= 99 ((aAbs & srcNaNCode) >> (srcSigBits - dstSigBits)) & dstNaNCode; 100 } else if (aAbs >= overflow) { 101 // a overflows to infinity. 102 absResult = (dst_rep_t)dstInfExp << dstSigBits; 103 } else { 104 // a underflows on conversion to the destination type or is an exact 105 // zero. The result may be a denormal or zero. Extract the exponent 106 // to get the shift amount for the denormalization. 107 const int aExp = aAbs >> srcSigBits; 108 const int shift = srcExpBias - dstExpBias - aExp + 1; 109 110 const src_rep_t significand = (aRep & srcSignificandMask) | srcMinNormal; 111 112 // Right shift by the denormalization amount with sticky. 113 if (shift > srcSigBits) { 114 absResult = 0; 115 } else { 116 const bool sticky = (significand << (srcBits - shift)) != 0; 117 src_rep_t denormalizedSignificand = significand >> shift | sticky; 118 absResult = denormalizedSignificand >> (srcSigBits - dstSigBits); 119 const src_rep_t roundBits = denormalizedSignificand & roundMask; 120 // Round to nearest 121 if (roundBits > halfway) 122 absResult++; 123 // Ties to even 124 else if (roundBits == halfway) 125 absResult += absResult & 1; 126 } 127 } 128 129 // Apply the signbit to the absolute value. 130 const dst_rep_t result = absResult | sign >> (srcBits - dstBits); 131 return dstFromRep(result); 132} 133