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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-exception6//7//===----------------------------------------------------------------------===//8//9// This file implements a fairly generic conversion from a wider to a narrower10// 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 below12// parameterize the conversion.13//14// This routine can be trivially adapted to support conversions to15// half-precision or from quad-precision. It does not support types that don't16// use the usual IEEE-754 interchange formats; specifically, some work would be17// needed to adapt it to (for example) the Intel 80-bit format or PowerPC18// double-double format.19//20// Note please, however, that this implementation is only intended to support21// *narrowing* operations; if you need to convert to a *wider* floating-point22// type (e.g. float -> double), then this routine will not do what you want it23// to.24//25// It also requires that integer types at least as large as both formats26// are available on the target platform; this may pose a problem when trying27// 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 the32// target platform.33//34// 2. Quiet NaNs, if supported, are indicated by the leading bit of the35// significand field being set.36//37//===----------------------------------------------------------------------===//38 39#include "fp_trunc.h"40 41// The destination type may use a usual IEEE-754 interchange format or Intel42// 80-bit format. In particular, for the destination type dstSigFracBits may be43// not equal to dstSigBits. The source type is assumed to be one of IEEE-75444// standard types.45static __inline dst_t __truncXfYf2__(src_t a) {46 // Various constants whose values follow from the type parameters.47 // Any reasonable optimizer will fold and propagate all of these.48 const int srcInfExp = (1 << srcExpBits) - 1;49 const int srcExpBias = srcInfExp >> 1;50 51 const src_rep_t srcMinNormal = SRC_REP_C(1) << srcSigFracBits;52 const src_rep_t roundMask =53 (SRC_REP_C(1) << (srcSigFracBits - dstSigFracBits)) - 1;54 const src_rep_t halfway = SRC_REP_C(1)55 << (srcSigFracBits - dstSigFracBits - 1);56 const src_rep_t srcQNaN = SRC_REP_C(1) << (srcSigFracBits - 1);57 const src_rep_t srcNaNCode = srcQNaN - 1;58 59 const int dstInfExp = (1 << dstExpBits) - 1;60 const int dstExpBias = dstInfExp >> 1;61 const int overflowExponent = srcExpBias + dstInfExp - dstExpBias;62 63 const dst_rep_t dstQNaN = DST_REP_C(1) << (dstSigFracBits - 1);64 const dst_rep_t dstNaNCode = dstQNaN - 1;65 66 const src_rep_t aRep = srcToRep(a);67 const src_rep_t srcSign = extract_sign_from_src(aRep);68 const src_rep_t srcExp = extract_exp_from_src(aRep);69 const src_rep_t srcSigFrac = extract_sig_frac_from_src(aRep);70 71 dst_rep_t dstSign = srcSign;72 dst_rep_t dstExp;73 dst_rep_t dstSigFrac;74 75 // Same size exponents and a's significand tail is 0.76 // The significand can be truncated and the exponent can be copied over.77 const int sigFracTailBits = srcSigFracBits - dstSigFracBits;78 if (srcExpBits == dstExpBits &&79 ((aRep >> sigFracTailBits) << sigFracTailBits) == aRep) {80 dstExp = srcExp;81 dstSigFrac = (dst_rep_t)(srcSigFrac >> sigFracTailBits);82 return dstFromRep(construct_dst_rep(dstSign, dstExp, dstSigFrac));83 }84 85 const int dstExpCandidate = ((int)srcExp - srcExpBias) + dstExpBias;86 if (dstExpCandidate >= 1 && dstExpCandidate < dstInfExp) {87 // The exponent of a is within the range of normal numbers in the88 // destination format. We can convert by simply right-shifting with89 // rounding and adjusting the exponent.90 dstExp = dstExpCandidate;91 dstSigFrac = (dst_rep_t)(srcSigFrac >> sigFracTailBits);92 93 const src_rep_t roundBits = srcSigFrac & roundMask;94 // Round to nearest.95 if (roundBits > halfway)96 dstSigFrac++;97 // Tie to even.98 else if (roundBits == halfway)99 dstSigFrac += dstSigFrac & 1;100 101 // Rounding has changed the exponent.102 if (dstSigFrac >= (DST_REP_C(1) << dstSigFracBits)) {103 dstExp += 1;104 dstSigFrac ^= (DST_REP_C(1) << dstSigFracBits);105 }106 } else if (srcExp == srcInfExp && srcSigFrac) {107 // a is NaN.108 // Conjure the result by beginning with infinity, setting the qNaN109 // bit and inserting the (truncated) trailing NaN field.110 dstExp = dstInfExp;111 dstSigFrac = dstQNaN;112 dstSigFrac |= ((srcSigFrac & srcNaNCode) >> sigFracTailBits) & dstNaNCode;113 } else if ((int)srcExp >= overflowExponent) {114 dstExp = dstInfExp;115 dstSigFrac = 0;116 } else {117 // a underflows on conversion to the destination type or is an exact118 // zero. The result may be a denormal or zero. Extract the exponent119 // to get the shift amount for the denormalization.120 src_rep_t significand = srcSigFrac;121 int shift = srcExpBias - dstExpBias - srcExp;122 123 if (srcExp) {124 // Set the implicit integer bit if the source is a normal number.125 significand |= srcMinNormal;126 shift += 1;127 }128 129 // Right shift by the denormalization amount with sticky.130 if (shift > srcSigFracBits) {131 dstExp = 0;132 dstSigFrac = 0;133 } else {134 dstExp = 0;135 const bool sticky = shift && ((significand << (srcBits - shift)) != 0);136 src_rep_t denormalizedSignificand = significand >> shift | sticky;137 dstSigFrac = denormalizedSignificand >> sigFracTailBits;138 const src_rep_t roundBits = denormalizedSignificand & roundMask;139 // Round to nearest140 if (roundBits > halfway)141 dstSigFrac++;142 // Ties to even143 else if (roundBits == halfway)144 dstSigFrac += dstSigFrac & 1;145 146 // Rounding has changed the exponent.147 if (dstSigFrac >= (DST_REP_C(1) << dstSigFracBits)) {148 dstExp += 1;149 dstSigFrac ^= (DST_REP_C(1) << dstSigFracBits);150 }151 }152 }153 154 return dstFromRep(construct_dst_rep(dstSign, dstExp, dstSigFrac));155}156