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1//===----- lib/fp_add_impl.inc - floaing point addition -----------*- C -*-===//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 soft-float addition with the IEEE-754 default rounding10// (to nearest, ties to even).11//12//===----------------------------------------------------------------------===//13 14#include "fp_lib.h"15#include "fp_mode.h"16 17static __inline fp_t __addXf3__(fp_t a, fp_t b) {18 rep_t aRep = toRep(a);19 rep_t bRep = toRep(b);20 const rep_t aAbs = aRep & absMask;21 const rep_t bAbs = bRep & absMask;22 23 // Detect if a or b is zero, infinity, or NaN.24 if (aAbs - REP_C(1) >= infRep - REP_C(1) ||25 bAbs - REP_C(1) >= infRep - REP_C(1)) {26 // NaN + anything = qNaN27 if (aAbs > infRep)28 return fromRep(toRep(a) | quietBit);29 // anything + NaN = qNaN30 if (bAbs > infRep)31 return fromRep(toRep(b) | quietBit);32 33 if (aAbs == infRep) {34 // +/-infinity + -/+infinity = qNaN35 if ((toRep(a) ^ toRep(b)) == signBit)36 return fromRep(qnanRep);37 // +/-infinity + anything remaining = +/- infinity38 else39 return a;40 }41 42 // anything remaining + +/-infinity = +/-infinity43 if (bAbs == infRep)44 return b;45 46 // zero + anything = anything47 if (!aAbs) {48 // We need to get the sign right for zero + zero.49 if (!bAbs)50 return fromRep(toRep(a) & toRep(b));51 else52 return b;53 }54 55 // anything + zero = anything56 if (!bAbs)57 return a;58 }59 60 // Swap a and b if necessary so that a has the larger absolute value.61 if (bAbs > aAbs) {62 const rep_t temp = aRep;63 aRep = bRep;64 bRep = temp;65 }66 67 // Extract the exponent and significand from the (possibly swapped) a and b.68 int aExponent = aRep >> significandBits & maxExponent;69 int bExponent = bRep >> significandBits & maxExponent;70 rep_t aSignificand = aRep & significandMask;71 rep_t bSignificand = bRep & significandMask;72 73 // Normalize any denormals, and adjust the exponent accordingly.74 if (aExponent == 0)75 aExponent = normalize(&aSignificand);76 if (bExponent == 0)77 bExponent = normalize(&bSignificand);78 79 // The sign of the result is the sign of the larger operand, a. If they80 // have opposite signs, we are performing a subtraction. Otherwise, we81 // perform addition.82 const rep_t resultSign = aRep & signBit;83 const bool subtraction = (aRep ^ bRep) & signBit;84 85 // Shift the significands to give us round, guard and sticky, and set the86 // implicit significand bit. If we fell through from the denormal path it87 // was already set by normalize( ), but setting it twice won't hurt88 // anything.89 aSignificand = (aSignificand | implicitBit) << 3;90 bSignificand = (bSignificand | implicitBit) << 3;91 92 // Shift the significand of b by the difference in exponents, with a sticky93 // bottom bit to get rounding correct.94 const unsigned int align = (unsigned int)(aExponent - bExponent);95 if (align) {96 if (align < typeWidth) {97 const bool sticky = (bSignificand << (typeWidth - align)) != 0;98 bSignificand = bSignificand >> align | sticky;99 } else {100 bSignificand = 1; // Set the sticky bit. b is known to be non-zero.101 }102 }103 if (subtraction) {104 aSignificand -= bSignificand;105 // If a == -b, return +zero.106 if (aSignificand == 0)107 return fromRep(0);108 109 // If partial cancellation occured, we need to left-shift the result110 // and adjust the exponent.111 if (aSignificand < implicitBit << 3) {112 const int shift = rep_clz(aSignificand) - rep_clz(implicitBit << 3);113 aSignificand <<= shift;114 aExponent -= shift;115 }116 } else /* addition */ {117 aSignificand += bSignificand;118 119 // If the addition carried up, we need to right-shift the result and120 // adjust the exponent.121 if (aSignificand & implicitBit << 4) {122 const bool sticky = aSignificand & 1;123 aSignificand = aSignificand >> 1 | sticky;124 aExponent += 1;125 }126 }127 128 // If we have overflowed the type, return +/- infinity.129 if (aExponent >= maxExponent)130 return fromRep(infRep | resultSign);131 132 if (aExponent <= 0) {133 // The result is denormal before rounding. The exponent is zero and we134 // need to shift the significand.135 const int shift = 1 - aExponent;136 const bool sticky = (aSignificand << (typeWidth - shift)) != 0;137 aSignificand = aSignificand >> shift | sticky;138 aExponent = 0;139 }140 141 // Low three bits are round, guard, and sticky.142 const int roundGuardSticky = aSignificand & 0x7;143 144 // Shift the significand into place, and mask off the implicit bit.145 rep_t result = aSignificand >> 3 & significandMask;146 147 // Insert the exponent and sign.148 result |= (rep_t)aExponent << significandBits;149 result |= resultSign;150 151 // Perform the final rounding. The result may overflow to infinity, but152 // that is the correct result in that case.153 switch (__fe_getround()) {154 case CRT_FE_TONEAREST:155 if (roundGuardSticky > 0x4)156 result++;157 if (roundGuardSticky == 0x4)158 result += result & 1;159 break;160 case CRT_FE_DOWNWARD:161 if (resultSign && roundGuardSticky) result++;162 break;163 case CRT_FE_UPWARD:164 if (!resultSign && roundGuardSticky) result++;165 break;166 case CRT_FE_TOWARDZERO:167 break;168 }169 if (roundGuardSticky)170 __fe_raise_inexact();171 return fromRep(result);172}173