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| //===----- lib/fp_add_impl.inc - floaing point addition -----------*- C -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This file implements soft-float addition with the IEEE-754 default rounding
// (to nearest, ties to even).
//
//===----------------------------------------------------------------------===//
#include "fp_lib.h"
#include "fp_mode.h"
static __inline fp_t __addXf3__(fp_t a, fp_t b) {
rep_t aRep = toRep(a);
rep_t bRep = toRep(b);
const rep_t aAbs = aRep & absMask;
const rep_t bAbs = bRep & absMask;
// Detect if a or b is zero, infinity, or NaN.
if (aAbs - REP_C(1) >= infRep - REP_C(1) ||
bAbs - REP_C(1) >= infRep - REP_C(1)) {
// NaN + anything = qNaN
if (aAbs > infRep)
return fromRep(toRep(a) | quietBit);
// anything + NaN = qNaN
if (bAbs > infRep)
return fromRep(toRep(b) | quietBit);
if (aAbs == infRep) {
// +/-infinity + -/+infinity = qNaN
if ((toRep(a) ^ toRep(b)) == signBit)
return fromRep(qnanRep);
// +/-infinity + anything remaining = +/- infinity
else
return a;
}
// anything remaining + +/-infinity = +/-infinity
if (bAbs == infRep)
return b;
// zero + anything = anything
if (!aAbs) {
// We need to get the sign right for zero + zero.
if (!bAbs)
return fromRep(toRep(a) & toRep(b));
else
return b;
}
// anything + zero = anything
if (!bAbs)
return a;
}
// Swap a and b if necessary so that a has the larger absolute value.
if (bAbs > aAbs) {
const rep_t temp = aRep;
aRep = bRep;
bRep = temp;
}
// Extract the exponent and significand from the (possibly swapped) a and b.
int aExponent = aRep >> significandBits & maxExponent;
int bExponent = bRep >> significandBits & maxExponent;
rep_t aSignificand = aRep & significandMask;
rep_t bSignificand = bRep & significandMask;
// Normalize any denormals, and adjust the exponent accordingly.
if (aExponent == 0)
aExponent = normalize(&aSignificand);
if (bExponent == 0)
bExponent = normalize(&bSignificand);
// The sign of the result is the sign of the larger operand, a. If they
// have opposite signs, we are performing a subtraction. Otherwise, we
// perform addition.
const rep_t resultSign = aRep & signBit;
const bool subtraction = (aRep ^ bRep) & signBit;
// Shift the significands to give us round, guard and sticky, and set the
// implicit significand bit. If we fell through from the denormal path it
// was already set by normalize( ), but setting it twice won't hurt
// anything.
aSignificand = (aSignificand | implicitBit) << 3;
bSignificand = (bSignificand | implicitBit) << 3;
// Shift the significand of b by the difference in exponents, with a sticky
// bottom bit to get rounding correct.
const unsigned int align = aExponent - bExponent;
if (align) {
if (align < typeWidth) {
const bool sticky = (bSignificand << (typeWidth - align)) != 0;
bSignificand = bSignificand >> align | sticky;
} else {
bSignificand = 1; // Set the sticky bit. b is known to be non-zero.
}
}
if (subtraction) {
aSignificand -= bSignificand;
// If a == -b, return +zero.
if (aSignificand == 0)
return fromRep(0);
// If partial cancellation occured, we need to left-shift the result
// and adjust the exponent.
if (aSignificand < implicitBit << 3) {
const int shift = rep_clz(aSignificand) - rep_clz(implicitBit << 3);
aSignificand <<= shift;
aExponent -= shift;
}
} else /* addition */ {
aSignificand += bSignificand;
// If the addition carried up, we need to right-shift the result and
// adjust the exponent.
if (aSignificand & implicitBit << 4) {
const bool sticky = aSignificand & 1;
aSignificand = aSignificand >> 1 | sticky;
aExponent += 1;
}
}
// If we have overflowed the type, return +/- infinity.
if (aExponent >= maxExponent)
return fromRep(infRep | resultSign);
if (aExponent <= 0) {
// The result is denormal before rounding. The exponent is zero and we
// need to shift the significand.
const int shift = 1 - aExponent;
const bool sticky = (aSignificand << (typeWidth - shift)) != 0;
aSignificand = aSignificand >> shift | sticky;
aExponent = 0;
}
// Low three bits are round, guard, and sticky.
const int roundGuardSticky = aSignificand & 0x7;
// Shift the significand into place, and mask off the implicit bit.
rep_t result = aSignificand >> 3 & significandMask;
// Insert the exponent and sign.
result |= (rep_t)aExponent << significandBits;
result |= resultSign;
// Perform the final rounding. The result may overflow to infinity, but
// that is the correct result in that case.
switch (__fe_getround()) {
case FE_TONEAREST:
if (roundGuardSticky > 0x4)
result++;
if (roundGuardSticky == 0x4)
result += result & 1;
break;
case FE_DOWNWARD:
if (resultSign && roundGuardSticky) result++;
break;
case FE_UPWARD:
if (!resultSign && roundGuardSticky) result++;
break;
case FE_TOWARDZERO:
break;
}
if (roundGuardSticky)
__fe_raise_inexact();
return fromRep(result);
}
|