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