lib/addsf3.c

/*
 *                     The LLVM Compiler Infrastructure
 *
 * This file is distributed under the University of Illinois Open Source
 * License. See LICENSE.TXT for details.
 */

#define SINGLE_PRECISION
#include "fp_lib.h"

// This file implements single-precision soft-float addition and subtraction
// with the IEEE-754 default rounding (to nearest, ties to even).

fp_t __addsf3(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 - 1U >= infRep - 1U || bAbs - 1U >= infRep - 1U) {
        
        // 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) {
            // but 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 addition.
    const rep_t resultSign = aRep & signBit;
    const bool subtraction = (aRep ^ bRep) & signBit;
    
    // Shift the significands to give us round, guard and sticky, and or in 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 int align = aExponent - bExponent;
    if (align) {
        if (align < typeWidth) {
            const bool sticky = bSignificand << (typeWidth - align);
            bSignificand = bSignificand >> align | sticky;
        } else {
            bSignificand = 1; // sticky; 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) {
        // 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);
        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;
    
    // Final rounding.  The result may overflow to infinity, but that is the
    // correct result in that case.
    if (roundGuardSticky > 0x4) result++;
    if (roundGuardSticky == 0x4) result += result & 1;
    return fromRep(result);
}

// Subtraction; flip the sign bit of b and add.
fp_t __subsf3(fp_t a, fp_t b) {
    return __addsf3(a, fromRep(toRep(b) ^ signBit));
}