120 lines
4.8 KiB
C
120 lines
4.8 KiB
C
//===-- lib/muldf3.c - Double-precision multiplication ------------*- C -*-===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file is distributed under the University of Illinois Open Source
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// License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// This file implements double-precision soft-float multiplication
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// with the IEEE-754 default rounding (to nearest, ties to even).
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//
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//===----------------------------------------------------------------------===//
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#define DOUBLE_PRECISION
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#include "fp_lib.h"
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fp_t __muldf3(fp_t a, fp_t b) {
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const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
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const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
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const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
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rep_t aSignificand = toRep(a) & significandMask;
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rep_t bSignificand = toRep(b) & significandMask;
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int scale = 0;
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// Detect if a or b is zero, denormal, infinity, or NaN.
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if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
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const rep_t aAbs = toRep(a) & absMask;
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const rep_t bAbs = toRep(b) & absMask;
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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 * non-zero = +/- infinity
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if (bAbs) return fromRep(aAbs | productSign);
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// infinity * zero = NaN
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else return fromRep(qnanRep);
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}
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if (bAbs == infRep) {
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// non-zero * infinity = +/- infinity
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if (aAbs) return fromRep(bAbs | productSign);
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// zero * infinity = NaN
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else return fromRep(qnanRep);
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}
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// zero * anything = +/- zero
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if (!aAbs) return fromRep(productSign);
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// anything * zero = +/- zero
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if (!bAbs) return fromRep(productSign);
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// one or both of a or b is denormal, the other (if applicable) is a
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// normal number. Renormalize one or both of a and b, and set scale to
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// include the necessary exponent adjustment.
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if (aAbs < implicitBit) scale += normalize(&aSignificand);
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if (bAbs < implicitBit) scale += normalize(&bSignificand);
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}
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// Or in the implicit significand bit. (If we fell through from the
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// denormal path it was already set by normalize( ), but setting it twice
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// won't hurt anything.)
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aSignificand |= implicitBit;
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bSignificand |= implicitBit;
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// Get the significand of a*b. Before multiplying the significands, shift
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// one of them left to left-align it in the field. Thus, the product will
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// have (exponentBits + 2) integral digits, all but two of which must be
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// zero. Normalizing this result is just a conditional left-shift by one
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// and bumping the exponent accordingly.
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rep_t productHi, productLo;
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wideMultiply(aSignificand, bSignificand << exponentBits,
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&productHi, &productLo);
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int productExponent = aExponent + bExponent - exponentBias + scale;
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// Normalize the significand, adjust exponent if needed.
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if (productHi & implicitBit) productExponent++;
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else wideLeftShift(&productHi, &productLo, 1);
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// If we have overflowed the type, return +/- infinity.
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if (productExponent >= maxExponent) return fromRep(infRep | productSign);
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if (productExponent <= 0) {
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// Result is denormal before rounding
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//
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// If the result is so small that it just underflows to zero, return
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// a zero of the appropriate sign. Mathematically there is no need to
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// handle this case separately, but we make it a special case to
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// simplify the shift logic.
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const int shift = 1 - productExponent;
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if (shift >= typeWidth) return fromRep(productSign);
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// Otherwise, shift the significand of the result so that the round
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// bit is the high bit of productLo.
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wideRightShiftWithSticky(&productHi, &productLo, shift);
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}
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else {
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// Result is normal before rounding; insert the exponent.
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productHi &= significandMask;
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productHi |= (rep_t)productExponent << significandBits;
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}
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// Insert the sign of the result:
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productHi |= productSign;
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// Final rounding. The final result may overflow to infinity, or underflow
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// to zero, but those are the correct results in those cases. We use the
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// default IEEE-754 round-to-nearest, ties-to-even rounding mode.
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if (productLo > signBit) productHi++;
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if (productLo == signBit) productHi += productHi & 1;
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return fromRep(productHi);
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}
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