1//===---- lib/fp_mul_impl.inc - floating point multiplication -----*- C -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is dual licensed under the MIT and the University of Illinois Open 6// Source Licenses. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file implements soft-float multiplication with the IEEE-754 default 11// rounding (to nearest, ties to even). 12// 13//===----------------------------------------------------------------------===// 14 15#include "fp_lib.h" 16 17static __inline fp_t __mulXf3__(fp_t a, fp_t b) { 18 const unsigned int aExponent = toRep(a) >> significandBits & maxExponent; 19 const unsigned int bExponent = toRep(b) >> significandBits & maxExponent; 20 const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit; 21 22 rep_t aSignificand = toRep(a) & significandMask; 23 rep_t bSignificand = toRep(b) & significandMask; 24 int scale = 0; 25 26 // Detect if a or b is zero, denormal, infinity, or NaN. 27 if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) { 28 29 const rep_t aAbs = toRep(a) & absMask; 30 const rep_t bAbs = toRep(b) & absMask; 31 32 // NaN * anything = qNaN 33 if (aAbs > infRep) return fromRep(toRep(a) | quietBit); 34 // anything * NaN = qNaN 35 if (bAbs > infRep) return fromRep(toRep(b) | quietBit); 36 37 if (aAbs == infRep) { 38 // infinity * non-zero = +/- infinity 39 if (bAbs) return fromRep(aAbs | productSign); 40 // infinity * zero = NaN 41 else return fromRep(qnanRep); 42 } 43 44 if (bAbs == infRep) { 45 //? non-zero * infinity = +/- infinity 46 if (aAbs) return fromRep(bAbs | productSign); 47 // zero * infinity = NaN 48 else return fromRep(qnanRep); 49 } 50 51 // zero * anything = +/- zero 52 if (!aAbs) return fromRep(productSign); 53 // anything * zero = +/- zero 54 if (!bAbs) return fromRep(productSign); 55 56 // one or both of a or b is denormal, the other (if applicable) is a 57 // normal number. Renormalize one or both of a and b, and set scale to 58 // include the necessary exponent adjustment. 59 if (aAbs < implicitBit) scale += normalize(&aSignificand); 60 if (bAbs < implicitBit) scale += normalize(&bSignificand); 61 } 62 63 // Or in the implicit significand bit. (If we fell through from the 64 // denormal path it was already set by normalize( ), but setting it twice 65 // won't hurt anything.) 66 aSignificand |= implicitBit; 67 bSignificand |= implicitBit; 68 69 // Get the significand of a*b. Before multiplying the significands, shift 70 // one of them left to left-align it in the field. Thus, the product will 71 // have (exponentBits + 2) integral digits, all but two of which must be 72 // zero. Normalizing this result is just a conditional left-shift by one 73 // and bumping the exponent accordingly. 74 rep_t productHi, productLo; 75 wideMultiply(aSignificand, bSignificand << exponentBits, 76 &productHi, &productLo); 77 78 int productExponent = aExponent + bExponent - exponentBias + scale; 79 80 // Normalize the significand, adjust exponent if needed. 81 if (productHi & implicitBit) productExponent++; 82 else wideLeftShift(&productHi, &productLo, 1); 83 84 // If we have overflowed the type, return +/- infinity. 85 if (productExponent >= maxExponent) return fromRep(infRep | productSign); 86 87 if (productExponent <= 0) { 88 // Result is denormal before rounding 89 // 90 // If the result is so small that it just underflows to zero, return 91 // a zero of the appropriate sign. Mathematically there is no need to 92 // handle this case separately, but we make it a special case to 93 // simplify the shift logic. 94 const unsigned int shift = REP_C(1) - (unsigned int)productExponent; 95 if (shift >= typeWidth) return fromRep(productSign); 96 97 // Otherwise, shift the significand of the result so that the round 98 // bit is the high bit of productLo. 99 wideRightShiftWithSticky(&productHi, &productLo, shift); 100 } 101 else { 102 // Result is normal before rounding; insert the exponent. 103 productHi &= significandMask; 104 productHi |= (rep_t)productExponent << significandBits; 105 } 106 107 // Insert the sign of the result: 108 productHi |= productSign; 109 110 // Final rounding. The final result may overflow to infinity, or underflow 111 // to zero, but those are the correct results in those cases. We use the 112 // default IEEE-754 round-to-nearest, ties-to-even rounding mode. 113 if (productLo > signBit) productHi++; 114 if (productLo == signBit) productHi += productHi & 1; 115 return fromRep(productHi); 116} 117