Joerg Sonnenberger | 493844d | 2014-05-28 15:08:05 +0000 | [diff] [blame] | 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 | |
Pirama Arumuga Nainar | 799172d | 2016-03-03 15:50:30 -0800 | [diff] [blame^] | 17 | static __inline fp_t __mulXf3__(fp_t a, fp_t b) { |
Joerg Sonnenberger | 493844d | 2014-05-28 15:08:05 +0000 | [diff] [blame] | 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 | } |