fp_mul_impl.inc revision 493844deb81978ef7fbcc09dd52dd7dca6858a98 
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