1//===-- lib/muldf3.c - Double-precision 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 double-precision soft-float multiplication
11// with the IEEE-754 default rounding (to nearest, ties to even).
12//
13//===----------------------------------------------------------------------===//
14
15#define DOUBLE_PRECISION
16#include "fp_lib.h"
17
18ARM_EABI_FNALIAS(dmul, muldf3)
19
20COMPILER_RT_ABI fp_t
21__muldf3(fp_t a, fp_t b) {
22
23    const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
24    const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
25    const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
26
27    rep_t aSignificand = toRep(a) & significandMask;
28    rep_t bSignificand = toRep(b) & significandMask;
29    int scale = 0;
30
31    // Detect if a or b is zero, denormal, infinity, or NaN.
32    if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
33
34        const rep_t aAbs = toRep(a) & absMask;
35        const rep_t bAbs = toRep(b) & absMask;
36
37        // NaN * anything = qNaN
38        if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
39        // anything * NaN = qNaN
40        if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
41
42        if (aAbs == infRep) {
43            // infinity * non-zero = +/- infinity
44            if (bAbs) return fromRep(aAbs | productSign);
45            // infinity * zero = NaN
46            else return fromRep(qnanRep);
47        }
48
49        if (bAbs == infRep) {
50            // non-zero * infinity = +/- infinity
51            if (aAbs) return fromRep(bAbs | productSign);
52            // zero * infinity = NaN
53            else return fromRep(qnanRep);
54        }
55
56        // zero * anything = +/- zero
57        if (!aAbs) return fromRep(productSign);
58        // anything * zero = +/- zero
59        if (!bAbs) return fromRep(productSign);
60
61        // one or both of a or b is denormal, the other (if applicable) is a
62        // normal number.  Renormalize one or both of a and b, and set scale to
63        // include the necessary exponent adjustment.
64        if (aAbs < implicitBit) scale += normalize(&aSignificand);
65        if (bAbs < implicitBit) scale += normalize(&bSignificand);
66    }
67
68    // Or in the implicit significand bit.  (If we fell through from the
69    // denormal path it was already set by normalize( ), but setting it twice
70    // won't hurt anything.)
71    aSignificand |= implicitBit;
72    bSignificand |= implicitBit;
73
74    // Get the significand of a*b.  Before multiplying the significands, shift
75    // one of them left to left-align it in the field.  Thus, the product will
76    // have (exponentBits + 2) integral digits, all but two of which must be
77    // zero.  Normalizing this result is just a conditional left-shift by one
78    // and bumping the exponent accordingly.
79    rep_t productHi, productLo;
80    wideMultiply(aSignificand, bSignificand << exponentBits,
81                 &productHi, &productLo);
82
83    int productExponent = aExponent + bExponent - exponentBias + scale;
84
85    // Normalize the significand, adjust exponent if needed.
86    if (productHi & implicitBit) productExponent++;
87    else wideLeftShift(&productHi, &productLo, 1);
88
89    // If we have overflowed the type, return +/- infinity.
90    if (productExponent >= maxExponent) return fromRep(infRep | productSign);
91
92    if (productExponent <= 0) {
93        // Result is denormal before rounding
94        //
95        // If the result is so small that it just underflows to zero, return
96        // a zero of the appropriate sign.  Mathematically there is no need to
97        // handle this case separately, but we make it a special case to
98        // simplify the shift logic.
99        const unsigned int shift = 1U - (unsigned int)productExponent;
100        if (shift >= typeWidth) return fromRep(productSign);
101
102        // Otherwise, shift the significand of the result so that the round
103        // bit is the high bit of productLo.
104        wideRightShiftWithSticky(&productHi, &productLo, shift);
105    }
106
107    else {
108        // Result is normal before rounding; insert the exponent.
109        productHi &= significandMask;
110        productHi |= (rep_t)productExponent << significandBits;
111    }
112
113    // Insert the sign of the result:
114    productHi |= productSign;
115
116    // Final rounding.  The final result may overflow to infinity, or underflow
117    // to zero, but those are the correct results in those cases.  We use the
118    // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
119    if (productLo > signBit) productHi++;
120    if (productLo == signBit) productHi += productHi & 1;
121    return fromRep(productHi);
122}
123