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
ARM_EABI_FNALIAS(dmul,muldf3)18 ARM_EABI_FNALIAS(dmul, muldf3)
19
20 COMPILER_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