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 #include "abi.h"
15
16 #define DOUBLE_PRECISION
17 #include "fp_lib.h"
18
19 ARM_EABI_FNALIAS(dmul, muldf3);
20
21 COMPILER_RT_ABI fp_t
__muldf3(fp_t a,fp_t b)22 __muldf3(fp_t a, fp_t b) {
23
24 const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
25 const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
26 const rep_t productSign = (toRep(a) ^ toRep(b)) & signBit;
27
28 rep_t aSignificand = toRep(a) & significandMask;
29 rep_t bSignificand = toRep(b) & significandMask;
30 int scale = 0;
31
32 // Detect if a or b is zero, denormal, infinity, or NaN.
33 if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
34
35 const rep_t aAbs = toRep(a) & absMask;
36 const rep_t bAbs = toRep(b) & absMask;
37
38 // NaN * anything = qNaN
39 if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
40 // anything * NaN = qNaN
41 if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
42
43 if (aAbs == infRep) {
44 // infinity * non-zero = +/- infinity
45 if (bAbs) return fromRep(aAbs | productSign);
46 // infinity * zero = NaN
47 else return fromRep(qnanRep);
48 }
49
50 if (bAbs == infRep) {
51 // non-zero * infinity = +/- infinity
52 if (aAbs) return fromRep(bAbs | productSign);
53 // zero * infinity = NaN
54 else return fromRep(qnanRep);
55 }
56
57 // zero * anything = +/- zero
58 if (!aAbs) return fromRep(productSign);
59 // anything * zero = +/- zero
60 if (!bAbs) return fromRep(productSign);
61
62 // one or both of a or b is denormal, the other (if applicable) is a
63 // normal number. Renormalize one or both of a and b, and set scale to
64 // include the necessary exponent adjustment.
65 if (aAbs < implicitBit) scale += normalize(&aSignificand);
66 if (bAbs < implicitBit) scale += normalize(&bSignificand);
67 }
68
69 // Or in the implicit significand bit. (If we fell through from the
70 // denormal path it was already set by normalize( ), but setting it twice
71 // won't hurt anything.)
72 aSignificand |= implicitBit;
73 bSignificand |= implicitBit;
74
75 // Get the significand of a*b. Before multiplying the significands, shift
76 // one of them left to left-align it in the field. Thus, the product will
77 // have (exponentBits + 2) integral digits, all but two of which must be
78 // zero. Normalizing this result is just a conditional left-shift by one
79 // and bumping the exponent accordingly.
80 rep_t productHi, productLo;
81 wideMultiply(aSignificand, bSignificand << exponentBits,
82 &productHi, &productLo);
83
84 int productExponent = aExponent + bExponent - exponentBias + scale;
85
86 // Normalize the significand, adjust exponent if needed.
87 if (productHi & implicitBit) productExponent++;
88 else wideLeftShift(&productHi, &productLo, 1);
89
90 // If we have overflowed the type, return +/- infinity.
91 if (productExponent >= maxExponent) return fromRep(infRep | productSign);
92
93 if (productExponent <= 0) {
94 // Result is denormal before rounding
95 //
96 // If the result is so small that it just underflows to zero, return
97 // a zero of the appropriate sign. Mathematically there is no need to
98 // handle this case separately, but we make it a special case to
99 // simplify the shift logic.
100 const int shift = 1 - productExponent;
101 if (shift >= typeWidth) return fromRep(productSign);
102
103 // Otherwise, shift the significand of the result so that the round
104 // bit is the high bit of productLo.
105 wideRightShiftWithSticky(&productHi, &productLo, shift);
106 }
107
108 else {
109 // Result is normal before rounding; insert the exponent.
110 productHi &= significandMask;
111 productHi |= (rep_t)productExponent << significandBits;
112 }
113
114 // Insert the sign of the result:
115 productHi |= productSign;
116
117 // Final rounding. The final result may overflow to infinity, or underflow
118 // to zero, but those are the correct results in those cases. We use the
119 // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
120 if (productLo > signBit) productHi++;
121 if (productLo == signBit) productHi += productHi & 1;
122 return fromRep(productHi);
123 }
124