GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libcompiler_rt/divdf3.c Lines: 0 56 0.0 %
Date: 2017-11-13 Branches: 0 32 0.0 %

Line Branch Exec Source
1
//===-- lib/divdf3.c - Double-precision division ------------------*- 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 division
11
// with the IEEE-754 default rounding (to nearest, ties to even).
12
//
13
// For simplicity, this implementation currently flushes denormals to zero.
14
// It should be a fairly straightforward exercise to implement gradual
15
// underflow with correct rounding.
16
//
17
//===----------------------------------------------------------------------===//
18
19
#define DOUBLE_PRECISION
20
#include "fp_lib.h"
21
22
ARM_EABI_FNALIAS(ddiv, divdf3)
23
24
COMPILER_RT_ABI fp_t
25
__divdf3(fp_t a, fp_t b) {
26
27
    const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
28
    const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
29
    const rep_t quotientSign = (toRep(a) ^ toRep(b)) & signBit;
30
31
    rep_t aSignificand = toRep(a) & significandMask;
32
    rep_t bSignificand = toRep(b) & significandMask;
33
    int scale = 0;
34
35
    // Detect if a or b is zero, denormal, infinity, or NaN.
36
    if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
37
38
        const rep_t aAbs = toRep(a) & absMask;
39
        const rep_t bAbs = toRep(b) & absMask;
40
41
        // NaN / anything = qNaN
42
        if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
43
        // anything / NaN = qNaN
44
        if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
45
46
        if (aAbs == infRep) {
47
            // infinity / infinity = NaN
48
            if (bAbs == infRep) return fromRep(qnanRep);
49
            // infinity / anything else = +/- infinity
50
            else return fromRep(aAbs | quotientSign);
51
        }
52
53
        // anything else / infinity = +/- 0
54
        if (bAbs == infRep) return fromRep(quotientSign);
55
56
        if (!aAbs) {
57
            // zero / zero = NaN
58
            if (!bAbs) return fromRep(qnanRep);
59
            // zero / anything else = +/- zero
60
            else return fromRep(quotientSign);
61
        }
62
        // anything else / zero = +/- infinity
63
        if (!bAbs) return fromRep(infRep | quotientSign);
64
65
        // one or both of a or b is denormal, the other (if applicable) is a
66
        // normal number.  Renormalize one or both of a and b, and set scale to
67
        // include the necessary exponent adjustment.
68
        if (aAbs < implicitBit) scale += normalize(&aSignificand);
69
        if (bAbs < implicitBit) scale -= normalize(&bSignificand);
70
    }
71
72
    // Or in the implicit significand bit.  (If we fell through from the
73
    // denormal path it was already set by normalize( ), but setting it twice
74
    // won't hurt anything.)
75
    aSignificand |= implicitBit;
76
    bSignificand |= implicitBit;
77
    int quotientExponent = aExponent - bExponent + scale;
78
79
    // Align the significand of b as a Q31 fixed-point number in the range
80
    // [1, 2.0) and get a Q32 approximate reciprocal using a small minimax
81
    // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2.  This
82
    // is accurate to about 3.5 binary digits.
83
    const uint32_t q31b = bSignificand >> 21;
84
    uint32_t recip32 = UINT32_C(0x7504f333) - q31b;
85
86
    // Now refine the reciprocal estimate using a Newton-Raphson iteration:
87
    //
88
    //     x1 = x0 * (2 - x0 * b)
89
    //
90
    // This doubles the number of correct binary digits in the approximation
91
    // with each iteration, so after three iterations, we have about 28 binary
92
    // digits of accuracy.
93
    uint32_t correction32;
94
    correction32 = -((uint64_t)recip32 * q31b >> 32);
95
    recip32 = (uint64_t)recip32 * correction32 >> 31;
96
    correction32 = -((uint64_t)recip32 * q31b >> 32);
97
    recip32 = (uint64_t)recip32 * correction32 >> 31;
98
    correction32 = -((uint64_t)recip32 * q31b >> 32);
99
    recip32 = (uint64_t)recip32 * correction32 >> 31;
100
101
    // recip32 might have overflowed to exactly zero in the preceding
102
    // computation if the high word of b is exactly 1.0.  This would sabotage
103
    // the full-width final stage of the computation that follows, so we adjust
104
    // recip32 downward by one bit.
105
    recip32--;
106
107
    // We need to perform one more iteration to get us to 56 binary digits;
108
    // The last iteration needs to happen with extra precision.
109
    const uint32_t q63blo = bSignificand << 11;
110
    uint64_t correction, reciprocal;
111
    correction = -((uint64_t)recip32*q31b + ((uint64_t)recip32*q63blo >> 32));
112
    uint32_t cHi = correction >> 32;
113
    uint32_t cLo = correction;
114
    reciprocal = (uint64_t)recip32*cHi + ((uint64_t)recip32*cLo >> 32);
115
116
    // We already adjusted the 32-bit estimate, now we need to adjust the final
117
    // 64-bit reciprocal estimate downward to ensure that it is strictly smaller
118
    // than the infinitely precise exact reciprocal.  Because the computation
119
    // of the Newton-Raphson step is truncating at every step, this adjustment
120
    // is small; most of the work is already done.
121
    reciprocal -= 2;
122
123
    // The numerical reciprocal is accurate to within 2^-56, lies in the
124
    // interval [0.5, 1.0), and is strictly smaller than the true reciprocal
125
    // of b.  Multiplying a by this reciprocal thus gives a numerical q = a/b
126
    // in Q53 with the following properties:
127
    //
128
    //    1. q < a/b
129
    //    2. q is in the interval [0.5, 2.0)
130
    //    3. the error in q is bounded away from 2^-53 (actually, we have a
131
    //       couple of bits to spare, but this is all we need).
132
133
    // We need a 64 x 64 multiply high to compute q, which isn't a basic
134
    // operation in C, so we need to be a little bit fussy.
135
    rep_t quotient, quotientLo;
136
    wideMultiply(aSignificand << 2, reciprocal, &quotient, &quotientLo);
137
138
    // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0).
139
    // In either case, we are going to compute a residual of the form
140
    //
141
    //     r = a - q*b
142
    //
143
    // We know from the construction of q that r satisfies:
144
    //
145
    //     0 <= r < ulp(q)*b
146
    //
147
    // if r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
148
    // already have the correct result.  The exact halfway case cannot occur.
149
    // We also take this time to right shift quotient if it falls in the [1,2)
150
    // range and adjust the exponent accordingly.
151
    rep_t residual;
152
    if (quotient < (implicitBit << 1)) {
153
        residual = (aSignificand << 53) - quotient * bSignificand;
154
        quotientExponent--;
155
    } else {
156
        quotient >>= 1;
157
        residual = (aSignificand << 52) - quotient * bSignificand;
158
    }
159
160
    const int writtenExponent = quotientExponent + exponentBias;
161
162
    if (writtenExponent >= maxExponent) {
163
        // If we have overflowed the exponent, return infinity.
164
        return fromRep(infRep | quotientSign);
165
    }
166
167
    else if (writtenExponent < 1) {
168
        // Flush denormals to zero.  In the future, it would be nice to add
169
        // code to round them correctly.
170
        return fromRep(quotientSign);
171
    }
172
173
    else {
174
        const bool round = (residual << 1) > bSignificand;
175
        // Clear the implicit bit
176
        rep_t absResult = quotient & significandMask;
177
        // Insert the exponent
178
        absResult |= (rep_t)writtenExponent << significandBits;
179
        // Round
180
        absResult += round;
181
        // Insert the sign and return
182
        const double result = fromRep(absResult | quotientSign);
183
        return result;
184
    }
185
}