fp80.c revision 9899:0392ef94d766 
1/*
2 * Copyright (c) 2013, Andreas Sandberg
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 *
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above
12 *    copyright notice, this list of conditions and the following
13 *    disclaimer in the documentation and/or other materials provided
14 *    with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
17 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
18 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
19 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
20 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
22 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
23 * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
25 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
27 * OF THE POSSIBILITY OF SUCH DAMAGE.
28 */
29
30#include <fputils/fp80.h>
31#include "fpbits.h"
32
33#include <assert.h>
34#include <stdint.h>
35
36#include <stdio.h>
37
38typedef union {
39    uint64_t bits;
40    double value;
41} fp64_t;
42
43
44const fp80_t fp80_pinf = BUILD_FP80(0, 0, FP80_EXP_SPECIAL);
45const fp80_t fp80_ninf = BUILD_FP80(1, 0, FP80_EXP_SPECIAL);
46const fp80_t fp80_qnan = BUILD_FP80(0,  FP80_FRAC_QNAN, FP80_EXP_SPECIAL);
47const fp80_t fp80_qnani = BUILD_FP80(1, FP80_FRAC_QNANI, FP80_EXP_SPECIAL);
48const fp80_t fp80_snan = BUILD_FP80(0, FP80_FRAC_SNAN, FP80_EXP_SPECIAL);
49const fp80_t fp80_nan = BUILD_FP80(0, FP80_FRAC_QNAN, FP80_EXP_SPECIAL);
50
51static const fp64_t fp64_pinf = BUILD_FP64(0, 0, FP64_EXP_SPECIAL);
52static const fp64_t fp64_ninf = BUILD_FP64(1, 0, FP64_EXP_SPECIAL);
53static const fp64_t fp64_qnan = BUILD_FP64(0,  FP64_FRAC_QNAN,
54                                           FP64_EXP_SPECIAL);
55static const fp64_t fp64_nqnan = BUILD_FP64(1,  FP64_FRAC_QNAN,
56                                            FP64_EXP_SPECIAL);
57static const fp64_t fp64_qnani = BUILD_FP64(1, FP64_FRAC_QNANI,
58                                            FP64_EXP_SPECIAL);
59static const fp64_t fp64_snan = BUILD_FP64(0, FP64_FRAC_SNAN,
60                                           FP64_EXP_SPECIAL);
61static const fp64_t fp64_nsnan = BUILD_FP64(1, FP64_FRAC_SNAN,
62                                            FP64_EXP_SPECIAL);
63
64static double
65build_fp64(int sign, uint64_t frac, int exp)
66{
67    const fp64_t f = BUILD_FP64(sign, frac, exp);
68
69    return f.value;
70}
71
72int
73fp80_sgn(fp80_t fp80)
74{
75    return (fp80.repr.se & FP80_SIGN_BIT) ? -1 : 1;
76}
77
78int
79fp80_isspecial(fp80_t fp80)
80{
81    const int exp = FP80_EXP(fp80);
82
83    return exp == FP80_EXP_SPECIAL;
84}
85
86int
87fp80_isinf(fp80_t fp80)
88{
89    const uint64_t frac = FP80_FRAC(fp80);
90
91    return fp80_isspecial(fp80) && frac == 0 ? fp80_sgn(fp80) : 0;
92}
93
94
95int
96fp80_isqnan(fp80_t fp80)
97{
98    const uint64_t frac = FP80_FRAC(fp80);
99
100    return fp80_isspecial(fp80) && (frac & FP80_QNAN_BIT);
101}
102
103int
104fp80_isqnani(fp80_t fp80)
105{
106    const uint64_t frac_low = fp80.repr.fi & (FP80_FRAC_MASK >> 1);
107
108    return fp80_isqnan(fp80) && (fp80.repr.se & FP80_SIGN_BIT) && !frac_low;
109}
110
111int
112fp80_issnan(fp80_t fp80)
113{
114    const uint64_t frac = FP80_FRAC(fp80);
115
116    return fp80_isspecial(fp80) && !(frac & FP80_QNAN_BIT) && frac;
117}
118
119int
120fp80_isfinite(fp80_t fp80)
121{
122    return !fp80_isnan(fp80) && !fp80_isinf(fp80);
123}
124
125int
126fp80_isnan(fp80_t fp80)
127{
128    return fp80_issnan(fp80) || fp80_isqnan(fp80) ? fp80_sgn(fp80) : 0;
129}
130
131int
132fp80_iszero(fp80_t fp80)
133{
134    return fp80.repr.fi == 0 && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0;
135}
136
137int
138fp80_isnormal(fp80_t fp80)
139{
140    return FP80_EXP(fp80) != 0 && !fp80_isspecial(fp80) ?
141        fp80_sgn(fp80) : 0;
142}
143
144int
145fp80_issubnormal(fp80_t fp80)
146{
147    return FP80_FRAC(fp80) && FP80_EXP(fp80) == 0 ? fp80_sgn(fp80) : 0;
148}
149
150int
151fp80_classify(fp80_t fp80)
152{
153    if (fp80_issubnormal(fp80)) {
154        return FP_SUBNORMAL;
155    } else if (fp80_iszero(fp80)) {
156        return FP_ZERO;
157    } else if (fp80_isinf(fp80)) {
158        return FP_INFINITE;
159    } else if (fp80_isnan(fp80)) {
160        return FP_NAN;
161    } else {
162        assert(fp80_isfinite(fp80));
163        return FP_NORMAL;
164    }
165}
166
167double
168fp80_cvtd(fp80_t fp80)
169{
170    const int sign = fp80.repr.se & FP80_SIGN_BIT;
171
172    if (!fp80_isspecial(fp80)) {
173        const uint64_t frac = fp80.repr.fi;
174        const int unb_exp = FP80_EXP(fp80) - FP80_EXP_BIAS;
175        const int fp64_exp = unb_exp + FP64_EXP_BIAS;
176        const uint64_t fp64_frac = frac >> (FP80_FRAC_BITS - FP64_FRAC_BITS);
177
178        if (fp64_exp > 0 && fp64_exp < FP64_EXP_SPECIAL) {
179            /* These numbers fall in the range of what we can express
180             * as normals */
181            return build_fp64(sign, fp64_frac, fp64_exp);
182        } else if (fp64_exp <= 0) {
183            uint64_t fp64_denormal_frac = fp64_frac >> (-fp64_exp);
184            /* Generate a denormal or zero */
185            return build_fp64(sign, fp64_denormal_frac, 0);
186        } else {
187            /* Infinity */
188            return build_fp64(sign, 0, FP64_EXP_SPECIAL);
189        }
190    } else {
191        if (fp80_isinf(fp80)) {
192            return build_fp64(sign, 0, FP64_EXP_SPECIAL);
193        } else if (fp80_issnan(fp80)) {
194            return fp80_sgn(fp80) > 0 ? fp64_snan.value : fp64_nsnan.value;
195        } else if (fp80_isqnani(fp80)) {
196            return fp64_qnani.value;
197        } else {
198            assert(fp80_isqnan(fp80));
199            return fp80_sgn(fp80) > 0 ? fp64_qnan.value : fp64_nqnan.value;
200        }
201    }
202}
203
204fp80_t
205fp80_cvfd(double value)
206{
207    const fp64_t fp64 = { .value = value };
208    const uint64_t frac = FP64_FRAC(fp64);
209    const unsigned exp = FP64_EXP(fp64);
210    const int unb_exp = exp - FP64_EXP_BIAS;
211    const uint64_t fp80_frac = frac << (FP80_FRAC_BITS - FP64_FRAC_BITS);
212
213    if (exp != 0) {
214        // Normal, inf, nan
215        const unsigned fp80_exp = exp == FP64_EXP_SPECIAL ?
216            FP80_EXP_SPECIAL : (unb_exp + FP80_EXP_BIAS);
217        const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT,
218                                       fp80_frac, fp80_exp);
219        return fp80;
220    } else if (exp == 0 && frac == 0) {
221        // Zero
222        const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT, 0, 0);
223        return fp80;
224    } else {
225        // Denormal
226        uint64_t fp80_fi = fp80_frac;
227        int shift_amt = 0;
228        while (!(fp80_fi & FP80_INT_BIT)) {
229            fp80_fi <<= 1;
230            ++shift_amt;
231        }
232        const unsigned fp80_exp = (unb_exp - shift_amt) + FP80_EXP_BIAS;
233        const fp80_t fp80 = BUILD_FP80(fp64.bits & FP64_SIGN_BIT,
234                                       fp80_fi, fp80_exp);
235        return fp80;
236    }
237}
238
239void
240fp80_debug_dump(FILE *fout, fp80_t fp80)
241{
242    fprintf(fout, "sgn: %i, int: %i, frac: 0x%llx, exp: 0x%x (%i)\n",
243            fp80_sgn(fp80), !!(fp80.repr.fi & FP80_INT_BIT), FP80_FRAC(fp80),
244            FP80_EXP(fp80), FP80_EXP(fp80) - FP80_EXP_BIAS);
245}
246