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}