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Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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1 /* origin: FreeBSD /usr/src/lib/msun/ld80/s_exp2l.c and /usr/src/lib/msun/ld128/ s_exp2l.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/ld80/s_exp2l.c and
2 * /usr/src/lib/msun/ld128/s_exp2l.c */
2 /*- 3 /*-
3 * Copyright (c) 2005-2008 David Schultz <das@FreeBSD.ORG> 4 * Copyright (c) 2005-2008 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved. 5 * All rights reserved.
5 * 6 *
6 * Redistribution and use in source and binary forms, with or without 7 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions 8 * modification, are permitted provided that the following conditions
8 * are met: 9 * are met:
9 * 1. Redistributions of source code must retain the above copyright 10 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer. 11 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright 12 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the 13 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution. 14 * documentation and/or other materials provided with the distribution.
14 * 15 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE. 26 * SUCH DAMAGE.
26 */ 27 */
27 28
28 #include "libm.h" 29 #include "libm.h"
29 30
30 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 31 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
31 long double exp2l(long double x) 32 long double exp2l(long double x) {
32 { 33 return exp2(x);
33 » return exp2(x);
34 } 34 }
35 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 35 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
36 #define TBLBITS 7 36 #define TBLBITS 7
37 #define TBLSIZE (1 << TBLBITS) 37 #define TBLSIZE (1 << TBLBITS)
38 38
39 static const double 39 static const double redux = 0x1.8p63 / TBLSIZE, P1 = 0x1.62e42fefa39efp-1,
40 redux = 0x1.8p63 / TBLSIZE, 40 P2 = 0x1.ebfbdff82c58fp-3, P3 = 0x1.c6b08d7049fap-5,
41 P1 = 0x1.62e42fefa39efp-1, 41 P4 = 0x1.3b2ab6fba4da5p-7, P5 = 0x1.5d8804780a736p-10,
42 P2 = 0x1.ebfbdff82c58fp-3, 42 P6 = 0x1.430918835e33dp-13;
43 P3 = 0x1.c6b08d7049fap-5,
44 P4 = 0x1.3b2ab6fba4da5p-7,
45 P5 = 0x1.5d8804780a736p-10,
46 P6 = 0x1.430918835e33dp-13;
47 43
48 static const double tbl[TBLSIZE * 2] = { 44 static const double tbl[TBLSIZE * 2] = {
49 0x1.6a09e667f3bcdp-1, -0x1.bdd3413b2648p-55, 45 0x1.6a09e667f3bcdp-1,
50 0x1.6c012750bdabfp-1, -0x1.2895667ff0cp-57, 46 -0x1.bdd3413b2648p-55,
51 0x1.6dfb23c651a2fp-1, -0x1.bbe3a683c88p-58, 47 0x1.6c012750bdabfp-1,
52 0x1.6ff7df9519484p-1, -0x1.83c0f25860fp-56, 48 -0x1.2895667ff0cp-57,
53 0x1.71f75e8ec5f74p-1, -0x1.16e4786887bp-56, 49 0x1.6dfb23c651a2fp-1,
54 0x1.73f9a48a58174p-1, -0x1.0a8d96c65d5p-55, 50 -0x1.bbe3a683c88p-58,
55 0x1.75feb564267c9p-1, -0x1.0245957316ep-55, 51 0x1.6ff7df9519484p-1,
56 0x1.780694fde5d3fp-1, 0x1.866b80a0216p-55, 52 -0x1.83c0f25860fp-56,
57 0x1.7a11473eb0187p-1, -0x1.41577ee0499p-56, 53 0x1.71f75e8ec5f74p-1,
58 0x1.7c1ed0130c132p-1, 0x1.f124cd1164ep-55, 54 -0x1.16e4786887bp-56,
59 0x1.7e2f336cf4e62p-1, 0x1.05d02ba157ap-57, 55 0x1.73f9a48a58174p-1,
60 0x1.80427543e1a12p-1, -0x1.27c86626d97p-55, 56 -0x1.0a8d96c65d5p-55,
61 0x1.82589994cce13p-1, -0x1.d4c1dd41533p-55, 57 0x1.75feb564267c9p-1,
62 0x1.8471a4623c7adp-1, -0x1.8d684a341cep-56, 58 -0x1.0245957316ep-55,
63 0x1.868d99b4492edp-1, -0x1.fc6f89bd4f68p-55, 59 0x1.780694fde5d3fp-1,
64 0x1.88ac7d98a6699p-1, 0x1.994c2f37cb5p-55, 60 0x1.866b80a0216p-55,
65 0x1.8ace5422aa0dbp-1, 0x1.6e9f156864bp-55, 61 0x1.7a11473eb0187p-1,
66 0x1.8cf3216b5448cp-1, -0x1.0d55e32e9e4p-57, 62 -0x1.41577ee0499p-56,
67 0x1.8f1ae99157736p-1, 0x1.5cc13a2e397p-56, 63 0x1.7c1ed0130c132p-1,
68 0x1.9145b0b91ffc6p-1, -0x1.dd6792e5825p-55, 64 0x1.f124cd1164ep-55,
69 0x1.93737b0cdc5e5p-1, -0x1.75fc781b58p-58, 65 0x1.7e2f336cf4e62p-1,
70 0x1.95a44cbc8520fp-1, -0x1.64b7c96a5fp-57, 66 0x1.05d02ba157ap-57,
71 0x1.97d829fde4e5p-1, -0x1.d185b7c1b86p-55, 67 0x1.80427543e1a12p-1,
72 0x1.9a0f170ca07bap-1, -0x1.173bd91cee6p-55, 68 -0x1.27c86626d97p-55,
73 0x1.9c49182a3f09p-1, 0x1.c7c46b071f2p-57, 69 0x1.82589994cce13p-1,
74 0x1.9e86319e32323p-1, 0x1.824ca78e64cp-57, 70 -0x1.d4c1dd41533p-55,
75 0x1.a0c667b5de565p-1, -0x1.359495d1cd5p-55, 71 0x1.8471a4623c7adp-1,
76 0x1.a309bec4a2d33p-1, 0x1.6305c7ddc368p-55, 72 -0x1.8d684a341cep-56,
77 0x1.a5503b23e255dp-1, -0x1.d2f6edb8d42p-55, 73 0x1.868d99b4492edp-1,
78 0x1.a799e1330b358p-1, 0x1.bcb7ecac564p-55, 74 -0x1.fc6f89bd4f68p-55,
79 0x1.a9e6b5579fdbfp-1, 0x1.0fac90ef7fdp-55, 75 0x1.88ac7d98a6699p-1,
80 0x1.ac36bbfd3f37ap-1, -0x1.f9234cae76dp-56, 76 0x1.994c2f37cb5p-55,
81 0x1.ae89f995ad3adp-1, 0x1.7a1cd345dcc8p-55, 77 0x1.8ace5422aa0dbp-1,
82 0x1.b0e07298db666p-1, -0x1.bdef54c80e4p-55, 78 0x1.6e9f156864bp-55,
83 0x1.b33a2b84f15fbp-1, -0x1.2805e3084d8p-58, 79 0x1.8cf3216b5448cp-1,
84 0x1.b59728de5593ap-1, -0x1.c71dfbbba6ep-55, 80 -0x1.0d55e32e9e4p-57,
85 0x1.b7f76f2fb5e47p-1, -0x1.5584f7e54acp-57, 81 0x1.8f1ae99157736p-1,
86 0x1.ba5b030a1064ap-1, -0x1.efcd30e5429p-55, 82 0x1.5cc13a2e397p-56,
87 0x1.bcc1e904bc1d2p-1, 0x1.23dd07a2d9fp-56, 83 0x1.9145b0b91ffc6p-1,
88 0x1.bf2c25bd71e09p-1, -0x1.efdca3f6b9c8p-55, 84 -0x1.dd6792e5825p-55,
89 0x1.c199bdd85529cp-1, 0x1.11065895049p-56, 85 0x1.93737b0cdc5e5p-1,
90 0x1.c40ab5fffd07ap-1, 0x1.b4537e083c6p-55, 86 -0x1.75fc781b58p-58,
91 0x1.c67f12e57d14bp-1, 0x1.2884dff483c8p-55, 87 0x1.95a44cbc8520fp-1,
92 0x1.c8f6d9406e7b5p-1, 0x1.1acbc48805cp-57, 88 -0x1.64b7c96a5fp-57,
93 0x1.cb720dcef9069p-1, 0x1.503cbd1e94ap-57, 89 0x1.97d829fde4e5p-1,
94 0x1.cdf0b555dc3fap-1, -0x1.dd83b53829dp-56, 90 -0x1.d185b7c1b86p-55,
95 0x1.d072d4a07897cp-1, -0x1.cbc3743797a8p-55, 91 0x1.9a0f170ca07bap-1,
96 0x1.d2f87080d89f2p-1, -0x1.d487b719d858p-55, 92 -0x1.173bd91cee6p-55,
97 0x1.d5818dcfba487p-1, 0x1.2ed02d75b37p-56, 93 0x1.9c49182a3f09p-1,
98 0x1.d80e316c98398p-1, -0x1.11ec18bedep-55, 94 0x1.c7c46b071f2p-57,
99 0x1.da9e603db3285p-1, 0x1.c2300696db5p-55, 95 0x1.9e86319e32323p-1,
100 0x1.dd321f301b46p-1, 0x1.2da5778f019p-55, 96 0x1.824ca78e64cp-57,
101 0x1.dfc97337b9b5fp-1, -0x1.1a5cd4f184b8p-55, 97 0x1.a0c667b5de565p-1,
102 0x1.e264614f5a129p-1, -0x1.7b627817a148p-55, 98 -0x1.359495d1cd5p-55,
103 0x1.e502ee78b3ff6p-1, 0x1.39e8980a9cdp-56, 99 0x1.a309bec4a2d33p-1,
104 0x1.e7a51fbc74c83p-1, 0x1.2d522ca0c8ep-55, 100 0x1.6305c7ddc368p-55,
105 0x1.ea4afa2a490dap-1, -0x1.e9c23179c288p-55, 101 0x1.a5503b23e255dp-1,
106 0x1.ecf482d8e67f1p-1, -0x1.c93f3b411ad8p-55, 102 -0x1.d2f6edb8d42p-55,
107 0x1.efa1bee615a27p-1, 0x1.dc7f486a4b68p-55, 103 0x1.a799e1330b358p-1,
108 0x1.f252b376bba97p-1, 0x1.3a1a5bf0d8e8p-55, 104 0x1.bcb7ecac564p-55,
109 0x1.f50765b6e454p-1, 0x1.9d3e12dd8a18p-55, 105 0x1.a9e6b5579fdbfp-1,
110 0x1.f7bfdad9cbe14p-1, -0x1.dbb12d00635p-55, 106 0x1.0fac90ef7fdp-55,
111 0x1.fa7c1819e90d8p-1, 0x1.74853f3a593p-56, 107 0x1.ac36bbfd3f37ap-1,
112 0x1.fd3c22b8f71f1p-1, 0x1.2eb74966578p-58, 108 -0x1.f9234cae76dp-56,
113 0x1p+0, 0x0p+0, 109 0x1.ae89f995ad3adp-1,
114 0x1.0163da9fb3335p+0, 0x1.b61299ab8cd8p-54, 110 0x1.7a1cd345dcc8p-55,
115 0x1.02c9a3e778061p+0, -0x1.19083535b08p-56, 111 0x1.b0e07298db666p-1,
116 0x1.04315e86e7f85p+0, -0x1.0a31c1977c98p-54, 112 -0x1.bdef54c80e4p-55,
117 0x1.059b0d3158574p+0, 0x1.d73e2a475b4p-55, 113 0x1.b33a2b84f15fbp-1,
118 0x1.0706b29ddf6dep+0, -0x1.c91dfe2b13cp-55, 114 -0x1.2805e3084d8p-58,
119 0x1.0874518759bc8p+0, 0x1.186be4bb284p-57, 115 0x1.b59728de5593ap-1,
120 0x1.09e3ecac6f383p+0, 0x1.14878183161p-54, 116 -0x1.c71dfbbba6ep-55,
121 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc61p-54, 117 0x1.b7f76f2fb5e47p-1,
122 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f8p-54, 118 -0x1.5584f7e54acp-57,
123 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c58p-59, 119 0x1.ba5b030a1064ap-1,
124 0x1.0fb66affed31bp+0, -0x1.b9bedc44ebcp-57, 120 -0x1.efcd30e5429p-55,
125 0x1.11301d0125b51p+0, -0x1.6c51039449bp-54, 121 0x1.bcc1e904bc1d2p-1,
126 0x1.12abdc06c31ccp+0, -0x1.1b514b36ca8p-58, 122 0x1.23dd07a2d9fp-56,
127 0x1.1429aaea92dep+0, -0x1.32fbf9af1368p-54, 123 0x1.bf2c25bd71e09p-1,
128 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeabp-55, 124 -0x1.efdca3f6b9c8p-55,
129 0x1.172b83c7d517bp+0, -0x1.19041b9d78ap-55, 125 0x1.c199bdd85529cp-1,
130 0x1.18af9388c8deap+0, -0x1.11023d1970f8p-54, 126 0x1.11065895049p-56,
131 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4969p-55, 127 0x1.c40ab5fffd07ap-1,
132 0x1.1bbe084045cd4p+0, -0x1.95386352ef6p-54, 128 0x1.b4537e083c6p-55,
133 0x1.1d4873168b9aap+0, 0x1.e016e00a264p-54, 129 0x1.c67f12e57d14bp-1,
134 0x1.1ed5022fcd91dp+0, -0x1.1df98027bb78p-54, 130 0x1.2884dff483c8p-55,
135 0x1.2063b88628cd6p+0, 0x1.dc775814a85p-55, 131 0x1.c8f6d9406e7b5p-1,
136 0x1.21f49917ddc96p+0, 0x1.2a97e9494a6p-55, 132 0x1.1acbc48805cp-57,
137 0x1.2387a6e756238p+0, 0x1.9b07eb6c7058p-54, 133 0x1.cb720dcef9069p-1,
138 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f5p-55, 134 0x1.503cbd1e94ap-57,
139 0x1.26b4565e27cddp+0, 0x1.2bd339940eap-55, 135 0x1.cdf0b555dc3fap-1,
140 0x1.284dfe1f56381p+0, -0x1.a4c3a8c3f0d8p-54, 136 -0x1.dd83b53829dp-56,
141 0x1.29e9df51fdee1p+0, 0x1.612e8afad12p-55, 137 0x1.d072d4a07897cp-1,
142 0x1.2b87fd0dad99p+0, -0x1.10adcd6382p-59, 138 -0x1.cbc3743797a8p-55,
143 0x1.2d285a6e4030bp+0, 0x1.0024754db42p-54, 139 0x1.d2f87080d89f2p-1,
144 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d524p-56, 140 -0x1.d487b719d858p-55,
145 0x1.306fe0a31b715p+0, 0x1.6f46ad23183p-55, 141 0x1.d5818dcfba487p-1,
146 0x1.32170fc4cd831p+0, 0x1.a9ce78e1804p-55, 142 0x1.2ed02d75b37p-56,
147 0x1.33c08b26416ffp+0, 0x1.327218436598p-54, 143 0x1.d80e316c98398p-1,
148 0x1.356c55f929ff1p+0, -0x1.b5cee5c4e46p-55, 144 -0x1.11ec18bedep-55,
149 0x1.371a7373aa9cbp+0, -0x1.63aeabf42ebp-54, 145 0x1.da9e603db3285p-1,
150 0x1.38cae6d05d866p+0, -0x1.e958d3c99048p-54, 146 0x1.c2300696db5p-55,
151 0x1.3a7db34e59ff7p+0, -0x1.5e436d661f6p-56, 147 0x1.dd321f301b46p-1,
152 0x1.3c32dc313a8e5p+0, -0x1.efff8375d2ap-54, 148 0x1.2da5778f019p-55,
153 0x1.3dea64c123422p+0, 0x1.ada0911f09fp-55, 149 0x1.dfc97337b9b5fp-1,
154 0x1.3fa4504ac801cp+0, -0x1.7d023f956fap-54, 150 -0x1.1a5cd4f184b8p-55,
155 0x1.4160a21f72e2ap+0, -0x1.ef3691c309p-58, 151 0x1.e264614f5a129p-1,
156 0x1.431f5d950a897p+0, -0x1.1c7dde35f7ap-55, 152 -0x1.7b627817a148p-55,
157 0x1.44e086061892dp+0, 0x1.89b7a04ef8p-59, 153 0x1.e502ee78b3ff6p-1,
158 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a8p-54, 154 0x1.39e8980a9cdp-56,
159 0x1.486a2b5c13cdp+0, 0x1.3c1a3b69062p-56, 155 0x1.e7a51fbc74c83p-1,
160 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be8p-54, 156 0x1.2d522ca0c8ep-55,
161 0x1.4bfdad5362a27p+0, 0x1.d4397afec42p-56, 157 0x1.ea4afa2a490dap-1,
162 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a78p-54, 158 -0x1.e9c23179c288p-55,
163 0x1.4f9b2769d2ca7p+0, -0x1.4b309d25958p-54, 159 0x1.ecf482d8e67f1p-1,
164 0x1.516daa2cf6642p+0, -0x1.f768569bd94p-55, 160 -0x1.c93f3b411ad8p-55,
165 0x1.5342b569d4f82p+0, -0x1.07abe1db13dp-55, 161 0x1.efa1bee615a27p-1,
166 0x1.551a4ca5d920fp+0, -0x1.d689cefede6p-55, 162 0x1.dc7f486a4b68p-55,
167 0x1.56f4736b527dap+0, 0x1.9bb2c011d938p-54, 163 0x1.f252b376bba97p-1,
168 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1ep-55, 164 0x1.3a1a5bf0d8e8p-55,
169 0x1.5ab07dd485429p+0, 0x1.6324c0546478p-54, 165 0x1.f50765b6e454p-1,
170 0x1.5c9268a5946b7p+0, 0x1.c4b1b81698p-60, 166 0x1.9d3e12dd8a18p-55,
171 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e68p-54, 167 0x1.f7bfdad9cbe14p-1,
172 0x1.605e1b976dc09p+0, -0x1.3e2429b56de8p-54, 168 -0x1.dbb12d00635p-55,
173 0x1.6247eb03a5585p+0, -0x1.383c17e40b48p-54, 169 0x1.fa7c1819e90d8p-1,
174 0x1.6434634ccc32p+0, -0x1.c483c759d89p-55, 170 0x1.74853f3a593p-56,
175 0x1.6623882552225p+0, -0x1.bb60987591cp-54, 171 0x1.fd3c22b8f71f1p-1,
176 0x1.68155d44ca973p+0, 0x1.038ae44f74p-57, 172 0x1.2eb74966578p-58,
173 0x1p+0,
174 0x0p+0,
175 0x1.0163da9fb3335p+0,
176 0x1.b61299ab8cd8p-54,
177 0x1.02c9a3e778061p+0,
178 -0x1.19083535b08p-56,
179 0x1.04315e86e7f85p+0,
180 -0x1.0a31c1977c98p-54,
181 0x1.059b0d3158574p+0,
182 0x1.d73e2a475b4p-55,
183 0x1.0706b29ddf6dep+0,
184 -0x1.c91dfe2b13cp-55,
185 0x1.0874518759bc8p+0,
186 0x1.186be4bb284p-57,
187 0x1.09e3ecac6f383p+0,
188 0x1.14878183161p-54,
189 0x1.0b5586cf9890fp+0,
190 0x1.8a62e4adc61p-54,
191 0x1.0cc922b7247f7p+0,
192 0x1.01edc16e24f8p-54,
193 0x1.0e3ec32d3d1a2p+0,
194 0x1.03a1727c58p-59,
195 0x1.0fb66affed31bp+0,
196 -0x1.b9bedc44ebcp-57,
197 0x1.11301d0125b51p+0,
198 -0x1.6c51039449bp-54,
199 0x1.12abdc06c31ccp+0,
200 -0x1.1b514b36ca8p-58,
201 0x1.1429aaea92dep+0,
202 -0x1.32fbf9af1368p-54,
203 0x1.15a98c8a58e51p+0,
204 0x1.2406ab9eeabp-55,
205 0x1.172b83c7d517bp+0,
206 -0x1.19041b9d78ap-55,
207 0x1.18af9388c8deap+0,
208 -0x1.11023d1970f8p-54,
209 0x1.1a35beb6fcb75p+0,
210 0x1.e5b4c7b4969p-55,
211 0x1.1bbe084045cd4p+0,
212 -0x1.95386352ef6p-54,
213 0x1.1d4873168b9aap+0,
214 0x1.e016e00a264p-54,
215 0x1.1ed5022fcd91dp+0,
216 -0x1.1df98027bb78p-54,
217 0x1.2063b88628cd6p+0,
218 0x1.dc775814a85p-55,
219 0x1.21f49917ddc96p+0,
220 0x1.2a97e9494a6p-55,
221 0x1.2387a6e756238p+0,
222 0x1.9b07eb6c7058p-54,
223 0x1.251ce4fb2a63fp+0,
224 0x1.ac155bef4f5p-55,
225 0x1.26b4565e27cddp+0,
226 0x1.2bd339940eap-55,
227 0x1.284dfe1f56381p+0,
228 -0x1.a4c3a8c3f0d8p-54,
229 0x1.29e9df51fdee1p+0,
230 0x1.612e8afad12p-55,
231 0x1.2b87fd0dad99p+0,
232 -0x1.10adcd6382p-59,
233 0x1.2d285a6e4030bp+0,
234 0x1.0024754db42p-54,
235 0x1.2ecafa93e2f56p+0,
236 0x1.1ca0f45d524p-56,
237 0x1.306fe0a31b715p+0,
238 0x1.6f46ad23183p-55,
239 0x1.32170fc4cd831p+0,
240 0x1.a9ce78e1804p-55,
241 0x1.33c08b26416ffp+0,
242 0x1.327218436598p-54,
243 0x1.356c55f929ff1p+0,
244 -0x1.b5cee5c4e46p-55,
245 0x1.371a7373aa9cbp+0,
246 -0x1.63aeabf42ebp-54,
247 0x1.38cae6d05d866p+0,
248 -0x1.e958d3c99048p-54,
249 0x1.3a7db34e59ff7p+0,
250 -0x1.5e436d661f6p-56,
251 0x1.3c32dc313a8e5p+0,
252 -0x1.efff8375d2ap-54,
253 0x1.3dea64c123422p+0,
254 0x1.ada0911f09fp-55,
255 0x1.3fa4504ac801cp+0,
256 -0x1.7d023f956fap-54,
257 0x1.4160a21f72e2ap+0,
258 -0x1.ef3691c309p-58,
259 0x1.431f5d950a897p+0,
260 -0x1.1c7dde35f7ap-55,
261 0x1.44e086061892dp+0,
262 0x1.89b7a04ef8p-59,
263 0x1.46a41ed1d0057p+0,
264 0x1.c944bd1648a8p-54,
265 0x1.486a2b5c13cdp+0,
266 0x1.3c1a3b69062p-56,
267 0x1.4a32af0d7d3dep+0,
268 0x1.9cb62f3d1be8p-54,
269 0x1.4bfdad5362a27p+0,
270 0x1.d4397afec42p-56,
271 0x1.4dcb299fddd0dp+0,
272 0x1.8ecdbbc6a78p-54,
273 0x1.4f9b2769d2ca7p+0,
274 -0x1.4b309d25958p-54,
275 0x1.516daa2cf6642p+0,
276 -0x1.f768569bd94p-55,
277 0x1.5342b569d4f82p+0,
278 -0x1.07abe1db13dp-55,
279 0x1.551a4ca5d920fp+0,
280 -0x1.d689cefede6p-55,
281 0x1.56f4736b527dap+0,
282 0x1.9bb2c011d938p-54,
283 0x1.58d12d497c7fdp+0,
284 0x1.295e15b9a1ep-55,
285 0x1.5ab07dd485429p+0,
286 0x1.6324c0546478p-54,
287 0x1.5c9268a5946b7p+0,
288 0x1.c4b1b81698p-60,
289 0x1.5e76f15ad2148p+0,
290 0x1.ba6f93080e68p-54,
291 0x1.605e1b976dc09p+0,
292 -0x1.3e2429b56de8p-54,
293 0x1.6247eb03a5585p+0,
294 -0x1.383c17e40b48p-54,
295 0x1.6434634ccc32p+0,
296 -0x1.c483c759d89p-55,
297 0x1.6623882552225p+0,
298 -0x1.bb60987591cp-54,
299 0x1.68155d44ca973p+0,
300 0x1.038ae44f74p-57,
177 }; 301 };
178 302
179 /* 303 /*
180 * exp2l(x): compute the base 2 exponential of x 304 * exp2l(x): compute the base 2 exponential of x
181 * 305 *
182 * Accuracy: Peak error < 0.511 ulp. 306 * Accuracy: Peak error < 0.511 ulp.
183 * 307 *
184 * Method: (equally-spaced tables) 308 * Method: (equally-spaced tables)
185 * 309 *
186 * Reduce x: 310 * Reduce x:
187 * x = 2**k + y, for integer k and |y| <= 1/2. 311 * x = 2**k + y, for integer k and |y| <= 1/2.
188 * Thus we have exp2l(x) = 2**k * exp2(y). 312 * Thus we have exp2l(x) = 2**k * exp2(y).
189 * 313 *
190 * Reduce y: 314 * Reduce y:
191 * y = i/TBLSIZE + z for integer i near y * TBLSIZE. 315 * y = i/TBLSIZE + z for integer i near y * TBLSIZE.
192 * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), 316 * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),
193 * with |z| <= 2**-(TBLBITS+1). 317 * with |z| <= 2**-(TBLBITS+1).
194 * 318 *
195 * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a 319 * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a
196 * degree-6 minimax polynomial with maximum error under 2**-69. 320 * degree-6 minimax polynomial with maximum error under 2**-69.
197 * The table entries each have 104 bits of accuracy, encoded as 321 * The table entries each have 104 bits of accuracy, encoded as
198 * a pair of double precision values. 322 * a pair of double precision values.
199 */ 323 */
200 long double exp2l(long double x) 324 long double exp2l(long double x) {
201 { 325 union ldshape u = {x};
202 » union ldshape u = {x}; 326 int e = u.i.se & 0x7fff;
203 » int e = u.i.se & 0x7fff; 327 long double r, z;
204 » long double r, z; 328 uint32_t i0;
205 » uint32_t i0; 329 union {
206 » union {uint32_t u; int32_t i;} k; 330 uint32_t u;
331 int32_t i;
332 } k;
207 333
208 » /* Filter out exceptional cases. */ 334 /* Filter out exceptional cases. */
209 » if (e >= 0x3fff + 13) { /* |x| >= 8192 or x is NaN */ 335 if (e >= 0x3fff + 13) { /* |x| >= 8192 or x is NaN */
210 » » if (u.i.se >= 0x3fff + 14 && u.i.se >> 15 == 0) 336 if (u.i.se >= 0x3fff + 14 && u.i.se >> 15 == 0)
211 » » » /* overflow */ 337 /* overflow */
212 » » » return x * 0x1p16383L; 338 return x * 0x1p16383L;
213 » » if (e == 0x7fff) /* -inf or -nan */ 339 if (e == 0x7fff) /* -inf or -nan */
214 » » » return -1/x; 340 return -1 / x;
215 » » if (x < -16382) { 341 if (x < -16382) {
216 » » » if (x <= -16446 || x - 0x1p63 + 0x1p63 != x) 342 if (x <= -16446 || x - 0x1p63 + 0x1p63 != x)
217 » » » » /* underflow */ 343 /* underflow */
218 » » » » FORCE_EVAL((float)(-0x1p-149/x)); 344 FORCE_EVAL((float)(-0x1p-149 / x));
219 » » » if (x <= -16446) 345 if (x <= -16446)
220 » » » » return 0; 346 return 0;
221 » » } 347 }
222 » } else if (e < 0x3fff - 64) { 348 } else if (e < 0x3fff - 64) {
223 » » return 1 + x; 349 return 1 + x;
224 » } 350 }
225 351
226 » /* 352 /*
227 » * Reduce x, computing z, i0, and k. The low bits of x + redux 353 * Reduce x, computing z, i0, and k. The low bits of x + redux
228 » * contain the 16-bit integer part of the exponent (k) followed by 354 * contain the 16-bit integer part of the exponent (k) followed by
229 » * TBLBITS fractional bits (i0). We use bit tricks to extract these 355 * TBLBITS fractional bits (i0). We use bit tricks to extract these
230 » * as integers, then set z to the remainder. 356 * as integers, then set z to the remainder.
231 » * 357 *
232 » * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8. 358 * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8.
233 » * Then the low-order word of x + redux is 0x000abc12, 359 * Then the low-order word of x + redux is 0x000abc12,
234 » * We split this into k = 0xabc and i0 = 0x12 (adjusted to 360 * We split this into k = 0xabc and i0 = 0x12 (adjusted to
235 » * index into the table), then we compute z = 0x0.003456p0. 361 * index into the table), then we compute z = 0x0.003456p0.
236 » */ 362 */
237 » u.f = x + redux; 363 u.f = x + redux;
238 » i0 = u.i.m + TBLSIZE / 2; 364 i0 = u.i.m + TBLSIZE / 2;
239 » k.u = i0 / TBLSIZE * TBLSIZE; 365 k.u = i0 / TBLSIZE * TBLSIZE;
240 » k.i /= TBLSIZE; 366 k.i /= TBLSIZE;
241 » i0 %= TBLSIZE; 367 i0 %= TBLSIZE;
242 » u.f -= redux; 368 u.f -= redux;
243 » z = x - u.f; 369 z = x - u.f;
244 370
245 » /* Compute r = exp2l(y) = exp2lt[i0] * p(z). */ 371 /* Compute r = exp2l(y) = exp2lt[i0] * p(z). */
246 » long double t_hi = tbl[2*i0]; 372 long double t_hi = tbl[2 * i0];
247 » long double t_lo = tbl[2*i0 + 1]; 373 long double t_lo = tbl[2 * i0 + 1];
248 » /* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */ 374 /* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */
249 » r = t_lo + (t_hi + t_lo) * z * (P1 + z * (P2 + z * (P3 + z * (P4 375 r = t_lo +
250 » + z * (P5 + z * P6))))) + t_hi; 376 (t_hi + t_lo) * z *
377 (P1 + z * (P2 + z * (P3 + z * (P4 + z * (P5 + z * P6))))) +
378 t_hi;
251 379
252 » return scalbnl(r, k.i); 380 return scalbnl(r, k.i);
253 } 381 }
254 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 382 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
255 #define TBLBITS 7 383 #define TBLBITS 7
256 #define TBLSIZE (1 << TBLBITS) 384 #define TBLSIZE (1 << TBLBITS)
257 385
258 static const long double 386 static const long double P1 = 0x1.62e42fefa39ef35793c7673007e6p-1L,
259 P1 = 0x1.62e42fefa39ef35793c7673007e6p-1L, 387 P2 = 0x1.ebfbdff82c58ea86f16b06ec9736p-3L,
260 P2 = 0x1.ebfbdff82c58ea86f16b06ec9736p-3L, 388 P3 = 0x1.c6b08d704a0bf8b33a762bad3459p-5L,
261 P3 = 0x1.c6b08d704a0bf8b33a762bad3459p-5L, 389 P4 = 0x1.3b2ab6fba4e7729ccbbe0b4f3fc2p-7L,
262 P4 = 0x1.3b2ab6fba4e7729ccbbe0b4f3fc2p-7L, 390 P5 = 0x1.5d87fe78a67311071dee13fd11d9p-10L,
263 P5 = 0x1.5d87fe78a67311071dee13fd11d9p-10L, 391 P6 = 0x1.430912f86c7876f4b663b23c5fe5p-13L;
264 P6 = 0x1.430912f86c7876f4b663b23c5fe5p-13L;
265 392
266 static const double 393 static const double P7 = 0x1.ffcbfc588b041p-17, P8 = 0x1.62c0223a5c7c7p-20,
267 P7 = 0x1.ffcbfc588b041p-17, 394 P9 = 0x1.b52541ff59713p-24, P10 = 0x1.e4cf56a391e22p-28,
268 P8 = 0x1.62c0223a5c7c7p-20, 395 redux = 0x1.8p112 / TBLSIZE;
269 P9 = 0x1.b52541ff59713p-24,
270 P10 = 0x1.e4cf56a391e22p-28,
271 redux = 0x1.8p112 / TBLSIZE;
272 396
273 static const long double tbl[TBLSIZE] = { 397 static const long double tbl[TBLSIZE] = {
274 0x1.6a09e667f3bcc908b2fb1366dfeap-1L, 398 0x1.6a09e667f3bcc908b2fb1366dfeap-1L, 0x1.6c012750bdabeed76a99800f4edep-1L,
275 0x1.6c012750bdabeed76a99800f4edep-1L, 399 0x1.6dfb23c651a2ef220e2cbe1bc0d4p-1L, 0x1.6ff7df9519483cf87e1b4f3e1e98p-1L,
276 0x1.6dfb23c651a2ef220e2cbe1bc0d4p-1L, 400 0x1.71f75e8ec5f73dd2370f2ef0b148p-1L, 0x1.73f9a48a58173bd5c9a4e68ab074p-1L,
277 0x1.6ff7df9519483cf87e1b4f3e1e98p-1L, 401 0x1.75feb564267c8bf6e9aa33a489a8p-1L, 0x1.780694fde5d3f619ae02808592a4p-1L,
278 0x1.71f75e8ec5f73dd2370f2ef0b148p-1L, 402 0x1.7a11473eb0186d7d51023f6ccb1ap-1L, 0x1.7c1ed0130c1327c49334459378dep-1L,
279 0x1.73f9a48a58173bd5c9a4e68ab074p-1L, 403 0x1.7e2f336cf4e62105d02ba1579756p-1L, 0x1.80427543e1a11b60de67649a3842p-1L,
280 0x1.75feb564267c8bf6e9aa33a489a8p-1L, 404 0x1.82589994cce128acf88afab34928p-1L, 0x1.8471a4623c7acce52f6b97c6444cp-1L,
281 0x1.780694fde5d3f619ae02808592a4p-1L, 405 0x1.868d99b4492ec80e41d90ac2556ap-1L, 0x1.88ac7d98a669966530bcdf2d4cc0p-1L,
282 0x1.7a11473eb0186d7d51023f6ccb1ap-1L, 406 0x1.8ace5422aa0db5ba7c55a192c648p-1L, 0x1.8cf3216b5448bef2aa1cd161c57ap-1L,
283 0x1.7c1ed0130c1327c49334459378dep-1L, 407 0x1.8f1ae991577362b982745c72eddap-1L, 0x1.9145b0b91ffc588a61b469f6b6a0p-1L,
284 0x1.7e2f336cf4e62105d02ba1579756p-1L, 408 0x1.93737b0cdc5e4f4501c3f2540ae8p-1L, 0x1.95a44cbc8520ee9b483695a0e7fep-1L,
285 0x1.80427543e1a11b60de67649a3842p-1L, 409 0x1.97d829fde4e4f8b9e920f91e8eb6p-1L, 0x1.9a0f170ca07b9ba3109b8c467844p-1L,
286 0x1.82589994cce128acf88afab34928p-1L, 410 0x1.9c49182a3f0901c7c46b071f28dep-1L, 0x1.9e86319e323231824ca78e64c462p-1L,
287 0x1.8471a4623c7acce52f6b97c6444cp-1L, 411 0x1.a0c667b5de564b29ada8b8cabbacp-1L, 0x1.a309bec4a2d3358c171f770db1f4p-1L,
288 0x1.868d99b4492ec80e41d90ac2556ap-1L, 412 0x1.a5503b23e255c8b424491caf88ccp-1L, 0x1.a799e1330b3586f2dfb2b158f31ep-1L,
289 0x1.88ac7d98a669966530bcdf2d4cc0p-1L, 413 0x1.a9e6b5579fdbf43eb243bdff53a2p-1L, 0x1.ac36bbfd3f379c0db966a3126988p-1L,
290 0x1.8ace5422aa0db5ba7c55a192c648p-1L, 414 0x1.ae89f995ad3ad5e8734d17731c80p-1L, 0x1.b0e07298db66590842acdfc6fb4ep-1L,
291 0x1.8cf3216b5448bef2aa1cd161c57ap-1L, 415 0x1.b33a2b84f15faf6bfd0e7bd941b0p-1L, 0x1.b59728de559398e3881111648738p-1L,
292 0x1.8f1ae991577362b982745c72eddap-1L, 416 0x1.b7f76f2fb5e46eaa7b081ab53ff6p-1L, 0x1.ba5b030a10649840cb3c6af5b74cp-1L,
293 0x1.9145b0b91ffc588a61b469f6b6a0p-1L, 417 0x1.bcc1e904bc1d2247ba0f45b3d06cp-1L, 0x1.bf2c25bd71e088408d7025190cd0p-1L,
294 0x1.93737b0cdc5e4f4501c3f2540ae8p-1L, 418 0x1.c199bdd85529c2220cb12a0916bap-1L, 0x1.c40ab5fffd07a6d14df820f17deap-1L,
295 0x1.95a44cbc8520ee9b483695a0e7fep-1L, 419 0x1.c67f12e57d14b4a2137fd20f2a26p-1L, 0x1.c8f6d9406e7b511acbc48805c3f6p-1L,
296 0x1.97d829fde4e4f8b9e920f91e8eb6p-1L, 420 0x1.cb720dcef90691503cbd1e949d0ap-1L, 0x1.cdf0b555dc3f9c44f8958fac4f12p-1L,
297 0x1.9a0f170ca07b9ba3109b8c467844p-1L, 421 0x1.d072d4a07897b8d0f22f21a13792p-1L, 0x1.d2f87080d89f18ade123989ea50ep-1L,
298 0x1.9c49182a3f0901c7c46b071f28dep-1L, 422 0x1.d5818dcfba48725da05aeb66dff8p-1L, 0x1.d80e316c98397bb84f9d048807a0p-1L,
299 0x1.9e86319e323231824ca78e64c462p-1L, 423 0x1.da9e603db3285708c01a5b6d480cp-1L, 0x1.dd321f301b4604b695de3c0630c0p-1L,
300 0x1.a0c667b5de564b29ada8b8cabbacp-1L, 424 0x1.dfc97337b9b5eb968cac39ed284cp-1L, 0x1.e264614f5a128a12761fa17adc74p-1L,
301 0x1.a309bec4a2d3358c171f770db1f4p-1L, 425 0x1.e502ee78b3ff6273d130153992d0p-1L, 0x1.e7a51fbc74c834b548b2832378a4p-1L,
302 0x1.a5503b23e255c8b424491caf88ccp-1L, 426 0x1.ea4afa2a490d9858f73a18f5dab4p-1L, 0x1.ecf482d8e67f08db0312fb949d50p-1L,
303 0x1.a799e1330b3586f2dfb2b158f31ep-1L, 427 0x1.efa1bee615a27771fd21a92dabb6p-1L, 0x1.f252b376bba974e8696fc3638f24p-1L,
304 0x1.a9e6b5579fdbf43eb243bdff53a2p-1L, 428 0x1.f50765b6e4540674f84b762861a6p-1L, 0x1.f7bfdad9cbe138913b4bfe72bd78p-1L,
305 0x1.ac36bbfd3f379c0db966a3126988p-1L, 429 0x1.fa7c1819e90d82e90a7e74b26360p-1L, 0x1.fd3c22b8f71f10975ba4b32bd006p-1L,
306 0x1.ae89f995ad3ad5e8734d17731c80p-1L, 430 0x1.0000000000000000000000000000p+0L, 0x1.0163da9fb33356d84a66ae336e98p+0L,
307 0x1.b0e07298db66590842acdfc6fb4ep-1L, 431 0x1.02c9a3e778060ee6f7caca4f7a18p+0L, 0x1.04315e86e7f84bd738f9a20da442p+0L,
308 0x1.b33a2b84f15faf6bfd0e7bd941b0p-1L, 432 0x1.059b0d31585743ae7c548eb68c6ap+0L, 0x1.0706b29ddf6ddc6dc403a9d87b1ep+0L,
309 0x1.b59728de559398e3881111648738p-1L, 433 0x1.0874518759bc808c35f25d942856p+0L, 0x1.09e3ecac6f3834521e060c584d5cp+0L,
310 0x1.b7f76f2fb5e46eaa7b081ab53ff6p-1L, 434 0x1.0b5586cf9890f6298b92b7184200p+0L, 0x1.0cc922b7247f7407b705b893dbdep+0L,
311 0x1.ba5b030a10649840cb3c6af5b74cp-1L, 435 0x1.0e3ec32d3d1a2020742e4f8af794p+0L, 0x1.0fb66affed31af232091dd8a169ep+0L,
312 0x1.bcc1e904bc1d2247ba0f45b3d06cp-1L, 436 0x1.11301d0125b50a4ebbf1aed9321cp+0L, 0x1.12abdc06c31cbfb92bad324d6f84p+0L,
313 0x1.bf2c25bd71e088408d7025190cd0p-1L, 437 0x1.1429aaea92ddfb34101943b2588ep+0L, 0x1.15a98c8a58e512480d573dd562aep+0L,
314 0x1.c199bdd85529c2220cb12a0916bap-1L, 438 0x1.172b83c7d517adcdf7c8c50eb162p+0L, 0x1.18af9388c8de9bbbf70b9a3c269cp+0L,
315 0x1.c40ab5fffd07a6d14df820f17deap-1L, 439 0x1.1a35beb6fcb753cb698f692d2038p+0L, 0x1.1bbe084045cd39ab1e72b442810ep+0L,
316 0x1.c67f12e57d14b4a2137fd20f2a26p-1L, 440 0x1.1d4873168b9aa7805b8028990be8p+0L, 0x1.1ed5022fcd91cb8819ff61121fbep+0L,
317 0x1.c8f6d9406e7b511acbc48805c3f6p-1L, 441 0x1.2063b88628cd63b8eeb0295093f6p+0L, 0x1.21f49917ddc962552fd29294bc20p+0L,
318 0x1.cb720dcef90691503cbd1e949d0ap-1L, 442 0x1.2387a6e75623866c1fadb1c159c0p+0L, 0x1.251ce4fb2a63f3582ab7de9e9562p+0L,
319 0x1.cdf0b555dc3f9c44f8958fac4f12p-1L, 443 0x1.26b4565e27cdd257a673281d3068p+0L, 0x1.284dfe1f5638096cf15cf03c9fa0p+0L,
320 0x1.d072d4a07897b8d0f22f21a13792p-1L, 444 0x1.29e9df51fdee12c25d15f5a25022p+0L, 0x1.2b87fd0dad98ffddea46538fca24p+0L,
321 0x1.d2f87080d89f18ade123989ea50ep-1L, 445 0x1.2d285a6e4030b40091d536d0733ep+0L, 0x1.2ecafa93e2f5611ca0f45d5239a4p+0L,
322 0x1.d5818dcfba48725da05aeb66dff8p-1L, 446 0x1.306fe0a31b7152de8d5a463063bep+0L, 0x1.32170fc4cd8313539cf1c3009330p+0L,
323 0x1.d80e316c98397bb84f9d048807a0p-1L, 447 0x1.33c08b26416ff4c9c8610d96680ep+0L, 0x1.356c55f929ff0c94623476373be4p+0L,
324 0x1.da9e603db3285708c01a5b6d480cp-1L, 448 0x1.371a7373aa9caa7145502f45452ap+0L, 0x1.38cae6d05d86585a9cb0d9bed530p+0L,
325 0x1.dd321f301b4604b695de3c0630c0p-1L, 449 0x1.3a7db34e59ff6ea1bc9299e0a1fep+0L, 0x1.3c32dc313a8e484001f228b58cf0p+0L,
326 0x1.dfc97337b9b5eb968cac39ed284cp-1L, 450 0x1.3dea64c12342235b41223e13d7eep+0L, 0x1.3fa4504ac801ba0bf701aa417b9cp+0L,
327 0x1.e264614f5a128a12761fa17adc74p-1L, 451 0x1.4160a21f72e29f84325b8f3dbacap+0L, 0x1.431f5d950a896dc704439410b628p+0L,
328 0x1.e502ee78b3ff6273d130153992d0p-1L, 452 0x1.44e086061892d03136f409df0724p+0L, 0x1.46a41ed1d005772512f459229f0ap+0L,
329 0x1.e7a51fbc74c834b548b2832378a4p-1L, 453 0x1.486a2b5c13cd013c1a3b69062f26p+0L, 0x1.4a32af0d7d3de672d8bcf46f99b4p+0L,
330 0x1.ea4afa2a490d9858f73a18f5dab4p-1L, 454 0x1.4bfdad5362a271d4397afec42e36p+0L, 0x1.4dcb299fddd0d63b36ef1a9e19dep+0L,
331 0x1.ecf482d8e67f08db0312fb949d50p-1L, 455 0x1.4f9b2769d2ca6ad33d8b69aa0b8cp+0L, 0x1.516daa2cf6641c112f52c84d6066p+0L,
332 0x1.efa1bee615a27771fd21a92dabb6p-1L, 456 0x1.5342b569d4f81df0a83c49d86bf4p+0L, 0x1.551a4ca5d920ec52ec620243540cp+0L,
333 0x1.f252b376bba974e8696fc3638f24p-1L, 457 0x1.56f4736b527da66ecb004764e61ep+0L, 0x1.58d12d497c7fd252bc2b7343d554p+0L,
334 0x1.f50765b6e4540674f84b762861a6p-1L, 458 0x1.5ab07dd48542958c93015191e9a8p+0L, 0x1.5c9268a5946b701c4b1b81697ed4p+0L,
335 0x1.f7bfdad9cbe138913b4bfe72bd78p-1L, 459 0x1.5e76f15ad21486e9be4c20399d12p+0L, 0x1.605e1b976dc08b076f592a487066p+0L,
336 0x1.fa7c1819e90d82e90a7e74b26360p-1L, 460 0x1.6247eb03a5584b1f0fa06fd2d9eap+0L, 0x1.6434634ccc31fc76f8714c4ee122p+0L,
337 0x1.fd3c22b8f71f10975ba4b32bd006p-1L, 461 0x1.66238825522249127d9e29b92ea2p+0L, 0x1.68155d44ca973081c57227b9f69ep+0L,
338 0x1.0000000000000000000000000000p+0L,
339 0x1.0163da9fb33356d84a66ae336e98p+0L,
340 0x1.02c9a3e778060ee6f7caca4f7a18p+0L,
341 0x1.04315e86e7f84bd738f9a20da442p+0L,
342 0x1.059b0d31585743ae7c548eb68c6ap+0L,
343 0x1.0706b29ddf6ddc6dc403a9d87b1ep+0L,
344 0x1.0874518759bc808c35f25d942856p+0L,
345 0x1.09e3ecac6f3834521e060c584d5cp+0L,
346 0x1.0b5586cf9890f6298b92b7184200p+0L,
347 0x1.0cc922b7247f7407b705b893dbdep+0L,
348 0x1.0e3ec32d3d1a2020742e4f8af794p+0L,
349 0x1.0fb66affed31af232091dd8a169ep+0L,
350 0x1.11301d0125b50a4ebbf1aed9321cp+0L,
351 0x1.12abdc06c31cbfb92bad324d6f84p+0L,
352 0x1.1429aaea92ddfb34101943b2588ep+0L,
353 0x1.15a98c8a58e512480d573dd562aep+0L,
354 0x1.172b83c7d517adcdf7c8c50eb162p+0L,
355 0x1.18af9388c8de9bbbf70b9a3c269cp+0L,
356 0x1.1a35beb6fcb753cb698f692d2038p+0L,
357 0x1.1bbe084045cd39ab1e72b442810ep+0L,
358 0x1.1d4873168b9aa7805b8028990be8p+0L,
359 0x1.1ed5022fcd91cb8819ff61121fbep+0L,
360 0x1.2063b88628cd63b8eeb0295093f6p+0L,
361 0x1.21f49917ddc962552fd29294bc20p+0L,
362 0x1.2387a6e75623866c1fadb1c159c0p+0L,
363 0x1.251ce4fb2a63f3582ab7de9e9562p+0L,
364 0x1.26b4565e27cdd257a673281d3068p+0L,
365 0x1.284dfe1f5638096cf15cf03c9fa0p+0L,
366 0x1.29e9df51fdee12c25d15f5a25022p+0L,
367 0x1.2b87fd0dad98ffddea46538fca24p+0L,
368 0x1.2d285a6e4030b40091d536d0733ep+0L,
369 0x1.2ecafa93e2f5611ca0f45d5239a4p+0L,
370 0x1.306fe0a31b7152de8d5a463063bep+0L,
371 0x1.32170fc4cd8313539cf1c3009330p+0L,
372 0x1.33c08b26416ff4c9c8610d96680ep+0L,
373 0x1.356c55f929ff0c94623476373be4p+0L,
374 0x1.371a7373aa9caa7145502f45452ap+0L,
375 0x1.38cae6d05d86585a9cb0d9bed530p+0L,
376 0x1.3a7db34e59ff6ea1bc9299e0a1fep+0L,
377 0x1.3c32dc313a8e484001f228b58cf0p+0L,
378 0x1.3dea64c12342235b41223e13d7eep+0L,
379 0x1.3fa4504ac801ba0bf701aa417b9cp+0L,
380 0x1.4160a21f72e29f84325b8f3dbacap+0L,
381 0x1.431f5d950a896dc704439410b628p+0L,
382 0x1.44e086061892d03136f409df0724p+0L,
383 0x1.46a41ed1d005772512f459229f0ap+0L,
384 0x1.486a2b5c13cd013c1a3b69062f26p+0L,
385 0x1.4a32af0d7d3de672d8bcf46f99b4p+0L,
386 0x1.4bfdad5362a271d4397afec42e36p+0L,
387 0x1.4dcb299fddd0d63b36ef1a9e19dep+0L,
388 0x1.4f9b2769d2ca6ad33d8b69aa0b8cp+0L,
389 0x1.516daa2cf6641c112f52c84d6066p+0L,
390 0x1.5342b569d4f81df0a83c49d86bf4p+0L,
391 0x1.551a4ca5d920ec52ec620243540cp+0L,
392 0x1.56f4736b527da66ecb004764e61ep+0L,
393 0x1.58d12d497c7fd252bc2b7343d554p+0L,
394 0x1.5ab07dd48542958c93015191e9a8p+0L,
395 0x1.5c9268a5946b701c4b1b81697ed4p+0L,
396 0x1.5e76f15ad21486e9be4c20399d12p+0L,
397 0x1.605e1b976dc08b076f592a487066p+0L,
398 0x1.6247eb03a5584b1f0fa06fd2d9eap+0L,
399 0x1.6434634ccc31fc76f8714c4ee122p+0L,
400 0x1.66238825522249127d9e29b92ea2p+0L,
401 0x1.68155d44ca973081c57227b9f69ep+0L,
402 }; 462 };
403 463
404 static const float eps[TBLSIZE] = { 464 static const float eps[TBLSIZE] = {
405 » -0x1.5c50p-101, 465 -0x1.5c50p-101, -0x1.5d00p-106, 0x1.8e90p-102, -0x1.5340p-103,
406 » -0x1.5d00p-106, 466 0x1.1bd0p-102, -0x1.4600p-105, -0x1.7a40p-104, 0x1.d590p-102,
407 » 0x1.8e90p-102, 467 -0x1.d590p-101, 0x1.b100p-103, -0x1.0d80p-105, 0x1.6b00p-103,
408 » -0x1.5340p-103, 468 -0x1.9f00p-105, 0x1.c400p-103, 0x1.e120p-103, -0x1.c100p-104,
409 » 0x1.1bd0p-102, 469 -0x1.9d20p-103, 0x1.a800p-108, 0x1.4c00p-106, -0x1.9500p-106,
410 » -0x1.4600p-105, 470 0x1.6900p-105, -0x1.29d0p-100, 0x1.4c60p-103, 0x1.13a0p-102,
411 » -0x1.7a40p-104, 471 -0x1.5b60p-103, -0x1.1c40p-103, 0x1.db80p-102, 0x1.91a0p-102,
412 » 0x1.d590p-102, 472 0x1.dc00p-105, 0x1.44c0p-104, 0x1.9710p-102, 0x1.8760p-103,
413 » -0x1.d590p-101, 473 -0x1.a720p-103, 0x1.ed20p-103, -0x1.49c0p-102, -0x1.e000p-111,
414 » 0x1.b100p-103, 474 0x1.86a0p-103, 0x1.2b40p-103, -0x1.b400p-108, 0x1.1280p-99,
415 » -0x1.0d80p-105, 475 -0x1.02d8p-102, -0x1.e3d0p-103, -0x1.b080p-105, -0x1.f100p-107,
416 » 0x1.6b00p-103, 476 -0x1.16c0p-105, -0x1.1190p-103, -0x1.a7d2p-100, 0x1.3450p-103,
417 » -0x1.9f00p-105, 477 -0x1.67c0p-105, 0x1.4b80p-104, -0x1.c4e0p-103, 0x1.6000p-108,
418 » 0x1.c400p-103, 478 -0x1.3f60p-105, 0x1.93f0p-104, 0x1.5fe0p-105, 0x1.6f80p-107,
419 » 0x1.e120p-103, 479 -0x1.7600p-106, 0x1.21e0p-106, -0x1.3a40p-106, -0x1.40c0p-104,
420 » -0x1.c100p-104, 480 -0x1.9860p-105, -0x1.5d40p-108, -0x1.1d70p-106, 0x1.2760p-105,
421 » -0x1.9d20p-103, 481 0x0.0000p+0, 0x1.21e2p-104, -0x1.9520p-108, -0x1.5720p-106,
422 » 0x1.a800p-108, 482 -0x1.4810p-106, -0x1.be00p-109, 0x1.0080p-105, -0x1.5780p-108,
423 » 0x1.4c00p-106, 483 -0x1.d460p-105, -0x1.6140p-105, 0x1.4630p-104, 0x1.ad50p-103,
424 » -0x1.9500p-106, 484 0x1.82e0p-105, 0x1.1d3cp-101, 0x1.6100p-107, 0x1.ec30p-104,
425 » 0x1.6900p-105, 485 0x1.f200p-108, 0x1.0b40p-103, 0x1.3660p-102, 0x1.d9d0p-103,
426 » -0x1.29d0p-100, 486 -0x1.02d0p-102, 0x1.b070p-103, 0x1.b9c0p-104, -0x1.01c0p-103,
427 » 0x1.4c60p-103, 487 -0x1.dfe0p-103, 0x1.1b60p-104, -0x1.ae94p-101, -0x1.3340p-104,
428 » 0x1.13a0p-102, 488 0x1.b3d8p-102, -0x1.6e40p-105, -0x1.3670p-103, 0x1.c140p-104,
429 » -0x1.5b60p-103, 489 0x1.1840p-101, 0x1.1ab0p-102, -0x1.a400p-104, 0x1.1f00p-104,
430 » -0x1.1c40p-103, 490 -0x1.7180p-103, 0x1.4ce0p-102, 0x1.9200p-107, -0x1.54c0p-103,
431 » 0x1.db80p-102, 491 0x1.1b80p-105, -0x1.1828p-101, 0x1.5720p-102, -0x1.a060p-100,
432 » 0x1.91a0p-102, 492 0x1.9160p-102, 0x1.a280p-104, 0x1.3400p-107, 0x1.2b20p-102,
433 » 0x1.dc00p-105, 493 0x1.7800p-108, 0x1.cfd0p-101, 0x1.2ef0p-102, -0x1.2760p-99,
434 » 0x1.44c0p-104, 494 0x1.b380p-104, 0x1.0048p-101, -0x1.60b0p-102, 0x1.a1ccp-100,
435 » 0x1.9710p-102, 495 -0x1.a640p-104, -0x1.08a0p-101, 0x1.7e60p-102, 0x1.22c0p-103,
436 » 0x1.8760p-103, 496 -0x1.7200p-106, 0x1.f0f0p-102, 0x1.eb4ep-99, 0x1.c6e0p-103,
437 » -0x1.a720p-103,
438 » 0x1.ed20p-103,
439 » -0x1.49c0p-102,
440 » -0x1.e000p-111,
441 » 0x1.86a0p-103,
442 » 0x1.2b40p-103,
443 » -0x1.b400p-108,
444 » 0x1.1280p-99,
445 » -0x1.02d8p-102,
446 » -0x1.e3d0p-103,
447 » -0x1.b080p-105,
448 » -0x1.f100p-107,
449 » -0x1.16c0p-105,
450 » -0x1.1190p-103,
451 » -0x1.a7d2p-100,
452 » 0x1.3450p-103,
453 » -0x1.67c0p-105,
454 » 0x1.4b80p-104,
455 » -0x1.c4e0p-103,
456 » 0x1.6000p-108,
457 » -0x1.3f60p-105,
458 » 0x1.93f0p-104,
459 » 0x1.5fe0p-105,
460 » 0x1.6f80p-107,
461 » -0x1.7600p-106,
462 » 0x1.21e0p-106,
463 » -0x1.3a40p-106,
464 » -0x1.40c0p-104,
465 » -0x1.9860p-105,
466 » -0x1.5d40p-108,
467 » -0x1.1d70p-106,
468 » 0x1.2760p-105,
469 » 0x0.0000p+0,
470 » 0x1.21e2p-104,
471 » -0x1.9520p-108,
472 » -0x1.5720p-106,
473 » -0x1.4810p-106,
474 » -0x1.be00p-109,
475 » 0x1.0080p-105,
476 » -0x1.5780p-108,
477 » -0x1.d460p-105,
478 » -0x1.6140p-105,
479 » 0x1.4630p-104,
480 » 0x1.ad50p-103,
481 » 0x1.82e0p-105,
482 » 0x1.1d3cp-101,
483 » 0x1.6100p-107,
484 » 0x1.ec30p-104,
485 » 0x1.f200p-108,
486 » 0x1.0b40p-103,
487 » 0x1.3660p-102,
488 » 0x1.d9d0p-103,
489 » -0x1.02d0p-102,
490 » 0x1.b070p-103,
491 » 0x1.b9c0p-104,
492 » -0x1.01c0p-103,
493 » -0x1.dfe0p-103,
494 » 0x1.1b60p-104,
495 » -0x1.ae94p-101,
496 » -0x1.3340p-104,
497 » 0x1.b3d8p-102,
498 » -0x1.6e40p-105,
499 » -0x1.3670p-103,
500 » 0x1.c140p-104,
501 » 0x1.1840p-101,
502 » 0x1.1ab0p-102,
503 » -0x1.a400p-104,
504 » 0x1.1f00p-104,
505 » -0x1.7180p-103,
506 » 0x1.4ce0p-102,
507 » 0x1.9200p-107,
508 » -0x1.54c0p-103,
509 » 0x1.1b80p-105,
510 » -0x1.1828p-101,
511 » 0x1.5720p-102,
512 » -0x1.a060p-100,
513 » 0x1.9160p-102,
514 » 0x1.a280p-104,
515 » 0x1.3400p-107,
516 » 0x1.2b20p-102,
517 » 0x1.7800p-108,
518 » 0x1.cfd0p-101,
519 » 0x1.2ef0p-102,
520 » -0x1.2760p-99,
521 » 0x1.b380p-104,
522 » 0x1.0048p-101,
523 » -0x1.60b0p-102,
524 » 0x1.a1ccp-100,
525 » -0x1.a640p-104,
526 » -0x1.08a0p-101,
527 » 0x1.7e60p-102,
528 » 0x1.22c0p-103,
529 » -0x1.7200p-106,
530 » 0x1.f0f0p-102,
531 » 0x1.eb4ep-99,
532 » 0x1.c6e0p-103,
533 }; 497 };
534 498
535 /* 499 /*
536 * exp2l(x): compute the base 2 exponential of x 500 * exp2l(x): compute the base 2 exponential of x
537 * 501 *
538 * Accuracy: Peak error < 0.502 ulp. 502 * Accuracy: Peak error < 0.502 ulp.
539 * 503 *
540 * Method: (accurate tables) 504 * Method: (accurate tables)
541 * 505 *
542 * Reduce x: 506 * Reduce x:
(...skipping 12 matching lines...) Expand all
555 * that exp2t[i] is accurate to 2**-122. 519 * that exp2t[i] is accurate to 2**-122.
556 * 520 *
557 * Note that the range of i is +-TBLSIZE/2, so we actually index the tables 521 * Note that the range of i is +-TBLSIZE/2, so we actually index the tables
558 * by i0 = i + TBLSIZE/2. 522 * by i0 = i + TBLSIZE/2.
559 * 523 *
560 * This method is due to Gal, with many details due to Gal and Bachelis: 524 * This method is due to Gal, with many details due to Gal and Bachelis:
561 * 525 *
562 * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library 526 * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library
563 * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). 527 * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991).
564 */ 528 */
565 long double 529 long double exp2l(long double x) {
566 exp2l(long double x) 530 union ldshape u = {x};
567 { 531 int e = u.i.se & 0x7fff;
568 » union ldshape u = {x}; 532 long double r, z, t;
569 » int e = u.i.se & 0x7fff; 533 uint32_t i0;
570 » long double r, z, t; 534 union {
571 » uint32_t i0; 535 uint32_t u;
572 » union {uint32_t u; int32_t i;} k; 536 int32_t i;
537 } k;
573 538
574 » /* Filter out exceptional cases. */ 539 /* Filter out exceptional cases. */
575 » if (e >= 0x3fff + 14) { /* |x| >= 16384 or x is NaN */ 540 if (e >= 0x3fff + 14) { /* |x| >= 16384 or x is NaN */
576 » » if (u.i.se >= 0x3fff + 15 && u.i.se >> 15 == 0) 541 if (u.i.se >= 0x3fff + 15 && u.i.se >> 15 == 0)
577 » » » /* overflow */ 542 /* overflow */
578 » » » return x * 0x1p16383L; 543 return x * 0x1p16383L;
579 » » if (e == 0x7fff) /* -inf or -nan */ 544 if (e == 0x7fff) /* -inf or -nan */
580 » » » return -1/x; 545 return -1 / x;
581 » » if (x < -16382) { 546 if (x < -16382) {
582 » » » if (x <= -16495 || x - 0x1p112 + 0x1p112 != x) 547 if (x <= -16495 || x - 0x1p112 + 0x1p112 != x)
583 » » » » /* underflow */ 548 /* underflow */
584 » » » » FORCE_EVAL((float)(-0x1p-149/x)); 549 FORCE_EVAL((float)(-0x1p-149 / x));
585 » » » if (x <= -16446) 550 if (x <= -16446)
586 » » » » return 0; 551 return 0;
587 » » } 552 }
588 » } else if (e < 0x3fff - 114) { 553 } else if (e < 0x3fff - 114) {
589 » » return 1 + x; 554 return 1 + x;
590 » } 555 }
591 556
592 » /* 557 /*
593 » * Reduce x, computing z, i0, and k. The low bits of x + redux 558 * Reduce x, computing z, i0, and k. The low bits of x + redux
594 » * contain the 16-bit integer part of the exponent (k) followed by 559 * contain the 16-bit integer part of the exponent (k) followed by
595 » * TBLBITS fractional bits (i0). We use bit tricks to extract these 560 * TBLBITS fractional bits (i0). We use bit tricks to extract these
596 » * as integers, then set z to the remainder. 561 * as integers, then set z to the remainder.
597 » * 562 *
598 » * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8. 563 * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8.
599 » * Then the low-order word of x + redux is 0x000abc12, 564 * Then the low-order word of x + redux is 0x000abc12,
600 » * We split this into k = 0xabc and i0 = 0x12 (adjusted to 565 * We split this into k = 0xabc and i0 = 0x12 (adjusted to
601 » * index into the table), then we compute z = 0x0.003456p0. 566 * index into the table), then we compute z = 0x0.003456p0.
602 » */ 567 */
603 » u.f = x + redux; 568 u.f = x + redux;
604 » i0 = u.i2.lo + TBLSIZE / 2; 569 i0 = u.i2.lo + TBLSIZE / 2;
605 » k.u = i0 / TBLSIZE * TBLSIZE; 570 k.u = i0 / TBLSIZE * TBLSIZE;
606 » k.i /= TBLSIZE; 571 k.i /= TBLSIZE;
607 » i0 %= TBLSIZE; 572 i0 %= TBLSIZE;
608 » u.f -= redux; 573 u.f -= redux;
609 » z = x - u.f; 574 z = x - u.f;
610 575
611 » /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ 576 /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */
612 » t = tbl[i0]; 577 t = tbl[i0];
613 » z -= eps[i0]; 578 z -= eps[i0];
614 » r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * (P5 + z * (P6 579 r = t +
615 » + z * (P7 + z * (P8 + z * (P9 + z * P10))))))))); 580 t * z *
581 (P1 +
582 z * (P2 +
583 z * (P3 +
584 z * (P4 +
585 z * (P5 +
586 z * (P6 +
587 z * (P7 +
588 z * (P8 + z * (P9 + z * P10)))))))));
616 589
617 » return scalbnl(r, k.i); 590 return scalbnl(r, k.i);
618 } 591 }
619 #endif 592 #endif
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