OLD | NEW |
1 /* origin: FreeBSD /usr/src/lib/msun/src/s_exp2.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_exp2.c */ |
2 /*- | 2 /*- |
3 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> | 3 * Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> |
4 * All rights reserved. | 4 * All rights reserved. |
5 * | 5 * |
6 * Redistribution and use in source and binary forms, with or without | 6 * Redistribution and use in source and binary forms, with or without |
7 * modification, are permitted provided that the following conditions | 7 * modification, are permitted provided that the following conditions |
8 * are met: | 8 * are met: |
9 * 1. Redistributions of source code must retain the above copyright | 9 * 1. Redistributions of source code must retain the above copyright |
10 * notice, this list of conditions and the following disclaimer. | 10 * notice, this list of conditions and the following disclaimer. |
(...skipping 11 matching lines...) Expand all Loading... |
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | 22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | 23 * 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 | 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
25 * SUCH DAMAGE. | 25 * SUCH DAMAGE. |
26 */ | 26 */ |
27 | 27 |
28 #include "libm.h" | 28 #include "libm.h" |
29 | 29 |
30 #define TBLSIZE 256 | 30 #define TBLSIZE 256 |
31 | 31 |
32 static const double | 32 static const double redux = 0x1.8p52 / TBLSIZE, P1 = 0x1.62e42fefa39efp-1, |
33 redux = 0x1.8p52 / TBLSIZE, | 33 P2 = 0x1.ebfbdff82c575p-3, P3 = 0x1.c6b08d704a0a6p-5, |
34 P1 = 0x1.62e42fefa39efp-1, | 34 P4 = 0x1.3b2ab88f70400p-7, P5 = 0x1.5d88003875c74p-10; |
35 P2 = 0x1.ebfbdff82c575p-3, | |
36 P3 = 0x1.c6b08d704a0a6p-5, | |
37 P4 = 0x1.3b2ab88f70400p-7, | |
38 P5 = 0x1.5d88003875c74p-10; | |
39 | 35 |
40 static const double tbl[TBLSIZE * 2] = { | 36 static const double tbl[TBLSIZE * 2] = { |
41 /* exp2(z + eps) eps */ | 37 /* exp2(z + eps) eps */ |
42 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, | 38 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, 0x1.6b052fa751744p-1, 0x1.8000p-50, |
43 0x1.6b052fa751744p-1, 0x1.8000p-50, | 39 0x1.6c012750bd9fep-1, -0x1.8780p-45, 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, |
44 0x1.6c012750bd9fep-1, -0x1.8780p-45, | 40 0x1.6dfb23c651a29p-1, -0x1.8000p-50, 0x1.6ef9298593ae3p-1, -0x1.c000p-52, |
45 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, | 41 0x1.6ff7df9519386p-1, -0x1.fd80p-45, 0x1.70f7466f42da3p-1, -0x1.c880p-45, |
46 0x1.6dfb23c651a29p-1, -0x1.8000p-50, | 42 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, 0x1.72f8286eacf05p-1, -0x1.8300p-44, |
47 0x1.6ef9298593ae3p-1, -0x1.c000p-52, | 43 0x1.73f9a48a58152p-1, -0x1.0c00p-47, 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, |
48 0x1.6ff7df9519386p-1, -0x1.fd80p-45, | 44 0x1.75feb564267f1p-1, 0x1.3e00p-47, 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, |
49 0x1.70f7466f42da3p-1, -0x1.c880p-45, | 45 0x1.780694fde5d38p-1, -0x1.d000p-50, 0x1.790b938ac1d00p-1, 0x1.3000p-49, |
50 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, | 46 0x1.7a11473eb0178p-1, -0x1.d000p-49, 0x1.7b17b0976d060p-1, 0x1.0400p-45, |
51 0x1.72f8286eacf05p-1, -0x1.8300p-44, | 47 0x1.7c1ed0130c133p-1, 0x1.0000p-53, 0x1.7d26a62ff8636p-1, -0x1.6900p-45, |
52 0x1.73f9a48a58152p-1, -0x1.0c00p-47, | 48 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, 0x1.7f3878491c3e8p-1, -0x1.4580p-45, |
53 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, | 49 0x1.80427543e1b4ep-1, 0x1.3000p-44, 0x1.814d2add1071ap-1, 0x1.f000p-47, |
54 0x1.75feb564267f1p-1, 0x1.3e00p-47, | 50 0x1.82589994ccd7ep-1, -0x1.1c00p-45, 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, |
55 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, | 51 0x1.8471a4623cab5p-1, 0x1.7100p-43, 0x1.857f4179f5bbcp-1, 0x1.2600p-45, |
56 0x1.780694fde5d38p-1, -0x1.d000p-50, | 52 0x1.868d99b4491afp-1, -0x1.2c40p-44, 0x1.879cad931a395p-1, -0x1.3000p-45, |
57 0x1.790b938ac1d00p-1, 0x1.3000p-49, | 53 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, 0x1.89bd0a4785800p-1, -0x1.d000p-49, |
58 0x1.7a11473eb0178p-1, -0x1.d000p-49, | 54 0x1.8ace5422aa223p-1, 0x1.3280p-44, 0x1.8be05bad619fap-1, 0x1.2b40p-43, |
59 0x1.7b17b0976d060p-1, 0x1.0400p-45, | 55 0x1.8cf3216b54383p-1, -0x1.ed00p-45, 0x1.8e06a5e08664cp-1, -0x1.0500p-45, |
60 0x1.7c1ed0130c133p-1, 0x1.0000p-53, | 56 0x1.8f1ae99157807p-1, 0x1.8280p-45, 0x1.902fed0282c0ep-1, -0x1.cb00p-46, |
61 0x1.7d26a62ff8636p-1, -0x1.6900p-45, | 57 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, 0x1.925c353aa2ff9p-1, 0x1.5400p-48, |
62 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, | 58 0x1.93737b0cdc64ap-1, 0x1.7200p-46, 0x1.948b82b5f98aep-1, -0x1.9000p-47, |
63 0x1.7f3878491c3e8p-1, -0x1.4580p-45, | 59 0x1.95a44cbc852cbp-1, 0x1.5680p-45, 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, |
64 0x1.80427543e1b4ep-1, 0x1.3000p-44, | 60 0x1.97d829fde4e2ap-1, -0x1.1000p-47, 0x1.98f33e47a23a3p-1, 0x1.d000p-45, |
65 0x1.814d2add1071ap-1, 0x1.f000p-47, | 61 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, |
66 0x1.82589994ccd7ep-1, -0x1.1c00p-45, | 62 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, 0x1.9d674194bb8c5p-1, -0x1.c000p-49, |
67 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, | 63 0x1.9e86319e3238ep-1, 0x1.7d00p-46, 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, |
68 0x1.8471a4623cab5p-1, 0x1.7100p-43, | 64 0x1.a0c667b5de54dp-1, -0x1.5000p-48, 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, |
69 0x1.857f4179f5bbcp-1, 0x1.2600p-45, | 65 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, 0x1.a42c980460a5dp-1, -0x1.af00p-46, |
70 0x1.868d99b4491afp-1, -0x1.2c40p-44, | 66 0x1.a5503b23e259bp-1, 0x1.b600p-47, 0x1.a674a8af46213p-1, 0x1.8880p-44, |
71 0x1.879cad931a395p-1, -0x1.3000p-45, | 67 0x1.a799e1330b3a7p-1, 0x1.1200p-46, 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, |
72 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, | 68 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, 0x1.ab0e521356fb8p-1, 0x1.b700p-45, |
73 0x1.89bd0a4785800p-1, -0x1.d000p-49, | 69 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, |
74 0x1.8ace5422aa223p-1, 0x1.3280p-44, | 70 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, 0x1.afb4ce622f367p-1, 0x1.6500p-46, |
75 0x1.8be05bad619fap-1, 0x1.2b40p-43, | 71 0x1.b0e07298db790p-1, 0x1.fd40p-45, 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, |
76 0x1.8cf3216b54383p-1, -0x1.ed00p-45, | 72 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, 0x1.b468415b747e7p-1, -0x1.8380p-44, |
77 0x1.8e06a5e08664cp-1, -0x1.0500p-45, | 73 0x1.b59728de5593ap-1, 0x1.8000p-54, 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, |
78 0x1.8f1ae99157807p-1, 0x1.8280p-45, | 74 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, 0x1.b928cf22749b2p-1, -0x1.4c00p-47, |
79 0x1.902fed0282c0ep-1, -0x1.cb00p-46, | 75 0x1.ba5b030a10603p-1, -0x1.d700p-47, 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, |
80 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, | 76 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, |
81 0x1.925c353aa2ff9p-1, 0x1.5400p-48, | 77 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, 0x1.c06286141b2e9p-1, -0x1.1400p-46, |
82 0x1.93737b0cdc64ap-1, 0x1.7200p-46, | 78 0x1.c199bdd8552e0p-1, 0x1.be00p-47, 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47, |
83 0x1.948b82b5f98aep-1, -0x1.9000p-47, | 79 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47, 0x1.c544778fafd15p-1, 0x1.9660p-44, |
84 0x1.95a44cbc852cbp-1, 0x1.5680p-45, | 80 0x1.c67f12e57d0cbp-1, -0x1.a100p-46, 0x1.c7ba88988c1b6p-1, -0x1.8458p-42, |
85 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, | 81 0x1.c8f6d9406e733p-1, -0x1.a480p-46, 0x1.ca3405751c4dfp-1, 0x1.b000p-51, |
86 0x1.97d829fde4e2ap-1, -0x1.1000p-47, | 82 0x1.cb720dcef9094p-1, 0x1.1400p-47, 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48, |
87 0x1.98f33e47a23a3p-1, 0x1.d000p-45, | 83 0x1.cdf0b555dc412p-1, 0x1.3600p-48, 0x1.cf3155b5bab3bp-1, -0x1.6900p-47, |
88 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, | 84 0x1.d072d4a0789bcp-1, 0x1.9a00p-47, 0x1.d1b532b08c8fap-1, -0x1.5e00p-46, |
89 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, | 85 0x1.d2f87080d8a85p-1, 0x1.d280p-46, 0x1.d43c8eacaa203p-1, 0x1.1a00p-47, |
90 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, | 86 0x1.d5818dcfba491p-1, 0x1.f000p-50, 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47, |
91 0x1.9d674194bb8c5p-1, -0x1.c000p-49, | 87 0x1.d80e316c9834ep-1, -0x1.cd80p-47, 0x1.d955d71ff6090p-1, 0x1.4c00p-48, |
92 0x1.9e86319e3238ep-1, 0x1.7d00p-46, | 88 0x1.da9e603db32aep-1, 0x1.f900p-48, 0x1.dbe7cd63a8325p-1, 0x1.9800p-49, |
93 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, | 89 0x1.dd321f301b445p-1, -0x1.5200p-48, 0x1.de7d5641c05bfp-1, -0x1.d700p-46, |
94 0x1.a0c667b5de54dp-1, -0x1.5000p-48, | 90 0x1.dfc97337b9aecp-1, -0x1.6140p-46, 0x1.e11676b197d5ep-1, 0x1.b480p-47, |
95 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, | 91 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43, 0x1.e3b333b16ee5cp-1, 0x1.c680p-47, |
96 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, | 92 0x1.e502ee78b3fb4p-1, -0x1.9300p-47, 0x1.e653924676d68p-1, -0x1.5000p-49, |
97 0x1.a42c980460a5dp-1, -0x1.af00p-46, | 93 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47, 0x1.e8f7977cdb726p-1, -0x1.3700p-48, |
98 0x1.a5503b23e259bp-1, 0x1.b600p-47, | 94 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49, 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46, |
99 0x1.a674a8af46213p-1, 0x1.8880p-44, | 95 0x1.ecf482d8e680dp-1, 0x1.5500p-48, 0x1.ee4aaa2188514p-1, 0x1.6400p-51, |
100 0x1.a799e1330b3a7p-1, 0x1.1200p-46, | 96 0x1.efa1bee615a13p-1, -0x1.e800p-49, 0x1.f0f9c1cb64106p-1, -0x1.a880p-48, |
101 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, | 97 0x1.f252b376bb963p-1, -0x1.c900p-45, 0x1.f3ac948dd7275p-1, 0x1.a000p-53, |
102 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, | 98 0x1.f50765b6e4524p-1, -0x1.4f00p-48, 0x1.f6632798844fdp-1, 0x1.a800p-51, |
103 0x1.ab0e521356fb8p-1, 0x1.b700p-45, | 99 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48, 0x1.f91d802243c82p-1, -0x1.4600p-50, |
104 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, | 100 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47, 0x1.fbdba3692d511p-1, -0x1.0e00p-51, |
105 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, | 101 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46, 0x1.fe9d96b2a23eep-1, 0x1.e430p-49, |
106 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, | 102 0x1.0000000000000p+0, 0x0.0000p+0, 0x1.00b1afa5abcbep+0, -0x1.3400p-52, |
107 0x1.afb4ce622f367p-1, 0x1.6500p-46, | 103 0x1.0163da9fb3303p+0, -0x1.2170p-46, 0x1.02168143b0282p+0, 0x1.a400p-52, |
108 0x1.b0e07298db790p-1, 0x1.fd40p-45, | 104 0x1.02c9a3e77806cp+0, 0x1.f980p-49, 0x1.037d42e11bbcap+0, -0x1.7400p-51, |
109 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, | 105 0x1.04315e86e7f89p+0, 0x1.8300p-50, 0x1.04e5f72f65467p+0, -0x1.a3f0p-46, |
110 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, | 106 0x1.059b0d315855ap+0, -0x1.2840p-47, 0x1.0650a0e3c1f95p+0, 0x1.1600p-48, |
111 0x1.b468415b747e7p-1, -0x1.8380p-44, | 107 0x1.0706b29ddf71ap+0, 0x1.5240p-46, 0x1.07bd42b72a82dp+0, -0x1.9a00p-49, |
112 0x1.b59728de5593ap-1, 0x1.8000p-54, | 108 0x1.0874518759bd0p+0, 0x1.6400p-49, 0x1.092bdf66607c8p+0, -0x1.0780p-47, |
113 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, | 109 0x1.09e3ecac6f383p+0, -0x1.8000p-54, 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48, |
114 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, | 110 0x1.0b5586cf988fcp+0, -0x1.ac80p-48, 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50, |
115 0x1.b928cf22749b2p-1, -0x1.4c00p-47, | 111 0x1.0cc922b724816p+0, 0x1.5200p-47, 0x1.0d83b23395dd8p+0, -0x1.ad00p-48, |
116 0x1.ba5b030a10603p-1, -0x1.d700p-47, | 112 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46, 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47, |
117 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, | 113 0x1.0fb66affed2f0p+0, -0x1.d300p-47, 0x1.1073028d7234bp+0, 0x1.1500p-48, |
118 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, | 114 0x1.11301d0125b5bp+0, 0x1.c000p-49, 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46, |
119 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, | 115 0x1.12abdc06c31d5p+0, 0x1.8400p-49, 0x1.136a814f2047dp+0, -0x1.ed00p-47, |
120 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, | 116 0x1.1429aaea92de9p+0, 0x1.8e00p-49, 0x1.14e95934f3138p+0, 0x1.b400p-49, |
121 0x1.c06286141b2e9p-1, -0x1.1400p-46, | 117 0x1.15a98c8a58e71p+0, 0x1.5300p-47, 0x1.166a45471c3dfp+0, 0x1.3380p-47, |
122 0x1.c199bdd8552e0p-1, 0x1.be00p-47, | 118 0x1.172b83c7d5211p+0, 0x1.8d40p-45, 0x1.17ed48695bb9fp+0, -0x1.5d00p-47, |
123 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47, | 119 0x1.18af9388c8d93p+0, -0x1.c880p-46, 0x1.1972658375d66p+0, 0x1.1f00p-46, |
124 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47, | 120 0x1.1a35beb6fcba7p+0, 0x1.0480p-46, 0x1.1af99f81387e3p+0, -0x1.7390p-43, |
125 0x1.c544778fafd15p-1, 0x1.9660p-44, | 121 0x1.1bbe084045d54p+0, 0x1.4e40p-45, 0x1.1c82f95281c43p+0, -0x1.a200p-47, |
126 0x1.c67f12e57d0cbp-1, -0x1.a100p-46, | 122 0x1.1d4873168b9b2p+0, 0x1.3800p-49, 0x1.1e0e75eb44031p+0, 0x1.ac00p-49, |
127 0x1.c7ba88988c1b6p-1, -0x1.8458p-42, | 123 0x1.1ed5022fcd938p+0, 0x1.1900p-47, 0x1.1f9c18438cdf7p+0, -0x1.b780p-46, |
128 0x1.c8f6d9406e733p-1, -0x1.a480p-46, | 124 0x1.2063b88628d8fp+0, 0x1.d940p-45, 0x1.212be3578a81ep+0, 0x1.8000p-50, |
129 0x1.ca3405751c4dfp-1, 0x1.b000p-51, | 125 0x1.21f49917ddd41p+0, 0x1.b340p-45, 0x1.22bdda2791323p+0, 0x1.9f80p-46, |
130 0x1.cb720dcef9094p-1, 0x1.1400p-47, | 126 0x1.2387a6e7561e7p+0, -0x1.9c80p-46, 0x1.2451ffb821427p+0, 0x1.2300p-47, |
131 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48, | 127 0x1.251ce4fb2a602p+0, -0x1.3480p-46, 0x1.25e85711eceb0p+0, 0x1.2700p-46, |
132 0x1.cdf0b555dc412p-1, 0x1.3600p-48, | 128 0x1.26b4565e27d16p+0, 0x1.1d00p-46, 0x1.2780e341de00fp+0, 0x1.1ee0p-44, |
133 0x1.cf3155b5bab3bp-1, -0x1.6900p-47, | 129 0x1.284dfe1f5633ep+0, -0x1.4c00p-46, 0x1.291ba7591bb30p+0, -0x1.3d80p-46, |
134 0x1.d072d4a0789bcp-1, 0x1.9a00p-47, | 130 0x1.29e9df51fdf09p+0, 0x1.8b00p-47, 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45, |
135 0x1.d1b532b08c8fap-1, -0x1.5e00p-46, | 131 0x1.2b87fd0dada3ap+0, 0x1.a340p-45, 0x1.2c57e39771af9p+0, -0x1.0800p-46, |
136 0x1.d2f87080d8a85p-1, 0x1.d280p-46, | 132 0x1.2d285a6e402d9p+0, -0x1.ed00p-47, 0x1.2df961f641579p+0, -0x1.4200p-48, |
137 0x1.d43c8eacaa203p-1, 0x1.1a00p-47, | 133 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45, 0x1.2f9d24abd8822p+0, -0x1.6300p-46, |
138 0x1.d5818dcfba491p-1, 0x1.f000p-50, | 134 0x1.306fe0a31b625p+0, -0x1.2360p-44, 0x1.31432edeea50bp+0, -0x1.0df8p-40, |
139 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47, | 135 0x1.32170fc4cd7b8p+0, -0x1.2480p-45, 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45, |
140 0x1.d80e316c9834ep-1, -0x1.cd80p-47, | 136 0x1.33c08b2641766p+0, 0x1.ed00p-46, 0x1.3496266e3fa27p+0, -0x1.c000p-50, |
141 0x1.d955d71ff6090p-1, 0x1.4c00p-48, | 137 0x1.356c55f929f0fp+0, -0x1.0d80p-44, 0x1.36431a2de88b9p+0, 0x1.2c80p-45, |
142 0x1.da9e603db32aep-1, 0x1.f900p-48, | 138 0x1.371a7373aaa39p+0, 0x1.0600p-45, 0x1.37f26231e74fep+0, -0x1.6600p-46, |
143 0x1.dbe7cd63a8325p-1, 0x1.9800p-49, | 139 0x1.38cae6d05d838p+0, -0x1.ae00p-47, 0x1.39a401b713ec3p+0, -0x1.4720p-43, |
144 0x1.dd321f301b445p-1, -0x1.5200p-48, | 140 0x1.3a7db34e5a020p+0, 0x1.8200p-47, 0x1.3b57fbfec6e95p+0, 0x1.e800p-44, |
145 0x1.de7d5641c05bfp-1, -0x1.d700p-46, | 141 0x1.3c32dc313a8f2p+0, 0x1.f800p-49, 0x1.3d0e544ede122p+0, -0x1.7a00p-46, |
146 0x1.dfc97337b9aecp-1, -0x1.6140p-46, | 142 0x1.3dea64c1234bbp+0, 0x1.6300p-45, 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, |
147 0x1.e11676b197d5ep-1, 0x1.b480p-47, | 143 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, 0x1.40822c367a0bbp+0, 0x1.5b80p-45, |
148 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43, | 144 0x1.4160a21f72e95p+0, 0x1.ec00p-46, 0x1.423fb27094646p+0, -0x1.3600p-46, |
149 0x1.e3b333b16ee5cp-1, 0x1.c680p-47, | 145 0x1.431f5d950a920p+0, 0x1.3980p-45, 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, |
150 0x1.e502ee78b3fb4p-1, -0x1.9300p-47, | 146 0x1.44e0860618919p+0, -0x1.6c00p-48, 0x1.45c2042a7d201p+0, -0x1.bc00p-47, |
151 0x1.e653924676d68p-1, -0x1.5000p-49, | 147 0x1.46a41ed1d0016p+0, -0x1.2800p-46, 0x1.4786d668b3326p+0, 0x1.0e00p-44, |
152 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47, | 148 0x1.486a2b5c13c00p+0, -0x1.d400p-45, 0x1.494e1e192af04p+0, 0x1.c200p-47, |
153 0x1.e8f7977cdb726p-1, -0x1.3700p-48, | 149 0x1.4a32af0d7d372p+0, -0x1.e500p-46, 0x1.4b17dea6db801p+0, 0x1.7800p-47, |
154 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49, | 150 0x1.4bfdad53629e1p+0, -0x1.3800p-46, 0x1.4ce41b817c132p+0, 0x1.0800p-47, |
155 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46, | 151 0x1.4dcb299fddddbp+0, 0x1.c700p-45, 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, |
156 0x1.ecf482d8e680dp-1, 0x1.5500p-48, | 152 0x1.4f9b2769d2d02p+0, 0x1.9200p-46, 0x1.508417f4531c1p+0, -0x1.8c00p-47, |
157 0x1.ee4aaa2188514p-1, 0x1.6400p-51, | 153 0x1.516daa2cf662ap+0, -0x1.a000p-48, 0x1.5257de83f51eap+0, 0x1.a080p-43, |
158 0x1.efa1bee615a13p-1, -0x1.e800p-49, | 154 0x1.5342b569d4edap+0, -0x1.6d80p-45, 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, |
159 0x1.f0f9c1cb64106p-1, -0x1.a880p-48, | 155 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, 0x1.56070dde9116bp+0, 0x1.4b00p-45, |
160 0x1.f252b376bb963p-1, -0x1.c900p-45, | 156 0x1.56f4736b529dep+0, 0x1.15a0p-43, 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, |
161 0x1.f3ac948dd7275p-1, 0x1.a000p-53, | 157 0x1.58d12d497c76fp+0, -0x1.3080p-45, 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, |
162 0x1.f50765b6e4524p-1, -0x1.4f00p-48, | 158 0x1.5ab07dd485427p+0, -0x1.4000p-51, 0x1.5ba11fba87af4p+0, 0x1.0080p-44, |
163 0x1.f6632798844fdp-1, 0x1.a800p-51, | 159 0x1.5c9268a59460bp+0, -0x1.6c80p-45, 0x1.5d84590998e3fp+0, 0x1.69a0p-43, |
164 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48, | 160 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, 0x1.5f6a320dcebcap+0, 0x1.7700p-46, |
165 0x1.f91d802243c82p-1, -0x1.4600p-50, | 161 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, 0x1.6152ae6cdf715p+0, 0x1.1000p-47, |
166 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47, | 162 0x1.6247eb03a5531p+0, -0x1.5d00p-46, 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, |
167 0x1.fbdba3692d511p-1, -0x1.0e00p-51, | 163 0x1.6434634ccc313p+0, -0x1.a800p-49, 0x1.652b9febc8efap+0, -0x1.8600p-45, |
168 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46, | 164 0x1.6623882553397p+0, 0x1.1fe0p-40, 0x1.671c1c708328ep+0, -0x1.7200p-44, |
169 0x1.fe9d96b2a23eep-1, 0x1.e430p-49, | 165 0x1.68155d44ca97ep+0, 0x1.6800p-49, 0x1.690f4b19e9471p+0, -0x1.9780p-45, |
170 0x1.0000000000000p+0, 0x0.0000p+0, | |
171 0x1.00b1afa5abcbep+0, -0x1.3400p-52, | |
172 0x1.0163da9fb3303p+0, -0x1.2170p-46, | |
173 0x1.02168143b0282p+0, 0x1.a400p-52, | |
174 0x1.02c9a3e77806cp+0, 0x1.f980p-49, | |
175 0x1.037d42e11bbcap+0, -0x1.7400p-51, | |
176 0x1.04315e86e7f89p+0, 0x1.8300p-50, | |
177 0x1.04e5f72f65467p+0, -0x1.a3f0p-46, | |
178 0x1.059b0d315855ap+0, -0x1.2840p-47, | |
179 0x1.0650a0e3c1f95p+0, 0x1.1600p-48, | |
180 0x1.0706b29ddf71ap+0, 0x1.5240p-46, | |
181 0x1.07bd42b72a82dp+0, -0x1.9a00p-49, | |
182 0x1.0874518759bd0p+0, 0x1.6400p-49, | |
183 0x1.092bdf66607c8p+0, -0x1.0780p-47, | |
184 0x1.09e3ecac6f383p+0, -0x1.8000p-54, | |
185 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48, | |
186 0x1.0b5586cf988fcp+0, -0x1.ac80p-48, | |
187 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50, | |
188 0x1.0cc922b724816p+0, 0x1.5200p-47, | |
189 0x1.0d83b23395dd8p+0, -0x1.ad00p-48, | |
190 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46, | |
191 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47, | |
192 0x1.0fb66affed2f0p+0, -0x1.d300p-47, | |
193 0x1.1073028d7234bp+0, 0x1.1500p-48, | |
194 0x1.11301d0125b5bp+0, 0x1.c000p-49, | |
195 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46, | |
196 0x1.12abdc06c31d5p+0, 0x1.8400p-49, | |
197 0x1.136a814f2047dp+0, -0x1.ed00p-47, | |
198 0x1.1429aaea92de9p+0, 0x1.8e00p-49, | |
199 0x1.14e95934f3138p+0, 0x1.b400p-49, | |
200 0x1.15a98c8a58e71p+0, 0x1.5300p-47, | |
201 0x1.166a45471c3dfp+0, 0x1.3380p-47, | |
202 0x1.172b83c7d5211p+0, 0x1.8d40p-45, | |
203 0x1.17ed48695bb9fp+0, -0x1.5d00p-47, | |
204 0x1.18af9388c8d93p+0, -0x1.c880p-46, | |
205 0x1.1972658375d66p+0, 0x1.1f00p-46, | |
206 0x1.1a35beb6fcba7p+0, 0x1.0480p-46, | |
207 0x1.1af99f81387e3p+0, -0x1.7390p-43, | |
208 0x1.1bbe084045d54p+0, 0x1.4e40p-45, | |
209 0x1.1c82f95281c43p+0, -0x1.a200p-47, | |
210 0x1.1d4873168b9b2p+0, 0x1.3800p-49, | |
211 0x1.1e0e75eb44031p+0, 0x1.ac00p-49, | |
212 0x1.1ed5022fcd938p+0, 0x1.1900p-47, | |
213 0x1.1f9c18438cdf7p+0, -0x1.b780p-46, | |
214 0x1.2063b88628d8fp+0, 0x1.d940p-45, | |
215 0x1.212be3578a81ep+0, 0x1.8000p-50, | |
216 0x1.21f49917ddd41p+0, 0x1.b340p-45, | |
217 0x1.22bdda2791323p+0, 0x1.9f80p-46, | |
218 0x1.2387a6e7561e7p+0, -0x1.9c80p-46, | |
219 0x1.2451ffb821427p+0, 0x1.2300p-47, | |
220 0x1.251ce4fb2a602p+0, -0x1.3480p-46, | |
221 0x1.25e85711eceb0p+0, 0x1.2700p-46, | |
222 0x1.26b4565e27d16p+0, 0x1.1d00p-46, | |
223 0x1.2780e341de00fp+0, 0x1.1ee0p-44, | |
224 0x1.284dfe1f5633ep+0, -0x1.4c00p-46, | |
225 0x1.291ba7591bb30p+0, -0x1.3d80p-46, | |
226 0x1.29e9df51fdf09p+0, 0x1.8b00p-47, | |
227 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45, | |
228 0x1.2b87fd0dada3ap+0, 0x1.a340p-45, | |
229 0x1.2c57e39771af9p+0, -0x1.0800p-46, | |
230 0x1.2d285a6e402d9p+0, -0x1.ed00p-47, | |
231 0x1.2df961f641579p+0, -0x1.4200p-48, | |
232 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45, | |
233 0x1.2f9d24abd8822p+0, -0x1.6300p-46, | |
234 0x1.306fe0a31b625p+0, -0x1.2360p-44, | |
235 0x1.31432edeea50bp+0, -0x1.0df8p-40, | |
236 0x1.32170fc4cd7b8p+0, -0x1.2480p-45, | |
237 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45, | |
238 0x1.33c08b2641766p+0, 0x1.ed00p-46, | |
239 0x1.3496266e3fa27p+0, -0x1.c000p-50, | |
240 0x1.356c55f929f0fp+0, -0x1.0d80p-44, | |
241 0x1.36431a2de88b9p+0, 0x1.2c80p-45, | |
242 0x1.371a7373aaa39p+0, 0x1.0600p-45, | |
243 0x1.37f26231e74fep+0, -0x1.6600p-46, | |
244 0x1.38cae6d05d838p+0, -0x1.ae00p-47, | |
245 0x1.39a401b713ec3p+0, -0x1.4720p-43, | |
246 0x1.3a7db34e5a020p+0, 0x1.8200p-47, | |
247 0x1.3b57fbfec6e95p+0, 0x1.e800p-44, | |
248 0x1.3c32dc313a8f2p+0, 0x1.f800p-49, | |
249 0x1.3d0e544ede122p+0, -0x1.7a00p-46, | |
250 0x1.3dea64c1234bbp+0, 0x1.6300p-45, | |
251 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, | |
252 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, | |
253 0x1.40822c367a0bbp+0, 0x1.5b80p-45, | |
254 0x1.4160a21f72e95p+0, 0x1.ec00p-46, | |
255 0x1.423fb27094646p+0, -0x1.3600p-46, | |
256 0x1.431f5d950a920p+0, 0x1.3980p-45, | |
257 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, | |
258 0x1.44e0860618919p+0, -0x1.6c00p-48, | |
259 0x1.45c2042a7d201p+0, -0x1.bc00p-47, | |
260 0x1.46a41ed1d0016p+0, -0x1.2800p-46, | |
261 0x1.4786d668b3326p+0, 0x1.0e00p-44, | |
262 0x1.486a2b5c13c00p+0, -0x1.d400p-45, | |
263 0x1.494e1e192af04p+0, 0x1.c200p-47, | |
264 0x1.4a32af0d7d372p+0, -0x1.e500p-46, | |
265 0x1.4b17dea6db801p+0, 0x1.7800p-47, | |
266 0x1.4bfdad53629e1p+0, -0x1.3800p-46, | |
267 0x1.4ce41b817c132p+0, 0x1.0800p-47, | |
268 0x1.4dcb299fddddbp+0, 0x1.c700p-45, | |
269 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, | |
270 0x1.4f9b2769d2d02p+0, 0x1.9200p-46, | |
271 0x1.508417f4531c1p+0, -0x1.8c00p-47, | |
272 0x1.516daa2cf662ap+0, -0x1.a000p-48, | |
273 0x1.5257de83f51eap+0, 0x1.a080p-43, | |
274 0x1.5342b569d4edap+0, -0x1.6d80p-45, | |
275 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, | |
276 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, | |
277 0x1.56070dde9116bp+0, 0x1.4b00p-45, | |
278 0x1.56f4736b529dep+0, 0x1.15a0p-43, | |
279 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, | |
280 0x1.58d12d497c76fp+0, -0x1.3080p-45, | |
281 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, | |
282 0x1.5ab07dd485427p+0, -0x1.4000p-51, | |
283 0x1.5ba11fba87af4p+0, 0x1.0080p-44, | |
284 0x1.5c9268a59460bp+0, -0x1.6c80p-45, | |
285 0x1.5d84590998e3fp+0, 0x1.69a0p-43, | |
286 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, | |
287 0x1.5f6a320dcebcap+0, 0x1.7700p-46, | |
288 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, | |
289 0x1.6152ae6cdf715p+0, 0x1.1000p-47, | |
290 0x1.6247eb03a5531p+0, -0x1.5d00p-46, | |
291 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, | |
292 0x1.6434634ccc313p+0, -0x1.a800p-49, | |
293 0x1.652b9febc8efap+0, -0x1.8600p-45, | |
294 0x1.6623882553397p+0, 0x1.1fe0p-40, | |
295 0x1.671c1c708328ep+0, -0x1.7200p-44, | |
296 0x1.68155d44ca97ep+0, 0x1.6800p-49, | |
297 0x1.690f4b19e9471p+0, -0x1.9780p-45, | |
298 }; | 166 }; |
299 | 167 |
300 /* | 168 /* |
301 * exp2(x): compute the base 2 exponential of x | 169 * exp2(x): compute the base 2 exponential of x |
302 * | 170 * |
303 * Accuracy: Peak error < 0.503 ulp for normalized results. | 171 * Accuracy: Peak error < 0.503 ulp for normalized results. |
304 * | 172 * |
305 * Method: (accurate tables) | 173 * Method: (accurate tables) |
306 * | 174 * |
307 * Reduce x: | 175 * Reduce x: |
(...skipping 13 matching lines...) Expand all Loading... |
321 * | 189 * |
322 * Note that the range of i is +-TBLSIZE/2, so we actually index the tables | 190 * Note that the range of i is +-TBLSIZE/2, so we actually index the tables |
323 * by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are | 191 * by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are |
324 * virtual tables, interleaved in the real table tbl[]. | 192 * virtual tables, interleaved in the real table tbl[]. |
325 * | 193 * |
326 * This method is due to Gal, with many details due to Gal and Bachelis: | 194 * This method is due to Gal, with many details due to Gal and Bachelis: |
327 * | 195 * |
328 * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library | 196 * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library |
329 * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). | 197 * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). |
330 */ | 198 */ |
331 double exp2(double x) | 199 double exp2(double x) { |
332 { | 200 double_t r, t, z; |
333 » double_t r, t, z; | 201 uint32_t ix, i0; |
334 » uint32_t ix, i0; | 202 union { |
335 » union {double f; uint64_t i;} u = {x}; | 203 double f; |
336 » union {uint32_t u; int32_t i;} k; | 204 uint64_t i; |
| 205 } u = {x}; |
| 206 union { |
| 207 uint32_t u; |
| 208 int32_t i; |
| 209 } k; |
337 | 210 |
338 » /* Filter out exceptional cases. */ | 211 /* Filter out exceptional cases. */ |
339 » ix = u.i>>32 & 0x7fffffff; | 212 ix = u.i >> 32 & 0x7fffffff; |
340 » if (ix >= 0x408ff000) { /* |x| >= 1022 or nan */ | 213 if (ix >= 0x408ff000) { /* |x| >= 1022 or nan */ |
341 » » if (ix >= 0x40900000 && u.i>>63 == 0) { /* x >= 1024 or nan */ | 214 if (ix >= 0x40900000 && u.i >> 63 == 0) { /* x >= 1024 or nan */ |
342 » » » /* overflow */ | 215 /* overflow */ |
343 » » » x *= 0x1p1023; | 216 x *= 0x1p1023; |
344 » » » return x; | 217 return x; |
345 » » } | 218 } |
346 » » if (ix >= 0x7ff00000) /* -inf or -nan */ | 219 if (ix >= 0x7ff00000) /* -inf or -nan */ |
347 » » » return -1/x; | 220 return -1 / x; |
348 » » if (u.i>>63) { /* x <= -1022 */ | 221 if (u.i >> 63) { /* x <= -1022 */ |
349 » » » /* underflow */ | 222 /* underflow */ |
350 » » » if (x <= -1075 || x - 0x1p52 + 0x1p52 != x) | 223 if (x <= -1075 || x - 0x1p52 + 0x1p52 != x) |
351 » » » » FORCE_EVAL((float)(-0x1p-149/x)); | 224 FORCE_EVAL((float)(-0x1p-149 / x)); |
352 » » » if (x <= -1075) | 225 if (x <= -1075) |
353 » » » » return 0; | 226 return 0; |
354 » » } | 227 } |
355 » } else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ | 228 } else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ |
356 » » return 1.0 + x; | 229 return 1.0 + x; |
357 » } | 230 } |
358 | 231 |
359 » /* Reduce x, computing z, i0, and k. */ | 232 /* Reduce x, computing z, i0, and k. */ |
360 » u.f = x + redux; | 233 u.f = x + redux; |
361 » i0 = u.i; | 234 i0 = u.i; |
362 » i0 += TBLSIZE / 2; | 235 i0 += TBLSIZE / 2; |
363 » k.u = i0 / TBLSIZE * TBLSIZE; | 236 k.u = i0 / TBLSIZE * TBLSIZE; |
364 » k.i /= TBLSIZE; | 237 k.i /= TBLSIZE; |
365 » i0 %= TBLSIZE; | 238 i0 %= TBLSIZE; |
366 » u.f -= redux; | 239 u.f -= redux; |
367 » z = x - u.f; | 240 z = x - u.f; |
368 | 241 |
369 » /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ | 242 /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ |
370 » t = tbl[2*i0]; /* exp2t[i0] */ | 243 t = tbl[2 * i0]; /* exp2t[i0] */ |
371 » z -= tbl[2*i0 + 1]; /* eps[i0] */ | 244 z -= tbl[2 * i0 + 1]; /* eps[i0] */ |
372 » r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); | 245 r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); |
373 | 246 |
374 » return scalbn(r, k.i); | 247 return scalbn(r, k.i); |
375 } | 248 } |
OLD | NEW |