1 | /* |
2 | * Shared data between exp, exp2 and pow. |
3 | * |
4 | * Copyright (c) 2018, Arm Limited. |
5 | * SPDX-License-Identifier: MIT |
6 | */ |
7 | |
8 | #include "exp_data.h" |
9 | |
10 | #define N (1 << EXP_TABLE_BITS) |
11 | |
12 | const struct exp_data __exp_data = { |
13 | // N/ln2 |
14 | .invln2N = 0x1.71547652b82fep0 * N, |
15 | // -ln2/N |
16 | .negln2hiN = -0x1.62e42fefa0000p-8, |
17 | .negln2loN = -0x1.cf79abc9e3b3ap-47, |
18 | // Used for rounding when !TOINT_INTRINSICS |
19 | #if EXP_USE_TOINT_NARROW |
20 | .shift = 0x1800000000.8p0, |
21 | #else |
22 | .shift = 0x1.8p52, |
23 | #endif |
24 | // exp polynomial coefficients. |
25 | .poly = { |
26 | // abs error: 1.555*2^-66 |
27 | // ulp error: 0.509 (0.511 without fma) |
28 | // if |x| < ln2/256+eps |
29 | // abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65 |
30 | // abs error if |x| < ln2/128: 1.7145*2^-56 |
31 | 0x1.ffffffffffdbdp-2, |
32 | 0x1.555555555543cp-3, |
33 | 0x1.55555cf172b91p-5, |
34 | 0x1.1111167a4d017p-7, |
35 | }, |
36 | .exp2_shift = 0x1.8p52 / N, |
37 | // exp2 polynomial coefficients. |
38 | .exp2_poly = { |
39 | // abs error: 1.2195*2^-65 |
40 | // ulp error: 0.507 (0.511 without fma) |
41 | // if |x| < 1/256 |
42 | // abs error if |x| < 1/128: 1.9941*2^-56 |
43 | 0x1.62e42fefa39efp-1, |
44 | 0x1.ebfbdff82c424p-3, |
45 | 0x1.c6b08d70cf4b5p-5, |
46 | 0x1.3b2abd24650ccp-7, |
47 | 0x1.5d7e09b4e3a84p-10, |
48 | }, |
49 | // 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N) |
50 | // tab[2*k] = asuint64(T[k]) |
51 | // tab[2*k+1] = asuint64(H[k]) - (k << 52)/N |
52 | .tab = { |
53 | 0x0, 0x3ff0000000000000, |
54 | 0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335, |
55 | 0xbc7160139cd8dc5d, 0x3fefec9a3e778061, |
56 | 0xbc905e7a108766d1, 0x3fefe315e86e7f85, |
57 | 0x3c8cd2523567f613, 0x3fefd9b0d3158574, |
58 | 0xbc8bce8023f98efa, 0x3fefd06b29ddf6de, |
59 | 0x3c60f74e61e6c861, 0x3fefc74518759bc8, |
60 | 0x3c90a3e45b33d399, 0x3fefbe3ecac6f383, |
61 | 0x3c979aa65d837b6d, 0x3fefb5586cf9890f, |
62 | 0x3c8eb51a92fdeffc, 0x3fefac922b7247f7, |
63 | 0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2, |
64 | 0xbc6a033489906e0b, 0x3fef9b66affed31b, |
65 | 0xbc9556522a2fbd0e, 0x3fef9301d0125b51, |
66 | 0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc, |
67 | 0xbc91c923b9d5f416, 0x3fef829aaea92de0, |
68 | 0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51, |
69 | 0xbc801b15eaa59348, 0x3fef72b83c7d517b, |
70 | 0xbc8f1ff055de323d, 0x3fef6af9388c8dea, |
71 | 0x3c8b898c3f1353bf, 0x3fef635beb6fcb75, |
72 | 0xbc96d99c7611eb26, 0x3fef5be084045cd4, |
73 | 0x3c9aecf73e3a2f60, 0x3fef54873168b9aa, |
74 | 0xbc8fe782cb86389d, 0x3fef4d5022fcd91d, |
75 | 0x3c8a6f4144a6c38d, 0x3fef463b88628cd6, |
76 | 0x3c807a05b0e4047d, 0x3fef3f49917ddc96, |
77 | 0x3c968efde3a8a894, 0x3fef387a6e756238, |
78 | 0x3c875e18f274487d, 0x3fef31ce4fb2a63f, |
79 | 0x3c80472b981fe7f2, 0x3fef2b4565e27cdd, |
80 | 0xbc96b87b3f71085e, 0x3fef24dfe1f56381, |
81 | 0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1, |
82 | 0xbc3d219b1a6fbffa, 0x3fef187fd0dad990, |
83 | 0x3c8b3782720c0ab4, 0x3fef1285a6e4030b, |
84 | 0x3c6e149289cecb8f, 0x3fef0cafa93e2f56, |
85 | 0x3c834d754db0abb6, 0x3fef06fe0a31b715, |
86 | 0x3c864201e2ac744c, 0x3fef0170fc4cd831, |
87 | 0x3c8fdd395dd3f84a, 0x3feefc08b26416ff, |
88 | 0xbc86a3803b8e5b04, 0x3feef6c55f929ff1, |
89 | 0xbc924aedcc4b5068, 0x3feef1a7373aa9cb, |
90 | 0xbc9907f81b512d8e, 0x3feeecae6d05d866, |
91 | 0xbc71d1e83e9436d2, 0x3feee7db34e59ff7, |
92 | 0xbc991919b3ce1b15, 0x3feee32dc313a8e5, |
93 | 0x3c859f48a72a4c6d, 0x3feedea64c123422, |
94 | 0xbc9312607a28698a, 0x3feeda4504ac801c, |
95 | 0xbc58a78f4817895b, 0x3feed60a21f72e2a, |
96 | 0xbc7c2c9b67499a1b, 0x3feed1f5d950a897, |
97 | 0x3c4363ed60c2ac11, 0x3feece086061892d, |
98 | 0x3c9666093b0664ef, 0x3feeca41ed1d0057, |
99 | 0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0, |
100 | 0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de, |
101 | 0x3c7690cebb7aafb0, 0x3feebfdad5362a27, |
102 | 0x3c931dbdeb54e077, 0x3feebcb299fddd0d, |
103 | 0xbc8f94340071a38e, 0x3feeb9b2769d2ca7, |
104 | 0xbc87deccdc93a349, 0x3feeb6daa2cf6642, |
105 | 0xbc78dec6bd0f385f, 0x3feeb42b569d4f82, |
106 | 0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f, |
107 | 0x3c93350518fdd78e, 0x3feeaf4736b527da, |
108 | 0x3c7b98b72f8a9b05, 0x3feead12d497c7fd, |
109 | 0x3c9063e1e21c5409, 0x3feeab07dd485429, |
110 | 0x3c34c7855019c6ea, 0x3feea9268a5946b7, |
111 | 0x3c9432e62b64c035, 0x3feea76f15ad2148, |
112 | 0xbc8ce44a6199769f, 0x3feea5e1b976dc09, |
113 | 0xbc8c33c53bef4da8, 0x3feea47eb03a5585, |
114 | 0xbc845378892be9ae, 0x3feea34634ccc320, |
115 | 0xbc93cedd78565858, 0x3feea23882552225, |
116 | 0x3c5710aa807e1964, 0x3feea155d44ca973, |
117 | 0xbc93b3efbf5e2228, 0x3feea09e667f3bcd, |
118 | 0xbc6a12ad8734b982, 0x3feea012750bdabf, |
119 | 0xbc6367efb86da9ee, 0x3fee9fb23c651a2f, |
120 | 0xbc80dc3d54e08851, 0x3fee9f7df9519484, |
121 | 0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74, |
122 | 0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174, |
123 | 0xbc8619321e55e68a, 0x3fee9feb564267c9, |
124 | 0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f, |
125 | 0xbc7b32dcb94da51d, 0x3feea11473eb0187, |
126 | 0x3c94ecfd5467c06b, 0x3feea1ed0130c132, |
127 | 0x3c65ebe1abd66c55, 0x3feea2f336cf4e62, |
128 | 0xbc88a1c52fb3cf42, 0x3feea427543e1a12, |
129 | 0xbc9369b6f13b3734, 0x3feea589994cce13, |
130 | 0xbc805e843a19ff1e, 0x3feea71a4623c7ad, |
131 | 0xbc94d450d872576e, 0x3feea8d99b4492ed, |
132 | 0x3c90ad675b0e8a00, 0x3feeaac7d98a6699, |
133 | 0x3c8db72fc1f0eab4, 0x3feeace5422aa0db, |
134 | 0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c, |
135 | 0x3c7bf68359f35f44, 0x3feeb1ae99157736, |
136 | 0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6, |
137 | 0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5, |
138 | 0xbc6c23f97c90b959, 0x3feeba44cbc8520f, |
139 | 0xbc92434322f4f9aa, 0x3feebd829fde4e50, |
140 | 0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba, |
141 | 0x3c71affc2b91ce27, 0x3feec49182a3f090, |
142 | 0x3c6dd235e10a73bb, 0x3feec86319e32323, |
143 | 0xbc87c50422622263, 0x3feecc667b5de565, |
144 | 0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33, |
145 | 0xbc91bbd1d3bcbb15, 0x3feed503b23e255d, |
146 | 0x3c90cc319cee31d2, 0x3feed99e1330b358, |
147 | 0x3c8469846e735ab3, 0x3feede6b5579fdbf, |
148 | 0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a, |
149 | 0x3c8c1a7792cb3387, 0x3feee89f995ad3ad, |
150 | 0xbc907b8f4ad1d9fa, 0x3feeee07298db666, |
151 | 0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb, |
152 | 0xbc90a40e3da6f640, 0x3feef9728de5593a, |
153 | 0xbc68d6f438ad9334, 0x3feeff76f2fb5e47, |
154 | 0xbc91eee26b588a35, 0x3fef05b030a1064a, |
155 | 0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2, |
156 | 0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09, |
157 | 0x3c736eae30af0cb3, 0x3fef199bdd85529c, |
158 | 0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a, |
159 | 0x3c84e08fd10959ac, 0x3fef27f12e57d14b, |
160 | 0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5, |
161 | 0x3c676b2c6c921968, 0x3fef3720dcef9069, |
162 | 0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa, |
163 | 0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c, |
164 | 0xbc900dae3875a949, 0x3fef4f87080d89f2, |
165 | 0x3c74a385a63d07a7, 0x3fef5818dcfba487, |
166 | 0xbc82919e2040220f, 0x3fef60e316c98398, |
167 | 0x3c8e5a50d5c192ac, 0x3fef69e603db3285, |
168 | 0x3c843a59ac016b4b, 0x3fef7321f301b460, |
169 | 0xbc82d52107b43e1f, 0x3fef7c97337b9b5f, |
170 | 0xbc892ab93b470dc9, 0x3fef864614f5a129, |
171 | 0x3c74b604603a88d3, 0x3fef902ee78b3ff6, |
172 | 0x3c83c5ec519d7271, 0x3fef9a51fbc74c83, |
173 | 0xbc8ff7128fd391f0, 0x3fefa4afa2a490da, |
174 | 0xbc8dae98e223747d, 0x3fefaf482d8e67f1, |
175 | 0x3c8ec3bc41aa2008, 0x3fefba1bee615a27, |
176 | 0x3c842b94c3a9eb32, 0x3fefc52b376bba97, |
177 | 0x3c8a64a931d185ee, 0x3fefd0765b6e4540, |
178 | 0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14, |
179 | 0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8, |
180 | 0x3c5305c14160cc89, 0x3feff3c22b8f71f1, |
181 | }, |
182 | }; |
183 | |