1.file "exp10l.s" 2 3 4// Copyright (c) 2000 - 2004, Intel Corporation 5// All rights reserved. 6// 7// 8// Redistribution and use in source and binary forms, with or without 9// modification, are permitted provided that the following conditions are 10// met: 11// 12// * Redistributions of source code must retain the above copyright 13// notice, this list of conditions and the following disclaimer. 14// 15// * Redistributions in binary form must reproduce the above copyright 16// notice, this list of conditions and the following disclaimer in the 17// documentation and/or other materials provided with the distribution. 18// 19// * The name of Intel Corporation may not be used to endorse or promote 20// products derived from this software without specific prior written 21// permission. 22 23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING 32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 34// 35// Intel Corporation is the author of this code, and requests that all 36// problem reports or change requests be submitted to it directly at 37// http://www.intel.com/software/products/opensource/libraries/num.htm. 38// 39// History 40//============================================================== 41// 08/25/00 Initial version 42// 05/20/02 Cleaned up namespace and sf0 syntax 43// 02/06/03 Reordered header: .section, .global, .proc, .align 44// 05/08/03 Reformatted assembly source; corrected overflow result for round to 45// -inf and round to zero; exact results now don't set inexact flag 46// 12/16/04 Call error handling on underflow. 47// 48// API 49//============================================================== 50// long double exp10l(long double) 51// 52// Overview of operation 53//============================================================== 54// Background 55// 56// Implementation 57// 58// Let x= (K + f + r)/log2(10), where 59// K is an integer, f= 0.b1 b2... b8 (f>= 0), 60// and |r|<2^{-9} 61// T is a table that stores 2^f (256 entries) rounded to 62// double extended precision (only mantissa is stored) 63// D stores (2^f/T [ f ] - 1), rounded to single precision 64// 65// 10^x is approximated as 66// 2^K * T [ f ] * ((1+c1*r+c2*r^2+...+c6*r^6)*(1+c1*e)+D [ f ] ), 67// where e= log2(10)_lo*x+(log2(10)_hi*x-RN(log2(10)_hi*x)) 68// 69 70 71 72// Special values 73//============================================================== 74// exp10(0)= 1 75// exp10(+inf)= inf 76// exp10(-inf)= 0 77// 78 79 80// Registers used 81//============================================================== 82// f6-f15, f32-f63 83// r14-r30, r32-r40 84// p6-p8, p11-p14 85// 86 87#include <shlib-compat.h> 88 89 90 FR_X = f10 91 FR_Y = f1 92 FR_RESULT = f8 93 94 FR_COEFF1 = f6 95 FR_COEFF2 = f7 96 FR_KF0 = f9 97 FR_LOG10 = f10 98 FR_CONST1 = f11 99 FR_XL10 = f12 100 FR_COEFF3 = f13 101 FR_COEFF4 = f14 102 FR_UF_TEST = f15 103 FR_OF_TEST = f32 104 FR_L10_LOW = f33 105 FR_COEFF5 = f34 106 FR_COEFF6 = f35 107 FR_L10 = f36 108 FR_C_L10 = f37 109 FR_XL10_H = f38 110 FR_XL10_L = f39 111 FR_KF = f40 112 FR_E = f41 113 FR_T = f42 114 FR_D = f43 115 FR_EXP_M_63 = f44 116 FR_R = f45 117 FR_E1 = f46 118 FR_COEFF2 = f47 119 FR_P34 = f48 120 FR_P56 = f49 121 FR_R2 = f50 122 FR_RE = f51 123 FR_D1 = f52 124 FR_P36 = f53 125 FR_R3E = f54 126 FR_P1 = f55 127 FR_P = f56 128 FR_T1 = f57 129 FR_XINT = f58 130 FR_XINTF = f59 131 FR_4 = f60 132 FR_28 = f61 133 FR_32 = f62 134 FR_SNORM_LIMIT = f63 135 136 137 GR_ADDR0 = r14 138 GR_D_ADDR = r15 139 GR_ADDR = r16 140 GR_B63 = r17 141 GR_KBITS = r18 142 GR_F = r19 143 GR_K = r20 144 GR_D = r21 145 GR_BM63 = r22 146 GR_T = r23 147 GR_CONST1 = r24 148 GR_EMIN = r25 149 GR_CONST2 = r26 150 GR_BM8 = r27 151 GR_SREG = r28 152 GR_4_BIAS = r29 153 GR_32_BIAS = r30 154 155 GR_SAVE_B0 = r33 156 GR_SAVE_PFS = r34 157 GR_SAVE_GP = r35 158 GR_SAVE_SP = r36 159 160 GR_Parameter_X = r37 161 GR_Parameter_Y = r38 162 GR_Parameter_RESULT= r39 163 GR_Parameter_TAG = r40 164 165 166// Data tables 167//============================================================== 168 169RODATA 170 171.align 16 172 173LOCAL_OBJECT_START(poly_coeffs) 174 175 data8 0xd49a784bcd1b8afe, 0x00004008 // log2(10)*2^8 176 data8 0x9a209a84fbcff798, 0x0000400b // overflow threshold 177 data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1 178 data8 0xf5fdeffc162c7541, 0x00003ffc // C_2 179 data8 0x3fac6b08d704a0c0 // C_3 180 data8 0x3f83b2ab6fba4e77 // C_4 181 data8 0x3f55d87fe78a6731 // C_5 182 data8 0x3f2430912f86c787 // C_6 183 data8 0x9257edfe9b5fb698, 0x00003fbf // log2(10)_low (bits 64...127) 184 data8 0x9a1bc98027a81918, 0x0000c00b // Smallest normal threshold 185LOCAL_OBJECT_END(poly_coeffs) 186 187 188LOCAL_OBJECT_START(T_table) 189 190 // 2^{0.b1 b2 b3 b4 b5 b6 b7 b8} 191 data8 0x8000000000000000, 0x8058d7d2d5e5f6b1 192 data8 0x80b1ed4fd999ab6c, 0x810b40a1d81406d4 193 data8 0x8164d1f3bc030773, 0x81bea1708dde6056 194 data8 0x8218af4373fc25ec, 0x8272fb97b2a5894c 195 data8 0x82cd8698ac2ba1d7, 0x83285071e0fc4547 196 data8 0x8383594eefb6ee37, 0x83dea15b9541b132 197 data8 0x843a28c3acde4046, 0x8495efb3303efd30 198 data8 0x84f1f656379c1a29, 0x854e3cd8f9c8c95d 199 data8 0x85aac367cc487b15, 0x86078a2f23642a9f 200 data8 0x8664915b923fba04, 0x86c1d919caef5c88 201 data8 0x871f61969e8d1010, 0x877d2afefd4e256c 202 data8 0x87db357ff698d792, 0x88398146b919f1d4 203 data8 0x88980e8092da8527, 0x88f6dd5af155ac6b 204 data8 0x8955ee03618e5fdd, 0x89b540a7902557a4 205 data8 0x8a14d575496efd9a, 0x8a74ac9a79896e47 206 data8 0x8ad4c6452c728924, 0x8b3522a38e1e1032 207 data8 0x8b95c1e3ea8bd6e7, 0x8bf6a434adde0085 208 data8 0x8c57c9c4646f4dde, 0x8cb932c1bae97a95 209 data8 0x8d1adf5b7e5ba9e6, 0x8d7ccfc09c50e2f8 210 data8 0x8ddf042022e69cd6, 0x8e417ca940e35a01 211 data8 0x8ea4398b45cd53c0, 0x8f073af5a2013520 212 data8 0x8f6a8117e6c8e5c4, 0x8fce0c21c6726481 213 data8 0x9031dc431466b1dc, 0x9095f1abc540ca6b 214 data8 0x90fa4c8beee4b12b, 0x915eed13c89689d3 215 data8 0x91c3d373ab11c336, 0x9228ffdc10a051ad 216 data8 0x928e727d9531f9ac, 0x92f42b88f673aa7c 217 data8 0x935a2b2f13e6e92c, 0x93c071a0eef94bc1 218 data8 0x9426ff0fab1c04b6, 0x948dd3ac8ddb7ed3 219 data8 0x94f4efa8fef70961, 0x955c5336887894d5 220 data8 0x95c3fe86d6cc7fef, 0x962bf1cbb8d97560 221 data8 0x96942d3720185a00, 0x96fcb0fb20ac4ba3 222 data8 0x97657d49f17ab08e, 0x97ce9255ec4357ab 223 data8 0x9837f0518db8a96f, 0x98a1976f7597e996 224 data8 0x990b87e266c189aa, 0x9975c1dd47518c77 225 data8 0x99e0459320b7fa65, 0x9a4b13371fd166ca 226 data8 0x9ab62afc94ff864a, 0x9b218d16f441d63d 227 data8 0x9b8d39b9d54e5539, 0x9bf93118f3aa4cc1 228 data8 0x9c6573682ec32c2d, 0x9cd200db8a0774cb 229 data8 0x9d3ed9a72cffb751, 0x9dabfdff6367a2aa 230 data8 0x9e196e189d472420, 0x9e872a276f0b98ff 231 data8 0x9ef5326091a111ae, 0x9f6386f8e28ba651 232 data8 0x9fd228256400dd06, 0xa041161b3d0121be 233 data8 0xa0b0510fb9714fc2, 0xa11fd9384a344cf7 234 data8 0xa18faeca8544b6e4, 0xa1ffd1fc25cea188 235 data8 0xa27043030c496819, 0xa2e102153e918f9e 236 data8 0xa3520f68e802bb93, 0xa3c36b345991b47c 237 data8 0xa43515ae09e6809e, 0xa4a70f0c95768ec5 238 data8 0xa5195786be9ef339, 0xa58bef536dbeb6ee 239 data8 0xa5fed6a9b15138ea, 0xa6720dc0be08a20c 240 data8 0xa6e594cfeee86b1e, 0xa7596c0ec55ff55b 241 data8 0xa7cd93b4e965356a, 0xa8420bfa298f70d1 242 data8 0xa8b6d5167b320e09, 0xa92bef41fa77771b 243 data8 0xa9a15ab4ea7c0ef8, 0xaa1717a7b5693979 244 data8 0xaa8d2652ec907629, 0xab0386ef48868de1 245 data8 0xab7a39b5a93ed337, 0xabf13edf162675e9 246 data8 0xac6896a4be3fe929, 0xace0413ff83e5d04 247 data8 0xad583eea42a14ac6, 0xadd08fdd43d01491 248 data8 0xae493452ca35b80e, 0xaec22c84cc5c9465 249 data8 0xaf3b78ad690a4375, 0xafb51906e75b8661 250 data8 0xb02f0dcbb6e04584, 0xb0a957366fb7a3c9 251 data8 0xb123f581d2ac2590, 0xb19ee8e8c94feb09 252 data8 0xb21a31a66618fe3b, 0xb295cff5e47db4a4 253 data8 0xb311c412a9112489, 0xb38e0e38419fae18 254 data8 0xb40aaea2654b9841, 0xb487a58cf4a9c180 255 data8 0xb504f333f9de6484, 0xb58297d3a8b9f0d2 256 data8 0xb60093a85ed5f76c, 0xb67ee6eea3b22b8f 257 data8 0xb6fd91e328d17791, 0xb77c94c2c9d725e9 258 data8 0xb7fbefca8ca41e7c, 0xb87ba337a1743834 259 data8 0xb8fbaf4762fb9ee9, 0xb97c143756844dbf 260 data8 0xb9fcd2452c0b9deb, 0xba7de9aebe5fea09 261 data8 0xbaff5ab2133e45fb, 0xbb81258d5b704b6f 262 data8 0xbc034a7ef2e9fb0d, 0xbc85c9c560e7b269 263 data8 0xbd08a39f580c36bf, 0xbd8bd84bb67ed483 264 data8 0xbe0f6809860993e2, 0xbe935317fc378238 265 data8 0xbf1799b67a731083, 0xbf9c3c248e2486f8 266 data8 0xc0213aa1f0d08db0, 0xc0a6956e8836ca8d 267 data8 0xc12c4cca66709456, 0xc1b260f5ca0fbb33 268 data8 0xc238d2311e3d6673, 0xc2bfa0bcfad907c9 269 data8 0xc346ccda24976407, 0xc3ce56c98d21b15d 270 data8 0xc4563ecc5334cb33, 0xc4de8523c2c07baa 271 data8 0xc5672a115506dadd, 0xc5f02dd6b0bbc3d9 272 data8 0xc67990b5aa245f79, 0xc70352f04336c51e 273 data8 0xc78d74c8abb9b15d, 0xc817f681416452b2 274 data8 0xc8a2d85c8ffe2c45, 0xc92e1a9d517f0ecc 275 data8 0xc9b9bd866e2f27a3, 0xca45c15afcc72624 276 data8 0xcad2265e4290774e, 0xcb5eecd3b38597c9 277 data8 0xcbec14fef2727c5d, 0xcc799f23d11510e5 278 data8 0xcd078b86503dcdd2, 0xcd95da6a9ff06445 279 data8 0xce248c151f8480e4, 0xceb3a0ca5dc6a55d 280 data8 0xcf4318cf191918c1, 0xcfd2f4683f94eeb5 281 data8 0xd06333daef2b2595, 0xd0f3d76c75c5db8d 282 data8 0xd184df6251699ac6, 0xd2164c023056bcab 283 data8 0xd2a81d91f12ae45a, 0xd33a5457a3029054 284 data8 0xd3ccf099859ac379, 0xd45ff29e0972c561 285 data8 0xd4f35aabcfedfa1f, 0xd5872909ab75d18a 286 data8 0xd61b5dfe9f9bce07, 0xd6aff9d1e13ba2fe 287 data8 0xd744fccad69d6af4, 0xd7da67311797f56a 288 data8 0xd870394c6db32c84, 0xd9067364d44a929c 289 data8 0xd99d15c278afd7b6, 0xda3420adba4d8704 290 data8 0xdacb946f2ac9cc72, 0xdb63714f8e295255 291 data8 0xdbfbb797daf23755, 0xdc9467913a4f1c92 292 data8 0xdd2d818508324c20, 0xddc705bcd378f7f0 293 data8 0xde60f4825e0e9124, 0xdefb4e1f9d1037f2 294 data8 0xdf9612deb8f04420, 0xe031430a0d99e627 295 data8 0xe0ccdeec2a94e111, 0xe168e6cfd3295d23 296 data8 0xe2055afffe83d369, 0xe2a23bc7d7d91226 297 data8 0xe33f8972be8a5a51, 0xe3dd444c46499619 298 data8 0xe47b6ca0373da88d, 0xe51a02ba8e26d681 299 data8 0xe5b906e77c8348a8, 0xe658797368b3a717 300 data8 0xe6f85aaaee1fce22, 0xe798aadadd5b9cbf 301 data8 0xe8396a503c4bdc68, 0xe8da9958464b42ab 302 data8 0xe97c38406c4f8c57, 0xea1e4756550eb27b 303 data8 0xeac0c6e7dd24392f, 0xeb63b74317369840 304 data8 0xec0718b64c1cbddc, 0xecaaeb8ffb03ab41 305 data8 0xed4f301ed9942b84, 0xedf3e6b1d418a491 306 data8 0xee990f980da3025b, 0xef3eab20e032bc6b 307 data8 0xefe4b99bdcdaf5cb, 0xf08b3b58cbe8b76a 308 data8 0xf13230a7ad094509, 0xf1d999d8b7708cc1 309 data8 0xf281773c59ffb13a, 0xf329c9233b6bae9c 310 data8 0xf3d28fde3a641a5b, 0xf47bcbbe6db9fddf 311 data8 0xf5257d152486cc2c, 0xf5cfa433e6537290 312 data8 0xf67a416c733f846e, 0xf7255510c4288239 313 data8 0xf7d0df730ad13bb9, 0xf87ce0e5b2094d9c 314 data8 0xf92959bb5dd4ba74, 0xf9d64a46eb939f35 315 data8 0xfa83b2db722a033a, 0xfb3193cc4227c3f4 316 data8 0xfbdfed6ce5f09c49, 0xfc8ec01121e447bb 317 data8 0xfd3e0c0cf486c175, 0xfdedd1b496a89f35 318 data8 0xfe9e115c7b8f884c, 0xff4ecb59511ec8a5 319LOCAL_OBJECT_END(T_table) 320 321 322LOCAL_OBJECT_START(D_table) 323 data4 0x00000000, 0x9f55c08f, 0x1e93ffa3, 0x1dcd43a8 324 data4 0x1f751f79, 0x9f3cdd88, 0x9f43d155, 0x1eda222c 325 data4 0x1ef35513, 0x9f597895, 0x9e698881, 0x1ec71073 326 data4 0x1e50e371, 0x9dc01e19, 0x1de74133, 0x1e2f028c 327 data4 0x9edefb47, 0x1ebbac48, 0x9e8b0330, 0x9e9e9314 328 data4 0x1edc1d11, 0x1f098529, 0x9f52827c, 0x1f50050d 329 data4 0x1f301e8e, 0x1f5b64d1, 0x9f45e3ee, 0x9ef64d6d 330 data4 0x1d6ec5e8, 0x9e61ad9a, 0x1d44ccbb, 0x9e4a8bbb 331 data4 0x9cf11576, 0x9dcce7e7, 0x9d02ac90, 0x1f26ccf0 332 data4 0x9f0877c6, 0x9ddd62ae, 0x9f4b7fc3, 0x1ea8ef6b 333 data4 0x1ea4378d, 0x1ef6fc38, 0x1db99fd9, 0x1f22bf6f 334 data4 0x1f53e172, 0x1e85504a, 0x9f37cc75, 0x1f0c5e17 335 data4 0x1dde8aac, 0x9cb42bb2, 0x1e153cd7, 0x1eb62bba 336 data4 0x9e9b941b, 0x9ea80e3c, 0x1f508823, 0x1ec3fd36 337 data4 0x1e9ffaa1, 0x1e21e2eb, 0x9d948b1d, 0x9e8ac93a 338 data4 0x1ef7ee6f, 0x9e80dda3, 0x1f0814be, 0x1dc5ddfe 339 data4 0x1eedb9d1, 0x9f2aaa26, 0x9ea5b0fc, 0x1edf702e 340 data4 0x9e391201, 0x1f1316bb, 0x1ea27fb7, 0x9e05ed18 341 data4 0x9f199ed2, 0x1ee7fd7c, 0x1f003db6, 0x9eac3793 342 data4 0x9e5b8c10, 0x9f3af17c, 0x1bc9a8be, 0x1ee3c004 343 data4 0x9f19b1b2, 0x9f242ce9, 0x9ce67dd1, 0x9e4f6275 344 data4 0x1e20742c, 0x1eb9328a, 0x9f477153, 0x1d969718 345 data4 0x9f1e6c43, 0x1f2f67f4, 0x9f39c7e4, 0x9e3c4feb 346 data4 0x1da3956b, 0x9e7c685d, 0x1f280911, 0x9f0d8afb 347 data4 0x1e314b40, 0x9eb4f250, 0x9f1a34ad, 0x1ef5d5e7 348 data4 0x9f145496, 0x1e604827, 0x9f1e5195, 0x1e9c1fc0 349 data4 0x1efde521, 0x1e69b385, 0x1f316830, 0x9f244eae 350 data4 0x1f1787ec, 0x9e939971, 0x1f0bb393, 0x9f0511d6 351 data4 0x1ed919de, 0x1d8b7b28, 0x1e5ca4a9, 0x1e7c357b 352 data4 0x9e3ff8e8, 0x1eef53b5, 0x9ed22ed7, 0x1f16659b 353 data4 0x9f2db102, 0x9e2c6a78, 0x1f328d7d, 0x9f2fec3c 354 data4 0x1eb395bd, 0x9f242b84, 0x9e2683e6, 0x1ed71e68 355 data4 0x1efd1df5, 0x9e9eeafd, 0x9ed2249c, 0x1eef129a 356 data4 0x1d1ea44c, 0x9e81f7ff, 0x1eaf77c9, 0x9ee7a285 357 data4 0x1e1864ed, 0x9ee7edbb, 0x9e15a27d, 0x9ae61655 358 data4 0x1f1ff1a2, 0x1da29755, 0x9e5f46fb, 0x1e901236 359 data4 0x9eecfb9b, 0x9f204d2f, 0x1ec64685, 0x9eb809bd 360 data4 0x9e0026c5, 0x1d9f1da1, 0x1f142b49, 0x9f20f22e 361 data4 0x1f24b067, 0x1f185a4c, 0x9f09765c, 0x9ece902f 362 data4 0x1e2ca5db, 0x1e6de464, 0x9f071f67, 0x1f1518c3 363 data4 0x1ea13ded, 0x1f0b8414, 0x1edb6ad4, 0x9e548740 364 data4 0x9ea10efb, 0x1ee48a60, 0x1e7954c5, 0x9edad013 365 data4 0x9f21517d, 0x9e9b6e0c, 0x9ee7f9a6, 0x9ebd4298 366 data4 0x9d65b24e, 0x1eed751f, 0x9f1573ea, 0x9d430377 367 data4 0x9e13fc0c, 0x1e47008a, 0x1e3d5c1d, 0x1ef41a91 368 data4 0x9e4a4ef7, 0x9e952f18, 0x1d620566, 0x1d9b8d33 369 data4 0x1db06247, 0x1e94b31e, 0x1f0730ad, 0x9d79ffb4 370 data4 0x1ed64d51, 0x9e91fd11, 0x9e28d35a, 0x9dea0ed9 371 data4 0x1e891def, 0x9ee28ac0, 0x1e1db99b, 0x9ee1ce38 372 data4 0x9bdd9bca, 0x1eb72cb9, 0x9e8c53c6, 0x1e0df6ca 373 data4 0x1e8f2ccd, 0x9e9b0886, 0x1eeb3bc7, 0x1ec7e772 374 data4 0x9e210776, 0x9daf246c, 0x1ea1f151, 0x1ece4dc6 375 data4 0x1ce741c8, 0x1ed3c88f, 0x9ec9a4fd, 0x9e0c8d30 376 data4 0x1d2fbb26, 0x9ef212a7, 0x1ee44f1c, 0x9e445550 377 data4 0x1e075f77, 0x9d9291a3, 0x1f09c2ee, 0x9e012c88 378 data4 0x1f057d62, 0x9e7bb0dc, 0x9d8758ee, 0x1ee8d6c1 379 data4 0x9e509a57, 0x9e4ca7b7, 0x1e2cb341, 0x9ec35106 380 data4 0x1ecf3baf, 0x1e11781c, 0x1ea0cc78, 0x1eb75ca6 381 data4 0x1e961e1a, 0x1eb88853, 0x1e7abf50, 0x1ee38704 382 data4 0x9dc5ab0f, 0x1afe197b, 0x9ec07523, 0x9d9b7f78 383 data4 0x1f011618, 0x1ed43b0b, 0x9f035945, 0x9e3fd014 384 data4 0x9bbda5cd, 0x9e83f8ab, 0x1e58a928, 0x1e392d61 385 data4 0x1efdbb52, 0x1ee310a8, 0x9ec7ecc1, 0x1e8c9ed6 386 data4 0x9ef82dee, 0x9e70545b, 0x9ea53fc4, 0x1e40f419 387LOCAL_OBJECT_END(D_table) 388 389 390 391.section .text 392GLOBAL_IEEE754_ENTRY(exp10l) 393 394{.mfi 395 alloc GR_SREG = ar.pfs, 1, 4, 4, 0 396 // will continue only for normal/denormal numbers 397 fclass.nm.unc p12, p7 = f8, 0x1b 398 // GR_ADDR0 = pointer to log2(10), C_1...C_6 followed by T_table 399 addl GR_ADDR0 = @ltoff(poly_coeffs), gp ;; 400} 401 402{.mfi 403 // load start address for C_1...C_6 followed by T_table 404 ld8 GR_ADDR0 = [ GR_ADDR0 ] 405 // X<0 ? 406 fcmp.lt.s1 p6, p8 = f8, f0 407 // GR_BM8 = bias-8 408 mov GR_BM8 = 0xffff-8 409} 410{.mlx 411 nop.m 0 412 // GR_EMIN = (-2^14-62)*2^{8} 413 movl GR_EMIN = 0xca807c00 ;; 414} 415 416{.mmb 417 // FR_CONST1 = 2^{-8} 418 setf.exp FR_CONST1 = GR_BM8 419 // load log2(10)*2^8 420 ldfe FR_LOG10 = [ GR_ADDR0 ], 16 421 (p12) br.cond.spnt SPECIAL_EXP10 ;; 422} 423 424{.mmf 425 setf.s FR_UF_TEST = GR_EMIN 426 // load overflow threshold 427 ldfe FR_OF_TEST = [ GR_ADDR0 ], 16 428 // normalize x 429 fma.s0 f8 = f8, f1, f0 ;; 430} 431 432{.mmi 433 // load C_1 434 ldfe FR_COEFF1 = [ GR_ADDR0 ], 16 ;; 435 // load C_2 436 ldfe FR_COEFF2 = [ GR_ADDR0 ], 16 437 nop.i 0 ;; 438} 439 440{.mmf 441 // GR_D_ADDR = pointer to D table 442 add GR_D_ADDR = 2048-64+96+32, GR_ADDR0 443 // load C_3, C_4 444 ldfpd FR_COEFF3, FR_COEFF4 = [ GR_ADDR0 ], 16 445 // y = x*log2(10)*2^8 446 fma.s1 FR_XL10 = f8, FR_LOG10, f0 ;; 447} 448 449{.mfi 450 // load C_5, C_6 451 ldfpd FR_COEFF5, FR_COEFF6 = [ GR_ADDR0 ], 16 452 // get int(x) 453 fcvt.fx.trunc.s1 FR_XINT = f8 454 nop.i 0 455} 456{.mfi 457 nop.m 0 458 // FR_LOG10 = log2(10) 459 fma.s1 FR_L10 = FR_LOG10, FR_CONST1, f0 460 nop.i 0 ;; 461} 462 463{.mfi 464 // load log2(10)_low 465 ldfe FR_L10_LOW = [ GR_ADDR0 ], 16 466 // y0 = x*log2(10) = x*log2(10)_hi 467 fma.s1 FR_LOG10 = f8, FR_L10, f0 468 mov GR_EMIN = 0xffff-63 469} 470{.mfi 471 mov GR_32_BIAS = 0xffff + 5 472 // (K+f)*2^8 = round_to_int(y) 473 fcvt.fx.s1 FR_KF0 = FR_XL10 474 mov GR_4_BIAS = 0xffff + 2;; 475} 476 477{.mfi 478 // load smallest normal limit 479 ldfe FR_SNORM_LIMIT = [ GR_ADDR0 ], 16 480 // x>overflow threshold ? 481 fcmp.gt.s1 p12, p7 = f8, FR_OF_TEST 482 nop.i 0 ;; 483} 484 485{.mfi 486 setf.exp FR_32 = GR_32_BIAS 487 // x<underflow threshold ? 488 (p7) fcmp.lt.s1 p12, p7 = FR_XL10, FR_UF_TEST 489 nop.i 0 ;; 490} 491 492{.mfi 493 setf.exp FR_4 = GR_4_BIAS 494 fcvt.xf FR_XINTF = FR_XINT 495 nop.i 0 496} 497{.mfi 498 nop.m 0 499 // FR_L10 = log2(10)_h*x-RN(log2(10)_h*x) 500 fms.s1 FR_L10 = f8, FR_L10, FR_LOG10 501 nop.i 0 ;; 502} 503 504{.mfi 505 getf.sig GR_BM8 = FR_KF0 506 fcvt.xf FR_KF0 = FR_KF0 507 mov GR_CONST2 = 255 ;; 508} 509 510{.mfi 511 // GR_CONST2 = f 512 and GR_CONST2 = GR_CONST2, GR_BM8 513 // FR_L10_LOW = e = log2(10)_l*x+(log2(10)_h*x-RN(log2(10)_h*x)) 514 fma.s1 FR_L10_LOW = FR_L10_LOW, f8, FR_L10 515 // GR_BM8 = K 516 shr GR_BM8 = GR_BM8, 8 ;; 517} 518 519{.mmi 520 // address of D 521 shladd GR_D_ADDR = GR_CONST2, 2, GR_D_ADDR 522 // K+ = bias-63 523 add GR_BM8 = GR_BM8, GR_EMIN 524 // address of T 525 shladd GR_ADDR0 = GR_CONST2, 3, GR_ADDR0 ;; 526} 527 528{.mfb 529 // load D 530 ldfs FR_OF_TEST = [ GR_D_ADDR ] 531 // is input an integer ? 532 fcmp.eq.s1 p13, p14 = f8, FR_XINTF 533 (p12) br.cond.spnt OUT_RANGE_EXP10 ;; 534} 535 536{.mmf 537 // load T 538 ldf8 FR_UF_TEST = [ GR_ADDR0 ] 539 // FR_XL10 = 2^{K-63} 540 setf.exp FR_XL10 = GR_BM8 541 // r = x*log2(10)_hi-2^{-10}* [ (K+f)*2^{10} ] 542 fnma.s1 FR_KF0 = FR_KF0, FR_CONST1, FR_LOG10 ;; 543} 544 545{.mfi 546 nop.m 0 547 // get 28.0 548 fms.s1 FR_28 = FR_32, f1, FR_4 549 nop.i 0 550} 551{.mfi 552 nop.m 0 553 // E = 1+C_1*e 554 fma.s1 FR_L10 = FR_L10_LOW, FR_COEFF1, f1 555 nop.i 0 ;; 556} 557 558{.mfi 559 nop.m 0 560 // P12 = C_1+C_2*r 561 fma.s1 FR_COEFF2 = FR_COEFF2, FR_KF0, FR_COEFF1 562 nop.i 0 563} 564{.mfi 565 nop.m 0 566 // P34 = C_3+C_4*r 567 fma.s1 FR_COEFF4 = FR_COEFF4, FR_KF0, FR_COEFF3 568 nop.i 0 ;; 569} 570 571{.mfi 572 nop.m 0 573 // P56 = C_5+C_6*r 574 fma.s1 FR_COEFF5 = FR_COEFF6, FR_KF0, FR_COEFF5 575 nop.i 0 576} 577{.mfi 578 nop.m 0 579 // GR_ADDR0 = r*r 580 fma.s1 FR_COEFF3 = FR_KF0, FR_KF0, f0 581 nop.i 0 ;; 582} 583 584{.mfi 585 nop.m 0 586 // if input is integer, is it positive ? 587 (p13) fcmp.ge.s1 p13, p14 = f8, f0 588 nop.i 0 589} 590{.mfi 591 nop.m 0 592 // r' = r*E 593 fma.s1 FR_KF0 = FR_KF0, FR_L10, f0 594 nop.i 0 ;; 595} 596 597{.mfi 598 nop.m 0 599 // D' = D+C_1*e 600 fma.s1 FR_OF_TEST = FR_L10_LOW, FR_COEFF1, FR_OF_TEST 601 nop.i 0 ;; 602} 603 604{.mfi 605 nop.m 0 606 // test if x >= smallest normal limit 607 fcmp.ge.s1 p11, p0 = f8, FR_SNORM_LIMIT 608 nop.i 0 ;; 609} 610 611{.mfi 612 nop.m 0 613 // P36 = P34+r2*P56 614 fma.s1 FR_COEFF4 = FR_COEFF5, FR_COEFF3, FR_COEFF4 615 nop.i 0 616} 617{.mfi 618 nop.m 0 619 // GR_D_ADDR = r'*r2 620 fma.s1 FR_COEFF3 = FR_COEFF3, FR_KF0, f0 621 nop.i 0 ;; 622} 623 624{.mfi 625 nop.m 0 626 // is input below 28.0 ? 627 (p13) fcmp.lt.s1 p13, p14 = f8, FR_28 628 nop.i 0 629} 630{.mfi 631 nop.m 0 632 // P' = P12*r'+D' 633 fma.s1 FR_COEFF2 = FR_COEFF2, FR_KF0, FR_OF_TEST 634 nop.i 0 ;; 635} 636 637{.mfi 638 nop.m 0 639 // P = P'+r3*P36 640 fma.s1 FR_COEFF3 = FR_COEFF3, FR_COEFF4, FR_COEFF2 641 nop.i 0 642} 643{.mfi 644 nop.m 0 645 // T = 2^{K-63}*T 646 fma.s1 FR_UF_TEST = FR_UF_TEST, FR_XL10, f0 647 nop.i 0 ;; 648} 649 650.pred.rel "mutex",p13,p14 651{.mfi 652 nop.m 0 653 (p13) fma.s1 f8 = FR_COEFF3, FR_UF_TEST, FR_UF_TEST 654 nop.i 0 655} 656{.mfb 657 nop.m 0 658 // result = T+T*P 659 (p14) fma.s0 f8 = FR_COEFF3, FR_UF_TEST, FR_UF_TEST 660 // return 661 (p11) br.ret.sptk b0 ;; // return, if result normal 662} 663 664// Here if result in denormal range (and not zero) 665{.mib 666 nop.m 0 667 mov GR_Parameter_TAG= 264 668 br.cond.sptk __libm_error_region // Branch to error handling 669} 670;; 671 672SPECIAL_EXP10: 673 674{.mfi 675 nop.m 0 676 // x = -Infinity ? 677 fclass.m p6, p0 = f8, 0x22 678 nop.i 0 ;; 679} 680 681{.mfi 682 nop.m 0 683 // x = +Infinity ? 684 fclass.m p7, p0 = f8, 0x21 685 nop.i 0 ;; 686} 687 688{.mfi 689 nop.m 0 690 // x = +/-Zero ? 691 fclass.m p8, p0 = f8, 0x7 692 nop.i 0 693} 694{.mfb 695 nop.m 0 696 // exp10(-Infinity) = 0 697 (p6) mov f8 = f0 698 (p6) br.ret.spnt b0 ;; 699} 700 701{.mfb 702 nop.m 0 703 // exp10(+Infinity) = +Infinity 704 nop.f 0 705 (p7) br.ret.spnt b0 ;; 706} 707 708{.mfb 709 nop.m 0 710 // exp10(+/-0) = 1 711 (p8) mov f8 = f1 712 (p8) br.ret.spnt b0 ;; 713} 714 715{.mfb 716 nop.m 0 717 // Remaining cases: NaNs 718 fma.s0 f8 = f8, f1, f0 719 br.ret.sptk b0 ;; 720} 721 722 723OUT_RANGE_EXP10: 724 725// underflow: p6 = 1 726// overflow: p8 = 1 727 728.pred.rel "mutex",p6,p8 729{.mmi 730 (p8) mov GR_CONST1 = 0x1fffe 731 (p6) mov GR_CONST1 = 1 732 nop.i 0 733} 734;; 735 736{.mii 737 setf.exp FR_KF0 = GR_CONST1 738 (p8) mov GR_Parameter_TAG = 165 739 (p6) mov GR_Parameter_TAG = 264 740} 741;; 742 743{.mfb 744 nop.m 999 745 fma.s0 f8 = FR_KF0, FR_KF0, f0 // Create overflow/underflow 746 br.cond.sptk __libm_error_region // Branch to error handling 747} 748;; 749 750GLOBAL_IEEE754_END(exp10l) 751libm_alias_ldouble_other (__exp10, exp10) 752#if SHLIB_COMPAT (libm, GLIBC_2_1, GLIBC_2_27) 753compat_symbol (libm, exp10l, pow10l, GLIBC_2_2) 754#endif 755 756 757LOCAL_LIBM_ENTRY(__libm_error_region) 758.prologue 759{.mfi 760 add GR_Parameter_Y = -32, sp // Parameter 2 value 761 nop.f 0 762.save ar.pfs, GR_SAVE_PFS 763 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs 764} 765 766{.mfi 767.fframe 64 768 add sp = -64, sp // Create new stack 769 nop.f 0 770 mov GR_SAVE_GP = gp ;; // Save gp 771} 772 773{.mmi 774 stfe [ GR_Parameter_Y ] = FR_Y, 16 // STORE Parameter 2 on stack 775 add GR_Parameter_X = 16, sp // Parameter 1 address 776.save b0, GR_SAVE_B0 777 mov GR_SAVE_B0 = b0 ;; // Save b0 778} 779 780.body 781{.mib 782 stfe [ GR_Parameter_X ] = FR_X // STORE Parameter 1 on stack 783 add GR_Parameter_RESULT = 0, GR_Parameter_Y // Parameter 3 address 784 nop.b 0 785} 786{.mib 787 stfe [ GR_Parameter_Y ] = FR_RESULT // STORE Parameter 3 on stack 788 add GR_Parameter_Y = -16, GR_Parameter_Y 789 br.call.sptk b0 = __libm_error_support# ;; // Call error handling function 790} 791 792{.mmi 793 add GR_Parameter_RESULT = 48, sp 794 nop.m 0 795 nop.i 0 ;; 796} 797 798{.mmi 799 ldfe f8 = [ GR_Parameter_RESULT ] // Get return result off stack 800.restore sp 801 add sp = 64, sp // Restore stack pointer 802 mov b0 = GR_SAVE_B0 ;; // Restore return address 803} 804 805{.mib 806 mov gp = GR_SAVE_GP // Restore gp 807 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 808 br.ret.sptk b0 ;; // Return 809} 810 811 812LOCAL_LIBM_END(__libm_error_region) 813.type __libm_error_support#, @function 814.global __libm_error_support# 815