1.file "exp2l.s" 2 3 4// Copyright (c) 2000 - 2003, 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// 07/27/00 Initial version 42// 08/15/00 Bundle added after call to __libm_error_support to properly 43// set [ the previously overwritten ] GR_Parameter_RESULT. 44// 02/02/01 Added libm_error_support calls for underflow 45// 05/20/02 Cleaned up namespace and sf0 syntax 46// 02/06/03 Reordered header: .section, .global, .proc, .align 47// 05/07/03 Reformatted assembly source 48// 49// API 50//============================================================== 51// long double exp2l(long double) 52// 53// Overview of operation 54//============================================================== 55// Background 56// 57// Implementation 58// 59// Let x= K + f + r, where 60// K is an integer, f= 0.b1 b2... b8 (f>= 0), 61// and |r|<2^{-8} 62// T is a table that stores 2^f (256 entries) rounded to 63// double extended precision (only mantissa is stored) 64// D stores (2^f/T [ f ] - 1), rounded to single precision 65// 66// 2^x is approximated as 67// 2^K * T [ f ] * (1+D [ f ] +c1*r+c2*r^2+...+c6*r^6) 68// 69 70 71 72// Special values 73//============================================================== 74// exp2(0)= 1 75// exp2(+inf)= inf 76// exp2(-inf)= 0 77// 78 79 80// Registers used 81//============================================================== 82// f6-f15, f32-f46 83// r2-r3, r8-r11, r14-r40 84// p6, p7, p8, p12 85 86 FR_X = f10 87 FR_Y = f1 88 FR_RESULT = f8 89 90 FR_KF0 = f6 91 FR_EXP63 = f7 92 FR_T = f9 93 FR_COEFF3 = f10 94 FR_COEFF4 = f11 95 FR_COEFF5 = f12 96 FR_COEFF6 = f13 97 FR_COEFF1 = f14 98 FR_COEFF2 = f15 99 FR_2P14 = f32 100 FR_UF_TEST = f33 101 FR_D = f34 102 FR_R = f35 103 FR_2EXP = f36 104 FR_EMIN = f37 105 FR_P34 = f38 106 FR_P56 = f39 107 FR_R2 = f40 108 FR_P12 = f41 109 FR_TS = f42 110 FR_P36 = f43 111 FR_P02 = f44 112 FR_R3 = f45 113 FR_P06 = f46 114 115 116 GR_ADDR0 = r2 117 GR_ADDR = r2 118 GR_D_ADDR0 = r3 119 GR_D_ADDR = r3 120 GR_LEADBITS = r8 121 GR_256 = r9 122 GR_EM63 = r10 123 GR_255 = r11 124 GR_EXPON = r14 125 GR_BM63 = r15 126 GR_UF_TEST = r16 127 GR_INDEX = r17 128 GR_K = r18 129 GR_KF = r19 130 GR_2P14 = r19 131 GR_EMIN = r20 132 GR_IT = r21 133 GR_ID = r22 134 GR_63 = r23 135 GR_CONST1 = r24 136 GR_EBIAS = r25 137 GR_CONST2 = r26 138 GR_CONST3 = r27 139 GR_SIGNIF = r28 140 GR_ARGEXP = r29 141 GR_SGN = r30 142 GR_EMIN1 = r31 143 GR_SREG = r32 144 145 GR_SAVE_B0 = r33 146 GR_SAVE_PFS = r34 147 GR_SAVE_GP = r35 148 GR_SAVE_SP = r36 149 150 GR_Parameter_X = r37 151 GR_Parameter_Y = r38 152 GR_Parameter_RESULT= r39 153 GR_Parameter_TAG = r40 154 155 156// Data tables 157//============================================================== 158 159RODATA 160 161.align 16 162 163LOCAL_OBJECT_START(poly_coeffs) 164 165 data8 0x3fac6b08d704a0c0 // C_3 166 data8 0x3f83b2ab6fba4e77 // C_4 167 data8 0x3f55d87fe78a6731 // C_5 168 data8 0x3f2430912f86c787 // C_6 169 data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1 170 data8 0xf5fdeffc162c7541, 0x00003ffc // C_2 171LOCAL_OBJECT_END(poly_coeffs) 172 173 174LOCAL_OBJECT_START(T_table) 175 176 data8 0x8000000000000000, 0x8058d7d2d5e5f6b1 177 data8 0x80b1ed4fd999ab6c, 0x810b40a1d81406d4 178 data8 0x8164d1f3bc030773, 0x81bea1708dde6056 179 data8 0x8218af4373fc25ec, 0x8272fb97b2a5894c 180 data8 0x82cd8698ac2ba1d7, 0x83285071e0fc4547 181 data8 0x8383594eefb6ee37, 0x83dea15b9541b132 182 data8 0x843a28c3acde4046, 0x8495efb3303efd30 183 data8 0x84f1f656379c1a29, 0x854e3cd8f9c8c95d 184 data8 0x85aac367cc487b15, 0x86078a2f23642a9f 185 data8 0x8664915b923fba04, 0x86c1d919caef5c88 186 data8 0x871f61969e8d1010, 0x877d2afefd4e256c 187 data8 0x87db357ff698d792, 0x88398146b919f1d4 188 data8 0x88980e8092da8527, 0x88f6dd5af155ac6b 189 data8 0x8955ee03618e5fdd, 0x89b540a7902557a4 190 data8 0x8a14d575496efd9a, 0x8a74ac9a79896e47 191 data8 0x8ad4c6452c728924, 0x8b3522a38e1e1032 192 data8 0x8b95c1e3ea8bd6e7, 0x8bf6a434adde0085 193 data8 0x8c57c9c4646f4dde, 0x8cb932c1bae97a95 194 data8 0x8d1adf5b7e5ba9e6, 0x8d7ccfc09c50e2f8 195 data8 0x8ddf042022e69cd6, 0x8e417ca940e35a01 196 data8 0x8ea4398b45cd53c0, 0x8f073af5a2013520 197 data8 0x8f6a8117e6c8e5c4, 0x8fce0c21c6726481 198 data8 0x9031dc431466b1dc, 0x9095f1abc540ca6b 199 data8 0x90fa4c8beee4b12b, 0x915eed13c89689d3 200 data8 0x91c3d373ab11c336, 0x9228ffdc10a051ad 201 data8 0x928e727d9531f9ac, 0x92f42b88f673aa7c 202 data8 0x935a2b2f13e6e92c, 0x93c071a0eef94bc1 203 data8 0x9426ff0fab1c04b6, 0x948dd3ac8ddb7ed3 204 data8 0x94f4efa8fef70961, 0x955c5336887894d5 205 data8 0x95c3fe86d6cc7fef, 0x962bf1cbb8d97560 206 data8 0x96942d3720185a00, 0x96fcb0fb20ac4ba3 207 data8 0x97657d49f17ab08e, 0x97ce9255ec4357ab 208 data8 0x9837f0518db8a96f, 0x98a1976f7597e996 209 data8 0x990b87e266c189aa, 0x9975c1dd47518c77 210 data8 0x99e0459320b7fa65, 0x9a4b13371fd166ca 211 data8 0x9ab62afc94ff864a, 0x9b218d16f441d63d 212 data8 0x9b8d39b9d54e5539, 0x9bf93118f3aa4cc1 213 data8 0x9c6573682ec32c2d, 0x9cd200db8a0774cb 214 data8 0x9d3ed9a72cffb751, 0x9dabfdff6367a2aa 215 data8 0x9e196e189d472420, 0x9e872a276f0b98ff 216 data8 0x9ef5326091a111ae, 0x9f6386f8e28ba651 217 data8 0x9fd228256400dd06, 0xa041161b3d0121be 218 data8 0xa0b0510fb9714fc2, 0xa11fd9384a344cf7 219 data8 0xa18faeca8544b6e4, 0xa1ffd1fc25cea188 220 data8 0xa27043030c496819, 0xa2e102153e918f9e 221 data8 0xa3520f68e802bb93, 0xa3c36b345991b47c 222 data8 0xa43515ae09e6809e, 0xa4a70f0c95768ec5 223 data8 0xa5195786be9ef339, 0xa58bef536dbeb6ee 224 data8 0xa5fed6a9b15138ea, 0xa6720dc0be08a20c 225 data8 0xa6e594cfeee86b1e, 0xa7596c0ec55ff55b 226 data8 0xa7cd93b4e965356a, 0xa8420bfa298f70d1 227 data8 0xa8b6d5167b320e09, 0xa92bef41fa77771b 228 data8 0xa9a15ab4ea7c0ef8, 0xaa1717a7b5693979 229 data8 0xaa8d2652ec907629, 0xab0386ef48868de1 230 data8 0xab7a39b5a93ed337, 0xabf13edf162675e9 231 data8 0xac6896a4be3fe929, 0xace0413ff83e5d04 232 data8 0xad583eea42a14ac6, 0xadd08fdd43d01491 233 data8 0xae493452ca35b80e, 0xaec22c84cc5c9465 234 data8 0xaf3b78ad690a4375, 0xafb51906e75b8661 235 data8 0xb02f0dcbb6e04584, 0xb0a957366fb7a3c9 236 data8 0xb123f581d2ac2590, 0xb19ee8e8c94feb09 237 data8 0xb21a31a66618fe3b, 0xb295cff5e47db4a4 238 data8 0xb311c412a9112489, 0xb38e0e38419fae18 239 data8 0xb40aaea2654b9841, 0xb487a58cf4a9c180 240 data8 0xb504f333f9de6484, 0xb58297d3a8b9f0d2 241 data8 0xb60093a85ed5f76c, 0xb67ee6eea3b22b8f 242 data8 0xb6fd91e328d17791, 0xb77c94c2c9d725e9 243 data8 0xb7fbefca8ca41e7c, 0xb87ba337a1743834 244 data8 0xb8fbaf4762fb9ee9, 0xb97c143756844dbf 245 data8 0xb9fcd2452c0b9deb, 0xba7de9aebe5fea09 246 data8 0xbaff5ab2133e45fb, 0xbb81258d5b704b6f 247 data8 0xbc034a7ef2e9fb0d, 0xbc85c9c560e7b269 248 data8 0xbd08a39f580c36bf, 0xbd8bd84bb67ed483 249 data8 0xbe0f6809860993e2, 0xbe935317fc378238 250 data8 0xbf1799b67a731083, 0xbf9c3c248e2486f8 251 data8 0xc0213aa1f0d08db0, 0xc0a6956e8836ca8d 252 data8 0xc12c4cca66709456, 0xc1b260f5ca0fbb33 253 data8 0xc238d2311e3d6673, 0xc2bfa0bcfad907c9 254 data8 0xc346ccda24976407, 0xc3ce56c98d21b15d 255 data8 0xc4563ecc5334cb33, 0xc4de8523c2c07baa 256 data8 0xc5672a115506dadd, 0xc5f02dd6b0bbc3d9 257 data8 0xc67990b5aa245f79, 0xc70352f04336c51e 258 data8 0xc78d74c8abb9b15d, 0xc817f681416452b2 259 data8 0xc8a2d85c8ffe2c45, 0xc92e1a9d517f0ecc 260 data8 0xc9b9bd866e2f27a3, 0xca45c15afcc72624 261 data8 0xcad2265e4290774e, 0xcb5eecd3b38597c9 262 data8 0xcbec14fef2727c5d, 0xcc799f23d11510e5 263 data8 0xcd078b86503dcdd2, 0xcd95da6a9ff06445 264 data8 0xce248c151f8480e4, 0xceb3a0ca5dc6a55d 265 data8 0xcf4318cf191918c1, 0xcfd2f4683f94eeb5 266 data8 0xd06333daef2b2595, 0xd0f3d76c75c5db8d 267 data8 0xd184df6251699ac6, 0xd2164c023056bcab 268 data8 0xd2a81d91f12ae45a, 0xd33a5457a3029054 269 data8 0xd3ccf099859ac379, 0xd45ff29e0972c561 270 data8 0xd4f35aabcfedfa1f, 0xd5872909ab75d18a 271 data8 0xd61b5dfe9f9bce07, 0xd6aff9d1e13ba2fe 272 data8 0xd744fccad69d6af4, 0xd7da67311797f56a 273 data8 0xd870394c6db32c84, 0xd9067364d44a929c 274 data8 0xd99d15c278afd7b6, 0xda3420adba4d8704 275 data8 0xdacb946f2ac9cc72, 0xdb63714f8e295255 276 data8 0xdbfbb797daf23755, 0xdc9467913a4f1c92 277 data8 0xdd2d818508324c20, 0xddc705bcd378f7f0 278 data8 0xde60f4825e0e9124, 0xdefb4e1f9d1037f2 279 data8 0xdf9612deb8f04420, 0xe031430a0d99e627 280 data8 0xe0ccdeec2a94e111, 0xe168e6cfd3295d23 281 data8 0xe2055afffe83d369, 0xe2a23bc7d7d91226 282 data8 0xe33f8972be8a5a51, 0xe3dd444c46499619 283 data8 0xe47b6ca0373da88d, 0xe51a02ba8e26d681 284 data8 0xe5b906e77c8348a8, 0xe658797368b3a717 285 data8 0xe6f85aaaee1fce22, 0xe798aadadd5b9cbf 286 data8 0xe8396a503c4bdc68, 0xe8da9958464b42ab 287 data8 0xe97c38406c4f8c57, 0xea1e4756550eb27b 288 data8 0xeac0c6e7dd24392f, 0xeb63b74317369840 289 data8 0xec0718b64c1cbddc, 0xecaaeb8ffb03ab41 290 data8 0xed4f301ed9942b84, 0xedf3e6b1d418a491 291 data8 0xee990f980da3025b, 0xef3eab20e032bc6b 292 data8 0xefe4b99bdcdaf5cb, 0xf08b3b58cbe8b76a 293 data8 0xf13230a7ad094509, 0xf1d999d8b7708cc1 294 data8 0xf281773c59ffb13a, 0xf329c9233b6bae9c 295 data8 0xf3d28fde3a641a5b, 0xf47bcbbe6db9fddf 296 data8 0xf5257d152486cc2c, 0xf5cfa433e6537290 297 data8 0xf67a416c733f846e, 0xf7255510c4288239 298 data8 0xf7d0df730ad13bb9, 0xf87ce0e5b2094d9c 299 data8 0xf92959bb5dd4ba74, 0xf9d64a46eb939f35 300 data8 0xfa83b2db722a033a, 0xfb3193cc4227c3f4 301 data8 0xfbdfed6ce5f09c49, 0xfc8ec01121e447bb 302 data8 0xfd3e0c0cf486c175, 0xfdedd1b496a89f35 303 data8 0xfe9e115c7b8f884c, 0xff4ecb59511ec8a5 304LOCAL_OBJECT_END(T_table) 305 306 307LOCAL_OBJECT_START(D_table) 308 309 data4 0x00000000, 0x9f55c08f, 0x1e93ffa3, 0x1dcd43a8 310 data4 0x1f751f79, 0x9f3cdd88, 0x9f43d155, 0x1eda222c 311 data4 0x1ef35513, 0x9f597895, 0x9e698881, 0x1ec71073 312 data4 0x1e50e371, 0x9dc01e19, 0x1de74133, 0x1e2f028c 313 data4 0x9edefb47, 0x1ebbac48, 0x9e8b0330, 0x9e9e9314 314 data4 0x1edc1d11, 0x1f098529, 0x9f52827c, 0x1f50050d 315 data4 0x1f301e8e, 0x1f5b64d1, 0x9f45e3ee, 0x9ef64d6d 316 data4 0x1d6ec5e8, 0x9e61ad9a, 0x1d44ccbb, 0x9e4a8bbb 317 data4 0x9cf11576, 0x9dcce7e7, 0x9d02ac90, 0x1f26ccf0 318 data4 0x9f0877c6, 0x9ddd62ae, 0x9f4b7fc3, 0x1ea8ef6b 319 data4 0x1ea4378d, 0x1ef6fc38, 0x1db99fd9, 0x1f22bf6f 320 data4 0x1f53e172, 0x1e85504a, 0x9f37cc75, 0x1f0c5e17 321 data4 0x1dde8aac, 0x9cb42bb2, 0x1e153cd7, 0x1eb62bba 322 data4 0x9e9b941b, 0x9ea80e3c, 0x1f508823, 0x1ec3fd36 323 data4 0x1e9ffaa1, 0x1e21e2eb, 0x9d948b1d, 0x9e8ac93a 324 data4 0x1ef7ee6f, 0x9e80dda3, 0x1f0814be, 0x1dc5ddfe 325 data4 0x1eedb9d1, 0x9f2aaa26, 0x9ea5b0fc, 0x1edf702e 326 data4 0x9e391201, 0x1f1316bb, 0x1ea27fb7, 0x9e05ed18 327 data4 0x9f199ed2, 0x1ee7fd7c, 0x1f003db6, 0x9eac3793 328 data4 0x9e5b8c10, 0x9f3af17c, 0x1bc9a8be, 0x1ee3c004 329 data4 0x9f19b1b2, 0x9f242ce9, 0x9ce67dd1, 0x9e4f6275 330 data4 0x1e20742c, 0x1eb9328a, 0x9f477153, 0x1d969718 331 data4 0x9f1e6c43, 0x1f2f67f4, 0x9f39c7e4, 0x9e3c4feb 332 data4 0x1da3956b, 0x9e7c685d, 0x1f280911, 0x9f0d8afb 333 data4 0x1e314b40, 0x9eb4f250, 0x9f1a34ad, 0x1ef5d5e7 334 data4 0x9f145496, 0x1e604827, 0x9f1e5195, 0x1e9c1fc0 335 data4 0x1efde521, 0x1e69b385, 0x1f316830, 0x9f244eae 336 data4 0x1f1787ec, 0x9e939971, 0x1f0bb393, 0x9f0511d6 337 data4 0x1ed919de, 0x1d8b7b28, 0x1e5ca4a9, 0x1e7c357b 338 data4 0x9e3ff8e8, 0x1eef53b5, 0x9ed22ed7, 0x1f16659b 339 data4 0x9f2db102, 0x9e2c6a78, 0x1f328d7d, 0x9f2fec3c 340 data4 0x1eb395bd, 0x9f242b84, 0x9e2683e6, 0x1ed71e68 341 data4 0x1efd1df5, 0x9e9eeafd, 0x9ed2249c, 0x1eef129a 342 data4 0x1d1ea44c, 0x9e81f7ff, 0x1eaf77c9, 0x9ee7a285 343 data4 0x1e1864ed, 0x9ee7edbb, 0x9e15a27d, 0x9ae61655 344 data4 0x1f1ff1a2, 0x1da29755, 0x9e5f46fb, 0x1e901236 345 data4 0x9eecfb9b, 0x9f204d2f, 0x1ec64685, 0x9eb809bd 346 data4 0x9e0026c5, 0x1d9f1da1, 0x1f142b49, 0x9f20f22e 347 data4 0x1f24b067, 0x1f185a4c, 0x9f09765c, 0x9ece902f 348 data4 0x1e2ca5db, 0x1e6de464, 0x9f071f67, 0x1f1518c3 349 data4 0x1ea13ded, 0x1f0b8414, 0x1edb6ad4, 0x9e548740 350 data4 0x9ea10efb, 0x1ee48a60, 0x1e7954c5, 0x9edad013 351 data4 0x9f21517d, 0x9e9b6e0c, 0x9ee7f9a6, 0x9ebd4298 352 data4 0x9d65b24e, 0x1eed751f, 0x9f1573ea, 0x9d430377 353 data4 0x9e13fc0c, 0x1e47008a, 0x1e3d5c1d, 0x1ef41a91 354 data4 0x9e4a4ef7, 0x9e952f18, 0x1d620566, 0x1d9b8d33 355 data4 0x1db06247, 0x1e94b31e, 0x1f0730ad, 0x9d79ffb4 356 data4 0x1ed64d51, 0x9e91fd11, 0x9e28d35a, 0x9dea0ed9 357 data4 0x1e891def, 0x9ee28ac0, 0x1e1db99b, 0x9ee1ce38 358 data4 0x9bdd9bca, 0x1eb72cb9, 0x9e8c53c6, 0x1e0df6ca 359 data4 0x1e8f2ccd, 0x9e9b0886, 0x1eeb3bc7, 0x1ec7e772 360 data4 0x9e210776, 0x9daf246c, 0x1ea1f151, 0x1ece4dc6 361 data4 0x1ce741c8, 0x1ed3c88f, 0x9ec9a4fd, 0x9e0c8d30 362 data4 0x1d2fbb26, 0x9ef212a7, 0x1ee44f1c, 0x9e445550 363 data4 0x1e075f77, 0x9d9291a3, 0x1f09c2ee, 0x9e012c88 364 data4 0x1f057d62, 0x9e7bb0dc, 0x9d8758ee, 0x1ee8d6c1 365 data4 0x9e509a57, 0x9e4ca7b7, 0x1e2cb341, 0x9ec35106 366 data4 0x1ecf3baf, 0x1e11781c, 0x1ea0cc78, 0x1eb75ca6 367 data4 0x1e961e1a, 0x1eb88853, 0x1e7abf50, 0x1ee38704 368 data4 0x9dc5ab0f, 0x1afe197b, 0x9ec07523, 0x9d9b7f78 369 data4 0x1f011618, 0x1ed43b0b, 0x9f035945, 0x9e3fd014 370 data4 0x9bbda5cd, 0x9e83f8ab, 0x1e58a928, 0x1e392d61 371 data4 0x1efdbb52, 0x1ee310a8, 0x9ec7ecc1, 0x1e8c9ed6 372 data4 0x9ef82dee, 0x9e70545b, 0x9ea53fc4, 0x1e40f419 373LOCAL_OBJECT_END(D_table) 374 375 376 377.section .text 378GLOBAL_LIBM_ENTRY(exp2l) 379 380{.mii 381 // get exponent 382 getf.exp GR_EBIAS = f8 383 // GR_D_ADDR0 = pointer to D_table 384 addl GR_D_ADDR0 = @ltoff(D_table), gp 385 // GR_ADDR0 = pointer to C_1...C_6 followed by T_table 386 addl GR_ADDR0 = @ltoff(poly_coeffs), gp ;; 387} 388 389{.mfi 390 // get significand 391 getf.sig GR_SIGNIF = f8 392 // will continue only for normal/denormal numbers 393 fclass.nm.unc p12, p7 = f8, 0x1b 394 mov GR_63 = 63 ;; 395} 396 397{.mfi 398 nop.m 0 399 nop.f 0 400 // GR_CONST2 = bias+63-8 401 mov GR_CONST2 = 0xffff+55 402} 403{.mfi 404 // GR_CONST1 = bias+15 405 mov GR_CONST1 = 0xffff+15 406 nop.f 0 407 mov GR_CONST3 = 0x1ffff ;; 408} 409 410{.mfi 411 // load start address for C_1...C_6 followed by T_table 412 ld8 GR_ADDR = [ GR_ADDR0 ] 413 nop.f 0 414 // get sign of argument 415 andcm GR_SGN = GR_EBIAS, GR_CONST3 416} 417{.mfi 418 // GR_D_ADDR = pointer to D_table 419 ld8 GR_D_ADDR = [ GR_D_ADDR0 ] 420 nop.f 0 421 // get argument exponent 422 and GR_ARGEXP = GR_CONST3, GR_EBIAS ;; 423} 424 425{.mfi 426 alloc GR_SREG = ar.pfs, 1, 4, 4, 0 427 nop.f 0 428 // p6 = 1 if sign = 1 429 cmp.ne p6, p8 = GR_SGN, r0 430} 431{.mfi 432 // p7 = 1 if exponent> = 15 (argument out of range) 433 cmp.ge p7, p0 = GR_ARGEXP, GR_CONST1 434 nop.f 0 435 sub GR_EXPON = GR_CONST2, GR_ARGEXP ;; 436} 437 438{.mib 439 // load C_3, C_4 440 ldfpd FR_COEFF3, FR_COEFF4 = [ GR_ADDR ], 16 441 // get first exponent+8 bits 442 shr.u GR_LEADBITS = GR_SIGNIF, GR_EXPON 443 (p12) br.cond.spnt SPECIAL_exp2l 444} 445{.mib 446 mov GR_256 = 256 447 // exponent- = 63 448 sub GR_EM63 = GR_EBIAS, GR_63 449 (p7) br.cond.spnt OUT_RANGE_exp2l ;; 450} 451 452{.mlx 453 // load C_5, C_6 454 ldfpd FR_COEFF5, FR_COEFF6 = [ GR_ADDR ], 16 455 // GR_2P14 = 2^14 456 movl GR_2P14 = 0x46800000 ;; 457} 458 459{.mfi 460 // load C_1 461 ldfe FR_COEFF1 = [ GR_ADDR ], 16 462 fma.s0 f8 = f8, f1, f0 463 // GR_BM63 = bias-63 464 mov GR_BM63 = 0xffff-63 ;; 465} 466 467{.mlx 468 setf.s FR_2P14 = GR_2P14 469 // GR_UF_TEST = -2^14-62 470 movl GR_UF_TEST = 0xc6807c00 471} 472{.mfi 473 // load C_2 474 ldfe FR_COEFF2 = [ GR_ADDR ], 16 475 nop.f 0 476 mov GR_255 = 255 ;; 477} 478 479{.mib 480 // get 8-bit index 481 and GR_INDEX = GR_255, GR_LEADBITS 482 // get K = integer part 483 shr.u GR_K = GR_LEADBITS, 8 484 nop.b 0 ;; 485} 486 487{.mmi 488 // if sign = 1 && f>0, set p7 = 1 489 (p6) cmp.gt.unc p7, p0 = GR_INDEX, r0 490 setf.s FR_UF_TEST = GR_UF_TEST 491 shl GR_KF = GR_LEADBITS, GR_EXPON ;; 492} 493 494{.mfi 495 // if sign = 1 && f>0, set f = 1-f 496 (p7) sub GR_INDEX = GR_256, GR_INDEX 497 nop.f 0 498 // if sign = 1 && f>0, set K = K+1 499 (p7) add GR_K = GR_K, r0, 1 ;; 500} 501 502{.mfi 503 // FR_EXP63 = 2^{expon-63} 504 setf.exp FR_EXP63 = GR_EM63 505 nop.f 0 506 nop.i 0 ;; 507} 508 509.pred.rel "mutex", p6, p8 510{.mfi 511 // if sign = 0, set scale factor exponent S = K+bias-63 512 (p8) add GR_K = GR_K, GR_BM63 513 nop.f 0 514 // if sign = 1, set scale factor exponent S = -K+bias-63 515 (p6) sub GR_K = GR_BM63, GR_K ;; 516} 517 518{.mmi 519 // FR_KF0 = 2^{63-expon}*(K+f) 520 setf.sig FR_KF0 = GR_KF 521 nop.m 0 522 // GR_EMIN = EMIN = 2-2^14 523 mov GR_EMIN = 0x18cfff ;; 524} 525 526{.mfi 527 // get T_table index 528 shladd GR_IT = GR_INDEX, 3, GR_ADDR 529 // p7 = 1 if x> = 2^10 530 fcmp.ge.s1 p7, p12 = f8, FR_2P14 531 // get D_table index 532 shladd GR_ID = GR_INDEX, 2, GR_D_ADDR ;; 533} 534 535{.mfi 536 // load T_table value 537 ldf8 FR_T = [ GR_IT ] 538 // p7 = 1 if x<-2^10-50 539 (p12) fcmp.lt.s1 p7, p0 = f8, FR_UF_TEST 540 // GR_EMIN1 = EMIN = 2-2^14 541 shl GR_EMIN1 = GR_EMIN, 11 ;; 542} 543 544{.mmb 545 // f50 = scale factor = 2^{K-63} 546 setf.exp FR_2EXP = GR_K 547 // load D_table value 548 ldfs FR_D = [ GR_ID ] 549 (p7) br.cond.spnt OUT_RANGE_exp2l ;; 550} 551 552{.mfi 553 nop.m 0 554 // get r = x-(K+f) 555 fnma.s1 FR_R = FR_KF0, FR_EXP63, f8 556 nop.i 0 ;; 557} 558 559{.mfi 560 // FR_EMIN = EMIN 561 setf.s FR_EMIN = GR_EMIN1 562 // P34 = C_4*r+C_3 563 fma.s1 FR_P34 = FR_COEFF4, FR_R, FR_COEFF3 564 nop.i 0 565} 566{.mfi 567 nop.m 0 568 // P56 = C_6*r+C_5 569 fma.s1 FR_P56 = FR_COEFF6, FR_R, FR_COEFF5 570 nop.i 0 ;; 571} 572 573{.mfi 574 nop.m 0 575 // r*r 576 fma.s1 FR_R2 = FR_R, FR_R, f0 577 nop.i 0 578} 579{.mfi 580 nop.m 0 581 // P12 = C_2*r+C_1 582 fma.s1 FR_P12 = FR_COEFF2, FR_R, FR_COEFF1 583 nop.i 0 ;; 584} 585 586{.mfi 587 nop.m 0 588 // T* = scaling factor 589 fma.s1 FR_TS = FR_T, FR_2EXP, f0 590 nop.i 0 591} 592{.mfi 593 nop.m 0 594 // P36 = P34+r2*P56 595 fma.s1 FR_P36 = FR_P56, FR_R2, FR_P34 596 nop.i 0 ;; 597} 598 599{.mfi 600 nop.m 0 601 // P02 = D+r*P12 602 fma.s1 FR_P02 = FR_P12, FR_R, FR_D 603 nop.i 0 604} 605{.mfi 606 nop.m 0 607 // GR_ID = r*r2 608 fma.s1 FR_R3 = FR_R2, FR_R, f0 609 nop.i 0 ;; 610} 611 612{.mfi 613 nop.m 0 614 // P06 = P02+r3*P36 615 fma.s1 FR_P06 = FR_P36, FR_R3, FR_P02 616 nop.i 0 ;; 617} 618 619{.mfi 620 nop.m 0 621 // underflow (x<EMIN) ? 622 fcmp.lt.s0 p6, p8 = f8, FR_EMIN 623 nop.i 0 ;; 624} 625 626{.mfb 627 nop.m 0 628 // result = T+T*P06 629 fma.s0 f8 = FR_TS, FR_P06, FR_TS 630 // return 631 (p8) br.ret.sptk b0 632} 633{.mfb 634 (p6) mov GR_Parameter_TAG = 160 635 nop.f 0 636 (p6) br.cond.sptk __libm_error_region ;; 637} 638 639 640SPECIAL_exp2l: 641 642{.mfi 643 nop.m 0 644 // x = -Infinity ? 645 fclass.m p6, p0 = f8, 0x22 646 nop.i 0 ;; 647} 648 649{.mfi 650 nop.m 0 651 // x = +Infinity ? 652 fclass.m p7, p0 = f8, 0x21 653 nop.i 0 ;; 654} 655 656{.mfi 657 nop.m 0 658 // x = +/-Zero ? 659 fclass.m p8, p0 = f8, 0x7 660 nop.i 0 661} 662{.mfb 663 nop.m 0 664 // exp2l(-Infinity) = 0 665 (p6) mov f8 = f0 666 (p6) br.ret.spnt b0 ;; 667} 668 669{.mfb 670 nop.m 0 671 // exp2l(+Infinity) = +Infinity 672 nop.f 0 673 (p7) br.ret.spnt b0 ;; 674} 675 676{.mfb 677 nop.m 0 678 // exp2l(+/-0) = 1 679 (p8) mov f8 = f1 680 (p8) br.ret.spnt b0 ;; 681} 682 683{.mfb 684 nop.m 0 685 // Remaining cases: NaNs 686 fma.s0 f8 = f8, f1, f0 687 br.ret.sptk b0 ;; 688} 689 690 691OUT_RANGE_exp2l: 692 693 694{.mfi 695 // overflow: p8 = 1 696 (p8) mov GR_EM63 = 0x1fffe 697 // normalize input, to detect pseudo-zeroes 698 fma.s0 f8 = f8, f1, f0 699 nop.i 0 ;; 700} 701 702{.mfi 703 nop.m 0 704 // f8 = 0? 705 fcmp.eq.s1 p7, p0 = f8, f0 706 nop.i 0 ;; 707} 708 709{.mmb 710 (p8) mov GR_Parameter_TAG = 159 711 (p8) setf.exp FR_TS = GR_EM63 712 nop.b 999 ;; 713} 714 715{.mfb 716 nop.m 0 717 // pseudo-zero 718 (p7) mov f8 = f1 719 (p7) br.ret.sptk b0 ;; 720} 721 722{.mfi 723 nop.m 999 724 (p8) fma.s0 f8 = FR_TS, FR_TS, f0 725 nop.i 999 726} 727{.mii 728 nop.m 0 729 // underflow: p6 = 1 730 (p6) mov GR_EM63 = 1 731 nop.i 0 ;; 732} 733 734{.mmb 735 (p6) mov GR_Parameter_TAG = 160 736 (p6) setf.exp FR_TS = GR_EM63 737 nop.b 999 ;; 738} 739 740{.mfb 741 nop.m 999 742 (p6) fma.s0 f8 = FR_TS, FR_TS, f0 743 nop.b 0 ;; 744} 745 746 747GLOBAL_LIBM_END(exp2l) 748libm_alias_ldouble_other (exp2, exp2) 749 750 751LOCAL_LIBM_ENTRY(__libm_error_region) 752.prologue 753{.mfi 754 add GR_Parameter_Y = -32, sp // Parameter 2 value 755 nop.f 0 756.save ar.pfs, GR_SAVE_PFS 757 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs 758} 759{.mfi 760.fframe 64 761 add sp = -64, sp // Create new stack 762 nop.f 0 763 mov GR_SAVE_GP = gp ;; // Save gp 764} 765 766{.mmi 767 stfe [ GR_Parameter_Y ] = FR_Y, 16 // STORE Parameter 2 on stack 768 add GR_Parameter_X = 16, sp // Parameter 1 address 769.save b0, GR_SAVE_B0 770 mov GR_SAVE_B0 = b0 ;; // Save b0 771} 772 773.body 774{.mib 775 stfe [ GR_Parameter_X ] = FR_X // STORE Parameter 1 on stack 776 add GR_Parameter_RESULT = 0, GR_Parameter_Y // Parameter 3 address 777 nop.b 0 778} 779{.mib 780 stfe [ GR_Parameter_Y ] = FR_RESULT // STORE Parameter 3 on stack 781 add GR_Parameter_Y = -16, GR_Parameter_Y 782 br.call.sptk b0 = __libm_error_support# ;; // Call error handling function 783} 784 785{.mmi 786 add GR_Parameter_RESULT = 48, sp 787 nop.m 0 788 nop.i 0 ;; 789} 790 791{.mmi 792 ldfe f8 = [ GR_Parameter_RESULT ] // Get return result off stack 793.restore sp 794 add sp = 64, sp // Restore stack pointer 795 mov b0 = GR_SAVE_B0 ;; // Restore return address 796} 797 798{.mib 799 mov gp = GR_SAVE_GP // Restore gp 800 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 801 br.ret.sptk b0 ;; // Return 802} 803 804 805LOCAL_LIBM_END(__libm_error_region) 806.type __libm_error_support#, @function 807.global __libm_error_support# 808