1.file "cbrtl.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// 04/28/00 Initial version 42// 05/20/02 Cleaned up namespace and sf0 syntax 43// 02/06/03 Reordered header:.section,.global,.proc,.align 44// 11/23/04 Reformatted routine and improved speed 45// 46// API 47//============================================================== 48// long double cbrtl(long double) 49// 50// Overview of operation 51//============================================================== 52// Background 53// 54// Implementation 55// 56// The result is computed as 57// cbrt(x)= cbrt(1 - (1 - x*y)) * (1/cbrt(y)) 58// where y = frcpa(x) = (-1)^sgn_y * 2^(3*k+j) * m_y, 59// m_y in [1,2), j in {0,1,2} 60// 61// cbrt(1 - (1 - x*y)) is approximated by a degree-6 polynomial 62// in r= 1 - x*y : 63// P = 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6 64// 65// 66// The values (1/cbrt(y)) are stored as two tables of constants T_hi 67// (double-extended precision) and D (single precision) as follows: 68// T_hi (1 + D)= 1/cbrt(y) to about 80 bits of accuracy 69// 70// The tables are only stored for three exponent values (i.e. 71// only for 2^j * m_y, where j in {0,1,2} and m_y covers the 256 72// possible mantissas for an frcpa result); the index is formed 73// by the 8 leading mantissa bits of x, which is the same index used 74// by the hardware to get frcpa(x). 75// 76// The table values are multiplied by 2^k where e is the exponent of 77// the input number. This multiplication is carried out in parallel with 78// the polynomial evaluation: 79// T= 2^(k) * T_hi 80// 81//======================================================================= 82 83//=============== 84// Special values 85//============================================================== 86 87// Registers used 88//============================================================== 89// p6, p7, p12 90 FR_R = f6 91 FR_C1 = f7 92 FR_C2 = f9 93 FR_C3 = f10 94 FR_C4 = f11 95 FR_C5 = f12 96 FR_C6 = f13 97 FR_XNORM = f14 98 FR_D = f15 99 FR_SPECIAL = f32 100 FR_RCP = f33 101 FR_R2 = f34 102 FR_P1 = f35 103 FR_P2 = f36 104 FR_P3 = f37 105 FR_P4 = f38 106 FR_P5 = f39 107 FR_R3 = f40 108 FR_T = f41 109 FR_TF = f42 110 FR_P = f43 111 FR_SGNEXP = f44 112 113 GR_ADDR = r2 114 GR_C_START = r2 115 GR_ARGSIG = r3 116 GR_NORMSIG = r15 117 GR_D_ADDR = r16 118 GR_D_START = r16 119 GR_INDEX2 = r17 120 GR_IX2 = r17 121 GR_NORMEXP = r18 122 GR_EXP5 = r19 123 GR_EXP3 = r20 124 GR_EXP6 = r20 125 GR_EXP17 = r21 126 GR_TMP1 = r21 127 GR_SGNMASK = r22 128 GR_T_INDEX = r23 129 GR_IX_T = r23 130 GR_IX_D = r24 131 GR_D_INDEX = r24 132 GR_TMP2 = r25 133 GR_TMP3 = r25 134 GR_TMP4 = r25 135 GR_EXP_RES = r26 136 GR_BIAS23 = r27 137 GR_EXPBIAS = r27 138 GR_EXP_MOD_3 = r28 139 GR_SIGN = r29 140 GR_EXPSIGNRES = r29 141 GR_REMTMP = r30 142 GR_NORMEXPSGN = r31 143 144 145// Data tables 146//============================================================== 147 148RODATA 149 150.align 16 151 152LOCAL_OBJECT_START(poly_coeffs) 153 154 data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1 155 data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2 156 data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4 157 data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6 158LOCAL_OBJECT_END(poly_coeffs) 159 160 161LOCAL_OBJECT_START(T_table) 162 163 data8 0x80155c748c374836, 0x8040404b0879f7f9 164 data8 0x806b5dce4b405c10, 0x8096b586974669b1 165 data8 0x80bcd273d952a028, 0x80e898c52813f2f3 166 data8 0x81149add67c2d208, 0x813b4e2c856b6e9a 167 data8 0x8167c1dde03de7aa, 0x818ed973b811135e 168 data8 0x81bbc0c33e13ec98, 0x81e33e69fbe7504a 169 data8 0x820aec524e3c23e9, 0x823880f78e70b805 170 data8 0x826097a62a8e5200, 0x8288dfe00e9b5eaf 171 data8 0x82b15a10c5371624, 0x82da06a527b18937 172 data8 0x8302e60b635ab394, 0x832bf8b2feec2f0e 173 data8 0x83553f0ce00e276b, 0x837eb98b50f8322a 174 data8 0x83a270f44c84f699, 0x83cc4d7cfcfac5ca 175 data8 0x83f65f78a8872b4c, 0x8420a75f2f7b53c8 176 data8 0x844510461ff14209, 0x846fbd91b930bed2 177 data8 0x84947e18234f3294, 0x84bf92755825045a 178 data8 0x84e4ac0ee112ba51, 0x8509ef44b86f20be 179 data8 0x85359d5d91768427, 0x855b3bd5b7384357 180 data8 0x858104f0c415f79a, 0x85a6f90390d29864 181 data8 0x85d3772fcd56a1dd, 0x85f9c982fcc002f3 182 data8 0x862047e0e7ea554b, 0x8646f2a26f7f5852 183 data8 0x866dca21754096b5, 0x8694ceb8dfd17a37 184 data8 0x86bc00c49e9307e8, 0x86dccd74fce79610 185 data8 0x870453c845acf90f, 0x872c089a1e90342c 186 data8 0x8753ec4a92d16c5e, 0x877bff3aca19f6b4 187 data8 0x879d88b6fe1c324c, 0x87c5f346dbf98c3a 188 data8 0x87e7c653efacef2c, 0x881089d4e73ffefc 189 data8 0x88397e6a366f2a8a, 0x885bc559e5e1c081 190 data8 0x887e2ee392bb7a93, 0x88a7a8587e404257 191 data8 0x88ca5eda67594784, 0x88f4356166bd590e 192 data8 0x89173a0acf5ce026, 0x893a62a098b6a57b 193 data8 0x895daf637236ae2c, 0x89883b9d1c2fa9c5 194 data8 0x89abd8dd374a5d7b, 0x89cf9b1dcd197fa0 195 data8 0x89f382a258ea79de, 0x8a178faf06648f29 196 data8 0x8a3bc288b3e1d18a, 0x8a601b74f4d1f835 197 data8 0x8a849aba14274764, 0x8aa9409f16cdbc9b 198 data8 0x8ace0d6bbe2cb316, 0x8af301688ab33558 199 data8 0x8b181cdebe6f3206, 0x8b3d60185fafcb7c 200 data8 0x8b62cb603bb2fad0, 0x8b80d7d6bc4104de 201 data8 0x8ba68bf73ac74f39, 0x8bcc68fb9f9f7335 202 data8 0x8bf26f31c534fca2, 0x8c10f86e13a1a1f9 203 data8 0x8c3749916cc6abb5, 0x8c5dc4c4f7706032 204 data8 0x8c7cac3a8c42e3e0, 0x8ca373f1b7bf2716 205 data8 0x8cc29907fb951294, 0x8ce9ae4e9492aac8 206 data8 0x8d0911dddbfdad0e, 0x8d3075c4f20f04ee 207 data8 0x8d5018a9d4de77d5, 0x8d77cc47dd143515 208 data8 0x8d97af6352739cb7, 0x8db7af523167800f 209 data8 0x8ddfd80bc68c32ff, 0x8e00197e1e7c88fe 210 data8 0x8e207859f77e20e7, 0x8e40f4ce60c9f8e2 211 data8 0x8e69ba46cf2fde4d, 0x8e8a7a00bd7ae63e 212 data8 0x8eab57ef1cf2f529, 0x8ecc5442cffb1dad 213 data8 0x8eed6f2d2a4acbfe, 0x8f0ea8dff24441ff 214 data8 0x8f385c95d696b817, 0x8f59dc43edd930f3 215 data8 0x8f7b7b5f5ffad1c4, 0x8f9d3a1bea165f38 216 data8 0x8fbf18adc34b66da, 0x8fe117499e356095 217 data8 0x90033624aa685f8d, 0x9025757495f36b86 218 data8 0x903f3a5dcc091203, 0x9061b2fceb2bdbab 219 data8 0x90844ca7211032a7, 0x90a7079403e6a15d 220 data8 0x90c9e3fbafd63799, 0x90ece216c8a16ee4 221 data8 0x9110021e7b516f0a, 0x912a708a39be9075 222 data8 0x914dcc7b31146370, 0x91714af8cfe984d5 223 data8 0x918c00a6f3795e97, 0x91afbc299ed0295d 224 data8 0x91d39add3e958db0, 0x91ee9920a8974d92 225 data8 0x9212b5fcac537c19, 0x9236f6b256923fcf 226 data8 0x92523ee6f90dcfc3, 0x9276bef031e6eb79 227 data8 0x929236ec237a24ad, 0x92b6f70b7efe9dc3 228 data8 0x92d29f61eec7dc2b, 0x92f7a05d5b8ba92f 229 data8 0x931379a403be5c16, 0x9338bc44de2e3f34 230 data8 0x9354c71412c69486, 0x937a4c273907e262 231 data8 0x93968919f6e7975d, 0x93bc516fdd4680c9 232 data8 0x93d8c123d9be59b2, 0x93f546c955e60076 233 data8 0x941b70a65879079f, 0x943829f337410591 234 data8 0x9454f995765bc4d2, 0x947b86b57f5842ed 235 data8 0x94988aeb23470f86, 0x94b5a5dc9695f42a 236 data8 0x94d2d7a9170d8b42, 0x94f9e87dd78bf019 237 data8 0x95175019a503d89e, 0x9534cefa625fcb3a 238 data8 0x955265405c491a25, 0x9570130c1f9bb857 239 data8 0x9597ca4119525184, 0x95b5af6fb5aa4d3c 240 data8 0x95d3ac9273aafd7a, 0x95f1c1cafdfd3684 241 data8 0x960fef3b430b8d5f, 0x962e350575b409c5 242 data8 0x964c934c0dfc1708, 0x966b0a31c9c6bc7d 243 data8 0x968999d9ad8d264e, 0x96a8426705198795 244 data8 0x96c703fd64445ee5, 0x96e5dec0a7b4268d 245 data8 0x9704d2d4f59f79f3, 0x9723e05ebe91b9b0 246 data8 0x97430782be323831, 0x97624865fc0df8bf 247 data8 0x9781a32dcc640b2a, 0x97a117ffd0f48e46 248 data8 0x97c0a701f9d263c9, 0x97e0505a8637a036 249 data8 0x97f57a9fb0b08c6e, 0x9815503365914a9d 250 data8 0x98354085054fd204, 0x98554bbbf8a77902 251 data8 0x987571fffb7f94f6, 0x9895b3791dd03c23 252 data8 0x98ab43a5fc65d0c8, 0x98cbb2d196bd713d 253 data8 0x98ec3d9ec7b6f21a, 0x990ce436db5e8344 254 data8 0x9922b8218160967a, 0x99438d686f75779d 255 data8 0x99647eea131fa20b, 0x997a85045a47c6d0 256 data8 0x999ba5f14f8add02, 0x99bce38b5465ecae 257 data8 0x99d31ca0887f30f9, 0x99f48a669c74c09e 258 data8 0x9a16154eb445c873, 0x9a2c822ec198d667 259 data8 0x9a4e3e080cd91b78, 0x9a70177afe52322e 260 data8 0x9a86b8fa94eebe10, 0x9aa8c42866ae2958 261 data8 0x9abf86f9e12fc45e, 0x9ae1c462fc05f49d 262 data8 0x9af8a8dc936b84d0, 0x9b1b19033be35730 263 data8 0x9b3da7daf04c2892, 0x9b54c2e4c8a9012b 264 data8 0x9b77854e6c661200, 0x9b8ec2e678d56d2f 265 data8 0x9ba60e6a5ca133b6, 0x9bc919ea66a151a4 266 data8 0x9be0887c09ef82bb, 0x9c03c8d5fffc3503 267 data8 0x9c1b5ad21a81cbb9, 0x9c3ed09216e9ca02 268 data8 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0xa0ccd82d1bd2f68b 289 data8 0xa0e77200215909e6, 0xa1021d760d584855 290 data8 0xa11cdaa36068a57d, 0xa137a99cbd3f880b 291 data8 0xa160019ed37fb4ae, 0xa1960b5966da4608 292 data8 0xa1cc5dbe6dc2aab4, 0xa202f97995b69c0d 293 data8 0xa232fe6eb0c0577d, 0xa26a2582012f6e17 294 data8 0xa2a197e5d10465cb, 0xa2d25a532efefbc8 295 data8 0xa30a5bd6e49e4ab8, 0xa33b9c9b59879e24 296 data8 0xa3742fca6a3c1f21, 0xa3a5f1273887bf22 297 data8 0xa3d7ef508ff11574, 0xa4115ce30548bc15 298 data8 0xa443df0e53df577a, 0xa4769fa5913c0ec3 299 data8 0xa4a99f303bc7def5, 0xa4dcde37779adf4b 300 data8 0xa5105d46152c938a, 0xa5441ce89825cb8d 301 data8 0xa5781dad3e54d899, 0xa5ac602406c4e68c 302 data8 0xa5d9601d95c2c0bc, 0xa60e1e1a2de14745 303 data8 0xa6431f6e3fbd9658, 0xa67864b0d432fda4 304 data8 0xa6a6444aa0243c0b, 0xa6dc094d10f25792 305 data8 0xa70a574cc02bba69, 0xa7409e2af9549084 306 data8 0xa76f5c64ca2cf13b, 0xa79e4f0babab5dc0 307 data8 0xa7d5579ae5164b85, 0xa804bd3c6fe61cc8 308 data8 0xa8345895e5250a5a, 0xa8642a122b44ef0b 309 data8 0xa89c38ca18f6108b, 0xa8cc81063b6e87ca 310 data8 0xa8fd00bfa409285e, 0xa92db8664d5516da 311 data8 0xa95ea86b75cc2c20, 0xa98fd141a4992deb 312 data8 0xa9c1335cae7446ba, 0xa9ea8686f556f645 313 data8 0xaa1c52d17906bb19, 0xaa4e59b046dab887 314 data8 0xaa809b9c60d1890b, 0xaab319102f3f9b33 315 data8 0xaadd5a18c1e21274, 0xab1045f2ac31bdf5 316 data8 0xab3ae3ab2df7231e, 0xab6e3f945d1e96fc 317 data8 0xaba1d953a08fa94e, 0xabcd090db7ef4c3f 318 data8 0xabf864602d7c323d, 0xac2ca5886ccf9b57 319 data8 0xac5861d4aa441f0f, 0xac8d183fe3a2fbed 320 data8 0xacb93703ff51571e, 0xace5830ad0c3f14b 321 data8 0xad11fca5d78b3ff2, 0xad4797fddf91a798 322 data8 0xad747701e559ebcb, 0xada184a47e9c7613 323 data8 0xadcec13ab0dda8ff, 0xadfc2d1a5fd21ba8 324 data8 0xae29c89a5053c33a, 0xae5794122b638df9 325 data8 0xae858fda8137ae0a, 0xaeb3bc4ccc56d3d1 326 data8 0xaee219c374c09920, 0xaf10a899d3235fe7 327 data8 0xaf3f692c341fe8b4, 0xaf6e5bd7db9ae6c2 328 data8 0xaf9d80fb081cd91b, 0xafc35ce063eb3787 329 data8 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0x9e73a0f5, 0x1d4e1d14 591 data4 0x9dd05b53, 0x1f2261e4, 0x9d4ee73d, 0x1ede515e 592 data4 0x1f22a573, 0x9ecac348, 0x1e6a2ac0, 0x1e2787d2 593 data4 0x9eb64b87, 0x1f0c69c6, 0x9f470a01, 0x9d7c1686 594 data4 0x1e468ebe, 0x9f21ee2f, 0x9ee52116, 0x9e20f715 595 data4 0x1ed18533, 0x9f005b38, 0x9f20cb95, 0x1da72967 596 data4 0x1f1ba5d7, 0x1e2f8b16, 0x9c794f96, 0x9ca74ea3 597 data4 0x1f410555, 0x9eff2b96, 0x1ce8f0b1, 0x1f0cee77 598 data4 0x1f191edd, 0x9ed5fcbc, 0x1f30f242, 0x9e0ad369 599 data4 0x1ed8f3c8, 0x1f52bb0e, 0x9e9ce408, 0x1f18907f 600 data4 0x9ecdad40, 0x9e8af91d, 0x1d46698a, 0x9f4b93d6 601 data4 0x9f3f5d33, 0x1e2e52f7, 0x9f13aeec, 0x9f3b1969 602 data4 0x1f0996f4, 0x9f2a03df, 0x1e264767, 0x1f3ab1fb 603 data4 0x9f3193c9, 0x9f21ce22, 0x9eab624c, 0x9ecd8fb1 604 data4 0x1eaf9a85, 0x1f0c6a2c, 0x1eecbe61, 0x1f3fead9 605 data4 0x1f1d3a29, 0x1e9099ce, 0x1eadd875, 0x1e4dbfb8 606 data4 0x9dc640d2, 0x1f413680, 0x9f3f57b3, 0x1dfa1553 607 data4 0x1ec71c6b, 0x1e00cc00, 0x9f271e55, 0x1e5a88bb 608 data4 0x1f46cc2b, 0x1ee80ff9, 0x9e29c6f3, 0x1f15e229 609 data4 0x9ea83d66, 0x1f37408e, 0x9dacb66e, 0x1e6f6259 610 data4 0x9f106973, 0x1dd4e5ac, 0x1cbfdcc8, 0x9f231c9f 611 data4 0x9e8677e4, 0x9e9e695a, 0x1efd782b, 0x9dd26959 612 data4 0x9e80af69, 0x1f386fb3, 0x1f022e8c, 0x9e839967 613 data4 0x1ce6796f, 0x1e4c22c2, 0x1e57ef24, 0x1e919804 614 data4 0x9d7ea090, 0x1e40140a, 0x1f261b46, 0x1db75be2 615 data4 0x1f145019, 0x9e3102b9, 0x9e22507b, 0x1eae813c 616 data4 0x1f117e97, 0x1f282296, 0x1f3814b3, 0x1e17977b 617 data4 0x1f39d6ff, 0x9f1c81b9, 0x9eb5bcad, 0x1f0f596e 618 data4 0x1e757fd5, 0x9f090daa, 0x9f2532fc, 0x9eebafbb 619 data4 0x1f086556, 0x9eeedde8, 0x9f32e174, 0x1e33c030 620 data4 0x1f1f145a, 0x1e6e556c, 0x1e419ffb, 0x9eb6019a 621 data4 0x9e872a2e, 0x1e113136, 0x1e93096f, 0x1f39be40 622 data4 0x1f1665ad, 0x9db81d7d, 0x9cd29091, 0x1e3f4af7 623 data4 0x9f23176c, 0x9eccf9b3, 0x1f34fc6c, 0x9ed36894 624 data4 0x1ef08e06, 0x9f3b46bb, 0x9f2c850b, 0x1f1565a4 625 data4 0x1e887bc3, 0x1e92629c, 0x9f11ac9e, 0x9e5579f3 626 data4 0x1e4d5790, 0x9ee1c3d1, 0x9e916aec, 0x9eb8d9b8 627 data4 0x1db46105, 0x1e168663, 0x1f26a942, 0x9f0f0383 628 data4 0x9f079032, 0x9ecae1d8, 0x1ed3b34c, 0x9edc5ee6 629 data4 0x9e8a75a7, 0x1f3c3de2, 0x9ee5041e, 0x1f08c727 630 data4 0x1d02d7ae, 0x9f36adda, 0x9ef9a857, 0x9ef5cb3a 631 data4 0x9eee73da, 0x9da5d629, 0x1e0e99be, 0x1e5159b9 632 data4 0x1f2eac89, 0x9e8eedc5, 0x1dd0ec90, 0x1f229aff 633 data4 0x1ed9c3e6, 0x1e95c55a, 0x9f0c24e4, 0x1e8afed6 634 data4 0x1e599a96, 0x1e881b21, 0x1eab84b9, 0x9ba2bb0e 635 data4 0x9e33ab10, 0x1f1710b5, 0x1ebfa271, 0x9e90bbc5 636 data4 0x9f32515b, 0x9b32aae8, 0x1eda455c, 0x1da8186e 637 data4 0x9e8917ff, 0x1ec4d08e, 0x1c90069d, 0x9f2f1d29 638 data4 0x9ecee86d, 0x9f234d1f, 0x1f370724, 0x1da87496 639 data4 0x1e7959f0, 0x9e8ada34, 0x1f1c7f6f, 0x1edd576b 640 data4 0x9de91e8b, 0x1ec4ef89, 0x1f32078a, 0x1e9925e2 641 data4 0x9d8eeccb, 0x9ea3d011, 0x1f231fdf, 0x9f1dbdfa 642 data4 0x1e7507a3, 0x1ec42614, 0x9e8693cb, 0x9ec68398 643 data4 0x1d5b05fb, 0x1de32119, 0x9f003429, 0x9ec16d92 644 data4 0x9f095315, 0x9f119d2c, 0x9ed0c984, 0x9f090662 645 data4 0x9e59aa1f, 0x9ed4e64a, 0x9f2798a7, 0x9f23624d 646 data4 0x1e0467d9, 0x1f22e7e7, 0x1e915256, 0x9cb4df70 647 data4 0x9e6f687c, 0x9e3c35e5, 0x9e5757ab, 0x9f031fa1 648 data4 0x1f25bff7, 0x1f0e58c2, 0x1ef3ce04, 0x1f002ecb 649 data4 0x9ebdc836, 0x9ed657dd, 0x9f149441, 0x9e8544b2 650 data4 0x1cd8ff1e, 0x1e9bb463, 0x1eaa1c5c, 0x1f200c1a 651 data4 0x1edbfbaf, 0x1f18724d, 0x9ed63c22, 0x9f08e045 652 data4 0x1f13ad07, 0x9e949311, 0x9f0c50d4, 0x1e824516 653 data4 0x1d5e52ba, 0x1d583fbd, 0x1e3b60a9, 0x9effe6d3 654 data4 0x1f0d0508, 0x1f00be77, 0x9e404bfa, 0x9e1ca381 655 data4 0x9f084dd8, 0x9e6db85d, 0x1db698e4, 0x9ebd1871 656 data4 0x9ecc2679, 0x1ee68442, 0x1edb1050, 0x9dbc96a4 657 data4 0x9f27c1f4, 0x1c99b756, 0x1eb4400a, 0x9f24390a 658 data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2 659 data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa 660 data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3 661 data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8 662 data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912 663 data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6 664 data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0 665 data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6 666 data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7 667 data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37 668 data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f 669 data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1 670 data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb 671 data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36 672 data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc 673 data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b 674 data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5 675 data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe 676 data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d 677 data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57 678 data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e 679 data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b 680 data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab 681 data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d 682 data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748 683 data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225 684 data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109 685 data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b 686 data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae 687 data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf 688 data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd 689 data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9 690 data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1 691 data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991 692 data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48 693 data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26 694 data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66 695 data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da 696 data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2 697 data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e 698 data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304 699 data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01 700 data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3 701 data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6 702 data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0 703 data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8 704 data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e 705 data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff 706 data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114 707 data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce 708 data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745 709 data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2 710 data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0 711 data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f 712 data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640 713 data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817 714 data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059 715 data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6 716 data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821 717 data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944 718 data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93 719 data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7 720 data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19 721 data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e 722 data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3 723 data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed 724 data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8 725 data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030 726 data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c 727 data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7 728 data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5 729 data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a 730 data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43 731 data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978 732 data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3 733 data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6 734 data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849 735 data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85 736 data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7 737 data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107 738 data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f 739 data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249 740 data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20 741 data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4 742 data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467 743 data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d 744LOCAL_OBJECT_END(D_table) 745 746 747.section .text 748GLOBAL_LIBM_ENTRY(cbrtl) 749 750{ .mfi 751 getf.sig GR_ARGSIG = f8 752 // will continue on main path only for normal/denormal numbers 753 // all other values will be filtered out and will exit early 754 fclass.nm.unc p12, p7 = f8, 0x1b 755 // GR_ADDR = pointer to C_1...C_6 followed by T_table 756 addl GR_ADDR = @ltoff(poly_coeffs), gp 757} 758{ .mfi 759 // GR_BIAS23 = 2/3*bias -63 = 0xaaaa-0x3f = 0xaa6b 760 mov GR_BIAS23 = 0xaa6b 761 // normalize a 762 fma.s1 FR_XNORM = f8, f1, f0 763 // GR_D_ADDR = pointer to D table 764 addl GR_D_ADDR = @ltoff(D_table), gp 765} 766;; 767 768{ .mmf 769 // load start address for C_1...C_6 followed by T_table 770 ld8 GR_C_START = [ GR_ADDR ] 771 // load start address of D table 772 ld8 GR_D_START = [ GR_D_ADDR ] 773 // y = frcpa(a) 774 frcpa.s1 FR_RCP, p6 = f1, f8 775} 776;; 777 778{ .mmi 779 // get normalized significand 780 getf.sig GR_NORMSIG = FR_XNORM 781 // get exponent 782 getf.exp GR_NORMEXPSGN = FR_XNORM 783 (p7) cmp.eq p12, p0 = GR_ARGSIG, r0 784} 785;; 786 787{ .mii 788 // load C_1 789 ldfe FR_C1 = [ GR_C_START ], 16 790 mov GR_SGNMASK = 0x20000 791 nop.i 0 792} 793;; 794 795{ .mfb 796 // load C_2 797 ldfe FR_C2 = [ GR_C_START ], 16 798 (p12) fma.s0 f8 = f8, f1, f0 799 // NaN/Infinities exit early 800 (p12) br.ret.spnt b0 801} 802;; 803 804{ .mfi 805 // load C_3, C_4 806 ldfpd FR_C3, FR_C4 = [ GR_C_START ], 16 807 // y = frcpa(a), set flags and result when argument is 0 808 // only used when p6=0 809 frcpa.s0 f8, p0 = f1, f8 810 nop.i 0 811} 812;; 813 814{ .mii 815 // get GR_SIGN = sign 816 and GR_SIGN = GR_NORMEXPSGN, GR_SGNMASK 817 // eliminate leading 1 from GR_NORMSIG = 2nd table index 818 shl GR_INDEX2 = GR_NORMSIG, 1 819 // eliminate sign from exponent 820 andcm GR_NORMEXP = GR_NORMEXPSGN, GR_SGNMASK 821} 822;; 823 824{ .mfi 825 // load C_5, C_6 826 (p6) ldfpd FR_C5, FR_C6 = [ GR_C_START ], 16 827 // r = 1-a*y 828 (p6) fnma.s1 FR_R = FR_RCP, FR_XNORM, f1 829 // Start computation of floor(exponent/3) by 830 // computing (2^20+2)/3*exponent = exponent*0x55556 831 // 1: exponent* = 5; 832 // (2^{16}-1)/3 = 0x5555: 833 // will form 0x5555*exponent by using shladd's 834 shladd GR_EXP5 = GR_NORMEXP, 2, GR_NORMEXP 835} 836;; 837 838{ .mib 839 // Next several integer steps compute floor(exponent/3) 840 // GR_TMP1 = (5*expon)*16 841 shladd GR_TMP1 = GR_EXP5, 4, r0 842 // GR_EXP3 = 3*exponent 843 shladd GR_EXP3 = GR_NORMEXP, 1, GR_NORMEXP 844 nop.b 0 845} 846;; 847 848{ .mmi 849 // GR_EXP6 = 6*exponent 850 shladd GR_EXP6 = GR_EXP3, 1, r0 851 // GR_EXP17 = 17*expon 852 add GR_EXP17 = GR_EXP5, GR_TMP1 853 // GR_IX2 = 2nd table index (8 bits) 854 shr.u GR_IX2 = GR_INDEX2, 56 855} 856;; 857 858{ .mmi 859 // adjust T_table pointer by 2nd index 860 shladd GR_T_INDEX = GR_IX2, 3, GR_C_START 861 // adjust D_table pointer by 2nd index 862 shladd GR_D_INDEX = GR_IX2, 2, GR_D_START 863 // GR_TMP2 = (17*expon)*16^2 864 shl GR_TMP2 = GR_EXP17, 8 865} 866;; 867 868{ .mmi 869 // GR_TMP3 = expon*(2^16-1)/3 870 add GR_TMP3 = GR_EXP17, GR_TMP2 871;; 872 // GR_TMP4 = expon*(2^20+2)/3 = expon*0x55556 873 shladd GR_TMP4 = GR_TMP3, 4, GR_EXP6 874 nop.i 0 875} 876;; 877 878{ .mii 879 nop.m 0 880 // GR_EXP_RES = floor(expon/3) 881 shr.u GR_EXP_RES = GR_TMP4, 20 882 nop.i 0 883} 884;; 885 886{ .mmi 887 nop.m 0 888 // r16 = 3*exponent 889 shladd r16 = GR_EXP_RES, 1, GR_EXP_RES 890 // bias exponent 891 add GR_EXPBIAS = GR_BIAS23, GR_EXP_RES 892} 893;; 894 895{ .mmi 896 // get remainder of exponent/3 897 sub GR_EXP_MOD_3 = GR_NORMEXP, r16 898;; 899 // add sign to exponent 900 or GR_EXPSIGNRES = GR_EXPBIAS, GR_SIGN 901 // remainder << = 8 902 shl GR_REMTMP = GR_EXP_MOD_3, 8 903} 904;; 905 906{ .mfi 907 // adjust D_table pointer by 1st index 908 shladd GR_IX_D = GR_REMTMP, 2, GR_D_INDEX 909 // P_1 = C_1+C_2*r 910 (p6) fma.s1 FR_P1 = FR_C2, FR_R, FR_C1 911 // adjust T_table pointer by 1st index 912 shladd GR_IX_T = GR_REMTMP, 3, GR_T_INDEX 913} 914{ .mfi 915 // FR_SGNEXP = sign*2^{exponent/3} 916 (p6) setf.exp FR_SGNEXP = GR_EXPSIGNRES 917 // r^2 = r*r 918 (p6) fma.s1 FR_R2 = FR_R, FR_R, f0 919 nop.i 0 920} 921;; 922 923{ .mfi 924 // load D 925 (p6) ldfs FR_D = [ GR_IX_D ] 926 // P_2 = C_3+C_4*r 927 (p6) fma.s1 FR_P2 = FR_C4, FR_R, FR_C3 928 nop.i 0 929} 930{ .mfi 931 // load T 932 (p6) ldf8 FR_T = [ GR_IX_T ] 933 // P_3 = C_5+C_6*r 934 (p6) fma.s1 FR_P3 = FR_C6, FR_R, FR_C5 935 nop.i 0 936} 937;; 938 939{ .mfi 940 nop.m 0 941 // P_4 = D-r*P_1 942 (p6) fnma.s1 FR_P4 = FR_R, FR_P1, FR_D 943 nop.i 0 944} 945{ .mfi 946 nop.m 0 947 // r^3 = r*r^2 948 (p6) fma.s1 FR_R3 = FR_R, FR_R2, f0 949 nop.i 0 950} 951;; 952 953{ .mfi 954 nop.m 0 955 // P_5 = P_2+r2*P_3 956 (p6) fma.s1 FR_P5 = FR_R2, FR_P3, FR_P2 957 nop.i 0 958} 959;; 960 961{ .mfi 962 nop.m 0 963 // T = T*(sign*2^{exponent/3}) 964 (p6) fma.s1 FR_TF = FR_T, FR_SGNEXP, f0 965 nop.i 0 966} 967{ .mfi 968 nop.m 0 969 // P = P_4-r3*P_5 970 (p6) fnma.s1 FR_P = FR_R3, FR_P5, FR_P4 971 nop.i 0 972} 973;; 974 975{ .mfb 976 nop.m 0 977 // result = T+T*p 978 (p6) fma.s0 f8 = FR_TF, FR_P, FR_TF 979 br.ret.sptk b0 980} 981;; 982 983GLOBAL_LIBM_END(cbrtl) 984libm_alias_ldouble_other (cbrt, cbrt) 985