1.file "asinl.s" 2 3 4// Copyright (c) 2001 - 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// 08/28/01 New version 42// 05/20/02 Cleaned up namespace and sf0 syntax 43// 02/06/03 Reordered header: .section, .global, .proc, .align 44// 45// API 46//============================================================== 47// long double asinl(long double) 48// 49// Overview of operation 50//============================================================== 51// Background 52// 53// Implementation 54// 55// For |s| in [2^{-4}, sqrt(2)/2]: 56// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52 57// asin(s)= asin(t)+asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e. 58// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1) 59// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9) 60// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table, 61// along with the high and low parts of asin(t) (stored as two double precision 62// values) 63// 64// |s| in (sqrt(2)/2, sqrt(255/256)): 65// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6.. 66// asin(|s|)= pi/2-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2) 67// To minimize accumulated errors, r is computed as 68// r= (t*s)_s-t^2*y*z+z*y*(t^2-1+s^2)_s+z*y*(1-s^2)_s*x+z'*y*(1-s^2)*PS29+ 69// +(t*s-(t*s)_s)+z*y*((t^2-1-(t^2-1+s^2)_s)+s^2)+z*y*(1-s^2-(1-s^2)_s)+ 70// +ez*z'*y*(1-s^2)*(1-x), 71// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits) 72// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2 73// 74// |s|<2^{-4}: evaluate as 17-degree polynomial 75// (or simply return s, if|s|<2^{-64}) 76// 77// |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-asin(sqrt(1-s^2)) 78// use 17-degree polynomial for asin(sqrt(1-s^2)), 79// 9-degree polynomial to evaluate sqrt(1-s^2) 80// High order term is (pi/2)_high-(y*(1-s^2))_high 81// 82 83 84 85// Registers used 86//============================================================== 87// f6-f15, f32-f36 88// r2-r3, r23-r23 89// p6, p7, p8, p12 90// 91 92 93 GR_SAVE_B0= r33 94 GR_SAVE_PFS= r34 95 GR_SAVE_GP= r35 // This reg. can safely be used 96 GR_SAVE_SP= r36 97 98 GR_Parameter_X= r37 99 GR_Parameter_Y= r38 100 GR_Parameter_RESULT= r39 101 GR_Parameter_TAG= r40 102 103 FR_X= f10 104 FR_Y= f1 105 FR_RESULT= f8 106 107 108 109RODATA 110 111.align 16 112 113 114 115LOCAL_OBJECT_START(T_table) 116 117// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2), 118// asin(t)_high (double precision), asin(t)_low (double precision) 119 120data8 0x80828692b71c4391, 0xff7ddcec2d87e879 121data8 0x3fb022bc0ae531a0, 0x3c9f599c7bb42af6 122data8 0x80869f0163d0b082, 0xff79cad2247914d3 123data8 0x3fb062dd26afc320, 0x3ca4eff21bd49c5c 124data8 0x808ac7d5a8690705, 0xff75a89ed6b626b9 125data8 0x3fb0a2ff4a1821e0, 0x3cb7e33b58f164cc 126data8 0x808f0112ad8ad2e0, 0xff7176517c2cc0cb 127data8 0x3fb0e32279319d80, 0x3caee31546582c43 128data8 0x80934abba8a1da0a, 0xff6d33e949b1ed31 129data8 0x3fb12346b8101da0, 0x3cb8bfe463d087cd 130data8 0x8097a4d3dbe63d8f, 0xff68e16571015c63 131data8 0x3fb1636c0ac824e0, 0x3c8870a7c5a3556f 132data8 0x809c0f5e9662b3dd, 0xff647ec520bca0f0 133data8 0x3fb1a392756ed280, 0x3c964f1a927461ae 134data8 0x80a08a5f33fadc66, 0xff600c07846a6830 135data8 0x3fb1e3b9fc19e580, 0x3c69eb3576d56332 136data8 0x80a515d91d71acd4, 0xff5b892bc475affa 137data8 0x3fb223e2a2dfbe80, 0x3c6a4e19fd972fb6 138data8 0x80a9b1cfc86ff7cd, 0xff56f631062cf93d 139data8 0x3fb2640c6dd76260, 0x3c62041160e0849e 140data8 0x80ae5e46b78b0d68, 0xff5253166bc17794 141data8 0x3fb2a43761187c80, 0x3cac61651af678c0 142data8 0x80b31b417a4b756b, 0xff4d9fdb14463dc8 143data8 0x3fb2e46380bb6160, 0x3cb06ef23eeba7a1 144data8 0x80b7e8c3ad33c369, 0xff48dc7e1baf6738 145data8 0x3fb32490d0d910c0, 0x3caa05f480b300d5 146data8 0x80bcc6d0f9c784d6, 0xff4408fe9ad13e37 147data8 0x3fb364bf558b3820, 0x3cb01e7e403aaab9 148data8 0x80c1b56d1692492d, 0xff3f255ba75f5f4e 149data8 0x3fb3a4ef12ec3540, 0x3cb4fe8fcdf5f5f1 150data8 0x80c6b49bc72ec446, 0xff3a319453ebd961 151data8 0x3fb3e5200d171880, 0x3caf2dc089b2b7e2 152data8 0x80cbc460dc4e0ae8, 0xff352da7afe64ac6 153data8 0x3fb425524827a720, 0x3cb75a855e7c6053 154data8 0x80d0e4c033bee9c4, 0xff301994c79afb32 155data8 0x3fb46585c83a5e00, 0x3cb3264981c019ab 156data8 0x80d615bdb87556db, 0xff2af55aa431f291 157data8 0x3fb4a5ba916c73c0, 0x3c994251d94427b5 158data8 0x80db575d6291fd8a, 0xff25c0f84bae0cb9 159data8 0x3fb4e5f0a7dbdb20, 0x3cbee2fcc4c786cb 160data8 0x80e0a9a33769e535, 0xff207c6cc0ec09fd 161data8 0x3fb526280fa74620, 0x3c940656e5549b91 162data8 0x80e60c93498e32cd, 0xff1b27b703a19c98 163data8 0x3fb56660ccee2740, 0x3ca7082374d7b2cd 164data8 0x80eb8031b8d4052d, 0xff15c2d6105c72f8 165data8 0x3fb5a69ae3d0b520, 0x3c7c4d46e09ac68a 166data8 0x80f10482b25c6c8a, 0xff104dc8e0813ed4 167data8 0x3fb5e6d6586fec20, 0x3c9aa84ffd9b4958 168data8 0x80f6998a709c7cfb, 0xff0ac88e6a4ab926 169data8 0x3fb627132eed9140, 0x3cbced2cbbbe7d16 170data8 0x80fc3f4d3b657c44, 0xff053325a0c8a2ec 171data8 0x3fb667516b6c34c0, 0x3c6489c5fc68595a 172data8 0x8101f5cf67ed2af8, 0xfeff8d8d73dec2bb 173data8 0x3fb6a791120f33a0, 0x3cbe12acf159dfad 174data8 0x8107bd1558d6291f, 0xfef9d7c4d043df29 175data8 0x3fb6e7d226fabba0, 0x3ca386d099cd0dc7 176data8 0x810d95237e38766a, 0xfef411ca9f80b5f7 177data8 0x3fb72814ae53cc20, 0x3cb9f35731e71dd6 178data8 0x81137dfe55aa0e29, 0xfeee3b9dc7eef009 179data8 0x3fb76858ac403a00, 0x3c74df3dd959141a 180data8 0x811977aa6a479f0f, 0xfee8553d2cb8122c 181data8 0x3fb7a89e24e6b0e0, 0x3ca6034406ee42bc 182data8 0x811f822c54bd5ef8, 0xfee25ea7add46a91 183data8 0x3fb7e8e51c6eb6a0, 0x3cb82f8f78e68ed7 184data8 0x81259d88bb4ffac1, 0xfedc57dc2809fb1d 185data8 0x3fb8292d9700ad60, 0x3cbebb73c0e653f9 186data8 0x812bc9c451e5a257, 0xfed640d974eb6068 187data8 0x3fb8697798c5d620, 0x3ca2feee76a9701b 188data8 0x813206e3da0f3124, 0xfed0199e6ad6b585 189data8 0x3fb8a9c325e852e0, 0x3cb9e88f2f4d0efe 190data8 0x813854ec231172f9, 0xfec9e229dcf4747d 191data8 0x3fb8ea1042932a00, 0x3ca5ff40d81f66fd 192data8 0x813eb3e209ee858f, 0xfec39a7a9b36538b 193data8 0x3fb92a5ef2f247c0, 0x3cb5e3bece4d6b07 194data8 0x814523ca796f56ce, 0xfebd428f72561efe 195data8 0x3fb96aaf3b3281a0, 0x3cb7b9e499436d7c 196data8 0x814ba4aa6a2d3ff9, 0xfeb6da672bd48fe4 197data8 0x3fb9ab011f819860, 0x3cb9168143cc1a7f 198data8 0x81523686e29bbdd7, 0xfeb062008df81f50 199data8 0x3fb9eb54a40e3ac0, 0x3cb6e544197eb1e1 200data8 0x8158d964f7124614, 0xfea9d95a5bcbd65a 201data8 0x3fba2ba9cd080800, 0x3ca9a717be8f7446 202data8 0x815f8d49c9d639e4, 0xfea34073551e1ac8 203data8 0x3fba6c009e9f9260, 0x3c741e989a60938a 204data8 0x8166523a8b24f626, 0xfe9c974a367f785c 205data8 0x3fbaac591d0661a0, 0x3cb2c1290107e57d 206data8 0x816d283c793e0114, 0xfe95ddddb94166cb 207data8 0x3fbaecb34c6ef600, 0x3c9c7d5fbaec405d 208data8 0x81740f54e06d55bd, 0xfe8f142c93750c50 209data8 0x3fbb2d0f310cca00, 0x3cbc09479a9cbcfb 210data8 0x817b07891b15cd5e, 0xfe883a3577e9fceb 211data8 0x3fbb6d6ccf1455e0, 0x3cb9450bff4ee307 212data8 0x818210de91bba6c8, 0xfe814ff7162cf62f 213data8 0x3fbbadcc2abb1180, 0x3c9227fda12a8d24 214data8 0x81892b5abb0f2bf9, 0xfe7a55701a8697b1 215data8 0x3fbbee2d48377700, 0x3cb6fad72acfe356 216data8 0x819057031bf7760e, 0xfe734a9f2dfa1810 217data8 0x3fbc2e902bc10600, 0x3cb4465b588d16ad 218data8 0x819793dd479d4fbe, 0xfe6c2f82f643f68b 219data8 0x3fbc6ef4d9904580, 0x3c8b9ac54823960d 220data8 0x819ee1eedf76367a, 0xfe65041a15d8a92c 221data8 0x3fbcaf5b55dec6a0, 0x3ca2b8d28a954db2 222data8 0x81a6413d934f7a66, 0xfe5dc8632be3477f 223data8 0x3fbcefc3a4e727a0, 0x3c9380da83713ab4 224data8 0x81adb1cf21597d4b, 0xfe567c5cd44431d5 225data8 0x3fbd302dcae51600, 0x3ca995b83421756a 226data8 0x81b533a9563310b8, 0xfe4f2005a78fb50f 227data8 0x3fbd7099cc155180, 0x3caefa2f7a817d5f 228data8 0x81bcc6d20cf4f373, 0xfe47b35c3b0caaeb 229data8 0x3fbdb107acb5ae80, 0x3cb455fc372dd026 230data8 0x81c46b4f2f3d6e68, 0xfe40365f20b316d6 231data8 0x3fbdf177710518c0, 0x3cbee3dcc5b01434 232data8 0x81cc2126b53c1144, 0xfe38a90ce72abf36 233data8 0x3fbe31e91d439620, 0x3cb3e131c950aebd 234data8 0x81d3e85ea5bd8ee2, 0xfe310b6419c9c33a 235data8 0x3fbe725cb5b24900, 0x3c01d3fac6029027 236data8 0x81dbc0fd1637b9c1, 0xfe295d6340932d15 237data8 0x3fbeb2d23e937300, 0x3c6304cc44aeedd1 238data8 0x81e3ab082ad5a0a4, 0xfe219f08e03580b3 239data8 0x3fbef349bc2a77e0, 0x3cac1d2d6abe9c72 240data8 0x81eba6861683cb97, 0xfe19d0537a0946e2 241data8 0x3fbf33c332bbe020, 0x3ca0909dba4e96ca 242data8 0x81f3b37d1afc9979, 0xfe11f1418c0f94e2 243data8 0x3fbf743ea68d5b60, 0x3c937fc12a2a779a 244data8 0x81fbd1f388d4be45, 0xfe0a01d190f09063 245data8 0x3fbfb4bc1be5c340, 0x3cbf51a504b55813 246data8 0x820401efbf87e248, 0xfe020201fff9efea 247data8 0x3fbff53b970d1e80, 0x3ca625444b260078 248data8 0x82106ad2ffdca049, 0xfdf5e3940a49135e 249data8 0x3fc02aff52065460, 0x3c9125d113e22a57 250data8 0x8221343d6ea1d3e2, 0xfde581a45429b0a0 251data8 0x3fc06b84f8e03220, 0x3caccf362295894b 252data8 0x82324434adbf99c2, 0xfdd4de1a001fb775 253data8 0x3fc0ac0ed1fe7240, 0x3cc22f676096b0af 254data8 0x82439aee8d0c7747, 0xfdc3f8e8269d1f03 255data8 0x3fc0ec9cee9e4820, 0x3cca147e2886a628 256data8 0x825538a1d0fcb2f0, 0xfdb2d201a9b1ba66 257data8 0x3fc12d2f6006f0a0, 0x3cc72b36633bc2d4 258data8 0x82671d86345c5cee, 0xfda1695934d723e7 259data8 0x3fc16dc63789de60, 0x3cb11f9c47c7b83f 260data8 0x827949d46a121770, 0xfd8fbee13cbbb823 261data8 0x3fc1ae618682e620, 0x3cce1b59020cef8e 262data8 0x828bbdc61eeab9ba, 0xfd7dd28bff0c9f34 263data8 0x3fc1ef015e586c40, 0x3cafec043e0225ee 264data8 0x829e7995fb6de9e1, 0xfd6ba44b823ee1ca 265data8 0x3fc22fa5d07b90c0, 0x3cba905409caf8e3 266data8 0x82b17d7fa5bbc982, 0xfd5934119557883a 267data8 0x3fc2704eee685da0, 0x3cb5ef21838a823e 268data8 0x82c4c9bfc373d276, 0xfd4681cfcfb2c161 269data8 0x3fc2b0fcc9a5f3e0, 0x3ccc7952c5e0e312 270data8 0x82d85e93fba50136, 0xfd338d7790ca0f41 271data8 0x3fc2f1af73c6ba00, 0x3cbecf5f977d1ca9 272data8 0x82ec3c3af8c76b32, 0xfd2056f9fff97727 273data8 0x3fc33266fe6889a0, 0x3c9d329c022ebdb5 274data8 0x830062f46abf6022, 0xfd0cde480c43b327 275data8 0x3fc373237b34de60, 0x3cc95806d4928adb 276data8 0x8314d30108ea35f0, 0xfcf923526c1562b2 277data8 0x3fc3b3e4fbe10520, 0x3cbc299fe7223d54 278data8 0x83298ca29434df97, 0xfce526099d0737ed 279data8 0x3fc3f4ab922e4a60, 0x3cb59d8bb8fdbccc 280data8 0x833e901bd93c7009, 0xfcd0e65de39f1f7c 281data8 0x3fc435774fea2a60, 0x3c9ec18b43340914 282data8 0x8353ddb0b278aad8, 0xfcbc643f4b106055 283data8 0x3fc4764846ee80a0, 0x3cb90402efd87ed6 284data8 0x836975a60a70c52e, 0xfca79f9da4fab13a 285data8 0x3fc4b71e8921b860, 0xbc58f23449ed6365 286data8 0x837f5841ddfa7a46, 0xfc92986889284148 287data8 0x3fc4f7fa2876fca0, 0xbc6294812bf43acd 288data8 0x839585cb3e839773, 0xfc7d4e8f554ab12f 289data8 0x3fc538db36ee6960, 0x3cb910b773d4c578 290data8 0x83abfe8a5466246f, 0xfc67c2012cb6fa68 291data8 0x3fc579c1c6953cc0, 0x3cc5ede909fc47fc 292data8 0x83c2c2c861474d91, 0xfc51f2acf82041d5 293data8 0x3fc5baade9860880, 0x3cac63cdfc3588e5 294data8 0x83d9d2cfc2813637, 0xfc3be08165519325 295data8 0x3fc5fb9fb1e8e3a0, 0x3cbf7c8466578c29 296data8 0x83f12eebf397daac, 0xfc258b6ce6e6822f 297data8 0x3fc63c9731f39d40, 0x3cb6d2a7ffca3e9e 298data8 0x8408d76990b9296e, 0xfc0ef35db402af94 299data8 0x3fc67d947be9eec0, 0x3cb1980da09e6566 300data8 0x8420cc9659487cd7, 0xfbf81841c8082dc4 301data8 0x3fc6be97a21daf00, 0x3cc2ac8330e59aa5 302data8 0x84390ec132759ecb, 0xfbe0fa06e24cc390 303data8 0x3fc6ffa0b6ef05e0, 0x3ccc1a030fee56c4 304data8 0x84519e3a29df811a, 0xfbc9989a85ce0954 305data8 0x3fc740afcccca000, 0x3cc19692a5301ca6 306data8 0x846a7b527842d61b, 0xfbb1f3e9f8e45dc4 307data8 0x3fc781c4f633e2c0, 0x3cc0e98f3868a508 308data8 0x8483a65c8434b5f0, 0xfb9a0be244f4af45 309data8 0x3fc7c2e045b12140, 0x3cb2a8d309754420 310data8 0x849d1fabe4e97dd7, 0xfb81e070362116d1 311data8 0x3fc80401cddfd120, 0x3ca7a44544aa4ce6 312data8 0x84b6e795650817ea, 0xfb6971805af8411e 313data8 0x3fc84529a16ac020, 0x3c9e3b709c7d6f94 314data8 0x84d0fe6f0589da92, 0xfb50beff0423a2f5 315data8 0x3fc88657d30c49e0, 0x3cc60d65a7f0a278 316data8 0x84eb649000a73014, 0xfb37c8d84414755c 317data8 0x3fc8c78c758e8e80, 0x3cc94b2ee984c2b7 318data8 0x85061a50ccd13781, 0xfb1e8ef7eeaf764b 319data8 0x3fc908c79bcba900, 0x3cc8540ae794a2fe 320data8 0x8521200b1fb8916e, 0xfb05114998f76a83 321data8 0x3fc94a0958ade6c0, 0x3ca127f49839fa9c 322data8 0x853c7619f1618bf6, 0xfaeb4fb898b65d19 323data8 0x3fc98b51bf2ffee0, 0x3c8c9ba7a803909a 324data8 0x85581cd97f45e274, 0xfad14a3004259931 325data8 0x3fc9cca0e25d4ac0, 0x3cba458e91d3bf54 326data8 0x857414a74f8446b4, 0xfab7009ab1945a54 327data8 0x3fca0df6d551fe80, 0x3cc78ea1d329d2b2 328data8 0x85905de2341dea46, 0xfa9c72e3370d2fbc 329data8 0x3fca4f53ab3b6200, 0x3ccf60dca86d57ef 330data8 0x85acf8ea4e423ff8, 0xfa81a0f3e9fa0ee9 331data8 0x3fca90b777580aa0, 0x3ca4c4e2ec8a867e 332data8 0x85c9e62111a92e7d, 0xfa668ab6dec711b1 333data8 0x3fcad2224cf814e0, 0x3c303de5980d071c 334data8 0x85e725e947fbee97, 0xfa4b3015e883dbfe 335data8 0x3fcb13943f7d5f80, 0x3cc29d4eefa5cb1e 336data8 0x8604b8a7144cd054, 0xfa2f90fa9883a543 337data8 0x3fcb550d625bc6a0, 0x3c9e01a746152daf 338data8 0x86229ebff69e2415, 0xfa13ad4e3dfbe1c1 339data8 0x3fcb968dc9195ea0, 0x3ccc091bd73ae518 340data8 0x8640d89acf78858c, 0xf9f784f9e5a1877b 341data8 0x3fcbd815874eb160, 0x3cb5f4b89875e187 342data8 0x865f669fe390c7f5, 0xf9db17e65944eacf 343data8 0x3fcc19a4b0a6f9c0, 0x3cc5c0bc2b0bbf14 344data8 0x867e4938df7dc45f, 0xf9be65fc1f6c2e6e 345data8 0x3fcc5b3b58e061e0, 0x3cc1ca70df8f57e7 346data8 0x869d80d0db7e4c0c, 0xf9a16f237aec427a 347data8 0x3fcc9cd993cc4040, 0x3cbae93acc85eccf 348data8 0x86bd0dd45f4f8265, 0xf98433446a806e70 349data8 0x3fccde7f754f5660, 0x3cb22f70e64568d0 350data8 0x86dcf0b16613e37a, 0xf966b246a8606170 351data8 0x3fcd202d11620fa0, 0x3c962030e5d4c849 352data8 0x86fd29d7624b3d5d, 0xf948ec11a9d4c45b 353data8 0x3fcd61e27c10c0a0, 0x3cc7083c91d59217 354data8 0x871db9b741dbe44a, 0xf92ae08c9eca4941 355data8 0x3fcda39fc97be7c0, 0x3cc9258579e57211 356data8 0x873ea0c3722d6af2, 0xf90c8f9e71633363 357data8 0x3fcde5650dd86d60, 0x3ca4755a9ea582a9 358data8 0x875fdf6fe45529e8, 0xf8edf92dc5875319 359data8 0x3fce27325d6fe520, 0x3cbc1e2b6c1954f9 360data8 0x878176321154e2bc, 0xf8cf1d20f87270b8 361data8 0x3fce6907cca0d060, 0x3cb6ca4804750830 362data8 0x87a36580fe6bccf5, 0xf8affb5e20412199 363data8 0x3fceaae56fdee040, 0x3cad6b310d6fd46c 364data8 0x87c5add5417a5cb9, 0xf89093cb0b7c0233 365data8 0x3fceeccb5bb33900, 0x3cc16e99cedadb20 366data8 0x87e84fa9057914ca, 0xf870e64d40a15036 367data8 0x3fcf2eb9a4bcb600, 0x3cc75ee47c8b09e9 368data8 0x880b4b780f02b709, 0xf850f2c9fdacdf78 369data8 0x3fcf70b05fb02e20, 0x3cad6350d379f41a 370data8 0x882ea1bfc0f228ac, 0xf830b926379e6465 371data8 0x3fcfb2afa158b8a0, 0x3cce0ccd9f829985 372data8 0x885252ff21146108, 0xf810394699fe0e8e 373data8 0x3fcff4b77e97f3e0, 0x3c9b30faa7a4c703 374data8 0x88765fb6dceebbb3, 0xf7ef730f865f6df0 375data8 0x3fd01b6406332540, 0x3cdc5772c9e0b9bd 376data8 0x88ad1f69be2cc730, 0xf7bdc59bc9cfbd97 377data8 0x3fd04cf8ad203480, 0x3caeef44fe21a74a 378data8 0x88f763f70ae2245e, 0xf77a91c868a9c54e 379data8 0x3fd08f23ce0162a0, 0x3cd6290ab3fe5889 380data8 0x89431fc7bc0c2910, 0xf73642973c91298e 381data8 0x3fd0d1610f0c1ec0, 0x3cc67401a01f08cf 382data8 0x8990573407c7738e, 0xf6f0d71d1d7a2dd6 383data8 0x3fd113b0c65d88c0, 0x3cc7aa4020fe546f 384data8 0x89df0eb108594653, 0xf6aa4e6a05cfdef2 385data8 0x3fd156134ada6fe0, 0x3cc87369da09600c 386data8 0x8a2f4ad16e0ed78a, 0xf662a78900c35249 387data8 0x3fd19888f43427a0, 0x3cc62b220f38e49c 388data8 0x8a811046373e0819, 0xf619e180181d97cc 389data8 0x3fd1db121aed7720, 0x3ca3ede7490b52f4 390data8 0x8ad463df6ea0fa2c, 0xf5cffb504190f9a2 391data8 0x3fd21daf185fa360, 0x3caafad98c1d6c1b 392data8 0x8b294a8cf0488daf, 0xf584f3f54b8604e6 393data8 0x3fd2606046bf95a0, 0x3cdb2d704eeb08fa 394data8 0x8b7fc95f35647757, 0xf538ca65c960b582 395data8 0x3fd2a32601231ec0, 0x3cc661619fa2f126 396data8 0x8bd7e588272276f8, 0xf4eb7d92ff39fccb 397data8 0x3fd2e600a3865760, 0x3c8a2a36a99aca4a 398data8 0x8c31a45bf8e9255e, 0xf49d0c68cd09b689 399data8 0x3fd328f08ad12000, 0x3cb9efaf1d7ab552 400data8 0x8c8d0b520a35eb18, 0xf44d75cd993cfad2 401data8 0x3fd36bf614dcc040, 0x3ccacbb590bef70d 402data8 0x8cea2005d068f23d, 0xf3fcb8a23ab4942b 403data8 0x3fd3af11a079a6c0, 0x3cd9775872cf037d 404data8 0x8d48e837c8cd5027, 0xf3aad3c1e2273908 405data8 0x3fd3f2438d754b40, 0x3ca03304f667109a 406data8 0x8da969ce732f3ac7, 0xf357c60202e2fd7e 407data8 0x3fd4358c3ca032e0, 0x3caecf2504ff1a9d 408data8 0x8e0baad75555e361, 0xf3038e323ae9463a 409data8 0x3fd478ec0fd419c0, 0x3cc64bdc3d703971 410data8 0x8e6fb18807ba877e, 0xf2ae2b1c3a6057f7 411data8 0x3fd4bc6369fa40e0, 0x3cbb7122ec245cf2 412data8 0x8ed5843f4bda74d5, 0xf2579b83aa556f0c 413data8 0x3fd4fff2af11e2c0, 0x3c9cfa2dc792d394 414data8 0x8f3d29862c861fef, 0xf1ffde2612ca1909 415data8 0x3fd5439a4436d000, 0x3cc38d46d310526b 416data8 0x8fa6a81128940b2d, 0xf1a6f1bac0075669 417data8 0x3fd5875a8fa83520, 0x3cd8bf59b8153f8a 418data8 0x901206c1686317a6, 0xf14cd4f2a730d480 419data8 0x3fd5cb33f8cf8ac0, 0x3c9502b5c4d0e431 420data8 0x907f4ca5fe9cf739, 0xf0f186784a125726 421data8 0x3fd60f26e847b120, 0x3cc8a1a5e0acaa33 422data8 0x90ee80fd34aeda5e, 0xf09504ef9a212f18 423data8 0x3fd65333c7e43aa0, 0x3cae5b029cb1f26e 424data8 0x915fab35e37421c6, 0xf0374ef5daab5c45 425data8 0x3fd6975b02b8e360, 0x3cd5aa1c280c45e6 426data8 0x91d2d2f0d894d73c, 0xefd86321822dbb51 427data8 0x3fd6db9d05213b20, 0x3cbecf2c093ccd8b 428data8 0x9248000249200009, 0xef7840021aca5a72 429data8 0x3fd71ffa3cc87fc0, 0x3cb8d273f08d00d9 430data8 0x92bf3a7351f081d2, 0xef16e42021d7cbd5 431data8 0x3fd7647318b1ad20, 0x3cbce099d79cdc46 432data8 0x93388a8386725713, 0xeeb44dfce6820283 433data8 0x3fd7a908093fc1e0, 0x3ccb033ec17a30d9 434data8 0x93b3f8aa8e653812, 0xee507c126774fa45 435data8 0x3fd7edb9803e3c20, 0x3cc10aedb48671eb 436data8 0x94318d99d341ade4, 0xedeb6cd32f891afb 437data8 0x3fd83287f0e9cf80, 0x3c994c0c1505cd2a 438data8 0x94b1523e3dedc630, 0xed851eaa3168f43c 439data8 0x3fd87773cff956e0, 0x3cda3b7bce6a6b16 440data8 0x95334fc20577563f, 0xed1d8ffaa2279669 441data8 0x3fd8bc7d93a70440, 0x3cd4922edc792ce2 442data8 0x95b78f8e8f92f274, 0xecb4bf1fd2be72da 443data8 0x3fd901a5b3b9cf40, 0x3cd3fea1b00f9d0d 444data8 0x963e1b4e63a87c3f, 0xec4aaa6d08694cc1 445data8 0x3fd946eca98f2700, 0x3cdba4032d968ff1 446data8 0x96c6fcef314074fc, 0xebdf502d53d65fea 447data8 0x3fd98c52f024e800, 0x3cbe7be1ab8c95c9 448data8 0x97523ea3eab028b2, 0xeb72aea36720793e 449data8 0x3fd9d1d904239860, 0x3cd72d08a6a22b70 450data8 0x97dfeae6f4ee4a9a, 0xeb04c4096a884e94 451data8 0x3fda177f63e8ef00, 0x3cd818c3c1ebfac7 452data8 0x98700c7c6d85d119, 0xea958e90cfe1efd7 453data8 0x3fda5d468f92a540, 0x3cdf45fbfaa080fe 454data8 0x9902ae7487a9caa1, 0xea250c6224aab21a 455data8 0x3fdaa32f090998e0, 0x3cd715a9353cede4 456data8 0x9997dc2e017a9550, 0xe9b33b9ce2bb7638 457data8 0x3fdae939540d3f00, 0x3cc545c014943439 458data8 0x9a2fa158b29b649b, 0xe9401a573f8aa706 459data8 0x3fdb2f65f63f6c60, 0x3cd4a63c2f2ca8e2 460data8 0x9aca09f835466186, 0xe8cba69df9f0bf35 461data8 0x3fdb75b5773075e0, 0x3cda310ce1b217ec 462data8 0x9b672266ab1e0136, 0xe855de74266193d4 463data8 0x3fdbbc28606babc0, 0x3cdc84b75cca6c44 464data8 0x9c06f7579f0b7bd5, 0xe7debfd2f98c060b 465data8 0x3fdc02bf3d843420, 0x3cd225d967ffb922 466data8 0x9ca995db058cabdc, 0xe76648a991511c6e 467data8 0x3fdc497a9c224780, 0x3cde08101c5b825b 468data8 0x9d4f0b605ce71e88, 0xe6ec76dcbc02d9a7 469data8 0x3fdc905b0c10d420, 0x3cb1abbaa3edf120 470data8 0x9df765b9eecad5e6, 0xe6714846bdda7318 471data8 0x3fdcd7611f4b8a00, 0x3cbf6217ae80aadf 472data8 0x9ea2b320350540fe, 0xe5f4bab71494cd6b 473data8 0x3fdd1e8d6a0d56c0, 0x3cb726e048cc235c 474data8 0x9f51023562fc5676, 0xe576cbf239235ecb 475data8 0x3fdd65e082df5260, 0x3cd9e66872bd5250 476data8 0xa002620915c2a2f6, 0xe4f779b15f5ec5a7 477data8 0x3fddad5b02a82420, 0x3c89743b0b57534b 478data8 0xa0b6e21c2caf9992, 0xe476c1a233a7873e 479data8 0x3fddf4fd84bbe160, 0x3cbf7adea9ee3338 480data8 0xa16e9264cc83a6b2, 0xe3f4a16696608191 481data8 0x3fde3cc8a6ec6ee0, 0x3cce46f5a51f49c6 482data8 0xa22983528f3d8d49, 0xe3711694552da8a8 483data8 0x3fde84bd099a6600, 0x3cdc78f6490a2d31 484data8 0xa2e7c5d2e2e69460, 0xe2ec1eb4e1e0a5fb 485data8 0x3fdeccdb4fc685c0, 0x3cdd3aedb56a4825 486data8 0xa3a96b5599bd2532, 0xe265b74506fbe1c9 487data8 0x3fdf15241f23b3e0, 0x3cd440f3c6d65f65 488data8 0xa46e85d1ae49d7de, 0xe1ddddb499b3606f 489data8 0x3fdf5d98202994a0, 0x3cd6c44bd3fb745a 490data8 0xa53727ca3e11b99e, 0xe1548f662951b00d 491data8 0x3fdfa637fe27bf60, 0x3ca8ad1cd33054dd 492data8 0xa6036453bdc20186, 0xe0c9c9aeabe5e481 493data8 0x3fdfef0467599580, 0x3cc0f1ac0685d78a 494data8 0xa6d34f1969dda338, 0xe03d89d5281e4f81 495data8 0x3fe01bff067d6220, 0x3cc0731e8a9ef057 496data8 0xa7a6fc62f7246ff3, 0xdfafcd125c323f54 497data8 0x3fe04092d1ae3b40, 0x3ccabda24b59906d 498data8 0xa87e811a861df9b9, 0xdf20909061bb9760 499data8 0x3fe0653df0fd9fc0, 0x3ce94c8dcc722278 500data8 0xa959f2d2dd687200, 0xde8fd16a4e5f88bd 501data8 0x3fe08a00c1cae320, 0x3ce6b888bb60a274 502data8 0xaa3967cdeea58bda, 0xddfd8cabd1240d22 503data8 0x3fe0aedba3221c00, 0x3ced5941cd486e46 504data8 0xab904fd587263c84, 0xdd1f4472e1cf64ed 505data8 0x3fe0e651e85229c0, 0x3cdb6701042299b1 506data8 0xad686d44dd5a74bb, 0xdbf173e1f6b46e92 507data8 0x3fe1309cbf4cdb20, 0x3cbf1be7bb3f0ec5 508data8 0xaf524e15640ebee4, 0xdabd54896f1029f6 509data8 0x3fe17b4ee1641300, 0x3ce81dd055b792f1 510data8 0xb14eca24ef7db3fa, 0xd982cb9ae2f47e41 511data8 0x3fe1c66b9ffd6660, 0x3cd98ea31eb5ddc7 512data8 0xb35ec807669920ce, 0xd841bd1b8291d0b6 513data8 0x3fe211f66db3a5a0, 0x3ca480c35a27b4a2 514data8 0xb5833e4755e04dd1, 0xd6fa0bd3150b6930 515data8 0x3fe25df2e05b6c40, 0x3ca4bc324287a351 516data8 0xb7bd34c8000b7bd3, 0xd5ab9939a7d23aa1 517data8 0x3fe2aa64b32f7780, 0x3cba67314933077c 518data8 0xba0dc64d126cc135, 0xd4564563ce924481 519data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec 520data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8 521data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac 522data8 0xbef78e31985291a9, 0xd19672e2182f78be 523data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c 524data8 0xc19368b2b0629572, 0xd02baca5427e436a 525data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689 526data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d 527data8 0x3fe4300c7e945020, 0x3cbd367143da6582 528data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a 529data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63 530data8 0xca14e1b0622de526, 0xcbbe13773c3c5338 531data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c 532data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9 533data8 0x3fe5206cc637e000, 0x3ce2798b38e54193 534data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0 535data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68 536data8 0xd3c0d9f50057adda, 0xc70901152d59d16b 537data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab 538data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828 539data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5 540data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02 541data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee 542data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af 543data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d 544data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b 545data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321 546data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91 547data8 0x3fe76840418978a0, 0x3ccda46e85432c3d 548data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3 549data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3 550data8 0xf049183c3f53c39b, 0xbad848720223d3a8 551data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b 552data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48 553data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f 554data8 0xfa718f05adbf2c33, 0xb70432500286b185 555data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9 556data8 0xfff200c3f5489608, 0xb509e6454dca33cc 557data8 0x3fe9211b54441080, 0x3cb789cb53515688 558// The following table entries are not used 559//data8 0x82e138a0fac48700, 0xb3044a513a8e6132 560//data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0 561//data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88 562//data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039 563//data8 0x89377c1387d5b908, 0xaed58e9a09014d5c 564//data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58 565//data8 0x8cad7a2c98dec333, 0xacab929ce114d451 566//data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f 567//data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec 568//data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5 569//data8 0x9446d8191f80dd42, 0xa82ff92687235baf 570//data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e 571//data8 0x98758ba086e4000a, 0xa5dd497a9c184f58 572//data8 0x3febb5f571cb0560, 0x3ce0c7774329a613 573//data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b 574//data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177 575//data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03 576//data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959 577//data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec 578//data8 0x3fece4f404e29b20, 0x3cea3413401132b5 579//data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c 580//data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276 581//data8 0xb265c39cbd80f97a, 0x99553d969fec7beb 582//data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2 583//data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c 584//data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71 585//data8 0xbfea427678945732, 0x93d5990f9ee787af 586//data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5 587//data8 0xc79611399b8c90c5, 0x90f72bde80febc31 588//data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56 589//data8 0xcffa8425040624d7, 0x8e02b4418574ebed 590//data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f 591//data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024 592//data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94 593//data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b 594//data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc 595//data8 0xeea6d733421da0a6, 0x84921bbe64ae029a 596//data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02 597//data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6 598//data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3 599//data8 0x84ac1fcec4203245, 0xfb73a828893df19e 600//data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de 601//data8 0x8ca50621110c60e6, 0xf438a14c158d867c 602//data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6 603//data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da 604//data8 0x3ff1717418520340, 0x3ca5c2732533177c 605//data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119 606//data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5 607//data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d 608//data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a 609//data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f 610//data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7 611//data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec 612//data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746 613//data8 0xdfe323b8653af367, 0xc19107d99ab27e42 614//data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02 615//data8 0xf93746caaba3e1f1, 0xb777744a9df03bff 616//data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43 617//data8 0x8ca77052f6c340f0, 0xacaf476f13806648 618//data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff 619//data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50 620//data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c 621//data8 0xbe45074b05579024, 0x9478e362a07dd287 622//data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12 623//data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b 624//data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69 625//data8 0x94503d69396d91c7, 0xedd2ce885ff04028 626//data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b 627//data8 0xced1d96c5bb209e6, 0xc965278083808702 628//data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c 629//data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd 630//data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e 631//data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4 632//data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb 633LOCAL_OBJECT_END(T_table) 634 635 636 637.align 16 638 639LOCAL_OBJECT_START(poly_coeffs) 640 // C_3 641data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc 642 // C_5 643data8 0x999999999999999a, 0x0000000000003ffb 644 // C_7, C_9 645data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8 646 // pi/2 (low, high) 647data8 0x3C91A62633145C07, 0x3FF921FB54442D18 648 // C_11, C_13 649data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e 650 // C_15, C_17 651data8 0x3f8c99999999999a, 0x3f87a87878787223 652LOCAL_OBJECT_END(poly_coeffs) 653 654 655R_DBL_S = r21 656R_EXP0 = r22 657R_EXP = r15 658R_SGNMASK = r23 659R_TMP = r24 660R_TMP2 = r25 661R_INDEX = r26 662R_TMP3 = r27 663R_TMP03 = r27 664R_TMP4 = r28 665R_TMP5 = r23 666R_TMP6 = r22 667R_TMP7 = r21 668R_T = r29 669R_BIAS = r20 670 671F_T = f6 672F_1S2 = f7 673F_1S2_S = f9 674F_INV_1T2 = f10 675F_SQRT_1T2 = f11 676F_S2T2 = f12 677F_X = f13 678F_D = f14 679F_2M64 = f15 680 681F_CS2 = f32 682F_CS3 = f33 683F_CS4 = f34 684F_CS5 = f35 685F_CS6 = f36 686F_CS7 = f37 687F_CS8 = f38 688F_CS9 = f39 689F_S23 = f40 690F_S45 = f41 691F_S67 = f42 692F_S89 = f43 693F_S25 = f44 694F_S69 = f45 695F_S29 = f46 696F_X2 = f47 697F_X4 = f48 698F_TSQRT = f49 699F_DTX = f50 700F_R = f51 701F_R2 = f52 702F_R3 = f53 703F_R4 = f54 704 705F_C3 = f55 706F_C5 = f56 707F_C7 = f57 708F_C9 = f58 709F_P79 = f59 710F_P35 = f60 711F_P39 = f61 712 713F_ATHI = f62 714F_ATLO = f63 715 716F_T1 = f64 717F_Y = f65 718F_Y2 = f66 719F_ANDMASK = f67 720F_ORMASK = f68 721F_S = f69 722F_05 = f70 723F_SQRT_1S2 = f71 724F_DS = f72 725F_Z = f73 726F_1T2 = f74 727F_DZ = f75 728F_ZE = f76 729F_YZ = f77 730F_Y1S2 = f78 731F_Y1S2X = f79 732F_1X = f80 733F_ST = f81 734F_1T2_ST = f82 735F_TSS = f83 736F_Y1S2X2 = f84 737F_DZ_TERM = f85 738F_DTS = f86 739F_DS2X = f87 740F_T2 = f88 741F_ZY1S2S = f89 742F_Y1S2_1X = f90 743F_TS = f91 744F_PI2_LO = f92 745F_PI2_HI = f93 746F_S19 = f94 747F_INV1T2_2 = f95 748F_CORR = f96 749F_DZ0 = f97 750 751F_C11 = f98 752F_C13 = f99 753F_C15 = f100 754F_C17 = f101 755F_P1113 = f102 756F_P1517 = f103 757F_P1117 = f104 758F_P317 = f105 759F_R8 = f106 760F_HI = f107 761F_1S2_HI = f108 762F_DS2 = f109 763F_Y2_2 = f110 764F_S2 = f111 765F_S_DS2 = f112 766F_S_1S2S = f113 767F_XL = f114 768F_2M128 = f115 769 770 771.section .text 772GLOBAL_LIBM_ENTRY(asinl) 773 774{.mfi 775 // get exponent, mantissa (rounded to double precision) of s 776 getf.d R_DBL_S = f8 777 // 1-s^2 778 fnma.s1 F_1S2 = f8, f8, f1 779 // r2 = pointer to T_table 780 addl r2 = @ltoff(T_table), gp 781} 782 783{.mfi 784 // sign mask 785 mov R_SGNMASK = 0x20000 786 nop.f 0 787 // bias-63-1 788 mov R_TMP03 = 0xffff-64;; 789} 790 791 792{.mfi 793 // get exponent of s 794 getf.exp R_EXP = f8 795 nop.f 0 796 // R_TMP4 = 2^45 797 shl R_TMP4 = R_SGNMASK, 45-17 798} 799 800{.mlx 801 // load bias-4 802 mov R_TMP = 0xffff-4 803 // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1) 804 movl R_TMP2 = 0x7fcd413cccfe779a;; 805} 806 807 808{.mfi 809 // load 2^{-64} in FP register 810 setf.exp F_2M64 = R_TMP03 811 nop.f 0 812 // index = (0x7-exponent)|b1 b2.. b6 813 extr.u R_INDEX = R_DBL_S, 46, 9 814} 815 816{.mfi 817 // get t = sign|exponent|b1 b2.. b6 1 x.. x 818 or R_T = R_DBL_S, R_TMP4 819 nop.f 0 820 // R_TMP4 = 2^45-1 821 sub R_TMP4 = R_TMP4, r0, 1;; 822} 823 824 825{.mfi 826 // get t = sign|exponent|b1 b2.. b6 1 0.. 0 827 andcm R_T = R_T, R_TMP4 828 nop.f 0 829 // eliminate sign from R_DBL_S (shift left by 1) 830 shl R_TMP3 = R_DBL_S, 1 831} 832 833{.mfi 834 // R_BIAS = 3*2^6 835 mov R_BIAS = 0xc0 836 nop.f 0 837 // eliminate sign from R_EXP 838 andcm R_EXP0 = R_EXP, R_SGNMASK;; 839} 840 841 842 843{.mfi 844 // load start address for T_table 845 ld8 r2 = [r2] 846 nop.f 0 847 // p8 = 1 if |s|> = sqrt(2)/2 848 cmp.geu p8, p0 = R_TMP3, R_TMP2 849} 850 851{.mlx 852 // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4) 853 cmp.lt p7, p0 = R_EXP0, R_TMP 854 // sqrt coefficient cs8 = -33*13/128 855 movl R_TMP2 = 0xc0568000;; 856} 857 858 859 860{.mbb 861 // load t in FP register 862 setf.d F_T = R_T 863 // if |s|<2^{-4}, take alternate path 864 (p7) br.cond.spnt SMALL_S 865 // if |s|> = sqrt(2)/2, take alternate path 866 (p8) br.cond.sptk LARGE_S 867} 868 869{.mlx 870 // index = (4-exponent)|b1 b2.. b6 871 sub R_INDEX = R_INDEX, R_BIAS 872 // sqrt coefficient cs9 = 55*13/128 873 movl R_TMP = 0x40b2c000;; 874} 875 876 877{.mfi 878 // sqrt coefficient cs8 = -33*13/128 879 setf.s F_CS8 = R_TMP2 880 nop.f 0 881 // shift R_INDEX by 5 882 shl R_INDEX = R_INDEX, 5 883} 884 885{.mfi 886 // sqrt coefficient cs3 = 0.5 (set exponent = bias-1) 887 mov R_TMP4 = 0xffff - 1 888 nop.f 0 889 // sqrt coefficient cs6 = -21/16 890 mov R_TMP6 = 0xbfa8;; 891} 892 893 894{.mlx 895 // table index 896 add r2 = r2, R_INDEX 897 // sqrt coefficient cs7 = 33/16 898 movl R_TMP2 = 0x40040000;; 899} 900 901 902{.mmi 903 // load cs9 = 55*13/128 904 setf.s F_CS9 = R_TMP 905 // sqrt coefficient cs5 = 7/8 906 mov R_TMP3 = 0x3f60 907 // sqrt coefficient cs6 = 21/16 908 shl R_TMP6 = R_TMP6, 16;; 909} 910 911 912{.mmi 913 // load significand of 1/(1-t^2) 914 ldf8 F_INV_1T2 = [r2], 8 915 // sqrt coefficient cs7 = 33/16 916 setf.s F_CS7 = R_TMP2 917 // sqrt coefficient cs4 = -5/8 918 mov R_TMP5 = 0xbf20;; 919} 920 921 922{.mmi 923 // load significand of sqrt(1-t^2) 924 ldf8 F_SQRT_1T2 = [r2], 8 925 // sqrt coefficient cs6 = 21/16 926 setf.s F_CS6 = R_TMP6 927 // sqrt coefficient cs5 = 7/8 928 shl R_TMP3 = R_TMP3, 16;; 929} 930 931 932{.mmi 933 // sqrt coefficient cs3 = 0.5 (set exponent = bias-1) 934 setf.exp F_CS3 = R_TMP4 935 // r3 = pointer to polynomial coefficients 936 addl r3 = @ltoff(poly_coeffs), gp 937 // sqrt coefficient cs4 = -5/8 938 shl R_TMP5 = R_TMP5, 16;; 939} 940 941 942{.mfi 943 // sqrt coefficient cs5 = 7/8 944 setf.s F_CS5 = R_TMP3 945 // d = s-t 946 fms.s1 F_D = f8, f1, F_T 947 // set p6 = 1 if s<0, p11 = 1 if s> = 0 948 cmp.ge p6, p11 = R_EXP, R_DBL_S 949} 950 951{.mfi 952 // r3 = load start address to polynomial coefficients 953 ld8 r3 = [r3] 954 // s+t 955 fma.s1 F_S2T2 = f8, f1, F_T 956 nop.i 0;; 957} 958 959 960{.mfi 961 // sqrt coefficient cs4 = -5/8 962 setf.s F_CS4 = R_TMP5 963 // s^2-t^2 964 fma.s1 F_S2T2 = F_S2T2, F_D, f0 965 nop.i 0;; 966} 967 968 969{.mfi 970 // load C3 971 ldfe F_C3 = [r3], 16 972 // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2)) 973 fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 974 nop.i 0;; 975} 976 977{.mfi 978 // load C_5 979 ldfe F_C5 = [r3], 16 980 // set correct exponent for sqrt(1-t^2) 981 fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 982 nop.i 0;; 983} 984 985 986{.mfi 987 // load C_7, C_9 988 ldfpd F_C7, F_C9 = [r3] 989 // x = -(s^2-t^2)/(1-t^2)/2 990 fnma.s1 F_X = F_INV_1T2, F_S2T2, f0 991 nop.i 0;; 992} 993 994 995{.mfi 996 // load asin(t)_high, asin(t)_low 997 ldfpd F_ATHI, F_ATLO = [r2] 998 // t*sqrt(1-t^2) 999 fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0 1000 nop.i 0;; 1001} 1002 1003 1004{.mfi 1005 nop.m 0 1006 // cs9*x+cs8 1007 fma.s1 F_S89 = F_CS9, F_X, F_CS8 1008 nop.i 0 1009} 1010 1011{.mfi 1012 nop.m 0 1013 // cs7*x+cs6 1014 fma.s1 F_S67 = F_CS7, F_X, F_CS6 1015 nop.i 0;; 1016} 1017 1018{.mfi 1019 nop.m 0 1020 // cs5*x+cs4 1021 fma.s1 F_S45 = F_CS5, F_X, F_CS4 1022 nop.i 0 1023} 1024 1025{.mfi 1026 nop.m 0 1027 // x*x 1028 fma.s1 F_X2 = F_X, F_X, f0 1029 nop.i 0;; 1030} 1031 1032 1033{.mfi 1034 nop.m 0 1035 // (s-t)-t*x 1036 fnma.s1 F_DTX = F_T, F_X, F_D 1037 nop.i 0 1038} 1039 1040{.mfi 1041 nop.m 0 1042 // cs3*x+cs2 (cs2 = -0.5 = -cs3) 1043 fms.s1 F_S23 = F_CS3, F_X, F_CS3 1044 nop.i 0;; 1045} 1046 1047 1048{.mfi 1049 nop.m 0 1050 // cs9*x^3+cs8*x^2+cs7*x+cs6 1051 fma.s1 F_S69 = F_S89, F_X2, F_S67 1052 nop.i 0 1053} 1054 1055{.mfi 1056 nop.m 0 1057 // x^4 1058 fma.s1 F_X4 = F_X2, F_X2, f0 1059 nop.i 0;; 1060} 1061 1062 1063{.mfi 1064 nop.m 0 1065 // t*sqrt(1-t^2)*x^2 1066 fma.s1 F_TSQRT = F_TSQRT, F_X2, f0 1067 nop.i 0 1068} 1069 1070{.mfi 1071 nop.m 0 1072 // cs5*x^3+cs4*x^2+cs3*x+cs2 1073 fma.s1 F_S25 = F_S45, F_X2, F_S23 1074 nop.i 0;; 1075} 1076 1077 1078{.mfi 1079 nop.m 0 1080 // ((s-t)-t*x)*sqrt(1-t^2) 1081 fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0 1082 nop.i 0;; 1083} 1084 1085 1086{.mfi 1087 nop.m 0 1088 // if sign is negative, negate table values: asin(t)_low 1089 (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0 1090 nop.i 0 1091} 1092 1093{.mfi 1094 nop.m 0 1095 // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2 1096 fma.s1 F_S29 = F_S69, F_X4, F_S25 1097 nop.i 0;; 1098} 1099 1100 1101{.mfi 1102 nop.m 0 1103 // if sign is negative, negate table values: asin(t)_high 1104 (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0 1105 nop.i 0 1106} 1107 1108{.mfi 1109 nop.m 0 1110 // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29 1111 fnma.s1 F_R = F_S29, F_TSQRT, F_DTX 1112 nop.i 0;; 1113} 1114 1115 1116{.mfi 1117 nop.m 0 1118 // R^2 1119 fma.s1 F_R2 = F_R, F_R, f0 1120 nop.i 0;; 1121} 1122 1123 1124{.mfi 1125 nop.m 0 1126 // c7+c9*R^2 1127 fma.s1 F_P79 = F_C9, F_R2, F_C7 1128 nop.i 0 1129} 1130 1131{.mfi 1132 nop.m 0 1133 // c3+c5*R^2 1134 fma.s1 F_P35 = F_C5, F_R2, F_C3 1135 nop.i 0;; 1136} 1137 1138{.mfi 1139 nop.m 0 1140 // R^3 1141 fma.s1 F_R4 = F_R2, F_R2, f0 1142 nop.i 0;; 1143} 1144 1145{.mfi 1146 nop.m 0 1147 // R^3 1148 fma.s1 F_R3 = F_R2, F_R, f0 1149 nop.i 0;; 1150} 1151 1152 1153 1154{.mfi 1155 nop.m 0 1156 // c3+c5*R^2+c7*R^4+c9*R^6 1157 fma.s1 F_P39 = F_P79, F_R4, F_P35 1158 nop.i 0;; 1159} 1160 1161 1162{.mfi 1163 nop.m 0 1164 // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) 1165 fma.s1 F_P39 = F_P39, F_R3, F_ATLO 1166 nop.i 0;; 1167} 1168 1169 1170{.mfi 1171 nop.m 0 1172 // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) 1173 fma.s1 F_P39 = F_P39, f1, F_R 1174 nop.i 0;; 1175} 1176 1177 1178{.mfb 1179 nop.m 0 1180 // result = asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) 1181 fma.s0 f8 = F_ATHI, f1, F_P39 1182 // return 1183 br.ret.sptk b0;; 1184} 1185 1186 1187 1188 1189LARGE_S: 1190 1191{.mfi 1192 // bias-1 1193 mov R_TMP3 = 0xffff - 1 1194 // y ~ 1/sqrt(1-s^2) 1195 frsqrta.s1 F_Y, p7 = F_1S2 1196 // c9 = 55*13*17/128 1197 mov R_TMP4 = 0x10af7b 1198} 1199 1200{.mlx 1201 // c8 = -33*13*15/128 1202 mov R_TMP5 = 0x184923 1203 movl R_TMP2 = 0xff00000000000000;; 1204} 1205 1206{.mfi 1207 // set p6 = 1 if s<0, p11 = 1 if s>0 1208 cmp.ge p6, p11 = R_EXP, R_DBL_S 1209 // 1-s^2 1210 fnma.s1 F_1S2 = f8, f8, f1 1211 // set p9 = 1 1212 cmp.eq p9, p0 = r0, r0;; 1213} 1214 1215 1216{.mfi 1217 // load 0.5 1218 setf.exp F_05 = R_TMP3 1219 // (1-s^2) rounded to single precision 1220 fnma.s.s1 F_1S2_S = f8, f8, f1 1221 // c9 = 55*13*17/128 1222 shl R_TMP4 = R_TMP4, 10 1223} 1224 1225{.mlx 1226 // AND mask for getting t ~ sqrt(1-s^2) 1227 setf.sig F_ANDMASK = R_TMP2 1228 // OR mask 1229 movl R_TMP2 = 0x0100000000000000;; 1230} 1231 1232 1233{.mfi 1234 nop.m 0 1235 // (s^2)_s 1236 fma.s.s1 F_S2 = f8, f8, f0 1237 nop.i 0;; 1238} 1239 1240 1241{.mmi 1242 // c9 = 55*13*17/128 1243 setf.s F_CS9 = R_TMP4 1244 // c7 = 33*13/16 1245 mov R_TMP4 = 0x41d68 1246 // c8 = -33*13*15/128 1247 shl R_TMP5 = R_TMP5, 11;; 1248} 1249 1250 1251{.mfi 1252 setf.sig F_ORMASK = R_TMP2 1253 // y^2 1254 fma.s1 F_Y2 = F_Y, F_Y, f0 1255 // c7 = 33*13/16 1256 shl R_TMP4 = R_TMP4, 12 1257} 1258 1259{.mfi 1260 // c6 = -33*7/16 1261 mov R_TMP6 = 0xc1670 1262 // y' ~ sqrt(1-s^2) 1263 fma.s1 F_T1 = F_Y, F_1S2, f0 1264 // c5 = 63/8 1265 mov R_TMP7 = 0x40fc;; 1266} 1267 1268 1269{.mlx 1270 // load c8 = -33*13*15/128 1271 setf.s F_CS8 = R_TMP5 1272 // c4 = -35/8 1273 movl R_TMP5 = 0xc08c0000;; 1274} 1275 1276{.mfi 1277 // r3 = pointer to polynomial coefficients 1278 addl r3 = @ltoff(poly_coeffs), gp 1279 // 1-(1-s^2)_s 1280 fnma.s1 F_DS = F_1S2_S, f1, f1 1281 // p9 = 0 if p7 = 1 (p9 = 1 for special cases only) 1282 (p7) cmp.ne p9, p0 = r0, r0 1283} 1284 1285{.mlx 1286 // load c7 = 33*13/16 1287 setf.s F_CS7 = R_TMP4 1288 // c3 = 5/2 1289 movl R_TMP4 = 0x40200000;; 1290} 1291 1292 1293{.mfi 1294 nop.m 0 1295 // 1-(s^2)_s 1296 fnma.s1 F_S_1S2S = F_S2, f1, f1 1297 nop.i 0 1298} 1299 1300{.mlx 1301 // load c4 = -35/8 1302 setf.s F_CS4 = R_TMP5 1303 // c2 = -3/2 1304 movl R_TMP5 = 0xbfc00000;; 1305} 1306 1307 1308{.mfi 1309 // load c3 = 5/2 1310 setf.s F_CS3 = R_TMP4 1311 // x = (1-s^2)_s*y^2-1 1312 fms.s1 F_X = F_1S2_S, F_Y2, f1 1313 // c6 = -33*7/16 1314 shl R_TMP6 = R_TMP6, 12 1315} 1316 1317{.mfi 1318 nop.m 0 1319 // y^2/2 1320 fma.s1 F_Y2_2 = F_Y2, F_05, f0 1321 nop.i 0;; 1322} 1323 1324 1325{.mfi 1326 // load c6 = -33*7/16 1327 setf.s F_CS6 = R_TMP6 1328 // eliminate lower bits from y' 1329 fand F_T = F_T1, F_ANDMASK 1330 // c5 = 63/8 1331 shl R_TMP7 = R_TMP7, 16 1332} 1333 1334{.mfb 1335 // r3 = load start address to polynomial coefficients 1336 ld8 r3 = [r3] 1337 // 1-(1-s^2)_s-s^2 1338 fnma.s1 F_DS = f8, f8, F_DS 1339 // p9 = 1 if s is a special input (NaN, or |s|> = 1) 1340 (p9) br.cond.spnt ASINL_SPECIAL_CASES;; 1341} 1342 1343{.mmf 1344 // get exponent, significand of y' (in single prec.) 1345 getf.s R_TMP = F_T1 1346 // load c3 = -3/2 1347 setf.s F_CS2 = R_TMP5 1348 // y*(1-s^2) 1349 fma.s1 F_Y1S2 = F_Y, F_1S2, f0;; 1350} 1351 1352 1353{.mfi 1354 nop.m 0 1355 // x' = (y^2/2)*(1-(s^2)_s)-0.5 1356 fms.s1 F_XL = F_Y2_2, F_S_1S2S, F_05 1357 nop.i 0 1358} 1359 1360{.mfi 1361 nop.m 0 1362 // s^2-(s^2)_s 1363 fms.s1 F_S_DS2 = f8, f8, F_S2 1364 nop.i 0;; 1365} 1366 1367 1368{.mfi 1369 nop.m 0 1370 // if s<0, set s = -s 1371 (p6) fnma.s1 f8 = f8, f1, f0 1372 nop.i 0;; 1373} 1374 1375{.mfi 1376 // load c5 = 63/8 1377 setf.s F_CS5 = R_TMP7 1378 // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2 1379 fma.s1 F_X = F_DS, F_Y2, F_X 1380 // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6 1381 extr.u R_INDEX = R_TMP, 17, 9;; 1382} 1383 1384 1385{.mmi 1386 // index = (4-exponent)|b1 b2.. b6 1387 sub R_INDEX = R_INDEX, R_BIAS 1388 nop.m 0 1389 // get exponent of y 1390 shr.u R_TMP2 = R_TMP, 23;; 1391} 1392 1393{.mmi 1394 // load C3 1395 ldfe F_C3 = [r3], 16 1396 // set p8 = 1 if y'<2^{-4} 1397 cmp.gt p8, p0 = 0x7b, R_TMP2 1398 // shift R_INDEX by 5 1399 shl R_INDEX = R_INDEX, 5;; 1400} 1401 1402 1403{.mfb 1404 // get table index for sqrt(1-t^2) 1405 add r2 = r2, R_INDEX 1406 // get t = 2^k*1.b1 b2.. b7 1 1407 for F_T = F_T, F_ORMASK 1408 (p8) br.cond.spnt VERY_LARGE_INPUT;; 1409} 1410 1411 1412 1413{.mmf 1414 // load C5 1415 ldfe F_C5 = [r3], 16 1416 // load 1/(1-t^2) 1417 ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16 1418 // x = ((1-s^2)*y^2-1)/2 1419 fma.s1 F_X = F_X, F_05, f0;; 1420} 1421 1422 1423 1424{.mmf 1425 nop.m 0 1426 // C7, C9 1427 ldfpd F_C7, F_C9 = [r3], 16 1428 // set correct exponent for t 1429 fmerge.se F_T = F_T1, F_T;; 1430} 1431 1432 1433 1434{.mfi 1435 // pi/2 (low, high) 1436 ldfpd F_PI2_LO, F_PI2_HI = [r3] 1437 // c9*x+c8 1438 fma.s1 F_S89 = F_X, F_CS9, F_CS8 1439 nop.i 0 1440} 1441 1442{.mfi 1443 nop.m 0 1444 // x^2 1445 fma.s1 F_X2 = F_X, F_X, f0 1446 nop.i 0;; 1447} 1448 1449 1450{.mfi 1451 nop.m 0 1452 // y*(1-s^2)*x 1453 fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 1454 nop.i 0 1455} 1456 1457{.mfi 1458 nop.m 0 1459 // c7*x+c6 1460 fma.s1 F_S67 = F_X, F_CS7, F_CS6 1461 nop.i 0;; 1462} 1463 1464 1465{.mfi 1466 nop.m 0 1467 // 1-x 1468 fnma.s1 F_1X = F_X, f1, f1 1469 nop.i 0 1470} 1471 1472{.mfi 1473 nop.m 0 1474 // c3*x+c2 1475 fma.s1 F_S23 = F_X, F_CS3, F_CS2 1476 nop.i 0;; 1477} 1478 1479 1480{.mfi 1481 nop.m 0 1482 // 1-t^2 1483 fnma.s1 F_1T2 = F_T, F_T, f1 1484 nop.i 0 1485} 1486 1487{.mfi 1488 // load asin(t)_high, asin(t)_low 1489 ldfpd F_ATHI, F_ATLO = [r2] 1490 // c5*x+c4 1491 fma.s1 F_S45 = F_X, F_CS5, F_CS4 1492 nop.i 0;; 1493} 1494 1495 1496 1497{.mfi 1498 nop.m 0 1499 // t*s 1500 fma.s1 F_TS = F_T, f8, f0 1501 nop.i 0 1502} 1503 1504{.mfi 1505 nop.m 0 1506 // 0.5/(1-t^2) 1507 fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 1508 nop.i 0;; 1509} 1510 1511{.mfi 1512 nop.m 0 1513 // z~sqrt(1-t^2), rounded to 24 significant bits 1514 fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0 1515 nop.i 0 1516} 1517 1518{.mfi 1519 nop.m 0 1520 // sqrt(1-t^2) 1521 fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 1522 nop.i 0;; 1523} 1524 1525 1526{.mfi 1527 nop.m 0 1528 // y*(1-s^2)*x^2 1529 fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 1530 nop.i 0 1531} 1532 1533{.mfi 1534 nop.m 0 1535 // x^4 1536 fma.s1 F_X4 = F_X2, F_X2, f0 1537 nop.i 0;; 1538} 1539 1540 1541{.mfi 1542 nop.m 0 1543 // s*t rounded to 24 significant bits 1544 fma.s.s1 F_TSS = F_T, f8, f0 1545 nop.i 0 1546} 1547 1548{.mfi 1549 nop.m 0 1550 // c9*x^3+..+c6 1551 fma.s1 F_S69 = F_X2, F_S89, F_S67 1552 nop.i 0;; 1553} 1554 1555 1556{.mfi 1557 nop.m 0 1558 // ST = (t^2-1+s^2) rounded to 24 significant bits 1559 fms.s.s1 F_ST = f8, f8, F_1T2 1560 nop.i 0 1561} 1562 1563{.mfi 1564 nop.m 0 1565 // c5*x^3+..+c2 1566 fma.s1 F_S25 = F_X2, F_S45, F_S23 1567 nop.i 0;; 1568} 1569 1570 1571{.mfi 1572 nop.m 0 1573 // 0.25/(1-t^2) 1574 fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0 1575 nop.i 0 1576} 1577 1578{.mfi 1579 nop.m 0 1580 // t*s-sqrt(1-t^2)*(1-s^2)*y 1581 fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS 1582 nop.i 0;; 1583} 1584 1585 1586{.mfi 1587 nop.m 0 1588 // z*0.5/(1-t^2) 1589 fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0 1590 nop.i 0 1591} 1592 1593{.mfi 1594 nop.m 0 1595 // z^2+t^2-1 1596 fms.s1 F_DZ0 = F_Z, F_Z, F_1T2 1597 nop.i 0;; 1598} 1599 1600 1601{.mfi 1602 nop.m 0 1603 // (1-s^2-(1-s^2)_s)*x 1604 fma.s1 F_DS2X = F_X, F_DS, f0 1605 nop.i 0;; 1606} 1607 1608 1609{.mfi 1610 nop.m 0 1611 // t*s-(t*s)_s 1612 fms.s1 F_DTS = F_T, f8, F_TSS 1613 nop.i 0 1614} 1615 1616{.mfi 1617 nop.m 0 1618 // c9*x^7+..+c2 1619 fma.s1 F_S29 = F_X4, F_S69, F_S25 1620 nop.i 0;; 1621} 1622 1623 1624{.mfi 1625 nop.m 0 1626 // y*z 1627 fma.s1 F_YZ = F_Z, F_Y, f0 1628 nop.i 0 1629} 1630 1631{.mfi 1632 nop.m 0 1633 // t^2 1634 fma.s1 F_T2 = F_T, F_T, f0 1635 nop.i 0;; 1636} 1637 1638 1639{.mfi 1640 nop.m 0 1641 // 1-t^2+ST 1642 fma.s1 F_1T2_ST = F_ST, f1, F_1T2 1643 nop.i 0;; 1644} 1645 1646 1647{.mfi 1648 nop.m 0 1649 // y*(1-s^2)(1-x) 1650 fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0 1651 nop.i 0 1652} 1653 1654{.mfi 1655 nop.m 0 1656 // dz ~ sqrt(1-t^2)-z 1657 fma.s1 F_DZ = F_DZ0, F_ZE, f0 1658 nop.i 0;; 1659} 1660 1661 1662{.mfi 1663 nop.m 0 1664 // -1+correction for sqrt(1-t^2)-z 1665 fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0 1666 nop.i 0;; 1667} 1668 1669 1670{.mfi 1671 nop.m 0 1672 // (PS29*x^2+x)*y*(1-s^2) 1673 fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X 1674 nop.i 0;; 1675} 1676 1677 1678{.mfi 1679 nop.m 0 1680 // z*y*(1-s^2)_s 1681 fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0 1682 nop.i 0 1683} 1684 1685{.mfi 1686 nop.m 0 1687 // s^2-(1-t^2+ST) 1688 fms.s1 F_1T2_ST = f8, f8, F_1T2_ST 1689 nop.i 0;; 1690} 1691 1692 1693{.mfi 1694 nop.m 0 1695 // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x 1696 fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS 1697 nop.i 0 1698} 1699 1700{.mfi 1701 nop.m 0 1702 // dz*y*(1-s^2)*(1-x) 1703 fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0 1704 nop.i 0;; 1705} 1706 1707 1708{.mfi 1709 nop.m 0 1710 // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19 1711 // (used for polynomial evaluation) 1712 fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS 1713 nop.i 0;; 1714} 1715 1716 1717{.mfi 1718 nop.m 0 1719 // (PS29*x^2)*y*(1-s^2) 1720 fma.s1 F_S29 = F_Y1S2X2, F_S29, f0 1721 nop.i 0 1722} 1723 1724{.mfi 1725 nop.m 0 1726 // apply correction to dz*y*(1-s^2)*(1-x) 1727 fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM 1728 nop.i 0;; 1729} 1730 1731 1732{.mfi 1733 nop.m 0 1734 // R^2 1735 fma.s1 F_R2 = F_R, F_R, f0 1736 nop.i 0;; 1737} 1738 1739 1740{.mfi 1741 nop.m 0 1742 // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x) 1743 fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS 1744 nop.i 0;; 1745} 1746 1747 1748{.mfi 1749 nop.m 0 1750 // c7+c9*R^2 1751 fma.s1 F_P79 = F_C9, F_R2, F_C7 1752 nop.i 0 1753} 1754 1755{.mfi 1756 nop.m 0 1757 // c3+c5*R^2 1758 fma.s1 F_P35 = F_C5, F_R2, F_C3 1759 nop.i 0;; 1760} 1761 1762{.mfi 1763 nop.m 0 1764 // asin(t)_low-(pi/2)_low 1765 fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO 1766 nop.i 0 1767} 1768 1769{.mfi 1770 nop.m 0 1771 // R^4 1772 fma.s1 F_R4 = F_R2, F_R2, f0 1773 nop.i 0;; 1774} 1775 1776{.mfi 1777 nop.m 0 1778 // R^3 1779 fma.s1 F_R3 = F_R2, F_R, f0 1780 nop.i 0;; 1781} 1782 1783 1784{.mfi 1785 nop.m 0 1786 // (t*s)_s-t^2*y*z 1787 fnma.s1 F_TSS = F_T2, F_YZ, F_TSS 1788 nop.i 0 1789} 1790 1791{.mfi 1792 nop.m 0 1793 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) 1794 fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM 1795 nop.i 0;; 1796} 1797 1798 1799{.mfi 1800 nop.m 0 1801 // (pi/2)_hi-asin(t)_hi 1802 fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI 1803 nop.i 0 1804} 1805 1806{.mfi 1807 nop.m 0 1808 // c3+c5*R^2+c7*R^4+c9*R^6 1809 fma.s1 F_P39 = F_P79, F_R4, F_P35 1810 nop.i 0;; 1811} 1812 1813 1814{.mfi 1815 nop.m 0 1816 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+ 1817 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 1818 fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM 1819 nop.i 0;; 1820} 1821 1822 1823{.mfi 1824 nop.m 0 1825 // (t*s)_s-t^2*y*z+z*y*ST 1826 fma.s1 F_TSS = F_YZ, F_ST, F_TSS 1827 nop.i 0 1828} 1829 1830{.mfi 1831 nop.m 0 1832 // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) 1833 fms.s1 F_P39 = F_P39, F_R3, F_ATLO 1834 nop.i 0;; 1835} 1836 1837 1838{.mfi 1839 nop.m 0 1840 // if s<0, change sign of F_ATHI 1841 (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0 1842 nop.i 0 1843} 1844 1845{.mfi 1846 nop.m 0 1847 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + 1848 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + 1849 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) 1850 fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM 1851 nop.i 0;; 1852} 1853 1854 1855{.mfi 1856 nop.m 0 1857 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + 1858 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x + 1859 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) 1860 fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM 1861 nop.i 0;; 1862} 1863 1864 1865{.mfi 1866 nop.m 0 1867 // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + 1868 // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x + 1869 // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) + 1870 // + (t*s)_s-t^2*y*z+z*y*ST 1871 fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM 1872 nop.i 0;; 1873} 1874 1875 1876.pred.rel "mutex", p6, p11 1877{.mfi 1878 nop.m 0 1879 // result: add high part of pi/2-table value 1880 // s>0 in this case 1881 (p11) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI 1882 nop.i 0 1883} 1884 1885{.mfb 1886 nop.m 0 1887 // result: add high part of pi/2-table value 1888 // if s<0 1889 (p6) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI 1890 br.ret.sptk b0;; 1891} 1892 1893 1894 1895 1896 1897 1898SMALL_S: 1899 1900 // use 15-term polynomial approximation 1901 1902{.mmi 1903 // r3 = pointer to polynomial coefficients 1904 addl r3 = @ltoff(poly_coeffs), gp;; 1905 // load start address for coefficients 1906 ld8 r3 = [r3] 1907 mov R_TMP = 0x3fbf;; 1908} 1909 1910 1911{.mmi 1912 add r2 = 64, r3 1913 ldfe F_C3 = [r3], 16 1914 // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64) 1915 cmp.lt p7, p0 = R_EXP0, R_TMP;; 1916} 1917 1918{.mmf 1919 ldfe F_C5 = [r3], 16 1920 ldfpd F_C11, F_C13 = [r2], 16 1921 // 2^{-128} 1922 fma.s1 F_2M128 = F_2M64, F_2M64, f0;; 1923} 1924 1925{.mmf 1926 ldfpd F_C7, F_C9 = [r3] 1927 ldfpd F_C15, F_C17 = [r2] 1928 // if |s|<2^{-64}, return s+2^{-128}*s 1929 (p7) fma.s0 f8 = f8, F_2M128, f8;; 1930} 1931 1932 1933 1934{.mfb 1935 nop.m 0 1936 // s^2 1937 fma.s1 F_R2 = f8, f8, f0 1938 // if |s|<2^{-64}, return s 1939 (p7) br.ret.spnt b0;; 1940} 1941 1942 1943{.mfi 1944 nop.m 0 1945 // s^3 1946 fma.s1 F_R3 = f8, F_R2, f0 1947 nop.i 0 1948} 1949 1950{.mfi 1951 nop.m 0 1952 // s^4 1953 fma.s1 F_R4 = F_R2, F_R2, f0 1954 nop.i 0;; 1955} 1956 1957 1958{.mfi 1959 nop.m 0 1960 // c3+c5*s^2 1961 fma.s1 F_P35 = F_C5, F_R2, F_C3 1962 nop.i 0 1963} 1964 1965{.mfi 1966 nop.m 0 1967 // c11+c13*s^2 1968 fma.s1 F_P1113 = F_C13, F_R2, F_C11 1969 nop.i 0;; 1970} 1971 1972 1973{.mfi 1974 nop.m 0 1975 // c7+c9*s^2 1976 fma.s1 F_P79 = F_C9, F_R2, F_C7 1977 nop.i 0 1978} 1979 1980{.mfi 1981 nop.m 0 1982 // c15+c17*s^2 1983 fma.s1 F_P1517 = F_C17, F_R2, F_C15 1984 nop.i 0;; 1985} 1986 1987 1988{.mfi 1989 nop.m 0 1990 // s^8 1991 fma.s1 F_R8 = F_R4, F_R4, f0 1992 nop.i 0;; 1993} 1994 1995 1996{.mfi 1997 nop.m 0 1998 // c3+c5*s^2+c7*s^4+c9*s^6 1999 fma.s1 F_P39 = F_P79, F_R4, F_P35 2000 nop.i 0 2001} 2002 2003{.mfi 2004 nop.m 0 2005 // c11+c13*s^2+c15*s^4+c17*s^6 2006 fma.s1 F_P1117 = F_P1517, F_R4, F_P1113 2007 nop.i 0;; 2008} 2009 2010 2011{.mfi 2012 nop.m 0 2013 // c3+..+c17*s^14 2014 fma.s1 F_P317 = F_R8, F_P1117, F_P39 2015 nop.i 0;; 2016} 2017 2018 2019{.mfb 2020 nop.m 0 2021 // result 2022 fma.s0 f8 = F_P317, F_R3, f8 2023 br.ret.sptk b0;; 2024} 2025 2026 2027{.mfb 2028 nop.m 0 2029 fma.s0 f8 = F_P317, F_R3, f0//F_P317, F_R3, F_S29 2030 // nop.f 0//fma.s0 f8 = f13, f6, f0 2031 br.ret.sptk b0;; 2032} 2033 2034 2035 2036 2037 2038 VERY_LARGE_INPUT: 2039 2040{.mfi 2041 nop.m 0 2042 // s rounded to 24 significant bits 2043 fma.s.s1 F_S = f8, f1, f0 2044 nop.i 0 2045} 2046 2047{.mfi 2048 // load C5 2049 ldfe F_C5 = [r3], 16 2050 // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2 2051 fnma.s1 F_X = F_S_DS2, F_Y2_2, F_XL 2052 nop.i 0;; 2053} 2054 2055 2056 2057{.mmf 2058 nop.m 0 2059 // C7, C9 2060 ldfpd F_C7, F_C9 = [r3], 16 2061 nop.f 0;; 2062} 2063 2064 2065 2066{.mfi 2067 // pi/2 (low, high) 2068 ldfpd F_PI2_LO, F_PI2_HI = [r3], 16 2069 // c9*x+c8 2070 fma.s1 F_S89 = F_X, F_CS9, F_CS8 2071 nop.i 0 2072} 2073 2074{.mfi 2075 nop.m 0 2076 // x^2 2077 fma.s1 F_X2 = F_X, F_X, f0 2078 nop.i 0;; 2079} 2080 2081 2082{.mfi 2083 nop.m 0 2084 // y*(1-s^2)*x 2085 fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 2086 nop.i 0 2087} 2088 2089{.mfi 2090 // C11, C13 2091 ldfpd F_C11, F_C13 = [r3], 16 2092 // c7*x+c6 2093 fma.s1 F_S67 = F_X, F_CS7, F_CS6 2094 nop.i 0;; 2095} 2096 2097 2098{.mfi 2099 // C15, C17 2100 ldfpd F_C15, F_C17 = [r3], 16 2101 // c3*x+c2 2102 fma.s1 F_S23 = F_X, F_CS3, F_CS2 2103 nop.i 0;; 2104} 2105 2106 2107{.mfi 2108 nop.m 0 2109 // c5*x+c4 2110 fma.s1 F_S45 = F_X, F_CS5, F_CS4 2111 nop.i 0;; 2112} 2113 2114 2115{.mfi 2116 nop.m 0 2117 // (s_s)^2 2118 fma.s1 F_DS = F_S, F_S, f0 2119 nop.i 0 2120} 2121 2122{.mfi 2123 nop.m 0 2124 // 1-(s_s)^2 2125 fnma.s1 F_1S2_S = F_S, F_S, f1 2126 nop.i 0;; 2127} 2128 2129 2130{.mfi 2131 nop.m 0 2132 // y*(1-s^2)*x^2 2133 fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 2134 nop.i 0 2135} 2136 2137{.mfi 2138 nop.m 0 2139 // x^4 2140 fma.s1 F_X4 = F_X2, F_X2, f0 2141 nop.i 0;; 2142} 2143 2144 2145{.mfi 2146 nop.m 0 2147 // c9*x^3+..+c6 2148 fma.s1 F_S69 = F_X2, F_S89, F_S67 2149 nop.i 0;; 2150} 2151 2152 2153{.mfi 2154 nop.m 0 2155 // c5*x^3+..+c2 2156 fma.s1 F_S25 = F_X2, F_S45, F_S23 2157 nop.i 0;; 2158} 2159 2160 2161{.mfi 2162 nop.m 0 2163 // ((s_s)^2-s^2) 2164 fnma.s1 F_DS = f8, f8, F_DS 2165 nop.i 0 2166} 2167 2168{.mfi 2169 nop.m 0 2170 // (pi/2)_high-y*(1-(s_s)^2) 2171 fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI 2172 nop.i 0;; 2173} 2174 2175 2176{.mfi 2177 nop.m 0 2178 // c9*x^7+..+c2 2179 fma.s1 F_S29 = F_X4, F_S69, F_S25 2180 nop.i 0;; 2181} 2182 2183 2184{.mfi 2185 nop.m 0 2186 // -(y*(1-(s_s)^2))_high 2187 fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI 2188 nop.i 0;; 2189} 2190 2191 2192{.mfi 2193 nop.m 0 2194 // (PS29*x^2+x)*y*(1-s^2) 2195 fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X 2196 nop.i 0;; 2197} 2198 2199 2200{.mfi 2201 nop.m 0 2202 // y*(1-(s_s)^2)-(y*(1-s^2))_high 2203 fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI 2204 nop.i 0;; 2205} 2206 2207 2208 2209{.mfi 2210 nop.m 0 2211 // R ~ sqrt(1-s^2) 2212 // (used for polynomial evaluation) 2213 fnma.s1 F_R = F_S19, f1, F_Y1S2 2214 nop.i 0;; 2215} 2216 2217 2218{.mfi 2219 nop.m 0 2220 // y*(1-s^2)-(y*(1-s^2))_high 2221 fma.s1 F_DS2 = F_Y, F_DS, F_DS2 2222 nop.i 0 2223} 2224 2225{.mfi 2226 nop.m 0 2227 // (pi/2)_low+(PS29*x^2)*y*(1-s^2) 2228 fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO 2229 nop.i 0;; 2230} 2231 2232 2233 2234{.mfi 2235 nop.m 0 2236 // R^2 2237 fma.s1 F_R2 = F_R, F_R, f0 2238 nop.i 0;; 2239} 2240 2241 2242{.mfi 2243 nop.m 0 2244 // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high) 2245 fms.s1 F_S29 = F_S29, f1, F_DS2 2246 nop.i 0;; 2247} 2248 2249 2250{.mfi 2251 nop.m 0 2252 // c7+c9*R^2 2253 fma.s1 F_P79 = F_C9, F_R2, F_C7 2254 nop.i 0 2255} 2256 2257{.mfi 2258 nop.m 0 2259 // c3+c5*R^2 2260 fma.s1 F_P35 = F_C5, F_R2, F_C3 2261 nop.i 0;; 2262} 2263 2264 2265 2266{.mfi 2267 nop.m 0 2268 // R^4 2269 fma.s1 F_R4 = F_R2, F_R2, f0 2270 nop.i 0 2271} 2272 2273{.mfi 2274 nop.m 0 2275 // R^3 2276 fma.s1 F_R3 = F_R2, F_R, f0 2277 nop.i 0;; 2278} 2279 2280 2281{.mfi 2282 nop.m 0 2283 // c11+c13*R^2 2284 fma.s1 F_P1113 = F_C13, F_R2, F_C11 2285 nop.i 0 2286} 2287 2288{.mfi 2289 nop.m 0 2290 // c15+c17*R^2 2291 fma.s1 F_P1517 = F_C17, F_R2, F_C15 2292 nop.i 0;; 2293} 2294 2295 2296{.mfi 2297 nop.m 0 2298 // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x 2299 fma.s1 F_S29 = F_Y1S2, F_X, F_S29 2300 nop.i 0;; 2301} 2302 2303 2304{.mfi 2305 nop.m 0 2306 // c11+c13*R^2+c15*R^4+c17*R^6 2307 fma.s1 F_P1117 = F_P1517, F_R4, F_P1113 2308 nop.i 0 2309} 2310 2311{.mfi 2312 nop.m 0 2313 // c3+c5*R^2+c7*R^4+c9*R^6 2314 fma.s1 F_P39 = F_P79, F_R4, F_P35 2315 nop.i 0;; 2316} 2317 2318 2319{.mfi 2320 nop.m 0 2321 // R^8 2322 fma.s1 F_R8 = F_R4, F_R4, f0 2323 nop.i 0;; 2324} 2325 2326 2327{.mfi 2328 nop.m 0 2329 // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14 2330 fma.s1 F_P317 = F_P1117, F_R8, F_P39 2331 nop.i 0;; 2332} 2333 2334 2335{.mfi 2336 nop.m 0 2337 // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)- 2338 // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17 2339 fnma.s1 F_S29 = F_P317, F_R3, F_S29 2340 nop.i 0;; 2341} 2342 2343{.mfi 2344 nop.m 0 2345 // set sign 2346 (p6) fnma.s1 F_S29 = F_S29, f1, f0 2347 nop.i 0 2348} 2349 2350{.mfi 2351 nop.m 0 2352 (p6) fnma.s1 F_HI = F_HI, f1, f0 2353 nop.i 0;; 2354} 2355 2356 2357{.mfb 2358 nop.m 0 2359 // Result: 2360 // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)- 2361 // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17 2362 // +(pi/2)_high-(y*(1-s^2))_high 2363 fma.s0 f8 = F_S29, f1, F_HI 2364 br.ret.sptk b0;; 2365} 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 ASINL_SPECIAL_CASES: 2376 2377{.mfi 2378 alloc r32 = ar.pfs, 1, 4, 4, 0 2379 // check if the input is a NaN, or unsupported format 2380 // (i.e. not infinity or normal/denormal) 2381 fclass.nm p7, p8 = f8, 0x3f 2382 // pointer to pi/2 2383 add r3 = 48, r3;; 2384} 2385 2386 2387{.mfi 2388 // load pi/2 2389 ldfpd F_PI2_HI, F_PI2_LO = [r3] 2390 // get |s| 2391 fmerge.s F_S = f0, f8 2392 nop.i 0 2393} 2394 2395{.mfb 2396 nop.m 0 2397 // if NaN, quietize it, and return 2398 (p7) fma.s0 f8 = f8, f1, f0 2399 (p7) br.ret.spnt b0;; 2400} 2401 2402 2403{.mfi 2404 nop.m 0 2405 // |s| = 1 ? 2406 fcmp.eq.s0 p9, p0 = F_S, f1 2407 nop.i 0 2408} 2409 2410{.mfi 2411 nop.m 0 2412 // load FR_X 2413 fma.s1 FR_X = f8, f1, f0 2414 // load error tag 2415 mov GR_Parameter_TAG = 60;; 2416} 2417 2418 2419{.mfb 2420 nop.m 0 2421 // change sign if s = -1 2422 (p6) fnma.s1 F_PI2_HI = F_PI2_HI, f1, f0 2423 nop.b 0 2424} 2425 2426{.mfb 2427 nop.m 0 2428 // change sign if s = -1 2429 (p6) fnma.s1 F_PI2_LO = F_PI2_LO, f1, f0 2430 nop.b 0;; 2431} 2432 2433{.mfb 2434 nop.m 0 2435 // if s = 1, result is pi/2 2436 (p9) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO 2437 // return if |s| = 1 2438 (p9) br.ret.sptk b0;; 2439} 2440 2441 2442{.mfi 2443 nop.m 0 2444 // get Infinity 2445 frcpa.s1 FR_RESULT, p0 = f1, f0 2446 nop.i 0;; 2447} 2448 2449 2450{.mfi 2451 nop.m 0 2452 // return QNaN indefinite (0*Infinity) 2453 fma.s0 FR_RESULT = f0, FR_RESULT, f0 2454 nop.i 0;; 2455} 2456 2457 2458GLOBAL_LIBM_END(asinl) 2459libm_alias_ldouble_other (asin, asin) 2460 2461 2462 2463LOCAL_LIBM_ENTRY(__libm_error_region) 2464.prologue 2465// (1) 2466{ .mfi 2467 add GR_Parameter_Y=-32,sp // Parameter 2 value 2468 nop.f 0 2469.save ar.pfs,GR_SAVE_PFS 2470 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs 2471} 2472{ .mfi 2473.fframe 64 2474 add sp=-64,sp // Create new stack 2475 nop.f 0 2476 mov GR_SAVE_GP=gp // Save gp 2477};; 2478 2479 2480// (2) 2481{ .mmi 2482 stfe [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack 2483 add GR_Parameter_X = 16,sp // Parameter 1 address 2484.save b0, GR_SAVE_B0 2485 mov GR_SAVE_B0=b0 // Save b0 2486};; 2487 2488.body 2489// (3) 2490{ .mib 2491 stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack 2492 add GR_Parameter_RESULT = 0,GR_Parameter_Y 2493 nop.b 0 // Parameter 3 address 2494} 2495{ .mib 2496 stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack 2497 add GR_Parameter_Y = -16,GR_Parameter_Y 2498 br.call.sptk b0=__libm_error_support# // Call error handling function 2499};; 2500{ .mmi 2501 nop.m 0 2502 nop.m 0 2503 add GR_Parameter_RESULT = 48,sp 2504};; 2505 2506// (4) 2507{ .mmi 2508 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack 2509.restore sp 2510 add sp = 64,sp // Restore stack pointer 2511 mov b0 = GR_SAVE_B0 // Restore return address 2512};; 2513 2514{ .mib 2515 mov gp = GR_SAVE_GP // Restore gp 2516 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 2517 br.ret.sptk b0 // Return 2518};; 2519 2520LOCAL_LIBM_END(__libm_error_region) 2521 2522.type __libm_error_support#,@function 2523.global __libm_error_support# 2524