| .file "asinl.s" |
| |
| |
| // Copyright (c) 2001 - 2003, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2001 by the Intel Numerics Group, Intel Corporation |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // |
| // * Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in the |
| // documentation and/or other materials provided with the distribution. |
| // |
| // * The name of Intel Corporation may not be used to endorse or promote |
| // products derived from this software without specific prior written |
| // permission. |
| |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
| // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
| // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
| // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Intel Corporation is the author of this code, and requests that all |
| // problem reports or change requests be submitted to it directly at |
| // http://www.intel.com/software/products/opensource/libraries/num.htm. |
| // |
| // History |
| //============================================================== |
| // 08/28/01 New version |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| // |
| // API |
| //============================================================== |
| // long double asinl(long double) |
| // |
| // Overview of operation |
| //============================================================== |
| // Background |
| // |
| // Implementation |
| // |
| // For |s| in [2^{-4}, sqrt(2)/2]: |
| // Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52 |
| // asin(s)= asin(t)+asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e. |
| // r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1) |
| // asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9) |
| // The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table, |
| // along with the high and low parts of asin(t) (stored as two double precision |
| // values) |
| // |
| // |s| in (sqrt(2)/2, sqrt(255/256)): |
| // Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6.. |
| // asin(|s|)= pi/2-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2) |
| // To minimize accumulated errors, r is computed as |
| // 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+ |
| // +(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)+ |
| // +ez*z'*y*(1-s^2)*(1-x), |
| // where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits) |
| // z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2 |
| // |
| // |s|<2^{-4}: evaluate as 17-degree polynomial |
| // (or simply return s, if|s|<2^{-64}) |
| // |
| // |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-asin(sqrt(1-s^2)) |
| // use 17-degree polynomial for asin(sqrt(1-s^2)), |
| // 9-degree polynomial to evaluate sqrt(1-s^2) |
| // High order term is (pi/2)_high-(y*(1-s^2))_high |
| // |
| |
| |
| |
| // Registers used |
| //============================================================== |
| // f6-f15, f32-f36 |
| // r2-r3, r23-r23 |
| // p6, p7, p8, p12 |
| // |
| |
| |
| GR_SAVE_B0= r33 |
| GR_SAVE_PFS= r34 |
| GR_SAVE_GP= r35 // This reg. can safely be used |
| GR_SAVE_SP= r36 |
| |
| GR_Parameter_X= r37 |
| GR_Parameter_Y= r38 |
| GR_Parameter_RESULT= r39 |
| GR_Parameter_TAG= r40 |
| |
| FR_X= f10 |
| FR_Y= f1 |
| FR_RESULT= f8 |
| |
| |
| |
| RODATA |
| |
| .align 16 |
| |
| |
| |
| LOCAL_OBJECT_START(T_table) |
| |
| // stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2), |
| // asin(t)_high (double precision), asin(t)_low (double precision) |
| |
| data8 0x80828692b71c4391, 0xff7ddcec2d87e879 |
| data8 0x3fb022bc0ae531a0, 0x3c9f599c7bb42af6 |
| data8 0x80869f0163d0b082, 0xff79cad2247914d3 |
| data8 0x3fb062dd26afc320, 0x3ca4eff21bd49c5c |
| data8 0x808ac7d5a8690705, 0xff75a89ed6b626b9 |
| data8 0x3fb0a2ff4a1821e0, 0x3cb7e33b58f164cc |
| data8 0x808f0112ad8ad2e0, 0xff7176517c2cc0cb |
| data8 0x3fb0e32279319d80, 0x3caee31546582c43 |
| data8 0x80934abba8a1da0a, 0xff6d33e949b1ed31 |
| data8 0x3fb12346b8101da0, 0x3cb8bfe463d087cd |
| data8 0x8097a4d3dbe63d8f, 0xff68e16571015c63 |
| data8 0x3fb1636c0ac824e0, 0x3c8870a7c5a3556f |
| data8 0x809c0f5e9662b3dd, 0xff647ec520bca0f0 |
| data8 0x3fb1a392756ed280, 0x3c964f1a927461ae |
| data8 0x80a08a5f33fadc66, 0xff600c07846a6830 |
| data8 0x3fb1e3b9fc19e580, 0x3c69eb3576d56332 |
| data8 0x80a515d91d71acd4, 0xff5b892bc475affa |
| data8 0x3fb223e2a2dfbe80, 0x3c6a4e19fd972fb6 |
| data8 0x80a9b1cfc86ff7cd, 0xff56f631062cf93d |
| data8 0x3fb2640c6dd76260, 0x3c62041160e0849e |
| data8 0x80ae5e46b78b0d68, 0xff5253166bc17794 |
| data8 0x3fb2a43761187c80, 0x3cac61651af678c0 |
| data8 0x80b31b417a4b756b, 0xff4d9fdb14463dc8 |
| data8 0x3fb2e46380bb6160, 0x3cb06ef23eeba7a1 |
| data8 0x80b7e8c3ad33c369, 0xff48dc7e1baf6738 |
| data8 0x3fb32490d0d910c0, 0x3caa05f480b300d5 |
| data8 0x80bcc6d0f9c784d6, 0xff4408fe9ad13e37 |
| data8 0x3fb364bf558b3820, 0x3cb01e7e403aaab9 |
| data8 0x80c1b56d1692492d, 0xff3f255ba75f5f4e |
| data8 0x3fb3a4ef12ec3540, 0x3cb4fe8fcdf5f5f1 |
| data8 0x80c6b49bc72ec446, 0xff3a319453ebd961 |
| data8 0x3fb3e5200d171880, 0x3caf2dc089b2b7e2 |
| data8 0x80cbc460dc4e0ae8, 0xff352da7afe64ac6 |
| data8 0x3fb425524827a720, 0x3cb75a855e7c6053 |
| data8 0x80d0e4c033bee9c4, 0xff301994c79afb32 |
| data8 0x3fb46585c83a5e00, 0x3cb3264981c019ab |
| data8 0x80d615bdb87556db, 0xff2af55aa431f291 |
| data8 0x3fb4a5ba916c73c0, 0x3c994251d94427b5 |
| data8 0x80db575d6291fd8a, 0xff25c0f84bae0cb9 |
| data8 0x3fb4e5f0a7dbdb20, 0x3cbee2fcc4c786cb |
| data8 0x80e0a9a33769e535, 0xff207c6cc0ec09fd |
| data8 0x3fb526280fa74620, 0x3c940656e5549b91 |
| data8 0x80e60c93498e32cd, 0xff1b27b703a19c98 |
| data8 0x3fb56660ccee2740, 0x3ca7082374d7b2cd |
| data8 0x80eb8031b8d4052d, 0xff15c2d6105c72f8 |
| data8 0x3fb5a69ae3d0b520, 0x3c7c4d46e09ac68a |
| data8 0x80f10482b25c6c8a, 0xff104dc8e0813ed4 |
| data8 0x3fb5e6d6586fec20, 0x3c9aa84ffd9b4958 |
| data8 0x80f6998a709c7cfb, 0xff0ac88e6a4ab926 |
| data8 0x3fb627132eed9140, 0x3cbced2cbbbe7d16 |
| data8 0x80fc3f4d3b657c44, 0xff053325a0c8a2ec |
| data8 0x3fb667516b6c34c0, 0x3c6489c5fc68595a |
| data8 0x8101f5cf67ed2af8, 0xfeff8d8d73dec2bb |
| data8 0x3fb6a791120f33a0, 0x3cbe12acf159dfad |
| data8 0x8107bd1558d6291f, 0xfef9d7c4d043df29 |
| data8 0x3fb6e7d226fabba0, 0x3ca386d099cd0dc7 |
| data8 0x810d95237e38766a, 0xfef411ca9f80b5f7 |
| data8 0x3fb72814ae53cc20, 0x3cb9f35731e71dd6 |
| data8 0x81137dfe55aa0e29, 0xfeee3b9dc7eef009 |
| data8 0x3fb76858ac403a00, 0x3c74df3dd959141a |
| data8 0x811977aa6a479f0f, 0xfee8553d2cb8122c |
| data8 0x3fb7a89e24e6b0e0, 0x3ca6034406ee42bc |
| data8 0x811f822c54bd5ef8, 0xfee25ea7add46a91 |
| data8 0x3fb7e8e51c6eb6a0, 0x3cb82f8f78e68ed7 |
| data8 0x81259d88bb4ffac1, 0xfedc57dc2809fb1d |
| data8 0x3fb8292d9700ad60, 0x3cbebb73c0e653f9 |
| data8 0x812bc9c451e5a257, 0xfed640d974eb6068 |
| data8 0x3fb8697798c5d620, 0x3ca2feee76a9701b |
| data8 0x813206e3da0f3124, 0xfed0199e6ad6b585 |
| data8 0x3fb8a9c325e852e0, 0x3cb9e88f2f4d0efe |
| data8 0x813854ec231172f9, 0xfec9e229dcf4747d |
| data8 0x3fb8ea1042932a00, 0x3ca5ff40d81f66fd |
| data8 0x813eb3e209ee858f, 0xfec39a7a9b36538b |
| data8 0x3fb92a5ef2f247c0, 0x3cb5e3bece4d6b07 |
| data8 0x814523ca796f56ce, 0xfebd428f72561efe |
| data8 0x3fb96aaf3b3281a0, 0x3cb7b9e499436d7c |
| data8 0x814ba4aa6a2d3ff9, 0xfeb6da672bd48fe4 |
| data8 0x3fb9ab011f819860, 0x3cb9168143cc1a7f |
| data8 0x81523686e29bbdd7, 0xfeb062008df81f50 |
| data8 0x3fb9eb54a40e3ac0, 0x3cb6e544197eb1e1 |
| data8 0x8158d964f7124614, 0xfea9d95a5bcbd65a |
| data8 0x3fba2ba9cd080800, 0x3ca9a717be8f7446 |
| data8 0x815f8d49c9d639e4, 0xfea34073551e1ac8 |
| data8 0x3fba6c009e9f9260, 0x3c741e989a60938a |
| data8 0x8166523a8b24f626, 0xfe9c974a367f785c |
| data8 0x3fbaac591d0661a0, 0x3cb2c1290107e57d |
| data8 0x816d283c793e0114, 0xfe95ddddb94166cb |
| data8 0x3fbaecb34c6ef600, 0x3c9c7d5fbaec405d |
| data8 0x81740f54e06d55bd, 0xfe8f142c93750c50 |
| data8 0x3fbb2d0f310cca00, 0x3cbc09479a9cbcfb |
| data8 0x817b07891b15cd5e, 0xfe883a3577e9fceb |
| data8 0x3fbb6d6ccf1455e0, 0x3cb9450bff4ee307 |
| data8 0x818210de91bba6c8, 0xfe814ff7162cf62f |
| data8 0x3fbbadcc2abb1180, 0x3c9227fda12a8d24 |
| data8 0x81892b5abb0f2bf9, 0xfe7a55701a8697b1 |
| data8 0x3fbbee2d48377700, 0x3cb6fad72acfe356 |
| data8 0x819057031bf7760e, 0xfe734a9f2dfa1810 |
| data8 0x3fbc2e902bc10600, 0x3cb4465b588d16ad |
| data8 0x819793dd479d4fbe, 0xfe6c2f82f643f68b |
| data8 0x3fbc6ef4d9904580, 0x3c8b9ac54823960d |
| data8 0x819ee1eedf76367a, 0xfe65041a15d8a92c |
| data8 0x3fbcaf5b55dec6a0, 0x3ca2b8d28a954db2 |
| data8 0x81a6413d934f7a66, 0xfe5dc8632be3477f |
| data8 0x3fbcefc3a4e727a0, 0x3c9380da83713ab4 |
| data8 0x81adb1cf21597d4b, 0xfe567c5cd44431d5 |
| data8 0x3fbd302dcae51600, 0x3ca995b83421756a |
| data8 0x81b533a9563310b8, 0xfe4f2005a78fb50f |
| data8 0x3fbd7099cc155180, 0x3caefa2f7a817d5f |
| data8 0x81bcc6d20cf4f373, 0xfe47b35c3b0caaeb |
| data8 0x3fbdb107acb5ae80, 0x3cb455fc372dd026 |
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| data8 0x81cc2126b53c1144, 0xfe38a90ce72abf36 |
| data8 0x3fbe31e91d439620, 0x3cb3e131c950aebd |
| data8 0x81d3e85ea5bd8ee2, 0xfe310b6419c9c33a |
| data8 0x3fbe725cb5b24900, 0x3c01d3fac6029027 |
| data8 0x81dbc0fd1637b9c1, 0xfe295d6340932d15 |
| data8 0x3fbeb2d23e937300, 0x3c6304cc44aeedd1 |
| data8 0x81e3ab082ad5a0a4, 0xfe219f08e03580b3 |
| data8 0x3fbef349bc2a77e0, 0x3cac1d2d6abe9c72 |
| data8 0x81eba6861683cb97, 0xfe19d0537a0946e2 |
| data8 0x3fbf33c332bbe020, 0x3ca0909dba4e96ca |
| data8 0x81f3b37d1afc9979, 0xfe11f1418c0f94e2 |
| data8 0x3fbf743ea68d5b60, 0x3c937fc12a2a779a |
| data8 0x81fbd1f388d4be45, 0xfe0a01d190f09063 |
| data8 0x3fbfb4bc1be5c340, 0x3cbf51a504b55813 |
| data8 0x820401efbf87e248, 0xfe020201fff9efea |
| data8 0x3fbff53b970d1e80, 0x3ca625444b260078 |
| data8 0x82106ad2ffdca049, 0xfdf5e3940a49135e |
| data8 0x3fc02aff52065460, 0x3c9125d113e22a57 |
| data8 0x8221343d6ea1d3e2, 0xfde581a45429b0a0 |
| data8 0x3fc06b84f8e03220, 0x3caccf362295894b |
| data8 0x82324434adbf99c2, 0xfdd4de1a001fb775 |
| data8 0x3fc0ac0ed1fe7240, 0x3cc22f676096b0af |
| data8 0x82439aee8d0c7747, 0xfdc3f8e8269d1f03 |
| data8 0x3fc0ec9cee9e4820, 0x3cca147e2886a628 |
| data8 0x825538a1d0fcb2f0, 0xfdb2d201a9b1ba66 |
| data8 0x3fc12d2f6006f0a0, 0x3cc72b36633bc2d4 |
| data8 0x82671d86345c5cee, 0xfda1695934d723e7 |
| data8 0x3fc16dc63789de60, 0x3cb11f9c47c7b83f |
| data8 0x827949d46a121770, 0xfd8fbee13cbbb823 |
| data8 0x3fc1ae618682e620, 0x3cce1b59020cef8e |
| data8 0x828bbdc61eeab9ba, 0xfd7dd28bff0c9f34 |
| data8 0x3fc1ef015e586c40, 0x3cafec043e0225ee |
| data8 0x829e7995fb6de9e1, 0xfd6ba44b823ee1ca |
| data8 0x3fc22fa5d07b90c0, 0x3cba905409caf8e3 |
| data8 0x82b17d7fa5bbc982, 0xfd5934119557883a |
| data8 0x3fc2704eee685da0, 0x3cb5ef21838a823e |
| data8 0x82c4c9bfc373d276, 0xfd4681cfcfb2c161 |
| data8 0x3fc2b0fcc9a5f3e0, 0x3ccc7952c5e0e312 |
| data8 0x82d85e93fba50136, 0xfd338d7790ca0f41 |
| data8 0x3fc2f1af73c6ba00, 0x3cbecf5f977d1ca9 |
| data8 0x82ec3c3af8c76b32, 0xfd2056f9fff97727 |
| data8 0x3fc33266fe6889a0, 0x3c9d329c022ebdb5 |
| data8 0x830062f46abf6022, 0xfd0cde480c43b327 |
| data8 0x3fc373237b34de60, 0x3cc95806d4928adb |
| data8 0x8314d30108ea35f0, 0xfcf923526c1562b2 |
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| data8 0x83298ca29434df97, 0xfce526099d0737ed |
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| data8 0x3fc435774fea2a60, 0x3c9ec18b43340914 |
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| data8 0x3fc538db36ee6960, 0x3cb910b773d4c578 |
| data8 0x83abfe8a5466246f, 0xfc67c2012cb6fa68 |
| data8 0x3fc579c1c6953cc0, 0x3cc5ede909fc47fc |
| data8 0x83c2c2c861474d91, 0xfc51f2acf82041d5 |
| data8 0x3fc5baade9860880, 0x3cac63cdfc3588e5 |
| data8 0x83d9d2cfc2813637, 0xfc3be08165519325 |
| data8 0x3fc5fb9fb1e8e3a0, 0x3cbf7c8466578c29 |
| data8 0x83f12eebf397daac, 0xfc258b6ce6e6822f |
| data8 0x3fc63c9731f39d40, 0x3cb6d2a7ffca3e9e |
| data8 0x8408d76990b9296e, 0xfc0ef35db402af94 |
| data8 0x3fc67d947be9eec0, 0x3cb1980da09e6566 |
| data8 0x8420cc9659487cd7, 0xfbf81841c8082dc4 |
| data8 0x3fc6be97a21daf00, 0x3cc2ac8330e59aa5 |
| data8 0x84390ec132759ecb, 0xfbe0fa06e24cc390 |
| data8 0x3fc6ffa0b6ef05e0, 0x3ccc1a030fee56c4 |
| data8 0x84519e3a29df811a, 0xfbc9989a85ce0954 |
| data8 0x3fc740afcccca000, 0x3cc19692a5301ca6 |
| data8 0x846a7b527842d61b, 0xfbb1f3e9f8e45dc4 |
| data8 0x3fc781c4f633e2c0, 0x3cc0e98f3868a508 |
| data8 0x8483a65c8434b5f0, 0xfb9a0be244f4af45 |
| data8 0x3fc7c2e045b12140, 0x3cb2a8d309754420 |
| data8 0x849d1fabe4e97dd7, 0xfb81e070362116d1 |
| data8 0x3fc80401cddfd120, 0x3ca7a44544aa4ce6 |
| data8 0x84b6e795650817ea, 0xfb6971805af8411e |
| data8 0x3fc84529a16ac020, 0x3c9e3b709c7d6f94 |
| data8 0x84d0fe6f0589da92, 0xfb50beff0423a2f5 |
| data8 0x3fc88657d30c49e0, 0x3cc60d65a7f0a278 |
| data8 0x84eb649000a73014, 0xfb37c8d84414755c |
| data8 0x3fc8c78c758e8e80, 0x3cc94b2ee984c2b7 |
| data8 0x85061a50ccd13781, 0xfb1e8ef7eeaf764b |
| data8 0x3fc908c79bcba900, 0x3cc8540ae794a2fe |
| data8 0x8521200b1fb8916e, 0xfb05114998f76a83 |
| data8 0x3fc94a0958ade6c0, 0x3ca127f49839fa9c |
| data8 0x853c7619f1618bf6, 0xfaeb4fb898b65d19 |
| data8 0x3fc98b51bf2ffee0, 0x3c8c9ba7a803909a |
| data8 0x85581cd97f45e274, 0xfad14a3004259931 |
| data8 0x3fc9cca0e25d4ac0, 0x3cba458e91d3bf54 |
| data8 0x857414a74f8446b4, 0xfab7009ab1945a54 |
| data8 0x3fca0df6d551fe80, 0x3cc78ea1d329d2b2 |
| data8 0x85905de2341dea46, 0xfa9c72e3370d2fbc |
| data8 0x3fca4f53ab3b6200, 0x3ccf60dca86d57ef |
| data8 0x85acf8ea4e423ff8, 0xfa81a0f3e9fa0ee9 |
| data8 0x3fca90b777580aa0, 0x3ca4c4e2ec8a867e |
| data8 0x85c9e62111a92e7d, 0xfa668ab6dec711b1 |
| data8 0x3fcad2224cf814e0, 0x3c303de5980d071c |
| data8 0x85e725e947fbee97, 0xfa4b3015e883dbfe |
| data8 0x3fcb13943f7d5f80, 0x3cc29d4eefa5cb1e |
| data8 0x8604b8a7144cd054, 0xfa2f90fa9883a543 |
| data8 0x3fcb550d625bc6a0, 0x3c9e01a746152daf |
| data8 0x86229ebff69e2415, 0xfa13ad4e3dfbe1c1 |
| data8 0x3fcb968dc9195ea0, 0x3ccc091bd73ae518 |
| data8 0x8640d89acf78858c, 0xf9f784f9e5a1877b |
| data8 0x3fcbd815874eb160, 0x3cb5f4b89875e187 |
| data8 0x865f669fe390c7f5, 0xf9db17e65944eacf |
| data8 0x3fcc19a4b0a6f9c0, 0x3cc5c0bc2b0bbf14 |
| data8 0x867e4938df7dc45f, 0xf9be65fc1f6c2e6e |
| data8 0x3fcc5b3b58e061e0, 0x3cc1ca70df8f57e7 |
| data8 0x869d80d0db7e4c0c, 0xf9a16f237aec427a |
| data8 0x3fcc9cd993cc4040, 0x3cbae93acc85eccf |
| data8 0x86bd0dd45f4f8265, 0xf98433446a806e70 |
| data8 0x3fccde7f754f5660, 0x3cb22f70e64568d0 |
| data8 0x86dcf0b16613e37a, 0xf966b246a8606170 |
| data8 0x3fcd202d11620fa0, 0x3c962030e5d4c849 |
| data8 0x86fd29d7624b3d5d, 0xf948ec11a9d4c45b |
| data8 0x3fcd61e27c10c0a0, 0x3cc7083c91d59217 |
| data8 0x871db9b741dbe44a, 0xf92ae08c9eca4941 |
| data8 0x3fcda39fc97be7c0, 0x3cc9258579e57211 |
| data8 0x873ea0c3722d6af2, 0xf90c8f9e71633363 |
| data8 0x3fcde5650dd86d60, 0x3ca4755a9ea582a9 |
| data8 0x875fdf6fe45529e8, 0xf8edf92dc5875319 |
| data8 0x3fce27325d6fe520, 0x3cbc1e2b6c1954f9 |
| data8 0x878176321154e2bc, 0xf8cf1d20f87270b8 |
| data8 0x3fce6907cca0d060, 0x3cb6ca4804750830 |
| data8 0x87a36580fe6bccf5, 0xf8affb5e20412199 |
| data8 0x3fceaae56fdee040, 0x3cad6b310d6fd46c |
| data8 0x87c5add5417a5cb9, 0xf89093cb0b7c0233 |
| data8 0x3fceeccb5bb33900, 0x3cc16e99cedadb20 |
| data8 0x87e84fa9057914ca, 0xf870e64d40a15036 |
| data8 0x3fcf2eb9a4bcb600, 0x3cc75ee47c8b09e9 |
| data8 0x880b4b780f02b709, 0xf850f2c9fdacdf78 |
| data8 0x3fcf70b05fb02e20, 0x3cad6350d379f41a |
| data8 0x882ea1bfc0f228ac, 0xf830b926379e6465 |
| data8 0x3fcfb2afa158b8a0, 0x3cce0ccd9f829985 |
| data8 0x885252ff21146108, 0xf810394699fe0e8e |
| data8 0x3fcff4b77e97f3e0, 0x3c9b30faa7a4c703 |
| data8 0x88765fb6dceebbb3, 0xf7ef730f865f6df0 |
| data8 0x3fd01b6406332540, 0x3cdc5772c9e0b9bd |
| data8 0x88ad1f69be2cc730, 0xf7bdc59bc9cfbd97 |
| data8 0x3fd04cf8ad203480, 0x3caeef44fe21a74a |
| data8 0x88f763f70ae2245e, 0xf77a91c868a9c54e |
| data8 0x3fd08f23ce0162a0, 0x3cd6290ab3fe5889 |
| data8 0x89431fc7bc0c2910, 0xf73642973c91298e |
| data8 0x3fd0d1610f0c1ec0, 0x3cc67401a01f08cf |
| data8 0x8990573407c7738e, 0xf6f0d71d1d7a2dd6 |
| data8 0x3fd113b0c65d88c0, 0x3cc7aa4020fe546f |
| data8 0x89df0eb108594653, 0xf6aa4e6a05cfdef2 |
| data8 0x3fd156134ada6fe0, 0x3cc87369da09600c |
| data8 0x8a2f4ad16e0ed78a, 0xf662a78900c35249 |
| data8 0x3fd19888f43427a0, 0x3cc62b220f38e49c |
| data8 0x8a811046373e0819, 0xf619e180181d97cc |
| data8 0x3fd1db121aed7720, 0x3ca3ede7490b52f4 |
| data8 0x8ad463df6ea0fa2c, 0xf5cffb504190f9a2 |
| data8 0x3fd21daf185fa360, 0x3caafad98c1d6c1b |
| data8 0x8b294a8cf0488daf, 0xf584f3f54b8604e6 |
| data8 0x3fd2606046bf95a0, 0x3cdb2d704eeb08fa |
| data8 0x8b7fc95f35647757, 0xf538ca65c960b582 |
| data8 0x3fd2a32601231ec0, 0x3cc661619fa2f126 |
| data8 0x8bd7e588272276f8, 0xf4eb7d92ff39fccb |
| data8 0x3fd2e600a3865760, 0x3c8a2a36a99aca4a |
| data8 0x8c31a45bf8e9255e, 0xf49d0c68cd09b689 |
| data8 0x3fd328f08ad12000, 0x3cb9efaf1d7ab552 |
| data8 0x8c8d0b520a35eb18, 0xf44d75cd993cfad2 |
| data8 0x3fd36bf614dcc040, 0x3ccacbb590bef70d |
| data8 0x8cea2005d068f23d, 0xf3fcb8a23ab4942b |
| data8 0x3fd3af11a079a6c0, 0x3cd9775872cf037d |
| data8 0x8d48e837c8cd5027, 0xf3aad3c1e2273908 |
| data8 0x3fd3f2438d754b40, 0x3ca03304f667109a |
| data8 0x8da969ce732f3ac7, 0xf357c60202e2fd7e |
| data8 0x3fd4358c3ca032e0, 0x3caecf2504ff1a9d |
| data8 0x8e0baad75555e361, 0xf3038e323ae9463a |
| data8 0x3fd478ec0fd419c0, 0x3cc64bdc3d703971 |
| data8 0x8e6fb18807ba877e, 0xf2ae2b1c3a6057f7 |
| data8 0x3fd4bc6369fa40e0, 0x3cbb7122ec245cf2 |
| data8 0x8ed5843f4bda74d5, 0xf2579b83aa556f0c |
| data8 0x3fd4fff2af11e2c0, 0x3c9cfa2dc792d394 |
| data8 0x8f3d29862c861fef, 0xf1ffde2612ca1909 |
| data8 0x3fd5439a4436d000, 0x3cc38d46d310526b |
| data8 0x8fa6a81128940b2d, 0xf1a6f1bac0075669 |
| data8 0x3fd5875a8fa83520, 0x3cd8bf59b8153f8a |
| data8 0x901206c1686317a6, 0xf14cd4f2a730d480 |
| data8 0x3fd5cb33f8cf8ac0, 0x3c9502b5c4d0e431 |
| data8 0x907f4ca5fe9cf739, 0xf0f186784a125726 |
| data8 0x3fd60f26e847b120, 0x3cc8a1a5e0acaa33 |
| data8 0x90ee80fd34aeda5e, 0xf09504ef9a212f18 |
| data8 0x3fd65333c7e43aa0, 0x3cae5b029cb1f26e |
| data8 0x915fab35e37421c6, 0xf0374ef5daab5c45 |
| data8 0x3fd6975b02b8e360, 0x3cd5aa1c280c45e6 |
| data8 0x91d2d2f0d894d73c, 0xefd86321822dbb51 |
| data8 0x3fd6db9d05213b20, 0x3cbecf2c093ccd8b |
| data8 0x9248000249200009, 0xef7840021aca5a72 |
| data8 0x3fd71ffa3cc87fc0, 0x3cb8d273f08d00d9 |
| data8 0x92bf3a7351f081d2, 0xef16e42021d7cbd5 |
| data8 0x3fd7647318b1ad20, 0x3cbce099d79cdc46 |
| data8 0x93388a8386725713, 0xeeb44dfce6820283 |
| data8 0x3fd7a908093fc1e0, 0x3ccb033ec17a30d9 |
| data8 0x93b3f8aa8e653812, 0xee507c126774fa45 |
| data8 0x3fd7edb9803e3c20, 0x3cc10aedb48671eb |
| data8 0x94318d99d341ade4, 0xedeb6cd32f891afb |
| data8 0x3fd83287f0e9cf80, 0x3c994c0c1505cd2a |
| data8 0x94b1523e3dedc630, 0xed851eaa3168f43c |
| data8 0x3fd87773cff956e0, 0x3cda3b7bce6a6b16 |
| data8 0x95334fc20577563f, 0xed1d8ffaa2279669 |
| data8 0x3fd8bc7d93a70440, 0x3cd4922edc792ce2 |
| data8 0x95b78f8e8f92f274, 0xecb4bf1fd2be72da |
| data8 0x3fd901a5b3b9cf40, 0x3cd3fea1b00f9d0d |
| data8 0x963e1b4e63a87c3f, 0xec4aaa6d08694cc1 |
| data8 0x3fd946eca98f2700, 0x3cdba4032d968ff1 |
| data8 0x96c6fcef314074fc, 0xebdf502d53d65fea |
| data8 0x3fd98c52f024e800, 0x3cbe7be1ab8c95c9 |
| data8 0x97523ea3eab028b2, 0xeb72aea36720793e |
| data8 0x3fd9d1d904239860, 0x3cd72d08a6a22b70 |
| data8 0x97dfeae6f4ee4a9a, 0xeb04c4096a884e94 |
| data8 0x3fda177f63e8ef00, 0x3cd818c3c1ebfac7 |
| data8 0x98700c7c6d85d119, 0xea958e90cfe1efd7 |
| data8 0x3fda5d468f92a540, 0x3cdf45fbfaa080fe |
| data8 0x9902ae7487a9caa1, 0xea250c6224aab21a |
| data8 0x3fdaa32f090998e0, 0x3cd715a9353cede4 |
| data8 0x9997dc2e017a9550, 0xe9b33b9ce2bb7638 |
| data8 0x3fdae939540d3f00, 0x3cc545c014943439 |
| data8 0x9a2fa158b29b649b, 0xe9401a573f8aa706 |
| data8 0x3fdb2f65f63f6c60, 0x3cd4a63c2f2ca8e2 |
| data8 0x9aca09f835466186, 0xe8cba69df9f0bf35 |
| data8 0x3fdb75b5773075e0, 0x3cda310ce1b217ec |
| data8 0x9b672266ab1e0136, 0xe855de74266193d4 |
| data8 0x3fdbbc28606babc0, 0x3cdc84b75cca6c44 |
| data8 0x9c06f7579f0b7bd5, 0xe7debfd2f98c060b |
| data8 0x3fdc02bf3d843420, 0x3cd225d967ffb922 |
| data8 0x9ca995db058cabdc, 0xe76648a991511c6e |
| data8 0x3fdc497a9c224780, 0x3cde08101c5b825b |
| data8 0x9d4f0b605ce71e88, 0xe6ec76dcbc02d9a7 |
| data8 0x3fdc905b0c10d420, 0x3cb1abbaa3edf120 |
| data8 0x9df765b9eecad5e6, 0xe6714846bdda7318 |
| data8 0x3fdcd7611f4b8a00, 0x3cbf6217ae80aadf |
| data8 0x9ea2b320350540fe, 0xe5f4bab71494cd6b |
| data8 0x3fdd1e8d6a0d56c0, 0x3cb726e048cc235c |
| data8 0x9f51023562fc5676, 0xe576cbf239235ecb |
| data8 0x3fdd65e082df5260, 0x3cd9e66872bd5250 |
| data8 0xa002620915c2a2f6, 0xe4f779b15f5ec5a7 |
| data8 0x3fddad5b02a82420, 0x3c89743b0b57534b |
| data8 0xa0b6e21c2caf9992, 0xe476c1a233a7873e |
| data8 0x3fddf4fd84bbe160, 0x3cbf7adea9ee3338 |
| data8 0xa16e9264cc83a6b2, 0xe3f4a16696608191 |
| data8 0x3fde3cc8a6ec6ee0, 0x3cce46f5a51f49c6 |
| data8 0xa22983528f3d8d49, 0xe3711694552da8a8 |
| data8 0x3fde84bd099a6600, 0x3cdc78f6490a2d31 |
| data8 0xa2e7c5d2e2e69460, 0xe2ec1eb4e1e0a5fb |
| data8 0x3fdeccdb4fc685c0, 0x3cdd3aedb56a4825 |
| data8 0xa3a96b5599bd2532, 0xe265b74506fbe1c9 |
| data8 0x3fdf15241f23b3e0, 0x3cd440f3c6d65f65 |
| data8 0xa46e85d1ae49d7de, 0xe1ddddb499b3606f |
| data8 0x3fdf5d98202994a0, 0x3cd6c44bd3fb745a |
| data8 0xa53727ca3e11b99e, 0xe1548f662951b00d |
| data8 0x3fdfa637fe27bf60, 0x3ca8ad1cd33054dd |
| data8 0xa6036453bdc20186, 0xe0c9c9aeabe5e481 |
| data8 0x3fdfef0467599580, 0x3cc0f1ac0685d78a |
| data8 0xa6d34f1969dda338, 0xe03d89d5281e4f81 |
| data8 0x3fe01bff067d6220, 0x3cc0731e8a9ef057 |
| data8 0xa7a6fc62f7246ff3, 0xdfafcd125c323f54 |
| data8 0x3fe04092d1ae3b40, 0x3ccabda24b59906d |
| data8 0xa87e811a861df9b9, 0xdf20909061bb9760 |
| data8 0x3fe0653df0fd9fc0, 0x3ce94c8dcc722278 |
| data8 0xa959f2d2dd687200, 0xde8fd16a4e5f88bd |
| data8 0x3fe08a00c1cae320, 0x3ce6b888bb60a274 |
| data8 0xaa3967cdeea58bda, 0xddfd8cabd1240d22 |
| data8 0x3fe0aedba3221c00, 0x3ced5941cd486e46 |
| data8 0xab904fd587263c84, 0xdd1f4472e1cf64ed |
| data8 0x3fe0e651e85229c0, 0x3cdb6701042299b1 |
| data8 0xad686d44dd5a74bb, 0xdbf173e1f6b46e92 |
| data8 0x3fe1309cbf4cdb20, 0x3cbf1be7bb3f0ec5 |
| data8 0xaf524e15640ebee4, 0xdabd54896f1029f6 |
| data8 0x3fe17b4ee1641300, 0x3ce81dd055b792f1 |
| data8 0xb14eca24ef7db3fa, 0xd982cb9ae2f47e41 |
| data8 0x3fe1c66b9ffd6660, 0x3cd98ea31eb5ddc7 |
| data8 0xb35ec807669920ce, 0xd841bd1b8291d0b6 |
| data8 0x3fe211f66db3a5a0, 0x3ca480c35a27b4a2 |
| data8 0xb5833e4755e04dd1, 0xd6fa0bd3150b6930 |
| data8 0x3fe25df2e05b6c40, 0x3ca4bc324287a351 |
| data8 0xb7bd34c8000b7bd3, 0xd5ab9939a7d23aa1 |
| data8 0x3fe2aa64b32f7780, 0x3cba67314933077c |
| data8 0xba0dc64d126cc135, 0xd4564563ce924481 |
| data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec |
| data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8 |
| data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac |
| data8 0xbef78e31985291a9, 0xd19672e2182f78be |
| data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c |
| data8 0xc19368b2b0629572, 0xd02baca5427e436a |
| data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689 |
| data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d |
| data8 0x3fe4300c7e945020, 0x3cbd367143da6582 |
| data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a |
| data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63 |
| data8 0xca14e1b0622de526, 0xcbbe13773c3c5338 |
| data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c |
| data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9 |
| data8 0x3fe5206cc637e000, 0x3ce2798b38e54193 |
| data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0 |
| data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68 |
| data8 0xd3c0d9f50057adda, 0xc70901152d59d16b |
| data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab |
| data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828 |
| data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5 |
| data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02 |
| data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee |
| data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af |
| data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d |
| data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b |
| data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321 |
| data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91 |
| data8 0x3fe76840418978a0, 0x3ccda46e85432c3d |
| data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3 |
| data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3 |
| data8 0xf049183c3f53c39b, 0xbad848720223d3a8 |
| data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b |
| data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48 |
| data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f |
| data8 0xfa718f05adbf2c33, 0xb70432500286b185 |
| data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9 |
| data8 0xfff200c3f5489608, 0xb509e6454dca33cc |
| data8 0x3fe9211b54441080, 0x3cb789cb53515688 |
| // The following table entries are not used |
| //data8 0x82e138a0fac48700, 0xb3044a513a8e6132 |
| //data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0 |
| //data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88 |
| //data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039 |
| //data8 0x89377c1387d5b908, 0xaed58e9a09014d5c |
| //data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58 |
| //data8 0x8cad7a2c98dec333, 0xacab929ce114d451 |
| //data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f |
| //data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec |
| //data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5 |
| //data8 0x9446d8191f80dd42, 0xa82ff92687235baf |
| //data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e |
| //data8 0x98758ba086e4000a, 0xa5dd497a9c184f58 |
| //data8 0x3febb5f571cb0560, 0x3ce0c7774329a613 |
| //data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b |
| //data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177 |
| //data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03 |
| //data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959 |
| //data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec |
| //data8 0x3fece4f404e29b20, 0x3cea3413401132b5 |
| //data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c |
| //data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276 |
| //data8 0xb265c39cbd80f97a, 0x99553d969fec7beb |
| //data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2 |
| //data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c |
| //data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71 |
| //data8 0xbfea427678945732, 0x93d5990f9ee787af |
| //data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5 |
| //data8 0xc79611399b8c90c5, 0x90f72bde80febc31 |
| //data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56 |
| //data8 0xcffa8425040624d7, 0x8e02b4418574ebed |
| //data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f |
| //data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024 |
| //data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94 |
| //data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b |
| //data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc |
| //data8 0xeea6d733421da0a6, 0x84921bbe64ae029a |
| //data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02 |
| //data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6 |
| //data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3 |
| //data8 0x84ac1fcec4203245, 0xfb73a828893df19e |
| //data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de |
| //data8 0x8ca50621110c60e6, 0xf438a14c158d867c |
| //data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6 |
| //data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da |
| //data8 0x3ff1717418520340, 0x3ca5c2732533177c |
| //data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119 |
| //data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5 |
| //data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d |
| //data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a |
| //data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f |
| //data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7 |
| //data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec |
| //data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746 |
| //data8 0xdfe323b8653af367, 0xc19107d99ab27e42 |
| //data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02 |
| //data8 0xf93746caaba3e1f1, 0xb777744a9df03bff |
| //data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43 |
| //data8 0x8ca77052f6c340f0, 0xacaf476f13806648 |
| //data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff |
| //data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50 |
| //data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c |
| //data8 0xbe45074b05579024, 0x9478e362a07dd287 |
| //data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12 |
| //data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b |
| //data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69 |
| //data8 0x94503d69396d91c7, 0xedd2ce885ff04028 |
| //data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b |
| //data8 0xced1d96c5bb209e6, 0xc965278083808702 |
| //data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c |
| //data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd |
| //data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e |
| //data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4 |
| //data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb |
| LOCAL_OBJECT_END(T_table) |
| |
| |
| |
| .align 16 |
| |
| LOCAL_OBJECT_START(poly_coeffs) |
| // C_3 |
| data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc |
| // C_5 |
| data8 0x999999999999999a, 0x0000000000003ffb |
| // C_7, C_9 |
| data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8 |
| // pi/2 (low, high) |
| data8 0x3C91A62633145C07, 0x3FF921FB54442D18 |
| // C_11, C_13 |
| data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e |
| // C_15, C_17 |
| data8 0x3f8c99999999999a, 0x3f87a87878787223 |
| LOCAL_OBJECT_END(poly_coeffs) |
| |
| |
| R_DBL_S = r21 |
| R_EXP0 = r22 |
| R_EXP = r15 |
| R_SGNMASK = r23 |
| R_TMP = r24 |
| R_TMP2 = r25 |
| R_INDEX = r26 |
| R_TMP3 = r27 |
| R_TMP03 = r27 |
| R_TMP4 = r28 |
| R_TMP5 = r23 |
| R_TMP6 = r22 |
| R_TMP7 = r21 |
| R_T = r29 |
| R_BIAS = r20 |
| |
| F_T = f6 |
| F_1S2 = f7 |
| F_1S2_S = f9 |
| F_INV_1T2 = f10 |
| F_SQRT_1T2 = f11 |
| F_S2T2 = f12 |
| F_X = f13 |
| F_D = f14 |
| F_2M64 = f15 |
| |
| F_CS2 = f32 |
| F_CS3 = f33 |
| F_CS4 = f34 |
| F_CS5 = f35 |
| F_CS6 = f36 |
| F_CS7 = f37 |
| F_CS8 = f38 |
| F_CS9 = f39 |
| F_S23 = f40 |
| F_S45 = f41 |
| F_S67 = f42 |
| F_S89 = f43 |
| F_S25 = f44 |
| F_S69 = f45 |
| F_S29 = f46 |
| F_X2 = f47 |
| F_X4 = f48 |
| F_TSQRT = f49 |
| F_DTX = f50 |
| F_R = f51 |
| F_R2 = f52 |
| F_R3 = f53 |
| F_R4 = f54 |
| |
| F_C3 = f55 |
| F_C5 = f56 |
| F_C7 = f57 |
| F_C9 = f58 |
| F_P79 = f59 |
| F_P35 = f60 |
| F_P39 = f61 |
| |
| F_ATHI = f62 |
| F_ATLO = f63 |
| |
| F_T1 = f64 |
| F_Y = f65 |
| F_Y2 = f66 |
| F_ANDMASK = f67 |
| F_ORMASK = f68 |
| F_S = f69 |
| F_05 = f70 |
| F_SQRT_1S2 = f71 |
| F_DS = f72 |
| F_Z = f73 |
| F_1T2 = f74 |
| F_DZ = f75 |
| F_ZE = f76 |
| F_YZ = f77 |
| F_Y1S2 = f78 |
| F_Y1S2X = f79 |
| F_1X = f80 |
| F_ST = f81 |
| F_1T2_ST = f82 |
| F_TSS = f83 |
| F_Y1S2X2 = f84 |
| F_DZ_TERM = f85 |
| F_DTS = f86 |
| F_DS2X = f87 |
| F_T2 = f88 |
| F_ZY1S2S = f89 |
| F_Y1S2_1X = f90 |
| F_TS = f91 |
| F_PI2_LO = f92 |
| F_PI2_HI = f93 |
| F_S19 = f94 |
| F_INV1T2_2 = f95 |
| F_CORR = f96 |
| F_DZ0 = f97 |
| |
| F_C11 = f98 |
| F_C13 = f99 |
| F_C15 = f100 |
| F_C17 = f101 |
| F_P1113 = f102 |
| F_P1517 = f103 |
| F_P1117 = f104 |
| F_P317 = f105 |
| F_R8 = f106 |
| F_HI = f107 |
| F_1S2_HI = f108 |
| F_DS2 = f109 |
| F_Y2_2 = f110 |
| F_S2 = f111 |
| F_S_DS2 = f112 |
| F_S_1S2S = f113 |
| F_XL = f114 |
| F_2M128 = f115 |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(asinl) |
| |
| {.mfi |
| // get exponent, mantissa (rounded to double precision) of s |
| getf.d R_DBL_S = f8 |
| // 1-s^2 |
| fnma.s1 F_1S2 = f8, f8, f1 |
| // r2 = pointer to T_table |
| addl r2 = @ltoff(T_table), gp |
| } |
| |
| {.mfi |
| // sign mask |
| mov R_SGNMASK = 0x20000 |
| nop.f 0 |
| // bias-63-1 |
| mov R_TMP03 = 0xffff-64;; |
| } |
| |
| |
| {.mfi |
| // get exponent of s |
| getf.exp R_EXP = f8 |
| nop.f 0 |
| // R_TMP4 = 2^45 |
| shl R_TMP4 = R_SGNMASK, 45-17 |
| } |
| |
| {.mlx |
| // load bias-4 |
| mov R_TMP = 0xffff-4 |
| // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1) |
| movl R_TMP2 = 0x7fcd413cccfe779a;; |
| } |
| |
| |
| {.mfi |
| // load 2^{-64} in FP register |
| setf.exp F_2M64 = R_TMP03 |
| nop.f 0 |
| // index = (0x7-exponent)|b1 b2.. b6 |
| extr.u R_INDEX = R_DBL_S, 46, 9 |
| } |
| |
| {.mfi |
| // get t = sign|exponent|b1 b2.. b6 1 x.. x |
| or R_T = R_DBL_S, R_TMP4 |
| nop.f 0 |
| // R_TMP4 = 2^45-1 |
| sub R_TMP4 = R_TMP4, r0, 1;; |
| } |
| |
| |
| {.mfi |
| // get t = sign|exponent|b1 b2.. b6 1 0.. 0 |
| andcm R_T = R_T, R_TMP4 |
| nop.f 0 |
| // eliminate sign from R_DBL_S (shift left by 1) |
| shl R_TMP3 = R_DBL_S, 1 |
| } |
| |
| {.mfi |
| // R_BIAS = 3*2^6 |
| mov R_BIAS = 0xc0 |
| nop.f 0 |
| // eliminate sign from R_EXP |
| andcm R_EXP0 = R_EXP, R_SGNMASK;; |
| } |
| |
| |
| |
| {.mfi |
| // load start address for T_table |
| ld8 r2 = [r2] |
| nop.f 0 |
| // p8 = 1 if |s|> = sqrt(2)/2 |
| cmp.geu p8, p0 = R_TMP3, R_TMP2 |
| } |
| |
| {.mlx |
| // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4) |
| cmp.lt p7, p0 = R_EXP0, R_TMP |
| // sqrt coefficient cs8 = -33*13/128 |
| movl R_TMP2 = 0xc0568000;; |
| } |
| |
| |
| |
| {.mbb |
| // load t in FP register |
| setf.d F_T = R_T |
| // if |s|<2^{-4}, take alternate path |
| (p7) br.cond.spnt SMALL_S |
| // if |s|> = sqrt(2)/2, take alternate path |
| (p8) br.cond.sptk LARGE_S |
| } |
| |
| {.mlx |
| // index = (4-exponent)|b1 b2.. b6 |
| sub R_INDEX = R_INDEX, R_BIAS |
| // sqrt coefficient cs9 = 55*13/128 |
| movl R_TMP = 0x40b2c000;; |
| } |
| |
| |
| {.mfi |
| // sqrt coefficient cs8 = -33*13/128 |
| setf.s F_CS8 = R_TMP2 |
| nop.f 0 |
| // shift R_INDEX by 5 |
| shl R_INDEX = R_INDEX, 5 |
| } |
| |
| {.mfi |
| // sqrt coefficient cs3 = 0.5 (set exponent = bias-1) |
| mov R_TMP4 = 0xffff - 1 |
| nop.f 0 |
| // sqrt coefficient cs6 = -21/16 |
| mov R_TMP6 = 0xbfa8;; |
| } |
| |
| |
| {.mlx |
| // table index |
| add r2 = r2, R_INDEX |
| // sqrt coefficient cs7 = 33/16 |
| movl R_TMP2 = 0x40040000;; |
| } |
| |
| |
| {.mmi |
| // load cs9 = 55*13/128 |
| setf.s F_CS9 = R_TMP |
| // sqrt coefficient cs5 = 7/8 |
| mov R_TMP3 = 0x3f60 |
| // sqrt coefficient cs6 = 21/16 |
| shl R_TMP6 = R_TMP6, 16;; |
| } |
| |
| |
| {.mmi |
| // load significand of 1/(1-t^2) |
| ldf8 F_INV_1T2 = [r2], 8 |
| // sqrt coefficient cs7 = 33/16 |
| setf.s F_CS7 = R_TMP2 |
| // sqrt coefficient cs4 = -5/8 |
| mov R_TMP5 = 0xbf20;; |
| } |
| |
| |
| {.mmi |
| // load significand of sqrt(1-t^2) |
| ldf8 F_SQRT_1T2 = [r2], 8 |
| // sqrt coefficient cs6 = 21/16 |
| setf.s F_CS6 = R_TMP6 |
| // sqrt coefficient cs5 = 7/8 |
| shl R_TMP3 = R_TMP3, 16;; |
| } |
| |
| |
| {.mmi |
| // sqrt coefficient cs3 = 0.5 (set exponent = bias-1) |
| setf.exp F_CS3 = R_TMP4 |
| // r3 = pointer to polynomial coefficients |
| addl r3 = @ltoff(poly_coeffs), gp |
| // sqrt coefficient cs4 = -5/8 |
| shl R_TMP5 = R_TMP5, 16;; |
| } |
| |
| |
| {.mfi |
| // sqrt coefficient cs5 = 7/8 |
| setf.s F_CS5 = R_TMP3 |
| // d = s-t |
| fms.s1 F_D = f8, f1, F_T |
| // set p6 = 1 if s<0, p11 = 1 if s> = 0 |
| cmp.ge p6, p11 = R_EXP, R_DBL_S |
| } |
| |
| {.mfi |
| // r3 = load start address to polynomial coefficients |
| ld8 r3 = [r3] |
| // s+t |
| fma.s1 F_S2T2 = f8, f1, F_T |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| // sqrt coefficient cs4 = -5/8 |
| setf.s F_CS4 = R_TMP5 |
| // s^2-t^2 |
| fma.s1 F_S2T2 = F_S2T2, F_D, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| // load C3 |
| ldfe F_C3 = [r3], 16 |
| // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2)) |
| fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| // load C_5 |
| ldfe F_C5 = [r3], 16 |
| // set correct exponent for sqrt(1-t^2) |
| fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| // load C_7, C_9 |
| ldfpd F_C7, F_C9 = [r3] |
| // x = -(s^2-t^2)/(1-t^2)/2 |
| fnma.s1 F_X = F_INV_1T2, F_S2T2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| // load asin(t)_high, asin(t)_low |
| ldfpd F_ATHI, F_ATLO = [r2] |
| // t*sqrt(1-t^2) |
| fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // cs9*x+cs8 |
| fma.s1 F_S89 = F_CS9, F_X, F_CS8 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // cs7*x+cs6 |
| fma.s1 F_S67 = F_CS7, F_X, F_CS6 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // cs5*x+cs4 |
| fma.s1 F_S45 = F_CS5, F_X, F_CS4 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // x*x |
| fma.s1 F_X2 = F_X, F_X, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (s-t)-t*x |
| fnma.s1 F_DTX = F_T, F_X, F_D |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // cs3*x+cs2 (cs2 = -0.5 = -cs3) |
| fms.s1 F_S23 = F_CS3, F_X, F_CS3 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // cs9*x^3+cs8*x^2+cs7*x+cs6 |
| fma.s1 F_S69 = F_S89, F_X2, F_S67 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // x^4 |
| fma.s1 F_X4 = F_X2, F_X2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // t*sqrt(1-t^2)*x^2 |
| fma.s1 F_TSQRT = F_TSQRT, F_X2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // cs5*x^3+cs4*x^2+cs3*x+cs2 |
| fma.s1 F_S25 = F_S45, F_X2, F_S23 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // ((s-t)-t*x)*sqrt(1-t^2) |
| fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // if sign is negative, negate table values: asin(t)_low |
| (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2 |
| fma.s1 F_S29 = F_S69, F_X4, F_S25 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // if sign is negative, negate table values: asin(t)_high |
| (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29 |
| fnma.s1 F_R = F_S29, F_TSQRT, F_DTX |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // R^2 |
| fma.s1 F_R2 = F_R, F_R, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c7+c9*R^2 |
| fma.s1 F_P79 = F_C9, F_R2, F_C7 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2 |
| fma.s1 F_P35 = F_C5, F_R2, F_C3 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // R^3 |
| fma.s1 F_R4 = F_R2, F_R2, f0 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // R^3 |
| fma.s1 F_R3 = F_R2, F_R, f0 |
| nop.i 0;; |
| } |
| |
| |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2+c7*R^4+c9*R^6 |
| fma.s1 F_P39 = F_P79, F_R4, F_P35 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) |
| fma.s1 F_P39 = F_P39, F_R3, F_ATLO |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) |
| fma.s1 F_P39 = F_P39, f1, F_R |
| nop.i 0;; |
| } |
| |
| |
| {.mfb |
| nop.m 0 |
| // result = asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) |
| fma.s0 f8 = F_ATHI, f1, F_P39 |
| // return |
| br.ret.sptk b0;; |
| } |
| |
| |
| |
| |
| LARGE_S: |
| |
| {.mfi |
| // bias-1 |
| mov R_TMP3 = 0xffff - 1 |
| // y ~ 1/sqrt(1-s^2) |
| frsqrta.s1 F_Y, p7 = F_1S2 |
| // c9 = 55*13*17/128 |
| mov R_TMP4 = 0x10af7b |
| } |
| |
| {.mlx |
| // c8 = -33*13*15/128 |
| mov R_TMP5 = 0x184923 |
| movl R_TMP2 = 0xff00000000000000;; |
| } |
| |
| {.mfi |
| // set p6 = 1 if s<0, p11 = 1 if s>0 |
| cmp.ge p6, p11 = R_EXP, R_DBL_S |
| // 1-s^2 |
| fnma.s1 F_1S2 = f8, f8, f1 |
| // set p9 = 1 |
| cmp.eq p9, p0 = r0, r0;; |
| } |
| |
| |
| {.mfi |
| // load 0.5 |
| setf.exp F_05 = R_TMP3 |
| // (1-s^2) rounded to single precision |
| fnma.s.s1 F_1S2_S = f8, f8, f1 |
| // c9 = 55*13*17/128 |
| shl R_TMP4 = R_TMP4, 10 |
| } |
| |
| {.mlx |
| // AND mask for getting t ~ sqrt(1-s^2) |
| setf.sig F_ANDMASK = R_TMP2 |
| // OR mask |
| movl R_TMP2 = 0x0100000000000000;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (s^2)_s |
| fma.s.s1 F_S2 = f8, f8, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mmi |
| // c9 = 55*13*17/128 |
| setf.s F_CS9 = R_TMP4 |
| // c7 = 33*13/16 |
| mov R_TMP4 = 0x41d68 |
| // c8 = -33*13*15/128 |
| shl R_TMP5 = R_TMP5, 11;; |
| } |
| |
| |
| {.mfi |
| setf.sig F_ORMASK = R_TMP2 |
| // y^2 |
| fma.s1 F_Y2 = F_Y, F_Y, f0 |
| // c7 = 33*13/16 |
| shl R_TMP4 = R_TMP4, 12 |
| } |
| |
| {.mfi |
| // c6 = -33*7/16 |
| mov R_TMP6 = 0xc1670 |
| // y' ~ sqrt(1-s^2) |
| fma.s1 F_T1 = F_Y, F_1S2, f0 |
| // c5 = 63/8 |
| mov R_TMP7 = 0x40fc;; |
| } |
| |
| |
| {.mlx |
| // load c8 = -33*13*15/128 |
| setf.s F_CS8 = R_TMP5 |
| // c4 = -35/8 |
| movl R_TMP5 = 0xc08c0000;; |
| } |
| |
| {.mfi |
| // r3 = pointer to polynomial coefficients |
| addl r3 = @ltoff(poly_coeffs), gp |
| // 1-(1-s^2)_s |
| fnma.s1 F_DS = F_1S2_S, f1, f1 |
| // p9 = 0 if p7 = 1 (p9 = 1 for special cases only) |
| (p7) cmp.ne p9, p0 = r0, r0 |
| } |
| |
| {.mlx |
| // load c7 = 33*13/16 |
| setf.s F_CS7 = R_TMP4 |
| // c3 = 5/2 |
| movl R_TMP4 = 0x40200000;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // 1-(s^2)_s |
| fnma.s1 F_S_1S2S = F_S2, f1, f1 |
| nop.i 0 |
| } |
| |
| {.mlx |
| // load c4 = -35/8 |
| setf.s F_CS4 = R_TMP5 |
| // c2 = -3/2 |
| movl R_TMP5 = 0xbfc00000;; |
| } |
| |
| |
| {.mfi |
| // load c3 = 5/2 |
| setf.s F_CS3 = R_TMP4 |
| // x = (1-s^2)_s*y^2-1 |
| fms.s1 F_X = F_1S2_S, F_Y2, f1 |
| // c6 = -33*7/16 |
| shl R_TMP6 = R_TMP6, 12 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // y^2/2 |
| fma.s1 F_Y2_2 = F_Y2, F_05, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| // load c6 = -33*7/16 |
| setf.s F_CS6 = R_TMP6 |
| // eliminate lower bits from y' |
| fand F_T = F_T1, F_ANDMASK |
| // c5 = 63/8 |
| shl R_TMP7 = R_TMP7, 16 |
| } |
| |
| {.mfb |
| // r3 = load start address to polynomial coefficients |
| ld8 r3 = [r3] |
| // 1-(1-s^2)_s-s^2 |
| fnma.s1 F_DS = f8, f8, F_DS |
| // p9 = 1 if s is a special input (NaN, or |s|> = 1) |
| (p9) br.cond.spnt ASINL_SPECIAL_CASES;; |
| } |
| |
| {.mmf |
| // get exponent, significand of y' (in single prec.) |
| getf.s R_TMP = F_T1 |
| // load c3 = -3/2 |
| setf.s F_CS2 = R_TMP5 |
| // y*(1-s^2) |
| fma.s1 F_Y1S2 = F_Y, F_1S2, f0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // x' = (y^2/2)*(1-(s^2)_s)-0.5 |
| fms.s1 F_XL = F_Y2_2, F_S_1S2S, F_05 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // s^2-(s^2)_s |
| fms.s1 F_S_DS2 = f8, f8, F_S2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // if s<0, set s = -s |
| (p6) fnma.s1 f8 = f8, f1, f0 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| // load c5 = 63/8 |
| setf.s F_CS5 = R_TMP7 |
| // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2 |
| fma.s1 F_X = F_DS, F_Y2, F_X |
| // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6 |
| extr.u R_INDEX = R_TMP, 17, 9;; |
| } |
| |
| |
| {.mmi |
| // index = (4-exponent)|b1 b2.. b6 |
| sub R_INDEX = R_INDEX, R_BIAS |
| nop.m 0 |
| // get exponent of y |
| shr.u R_TMP2 = R_TMP, 23;; |
| } |
| |
| {.mmi |
| // load C3 |
| ldfe F_C3 = [r3], 16 |
| // set p8 = 1 if y'<2^{-4} |
| cmp.gt p8, p0 = 0x7b, R_TMP2 |
| // shift R_INDEX by 5 |
| shl R_INDEX = R_INDEX, 5;; |
| } |
| |
| |
| {.mfb |
| // get table index for sqrt(1-t^2) |
| add r2 = r2, R_INDEX |
| // get t = 2^k*1.b1 b2.. b7 1 |
| for F_T = F_T, F_ORMASK |
| (p8) br.cond.spnt VERY_LARGE_INPUT;; |
| } |
| |
| |
| |
| {.mmf |
| // load C5 |
| ldfe F_C5 = [r3], 16 |
| // load 1/(1-t^2) |
| ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16 |
| // x = ((1-s^2)*y^2-1)/2 |
| fma.s1 F_X = F_X, F_05, f0;; |
| } |
| |
| |
| |
| {.mmf |
| nop.m 0 |
| // C7, C9 |
| ldfpd F_C7, F_C9 = [r3], 16 |
| // set correct exponent for t |
| fmerge.se F_T = F_T1, F_T;; |
| } |
| |
| |
| |
| {.mfi |
| // pi/2 (low, high) |
| ldfpd F_PI2_LO, F_PI2_HI = [r3] |
| // c9*x+c8 |
| fma.s1 F_S89 = F_X, F_CS9, F_CS8 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // x^2 |
| fma.s1 F_X2 = F_X, F_X, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-s^2)*x |
| fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c7*x+c6 |
| fma.s1 F_S67 = F_X, F_CS7, F_CS6 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // 1-x |
| fnma.s1 F_1X = F_X, f1, f1 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c3*x+c2 |
| fma.s1 F_S23 = F_X, F_CS3, F_CS2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // 1-t^2 |
| fnma.s1 F_1T2 = F_T, F_T, f1 |
| nop.i 0 |
| } |
| |
| {.mfi |
| // load asin(t)_high, asin(t)_low |
| ldfpd F_ATHI, F_ATLO = [r2] |
| // c5*x+c4 |
| fma.s1 F_S45 = F_X, F_CS5, F_CS4 |
| nop.i 0;; |
| } |
| |
| |
| |
| {.mfi |
| nop.m 0 |
| // t*s |
| fma.s1 F_TS = F_T, f8, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // 0.5/(1-t^2) |
| fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // z~sqrt(1-t^2), rounded to 24 significant bits |
| fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // sqrt(1-t^2) |
| fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-s^2)*x^2 |
| fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // x^4 |
| fma.s1 F_X4 = F_X2, F_X2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // s*t rounded to 24 significant bits |
| fma.s.s1 F_TSS = F_T, f8, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c9*x^3+..+c6 |
| fma.s1 F_S69 = F_X2, F_S89, F_S67 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // ST = (t^2-1+s^2) rounded to 24 significant bits |
| fms.s.s1 F_ST = f8, f8, F_1T2 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c5*x^3+..+c2 |
| fma.s1 F_S25 = F_X2, F_S45, F_S23 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // 0.25/(1-t^2) |
| fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // t*s-sqrt(1-t^2)*(1-s^2)*y |
| fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // z*0.5/(1-t^2) |
| fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // z^2+t^2-1 |
| fms.s1 F_DZ0 = F_Z, F_Z, F_1T2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (1-s^2-(1-s^2)_s)*x |
| fma.s1 F_DS2X = F_X, F_DS, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // t*s-(t*s)_s |
| fms.s1 F_DTS = F_T, f8, F_TSS |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c9*x^7+..+c2 |
| fma.s1 F_S29 = F_X4, F_S69, F_S25 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*z |
| fma.s1 F_YZ = F_Z, F_Y, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // t^2 |
| fma.s1 F_T2 = F_T, F_T, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // 1-t^2+ST |
| fma.s1 F_1T2_ST = F_ST, f1, F_1T2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-s^2)(1-x) |
| fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // dz ~ sqrt(1-t^2)-z |
| fma.s1 F_DZ = F_DZ0, F_ZE, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // -1+correction for sqrt(1-t^2)-z |
| fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (PS29*x^2+x)*y*(1-s^2) |
| fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // z*y*(1-s^2)_s |
| fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // s^2-(1-t^2+ST) |
| fms.s1 F_1T2_ST = f8, f8, F_1T2_ST |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x |
| fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // dz*y*(1-s^2)*(1-x) |
| fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19 |
| // (used for polynomial evaluation) |
| fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (PS29*x^2)*y*(1-s^2) |
| fma.s1 F_S29 = F_Y1S2X2, F_S29, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // apply correction to dz*y*(1-s^2)*(1-x) |
| fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // R^2 |
| fma.s1 F_R2 = F_R, F_R, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x) |
| fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c7+c9*R^2 |
| fma.s1 F_P79 = F_C9, F_R2, F_C7 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2 |
| fma.s1 F_P35 = F_C5, F_R2, F_C3 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // asin(t)_low-(pi/2)_low |
| fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // R^4 |
| fma.s1 F_R4 = F_R2, F_R2, f0 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // R^3 |
| fma.s1 F_R3 = F_R2, F_R, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (t*s)_s-t^2*y*z |
| fnma.s1 F_TSS = F_T2, F_YZ, F_TSS |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) |
| fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (pi/2)_hi-asin(t)_hi |
| fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2+c7*R^4+c9*R^6 |
| fma.s1 F_P39 = F_P79, F_R4, F_P35 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+ |
| // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 |
| fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (t*s)_s-t^2*y*z+z*y*ST |
| fma.s1 F_TSS = F_YZ, F_ST, F_TSS |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) |
| fms.s1 F_P39 = F_P39, F_R3, F_ATLO |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // if s<0, change sign of F_ATHI |
| (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + |
| // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + |
| // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) |
| fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + |
| // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x + |
| // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) |
| fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + |
| // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x + |
| // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) + |
| // + (t*s)_s-t^2*y*z+z*y*ST |
| fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM |
| nop.i 0;; |
| } |
| |
| |
| .pred.rel "mutex", p6, p11 |
| {.mfi |
| nop.m 0 |
| // result: add high part of pi/2-table value |
| // s>0 in this case |
| (p11) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI |
| nop.i 0 |
| } |
| |
| {.mfb |
| nop.m 0 |
| // result: add high part of pi/2-table value |
| // if s<0 |
| (p6) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI |
| br.ret.sptk b0;; |
| } |
| |
| |
| |
| |
| |
| |
| SMALL_S: |
| |
| // use 15-term polynomial approximation |
| |
| {.mmi |
| // r3 = pointer to polynomial coefficients |
| addl r3 = @ltoff(poly_coeffs), gp;; |
| // load start address for coefficients |
| ld8 r3 = [r3] |
| mov R_TMP = 0x3fbf;; |
| } |
| |
| |
| {.mmi |
| add r2 = 64, r3 |
| ldfe F_C3 = [r3], 16 |
| // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64) |
| cmp.lt p7, p0 = R_EXP0, R_TMP;; |
| } |
| |
| {.mmf |
| ldfe F_C5 = [r3], 16 |
| ldfpd F_C11, F_C13 = [r2], 16 |
| // 2^{-128} |
| fma.s1 F_2M128 = F_2M64, F_2M64, f0;; |
| } |
| |
| {.mmf |
| ldfpd F_C7, F_C9 = [r3] |
| ldfpd F_C15, F_C17 = [r2] |
| // if |s|<2^{-64}, return s+2^{-128}*s |
| (p7) fma.s0 f8 = f8, F_2M128, f8;; |
| } |
| |
| |
| |
| {.mfb |
| nop.m 0 |
| // s^2 |
| fma.s1 F_R2 = f8, f8, f0 |
| // if |s|<2^{-64}, return s |
| (p7) br.ret.spnt b0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // s^3 |
| fma.s1 F_R3 = f8, F_R2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // s^4 |
| fma.s1 F_R4 = F_R2, F_R2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*s^2 |
| fma.s1 F_P35 = F_C5, F_R2, F_C3 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c11+c13*s^2 |
| fma.s1 F_P1113 = F_C13, F_R2, F_C11 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c7+c9*s^2 |
| fma.s1 F_P79 = F_C9, F_R2, F_C7 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c15+c17*s^2 |
| fma.s1 F_P1517 = F_C17, F_R2, F_C15 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // s^8 |
| fma.s1 F_R8 = F_R4, F_R4, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*s^2+c7*s^4+c9*s^6 |
| fma.s1 F_P39 = F_P79, F_R4, F_P35 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c11+c13*s^2+c15*s^4+c17*s^6 |
| fma.s1 F_P1117 = F_P1517, F_R4, F_P1113 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c3+..+c17*s^14 |
| fma.s1 F_P317 = F_R8, F_P1117, F_P39 |
| nop.i 0;; |
| } |
| |
| |
| {.mfb |
| nop.m 0 |
| // result |
| fma.s0 f8 = F_P317, F_R3, f8 |
| br.ret.sptk b0;; |
| } |
| |
| |
| {.mfb |
| nop.m 0 |
| fma.s0 f8 = F_P317, F_R3, f0//F_P317, F_R3, F_S29 |
| // nop.f 0//fma.s0 f8 = f13, f6, f0 |
| br.ret.sptk b0;; |
| } |
| |
| |
| |
| |
| |
| VERY_LARGE_INPUT: |
| |
| {.mfi |
| nop.m 0 |
| // s rounded to 24 significant bits |
| fma.s.s1 F_S = f8, f1, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| // load C5 |
| ldfe F_C5 = [r3], 16 |
| // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2 |
| fnma.s1 F_X = F_S_DS2, F_Y2_2, F_XL |
| nop.i 0;; |
| } |
| |
| |
| |
| {.mmf |
| nop.m 0 |
| // C7, C9 |
| ldfpd F_C7, F_C9 = [r3], 16 |
| nop.f 0;; |
| } |
| |
| |
| |
| {.mfi |
| // pi/2 (low, high) |
| ldfpd F_PI2_LO, F_PI2_HI = [r3], 16 |
| // c9*x+c8 |
| fma.s1 F_S89 = F_X, F_CS9, F_CS8 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // x^2 |
| fma.s1 F_X2 = F_X, F_X, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-s^2)*x |
| fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| // C11, C13 |
| ldfpd F_C11, F_C13 = [r3], 16 |
| // c7*x+c6 |
| fma.s1 F_S67 = F_X, F_CS7, F_CS6 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| // C15, C17 |
| ldfpd F_C15, F_C17 = [r3], 16 |
| // c3*x+c2 |
| fma.s1 F_S23 = F_X, F_CS3, F_CS2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c5*x+c4 |
| fma.s1 F_S45 = F_X, F_CS5, F_CS4 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (s_s)^2 |
| fma.s1 F_DS = F_S, F_S, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // 1-(s_s)^2 |
| fnma.s1 F_1S2_S = F_S, F_S, f1 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-s^2)*x^2 |
| fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // x^4 |
| fma.s1 F_X4 = F_X2, F_X2, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c9*x^3+..+c6 |
| fma.s1 F_S69 = F_X2, F_S89, F_S67 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c5*x^3+..+c2 |
| fma.s1 F_S25 = F_X2, F_S45, F_S23 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // ((s_s)^2-s^2) |
| fnma.s1 F_DS = f8, f8, F_DS |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // (pi/2)_high-y*(1-(s_s)^2) |
| fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c9*x^7+..+c2 |
| fma.s1 F_S29 = F_X4, F_S69, F_S25 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // -(y*(1-(s_s)^2))_high |
| fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (PS29*x^2+x)*y*(1-s^2) |
| fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-(s_s)^2)-(y*(1-s^2))_high |
| fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI |
| nop.i 0;; |
| } |
| |
| |
| |
| {.mfi |
| nop.m 0 |
| // R ~ sqrt(1-s^2) |
| // (used for polynomial evaluation) |
| fnma.s1 F_R = F_S19, f1, F_Y1S2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // y*(1-s^2)-(y*(1-s^2))_high |
| fma.s1 F_DS2 = F_Y, F_DS, F_DS2 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // (pi/2)_low+(PS29*x^2)*y*(1-s^2) |
| fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO |
| nop.i 0;; |
| } |
| |
| |
| |
| {.mfi |
| nop.m 0 |
| // R^2 |
| fma.s1 F_R2 = F_R, F_R, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high) |
| fms.s1 F_S29 = F_S29, f1, F_DS2 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c7+c9*R^2 |
| fma.s1 F_P79 = F_C9, F_R2, F_C7 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2 |
| fma.s1 F_P35 = F_C5, F_R2, F_C3 |
| nop.i 0;; |
| } |
| |
| |
| |
| {.mfi |
| nop.m 0 |
| // R^4 |
| fma.s1 F_R4 = F_R2, F_R2, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // R^3 |
| fma.s1 F_R3 = F_R2, F_R, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c11+c13*R^2 |
| fma.s1 F_P1113 = F_C13, F_R2, F_C11 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c15+c17*R^2 |
| fma.s1 F_P1517 = F_C17, F_R2, F_C15 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x |
| fma.s1 F_S29 = F_Y1S2, F_X, F_S29 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c11+c13*R^2+c15*R^4+c17*R^6 |
| fma.s1 F_P1117 = F_P1517, F_R4, F_P1113 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2+c7*R^4+c9*R^6 |
| fma.s1 F_P39 = F_P79, F_R4, F_P35 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // R^8 |
| fma.s1 F_R8 = F_R4, F_R4, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14 |
| fma.s1 F_P317 = F_P1117, F_R8, F_P39 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)- |
| // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17 |
| fnma.s1 F_S29 = F_P317, F_R3, F_S29 |
| nop.i 0;; |
| } |
| |
| {.mfi |
| nop.m 0 |
| // set sign |
| (p6) fnma.s1 F_S29 = F_S29, f1, f0 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| (p6) fnma.s1 F_HI = F_HI, f1, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfb |
| nop.m 0 |
| // Result: |
| // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)- |
| // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17 |
| // +(pi/2)_high-(y*(1-s^2))_high |
| fma.s0 f8 = F_S29, f1, F_HI |
| br.ret.sptk b0;; |
| } |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| ASINL_SPECIAL_CASES: |
| |
| {.mfi |
| alloc r32 = ar.pfs, 1, 4, 4, 0 |
| // check if the input is a NaN, or unsupported format |
| // (i.e. not infinity or normal/denormal) |
| fclass.nm p7, p8 = f8, 0x3f |
| // pointer to pi/2 |
| add r3 = 48, r3;; |
| } |
| |
| |
| {.mfi |
| // load pi/2 |
| ldfpd F_PI2_HI, F_PI2_LO = [r3] |
| // get |s| |
| fmerge.s F_S = f0, f8 |
| nop.i 0 |
| } |
| |
| {.mfb |
| nop.m 0 |
| // if NaN, quietize it, and return |
| (p7) fma.s0 f8 = f8, f1, f0 |
| (p7) br.ret.spnt b0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // |s| = 1 ? |
| fcmp.eq.s0 p9, p0 = F_S, f1 |
| nop.i 0 |
| } |
| |
| {.mfi |
| nop.m 0 |
| // load FR_X |
| fma.s1 FR_X = f8, f1, f0 |
| // load error tag |
| mov GR_Parameter_TAG = 60;; |
| } |
| |
| |
| {.mfb |
| nop.m 0 |
| // change sign if s = -1 |
| (p6) fnma.s1 F_PI2_HI = F_PI2_HI, f1, f0 |
| nop.b 0 |
| } |
| |
| {.mfb |
| nop.m 0 |
| // change sign if s = -1 |
| (p6) fnma.s1 F_PI2_LO = F_PI2_LO, f1, f0 |
| nop.b 0;; |
| } |
| |
| {.mfb |
| nop.m 0 |
| // if s = 1, result is pi/2 |
| (p9) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO |
| // return if |s| = 1 |
| (p9) br.ret.sptk b0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // get Infinity |
| frcpa.s1 FR_RESULT, p0 = f1, f0 |
| nop.i 0;; |
| } |
| |
| |
| {.mfi |
| nop.m 0 |
| // return QNaN indefinite (0*Infinity) |
| fma.s0 FR_RESULT = f0, FR_RESULT, f0 |
| nop.i 0;; |
| } |
| |
| |
| GLOBAL_LIBM_END(asinl) |
| |
| |
| |
| LOCAL_LIBM_ENTRY(__libm_error_region) |
| .prologue |
| // (1) |
| { .mfi |
| add GR_Parameter_Y=-32,sp // Parameter 2 value |
| nop.f 0 |
| .save ar.pfs,GR_SAVE_PFS |
| mov GR_SAVE_PFS=ar.pfs // Save ar.pfs |
| } |
| { .mfi |
| .fframe 64 |
| add sp=-64,sp // Create new stack |
| nop.f 0 |
| mov GR_SAVE_GP=gp // Save gp |
| };; |
| |
| |
| // (2) |
| { .mmi |
| stfe [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack |
| add GR_Parameter_X = 16,sp // Parameter 1 address |
| .save b0, GR_SAVE_B0 |
| mov GR_SAVE_B0=b0 // Save b0 |
| };; |
| |
| .body |
| // (3) |
| { .mib |
| stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack |
| add GR_Parameter_RESULT = 0,GR_Parameter_Y |
| nop.b 0 // Parameter 3 address |
| } |
| { .mib |
| stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack |
| add GR_Parameter_Y = -16,GR_Parameter_Y |
| br.call.sptk b0=__libm_error_support# // Call error handling function |
| };; |
| { .mmi |
| nop.m 0 |
| nop.m 0 |
| add GR_Parameter_RESULT = 48,sp |
| };; |
| |
| // (4) |
| { .mmi |
| ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack |
| .restore sp |
| add sp = 64,sp // Restore stack pointer |
| mov b0 = GR_SAVE_B0 // Restore return address |
| };; |
| |
| { .mib |
| mov gp = GR_SAVE_GP // Restore gp |
| mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs |
| br.ret.sptk b0 // Return |
| };; |
| |
| LOCAL_LIBM_END(__libm_error_region) |
| |
| .type __libm_error_support#,@function |
| .global __libm_error_support# |
| |
| |
| |
| |
| |
