.file "cbrtf.s"// Copyright (c) 2000 - 2003, Intel Corporation// All rights reserved.//// Contributed 2000 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//==============================================================// 02/02/00 Initial version// 05/18/00 New version (modified algorithm)// 05/20/02 Cleaned up namespace and sf0 syntax// 01/28/03 Rescheduled some instructions for better performance//          on Itanium 2, and reformatted//// API//==============================================================// float cbrtf(float)//// Overview of operation//==============================================================// Background//// Implementation//// Let y= frcpa(a), where a is the argument//// cbrt(a)= cbrt(a*y)/cbrt(y) = cbrt(1 - (1-a*y)) * (1/cbrt(y))//// For all values of y, the 3 possible significands of 1/cbrt(y)// are stored in a table (T0) to 64 bits of accuracy. (There are// 3 possible significands because the exponent of y modulo 3// can be 0, 1, or 2.)////// * cbrt(1 - (1-a*y)) is approximated by a degree-2 polynomial//// 1 - (1/3)*r - (1/9)*r^2//// in r = 1-a*y.//// The table values are stored for three exponent values and are// then multiplied by 2^(e/3) where e is the exponent of the input number.// This computation is carried out in parallel with the polynomial// evaluation://// T= 2^(e/3) * T0//===============// input= x// C= frcpa(x)// r= 1 - C * x//// Special values//==============================================================// Registers used//==============================================================// p6, p7, p8, p12       FR_R      = f6       FR_COEFF1 = f7       FR_COEFF2 = f9       FR_T0     = f10       FR_T1     = f11       FR_T2     = f12       FR_2M63   = f13       FR_ARG    = f14       FR_Y      = f15       GR_GP     = r2       GR_ADDR   = r2       GR_TMP5   = r3       GR_CONST  = r8       GR_TMP63  = r8       GR_SIGN   = r9       GR_CT2    = r10       GR_CT3    = r11       GR_TMP4   = r14       GR_EBIAS3 = r15       GR_REM    = r16       GR_SEXP   = r17       GR_2P63   = r18       GR_SIGNIF = r19       GR_I1     = r20       GR_EBIAS  = r21       GR_EXP    = r22       GR_IT1    = r23       GR_E5     = r24       GR_IT1_3  = r25       GR_TP1    = r26       GR_TMP    = r27       GR_TMP2   = r28       GR_TMP3   = r29       GR_EXP3   = r30       GR_ARGEXP = r31// Data tables//==============================================================RODATA.align 16LOCAL_OBJECT_START(poly_coeffs)       data8 0xaaaab19b7e1f5ef9, 0x00003ffd // ~ 1/3       data8 0xe38e5192a5a8e56c, 0x00003ffb // ~ 1/9LOCAL_OBJECT_END(poly_coeffs)//   For every entry B in the frcpa table, this table contains// the significands of cbrt(1/B), cbrt(2/B), cbrt(4/B).// The index to this table is the same as the frcpa index.LOCAL_OBJECT_START(T_table)       data8 0x80155c748c374836, 0xa160019ed37fb4ae       data8 0xcb51ddcb9e93095e, 0x8040404b0879f7f9       data8 0xa1960b5966da4608, 0xcb95f333968ad59b       data8 0x806b5dce4b405c10, 0xa1cc5dbe6dc2aab4       data8 0xcbda64292d3ffd97, 0x8096b586974669b1       data8 0xa202f97995b69c0d, 0xcc1f3184af961596       data8 0x80bcd273d952a028, 0xa232fe6eb0c0577d       data8 0xcc5bb1ac954d33e2, 0x80e898c52813f2f3       data8 0xa26a2582012f6e17, 0xcca12e9831fc6402       data8 0x81149add67c2d208, 0xa2a197e5d10465cb       data8 0xcce70a67b64f24ad, 0x813b4e2c856b6e9a       data8 0xa2d25a532efefbc8, 0xcd24794726477ea5       data8 0x8167c1dde03de7aa, 0xa30a5bd6e49e4ab8       data8 0xcd6b096a0b70ee87, 0x818ed973b811135e       data8 0xa33b9c9b59879e24, 0xcda9177738b15a90       data8 0x81bbc0c33e13ec98, 0xa3742fca6a3c1f21       data8 0xcdf05f2247dffab9, 0x81e33e69fbe7504a       data8 0xa3a5f1273887bf22, 0xce2f0f347f96f906       data8 0x820aec524e3c23e9, 0xa3d7ef508ff11574       data8 0xce6e0be0cd551a61, 0x823880f78e70b805       data8 0xa4115ce30548bc15, 0xceb666b2c347d1de       data8 0x826097a62a8e5200, 0xa443df0e53df577a       data8 0xcef609b0cb874f00, 0x8288dfe00e9b5eaf       data8 0xa4769fa5913c0ec3, 0xcf35fb5447e5c765       data8 0x82b15a10c5371624, 0xa4a99f303bc7def5       data8 0xcf763c47ee869f00, 0x82da06a527b18937       data8 0xa4dcde37779adf4b, 0xcfb6cd3888d71785       data8 0x8302e60b635ab394, 0xa5105d46152c938a       data8 0xcff7aed4fbfbb447, 0x832bf8b2feec2f0e       data8 0xa5441ce89825cb8d, 0xd038e1ce5167e3c6       data8 0x83553f0ce00e276b, 0xa5781dad3e54d899       data8 0xd07a66d7bfa0ebba, 0x837eb98b50f8322a       data8 0xa5ac602406c4e68c, 0xd0bc3ea6b32d1b21       data8 0x83a270f44c84f699, 0xa5d9601d95c2c0bc       data8 0xd0f4f0e8f36c1bf8, 0x83cc4d7cfcfac5ca       data8 0xa60e1e1a2de14745, 0xd1376458e34b037e       data8 0x83f65f78a8872b4c, 0xa6431f6e3fbd9658       data8 0xd17a2ca133f78572, 0x8420a75f2f7b53c8       data8 0xa67864b0d432fda4, 0xd1bd4a80301c5715       data8 0x844510461ff14209, 0xa6a6444aa0243c0b       data8 0xd1f71682b2fa4575, 0x846fbd91b930bed2       data8 0xa6dc094d10f25792, 0xd23ad555f773f059       data8 0x84947e18234f3294, 0xa70a574cc02bba69       data8 0xd2752c7039a5bf73, 0x84bf92755825045a       data8 0xa7409e2af9549084, 0xd2b98ee008c06b59       data8 0x84e4ac0ee112ba51, 0xa76f5c64ca2cf13b       data8 0xd2f4735ffd700280, 0x8509ef44b86f20be       data8 0xa79e4f0babab5dc0, 0xd32f99ed6d9ac0e1       data8 0x85359d5d91768427, 0xa7d5579ae5164b85       data8 0xd374f0666c75d51c, 0x855b3bd5b7384357       data8 0xa804bd3c6fe61cc8, 0xd3b0a7d13618e4a1       data8 0x858104f0c415f79a, 0xa8345895e5250a5a       data8 0xd3eca2ea53bcec0c, 0x85a6f90390d29864       data8 0xa8642a122b44ef0b, 0xd428e23874f13a17       data8 0x85d3772fcd56a1dd, 0xa89c38ca18f6108b       data8 0xd46f82fe293bc6d3, 0x85f9c982fcc002f3       data8 0xa8cc81063b6e87ca, 0xd4ac57e9b7186420       data8 0x862047e0e7ea554b, 0xa8fd00bfa409285e       data8 0xd4e972becb04e8b8, 0x8646f2a26f7f5852       data8 0xa92db8664d5516da, 0xd526d40a7a9b43a3       data8 0x866dca21754096b5, 0xa95ea86b75cc2c20       data8 0xd5647c5b73917370, 0x8694ceb8dfd17a37       data8 0xa98fd141a4992deb, 0xd5a26c4201bd6d13       data8 0x86bc00c49e9307e8, 0xa9c1335cae7446ba       data8 0xd5e0a45015350a7e, 0x86dccd74fce79610       data8 0xa9ea8686f556f645, 0xd614b539c6194104       data8 0x870453c845acf90f, 0xaa1c52d17906bb19       data8 0xd6537310e224283f, 0x872c089a1e90342c       data8 0xaa4e59b046dab887, 0xd6927ab62244c917       data8 0x8753ec4a92d16c5e, 0xaa809b9c60d1890b       data8 0xd6d1ccc1fc4ef4b7, 0x877bff3aca19f6b4       data8 0xaab319102f3f9b33, 0xd71169cea98fdded       data8 0x879d88b6fe1c324c, 0xaadd5a18c1e21274       data8 0xd746a66a5bc9f6d9, 0x87c5f346dbf98c3a       data8 0xab1045f2ac31bdf5, 0xd786ce8f0fae5317       data8 0x87e7c653efacef2c, 0xab3ae3ab2df7231e       data8 0xd7bc7ff214c4e75a, 0x881089d4e73ffefc       data8 0xab6e3f945d1e96fc, 0xd7fd35467a517ed1       data8 0x88397e6a366f2a8a, 0xaba1d953a08fa94e       data8 0xd83e38838648d815, 0x885bc559e5e1c081       data8 0xabcd090db7ef4c3f, 0xd874a1db598b8951       data8 0x887e2ee392bb7a93, 0xabf864602d7c323d       data8 0xd8ab42205b80edaf, 0x88a7a8587e404257       data8 0xac2ca5886ccf9b57, 0xd8ed1849d202f965       data8 0x88ca5eda67594784, 0xac5861d4aa441f0f       data8 0xd92432bd5a173685, 0x88f4356166bd590e       data8 0xac8d183fe3a2fbed, 0xd9669ca45b03c23e       data8 0x89173a0acf5ce026, 0xacb93703ff51571e       data8 0xd99e3327cf89574e, 0x893a62a098b6a57b       data8 0xace5830ad0c3f14b, 0xd9d602b19b100466       data8 0x895daf637236ae2c, 0xad11fca5d78b3ff2       data8 0xda0e0ba86c096841, 0x89883b9d1c2fa9c5       data8 0xad4797fddf91a798, 0xda5195fcdb1c3dce       data8 0x89abd8dd374a5d7b, 0xad747701e559ebcb       data8 0xda8a1eb87a491f6c, 0x89cf9b1dcd197fa0       data8 0xada184a47e9c7613, 0xdac2e230b91c3f84       data8 0x89f382a258ea79de, 0xadcec13ab0dda8ff       data8 0xdafbe0d0b66aea30, 0x8a178faf06648f29       data8 0xadfc2d1a5fd21ba8, 0xdb351b04a8fafced       data8 0x8a3bc288b3e1d18a, 0xae29c89a5053c33a       data8 0xdb6e9139e33cdd8e, 0x8a601b74f4d1f835       data8 0xae5794122b638df9, 0xdba843ded7151ea1       data8 0x8a849aba14274764, 0xae858fda8137ae0a       data8 0xdbe2336319b61fc8, 0x8aa9409f16cdbc9b       data8 0xaeb3bc4ccc56d3d1, 0xdc1c60376789fa68       data8 0x8ace0d6bbe2cb316, 0xaee219c374c09920       data8 0xdc56cacda82d0cd5, 0x8af301688ab33558       data8 0xaf10a899d3235fe7, 0xdc917398f2797814       data8 0x8b181cdebe6f3206, 0xaf3f692c341fe8b4       data8 0xdccc5b0d90a3e628, 0x8b3d60185fafcb7c       data8 0xaf6e5bd7db9ae6c2, 0xdd0781a10469f0f2       data8 0x8b62cb603bb2fad0, 0xaf9d80fb081cd91b       data8 0xdd42e7ca0b52838f, 0x8b80d7d6bc4104de       data8 0xafc35ce063eb3787, 0xdd729ad01c69114d       data8 0x8ba68bf73ac74f39, 0xaff2ddcb5f28f03d       data8 0xddae749c001fbf5e, 0x8bcc68fb9f9f7335       data8 0xb022923b148e05c5, 0xddea8f50a51c69b1       data8 0x8bf26f31c534fca2, 0xb0527a919adbf58b       data8 0xde26eb69a0f0f111, 0x8c10f86e13a1a1f9       data8 0xb078f3ab1d701c65, 0xde576480262399bc       data8 0x8c3749916cc6abb5, 0xb0a93a6870649f31       data8 0xde943789645933c8, 0x8c5dc4c4f7706032       data8 0xb0d9b624d62ec856, 0xded14d58139a28af       data8 0x8c7cac3a8c42e3e0, 0xb100a5f53fb3c8e1       data8 0xdf025c00bbf2b5c7, 0x8ca373f1b7bf2716       data8 0xb131821882f5540a, 0xdf3feb44d723a713       data8 0x8cc29907fb951294, 0xb158bf8e4cb04055       data8 0xdf715bc16c159be0, 0x8ce9ae4e9492aac8       data8 0xb189fd69d56b238f, 0xdfaf66240e29cda8       data8 0x8d0911dddbfdad0e, 0xb1b189958e8108e4       data8 0xdfe139cbf6e19bdc, 0x8d3075c4f20f04ee       data8 0xb1e32a8165b09832, 0xe01fc0fe94d9fc52       data8 0x8d5018a9d4de77d5, 0xb20b0678fc271eec       data8 0xe051f92ffcc0bd60, 0x8d77cc47dd143515       data8 0xb23d0bd3f7592b6e, 0xe090feec9c9a06ac       data8 0x8d97af6352739cb7, 0xb26538b2db8420dc       data8 0xe0c39d0c9ff862d6, 0x8db7af523167800f       data8 0xb28d89e339ceca14, 0xe0f668eeb99f188d       data8 0x8ddfd80bc68c32ff, 0xb2c022ca12e55a16       data8 0xe1362890eb663139, 0x8e00197e1e7c88fe       data8 0xb2e8c6852c6b03f1, 0xe1695c7212aecbaa       data8 0x8e207859f77e20e7, 0xb3118f4eda9fe40f       data8 0xe19cbf0391bbbbe9, 0x8e40f4ce60c9f8e2       data8 0xb33a7d6268109ebe, 0xe1d050901c531e85       data8 0x8e69ba46cf2fde4d, 0xb36ddbc5ea70ec55       data8 0xe2110903b4f4047a, 0x8e8a7a00bd7ae63e       data8 0xb3971e9b39264023, 0xe2450559b4d80b6d       data8 0x8eab57ef1cf2f529, 0xb3c0877ecc18e24a       data8 0xe27931a231554ef3, 0x8ecc5442cffb1dad       data8 0xb3ea16ae3a6c905f, 0xe2ad8e2ac3c5b04b       data8 0x8eed6f2d2a4acbfe, 0xb413cc67aa0e4d2d       data8 0xe2e21b41b9694cce, 0x8f0ea8dff24441ff       data8 0xb43da8e9d163e1af, 0xe316d93615862714       data8 0x8f385c95d696b817, 0xb47233773b84d425       data8 0xe3590bd86a0d30f9, 0x8f59dc43edd930f3       data8 0xb49c6825430fe730, 0xe38e38e38e38e38e       data8 0x8f7b7b5f5ffad1c4, 0xb4c6c46bcdb27dcf       data8 0xe3c397d1e6db7839, 0x8f9d3a1bea165f38       data8 0xb4f1488c0b35d26f, 0xe3f928f5953feb9e       data8 0x8fbf18adc34b66da, 0xb51bf4c7c51f0168       data8 0xe42eeca17c62886c, 0x8fe117499e356095       data8 0xb546c9616087ab9c, 0xe464e32943446305       data8 0x90033624aa685f8d, 0xb571c69bdffd9a70       data8 0xe49b0ce15747a8a2, 0x9025757495f36b86       data8 0xb59cecbae56984c3, 0xe4d16a1eee94e9d4       data8 0x903f3a5dcc091203, 0xb5bd64512bb14bb7       data8 0xe4fa52107353f67d, 0x9061b2fceb2bdbab       data8 0xb5e8d2a4bf5ba416, 0xe5310a471f4d2dc3       data8 0x90844ca7211032a7, 0xb6146a9a1bc47819       data8 0xe567f6f1c2b9c224, 0x90a7079403e6a15d       data8 0xb6402c7749d621c0, 0xe59f18689a9e4c9a       data8 0x90c9e3fbafd63799, 0xb66c1882fb435ea2       data8 0xe5d66f04b8a68ecf, 0x90ece216c8a16ee4       data8 0xb6982f048c999a56, 0xe60dfb2005c192e9       data8 0x9110021e7b516f0a, 0xb6c47044075b4142       data8 0xe645bd1544c7ea51, 0x912a708a39be9075       data8 0xb6e5bd6bfd02bafd, 0xe66fb21b505b20a0       data8 0x914dcc7b31146370, 0xb7124a2736ff8ef2       data8 0xe6a7d32af4a7c59a, 0x91714af8cfe984d5       data8 0xb73f026a01e94177, 0xe6e02b129c6a5ae4       data8 0x918c00a6f3795e97, 0xb760a959f1d0a7a7       data8 0xe70a9136a7403039, 0x91afbc299ed0295d       data8 0xb78dae7e06868ab0, 0xe74349fb2d92a589       data8 0x91d39add3e958db0, 0xb7badff8ad9e4e02       data8 0xe77c3a9c86ed7d42, 0x91ee9920a8974d92       data8 0xb7dce25b8e17ae9f, 0xe7a713f88151518a       data8 0x9212b5fcac537c19, 0xb80a6226904045e2       data8 0xe7e067453317ed2b, 0x9236f6b256923fcf       data8 0xb8380f1cafd73c1c, 0xe819f37a81871bb5       data8 0x92523ee6f90dcfc3, 0xb85a6ea8e321b4d8       data8 0xe8454236bfaeca14, 0x9276bef031e6eb79       data8 0xb8886b684ae7d2fa, 0xe87f32f24c3fc90e       data8 0x929236ec237a24ad, 0xb8ab0726fa00cf5d       data8 0xe8aacd8688892ba6, 0x92b6f70b7efe9dc3       data8 0xb8d954a4d13b7cb1, 0xe8e523fd32f606f7       data8 0x92d29f61eec7dc2b, 0xb8fc2d4f6cd9f04a       data8 0xe9110b5311407927, 0x92f7a05d5b8ba92f       data8 0xb92acc851476b1ab, 0xe94bc8bf0c108fa3       data8 0x931379a403be5c16, 0xb94de2d841a184c2       data8 0xe977fdc439c2ca3c, 0x9338bc44de2e3f34       data8 0xb97cd4c36c92693c, 0xe9b3236528fc349e       data8 0x9354c71412c69486, 0xb9a0297f172665e3       data8 0xe9dfa70b745ac1b4, 0x937a4c273907e262       data8 0xb9cf6f21e36c3924, 0xea1b36268d0eaa38       data8 0x93968919f6e7975d, 0xb9f3030951267208       data8 0xea480963fd394197, 0x93bc516fdd4680c9       data8 0xba229d6a618e7c59, 0xea84034425f27484       data8 0x93d8c123d9be59b2, 0xba467144459f9855       data8 0xeab12713138dd1cc, 0x93f546c955e60076       data8 0xba6a60c3c48f1a4b, 0xeade6db73a5e503b       data8 0x941b70a65879079f, 0xba9a76056b67ee7a       data8 0xeb1b0268343b121b, 0x943829f337410591       data8 0xbabea699563ada6e, 0xeb489b0b2bdb5f14       data8 0x9454f995765bc4d2, 0xbae2f350b262cc4b       data8 0xeb765721e85f03d0, 0x947b86b57f5842ed       data8 0xbb1385a23be24e57, 0xebb389645f222f62       data8 0x94988aeb23470f86, 0xbb3814975e17c680       data8 0xebe198f090607e0c, 0x94b5a5dc9695f42a       data8 0xbb5cc031009bf467, 0xec0fcc9321024509       data8 0x94d2d7a9170d8b42, 0xbb81889680024764       data8 0xec3e247da8b82f61, 0x94f9e87dd78bf019       data8 0xbbb2c0d8703ae95d, 0xec7c27d21321c9f7       data8 0x95175019a503d89e, 0xbbd7cd09ba3c5463       data8 0xecaad5278824e453, 0x9534cefa625fcb3a       data8 0xbbfcf68c4977718f, 0xecd9a76d097d4e77       data8 0x955265405c491a25, 0xbc223d88cfc88eee