.file "cbrt.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 // 05/19/00 New version (modified algorithm) // 05/20/02 Cleaned up namespace and sf0 syntax // 01/28/03 Updated polynomial coefficients (changed to Remez coefficients), // to slightly improve accuracy // // API //============================================================== // double cbrt(double) // // 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-5 polynomial ~ // // ~ 1 - (1/3)*r - (1/9)*r^2 - (5/81)*r^3 - (10/243)*r^4 - (22/729)*r^5 // // in r = 1-a*y. // // // The table values are stored for three exponent values and are // then multiplied by 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 //============================================================== // f6-f15 // GR_GP, r23-r26, r28-r30 // p6, p7, p8, p12 FR_R = f6 FR_COEFF1 = f7 FR_COEFF2 = f9 FR_COEFF3 = f10 FR_COEFF4 = f11 FR_COEFF5 = f12 FR_R2 = f13 FR_ARG = f14 FR_P23 = f15 FR_P25 = f32 FR_P15 = f33 FR_P1 = f34 FR_P45 = f35 FR_2EXP = f36 FR_TMP63 = f37 GR_GP = r2 GR_ADDR = r2 GR_CONST1 = r3 GR_I1 = r8 GR_EXP = r9 GR_ADDR2 = r10 GR_IT1 = r11 GR_TMP2 = r11 GR_EXPON = r15 GR_TMP1 = r16 GR_TMP6 = r16 GR_ITB1 = r17 GR_TMP3 = r18 GR_TMP4 = r19 GR_TMP63 = r19 GR_TMP5 = r20 GR_EXP_BY_3 = r20 GR_CONST4 = r21 GR_TMP6 = r22 GR_INDEX = r23 GR_EBIAS = r24 GR_SIGNIF = r25 GR_SIGNIF2 = r25 GR_TEST = r25 GR_ARGEXP = r26 GR_CONST2 = r27 GR_SIGN = r28 GR_REM = r29 GR_CONST3 = r30 GR_SEXP = r31 // Data tables //============================================================== RODATA .align 16 LOCAL_OBJECT_START(poly_coeffs) data8 0xaaaaaaaaaaaaaab4, 0x0000bffd // ~ 1/3 data8 0xbfbc71c71c718e45, 0xbfaf9add3c0bbb43 data8 0xbfa511edb93dc98d, 0xbf9ee71c45f0dfbc LOCAL_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, 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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, 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0xc84b978847a06b87 data8 0xfc5b32968f99b21c, 0x9f12e05a4759ec25 data8 0xc86b9bf1ee817bc6, 0xfc83896bc861ab08 data8 0x9f2c5a20f4da6668, 0xc88bb4de3667cdf4 data8 0xfcabfa1861ed4815, 0x9f52af78ed1733ca data8 0xc8bc00e7fe9e23a3, 0xfce8d3cea7d3163e data8 0x9f6c52426a39d003, 0xc8dc4d7ff2d25232 data8 0xfd118595143ee273, 0x9f860593d42fd7f3 data8 0xc8fcaeebcb40eb47, 0xfd3a519943d4865a data8 0x9f9fc97fdb96bd51, 0xc91d25431426a663 data8 0xfd6337f8e1ae5a4b, 0x9fb99e194f4a7037 data8 0xc93db09d7fdb2949, 0xfd8c38d1c8e927eb data8 0x9fd383731ca51db9, 0xc95e5112e721582a data8 0xfdb5544205095a53, 0x9fed79a04fbf9423 data8 0xc97f06bb49787677, 0xfdde8a67d2613531 data8 0xa00780b413b24ee8, 0xc99fd1aecd6e1b06 data8 0xfe07db619e781611, 0xa02eab2c4474b0cd data8 0xc9d12a3e27bb1625, 0xfe460768d80bf758 data8 0xa048dcd51ccfd142, 0xc9f22ad82ba3d5f0 data8 0xfe6f9bfb06cd32f6, 0xa0631fa894b11b8d data8 0xca134113105e67b2, 0xfe994bcd3d14fcc2 data8 0xa07d73ba65e680af, 0xca346d07b045a876 data8 0xfec316fecaf3f2ab, 0xa097d91e6aaf71b0 data8 0xca55aecf0e94bb88, 0xfeecfdaf33fadb80 data8 0xa0b24fe89e02602f, 0xca77068257be9bab data8 0xff16fffe2fa8fad6, 0xa0ccd82d1bd2f68b data8 0xca98743ae1c693a8, 0xff411e0ba9db886d data8 0xa0e77200215909e6, 0xcab9f8122c99a101 data8 0xff6b57f7c33e4e9a, 0xa1021d760d584855 data8 0xcadb9221e268c3b5, 0xff95ade2d1bd7358 data8 0xa11cdaa36068a57d, 0xcafd4283d8043dfd data8 0xffc01fed60f86fb5, 0xa137a99cbd3f880b data8 0xcb1f09520d37c6fb, 0xffeaae3832b63956 LOCAL_OBJECT_END(T_table) .section .text GLOBAL_LIBM_ENTRY(cbrt) {.mfi // get significand getf.sig GR_SIGNIF = f8 // normalize a fma.s1 FR_ARG = f8, f1, f0 // GR_GP = pointer to C_1,..., C_5 followed by T_table addl GR_GP = @ltoff(poly_coeffs), gp ;; } {.mfi // get exponent getf.exp GR_ARGEXP = f8 // will continue only for normal/denormal numbers fclass.m.unc p12, p13 = f8, 0x1e7 // GR_CONST4 = bias-((2^{12}-1)/3)-63 = 0xffff-0x555-0x3f = 0xfa6b mov GR_CONST4 = 0xfa6b ;; } {.mlx mov GR_CONST2 = 0x20000 // GR_CONST3 = 2^52 movl GR_CONST3 = 0x8000000000000000 ;; } .pred.rel "mutex", p12, p13 {.mfi // load start address for C_1,..., C_5 followed by T_table ld8 GR_ADDR = [ GR_GP ] // y = frcpa(a) (p13) frcpa.s0 f8, p0 = f1, f8 // p7 = 1 if denormal input cmp.gtu p7, p0 = GR_CONST3, GR_SIGNIF } {.mfb nop.m 0 // if argument is 0, +/-Infinity, NaN, or NaTVal, then return (p12) fma.d.s0 f8 = f8, f1, f0 (p12) br.ret.spnt b0 ;; } {.mmi // get exponent (for denormal input) (p7) getf.exp GR_ARGEXP = FR_ARG // get normalized significand (for denormal input) (p7) getf.sig GR_SIGNIF = FR_ARG // GR_CONST1 = bias-(2^{12}-1) mov GR_CONST1 = 0xf000 ;; } {.mii // get GR_SIGN = sign and GR_SIGN = GR_ARGEXP, GR_CONST2 // eliminate leading 1 from GR_I1 = 1st table index shl GR_I1 = GR_SIGNIF, 1 // eliminate sign from exponent andcm GR_EXP = GR_ARGEXP, GR_CONST2 ;; } {.mib add GR_ADDR2 = 32, GR_ADDR // GR_IT1 = 1st table index (y_index, 8 bits) shr.u GR_IT1 = GR_I1, 56 nop.b 0 } {.mib // load C_1 ldfe FR_COEFF1 = [ GR_ADDR ], 16 // subtract bias from GR_EXPON = exponent sub GR_EXPON = GR_EXP, GR_CONST1 nop.b 0 ;; } {.mib // load C_2, C_3 ldfpd FR_COEFF2, FR_COEFF3 = [ GR_ADDR ] // 1: exponent* = 5; // (2^{16}-1)/3 = 0x5555 shladd GR_TMP1 = GR_EXPON, 2, GR_EXPON nop.b 0 } {.mib // load C_4, C_5 ldfpd FR_COEFF4, FR_COEFF5 = [ GR_ADDR2 ], 16 // GR_TMP2 = 3*y_index shladd GR_TMP2 = GR_IT1, 1, GR_IT1 nop.b 0 ;; } {.mfi // GR_TMP6 = (5*expon)*16+5*expon = (0x55)*expon shladd GR_TMP6 = GR_TMP1, 4, GR_TMP1 // r = 1-a*y fnma.s1 FR_R = f8, FR_ARG, f1 // adjust T_table pointer by 1st index shladd GR_ITB1 = GR_TMP2, 3, GR_ADDR2 ;; } {.mii // eliminate leading 1 from significand add GR_SIGNIF2 = GR_SIGNIF, GR_SIGNIF // GR_TMP3 = (0x5500)*expon shl GR_TMP3 = GR_TMP6, 8 ;; // GR_TMP4 = (0x5555)*expon add GR_TMP4 = GR_TMP3, GR_TMP6 ;; } {.mii // GR_TMP5 = (0x5556)*expon // 0x5556 = (2^{16}+2)/3 add GR_TMP5 = GR_TMP4, GR_EXPON nop.i 0 ;; // GR_EXP_BY_3 = floor(expon/3) shr GR_EXP_BY_3 = GR_TMP5, 16 ;; } {.mfi // GR_TMP6 = 3*exponent shladd GR_TMP6 = GR_EXP_BY_3, 1, GR_EXP_BY_3 // r*r fma.s1 FR_R2 = FR_R, FR_R, f0 // bias exponent add GR_EBIAS = GR_CONST4, GR_EXP_BY_3 ;; } {.mfi // get remainder of exponent/3 sub GR_REM = GR_EXPON, GR_TMP6 // c2+c3*r fma.s1 FR_P23 = FR_COEFF3, FR_R, FR_COEFF2 nop.i 0 } {.mfi // add sign to exponent or GR_SEXP = GR_EBIAS, GR_SIGN // c4+c5*r fma.s1 FR_P45 = FR_COEFF5, FR_R, FR_COEFF4 mov GR_TMP63 = 63+0xffff ;; } {.mmi // FR_2EXP = sign*2^{exponent/3} setf.exp FR_2EXP = GR_SEXP // adjust T_table pointer by 2nd index shladd GR_INDEX = GR_REM, 3, GR_ITB1 // is the argument of the form 2^(3*k) ? // get (significand - leading 1) | (exponent mod 3) or GR_TEST = GR_REM, GR_SIGNIF2 ;; } {.mmi // 2^63 setf.exp FR_TMP63 = GR_TMP63 // load T ldf8 f8 = [ GR_INDEX ] // is the argument of the form 2^(3*k) ? cmp.eq p14, p0 = GR_TEST, r0 ;; } {.mfi nop.m 0 // (c2+c3*r)+r^2*(c4+c5*r) fma.s1 FR_P25 = FR_P45, FR_R2, FR_P23 nop.i 0 } {.mfi nop.m 0 // c1*r fma.s1 FR_P1 = FR_COEFF1, FR_R, f0 nop.i 0 ;; } {.mfb nop.m 0 (p14) fma.d.s0 f8 = FR_2EXP, FR_TMP63, f0 (p14) br.ret.spnt b0 ;; } {.mfi nop.m 0 // P = c1*r+r^2* [ (c2+c3*r)+r^2*(c4+c5*r) ] fma.s1 FR_P15 = FR_P25, FR_R2, FR_P1 nop.i 0 } {.mfi nop.m 0 // T' = T*(2^exp) fma.s1 f8 = f8, FR_2EXP, f0 nop.i 0 ;; } {.mfb nop.m 0 // result = T'+T'*P fma.d.s0 f8 = f8, FR_P15, f8 br.ret.sptk b0 ;; } GLOBAL_LIBM_END(cbrt)