diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_cbrt.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cbrt.S | 1224 |
1 files changed, 651 insertions, 573 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrt.S b/sysdeps/ia64/fpu/s_cbrt.S index 1e23b6024d..7a74ac19be 100644 --- a/sysdeps/ia64/fpu/s_cbrt.S +++ b/sysdeps/ia64/fpu/s_cbrt.S @@ -1,11 +1,10 @@ -.file "cbrt.asm" +.file "cbrt.s" -// Copyright (C) 2000, 2001, Intel Corporation + +// Copyright (c) 2000 - 2003, Intel Corporation // All rights reserved. -// -// Contributed 2/2/2000 by John Harrison, Cristina Iordache, Ted Kubaska, -// Bob Norin, Shane Story, and Ping Tak Peter Tang -// of the Computational Software Lab, Intel Corporation. +// +// 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 @@ -21,27 +20,30 @@ // * 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 + +// 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 +// 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 +// 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. -// +// 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://developer.intel.com/opensource. +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. // // History //============================================================== -// 2/02/00: Initial version -// 5/19/00: New version (modified algorithm) +// 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 //============================================================== @@ -53,637 +55,713 @@ // // Implementation // -// cbrt(a) = cbrt(a y) / cbrt(y) -// = cbrt(1 - (1 - a y)) * 1/cbrt(y) +// 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.) // -// where y = frcpa(a). // -// * 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. +// * 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 values 1/cbrt(y) are stored in a table of constants T0 -// to 64 bits of accuracy // // 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 +// T= 2^(e/3) * T0 //=============== -// input = x -// C = frcpa(x) -// r = 1 - C * x +// input= x +// C= frcpa(x) +// r= 1 - C * x // -// Special values +// Special values //============================================================== // Registers used //============================================================== -// f6-f15 -// r2, r23-r26, r28-r30 -// p6,p7,p8,p12 +// 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 + + + -#include "libm_support.h" // Data tables //============================================================== -#ifdef _LIBC -.rodata -#else -.data -#endif +RODATA .align 16 -poly_coeffs: -ASM_TYPE_DIRECTIVE(poly_coeffs,@object) -data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // 1/3 -data8 0x3fbc71c71c71c71d, 0x3faf9add3c0ca459 -data8 0x3fa511e8d2b3183b, 0x3f9ee7113506ac13 -ASM_SIZE_DIRECTIVE(poly_coeffs) - -T_table: -ASM_TYPE_DIRECTIVE(T_table,@object) - -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 -data8 0xed089ed5dcd99446, 0x9570130c1f9bb857 -data8 0xbc47a2284fee4ff8, 0xed37bb95add09a1c -data8 0x9597ca4119525184, 0xbc79ac0916ed7b8a -data8 0xed76c70508f904b6, 0x95b5af6fb5aa4d3c -data8 0xbc9f5670d1a13030, 0xeda63bb05e7f93c6 -data8 0x95d3ac9273aafd7a, 0xbcc51f068cb95c1d -data8 0xedd5d661daed2dc4, 0x95f1c1cafdfd3684 -data8 0xbceb05f4b30a9bc0, 0xee05974eef86b903 -data8 0x960fef3b430b8d5f, 0xbd110b6604c7d306 -data8 0xee357ead791fc670, 0x962e350575b409c5 -data8 0xbd372f8598620f19, 0xee658cb3c134a463 -data8 0x964c934c0dfc1708, 0xbd5d727edb6b3c7e -data8 0xee95c1987f080211, 0x966b0a31c9c6bc7d -data8 0xbd83d47d937bbc6d, 0xeec61d92d8c4314f -data8 0x968999d9ad8d264e, 0xbdaa55addf1ae47d -data8 0xeef6a0da64a014ac, 0x96a8426705198795 -data8 0xbdd0f63c36aa73f0, 0xef274ba72a07c811 -data8 0x96c703fd64445ee5, 0xbdf7b6556d550a15 -data8 0xef581e31a2c91260, 0x96e5dec0a7b4268d -data8 0xbe1e9626b1ffa96b, 0xef8918b2bc43aec6 -data8 0x9704d2d4f59f79f3, 0xbe4595dd903e5371 -data8 0xefba3b63d89d7cbf, 0x9723e05ebe91b9b0 -data8 0xbe6cb5a7f14bc935, 0xefeb867ecffaa607 -data8 0x97430782be323831, 0xbe93f5b41d047cf7 -data8 0xf01cfa3df1b9c9fa, 0x97624865fc0df8bf -data8 0xbebb5630bae4c15f, 0xf04e96dc05b43e2d -data8 0x9781a32dcc640b2a, 0xbee2d74cd30a430c -data8 0xf0805c944d827454, 0x97a117ffd0f48e46 -data8 0xbf0a7937cf38d981, 0xf0b24ba285c495cb -data8 0x97c0a701f9d263c9, 0xbf323c217be2bc8c -data8 0xf0e46442e76f6569, 0x97e0505a8637a036 -data8 0xbf5a203a09342bbb, 0xf116a6b2291d7896 -data8 0x97f57a9fb0b08c6e, 0xbf74cad1c14ebfc4 -data8 0xf1383fa9e9b5b381, 0x9815503365914a9d -data8 0xbf9ce6a497a89f78, 0xf16ac84f90083b9b -data8 0x98354085054fd204, 0xbfc52428bec6e72f -data8 0xf19d7b686dcb03d7, 0x98554bbbf8a77902 -data8 0xbfed838fddab024b, 0xf1d0593311db1757 -data8 0x987571fffb7f94f6, 0xc016050c0420981a -data8 0xf20361ee8f1c711e, 0x9895b3791dd03c23 -data8 0xc03ea8cfabddc330, 0xf23695da7de51d3f -data8 0x98ab43a5fc65d0c8, 0xc059d3cbd65ddbce -data8 0xf258d095e465cc35, 0x98cbb2d196bd713d -data8 0xc082b122a3c78c9d, 0xf28c4d0bfc982b34 -data8 0x98ec3d9ec7b6f21a, 0xc0abb1499ae736c4 -data8 0xf2bff55eb3f0ea71, 0x990ce436db5e8344 -data8 0xc0d4d474c3aedaaf, 0xf2f3c9cf9884636e -data8 0x9922b8218160967a, 0xc0f054ca33eb3437 -data8 0xf31670135ab9cc0f, 0x99438d686f75779d -data8 0xc119b2c67e600ed0, 0xf34a8e9f0b54cdfb -data8 0x99647eea131fa20b, 0xc1433453de2033ff -data8 0xf37ed9fa6b8add3f, 0x997a85045a47c6d0 -data8 0xc15ef3e44e10032d, 0xf3a1cfe884ef6bb6 -data8 0x999ba5f14f8add02, 0xc188b130431d80e6 -data8 0xf3d66689dcc8e8d3, 0x99bce38b5465ecae -data8 0xc1b2929d6067730e, 0xf40b2ab069d5c96a -data8 0x99d31ca0887f30f9, 0xc1ce9268f31cc734 -data8 0xf42e718b90c8bc16, 0x99f48a669c74c09e -data8 0xc1f8b0877c1b0c08, 0xf463822a0a3b4b00 -data8 0x9a16154eb445c873, 0xc222f35a87b415ba -data8 0xf498c1076015faf8, 0x9a2c822ec198d667 -data8 0xc23f3467349e5c88, 0xf4bc5a19a33990b5 -data8 0x9a4e3e080cd91b78, 0xc269b4e40e088c01 -data8 0xf4f1e6a7d6f5425f, 0x9a70177afe52322e -data8 0xc2945aac24daaf6e, 0xf527a232cf6be334 -data8 0x9a86b8fa94eebe10, 0xc2b0de05e43c1d66 -data8 0xf54b8ecdcda90851, 0x9aa8c42866ae2958 -data8 0xc2dbc275e1229d09, 0xf5819949c7ad87b4 -data8 0x9abf86f9e12fc45e, 0xc2f86fca9d80eeff -data8 0xf5a5bac9213b48a9, 0x9ae1c462fc05f49d -data8 0xc323938449a2587e, 0xf5dc1501f324a812 -data8 0x9af8a8dc936b84d0, 0xc3406b40a538ed20 -data8 0xf6006bee86b5589e, 0x9b1b19033be35730 -data8 0xc36bcee8211d15e0, 0xf63716b2fa067fa4 -data8 0x9b3da7daf04c2892, 0xc397593adf2ba366 -data8 0xf66df22fb6132b9c, 0x9b54c2e4c8a9012b -data8 0xc3b475b6206155d5, 0xf6929fb98225deb1 -data8 0x9b77854e6c661200, 0xc3e0410243b97383 -data8 0xf6c9cd13021e3fea, 0x9b8ec2e678d56d2f -data8 0xc3fd890709833d37, 0xf6eeb177472cedae -data8 0x9ba60e6a5ca133b6, 0xc41ae295f7e7fa06 -data8 0xf713abf4cb0b3afb, 0x9bc919ea66a151a4 -data8 0xc44709f7bb8a4dd2, 0xf74b4d5333684ef1 -data8 0x9be0887c09ef82bb, 0xc4648fb0e0bec4c1 -data8 0xf7707f75a72f8e94, 0x9c03c8d5fffc3503 -data8 0xc490f9a94695ba14, 0xf7a874b97927af44 -data8 0x9c1b5ad21a81cbb9, 0xc4aeac0173b7d390 -data8 0xf7cddf140aedf1d8, 0x9c3ed09216e9ca02 -data8 0xc4db5941007aa853, 0xf806291bacb7f7a9 -data8 0x9c568656c0423def, 0xc4f938aec206291a -data8 0xf82bcc43b92eafef, 0x9c7a320af242ce60 -data8 0xc52629e899dfd622, 0xf8646bf0defb759e -data8 0x9c920bf7a8c01dc2, 0xc54436e44043b965 -data8 0xf88a487dfc3ff5f7, 0x9ca9f475d98b159c -data8 0xc562563abf9ea07f, 0xf8b03c2b46cdc17f -data8 0x9ccdeca60e80b5f8, 0xc58fa7d1dc42921c -data8 0xf8e95541c152ae7a, 0x9ce5f9d4653d4902 -data8 0xc5adf561b91e110a, 0xf90f832c2700c160 -data8 0x9cfe15cb38bfdd8e, 0xc5cc5591bdbd82fa -data8 0xf935c88e0c7f419b, 0x9d225b983f6c1f96 -data8 0xc5fa08f1ff20593c, 0xf96f5cd84fd86873 -data8 0x9d3a9cca32261ed7, 0xc618980a79ce6862 -data8 0xf995dd53ebdd9d6d, 0x9d52ecfccebe1768 -data8 0xc6373a09e34b50fa, 0xf9bc75a034436a41 -data8 0x9d77818d95b82f86, 0xc66550a6e0baaf35 -data8 0xf9f686f26d5518de, 0x9d8ff7893fa4706c -data8 0xc6842241926342c9, 0xfa1d5b39b910a8c5 -data8 0x9da87cbef36f2a5e, 0xc6a3070b7c93bb9e -data8 0xfa4447acc4ecbfd2, 0x9dcd6140b4a35aeb -data8 0xc6d18260bb84081b, 0xfa7ed7e51e6fdfb4 -data8 0x9de60cd06dc6e2d4, 0xc6f0977c9416828b -data8 0xfaa601394d49a1a0, 0x9dfec7d4cc43b76f -data8 0xc70fc0117c641630, 0xfacd431644ce0e40 -data8 0x9e17925ec9fccc4a, 0xc72efc34d7e615be -data8 0xfaf49d96f7a75909, 0x9e3cdf6db57dc075 -data8 0xc75dfb441594141e, 0xfb2fd3c65e562fd5 -data8 0x9e55d110b63637a8, 0xc77d68aa019bda4c -data8 0xfb576c5762024805, 0x9e6ed27594550d2e -data8 0xc79ce9ea478dbc4f, 0xfb7f1debc22c4040 -data8 0x9e87e3adc385d393, 0xc7bc7f1ae453219d -data8 0xfba6e89f32d0190a, 0x9ead9b54b37a1055 -data8 0xc7ec0476e15e141a, 0xfbe2c803a0894893 -data8 0x9ec6d46a3d7de215, 0xc80bcbe16f1d540f -data8 0xfc0ad1ff0ed9ecf0, 0x9ee01d9108be3154 -data8 0xc82ba78a5d349735, 0xfc32f57bdfbcbe7f -data8 0x9ef976db07288d04, 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 -ASM_SIZE_DIRECTIVE(T_table) - - - - - - -.align 32 -.global cbrt# +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 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0xfaf49d96f7a75909, 0x9e3cdf6db57dc075 + data8 0xc75dfb441594141e, 0xfb2fd3c65e562fd5 + data8 0x9e55d110b63637a8, 0xc77d68aa019bda4c + data8 0xfb576c5762024805, 0x9e6ed27594550d2e + data8 0xc79ce9ea478dbc4f, 0xfb7f1debc22c4040 + data8 0x9e87e3adc385d393, 0xc7bc7f1ae453219d + data8 0xfba6e89f32d0190a, 0x9ead9b54b37a1055 + data8 0xc7ec0476e15e141a, 0xfbe2c803a0894893 + data8 0x9ec6d46a3d7de215, 0xc80bcbe16f1d540f + data8 0xfc0ad1ff0ed9ecf0, 0x9ee01d9108be3154 + data8 0xc82ba78a5d349735, 0xfc32f57bdfbcbe7f + data8 0x9ef976db07288d04, 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 -.proc cbrt# -.align 32 -cbrt: - - -{ .mfi - // get significand - getf.sig r23=f8 - // will continue only for normal/denormal numbers - (p0) fclass.nm.unc p12,p0 = f8, 0x1b - // r2 = pointer to C_1,...,C_5 followed by T_table - addl r2 = @ltoff(poly_coeffs), gp +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 r24=f8 - // normalize a - fma.s1 f14=f8,f1,f0 - // r29=bias-((2^{12}-1)/3) -63=0xffff-0x555-0x3f=0xfa6b - mov r29=0xfa6b;; + // 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 r25=0x20000 - // r28=2^52 - movl r28=0x8000000000000000;; -} -{.mfb - // load start address for C_1,...,C_5 followed by T_table - ld8 r3=[r2] - (p12) fma.d.s0 f8=f8,f1,f0 - (p12) br.ret.spnt b0 + mov GR_CONST2 = 0x20000 + // GR_CONST3 = 2^52 + movl GR_CONST3 = 0x8000000000000000 ;; } + +.pred.rel "mutex", p12, p13 {.mfi - nop.m 0 - // y=frcpa(a) - frcpa.s0 f8,p6=f1,f8 - // p7=1 if denormal input - cmp.gtu p7,p0=r28,r23;; + // 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 - (p7) getf.exp r24=f14 - // get normalized significand - (p7) getf.sig r23=f14 - // r28=bias-(2^{12}-1) - mov r28=0xf000;; + // 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 r26=sign - and r26=r24,r25 - // eliminate leading 1 from r23=1st table index - shl r23=r23,1 - // eliminate sign from exponent (r25) - andcm r25=r24,r25;; + // 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 r2=32,r3 - // r23=1st table index (y_index,8 bits) - shr.u r23=r23,56 - nop.b 0 + 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 f7=[r3],16 - // subtract bias from r25=exponent - sub r25=r25,r28 - nop.b 0;; + // 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 f9,f10=[r3] - // 1: exponent*=5; // (2^{16}-1)/3=0x5555 - shladd r24=r25,2,r25 - nop.b 0 + // 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 f11,f12=[r2],16 - // r23=3*y_index - shladd r23=r23,1,r23 - nop.b 0;; + // 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 - // r30=(5*expon)*16+5*expon=(0x55)*expon - shladd r30=r24,4,r24 - // r=1-a*y - (p6) fnma.s1 f6=f8,f14,f1 - // adjust T_table pointer by 1st index - shladd r2=r23,3,r2;; + // 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 - nop.m 0 - // r24=(0x5500)*expon - shl r24=r30,8;; - // r24=(0x5555)*expon - add r24=r24,r30;; + // 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 - // r24=(0x5556)*expon // 0x5556=(2^{16}+2)/3 - add r24=r24,r25 - nop.i 0;; - // r24=floor(expon/3) - shr r24=r24,16;; + // 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 - // r28=3*exponent - shladd r28=r24,1,r24 - // r2=r*r - (p6) fma.s1 f13=f6,f6,f0 - // bias exponent - add r24=r29,r24;; + // 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 : r25-r28 - sub r25=r25,r28 - // c2+c3*r - (p6) fma.s1 f9=f10,f6,f9 - // add sign to exponent - or r24=r24,r26 + // 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 - nop.m 0 - // c4+c5*r - (p6) fma.s1 f11=f12,f6,f11 - nop.i 0;; + // 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 - // f14=sign*2^{exponent/3} - (p6) setf.exp f14=r24 - // adjust T_table pointer by 2nd index - shladd r2=r25,3,r2 - nop.i 0;; + // 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 - // load T - (p6) ldf8 f8=[r2] - nop.m 0 - nop.i 0;; + // 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) - (p6) fma.s1 f9=f11,f13,f9 - nop.i 0 + 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 - (p6) fma.s1 f7=f7,f6,f0 - nop.i 0;; + 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)] - (p6) fma.s1 f9=f9,f13,f7 - nop.i 0 + 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) - (p6) fma.s1 f8=f8,f14,f0 - nop.i 0;; + 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 - (p6) fnma.d.s0 f8=f8,f9,f8 - br.ret.sptk b0;; + nop.m 0 + // result = T'+T'*P + fma.d.s0 f8 = f8, FR_P15, f8 + br.ret.sptk b0 ;; } -.endp cbrt -ASM_SIZE_DIRECTIVE(cbrt) + + +GLOBAL_LIBM_END(cbrt) |