diff options
Diffstat (limited to 'sysdeps/ia64/fpu/s_cbrtf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cbrtf.S | 1227 |
1 files changed, 565 insertions, 662 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrtf.S b/sysdeps/ia64/fpu/s_cbrtf.S index 612fb85ea3..20167797b8 100644 --- a/sysdeps/ia64/fpu/s_cbrtf.S +++ b/sysdeps/ia64/fpu/s_cbrtf.S @@ -1,10 +1,11 @@ -.file "cbrtf.s" +.file "cbrtf.asm" - -// Copyright (c) 2000 - 2003, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation +// +// 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. // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are @@ -20,30 +21,27 @@ // * 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://www.intel.com/software/products/opensource/libraries/num.htm. +// problem reports or change requests be submitted to it directly at +// http://developer.intel.com/opensource. // // 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 +// 2/02/00: Initial version +// 5/18/00: New version (modified algorithm) // // API //============================================================== @@ -55,711 +53,616 @@ // // 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) // -// cbrt(a)= cbrt(a*y)/cbrt(y) = cbrt(1 - (1-a*y)) * (1/cbrt(y)) +// where y = frcpa(a). // -// 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. // -// -// * 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 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 2^(e/3) where e is the exponent of the input number. +// 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 //============================================================== -// 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 - - +// f6-f15 +// r2, r23-r26, r28-r30 +// p6,p7,p8,p12 +#include "libm_support.h" // Data tables //============================================================== -RODATA +#ifdef _LIBC +.rodata +#else +.data +#endif .align 16 -LOCAL_OBJECT_START(poly_coeffs) - - data8 0xaaaab19b7e1f5ef9, 0x00003ffd // ~ 1/3 - data8 0xe38e5192a5a8e56c, 0x00003ffb // ~ 1/9 -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 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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 -LOCAL_OBJECT_END(T_table) - - - - - - +poly_coeffs: +ASM_TYPE_DIRECTIVE(poly_coeffs,@object) +data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // 1/3 +data8 0xe38e38e38e38e38e, 0x00003ffb // 1/9 +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, 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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 cbrtf# .section .text -GLOBAL_LIBM_ENTRY(cbrtf) +.proc cbrtf# +.align 32 +cbrtf: -{.mfi - getf.sig GR_SIGNIF = f8 - // will continue only for normal/denormal numbers - fclass.nm.unc p12, p7 = f8, 0x1b - // GR_GP = pointer to C_1, C_2 followed by T_table - nop.i 0 +{ .mfi + getf.sig r28=f8 + // will continue only for normal/denormal numbers +(p0) fclass.nm.unc p12,p7 = f8, 0x1b + // r2 = pointer to C_1,C_2 followed by T_table + addl r2 = @ltoff(poly_coeffs), gp } {.mfi - addl GR_GP = @ltoff(poly_coeffs), gp - // normalize a - fma.s1 FR_ARG = f8, f1, f0 - // GR_CT3 = bias-((2^8-1)/3) -63 = 0xffff-0x55-0x3f = 0xff6b - mov GR_CT3 = 0xff6b ;; -} - -{.mmi - // get exponent - getf.exp GR_ARGEXP = f8 - // load start address for C_1, C_2 followed by T_table - ld8 GR_ADDR = [ GR_GP ] - nop.i 0 ;; -} - -{.mlx - // check if input significand is 0 - (p7) cmp.eq p12, p7 = GR_SIGNIF, r0 - // GR_2P63 = 2^63 - movl GR_2P63 = 0x8000000000000000 ;; + // r29=bias-((2^8-1)/3) -63=0xffff-0x55-0x3f=0xff6b + mov r29=0xff6b + // normalize a + fma.s1 f14=f8,f1,f0 + nop.i 0;; } - -{.mfi - nop.m 0 - // y = frcpa(a) - // p7 = 1 for normal and denormal (but non-zero) arguments - (p7) frcpa.s0 FR_Y, p0 = f1, f8 - // p9 = 1 if denormal input - cmp.gtu p9, p0 = GR_2P63, GR_SIGNIF +{.mib + nop.m 0 + (p7) cmp.eq p12,p0=r28,r0 + nop.b 0;; } {.mfb - // load C_1 - ldfe FR_COEFF1 = [ GR_ADDR ], 16 - // if argument is 0, +/-Infinity, or NaN, return - (p12) fma.s.s0 f8 = f8, f1, f0 - (p12) br.ret.spnt b0 ;; + // load start address for C_1,C_2 followed by T_table + ld8 r2=[r2] + (p12) fma.s.s0 f8=f8,f1,f0 + (p12) br.ret.spnt b0;; +} +{.mmf + // load C_1 + ldfe f7=[r2],16 + nop.m 0 + // y=frcpa(a) + frcpa.s0 f8,p6=f1,f8;; } - {.mmi - // get normalized significand (for denormal inputs only) - (p9) getf.sig GR_SIGNIF = FR_ARG - // load C_2 - ldfe FR_COEFF2 = [ GR_ADDR ], 16 - // GR_CT2 = bias-(2^8-1) - mov GR_CT2 = 0xff00 + // load C_2 + ldfe f9=[r2],16 + // r28=bias-(2^8-1) + mov r28=0xff00 + nop.i 0;; } - -{.mii - // get exponent (for denormal inputs only) - (p9) getf.exp GR_ARGEXP = FR_ARG - nop.i 0 - mov GR_CONST = 0x20000 ;; +{.mmi + // get normalized significand + getf.sig r23=f14 + // get exponent + getf.exp r24=f14 + mov r25=0x20000;; } - - {.mii - // get GR_SIGN = sign - and GR_SIGN = GR_ARGEXP, GR_CONST - // eliminate leading 1 from GR_I1 = 1st table index - shl GR_I1 = GR_SIGNIF, 1 - // eliminate sign from exponent - andcm GR_EBIAS = GR_ARGEXP, GR_CONST ;; + // 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;; } - - {.mfi - // subtract bias from GR_EXP = exponent - sub GR_EXP = GR_EBIAS, GR_CT2 - // r = 1-a*y - fnma.s1 FR_R = FR_Y, FR_ARG, f1 - // GR_IT1 = 1st table index (y_index8 bits) - shr.u GR_IT1 = GR_I1, 56 ;; + // subtract bias from r25=exponent + sub r25=r25,r28 + // r=1-a*y + (p6) fnma.s1 f6=f8,f14,f1 + // r23=1st table index (y_index8 bits) + shr.u r23=r23,56;; } - - {.mii - // 1: exponent* = 5; // (2^{16}-1)/3 = 0x5555 - shladd GR_E5 = GR_EXP, 2, GR_EXP - // GR_IT1_3 = 3*y_index - shladd GR_IT1_3 = GR_IT1, 1, GR_IT1 - nop.i 0 ;; -} - - -{.mmi - // GR_TMP5 = (5*expon)*16+5*expon = (0x55)*expon - shladd GR_TMP5 = GR_E5, 4, GR_E5 - // adjust T_table pointer by 1st index - shladd GR_TP1 = GR_IT1_3, 3, GR_ADDR - nop.i 0 ;; + // 1: exponent*=5; // (2^{16}-1)/3=0x5555 + shladd r24=r25,2,r25 + // r23=3*y_index + shladd r23=r23,1,r23;; + // r30=(5*expon)*16+5*expon=(0x55)*expon + shladd r30=r24,4,r24;; } - - {.mmi - // FR_T0 = T [ 0 ] [ y ] - ldf8 FR_T0 = [ GR_TP1 ], 8 - // get 2^{-63} - mov GR_TMP63 = 0xffff + 63 - // GR_TMP = (0x5500)*expon - shl GR_TMP = GR_TMP5, 8 ;; + // adjust T_table pointer by 1st index + shladd r2=r23,3,r2;; + // f10=T[0][y] + (p6) ldf8 f10=[r2],8 + // r24=(0x5500)*expon + shl r24=r30,8;; } - - {.mfi - // FR_T1 = T [ 1 ] [ y ] - ldf8 FR_T1 = [ GR_TP1 ], 8 - // P_1 = C_1+C_2*r - fma.s1 FR_COEFF1 = FR_COEFF2, FR_R, FR_COEFF1 - // GR_TMP2 = (0x5555)*expon - add GR_TMP2 = GR_TMP, GR_TMP5 ;; + // f11=T[1][y] + (p6) ldf8 f11=[r2],8 + // P_1=C_1+C_2*r + (p6) fma.s1 f7=f9,f6,f7 + // r24=(0x5555)*expon + add r24=r24,r30;; } - - {.mmi - // GR_TMP3 = (0x5556)*expon // 0x5556 = (2^{16}+2)/3 - add GR_TMP3 = GR_TMP2, GR_EXP ;; - // FR_T2 = T [ 2 ] [ y ] - ldf8 FR_T2 = [ GR_TP1 ] - // GR_EXP3 = floor(expon/3) - shr GR_EXP3 = GR_TMP3, 16 ;; + // r24=(0x5556)*expon // 0x5556=(2^{16}+2)/3 + add r24=r24,r25;; + // f8=T[2][y] + (p6) ldf8 f8=[r2] + // r24=floor(expon/3) + shr r24=r24,16;; } - - {.mmi - setf.exp FR_2M63 = GR_TMP63 - // GR_TMP4 = 3*exponent - shladd GR_TMP4 = GR_EXP3, 1, GR_EXP3 - // bias exponent - add GR_EBIAS3 = GR_CT3, GR_EXP3 ;; -} - - -{.mmf - // get remainder of exponent/3 - sub GR_REM = GR_EXP, GR_TMP4 - // add sign to exponent - or GR_SEXP = GR_EBIAS3, GR_SIGN - // P_2 = -r*P_1 - fnma.s1 FR_R = FR_COEFF1, FR_R, f0 ;; + nop.m 0 + // r28=3*exponent + shladd r28=r24,1,r24 + // bias exponent + add r24=r29,r24;; } - - - {.mmi - // FR_ARG = sign*2^{exponent/3} - setf.exp FR_ARG = GR_SEXP - nop.m 0 - // remainder = 0 ? - // p7=1 if input exponent is 3*j (remainder is 0) - cmp.eq.unc p7, p8 = r0, GR_REM ;; + // get remainder of exponent/3 + sub r25=r25,r28 + // add sign to exponent + or r24=r24,r26 + nop.i 0;; +} +{.mfi + nop.m 0 + // P_2=-r*P_1 + (p6) fnma.s1 f6=f7,f6,f0 + // remainder=0 ? + (p6) cmp.eq.unc p7,p8=r0,r25;; } - - {.mfi - // remainder = 1 ? - // p8=1 if input exponent is 3*j+1 (remainder is 1) - // p12=1 if input exponent is 3*j+2 (remainder is 2) - (p8) cmp.eq.unc p8, p12 = 1, GR_REM - // p7=1 -> remainder = 0 -> use T = FR_T0 - (p7) fma.s1 f8 = FR_T0, FR_R, FR_T0 - // argument is of the form 2^(3*k) ? - // ( GR_I1 holds significand bits, without the leading 1) - or GR_I1 = GR_I1, GR_REM ;; + // f14=sign*2^{exponent/3} + (p6) setf.exp f14=r24 + nop.f 0 + // remainder = 1 ? + (p8) cmp.eq.unc p8,p12=1,r25;; } - - -.pred.rel "mutex", p12, p8 +.pred.rel "mutex",p7,p8 {.mfi - nop.m 0 - // p8=1 -> remainder = 1 -> use FR_T1 - (p8) fma.s1 f8 = FR_T1, FR_R, FR_T1 - // argument is of the form 2^(3*k) ? - cmp.eq p14, p7 = GR_I1, r0 + nop.m 0 + // remainder=0 -> use T=f10 + (p7) fma.s1 f8=f10,f6,f10 + nop.i 0 } - - {.mfi - nop.m 0 - // p12=1 -> remainder=2 -> result = T+T*P_2 - (p12) fma.s1 f8 = FR_T2, FR_R, FR_T2 - nop.i 0 ;; + nop.m 0 + // remainder =1 -> use f11 + (p8) fma.s1 f8=f11,f6,f11 + nop.i 0;; } - - -.pred.rel "mutex", p14, p7 {.mfi - nop.m 0 - // if argument is sgn*2^{3*(expon/3)} - (p14) fma.s.s0 f8 = FR_2M63, FR_ARG, f0 - nop.i 0 + nop.m 0 + // result=T+T*P_2 + (p12) fma.s.s0 f8=f8,f6,f8 + nop.i 0;; } {.mfb - nop.m 0 - // T* = sgn*2^{expon/3} - (p7) fma.s.s0 f8 = f8, FR_ARG, f0 - br.ret.sptk b0 ;; + nop.m 0 + // T*=sgn*2^{expon/3} + (p6) fma.s.s0 f8=f8,f14,f0 + br.ret.sptk b0;; } - - -GLOBAL_LIBM_END(cbrtf) - - - - +.endp cbrtf +ASM_SIZE_DIRECTIVE(cbrtf) |