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Diffstat (limited to 'sysdeps/ia64/fpu/s_cbrt.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_cbrt.S | 767 |
1 files changed, 0 insertions, 767 deletions
diff --git a/sysdeps/ia64/fpu/s_cbrt.S b/sysdeps/ia64/fpu/s_cbrt.S deleted file mode 100644 index 7a74ac19be..0000000000 --- a/sysdeps/ia64/fpu/s_cbrt.S +++ /dev/null @@ -1,767 +0,0 @@ -.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 - 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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 -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) |