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Diffstat (limited to 'sysdeps/ia64/fpu/e_acosl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_acosl.S | 2917 |
1 files changed, 736 insertions, 2181 deletions
diff --git a/sysdeps/ia64/fpu/e_acosl.S b/sysdeps/ia64/fpu/e_acosl.S index 4fd345bedd..ab1bbf41a7 100644 --- a/sysdeps/ia64/fpu/e_acosl.S +++ b/sysdeps/ia64/fpu/e_acosl.S @@ -1,10 +1,10 @@ .file "acosl.s" - -// Copyright (c) 2001 - 2003, Intel Corporation +// Copyright (C) 2000, 2001, Intel Corporation // All rights reserved. -// -// Contributed 2001 by the Intel Numerics Group, Intel Corporation +// +// Contributed 2/2/2000 by John Harrison, 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 @@ -20,2470 +20,1027 @@ // * 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 //============================================================== -// 08/28/01 New version -// 05/20/02 Cleaned up namespace and sf0 syntax -// 02/06/03 Reordered header: .section, .global, .proc, .align +// 2/02/00 Initial version +// 2/07/00 Modified calculation of acos_corr to correct acosl +// 4/04/00 Unwind support added +// 8/15/00 Bundle added after call to __libm_error_support to properly +// set [the previously overwritten] GR_Parameter_RESULT. +// 12/20/00 Set denormal flag properly. // // API //============================================================== -// long double acosl(long double) +// double-extended = acosl (double-extended) +// input floating point f8 +// output floating point f8 // -// Overview of operation +// Registers used //============================================================== -// Background // -// Implementation +// predicate registers used: +// p6 -> p12 // -// For |s| in [2^{-4}, sqrt(2)/2]: -// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52 -// acos(s)= pi/2-asin(t)-asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e. -// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1) -// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9) -// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table, -// along with the high and low parts of asin(t) (stored as two double precision -// values) +// floating-point registers used: +// f8 has input, then output +// f8 -> f15, f32 ->f99 // -// |s| in (sqrt(2)/2, sqrt(255/256)): -// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6.. -// acos(|s|)= asin(t)-asin(r) -// acos(-|s|)=pi-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2) -// To minimize accumulated errors, r is computed as -// r= (t*s)_s-t^2*y*z+z*y*(t^2-1+s^2)_s+z*y*(1-s^2)_s*x+z'*y*(1-s^2)*PS29+ -// +(t*s-(t*s)_s)+z*y*((t^2-1-(t^2-1+s^2)_s)+s^2)+z*y*(1-s^2-(1-s^2)_s)+ -// +ez*z'*y*(1-s^2)*(1-x), -// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits) -// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2 +// general registers used: +// r32 -> r48 // -// |s|<2^{-4}: evaluate asin(s) as 17-degree polynomial, return pi/2-asin(s) -// (or simply return pi/2-s, if|s|<2^{-64}) -// -// |s| in [sqrt(255/256), 1): acos(|s|)= asin(sqrt(1-s^2)) -// acos(-|s|)= pi-asin(sqrt(1-s^2)) -// use 17-degree polynomial for asin(sqrt(1-s^2)), -// 9-degree polynomial to evaluate sqrt(1-s^2) -// High order term is (pi)_high-(y*(1-s^2))_high, for s<0, -// or y*(1-s^2)_s, for s>0 -// - - - -// Registers used +// Overview of operation //============================================================== -// f6-f15, f32-f36 -// r2-r3, r23-r23 -// p6, p7, p8, p12 -// - - - GR_SAVE_B0= r33 - GR_SAVE_PFS= r34 - GR_SAVE_GP= r35 // This reg. can safely be used - GR_SAVE_SP= r36 - - GR_Parameter_X= r37 - GR_Parameter_Y= r38 - GR_Parameter_RESULT= r39 - GR_Parameter_TAG= r40 - - FR_X= f10 - FR_Y= f1 - FR_RESULT= f8 - - +// There are three paths +// 1. |x| < 2^-25 ACOS_TINY +// 2. 2^-25 <= |x| < 1/4 ACOS_POLY +// 3. 1/4 <= |x| < 1 ACOS_ATAN -RODATA - -.align 16 - -LOCAL_OBJECT_START(T_table) - -// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2), -// asin(t)_high (double precision), asin(t)_low (double precision) - -data8 0x80828692b71c4391, 0xff7ddcec2d87e879 -data8 0x3fb022bc0ae531a0, 0x3c9f599c7bb42af6 -data8 0x80869f0163d0b082, 0xff79cad2247914d3 -data8 0x3fb062dd26afc320, 0x3ca4eff21bd49c5c -data8 0x808ac7d5a8690705, 0xff75a89ed6b626b9 -data8 0x3fb0a2ff4a1821e0, 0x3cb7e33b58f164cc -data8 0x808f0112ad8ad2e0, 0xff7176517c2cc0cb -data8 0x3fb0e32279319d80, 0x3caee31546582c43 -data8 0x80934abba8a1da0a, 0xff6d33e949b1ed31 -data8 0x3fb12346b8101da0, 0x3cb8bfe463d087cd -data8 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0x3fe2aa64b32f7780, 0x3cba67314933077c -data8 0xba0dc64d126cc135, 0xd4564563ce924481 -data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec -data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8 -data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac -data8 0xbef78e31985291a9, 0xd19672e2182f78be -data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c -data8 0xc19368b2b0629572, 0xd02baca5427e436a -data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689 -data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d -data8 0x3fe4300c7e945020, 0x3cbd367143da6582 -data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a -data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63 -data8 0xca14e1b0622de526, 0xcbbe13773c3c5338 -data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c -data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9 -data8 0x3fe5206cc637e000, 0x3ce2798b38e54193 -data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0 -data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68 -data8 0xd3c0d9f50057adda, 0xc70901152d59d16b -data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab -data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828 -data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5 -data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02 -data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee -data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af -data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d -data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b -data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321 -data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91 -data8 0x3fe76840418978a0, 0x3ccda46e85432c3d -data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3 -data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3 -data8 0xf049183c3f53c39b, 0xbad848720223d3a8 -data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b -data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48 -data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f -data8 0xfa718f05adbf2c33, 0xb70432500286b185 -data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9 -data8 0xfff200c3f5489608, 0xb509e6454dca33cc -data8 0x3fe9211b54441080, 0x3cb789cb53515688 -// The following table entries are not used -//data8 0x82e138a0fac48700, 0xb3044a513a8e6132 -//data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0 -//data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88 -//data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039 -//data8 0x89377c1387d5b908, 0xaed58e9a09014d5c -//data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58 -//data8 0x8cad7a2c98dec333, 0xacab929ce114d451 -//data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f -//data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec -//data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5 -//data8 0x9446d8191f80dd42, 0xa82ff92687235baf -//data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e -//data8 0x98758ba086e4000a, 0xa5dd497a9c184f58 -//data8 0x3febb5f571cb0560, 0x3ce0c7774329a613 -//data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b -//data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177 -//data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03 -//data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959 -//data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec -//data8 0x3fece4f404e29b20, 0x3cea3413401132b5 -//data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c -//data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276 -//data8 0xb265c39cbd80f97a, 0x99553d969fec7beb -//data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2 -//data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c -//data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71 -//data8 0xbfea427678945732, 0x93d5990f9ee787af -//data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5 -//data8 0xc79611399b8c90c5, 0x90f72bde80febc31 -//data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56 -//data8 0xcffa8425040624d7, 0x8e02b4418574ebed -//data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f -//data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024 -//data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94 -//data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b -//data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc -//data8 0xeea6d733421da0a6, 0x84921bbe64ae029a -//data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02 -//data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6 -//data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3 -//data8 0x84ac1fcec4203245, 0xfb73a828893df19e -//data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de -//data8 0x8ca50621110c60e6, 0xf438a14c158d867c -//data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6 -//data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da -//data8 0x3ff1717418520340, 0x3ca5c2732533177c -//data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119 -//data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5 -//data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d -//data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a -//data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f -//data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7 -//data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec -//data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746 -//data8 0xdfe323b8653af367, 0xc19107d99ab27e42 -//data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02 -//data8 0xf93746caaba3e1f1, 0xb777744a9df03bff -//data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43 -//data8 0x8ca77052f6c340f0, 0xacaf476f13806648 -//data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff -//data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50 -//data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c -//data8 0xbe45074b05579024, 0x9478e362a07dd287 -//data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12 -//data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b -//data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69 -//data8 0x94503d69396d91c7, 0xedd2ce885ff04028 -//data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b -//data8 0xced1d96c5bb209e6, 0xc965278083808702 -//data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c -//data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd -//data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e -//data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4 -//data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb -LOCAL_OBJECT_END(T_table) - - - -.align 16 +#include "libm_support.h" -LOCAL_OBJECT_START(poly_coeffs) - // C_3 -data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc - // C_5 -data8 0x999999999999999a, 0x0000000000003ffb - // C_7, C_9 -data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8 - // pi/2 (low, high) -data8 0x3C91A62633145C07, 0x3FF921FB54442D18 - // C_11, C_13 -data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e - // C_15, C_17 -data8 0x3f8c99999999999a, 0x3f87a87878787223 - // pi (low, high) -data8 0x3CA1A62633145C07, 0x400921FB54442D18 -LOCAL_OBJECT_END(poly_coeffs) - - -R_DBL_S = r21 -R_EXP0 = r22 -R_EXP = r15 -R_SGNMASK = r23 -R_TMP = r24 -R_TMP2 = r25 -R_INDEX = r26 -R_TMP3 = r27 -R_TMP03 = r27 -R_TMP4 = r28 -R_TMP5 = r23 -R_TMP6 = r22 -R_TMP7 = r21 -R_T = r29 -R_BIAS = r20 - -F_T = f6 -F_1S2 = f7 -F_1S2_S = f9 -F_INV_1T2 = f10 -F_SQRT_1T2 = f11 -F_S2T2 = f12 -F_X = f13 -F_D = f14 -F_2M64 = f15 - -F_CS2 = f32 -F_CS3 = f33 -F_CS4 = f34 -F_CS5 = f35 -F_CS6 = f36 -F_CS7 = f37 -F_CS8 = f38 -F_CS9 = f39 -F_S23 = f40 -F_S45 = f41 -F_S67 = f42 -F_S89 = f43 -F_S25 = f44 -F_S69 = f45 -F_S29 = f46 -F_X2 = f47 -F_X4 = f48 -F_TSQRT = f49 -F_DTX = f50 -F_R = f51 -F_R2 = f52 -F_R3 = f53 -F_R4 = f54 - -F_C3 = f55 -F_C5 = f56 -F_C7 = f57 -F_C9 = f58 -F_P79 = f59 -F_P35 = f60 -F_P39 = f61 - -F_ATHI = f62 -F_ATLO = f63 - -F_T1 = f64 -F_Y = f65 -F_Y2 = f66 -F_ANDMASK = f67 -F_ORMASK = f68 -F_S = f69 -F_05 = f70 -F_SQRT_1S2 = f71 -F_DS = f72 -F_Z = f73 -F_1T2 = f74 -F_DZ = f75 -F_ZE = f76 -F_YZ = f77 -F_Y1S2 = f78 -F_Y1S2X = f79 -F_1X = f80 -F_ST = f81 -F_1T2_ST = f82 -F_TSS = f83 -F_Y1S2X2 = f84 -F_DZ_TERM = f85 -F_DTS = f86 -F_DS2X = f87 -F_T2 = f88 -F_ZY1S2S = f89 -F_Y1S2_1X = f90 -F_TS = f91 -F_PI2_LO = f92 -F_PI2_HI = f93 -F_S19 = f94 -F_INV1T2_2 = f95 -F_CORR = f96 -F_DZ0 = f97 - -F_C11 = f98 -F_C13 = f99 -F_C15 = f100 -F_C17 = f101 -F_P1113 = f102 -F_P1517 = f103 -F_P1117 = f104 -F_P317 = f105 -F_R8 = f106 -F_HI = f107 -F_1S2_HI = f108 -F_DS2 = f109 -F_Y2_2 = f110 -//F_S2 = f111 -//F_S_DS2 = f112 -F_S_1S2S = f113 -F_XL = f114 -F_2M128 = f115 -F_1AS = f116 -F_AS = f117 - - - -.section .text -GLOBAL_LIBM_ENTRY(acosl) - -{.mfi - // get exponent, mantissa (rounded to double precision) of s - getf.d R_DBL_S = f8 - // 1-s^2 - fnma.s1 F_1S2 = f8, f8, f1 - // r2 = pointer to T_table - addl r2 = @ltoff(T_table), gp -} - -{.mfi - // sign mask - mov R_SGNMASK = 0x20000 - nop.f 0 - // bias-63-1 - mov R_TMP03 = 0xffff-64;; -} - - -{.mfi - // get exponent of s - getf.exp R_EXP = f8 - nop.f 0 - // R_TMP4 = 2^45 - shl R_TMP4 = R_SGNMASK, 45-17 -} - -{.mlx - // load bias-4 - mov R_TMP = 0xffff-4 - // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1) - movl R_TMP2 = 0x7fcd413cccfe779a;; -} - - -{.mfi - // load 2^{-64} in FP register - setf.exp F_2M64 = R_TMP03 - nop.f 0 - // index = (0x7-exponent)|b1 b2.. b6 - extr.u R_INDEX = R_DBL_S, 46, 9 -} - -{.mfi - // get t = sign|exponent|b1 b2.. b6 1 x.. x - or R_T = R_DBL_S, R_TMP4 - nop.f 0 - // R_TMP4 = 2^45-1 - sub R_TMP4 = R_TMP4, r0, 1;; -} - - -{.mfi - // get t = sign|exponent|b1 b2.. b6 1 0.. 0 - andcm R_T = R_T, R_TMP4 - nop.f 0 - // eliminate sign from R_DBL_S (shift left by 1) - shl R_TMP3 = R_DBL_S, 1 -} - -{.mfi - // R_BIAS = 3*2^6 - mov R_BIAS = 0xc0 - nop.f 0 - // eliminate sign from R_EXP - andcm R_EXP0 = R_EXP, R_SGNMASK;; -} - - - -{.mfi - // load start address for T_table - ld8 r2 = [r2] - nop.f 0 - // p8 = 1 if |s|> = sqrt(2)/2 - cmp.geu p8, p0 = R_TMP3, R_TMP2 -} - -{.mlx - // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4) - cmp.lt p7, p0 = R_EXP0, R_TMP - // sqrt coefficient cs8 = -33*13/128 - movl R_TMP2 = 0xc0568000;; -} - - - -{.mbb - // load t in FP register - setf.d F_T = R_T - // if |s|<2^{-4}, take alternate path - (p7) br.cond.spnt SMALL_S - // if |s|> = sqrt(2)/2, take alternate path - (p8) br.cond.sptk LARGE_S -} - -{.mlx - // index = (4-exponent)|b1 b2.. b6 - sub R_INDEX = R_INDEX, R_BIAS - // sqrt coefficient cs9 = 55*13/128 - movl R_TMP = 0x40b2c000;; -} - - -{.mfi - // sqrt coefficient cs8 = -33*13/128 - setf.s F_CS8 = R_TMP2 - nop.f 0 - // shift R_INDEX by 5 - shl R_INDEX = R_INDEX, 5 -} - -{.mfi - // sqrt coefficient cs3 = 0.5 (set exponent = bias-1) - mov R_TMP4 = 0xffff - 1 - nop.f 0 - // sqrt coefficient cs6 = -21/16 - mov R_TMP6 = 0xbfa8;; -} - - -{.mlx - // table index - add r2 = r2, R_INDEX - // sqrt coefficient cs7 = 33/16 - movl R_TMP2 = 0x40040000;; -} - - -{.mmi - // load cs9 = 55*13/128 - setf.s F_CS9 = R_TMP - // sqrt coefficient cs5 = 7/8 - mov R_TMP3 = 0x3f60 - // sqrt coefficient cs6 = 21/16 - shl R_TMP6 = R_TMP6, 16;; -} - - -{.mmi - // load significand of 1/(1-t^2) - ldf8 F_INV_1T2 = [r2], 8 - // sqrt coefficient cs7 = 33/16 - setf.s F_CS7 = R_TMP2 - // sqrt coefficient cs4 = -5/8 - mov R_TMP5 = 0xbf20;; -} - - -{.mmi - // load significand of sqrt(1-t^2) - ldf8 F_SQRT_1T2 = [r2], 8 - // sqrt coefficient cs6 = 21/16 - setf.s F_CS6 = R_TMP6 - // sqrt coefficient cs5 = 7/8 - shl R_TMP3 = R_TMP3, 16;; -} - - -{.mmi - // sqrt coefficient cs3 = 0.5 (set exponent = bias-1) - setf.exp F_CS3 = R_TMP4 - // r3 = pointer to polynomial coefficients - addl r3 = @ltoff(poly_coeffs), gp - // sqrt coefficient cs4 = -5/8 - shl R_TMP5 = R_TMP5, 16;; -} - - -{.mfi - // sqrt coefficient cs5 = 7/8 - setf.s F_CS5 = R_TMP3 - // d = s-t - fms.s1 F_D = f8, f1, F_T - // set p6 = 1 if s<0, p11 = 1 if s> = 0 - cmp.ge p6, p11 = R_EXP, R_DBL_S -} - -{.mfi - // r3 = load start address to polynomial coefficients - ld8 r3 = [r3] - // s+t - fma.s1 F_S2T2 = f8, f1, F_T - nop.i 0;; -} - - -{.mfi - // sqrt coefficient cs4 = -5/8 - setf.s F_CS4 = R_TMP5 - // s^2-t^2 - fma.s1 F_S2T2 = F_S2T2, F_D, f0 - nop.i 0;; -} - - -{.mfi - // load C3 - ldfe F_C3 = [r3], 16 - // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2)) - fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 - nop.i 0;; -} - -{.mfi - // load C_5 - ldfe F_C5 = [r3], 16 - // set correct exponent for sqrt(1-t^2) - fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 - nop.i 0;; -} - - -{.mfi - // load C_7, C_9 - ldfpd F_C7, F_C9 = [r3], 16 - // x = -(s^2-t^2)/(1-t^2)/2 - fnma.s1 F_X = F_INV_1T2, F_S2T2, f0 - nop.i 0;; -} - - -{.mmf - // load asin(t)_high, asin(t)_low - ldfpd F_ATHI, F_ATLO = [r2] - // load pi/2 - ldfpd F_PI2_LO, F_PI2_HI = [r3] - // t*sqrt(1-t^2) - fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0;; -} - - -{.mfi - nop.m 0 - // cs9*x+cs8 - fma.s1 F_S89 = F_CS9, F_X, F_CS8 - nop.i 0 -} - -{.mfi - nop.m 0 - // cs7*x+cs6 - fma.s1 F_S67 = F_CS7, F_X, F_CS6 - nop.i 0;; -} - -{.mfi - nop.m 0 - // cs5*x+cs4 - fma.s1 F_S45 = F_CS5, F_X, F_CS4 - nop.i 0 -} - -{.mfi - nop.m 0 - // x*x - fma.s1 F_X2 = F_X, F_X, f0 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // (s-t)-t*x - fnma.s1 F_DTX = F_T, F_X, F_D - nop.i 0 -} - -{.mfi - nop.m 0 - // cs3*x+cs2 (cs2 = -0.5 = -cs3) - fms.s1 F_S23 = F_CS3, F_X, F_CS3 - nop.i 0;; -} - -{.mfi - nop.m 0 - // if sign is negative, negate table values: asin(t)_low - (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0 - nop.i 0 -} - -{.mfi - nop.m 0 - // if sign is negative, negate table values: asin(t)_high - (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // cs9*x^3+cs8*x^2+cs7*x+cs6 - fma.s1 F_S69 = F_S89, F_X2, F_S67 - nop.i 0 -} - -{.mfi - nop.m 0 - // x^4 - fma.s1 F_X4 = F_X2, F_X2, f0 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // t*sqrt(1-t^2)*x^2 - fma.s1 F_TSQRT = F_TSQRT, F_X2, f0 - nop.i 0 -} - -{.mfi - nop.m 0 - // cs5*x^3+cs4*x^2+cs3*x+cs2 - fma.s1 F_S25 = F_S45, F_X2, F_S23 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // ((s-t)-t*x)*sqrt(1-t^2) - fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0 - nop.i 0;; -} - -{.mfi - nop.m 0 - // (pi/2)_high - asin(t)_high - fnma.s1 F_ATHI = F_ATHI, f1, F_PI2_HI - nop.i 0 -} - -{.mfi - nop.m 0 - // asin(t)_low - (pi/2)_low - fnma.s1 F_ATLO = F_PI2_LO, f1, F_ATLO - nop.i 0;; -} - - -{.mfi - nop.m 0 - // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2 - fma.s1 F_S29 = F_S69, F_X4, F_S25 - nop.i 0;; -} - - - -{.mfi - nop.m 0 - // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29 - fnma.s1 F_R = F_S29, F_TSQRT, F_DTX - nop.i 0;; -} - - -{.mfi - nop.m 0 - // R^2 - fma.s1 F_R2 = F_R, F_R, f0 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // c7+c9*R^2 - fma.s1 F_P79 = F_C9, F_R2, F_C7 - nop.i 0 -} - -{.mfi - nop.m 0 - // c3+c5*R^2 - fma.s1 F_P35 = F_C5, F_R2, F_C3 - nop.i 0;; -} - -{.mfi - nop.m 0 - // R^3 - fma.s1 F_R4 = F_R2, F_R2, f0 - nop.i 0;; -} - -{.mfi - nop.m 0 - // R^3 - fma.s1 F_R3 = F_R2, F_R, f0 - nop.i 0;; -} - - - -{.mfi - nop.m 0 - // c3+c5*R^2+c7*R^4+c9*R^6 - fma.s1 F_P39 = F_P79, F_R4, F_P35 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fma.s1 F_P39 = F_P39, F_R3, F_ATLO - nop.i 0;; -} - - -{.mfi - nop.m 0 - // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fma.s1 F_P39 = F_P39, f1, F_R - nop.i 0;; -} - - -{.mfb - nop.m 0 - // result = (pi/2)-asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fnma.s0 f8 = F_P39, f1, F_ATHI - // return - br.ret.sptk b0;; -} - - - - -LARGE_S: - -{.mfi - // bias-1 - mov R_TMP3 = 0xffff - 1 - // y ~ 1/sqrt(1-s^2) - frsqrta.s1 F_Y, p7 = F_1S2 - // c9 = 55*13*17/128 - mov R_TMP4 = 0x10af7b -} - -{.mlx - // c8 = -33*13*15/128 - mov R_TMP5 = 0x184923 - movl R_TMP2 = 0xff00000000000000;; -} - -{.mfi - // set p6 = 1 if s<0, p11 = 1 if s>0 - cmp.ge p6, p11 = R_EXP, R_DBL_S - // 1-s^2 - fnma.s1 F_1S2 = f8, f8, f1 - // set p9 = 1 - cmp.eq p9, p0 = r0, r0;; -} - - -{.mfi - // load 0.5 - setf.exp F_05 = R_TMP3 - // (1-s^2) rounded to single precision - fnma.s.s1 F_1S2_S = f8, f8, f1 - // c9 = 55*13*17/128 - shl R_TMP4 = R_TMP4, 10 -} - -{.mlx - // AND mask for getting t ~ sqrt(1-s^2) - setf.sig F_ANDMASK = R_TMP2 - // OR mask - movl R_TMP2 = 0x0100000000000000;; -} - -.pred.rel "mutex", p6, p11 -{.mfi - nop.m 0 - // 1-|s| - (p6) fma.s1 F_1AS = f8, f1, f1 - nop.i 0 -} - -{.mfi - nop.m 0 - // 1-|s| - (p11) fnma.s1 F_1AS = f8, f1, f1 - nop.i 0;; -} - - -{.mfi - // c9 = 55*13*17/128 - setf.s F_CS9 = R_TMP4 - // |s| - (p6) fnma.s1 F_AS = f8, f1, f0 - // c8 = -33*13*15/128 - shl R_TMP5 = R_TMP5, 11 -} +// Assembly macros +//============================================================== -{.mfi - // c7 = 33*13/16 - mov R_TMP4 = 0x41d68 - // |s| - (p11) fma.s1 F_AS = f8, f1, f0 - nop.i 0;; -} +// f8 is input, but acos_V must be put in f8 +// when __libm_atan2_reg is called, f8 must get V +// f9 gets U when __libm_atan2_reg is called -{.mfi - setf.sig F_ORMASK = R_TMP2 - // y^2 - fma.s1 F_Y2 = F_Y, F_Y, f0 - // c7 = 33*13/16 - shl R_TMP4 = R_TMP4, 12 -} +// __libm_atan2_reg returns +// f8 = Z_hi +// f10 = Z_lo +// f11 = s_lo -{.mfi - // c6 = -33*7/16 - mov R_TMP6 = 0xc1670 - // y' ~ sqrt(1-s^2) - fma.s1 F_T1 = F_Y, F_1S2, f0 - // c5 = 63/8 - mov R_TMP7 = 0x40fc;; -} +acos_Z_hi = f8 +acos_Z_lo = f10 +acos_S_lo = f11 +// When we call __libm_atan2_reg, we must save +// the following: -{.mlx - // load c8 = -33*13*15/128 - setf.s F_CS8 = R_TMP5 - // c4 = -35/8 - movl R_TMP5 = 0xc08c0000;; -} +acos_corr = f12 +acos_X = f13 +acos_pi_hi = f14 +acos_pi_lo = f15 -{.mfi - // r3 = pointer to polynomial coefficients - addl r3 = @ltoff(poly_coeffs), gp - // 1-s-(1-s^2)_s - fnma.s1 F_DS = F_1S2_S, f1, F_1AS - // p9 = 0 if p7 = 1 (p9 = 1 for special cases only) - (p7) cmp.ne p9, p0 = r0, r0 -} +// The rest of the assembly macros + +acos_P79 = f32 +acos_P59 = f33 +acos_P39 = f34 +acos_P19 = f35 -{.mlx - // load c7 = 33*13/16 - setf.s F_CS7 = R_TMP4 - // c3 = 5/2 - movl R_TMP4 = 0x40200000;; -} +acos_P810 = f36 +acos_P610 = f37 +acos_P410 = f38 +acos_P210 = f39 +acos_A1 = f41 +acos_A2 = f42 +acos_A3 = f43 +acos_A4 = f44 +acos_A5 = f45 +acos_A6 = f46 +acos_A7 = f47 +acos_A8 = f48 +acos_A9 = f49 +acos_A10 = f50 -{.mlx - // load c4 = -35/8 - setf.s F_CS4 = R_TMP5 - // c2 = -3/2 - movl R_TMP5 = 0xbfc00000;; -} +acos_X2 = f51 +acos_X4 = f52 +acos_B = f53 +acos_Bb = f54 +acos_A = f55 +acos_Aa = f56 -{.mfi - // load c3 = 5/2 - setf.s F_CS3 = R_TMP4 - // x = (1-s^2)_s*y^2-1 - fms.s1 F_X = F_1S2_S, F_Y2, f1 - // c6 = -33*7/16 - shl R_TMP6 = R_TMP6, 12 -} +acos_1mA = f57 -{.mfi - nop.m 0 - // y^2/2 - fma.s1 F_Y2_2 = F_Y2, F_05, f0 - nop.i 0;; -} +acos_W = f58 +acos_Ww = f59 +acos_y0 = f60 +acos_y1 = f61 +acos_y2 = f62 -{.mfi - // load c6 = -33*7/16 - setf.s F_CS6 = R_TMP6 - // eliminate lower bits from y' - fand F_T = F_T1, F_ANDMASK - // c5 = 63/8 - shl R_TMP7 = R_TMP7, 16 -} +acos_H = f63 +acos_Hh = f64 +acos_t1 = f65 +acos_t2 = f66 +acos_t3 = f67 +acos_t4 = f68 +acos_t5 = f69 -{.mfb - // r3 = load start address to polynomial coefficients - ld8 r3 = [r3] - // 1-(1-s^2)_s-s^2 - fma.s1 F_DS = F_AS, F_1AS, F_DS - // p9 = 1 if s is a special input (NaN, or |s|> = 1) - (p9) br.cond.spnt acosl_SPECIAL_CASES;; -} +acos_Pseries = f70 +acos_NORM_f8 = f71 +acos_ABS_NORM_f8 = f72 -{.mmf - // get exponent, significand of y' (in single prec.) - getf.s R_TMP = F_T1 - // load c3 = -3/2 - setf.s F_CS2 = R_TMP5 - // y*(1-s^2) - fma.s1 F_Y1S2 = F_Y, F_1S2, f0;; -} +acos_2 = f73 +acos_P1P2 = f74 +acos_HALF = f75 +acos_U = f76 +acos_1mB = f77 +acos_V = f78 +acos_S = f79 +acos_BmUU = f80 +acos_BmUUpb = f81 +acos_2U = f82 +acos_1d2U = f83 -{.mfi - nop.m 0 - // if s<0, set s = -s - (p6) fnma.s1 f8 = f8, f1, f0 - nop.i 0;; -} - - -{.mfi - // load c5 = 63/8 - setf.s F_CS5 = R_TMP7 - // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2 - fma.s1 F_X = F_DS, F_Y2, F_X - // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6 - extr.u R_INDEX = R_TMP, 17, 9;; -} +acos_Dd = f84 +acos_pi_by_2_hi = f85 +acos_pi_by_2_lo = f86 +acos_xmpi_by_2_lo = f87 +acos_xPmw = f88 -{.mmi - // index = (4-exponent)|b1 b2.. b6 - sub R_INDEX = R_INDEX, R_BIAS - nop.m 0 - // get exponent of y - shr.u R_TMP2 = R_TMP, 23;; -} - -{.mmi - // load C3 - ldfe F_C3 = [r3], 16 - // set p8 = 1 if y'<2^{-4} - cmp.gt p8, p0 = 0x7b, R_TMP2 - // shift R_INDEX by 5 - shl R_INDEX = R_INDEX, 5;; -} +acos_Uu = f89 +acos_AmVV = f90 +acos_AmVVpa = f91 +acos_2V = f92 +acos_1d2V = f93 +acos_Vv = f94 -{.mfb - // get table index for sqrt(1-t^2) - add r2 = r2, R_INDEX - // get t = 2^k*1.b1 b2.. b7 1 - for F_T = F_T, F_ORMASK - (p8) br.cond.spnt VERY_LARGE_INPUT;; -} - - - -{.mmf - // load C5 - ldfe F_C5 = [r3], 16 - // load 1/(1-t^2) - ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16 - // x = ((1-s^2)*y^2-1)/2 - fma.s1 F_X = F_X, F_05, f0;; -} - +acos_Vu = f95 +acos_Uv = f96 + +acos_2_Z_hi = f97 +acos_s_lo_Z_lo = f98 +acos_result_lo = f99 + +acos_Z_hi = f8 +acos_Z_lo = f10 +acos_s_lo = f11 + +acos_GR_17_ones = r33 +acos_GR_16_ones = r34 +acos_GR_signexp_f8 = r35 +acos_GR_exp = r36 +acos_GR_true_exp = r37 +acos_GR_fffe = r38 + +GR_SAVE_PFS = r43 +GR_SAVE_B0 = r39 +GR_SAVE_GP = r41 + +// r40 is address of table of coefficients +// r42 + +GR_Parameter_X = r44 +GR_Parameter_Y = r45 +GR_Parameter_RESULT = r46 +GR_Parameter_TAG = r47 + + +// 2^-40: +// A true exponent of -40 is +// : -40 + register_bias +// : -28 + ffff = ffd7 +// A true exponent of 1 is +// : 1 + register_bias +// : 1 + ffff = 10000 -{.mmf - nop.m 0 - // C7, C9 - ldfpd F_C7, F_C9 = [r3], 16 - // set correct exponent for t - fmerge.se F_T = F_T1, F_T;; -} +// Data tables +//============================================================== +#ifdef _LIBC +.rodata +#else +.data +#endif +.align 16 -{.mfi - // get address for loading pi - add r3 = 48, r3 - // c9*x+c8 - fma.s1 F_S89 = F_X, F_CS9, F_CS8 - nop.i 0 -} +acos_coefficients: +ASM_TYPE_DIRECTIVE(acos_coefficients,@object) +data8 0xc90fdaa22168c234, 0x00003FFF // pi_by_2_hi +data8 0xc4c6628b80dc1cd1, 0x00003FBF // pi_by_2_lo +data8 0xc90fdaa22168c234, 0x00004000 // pi_hi +data8 0xc4c6628b80dc1cd1, 0x00003FC0 // pi_lo + +data8 0xBB08911F2013961E, 0x00003FF8 // A10 +data8 0x981F1095A23A87D3, 0x00003FF8 // A9 +data8 0xBDF09C6C4177BCC6, 0x00003FF8 // A8 +data8 0xE4C3A60B049ACCEA, 0x00003FF8 // A7 +data8 0x8E2789F4E8A8F1AD, 0x00003FF9 // A6 +data8 0xB745D09B2B0E850B, 0x00003FF9 // A5 +data8 0xF8E38E3BC4C50920, 0x00003FF9 // A4 +data8 0xB6DB6DB6D89FCD81, 0x00003FFA // A3 +data8 0x99999999999AF376, 0x00003FFB // A2 +data8 0xAAAAAAAAAAAAAA71, 0x00003FFC // A1 +ASM_SIZE_DIRECTIVE(acos_coefficients) + + +.align 32 +.global acosl# +ASM_TYPE_DIRECTIVE(acosl#,@function) -{.mfi - nop.m 0 - // x^2 - fma.s1 F_X2 = F_X, F_X, f0 - nop.i 0;; -} +.section .text +.proc acosl# +.align 32 -{.mfi - // pi (low, high) - ldfpd F_PI2_LO, F_PI2_HI = [r3] - // y*(1-s^2)*x - fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 - nop.i 0 -} +acosl: -{.mfi - nop.m 0 - // c7*x+c6 - fma.s1 F_S67 = F_X, F_CS7, F_CS6 - nop.i 0;; +// After normalizing f8, get its true exponent +{ .mfi + alloc r32 = ar.pfs,1,11,4,0 +(p0) fnorm.s1 acos_NORM_f8 = f8 +(p0) mov acos_GR_17_ones = 0x1ffff } - -{.mfi - nop.m 0 - // 1-x - fnma.s1 F_1X = F_X, f1, f1 - nop.i 0 +{ .mmi +(p0) mov acos_GR_16_ones = 0xffff +(p0) addl r40 = @ltoff(acos_coefficients), gp + nop.i 999 } +;; -{.mfi - nop.m 0 - // c3*x+c2 - fma.s1 F_S23 = F_X, F_CS3, F_CS2 - nop.i 0;; +// Set denormal flag on denormal input with fcmp +{ .mfi + ld8 r40 = [r40] + fcmp.eq p6,p0 = f8,f0 + nop.i 999 } +;; -{.mfi - nop.m 0 - // 1-t^2 - fnma.s1 F_1T2 = F_T, F_T, f1 - nop.i 0 -} +// Load the constants pi_by_2 and pi. +// Each is stored as hi and lo values +// Also load the coefficients for ACOS_POLY -{.mfi - // load asin(t)_high, asin(t)_low - ldfpd F_ATHI, F_ATLO = [r2] - // c5*x+c4 - fma.s1 F_S45 = F_X, F_CS5, F_CS4 - nop.i 0;; +{ .mmi +(p0) ldfe acos_pi_by_2_hi = [r40],16 ;; +(p0) ldfe acos_pi_by_2_lo = [r40],16 + nop.i 999 ;; } - - -{.mfi - nop.m 0 - // t*s - fma.s1 F_TS = F_T, f8, f0 - nop.i 0 +{ .mmi +(p0) ldfe acos_pi_hi = [r40],16 ;; +(p0) ldfe acos_pi_lo = [r40],16 + nop.i 999 ;; } -{.mfi - nop.m 0 - // 0.5/(1-t^2) - fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 - nop.i 0;; +{ .mmi +(p0) ldfe acos_A10 = [r40],16 ;; +(p0) ldfe acos_A9 = [r40],16 + nop.i 999 ;; } -{.mfi - nop.m 0 - // z~sqrt(1-t^2), rounded to 24 significant bits - fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0 - nop.i 0 +// Take the absolute value of f8 +{ .mmf + nop.m 999 +(p0) getf.exp acos_GR_signexp_f8 = acos_NORM_f8 +(p0) fmerge.s acos_ABS_NORM_f8 = f0, acos_NORM_f8 } -{.mfi - nop.m 0 - // sqrt(1-t^2) - fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 - nop.i 0;; +{ .mii +(p0) ldfe acos_A8 = [r40],16 + nop.i 999 ;; +(p0) and acos_GR_exp = acos_GR_signexp_f8, acos_GR_17_ones ;; } +// case 1: |x| < 2^-25 ==> p6 ACOS_TINY +// case 2: 2^-25 <= |x| < 2^-2 ==> p8 ACOS_POLY +// case 3: 2^-2 <= |x| < 1 ==> p9 ACOS_ATAN +// case 4: 1 <= |x| ==> p11 ACOS_ERROR_RETURN +// Admittedly |x| = 1 is not an error but this is where that case is +// handled. -{.mfi - nop.m 0 - // y*(1-s^2)*x^2 - fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 - nop.i 0 +{ .mii +(p0) ldfe acos_A7 = [r40],16 +(p0) sub acos_GR_true_exp = acos_GR_exp, acos_GR_16_ones ;; +(p0) cmp.ge.unc p6, p7 = -26, acos_GR_true_exp ;; } -{.mfi - nop.m 0 - // x^4 - fma.s1 F_X4 = F_X2, F_X2, f0 - nop.i 0;; +{ .mii +(p0) ldfe acos_A6 = [r40],16 +(p7) cmp.ge.unc p8, p9 = -3, acos_GR_true_exp ;; +(p9) cmp.ge.unc p10, p11 = -1, acos_GR_true_exp } - -{.mfi - nop.m 0 - // s*t rounded to 24 significant bits - fma.s.s1 F_TSS = F_T, f8, f0 - nop.i 0 -} - -{.mfi - nop.m 0 - // c9*x^3+..+c6 - fma.s1 F_S69 = F_X2, F_S89, F_S67 - nop.i 0;; +{ .mmi +(p0) ldfe acos_A5 = [r40],16 ;; +(p0) ldfe acos_A4 = [r40],16 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // ST = (t^2-1+s^2) rounded to 24 significant bits - fms.s.s1 F_ST = f8, f8, F_1T2 - nop.i 0 +{ .mmi +(p0) ldfe acos_A3 = [r40],16 ;; +(p0) ldfe acos_A2 = [r40],16 + nop.i 999 ;; } -{.mfi - nop.m 0 - // c5*x^3+..+c2 - fma.s1 F_S25 = F_X2, F_S45, F_S23 - nop.i 0;; +// ACOS_ERROR_RETURN ==> p11 is true +// case 4: |x| >= 1 +{ .mib +(p0) ldfe acos_A1 = [r40],16 + nop.i 999 +(p11) br.spnt L(ACOS_ERROR_RETURN) ;; } - -{.mfi - nop.m 0 - // 0.25/(1-t^2) - fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0 - nop.i 0 +// ACOS_TINY ==> p6 is true +// case 1: |x| < 2^-25 +{ .mfi + nop.m 999 +(p6) fms.s1 acos_xmpi_by_2_lo = acos_NORM_f8,f1, acos_pi_by_2_lo + nop.i 999 ;; } -{.mfi - nop.m 0 - // t*s-sqrt(1-t^2)*(1-s^2)*y - fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS - nop.i 0;; +{ .mfb + nop.m 999 +(p6) fms.s0 f8 = acos_pi_by_2_hi,f1, acos_xmpi_by_2_lo +(p6) br.ret.spnt b0 ;; } -{.mfi - nop.m 0 - // z*0.5/(1-t^2) - fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0 - nop.i 0 -} -{.mfi - nop.m 0 - // z^2+t^2-1 - fms.s1 F_DZ0 = F_Z, F_Z, F_1T2 - nop.i 0;; +// ACOS_POLY ==> p8 is true +// case 2: 2^-25 <= |x| < 2^-2 +{ .mfi + nop.m 999 +(p8) fms.s1 acos_W = acos_pi_by_2_hi, f1, acos_NORM_f8 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // (1-s^2-(1-s^2)_s)*x - fma.s1 F_DS2X = F_X, F_DS, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_X2 = f8,f8, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // t*s-(t*s)_s - fms.s1 F_DTS = F_T, f8, F_TSS - nop.i 0 +{ .mfi + nop.m 999 +(p8) fms.s1 acos_Ww = acos_pi_by_2_hi, f1, acos_W + nop.i 999 ;; } -{.mfi - nop.m 0 - // c9*x^7+..+c2 - fma.s1 F_S29 = F_X4, F_S69, F_S25 - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_X4 = acos_X2,acos_X2, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // y*z - fma.s1 F_YZ = F_Z, F_Y, f0 - nop.i 0 +{ .mfi + nop.m 999 +(p8) fms.s1 acos_Ww = acos_Ww, f1, acos_NORM_f8 + nop.i 999 ;; } -{.mfi - nop.m 0 - // t^2 - fma.s1 F_T2 = F_T, F_T, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P810 = acos_X4, acos_A10, acos_A8 + nop.i 999 } - -{.mfi - nop.m 0 - // 1-t^2+ST - fma.s1 F_1T2_ST = F_ST, f1, F_1T2 - nop.i 0;; +// acos_P79 = X4*A9 + A7 +// acos_P810 = X4*A10 + A8 +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P79 = acos_X4, acos_A9, acos_A7 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // y*(1-s^2)(1-x) - fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0 - nop.i 0 +{ .mfi + nop.m 999 +(p8) fma.s1 acos_Ww = acos_Ww, f1, acos_pi_by_2_lo + nop.i 999 ;; } -{.mfi - nop.m 0 - // dz ~ sqrt(1-t^2)-z - fma.s1 F_DZ = F_DZ0, F_ZE, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P610 = acos_X4, acos_P810, acos_A6 + nop.i 999 } -{.mfi - nop.m 0 - // -1+correction for sqrt(1-t^2)-z - fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0 - nop.i 0;; +// acos_P59 = X4*(X4*A9 + A7) + A5 +// acos_P610 = X4*(X4*A10 + A8) + A6 +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P59 = acos_X4, acos_P79, acos_A5 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // (PS29*x^2+x)*y*(1-s^2) - fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P410 = acos_X4, acos_P610, acos_A4 + nop.i 999 } -{.mfi - nop.m 0 - // z*y*(1-s^2)_s - fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0 - nop.i 0 +// acos_P39 = X4*(X4*(X4*A9 + A7) + A5) + A3 +// acos_P410 = X4*(X4*(X4*A10 + A8) + A6) + A4 +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P39 = acos_X4, acos_P59, acos_A3 + nop.i 999 ;; } -{.mfi - nop.m 0 - // s^2-(1-t^2+ST) - fms.s1 F_1T2_ST = f8, f8, F_1T2_ST - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P210 = acos_X4, acos_P410, acos_A2 + nop.i 999 } - -{.mfi - nop.m 0 - // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x - fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS - nop.i 0 +// acos_P19 = X4*(X4*(X4*(X4*A9 + A7) + A5) + A3) + A1 = P1 +// acos_P210 = X4*(X4*(X4*(X4*A10 + A8) + A6) + A4) + A2 = P2 +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P19 = acos_X4, acos_P39, acos_A1 + nop.i 999 ;; } -{.mfi - nop.m 0 - // dz*y*(1-s^2)*(1-x) - fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0 - nop.i 0;; +// acos_P1P2 = Xsq*P2 + P1 +// acos_P1P2 = Xsq*(Xsq*P2 + P1) +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P1P2 = acos_X2, acos_P210, acos_P19 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19 - // (used for polynomial evaluation) - fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS - nop.i 0;; +{ .mfi + nop.m 999 +(p8) fma.s1 acos_P1P2 = acos_X2, acos_P1P2, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // (PS29*x^2)*y*(1-s^2) - fma.s1 F_S29 = F_Y1S2X2, F_S29, f0 - nop.i 0 +{ .mfi + nop.m 999 +(p8) fms.s1 acos_xPmw = acos_NORM_f8, acos_P1P2, acos_Ww + nop.i 999 ;; } -{.mfi - nop.m 0 - // apply correction to dz*y*(1-s^2)*(1-x) - fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM - nop.i 0;; +{ .mfb + nop.m 999 +(p8) fms.s0 f8 = acos_W, f1, acos_xPmw +(p8) br.ret.spnt b0 ;; } -{.mfi - nop.m 0 - // R^2 - fma.s1 F_R2 = F_R, F_R, f0 - nop.i 0;; -} +// ACOS_ATAN +// case 3: 2^-2 <= |x| < 1 +// case 3: 2^-2 <= |x| < 1 ==> p9 ACOS_ATAN +// Step 1.1: Get A,B and a,b +// A + a = 1- |X| +// B + b = 1+ |X| +// Note also that we will use acos_corr (f13) +// and acos_W -{.mfi - nop.m 0 - // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x) - fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS - nop.i 0;; -} +// Step 2 +// Call __libm_atan2_reg -{.mfi - nop.m 0 - // c7+c9*R^2 - fma.s1 F_P79 = F_C9, F_R2, F_C7 - nop.i 0 -} - -{.mfi - nop.m 0 - // c3+c5*R^2 - fma.s1 F_P35 = F_C5, F_R2, F_C3 - nop.i 0;; +{ .mfi +(p0) mov acos_GR_fffe = 0xfffe +(p0) fma.s1 acos_B = f1,f1, acos_ABS_NORM_f8 +(p0) mov GR_SAVE_B0 = b0 ;; } -{.mfi - nop.m 0 - // asin(t)_low-(pi)_low (if s<0) - (p6) fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO - nop.i 0 +{ .mmf +(p0) mov GR_SAVE_GP = gp + nop.m 999 +(p0) fms.s1 acos_A = f1,f1, acos_ABS_NORM_f8 } -{.mfi - nop.m 0 - // R^4 - fma.s1 F_R4 = F_R2, F_R2, f0 - nop.i 0;; +{ .mfi +(p0) setf.exp acos_HALF = acos_GR_fffe + nop.f 999 + nop.i 999 ;; } -{.mfi - nop.m 0 - // R^3 - fma.s1 F_R3 = F_R2, F_R, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fms.s1 acos_1mB = f1,f1, acos_B + nop.i 999 ;; } +// We want atan2(V,U) +// so put V in f8 and U in f9 +// but save X in acos_X -{.mfi - nop.m 0 - // (t*s)_s-t^2*y*z - fnma.s1 F_TSS = F_T2, F_YZ, F_TSS - nop.i 0 -} - -{.mfi - nop.m 0 - // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) - fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fmerge.se acos_X = f8, f8 + nop.i 999 ;; } +// Step 1.2: +///////////////////////// +// Get U = sqrt(B) +///////////////////////// -{.mfi - nop.m 0 - // (pi)_hi-asin(t)_hi (if s<0) - (p6) fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI - nop.i 0 +{ .mfi + nop.m 999 +(p0) frsqrta.s1 acos_y0,p8 = acos_B + nop.i 999 } -{.mfi - nop.m 0 - // c3+c5*R^2+c7*R^4+c9*R^6 - fma.s1 F_P39 = F_P79, F_R4, F_P35 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fms.s1 acos_1mA = f1,f1, acos_A + nop.i 999 ;; } - -{.mfi - nop.m 0 - // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+ - // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 - fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_Bb = acos_1mB,f1, acos_ABS_NORM_f8 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // (t*s)_s-t^2*y*z+z*y*ST - fma.s1 F_TSS = F_YZ, F_ST, F_TSS - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_Hh = acos_HALF, acos_B, f0 + nop.i 999 ;; } -{.mfi - nop.m 0 - // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fms.s1 F_P39 = F_P39, F_R3, F_ATLO - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_t1 = acos_y0, acos_y0, f0 + nop.i 999 } - -{.mfi - nop.m 0 - // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + - // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + - // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fms.s1 acos_Aa = acos_1mA,f1, acos_ABS_NORM_f8 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + - // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x + - // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_t2 = acos_t1, acos_Hh, acos_HALF + nop.i 999 ;; } - -{.mfi - nop.m 0 - // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) + - // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x + - // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) + - // + (t*s)_s-t^2*y*z+z*y*ST - fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_y1 = acos_t2, acos_y0, acos_y0 + nop.i 999 } -.pred.rel "mutex", p6, p11 -{.mfi - nop.m 0 - // result: add high part of table value - // s>0 in this case - (p11) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI - nop.i 0 +// Step 1.2: +///////////////////////// +// Get V = sqrt(A) +///////////////////////// +{ .mfi + nop.m 999 +(p0) frsqrta.s1 acos_y0,p8 = acos_A + nop.i 999 ;; } -{.mfb - nop.m 0 - // result: add high part of pi-table value - // if s<0 - (p6) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI - br.ret.sptk b0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_t3 = acos_y1, acos_Hh, f0 + nop.i 999 ;; } - - - - - -SMALL_S: - - // use 15-term polynomial approximation - -{.mmi - // r3 = pointer to polynomial coefficients - addl r3 = @ltoff(poly_coeffs), gp;; - // load start address for coefficients - ld8 r3 = [r3] - mov R_TMP = 0x3fbf;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_t1 = acos_y0, acos_y0, f0 + nop.i 999 ;; } - -{.mmi - add r2 = 64, r3 - ldfe F_C3 = [r3], 16 - // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64) - cmp.lt p7, p0 = R_EXP0, R_TMP;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_t4 = acos_t3, acos_y1, acos_HALF + nop.i 999 ;; } -{.mmf - ldfe F_C5 = [r3], 16 - ldfpd F_C11, F_C13 = [r2], 16 - nop.f 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_y2 = acos_t4, acos_y1, acos_y1 + nop.i 999 ;; } -{.mmf - ldfpd F_C7, F_C9 = [r3], 16 - ldfpd F_C15, F_C17 = [r2] - nop.f 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_S = acos_B, acos_y2, f0 + nop.i 999 } - - -{.mfb - // load pi/2 - ldfpd F_PI2_LO, F_PI2_HI = [r3] - // s^2 - fma.s1 F_R2 = f8, f8, f0 - // |s|<2^{-64} - (p7) br.cond.spnt RETURN_PI2;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_H = acos_y2, acos_HALF, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // s^3 - fma.s1 F_R3 = f8, F_R2, f0 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_t5 = acos_Hh, acos_y2, f0 + nop.i 999 } -{.mfi - nop.m 0 - // s^4 - fma.s1 F_R4 = F_R2, F_R2, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_Hh = acos_HALF, acos_A, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c3+c5*s^2 - fma.s1 F_P35 = F_C5, F_R2, F_C3 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_Dd = acos_S, acos_S, acos_B + nop.i 999 ;; } -{.mfi - nop.m 0 - // c11+c13*s^2 - fma.s1 F_P1113 = F_C13, F_R2, F_C11 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_t2 = acos_t1, acos_Hh, acos_HALF + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c7+c9*s^2 - fma.s1 F_P79 = F_C9, F_R2, F_C7 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_U = acos_Dd, acos_H, acos_S + nop.i 999 ;; } -{.mfi - nop.m 0 - // c15+c17*s^2 - fma.s1 F_P1517 = F_C17, F_R2, F_C15 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_y1 = acos_t2, acos_y0, acos_y0 + nop.i 999 ;; } -{.mfi - nop.m 0 - // (pi/2)_high-s_high - fnma.s1 F_T = f8, f1, F_PI2_HI - nop.i 0 -} -{.mfi - nop.m 0 - // s^8 - fma.s1 F_R8 = F_R4, F_R4, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_2U = acos_U, f1, acos_U + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c3+c5*s^2+c7*s^4+c9*s^6 - fma.s1 F_P39 = F_P79, F_R4, F_P35 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_t3 = acos_y1, acos_Hh, f0 + nop.i 999 } -{.mfi - nop.m 0 - // c11+c13*s^2+c15*s^4+c17*s^6 - fma.s1 F_P1117 = F_P1517, F_R4, F_P1113 - nop.i 0;; -} -{.mfi - nop.m 0 - // -s_high - fms.s1 F_S = F_T, f1, F_PI2_HI - nop.i 0;; -} +// Step 1.3: +// sqrt(A + a) = V + v +// sqrt(B + b) = U + u -{.mfi - nop.m 0 - // c3+..+c17*s^14 - fma.s1 F_P317 = F_R8, F_P1117, F_P39 - nop.i 0;; -} +///////////////////////// +// Get u +///////////////////////// -{.mfi - nop.m 0 - // s_low - fma.s1 F_DS = f8, f1, F_S - nop.i 0;; -} - -{.mfi - nop.m 0 - // (pi/2)_low-s^3*(c3+..+c17*s^14) - fnma.s0 F_P317 = F_P317, F_R3, F_PI2_LO - nop.i 0;; -} +// acos_BmUU = B - UU +// acos_BmUUpb = (B - UU) + b -{.mfi - nop.m 0 - // (pi/2)_low-s_low-s^3*(c3+..+c17*s^14) - fms.s1 F_P317 = F_P317, f1, F_DS - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_BmUU = acos_U, acos_U, acos_B + nop.i 999 ;; } -{.mfb - nop.m 0 - // result: pi/2-s-c3*s^3-..-c17*s^17 - fma.s0 f8 = F_T, f1, F_P317 - br.ret.sptk b0;; +{ .mfi + nop.m 999 +(p0) fmerge.se f9 = acos_U, acos_U + nop.i 999 ;; } - - - - -RETURN_PI2: - -{.mfi - nop.m 0 - // (pi/2)_low-s - fms.s0 F_PI2_LO = F_PI2_LO, f1, f8 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_t4 = acos_t3, acos_y1, acos_HALF + nop.i 999 ;; } -{.mfb - nop.m 0 - // (pi/2)-s - fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO - br.ret.sptk b0;; +// acos_1d2U = frcpa(2U) +{ .mfi + nop.m 999 +(p0) frcpa.s1 acos_1d2U,p9 = f1, acos_2U + nop.i 999 } - - - - -VERY_LARGE_INPUT: - - -{.mmf - // pointer to pi_low, pi_high - add r2 = 80, r3 - // load C5 - ldfe F_C5 = [r3], 16 - // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2 - fma.s1 F_X = F_X, F_05, f0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_BmUUpb = acos_BmUU, f1, acos_Bb + nop.i 999 ;; } -.pred.rel "mutex", p6, p11 -{.mmf - // load pi (low, high), if s<0 - (p6) ldfpd F_PI2_LO, F_PI2_HI = [r2] - // C7, C9 - ldfpd F_C7, F_C9 = [r3], 16 - // if s>0, set F_PI2_LO=0 - (p11) fma.s1 F_PI2_HI = f0, f0, f0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_y2 = acos_t4, acos_y1, acos_y1 + nop.i 999 ;; } -{.mfi - nop.m 0 - (p11) fma.s1 F_PI2_LO = f0, f0, f0 - nop.i 0;; +{ .mfi + nop.m 999 +// acos_Uu = ((B - UU) + b) * frcpa(2U) +(p0) fma.s1 acos_Uu = acos_BmUUpb, acos_1d2U, f0 + nop.i 999 ;; } -{.mfi - // adjust address for C_11 - add r3 = 16, r3 - // c9*x+c8 - fma.s1 F_S89 = F_X, F_CS9, F_CS8 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_S = acos_A, acos_y2, f0 + nop.i 999 } -{.mfi - nop.m 0 - // x^2 - fma.s1 F_X2 = F_X, F_X, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_H = acos_y2, acos_HALF, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // y*(1-s^2)*x - fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_t5 = acos_Hh, acos_y2, f0 + nop.i 999 ;; } -{.mfi - // C11, C13 - ldfpd F_C11, F_C13 = [r3], 16 - // c7*x+c6 - fma.s1 F_S67 = F_X, F_CS7, F_CS6 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_Dd = acos_S, acos_S, acos_A + nop.i 999 ;; } - -{.mfi - // C15, C17 - ldfpd F_C15, F_C17 = [r3], 16 - // c3*x+c2 - fma.s1 F_S23 = F_X, F_CS3, F_CS2 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_V = acos_Dd, acos_H, acos_S + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c5*x+c4 - fma.s1 F_S45 = F_X, F_CS5, F_CS4 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_2V = acos_V, f1, acos_V + nop.i 999 } +// Step 3 +///////////////////////// +// Calculate the correction, acos_corr +///////////////////////// +// acos_corr = U*v - (V*u) - - -{.mfi - nop.m 0 - // y*(1-s^2)*x^2 - fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 - nop.i 0 -} - -{.mfi - nop.m 0 - // x^4 - fma.s1 F_X4 = F_X2, F_X2, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_Vu = acos_V,acos_Uu, f0 + nop.i 999 ;; } +///////////////////////// +// Get v +///////////////////////// +// acos_AmVV = A - VV +// acos_AmVVpa = (A - VV) + a -{.mfi - nop.m 0 - // c9*x^3+..+c6 - fma.s1 F_S69 = F_X2, F_S89, F_S67 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fnma.s1 acos_AmVV = acos_V, acos_V, acos_A + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c5*x^3+..+c2 - fma.s1 F_S25 = F_X2, F_S45, F_S23 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fmerge.se f8 = acos_V, acos_V + nop.i 999 ;; } - - -{.mfi - nop.m 0 - // (pi)_high-y*(1-s^2)_s - fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_AmVVpa = acos_AmVV, f1, acos_Aa + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c9*x^7+..+c2 - fma.s1 F_S29 = F_X4, F_S69, F_S25 - nop.i 0;; +// acos_1d2V = frcpa(2V) +{ .mfi + nop.m 999 +(p0) frcpa.s1 acos_1d2V,p9 = f1, acos_2V + nop.i 999 ;; } - -{.mfi - nop.m 0 - // -(y*(1-s^2)_s)_high - fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI - nop.i 0;; +// acos_Vv = ((A - VV) + a) * frcpa(2V) +{ .mfi + nop.m 999 +(p0) fma.s1 acos_Vv = acos_AmVVpa, acos_1d2V, f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // (PS29*x^2+x)*y*(1-s^2) - fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_Uv = acos_U,acos_Vv, f0 + nop.i 999 ;; } -{.mfi - nop.m 0 - // y*(1-s^2)_s-(y*(1-s^2))_high - fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI - nop.i 0;; -} +.endp acosl# +ASM_SIZE_DIRECTIVE(acosl#) - -{.mfi - nop.m 0 - // R ~ sqrt(1-s^2) - // (used for polynomial evaluation) - fnma.s1 F_R = F_S19, f1, F_Y1S2 - nop.i 0;; +.proc __libm_callout +__libm_callout: +.prologue +{ .mfi + nop.m 0 + nop.f 0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs } +;; - -{.mfi - nop.m 0 - // y*(1-s^2)-(y*(1-s^2))_high - fma.s1 F_DS2 = F_Y, F_DS, F_DS2 - nop.i 0 +{ .mfi + mov GR_SAVE_GP=gp + nop.f 0 +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 } -{.mfi - nop.m 0 - // (pi)_low+(PS29*x^2)*y*(1-s^2) - fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO - nop.i 0;; +.body +{ .mfb + nop.m 999 +(p0) fms.s1 acos_corr = acos_Uv,f1, acos_Vu +(p0) br.call.sptk.many b0=__libm_atan2_reg# ;; } -{.mfi - nop.m 0 - // R^2 - fma.s1 F_R2 = F_R, F_R, f0 - nop.i 0;; -} - +// p6 ==> X is negative +// p7 ==> x is positive +// We know that |X| >= 1/4 -{.mfi - nop.m 0 - // if s<0 - // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high) - fms.s1 F_S29 = F_S29, f1, F_DS2 - nop.i 0;; +{ .mfi +(p0) mov gp = GR_SAVE_GP +(p0) fcmp.lt.unc p6,p7 = acos_X , f0 +(p0) mov b0 = GR_SAVE_B0 ;; } +// acos_2_Z_hi = 2 * acos_Z_hi +// acos_s_lo_Z_lo = s_lo * Z_lo -{.mfi - nop.m 0 - // c7+c9*R^2 - fma.s1 F_P79 = F_C9, F_R2, F_C7 - nop.i 0 -} - -{.mfi - nop.m 0 - // c3+c5*R^2 - fma.s1 F_P35 = F_C5, F_R2, F_C3 - nop.i 0;; +{ .mfi + nop.m 999 +(p0) fma.s1 acos_2_Z_hi = acos_Z_hi, f1, acos_Z_hi +(p0) mov ar.pfs = GR_SAVE_PFS } - - -{.mfi - nop.m 0 - // R^4 - fma.s1 F_R4 = F_R2, F_R2, f0 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fma.s1 acos_s_lo_Z_lo = acos_s_lo, acos_Z_lo, f0 + nop.i 999 ;; } -{.mfi - nop.m 0 - // R^3 - fma.s1 F_R3 = F_R2, F_R, f0 - nop.i 0;; +// 2 is a constant needed later +{ .mfi + nop.m 999 +(p0) fma.s1 acos_2 = f1,f1,f1 + nop.i 999 ;; } +// X >= 1/4 +// acos_result_lo = 2(s_lo * Z_lo) - corr +// f8 = (2*Z_hi) + (2(s_lo * Z_lo) - corr) -{.mfi - nop.m 0 - // c11+c13*R^2 - fma.s1 F_P1113 = F_C13, F_R2, F_C11 - nop.i 0 +{ .mfi + nop.m 999 +(p7) fma.s1 acos_result_lo = acos_s_lo_Z_lo, acos_2, acos_corr + nop.i 999 ;; } -{.mfi - nop.m 0 - // c15+c17*R^2 - fma.s1 F_P1517 = F_C17, F_R2, F_C15 - nop.i 0;; +{ .mfi + nop.m 999 +(p7) fma.s0 f8 = acos_2_Z_hi, f1, acos_result_lo + nop.i 999 } - -{.mfi - nop.m 0 - // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x - fma.s1 F_S29 = F_Y1S2, F_X, F_S29 - nop.i 0;; +// acos_result_lo = (pi_lo - corr) +// acos_result_lo = (pi_lo - corr) + acos_Ww +{ .mfi + nop.m 999 +(p6) fms.s1 acos_result_lo = acos_pi_lo, f1, acos_corr + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c11+c13*R^2+c15*R^4+c17*R^6 - fma.s1 F_P1117 = F_P1517, F_R4, F_P1113 - nop.i 0 +// X <= -1/4 +// acos_W = pi_hi - 2 * Z_hi +{ .mfi + nop.m 999 +(p6) fnma.s1 acos_W = acos_2, acos_Z_hi, acos_pi_hi + nop.i 999 ;; } -{.mfi - nop.m 0 - // c3+c5*R^2+c7*R^4+c9*R^6 - fma.s1 F_P39 = F_P79, F_R4, F_P35 - nop.i 0;; +// acos_Ww = pi_hi - W +// acos_Ww = (pi_hi - W) + (2 * Z_hi) +{ .mfi + nop.m 999 +(p6) fms.s1 acos_Ww = acos_pi_hi, f1, acos_W + nop.i 999 ;; } - - -{.mfi - nop.m 0 - // R^8 - fma.s1 F_R8 = F_R4, F_R4, f0 - nop.i 0;; +{ .mfi + nop.m 999 +(p6) fms.s1 acos_Ww = acos_Ww, f1, acos_2_Z_hi + nop.i 999 ;; } - -{.mfi - nop.m 0 - // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14 - fma.s1 F_P317 = F_P1117, F_R8, F_P39 - nop.i 0;; +{ .mfi + nop.m 999 +(p6) fma.s1 acos_result_lo = acos_result_lo, f1, acos_Ww + nop.i 999 ;; } - -{.mfi - nop.m 0 - // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)- - // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17 - fnma.s1 F_S29 = F_P317, F_R3, F_S29 - nop.i 0;; +// acos_Z_lo = ((pi_lo - corr) + acos_Ww) - 2 * (s_lo * Z_lo) +{ .mfi + nop.m 999 +(p6) fnma.s1 acos_Z_lo = acos_s_lo_Z_lo, acos_2, acos_result_lo + nop.i 999 ;; } -.pred.rel "mutex", p6, p11 -{.mfi - nop.m 0 - // Result (if s<0): - // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)- - // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17 - // +(pi)_high-(y*(1-s^2))_high - (p6) fma.s0 f8 = F_S29, f1, F_HI - nop.i 0 +{ .mfb + nop.m 999 +(p6) fma.s0 f8 = acos_W, f1, acos_Z_lo +(p0) br.ret.sptk b0 ;; } +.endp __libm_callout +ASM_SIZE_DIRECTIVE(__libm_callout) -{.mfb - nop.m 0 - // Result (if s>0): - // (PS29*x^2)*y*(1-s^2)- - // -y*(1-s^2)*x + P3, 17 - // +(y*(1-s^2)) - (p11) fms.s0 f8 = F_Y, F_1S2_S, F_S29 - br.ret.sptk b0;; +.proc SPECIAL +SPECIAL: +L(ACOS_NAN): +{ .mfb + nop.m 999 +(p0) fma.s0 f8 = f8,f1,f0 +(p0) br.ret.sptk b0 ;; } +L(ACOS_ERROR_RETURN): +// Save ar.pfs, b0, and gp; restore on exit +// qnan snan inf norm unorm 0 -+ +// 1 1 0 0 0 0 11 = 0xc3 +// Coming in as X = +- 1 +// What should we return? +// If X is 1, return (sign of X)pi/2 -acosl_SPECIAL_CASES: - -{.mfi - alloc r32 = ar.pfs, 1, 4, 4, 0 - // check if the input is a NaN, or unsupported format - // (i.e. not infinity or normal/denormal) - fclass.nm p7, p8 = f8, 0x3f - // pointer to pi/2 - add r3 = 96, r3;; -} - - -{.mfi - // load pi/2 - ldfpd F_PI2_HI, F_PI2_LO = [r3] - // get |s| - fmerge.s F_S = f0, f8 - nop.i 0 -} - -{.mfb - nop.m 0 - // if NaN, quietize it, and return - (p7) fma.s0 f8 = f8, f1, f0 - (p7) br.ret.spnt b0;; -} - - -{.mfi - nop.m 0 - // |s| = 1 ? - fcmp.eq.s0 p9, p10 = F_S, f1 - nop.i 0 +{ .mfi + nop.m 999 +(p0) fcmp.eq.unc p6,p7 = acos_ABS_NORM_f8,f1 + nop.i 999 ;; } -{.mfi - nop.m 0 - // load FR_X - fma.s1 FR_X = f8, f1, f0 - // load error tag - mov GR_Parameter_TAG = 57;; +{ .mfi + nop.m 999 +(p6) fcmp.lt.unc p8,p9 = f8,f0 + nop.i 999 ;; } - -{.mfi - nop.m 0 - // if s = 1, result is 0 - (p9) fma.s0 f8 = f0, f0, f0 - // set p6=0 for |s|>1 - (p10) cmp.ne p6, p0 = r0, r0;; +{ .mfi + nop.m 999 +(p8) fma.s0 f8 = acos_pi_hi, f1, acos_pi_lo + nop.i 999 } - -{.mfb - nop.m 0 - // if s = -1, result is pi - (p6) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO - // return if |s| = 1 - (p9) br.ret.sptk b0;; +{ .mfb + nop.m 999 +(p9) fmerge.s f8 = f8,f0 +(p6) br.ret.spnt b0 ;; } - -{.mfi - nop.m 0 - // get Infinity - frcpa.s1 FR_RESULT, p0 = f1, f0 - nop.i 0;; +// If X is a NAN, leave +{ .mfi + nop.m 999 +(p0) fclass.m.unc p12,p0 = f8, 0xc3 + nop.i 999 ;; } - -{.mfb - nop.m 0 - // return QNaN indefinite (0*Infinity) - fma.s0 FR_RESULT = f0, FR_RESULT, f0 - nop.b 0;; +{ .mfb + nop.m 999 +(p12) fma.s0 f8 = f8,f1,f0 +(p12) br.ret.spnt b0 ;; } +{ .mfi +(p0) mov GR_Parameter_TAG = 57 +(p0) frcpa f10, p6 = f0, f0 +nop.i 999 +};; -GLOBAL_LIBM_END(acosl) - +.endp SPECIAL +ASM_SIZE_DIRECTIVE(SPECIAL) -LOCAL_LIBM_ENTRY(__libm_error_region) +.proc __libm_error_region +__libm_error_region: .prologue // (1) { .mfi @@ -2511,12 +1068,12 @@ LOCAL_LIBM_ENTRY(__libm_error_region) .body // (3) { .mib - stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack + stfe [GR_Parameter_X] = f8 // Store Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y nop.b 0 // Parameter 3 address } { .mib - stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack + stfe [GR_Parameter_Y] = f10 // Store Parameter 3 on stack add GR_Parameter_Y = -16,GR_Parameter_Y br.call.sptk b0=__libm_error_support# // Call error handling function };; @@ -2540,13 +1097,11 @@ LOCAL_LIBM_ENTRY(__libm_error_region) br.ret.sptk b0 // Return };; -LOCAL_LIBM_END(__libm_error_region) +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# - - - - - +.type __libm_atan2_reg#,@function +.global __libm_atan2_reg# |