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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, 2181 insertions, 736 deletions
diff --git a/sysdeps/ia64/fpu/e_acosl.S b/sysdeps/ia64/fpu/e_acosl.S index ab1bbf4..4fd345b 100644 --- a/sysdeps/ia64/fpu/e_acosl.S +++ b/sysdeps/ia64/fpu/e_acosl.S @@ -1,10 +1,10 @@ .file "acosl.s" -// Copyright (C) 2000, 2001, Intel Corporation + +// Copyright (c) 2001 - 2003, Intel Corporation // All rights reserved. -// -// 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. +// +// Contributed 2001 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 @@ -20,1027 +20,2470 @@ // * The name of Intel Corporation may not be used to endorse or promote // products derived from this software without specific prior written // permission. -// -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// // Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://developer.intel.com/opensource. +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. // // History //============================================================== -// 2/02/00 Initial version -// 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. +// 08/28/01 New version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/06/03 Reordered header: .section, .global, .proc, .align // // API //============================================================== -// double-extended = acosl (double-extended) -// input floating point f8 -// output floating point f8 +// long double acosl(long double) // -// Registers used +// Overview of operation //============================================================== +// Background // -// predicate registers used: -// p6 -> p12 +// Implementation // -// floating-point registers used: -// f8 has input, then output -// f8 -> f15, f32 ->f99 +// 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) // -// general registers used: -// r32 -> r48 +// |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 +// +// |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 // -// Overview of operation -//============================================================== -// 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 -#include "libm_support.h" -// Assembly macros + +// Registers used //============================================================== +// f6-f15, f32-f36 +// r2-r3, r23-r23 +// p6, p7, p8, p12 +// -// 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 + GR_SAVE_B0= r33 + GR_SAVE_PFS= r34 + GR_SAVE_GP= r35 // This reg. can safely be used + GR_SAVE_SP= r36 -// __libm_atan2_reg returns -// f8 = Z_hi -// f10 = Z_lo -// f11 = s_lo + GR_Parameter_X= r37 + GR_Parameter_Y= r38 + GR_Parameter_RESULT= r39 + GR_Parameter_TAG= r40 -acos_Z_hi = f8 -acos_Z_lo = f10 -acos_S_lo = f11 + FR_X= f10 + FR_Y= f1 + FR_RESULT= f8 -// When we call __libm_atan2_reg, we must save -// the following: -acos_corr = f12 -acos_X = f13 -acos_pi_hi = f14 -acos_pi_lo = f15 -// The rest of the assembly macros - -acos_P79 = f32 -acos_P59 = f33 -acos_P39 = f34 -acos_P19 = f35 +RODATA -acos_P810 = f36 -acos_P610 = f37 -acos_P410 = f38 -acos_P210 = f39 +.align 16 -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 +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 0x8097a4d3dbe63d8f, 0xff68e16571015c63 +data8 0x3fb1636c0ac824e0, 0x3c8870a7c5a3556f +data8 0x809c0f5e9662b3dd, 0xff647ec520bca0f0 +data8 0x3fb1a392756ed280, 0x3c964f1a927461ae +data8 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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) -acos_X2 = f51 -acos_X4 = f52 -acos_B = f53 -acos_Bb = f54 -acos_A = f55 -acos_Aa = f56 -acos_1mA = f57 +.align 16 -acos_W = f58 -acos_Ww = f59 +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 -acos_y0 = f60 -acos_y1 = f61 -acos_y2 = f62 -acos_H = f63 -acos_Hh = f64 -acos_t1 = f65 -acos_t2 = f66 -acos_t3 = f67 -acos_t4 = f68 -acos_t5 = f69 +.section .text +GLOBAL_LIBM_ENTRY(acosl) -acos_Pseries = f70 -acos_NORM_f8 = f71 -acos_ABS_NORM_f8 = f72 +{.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 +} -acos_2 = f73 -acos_P1P2 = f74 -acos_HALF = f75 -acos_U = f76 +{.mfi + // sign mask + mov R_SGNMASK = 0x20000 + nop.f 0 + // bias-63-1 + mov R_TMP03 = 0xffff-64;; +} -acos_1mB = f77 -acos_V = f78 -acos_S = f79 -acos_BmUU = f80 -acos_BmUUpb = f81 -acos_2U = f82 -acos_1d2U = f83 +{.mfi + // get exponent of s + getf.exp R_EXP = f8 + nop.f 0 + // R_TMP4 = 2^45 + shl R_TMP4 = R_SGNMASK, 45-17 +} -acos_Dd = f84 +{.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;; +} -acos_pi_by_2_hi = f85 -acos_pi_by_2_lo = f86 -acos_xmpi_by_2_lo = f87 -acos_xPmw = f88 -acos_Uu = f89 -acos_AmVV = f90 -acos_AmVVpa = f91 +{.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 +} -acos_2V = f92 -acos_1d2V = f93 -acos_Vv = f94 +{.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;; +} -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 +{.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 +} -// Data tables -//============================================================== +{.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;; +} -#ifdef _LIBC -.rodata -#else -.data -#endif -.align 16 -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 + // 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 +} -.section .text -.proc acosl# -.align 32 +{.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;; +} -acosl: -// 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 +{.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 } -{ .mmi -(p0) mov acos_GR_16_ones = 0xffff -(p0) addl r40 = @ltoff(acos_coefficients), gp - nop.i 999 +{.mlx + // index = (4-exponent)|b1 b2.. b6 + sub R_INDEX = R_INDEX, R_BIAS + // sqrt coefficient cs9 = 55*13/128 + movl R_TMP = 0x40b2c000;; } -;; -// Set denormal flag on denormal input with fcmp -{ .mfi - ld8 r40 = [r40] - fcmp.eq p6,p0 = f8,f0 - nop.i 999 + +{.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;; +} -// Load the constants pi_by_2 and pi. -// Each is stored as hi and lo values -// Also load the coefficients for ACOS_POLY -{ .mmi -(p0) ldfe acos_pi_by_2_hi = [r40],16 ;; -(p0) ldfe acos_pi_by_2_lo = [r40],16 - nop.i 999 ;; +{.mlx + // table index + add r2 = r2, R_INDEX + // sqrt coefficient cs7 = 33/16 + movl R_TMP2 = 0x40040000;; } -{ .mmi -(p0) ldfe acos_pi_hi = [r40],16 ;; -(p0) ldfe acos_pi_lo = [r40],16 - nop.i 999 ;; + +{.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 -(p0) ldfe acos_A10 = [r40],16 ;; -(p0) ldfe acos_A9 = [r40],16 - nop.i 999 ;; + +{.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;; } -// 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 + +{.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;; } -{ .mii -(p0) ldfe acos_A8 = [r40],16 - nop.i 999 ;; -(p0) and acos_GR_exp = acos_GR_signexp_f8, acos_GR_17_ones ;; + +{.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;; } -// 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. -{ .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 + // 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 } -{ .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 + // r3 = load start address to polynomial coefficients + ld8 r3 = [r3] + // s+t + fma.s1 F_S2T2 = f8, f1, F_T + nop.i 0;; } -{ .mmi -(p0) ldfe acos_A5 = [r40],16 ;; -(p0) ldfe acos_A4 = [r40],16 - nop.i 999 ;; + +{.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;; } -{ .mmi -(p0) ldfe acos_A3 = [r40],16 ;; -(p0) ldfe acos_A2 = [r40],16 - nop.i 999 ;; + +{.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;; } -// 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 + // 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;; } -// 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 + // 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;; } -{ .mfb - nop.m 999 -(p6) fms.s0 f8 = acos_pi_by_2_hi,f1, acos_xmpi_by_2_lo -(p6) br.ret.spnt b0 ;; + +{.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 +} -// 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 + // cs7*x+cs6 + fma.s1 F_S67 = F_CS7, F_X, F_CS6 + nop.i 0;; } -{ .mfi - nop.m 999 -(p8) fma.s1 acos_X2 = f8,f8, f0 - nop.i 999 ;; +{.mfi + nop.m 0 + // cs5*x+cs4 + fma.s1 F_S45 = F_CS5, F_X, F_CS4 + 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 + // x*x + fma.s1 F_X2 = F_X, F_X, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p8) fma.s1 acos_X4 = acos_X2,acos_X2, f0 - nop.i 999 ;; + +{.mfi + nop.m 0 + // (s-t)-t*x + fnma.s1 F_DTX = F_T, F_X, F_D + 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 + // cs3*x+cs2 (cs2 = -0.5 = -cs3) + fms.s1 F_S23 = F_CS3, F_X, F_CS3 + 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 + // if sign is negative, negate table values: asin(t)_low + (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0 + 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 + // 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 999 -(p8) fma.s1 acos_Ww = acos_Ww, f1, acos_pi_by_2_lo - nop.i 999 ;; + +{.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 999 -(p8) fma.s1 acos_P610 = acos_X4, acos_P810, acos_A6 - nop.i 999 +{.mfi + nop.m 0 + // x^4 + fma.s1 F_X4 = F_X2, F_X2, 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 + // t*sqrt(1-t^2)*x^2 + fma.s1 F_TSQRT = F_TSQRT, F_X2, f0 + 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 + // cs5*x^3+cs4*x^2+cs3*x+cs2 + fma.s1 F_S25 = F_S45, F_X2, F_S23 + 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-t)-t*x)*sqrt(1-t^2) + fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0 + 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 + // (pi/2)_high - asin(t)_high + fnma.s1 F_ATHI = F_ATHI, f1, F_PI2_HI + 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 + // asin(t)_low - (pi/2)_low + fnma.s1 F_ATLO = F_PI2_LO, f1, F_ATLO + 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 + // 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 999 -(p8) fma.s1 acos_P1P2 = acos_X2, acos_P1P2, f0 - nop.i 999 ;; + + +{.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 999 -(p8) fms.s1 acos_xPmw = acos_NORM_f8, acos_P1P2, acos_Ww - nop.i 999 ;; + +{.mfi + nop.m 0 + // R^2 + fma.s1 F_R2 = F_R, F_R, f0 + 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 + // 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;; +} -// ACOS_ATAN -// case 3: 2^-2 <= |x| < 1 -// case 3: 2^-2 <= |x| < 1 ==> p9 ACOS_ATAN +{.mfi + nop.m 0 + // R^3 + fma.s1 F_R4 = F_R2, F_R2, f0 + nop.i 0;; +} -// 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 + // R^3 + fma.s1 F_R3 = F_R2, F_R, f0 + nop.i 0;; +} -// Step 2 -// Call __libm_atan2_reg -{ .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 + // c3+c5*R^2+c7*R^4+c9*R^6 + fma.s1 F_P39 = F_P79, F_R4, F_P35 + 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 + // 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 -(p0) setf.exp acos_HALF = acos_GR_fffe - nop.f 999 - nop.i 999 ;; + +{.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;; } -{ .mfi - nop.m 999 -(p0) fms.s1 acos_1mB = f1,f1, acos_B - nop.i 999 ;; + +{.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;; } -// We want atan2(V,U) -// so put V in f8 and U in f9 -// but save X in acos_X -{ .mfi - nop.m 999 -(p0) fmerge.se acos_X = f8, f8 - nop.i 999 ;; + + +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 } -// Step 1.2: -///////////////////////// -// Get U = sqrt(B) -///////////////////////// +{.mlx + // c8 = -33*13*15/128 + mov R_TMP5 = 0x184923 + movl R_TMP2 = 0xff00000000000000;; +} -{ .mfi - nop.m 999 -(p0) frsqrta.s1 acos_y0,p8 = acos_B - nop.i 999 +{.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 - nop.m 999 -(p0) fms.s1 acos_1mA = f1,f1, acos_A - nop.i 999 ;; + +{.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 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_Bb = acos_1mB,f1, acos_ABS_NORM_f8 - nop.i 999 ;; +{.mlx + // AND mask for getting t ~ sqrt(1-s^2) + setf.sig F_ANDMASK = R_TMP2 + // OR mask + movl R_TMP2 = 0x0100000000000000;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_Hh = acos_HALF, acos_B, f0 - nop.i 999 ;; +.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 999 -(p0) fma.s1 acos_t1 = acos_y0, acos_y0, f0 - nop.i 999 +{.mfi + nop.m 0 + // 1-|s| + (p11) fnma.s1 F_1AS = f8, f1, f1 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fms.s1 acos_Aa = acos_1mA,f1, acos_ABS_NORM_f8 - nop.i 999 ;; + +{.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 } -{ .mfi - nop.m 999 -(p0) fnma.s1 acos_t2 = acos_t1, acos_Hh, acos_HALF - nop.i 999 ;; +{.mfi + // c7 = 33*13/16 + mov R_TMP4 = 0x41d68 + // |s| + (p11) fma.s1 F_AS = f8, f1, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_y1 = acos_t2, acos_y0, acos_y0 - nop.i 999 + +{.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 } +{.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;; +} -// Step 1.2: -///////////////////////// -// Get V = sqrt(A) -///////////////////////// -{ .mfi - nop.m 999 -(p0) frsqrta.s1 acos_y0,p8 = acos_A - nop.i 999 ;; + +{.mlx + // load c8 = -33*13*15/128 + setf.s F_CS8 = R_TMP5 + // c4 = -35/8 + movl R_TMP5 = 0xc08c0000;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_t3 = acos_y1, acos_Hh, f0 - nop.i 999 ;; +{.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 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_t1 = acos_y0, acos_y0, f0 - nop.i 999 ;; +{.mlx + // load c7 = 33*13/16 + setf.s F_CS7 = R_TMP4 + // c3 = 5/2 + movl R_TMP4 = 0x40200000;; } -{ .mfi - nop.m 999 -(p0) fnma.s1 acos_t4 = acos_t3, acos_y1, acos_HALF - nop.i 999 ;; + +{.mlx + // load c4 = -35/8 + setf.s F_CS4 = R_TMP5 + // c2 = -3/2 + movl R_TMP5 = 0xbfc00000;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_y2 = acos_t4, acos_y1, acos_y1 - nop.i 999 ;; + +{.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 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_S = acos_B, acos_y2, f0 - nop.i 999 +{.mfi + nop.m 0 + // y^2/2 + fma.s1 F_Y2_2 = F_Y2, F_05, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_H = acos_y2, acos_HALF, f0 - nop.i 999 ;; + +{.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 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_t5 = acos_Hh, acos_y2, f0 - nop.i 999 + +{.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;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_Hh = acos_HALF, acos_A, f0 - nop.i 999 ;; +{.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;; } -{ .mfi - nop.m 999 -(p0) fnma.s1 acos_Dd = acos_S, acos_S, acos_B - nop.i 999 ;; + + +{.mfi + nop.m 0 + // if s<0, set s = -s + (p6) fnma.s1 f8 = f8, f1, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fnma.s1 acos_t2 = acos_t1, acos_Hh, acos_HALF - nop.i 999 ;; + +{.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;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_U = acos_Dd, acos_H, acos_S - nop.i 999 ;; + +{.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;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_y1 = acos_t2, acos_y0, acos_y0 - nop.i 999 ;; +{.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;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_2U = acos_U, f1, acos_U - nop.i 999 ;; + +{.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;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_t3 = acos_y1, acos_Hh, f0 - nop.i 999 + + +{.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;; } -// Step 1.3: -// sqrt(A + a) = V + v -// sqrt(B + b) = U + u -///////////////////////// -// Get u -///////////////////////// +{.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;; +} -// acos_BmUU = B - UU -// acos_BmUUpb = (B - UU) + b -{ .mfi - nop.m 999 -(p0) fnma.s1 acos_BmUU = acos_U, acos_U, acos_B - nop.i 999 ;; + +{.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 } -{ .mfi - nop.m 999 -(p0) fmerge.se f9 = acos_U, acos_U - 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) fnma.s1 acos_t4 = acos_t3, acos_y1, acos_HALF - nop.i 999 ;; + +{.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 } -// acos_1d2U = frcpa(2U) -{ .mfi - nop.m 999 -(p0) frcpa.s1 acos_1d2U,p9 = f1, acos_2U - nop.i 999 +{.mfi + nop.m 0 + // c7*x+c6 + fma.s1 F_S67 = F_X, F_CS7, F_CS6 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_BmUUpb = acos_BmUU, f1, acos_Bb - nop.i 999 ;; + +{.mfi + nop.m 0 + // 1-x + fnma.s1 F_1X = F_X, f1, f1 + nop.i 0 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_y2 = acos_t4, acos_y1, acos_y1 - nop.i 999 ;; +{.mfi + nop.m 0 + // c3*x+c2 + fma.s1 F_S23 = F_X, F_CS3, F_CS2 + 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 + nop.m 0 + // 1-t^2 + fnma.s1 F_1T2 = F_T, F_T, f1 + nop.i 0 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_S = acos_A, acos_y2, f0 - nop.i 999 +{.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;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_H = acos_y2, acos_HALF, f0 - nop.i 999 ;; + + +{.mfi + nop.m 0 + // t*s + fma.s1 F_TS = F_T, f8, 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 + // 0.5/(1-t^2) + fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fnma.s1 acos_Dd = acos_S, acos_S, acos_A - 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 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_V = acos_Dd, acos_H, acos_S - nop.i 999 ;; +{.mfi + nop.m 0 + // sqrt(1-t^2) + fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_2V = acos_V, f1, acos_V - nop.i 999 + +{.mfi + nop.m 0 + // y*(1-s^2)*x^2 + fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0 + nop.i 0 } -// Step 3 -///////////////////////// -// Calculate the correction, acos_corr -///////////////////////// -// acos_corr = U*v - (V*u) +{.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 ;; + +{.mfi + nop.m 0 + // s*t rounded to 24 significant bits + fma.s.s1 F_TSS = F_T, f8, f0 + nop.i 0 } -///////////////////////// -// 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 + // ST = (t^2-1+s^2) rounded to 24 significant bits + fms.s.s1 F_ST = f8, f8, F_1T2 + nop.i 0 } -{ .mfi - nop.m 999 -(p0) fmerge.se f8 = acos_V, acos_V - 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) fma.s1 acos_AmVVpa = acos_AmVV, f1, acos_Aa - nop.i 999 ;; + +{.mfi + nop.m 0 + // 0.25/(1-t^2) + fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0 + 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 + // t*s-sqrt(1-t^2)*(1-s^2)*y + fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS + 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 + // z*0.5/(1-t^2) + fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0 + nop.i 0 } -{ .mfi - nop.m 999 -(p0) fma.s1 acos_Uv = acos_U,acos_Vv, f0 - nop.i 999 ;; +{.mfi + nop.m 0 + // z^2+t^2-1 + fms.s1 F_DZ0 = F_Z, F_Z, F_1T2 + nop.i 0;; } -.endp acosl# -ASM_SIZE_DIRECTIVE(acosl#) +{.mfi + nop.m 0 + // (1-s^2-(1-s^2)_s)*x + fma.s1 F_DS2X = F_X, F_DS, f0 + 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 + // t*s-(t*s)_s + fms.s1 F_DTS = F_T, f8, F_TSS + 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 + // c9*x^7+..+c2 + fma.s1 F_S29 = F_X4, F_S69, F_S25 + 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 + // y*z + fma.s1 F_YZ = F_Z, F_Y, f0 + nop.i 0 } +{.mfi + nop.m 0 + // t^2 + fma.s1 F_T2 = F_T, F_T, f0 + nop.i 0;; +} -// p6 ==> X is negative -// p7 ==> x is positive -// We know that |X| >= 1/4 -{ .mfi -(p0) mov gp = GR_SAVE_GP -(p0) fcmp.lt.unc p6,p7 = acos_X , f0 -(p0) mov b0 = GR_SAVE_B0 ;; +{.mfi + nop.m 0 + // 1-t^2+ST + fma.s1 F_1T2_ST = F_ST, f1, F_1T2 + nop.i 0;; } -// acos_2_Z_hi = 2 * acos_Z_hi -// acos_s_lo_Z_lo = s_lo * Z_lo -{ .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 + // y*(1-s^2)(1-x) + fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, 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 + // dz ~ sqrt(1-t^2)-z + fma.s1 F_DZ = F_DZ0, F_ZE, 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 ;; + +{.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;; } -// 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 999 -(p7) fma.s1 acos_result_lo = acos_s_lo_Z_lo, acos_2, acos_corr - 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 -(p7) fma.s0 f8 = acos_2_Z_hi, f1, acos_result_lo - 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_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 + // s^2-(1-t^2+ST) + fms.s1 F_1T2_ST = f8, f8, F_1T2_ST + 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 + // (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_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 + // dz*y*(1-s^2)*(1-x) + fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, 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 + // 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 -(p6) fma.s1 acos_result_lo = acos_result_lo, f1, acos_Ww - 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 } -// 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 ;; +{.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 -(p6) fma.s0 f8 = acos_W, f1, acos_Z_lo -(p0) br.ret.sptk b0 ;; + +{.mfi + nop.m 0 + // R^2 + fma.s1 F_R2 = F_R, F_R, f0 + nop.i 0;; } -.endp __libm_callout -ASM_SIZE_DIRECTIVE(__libm_callout) -.proc SPECIAL -SPECIAL: -L(ACOS_NAN): -{ .mfb - nop.m 999 -(p0) fma.s0 f8 = f8,f1,f0 -(p0) br.ret.sptk b0 ;; + +{.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;; } -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 +{.mfi + nop.m 0 + // c7+c9*R^2 + fma.s1 F_P79 = F_C9, F_R2, F_C7 + nop.i 0 +} -// Coming in as X = +- 1 -// What should we return? +{.mfi + nop.m 0 + // c3+c5*R^2 + fma.s1 F_P35 = F_C5, F_R2, F_C3 + nop.i 0;; +} -// If X is 1, return (sign of X)pi/2 +{.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 +} +{.mfi + nop.m 0 + // R^4 + fma.s1 F_R4 = F_R2, F_R2, f0 + 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 + // R^3 + fma.s1 F_R3 = F_R2, F_R, f0 + nop.i 0;; } -{ .mfi - nop.m 999 -(p6) fcmp.lt.unc p8,p9 = f8,f0 - nop.i 999 ;; + +{.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 999 -(p8) fma.s0 f8 = acos_pi_hi, f1, acos_pi_lo - 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) + fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM + nop.i 0;; } -{ .mfb - nop.m 999 -(p9) fmerge.s f8 = f8,f0 -(p6) br.ret.spnt b0 ;; + +{.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 } -// If X is a NAN, leave -{ .mfi - nop.m 999 -(p0) fclass.m.unc p12,p0 = f8, 0xc3 - 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;; } -{ .mfb - nop.m 999 -(p12) fma.s0 f8 = f8,f1,f0 -(p12) br.ret.spnt b0 ;; + +{.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 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 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 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 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 -(p0) mov GR_Parameter_TAG = 57 -(p0) frcpa f10, p6 = f0, f0 -nop.i 999 -};; -.endp SPECIAL -ASM_SIZE_DIRECTIVE(SPECIAL) +{.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;; +} + + +.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 +} + +{.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;; +} + + + + + + +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;; +} + + +{.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;; +} + +{.mmf + ldfe F_C5 = [r3], 16 + ldfpd F_C11, F_C13 = [r2], 16 + nop.f 0;; +} + +{.mmf + ldfpd F_C7, F_C9 = [r3], 16 + ldfpd F_C15, F_C17 = [r2] + nop.f 0;; +} + + + +{.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 0 + // s^3 + fma.s1 F_R3 = f8, F_R2, f0 + nop.i 0 +} + +{.mfi + nop.m 0 + // s^4 + fma.s1 F_R4 = F_R2, F_R2, f0 + nop.i 0;; +} + + +{.mfi + nop.m 0 + // c3+c5*s^2 + fma.s1 F_P35 = F_C5, F_R2, F_C3 + nop.i 0 +} + +{.mfi + nop.m 0 + // c11+c13*s^2 + fma.s1 F_P1113 = F_C13, F_R2, F_C11 + nop.i 0;; +} + + +{.mfi + nop.m 0 + // c7+c9*s^2 + fma.s1 F_P79 = F_C9, F_R2, F_C7 + nop.i 0 +} + +{.mfi + nop.m 0 + // c15+c17*s^2 + fma.s1 F_P1517 = F_C17, F_R2, F_C15 + nop.i 0;; +} + +{.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 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 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;; +} + +{.mfi + nop.m 0 + // c3+..+c17*s^14 + fma.s1 F_P317 = F_R8, F_P1117, F_P39 + nop.i 0;; +} + +{.mfi + nop.m 0 + // s_low + fma.s1 F_DS = f8, f1, F_S + nop.i 0;; +} -.proc __libm_error_region -__libm_error_region: +{.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;; +} + +{.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;; +} + +{.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;; +} + + + + + +RETURN_PI2: + +{.mfi + nop.m 0 + // (pi/2)_low-s + fms.s0 F_PI2_LO = F_PI2_LO, f1, f8 + nop.i 0;; +} + +{.mfb + nop.m 0 + // (pi/2)-s + fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO + br.ret.sptk b0;; +} + + + + + +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;; +} + +.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 0 + (p11) fma.s1 F_PI2_LO = f0, f0, f0 + nop.i 0;; +} + +{.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 0 + // x^2 + fma.s1 F_X2 = F_X, F_X, f0 + nop.i 0;; +} + + +{.mfi + nop.m 0 + // y*(1-s^2)*x + fma.s1 F_Y1S2X = F_Y1S2, F_X, f0 + nop.i 0 +} + +{.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 + // 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 0 + // c5*x+c4 + fma.s1 F_S45 = F_X, F_CS5, F_CS4 + nop.i 0;; +} + + + + +{.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 0 + // c9*x^3+..+c6 + fma.s1 F_S69 = F_X2, F_S89, F_S67 + nop.i 0;; +} + + +{.mfi + nop.m 0 + // c5*x^3+..+c2 + fma.s1 F_S25 = F_X2, F_S45, F_S23 + nop.i 0;; +} + + + +{.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 0 + // c9*x^7+..+c2 + fma.s1 F_S29 = F_X4, F_S69, F_S25 + nop.i 0;; +} + + +{.mfi + nop.m 0 + // -(y*(1-s^2)_s)_high + fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI + nop.i 0;; +} + + +{.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 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;; +} + + + +{.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;; +} + + +{.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 + 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;; +} + + +{.mfi + nop.m 0 + // R^2 + fma.s1 F_R2 = F_R, F_R, f0 + nop.i 0;; +} + + +{.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 + 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^4 + 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 + // c11+c13*R^2 + fma.s1 F_P1113 = F_C13, F_R2, F_C11 + nop.i 0 +} + +{.mfi + nop.m 0 + // c15+c17*R^2 + fma.s1 F_P1517 = F_C17, F_R2, F_C15 + nop.i 0;; +} + + +{.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;; +} + + +{.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 +} + +{.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 + // R^8 + fma.s1 F_R8 = F_R4, F_R4, f0 + nop.i 0;; +} + + +{.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 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;; +} + +.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 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;; +} + + + + + + +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 0 + // load FR_X + fma.s1 FR_X = f8, f1, f0 + // load error tag + mov GR_Parameter_TAG = 57;; +} + + +{.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;; +} + + +{.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;; +} + + +{.mfi + nop.m 0 + // get Infinity + frcpa.s1 FR_RESULT, p0 = f1, f0 + nop.i 0;; +} + + +{.mfb + nop.m 0 + // return QNaN indefinite (0*Infinity) + fma.s0 FR_RESULT = f0, FR_RESULT, f0 + nop.b 0;; +} + + +GLOBAL_LIBM_END(acosl) + + +LOCAL_LIBM_ENTRY(__libm_error_region) .prologue // (1) { .mfi @@ -1068,12 +2511,12 @@ __libm_error_region: .body // (3) { .mib - stfe [GR_Parameter_X] = f8 // Store Parameter 1 on stack + stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y nop.b 0 // Parameter 3 address } { .mib - stfe [GR_Parameter_Y] = f10 // Store Parameter 3 on stack + stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack add GR_Parameter_Y = -16,GR_Parameter_Y br.call.sptk b0=__libm_error_support# // Call error handling function };; @@ -1097,11 +2540,13 @@ __libm_error_region: br.ret.sptk b0 // Return };; -.endp __libm_error_region -ASM_SIZE_DIRECTIVE(__libm_error_region) +LOCAL_LIBM_END(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support# -.type __libm_atan2_reg#,@function -.global __libm_atan2_reg# + + + + + |