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Diffstat (limited to 'sysdeps/ia64/fpu/e_asinl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_asinl.S | 2528 |
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diff --git a/sysdeps/ia64/fpu/e_asinl.S b/sysdeps/ia64/fpu/e_asinl.S deleted file mode 100644 index ad65a73..0000000 --- a/sysdeps/ia64/fpu/e_asinl.S +++ /dev/null @@ -1,2528 +0,0 @@ -.file "asinl.s" - - -// Copyright (c) 2001 - 2003, Intel Corporation -// All rights reserved. -// -// 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 -// met: -// -// * Redistributions of source code must retain the above copyright -// notice, this list of conditions and the following disclaimer. -// -// * Redistributions in binary form must reproduce the above copyright -// notice, this list of conditions and the following disclaimer in the -// documentation and/or other materials provided with the distribution. -// -// * The name of Intel Corporation may not be used to endorse or promote -// products derived from this software without specific prior written -// permission. - -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS -// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY -// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// -// Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://www.intel.com/software/products/opensource/libraries/num.htm. -// -// History -//============================================================== -// 08/28/01 New version -// 05/20/02 Cleaned up namespace and sf0 syntax -// 02/06/03 Reordered header: .section, .global, .proc, .align -// -// API -//============================================================== -// long double asinl(long double) -// -// Overview of operation -//============================================================== -// Background -// -// Implementation -// -// 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 -// asin(s)= 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) -// -// |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.. -// asin(|s|)= pi/2-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 as 17-degree polynomial -// (or simply return s, if|s|<2^{-64}) -// -// |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-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/2)_high-(y*(1-s^2))_high -// - - - -// Registers used -//============================================================== -// 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 - - - -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 0x8097a4d3dbe63d8f, 0xff68e16571015c63 -data8 0x3fb1636c0ac824e0, 0x3c8870a7c5a3556f -data8 0x809c0f5e9662b3dd, 0xff647ec520bca0f0 -data8 0x3fb1a392756ed280, 0x3c964f1a927461ae -data8 0x80a08a5f33fadc66, 0xff600c07846a6830 -data8 0x3fb1e3b9fc19e580, 0x3c69eb3576d56332 -data8 0x80a515d91d71acd4, 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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 - -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 -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 - - -.section .text -GLOBAL_LIBM_ENTRY(asinl) - -{.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] - // x = -(s^2-t^2)/(1-t^2)/2 - fnma.s1 F_X = F_INV_1T2, F_S2T2, f0 - nop.i 0;; -} - - -{.mfi - // load asin(t)_high, asin(t)_low - ldfpd F_ATHI, F_ATLO = [r2] - // t*sqrt(1-t^2) - fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0 - nop.i 0;; -} - - -{.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 - // 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 - // 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 - // 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 - // 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 - // 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 = asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) - fma.s0 f8 = F_ATHI, f1, F_P39 - // 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;; -} - - -{.mfi - nop.m 0 - // (s^2)_s - fma.s.s1 F_S2 = f8, f8, f0 - nop.i 0;; -} - - -{.mmi - // c9 = 55*13*17/128 - setf.s F_CS9 = R_TMP4 - // c7 = 33*13/16 - mov R_TMP4 = 0x41d68 - // c8 = -33*13*15/128 - shl R_TMP5 = R_TMP5, 11;; -} - - -{.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;; -} - - -{.mlx - // load c8 = -33*13*15/128 - setf.s F_CS8 = R_TMP5 - // c4 = -35/8 - movl R_TMP5 = 0xc08c0000;; -} - -{.mfi - // r3 = pointer to polynomial coefficients - addl r3 = @ltoff(poly_coeffs), gp - // 1-(1-s^2)_s - fnma.s1 F_DS = F_1S2_S, f1, f1 - // p9 = 0 if p7 = 1 (p9 = 1 for special cases only) - (p7) cmp.ne p9, p0 = r0, r0 -} - -{.mlx - // load c7 = 33*13/16 - setf.s F_CS7 = R_TMP4 - // c3 = 5/2 - movl R_TMP4 = 0x40200000;; -} - - -{.mfi - nop.m 0 - // 1-(s^2)_s - fnma.s1 F_S_1S2S = F_S2, f1, f1 - nop.i 0 -} - -{.mlx - // load c4 = -35/8 - setf.s F_CS4 = R_TMP5 - // c2 = -3/2 - movl R_TMP5 = 0xbfc00000;; -} - - -{.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 0 - // y^2/2 - fma.s1 F_Y2_2 = F_Y2, F_05, f0 - nop.i 0;; -} - - -{.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 -} - -{.mfb - // r3 = load start address to polynomial coefficients - ld8 r3 = [r3] - // 1-(1-s^2)_s-s^2 - fnma.s1 F_DS = f8, f8, F_DS - // p9 = 1 if s is a special input (NaN, or |s|> = 1) - (p9) br.cond.spnt ASINL_SPECIAL_CASES;; -} - -{.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 0 - // x' = (y^2/2)*(1-(s^2)_s)-0.5 - fms.s1 F_XL = F_Y2_2, F_S_1S2S, F_05 - nop.i 0 -} - -{.mfi - nop.m 0 - // s^2-(s^2)_s - fms.s1 F_S_DS2 = f8, f8, F_S2 - nop.i 0;; -} - - -{.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;; -} - - -{.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;; -} - - -{.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;; -} - - - -{.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;; -} - - - -{.mfi - // pi/2 (low, high) - ldfpd F_PI2_LO, F_PI2_HI = [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 - nop.m 0 - // c7*x+c6 - fma.s1 F_S67 = F_X, F_CS7, F_CS6 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // 1-x - fnma.s1 F_1X = F_X, f1, f1 - nop.i 0 -} - -{.mfi - nop.m 0 - // c3*x+c2 - fma.s1 F_S23 = F_X, F_CS3, F_CS2 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // 1-t^2 - fnma.s1 F_1T2 = F_T, F_T, f1 - nop.i 0 -} - -{.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 0 - // t*s - fma.s1 F_TS = F_T, f8, f0 - nop.i 0 -} - -{.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 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 0 - // sqrt(1-t^2) - fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0 - 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 - // 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;; -} - - -{.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 0 - // c5*x^3+..+c2 - fma.s1 F_S25 = F_X2, F_S45, F_S23 - nop.i 0;; -} - - -{.mfi - nop.m 0 - // 0.25/(1-t^2) - fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0 - nop.i 0 -} - -{.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;; -} - - -{.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;; -} - - -{.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 0 - // t*s-(t*s)_s - fms.s1 F_DTS = F_T, f8, F_TSS - 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*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;; -} - - -{.mfi - nop.m 0 - // 1-t^2+ST - fma.s1 F_1T2_ST = F_ST, f1, F_1T2 - nop.i 0;; -} - - -{.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 0 - // dz ~ sqrt(1-t^2)-z - fma.s1 F_DZ = F_DZ0, F_ZE, f0 - nop.i 0;; -} - - -{.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;; -} - - -{.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 - // z*y*(1-s^2)_s - fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0 - nop.i 0 -} - -{.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 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 -} - -{.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 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 0 - // (PS29*x^2)*y*(1-s^2) - fma.s1 F_S29 = F_Y1S2X2, F_S29, f0 - nop.i 0 -} - -{.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;; -} - - -{.mfi - nop.m 0 - // R^2 - fma.s1 F_R2 = F_R, F_R, f0 - nop.i 0;; -} - - -{.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;; -} - - -{.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 - // asin(t)_low-(pi/2)_low - 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 0 - // R^3 - fma.s1 F_R3 = F_R2, F_R, f0 - nop.i 0;; -} - - -{.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 0 - // (pi/2)_hi-asin(t)_hi - fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI - 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 - // 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 - // if s<0, change sign of F_ATHI - (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0 - 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 - 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 pi/2-table value - // s>0 in this case - (p11) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI - nop.i 0 -} - -{.mfb - nop.m 0 - // result: add high part of pi/2-table value - // if s<0 - (p6) fnma.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 - // 2^{-128} - fma.s1 F_2M128 = F_2M64, F_2M64, f0;; -} - -{.mmf - ldfpd F_C7, F_C9 = [r3] - ldfpd F_C15, F_C17 = [r2] - // if |s|<2^{-64}, return s+2^{-128}*s - (p7) fma.s0 f8 = f8, F_2M128, f8;; -} - - - -{.mfb - nop.m 0 - // s^2 - fma.s1 F_R2 = f8, f8, f0 - // if |s|<2^{-64}, return s - (p7) br.ret.spnt b0;; -} - - -{.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 - // 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 - // c3+..+c17*s^14 - fma.s1 F_P317 = F_R8, F_P1117, F_P39 - nop.i 0;; -} - - -{.mfb - nop.m 0 - // result - fma.s0 f8 = F_P317, F_R3, f8 - br.ret.sptk b0;; -} - - -{.mfb - nop.m 0 - fma.s0 f8 = F_P317, F_R3, f0//F_P317, F_R3, F_S29 - // nop.f 0//fma.s0 f8 = f13, f6, f0 - br.ret.sptk b0;; -} - - - - - - VERY_LARGE_INPUT: - -{.mfi - nop.m 0 - // s rounded to 24 significant bits - fma.s.s1 F_S = f8, f1, f0 - nop.i 0 -} - -{.mfi - // load C5 - ldfe F_C5 = [r3], 16 - // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2 - fnma.s1 F_X = F_S_DS2, F_Y2_2, F_XL - nop.i 0;; -} - - - -{.mmf - nop.m 0 - // C7, C9 - ldfpd F_C7, F_C9 = [r3], 16 - nop.f 0;; -} - - - -{.mfi - // pi/2 (low, high) - ldfpd F_PI2_LO, F_PI2_HI = [r3], 16 - // 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 - // (s_s)^2 - fma.s1 F_DS = F_S, F_S, f0 - nop.i 0 -} - -{.mfi - nop.m 0 - // 1-(s_s)^2 - fnma.s1 F_1S2_S = F_S, F_S, f1 - 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 - // ((s_s)^2-s^2) - fnma.s1 F_DS = f8, f8, F_DS - nop.i 0 -} - -{.mfi - nop.m 0 - // (pi/2)_high-y*(1-(s_s)^2) - 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_s)^2))_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_s)^2)-(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/2)_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 - // (pi/2)_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/2)_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/2)_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;; -} - -{.mfi - nop.m 0 - // set sign - (p6) fnma.s1 F_S29 = F_S29, f1, f0 - nop.i 0 -} - -{.mfi - nop.m 0 - (p6) fnma.s1 F_HI = F_HI, f1, f0 - nop.i 0;; -} - - -{.mfb - nop.m 0 - // Result: - // (pi/2)_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/2)_high-(y*(1-s^2))_high - fma.s0 f8 = F_S29, f1, F_HI - br.ret.sptk b0;; -} - - - - - - - - - - ASINL_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 = 48, 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, p0 = 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 = 60;; -} - - -{.mfb - nop.m 0 - // change sign if s = -1 - (p6) fnma.s1 F_PI2_HI = F_PI2_HI, f1, f0 - nop.b 0 -} - -{.mfb - nop.m 0 - // change sign if s = -1 - (p6) fnma.s1 F_PI2_LO = F_PI2_LO, f1, f0 - nop.b 0;; -} - -{.mfb - nop.m 0 - // if s = 1, result is pi/2 - (p9) 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;; -} - - -{.mfi - nop.m 0 - // return QNaN indefinite (0*Infinity) - fma.s0 FR_RESULT = f0, FR_RESULT, f0 - nop.i 0;; -} - - -GLOBAL_LIBM_END(asinl) - - - -LOCAL_LIBM_ENTRY(__libm_error_region) -.prologue -// (1) -{ .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value - nop.f 0 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -} -{ .mfi -.fframe 64 - add sp=-64,sp // Create new stack - nop.f 0 - mov GR_SAVE_GP=gp // Save gp -};; - - -// (2) -{ .mmi - stfe [GR_Parameter_Y] = f1,16 // Store Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 -};; - -.body -// (3) -{ .mib - 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] = 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 -};; -{ .mmi - nop.m 0 - nop.m 0 - add GR_Parameter_RESULT = 48,sp -};; - -// (4) -{ .mmi - ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack -.restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address -};; - -{ .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return -};; - -LOCAL_LIBM_END(__libm_error_region) - -.type __libm_error_support#,@function -.global __libm_error_support# - - - - - |