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| author | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
|---|---|---|
| committer | Zack Weinberg <zackw@panix.com> | 2017-06-08 15:39:03 -0400 |
| commit | 5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch) | |
| tree | 4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ia64/fpu/e_acosl.S | |
| parent | 199fc19d3aaaf57944ef036e15904febe877fc93 (diff) | |
| download | glibc-5046dbb4a7eba5eccfd258f92f4735c9ffc8d069.tar.gz glibc-5046dbb4a7eba5eccfd258f92f4735c9ffc8d069.tar.xz glibc-5046dbb4a7eba5eccfd258f92f4735c9ffc8d069.zip | |
Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ia64/fpu/e_acosl.S')
| -rw-r--r-- | REORG.TODO/sysdeps/ia64/fpu/e_acosl.S | 2546 |
1 files changed, 2546 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ia64/fpu/e_acosl.S b/REORG.TODO/sysdeps/ia64/fpu/e_acosl.S new file mode 100644 index 0000000000..8c5155a2ec --- /dev/null +++ b/REORG.TODO/sysdeps/ia64/fpu/e_acosl.S @@ -0,0 +1,2546 @@ +.file "acosl.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 acosl(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 +// 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) +// +// |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 +// + + + +// 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, 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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 + +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 +} + +{.mfi + // c7 = 33*13/16 + mov R_TMP4 = 0x41d68 + // |s| + (p11) fma.s1 F_AS = f8, f1, f0 + nop.i 0;; +} + + +{.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-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 +} + +{.mlx + // load c7 = 33*13/16 + setf.s F_CS7 = R_TMP4 + // c3 = 5/2 + movl R_TMP4 = 0x40200000;; +} + + +{.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 + 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;; +} + +{.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 + // 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 + // 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 0 + // x^2 + fma.s1 F_X2 = F_X, F_X, f0 + nop.i 0;; +} + + +{.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 +} + +{.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)_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 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)_hi-asin(t)_hi (if s<0) + (p6) 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 + // 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 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;; +} + +{.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 + 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# |