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| author | Andrew Senkevich <andrew.senkevich@intel.com> | 2015-06-18 20:11:27 +0300 |
|---|---|---|
| committer | Andrew Senkevich <andrew.senkevich@intel.com> | 2015-06-18 20:11:27 +0300 |
| commit | a6336cc446a7ed682cb9dbc47cc56ebf9f9a4229 (patch) | |
| tree | 3b89c96ee406327a8ad942cb1f4923fe33c0558e | |
| parent | c9a8c526acd185176e486bee4624039740f8c435 (diff) | |
| download | glibc-a6336cc446a7ed682cb9dbc47cc56ebf9f9a4229.tar glibc-a6336cc446a7ed682cb9dbc47cc56ebf9f9a4229.tar.gz glibc-a6336cc446a7ed682cb9dbc47cc56ebf9f9a4229.tar.bz2 glibc-a6336cc446a7ed682cb9dbc47cc56ebf9f9a4229.zip | |
Vector sincosf for x86_64 and tests.
Here is implementation of vectorized sincosf containing SSE, AVX,
AVX2 and AVX512 versions according to Vector ABI
<https://groups.google.com/forum/#!topic/x86-64-abi/LmppCfN1rZ4>.
* NEWS: Mention addition of x86_64 vector sincosf.
* math/test-float-vlen16.h: Added wrapper for sincosf tests.
* math/test-float-vlen4.h: Likewise.
* math/test-float-vlen8.h: Likewise.
* sysdeps/unix/sysv/linux/x86_64/libmvec.abilist: New symbols added.
* sysdeps/x86/fpu/bits/math-vector.h: Added sincosf SIMD declaration.
* sysdeps/x86_64/fpu/Makefile (libmvec-support): Added new files.
* sysdeps/x86_64/fpu/Versions: New versions added.
* sysdeps/x86_64/fpu/libm-test-ulps: Regenerated.
* sysdeps/x86_64/fpu/multiarch/Makefile (libmvec-sysdep_routines):
Added build of SSE, AVX2 and AVX512 IFUNC versions.
* sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core.S
* sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core_avx512.S
* sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core.S
* sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core_sse4.S
* sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core.S
* sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core_avx2.S
* sysdeps/x86_64/fpu/svml_s_sincosf16_core.S
* sysdeps/x86_64/fpu/svml_s_sincosf4_core.S
* sysdeps/x86_64/fpu/svml_s_sincosf8_core.S
* sysdeps/x86_64/fpu/svml_s_sincosf8_core_avx.S
* sysdeps/x86_64/fpu/svml_s_sincosf_data.S: New file.
* sysdeps/x86_64/fpu/svml_s_sincosf_data.h: New file.
* sysdeps/x86_64/fpu/svml_s_wrapper_impl.h: Added 3 argument wrappers.
* sysdeps/x86_64/fpu/test-float-vlen16.c: : Vector sincosf tests.
* sysdeps/x86_64/fpu/test-float-vlen16-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-float-vlen4-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-float-vlen4.c: Likewise.
* sysdeps/x86_64/fpu/test-float-vlen8-avx2-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-float-vlen8-avx2.c: Likewise.
* sysdeps/x86_64/fpu/test-float-vlen8-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-float-vlen8.c: Likewise.
32 files changed, 2706 insertions, 43 deletions
@@ -1,5 +1,38 @@ 2015-06-18 Andrew Senkevich <andrew.senkevich@intel.com> + * NEWS: Mention addition of x86_64 vector sincosf. + * math/test-float-vlen16.h: Added wrapper for sincosf tests. + * math/test-float-vlen4.h: Likewise. + * math/test-float-vlen8.h: Likewise. + * sysdeps/unix/sysv/linux/x86_64/libmvec.abilist: New symbols added. + * sysdeps/x86/fpu/bits/math-vector.h: Added sincosf SIMD declaration. + * sysdeps/x86_64/fpu/Makefile (libmvec-support): Added new files. + * sysdeps/x86_64/fpu/Versions: New versions added. + * sysdeps/x86_64/fpu/libm-test-ulps: Regenerated. + * sysdeps/x86_64/fpu/multiarch/Makefile (libmvec-sysdep_routines): + Added build of SSE, AVX2 and AVX512 IFUNC versions. + * sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core.S + * sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core_avx512.S + * sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core.S + * sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core_sse4.S + * sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core.S + * sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core_avx2.S + * sysdeps/x86_64/fpu/svml_s_sincosf16_core.S + * sysdeps/x86_64/fpu/svml_s_sincosf4_core.S + * sysdeps/x86_64/fpu/svml_s_sincosf8_core.S + * sysdeps/x86_64/fpu/svml_s_sincosf8_core_avx.S + * sysdeps/x86_64/fpu/svml_s_sincosf_data.S: New file. + * sysdeps/x86_64/fpu/svml_s_sincosf_data.h: New file. + * sysdeps/x86_64/fpu/svml_s_wrapper_impl.h: Added 3 argument wrappers. + * sysdeps/x86_64/fpu/test-float-vlen16.c: : Vector sincosf tests. + * sysdeps/x86_64/fpu/test-float-vlen16-wrappers.c: Likewise. + * sysdeps/x86_64/fpu/test-float-vlen4-wrappers.c: Likewise. + * sysdeps/x86_64/fpu/test-float-vlen4.c: Likewise. + * sysdeps/x86_64/fpu/test-float-vlen8-avx2-wrappers.c: Likewise. + * sysdeps/x86_64/fpu/test-float-vlen8-avx2.c: Likewise. + * sysdeps/x86_64/fpu/test-float-vlen8-wrappers.c: Likewise. + * sysdeps/x86_64/fpu/test-float-vlen8.c: Likewise. + * NEWS: Mention addition of x86_64 vector sincos. * bits/libm-simd-decl-stubs.h: Added stubs for sincos. * math/math.h (__MATHDECL_VEC): New macro. @@ -55,8 +55,8 @@ Version 2.22 condition in some applications. * Added vector math library named libmvec with the following vectorized x86_64 - implementations: cos, cosf, sin, sinf, sincos, log, logf, exp, expf, pow, - powf. + implementations: cos, cosf, sin, sinf, sincos, sincosf, log, logf, exp, expf, + pow, powf. The library can be disabled with --disable-mathvec. Use of the functions is enabled with -fopenmp -ffast-math starting from -O1 for GCC version >= 4.9.0. The library is linked in as needed when using -lm (no need to specify -lmvec diff --git a/math/test-float-vlen16.h b/math/test-float-vlen16.h index 802ae7bda2..b1890f3740 100644 --- a/math/test-float-vlen16.h +++ b/math/test-float-vlen16.h @@ -44,6 +44,7 @@ #define WRAPPER_DECL(func) extern FLOAT func (FLOAT x); #define WRAPPER_DECL_ff(func) extern FLOAT func (FLOAT x, FLOAT y); +#define WRAPPER_DECL_fFF(function) extern void function (FLOAT, FLOAT *, FLOAT *); // Wrapper from scalar to vector function with vector length 16. #define VECTOR_WRAPPER(scalar_func, vector_func) \ @@ -71,3 +72,19 @@ FLOAT scalar_func (FLOAT x, FLOAT y) \ TEST_VEC_LOOP (mr, 16); \ return ((FLOAT) mr[0]); \ } + +// Wrapper from scalar 3 argument function to vector one. +#define VECTOR_WRAPPER_fFF(scalar_func, vector_func) \ +extern void vector_func (VEC_TYPE, VEC_TYPE *, VEC_TYPE *); \ +void scalar_func (FLOAT x, FLOAT * r, FLOAT * r1) \ +{ \ + int i; \ + VEC_TYPE mx, mr, mr1; \ + INIT_VEC_LOOP (mx, x, 16); \ + vector_func (mx, &mr, &mr1); \ + TEST_VEC_LOOP (mr, 16); \ + TEST_VEC_LOOP (mr1, 16); \ + *r = (FLOAT) mr[0]; \ + *r1 = (FLOAT) mr1[0]; \ + return; \ +} diff --git a/math/test-float-vlen4.h b/math/test-float-vlen4.h index f5e530b756..213ae78e71 100644 --- a/math/test-float-vlen4.h +++ b/math/test-float-vlen4.h @@ -44,6 +44,7 @@ #define WRAPPER_DECL(function) extern FLOAT function (FLOAT); #define WRAPPER_DECL_ff(function) extern FLOAT function (FLOAT, FLOAT); +#define WRAPPER_DECL_fFF(function) extern void function (FLOAT, FLOAT *, FLOAT *); // Wrapper from scalar to vector function with vector length 4. #define VECTOR_WRAPPER(scalar_func, vector_func) \ @@ -71,3 +72,19 @@ FLOAT scalar_func (FLOAT x, FLOAT y) \ TEST_VEC_LOOP (mr, 4); \ return ((FLOAT) mr[0]); \ } + +// Wrapper from scalar 3 argument function to vector one. +#define VECTOR_WRAPPER_fFF(scalar_func, vector_func) \ +extern void vector_func (VEC_TYPE, VEC_TYPE *, VEC_TYPE *); \ +void scalar_func (FLOAT x, FLOAT * r, FLOAT * r1) \ +{ \ + int i; \ + VEC_TYPE mx, mr, mr1; \ + INIT_VEC_LOOP (mx, x, 4); \ + vector_func (mx, &mr, &mr1); \ + TEST_VEC_LOOP (mr, 4); \ + TEST_VEC_LOOP (mr1, 4); \ + *r = (FLOAT) mr[0]; \ + *r1 = (FLOAT) mr1[0]; \ + return; \ +} diff --git a/math/test-float-vlen8.h b/math/test-float-vlen8.h index 697849f070..dd2fb287ad 100644 --- a/math/test-float-vlen8.h +++ b/math/test-float-vlen8.h @@ -44,6 +44,7 @@ #define WRAPPER_DECL(function) extern FLOAT function (FLOAT); #define WRAPPER_DECL_ff(function) extern FLOAT function (FLOAT, FLOAT); +#define WRAPPER_DECL_fFF(function) extern void function (FLOAT, FLOAT *, FLOAT *); // Wrapper from scalar to vector function with vector length 8. #define VECTOR_WRAPPER(scalar_func, vector_func) \ @@ -71,3 +72,19 @@ FLOAT scalar_func (FLOAT x, FLOAT y) \ TEST_VEC_LOOP (mr, 8); \ return ((FLOAT) mr[0]); \ } + +// Wrapper from scalar 3 argument function to vector one. +#define VECTOR_WRAPPER_fFF(scalar_func, vector_func) \ +extern void vector_func (VEC_TYPE, VEC_TYPE *, VEC_TYPE *); \ +void scalar_func (FLOAT x, FLOAT * r, FLOAT * r1) \ +{ \ + int i; \ + VEC_TYPE mx, mr, mr1; \ + INIT_VEC_LOOP (mx, x, 8); \ + vector_func (mx, &mr, &mr1); \ + TEST_VEC_LOOP (mr, 8); \ + TEST_VEC_LOOP (mr1, 8); \ + *r = (FLOAT) mr[0]; \ + *r1 = (FLOAT) mr1[0]; \ + return; \ +} diff --git a/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist b/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist index 6c4584448e..b7efeab3ad 100644 --- a/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist +++ b/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist @@ -11,6 +11,7 @@ GLIBC_2.22 _ZGVbN4v_logf F _ZGVbN4v_sinf F _ZGVbN4vv_powf F + _ZGVbN4vvv_sincosf F _ZGVcN4v_cos F _ZGVcN4v_exp F _ZGVcN4v_log F @@ -22,6 +23,7 @@ GLIBC_2.22 _ZGVcN8v_logf F _ZGVcN8v_sinf F _ZGVcN8vv_powf F + _ZGVcN8vvv_sincosf F _ZGVdN4v_cos F _ZGVdN4v_exp F _ZGVdN4v_log F @@ -33,11 +35,13 @@ GLIBC_2.22 _ZGVdN8v_logf F _ZGVdN8v_sinf F _ZGVdN8vv_powf F + _ZGVdN8vvv_sincosf F _ZGVeN16v_cosf F _ZGVeN16v_expf F _ZGVeN16v_logf F _ZGVeN16v_sinf F _ZGVeN16vv_powf F + _ZGVeN16vvv_sincosf F _ZGVeN8v_cos F _ZGVeN8v_exp F _ZGVeN8v_log F diff --git a/sysdeps/x86/fpu/bits/math-vector.h b/sysdeps/x86/fpu/bits/math-vector.h index f684ff50be..f9e798b556 100644 --- a/sysdeps/x86/fpu/bits/math-vector.h +++ b/sysdeps/x86/fpu/bits/math-vector.h @@ -38,6 +38,8 @@ # define __DECL_SIMD_sinf __DECL_SIMD_x86_64 # undef __DECL_SIMD_sincos # define __DECL_SIMD_sincos __DECL_SIMD_x86_64 +# undef __DECL_SIMD_sincosf +# define __DECL_SIMD_sincosf __DECL_SIMD_x86_64 # undef __DECL_SIMD_log # define __DECL_SIMD_log __DECL_SIMD_x86_64 # undef __DECL_SIMD_logf diff --git a/sysdeps/x86_64/fpu/Makefile b/sysdeps/x86_64/fpu/Makefile index 9c28d62ee5..c6912cbadd 100644 --- a/sysdeps/x86_64/fpu/Makefile +++ b/sysdeps/x86_64/fpu/Makefile @@ -19,7 +19,9 @@ libmvec-support += svml_d_cos2_core svml_d_cos4_core_avx \ svml_d_pow4_core_avx svml_d_pow4_core svml_d_pow8_core \ svml_d_pow_data svml_s_powf4_core svml_s_powf8_core_avx \ svml_s_powf8_core svml_s_powf16_core svml_s_powf_data \ - init-arch + svml_s_sincosf4_core svml_s_sincosf8_core_avx \ + svml_s_sincosf8_core svml_s_sincosf16_core \ + svml_s_sincosf_data init-arch endif # Variables for libmvec tests. diff --git a/sysdeps/x86_64/fpu/Versions b/sysdeps/x86_64/fpu/Versions index d950f5852b..08132045d6 100644 --- a/sysdeps/x86_64/fpu/Versions +++ b/sysdeps/x86_64/fpu/Versions @@ -11,5 +11,6 @@ libmvec { _ZGVbN4v_logf; _ZGVcN8v_logf; _ZGVdN8v_logf; _ZGVeN16v_logf; _ZGVbN4v_expf; _ZGVcN8v_expf; _ZGVdN8v_expf; _ZGVeN16v_expf; _ZGVbN4vv_powf; _ZGVcN8vv_powf; _ZGVdN8vv_powf; _ZGVeN16vv_powf; + _ZGVbN4vvv_sincosf; _ZGVcN8vvv_sincosf; _ZGVdN8vvv_sincosf; _ZGVeN16vvv_sincosf; } } diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index 74b1af5bbc..2e2722df4b 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -2031,17 +2031,25 @@ idouble: 1 ildouble: 3 ldouble: 3 +Function: "sincos_vlen16": +float: 1 + Function: "sincos_vlen2": double: 1 Function: "sincos_vlen4": double: 1 +float: 1 Function: "sincos_vlen4_avx2": double: 1 Function: "sincos_vlen8": double: 1 +float: 1 + +Function: "sincos_vlen8_avx2": +float: 1 Function: "sinh": double: 2 diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile index 9e510db365..86ea473b4f 100644 --- a/sysdeps/x86_64/fpu/multiarch/Makefile +++ b/sysdeps/x86_64/fpu/multiarch/Makefile @@ -69,5 +69,6 @@ libmvec-sysdep_routines += svml_d_cos2_core_sse4 svml_d_cos4_core_avx2 \ svml_s_expf16_core_avx512 svml_d_pow2_core_sse4 \ svml_d_pow4_core_avx2 svml_d_pow8_core_avx512 \ svml_s_powf4_core_sse4 svml_s_powf8_core_avx2 \ - svml_s_powf16_core_avx512 + svml_s_powf16_core_avx512 svml_s_sincosf4_core_sse4 \ + svml_s_sincosf8_core_avx2 svml_s_sincosf16_core_avx512 endif diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core.S b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core.S new file mode 100644 index 0000000000..0a1753eab7 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core.S @@ -0,0 +1,39 @@ +/* Multiple versions of vectorized sincosf. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include <init-arch.h> + + .text +ENTRY (_ZGVeN16vvv_sincosf) + .type _ZGVeN16vvv_sincosf, @gnu_indirect_function + cmpl $0, KIND_OFFSET+__cpu_features(%rip) + jne 1 + call __init_cpu_features +1: leaq _ZGVeN16vvv_sincosf_skx(%rip), %rax + testl $bit_AVX512DQ_Usable, __cpu_features+FEATURE_OFFSET+index_AVX512DQ_Usable(%rip) + jnz 3 +2: leaq _ZGVeN16vvv_sincosf_knl(%rip), %rax + testl $bit_AVX512F_Usable, __cpu_features+FEATURE_OFFSET+index_AVX512F_Usable(%rip) + jnz 3 + leaq _ZGVeN16vvv_sincosf_avx2_wrapper(%rip), %rax +3: ret +END (_ZGVeN16vvv_sincosf) + +#define _ZGVeN16vvv_sincosf _ZGVeN16vvv_sincosf_avx2_wrapper +#include "../svml_s_sincosf16_core.S" diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core_avx512.S new file mode 100644 index 0000000000..cae49f63a6 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf16_core_avx512.S @@ -0,0 +1,504 @@ +/* Function sincosf vectorized with AVX-512. KNL and SKX versions. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_s_sincosf_data.h" +#include "svml_s_wrapper_impl.h" + +/* + ALGORITHM DESCRIPTION: + + 1) Range reduction to [-Pi/4; +Pi/4] interval + a) Grab sign from source argument and save it. + b) Remove sign using AND operation + c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value + e) Treat obtained value as integer S for destination sign setting. + SS = ((S-S&1)&2)<<30; For sin part + SC = ((S+S&1)&2)<<30; For cos part + f) Change destination sign if source sign is negative + using XOR operation. + g) Subtract "Right Shifter" (0x4B000000) value + h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 4 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3 - Y*PI4; + 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))); + c) Swap RS & RC if if first bit of obtained value after + Right Shifting is set to 1. Using And, Andnot & Or operations. + 3) Destination sign setting + a) Set shifted destination sign using XOR operation: + R1 = XOR( RS, SS ); + R2 = XOR( RC, SC ). */ + + .text +ENTRY (_ZGVeN16vvv_sincosf_knl) +#ifndef HAVE_AVX512_ASM_SUPPORT +WRAPPER_IMPL_AVX512_fFF _ZGVdN8vvv_sincosf +#else + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $1344, %rsp + movq __svml_ssincos_data@GOTPCREL(%rip), %rax + vmovaps %zmm0, %zmm2 + movl $-1, %edx + vmovups __sAbsMask(%rax), %zmm0 + vmovups __sInvPI(%rax), %zmm3 + +/* Absolute argument computation */ + vpandd %zmm0, %zmm2, %zmm1 + vmovups __sPI1_FMA(%rax), %zmm5 + vmovups __sSignMask(%rax), %zmm9 + vpandnd %zmm2, %zmm0, %zmm0 + +/* h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 3 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3 */ + vmovaps %zmm1, %zmm6 + vmovaps %zmm1, %zmm8 + +/* c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value */ + vfmadd213ps __sRShifter(%rax), %zmm1, %zmm3 + vmovups __sPI3_FMA(%rax), %zmm7 + +/* g) Subtract "Right Shifter" (0x4B000000) value */ + vsubps __sRShifter(%rax), %zmm3, %zmm12 + +/* e) Treat obtained value as integer S for destination sign setting */ + vpslld $31, %zmm3, %zmm13 + vmovups __sA7_FMA(%rax), %zmm14 + vfnmadd231ps %zmm12, %zmm5, %zmm6 + +/* 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))) */ + vmovaps %zmm14, %zmm15 + vmovups __sA9_FMA(%rax), %zmm3 + vcmpps $22, __sRangeReductionVal(%rax), %zmm1, %k1 + vpbroadcastd %edx, %zmm1{%k1}{z} + vfnmadd231ps __sPI2_FMA(%rax), %zmm12, %zmm6 + vptestmd %zmm1, %zmm1, %k0 + vpandd %zmm6, %zmm9, %zmm11 + kmovw %k0, %ecx + vpxord __sOneHalf(%rax), %zmm11, %zmm4 + +/* Result sign calculations */ + vpternlogd $150, %zmm13, %zmm9, %zmm11 + +/* Add correction term 0.5 for cos() part */ + vaddps %zmm4, %zmm12, %zmm10 + vfnmadd213ps %zmm6, %zmm7, %zmm12 + vfnmadd231ps %zmm10, %zmm5, %zmm8 + vpxord %zmm13, %zmm12, %zmm13 + vmulps %zmm13, %zmm13, %zmm12 + vfnmadd231ps __sPI2_FMA(%rax), %zmm10, %zmm8 + vfmadd231ps __sA9_FMA(%rax), %zmm12, %zmm15 + vfnmadd213ps %zmm8, %zmm7, %zmm10 + vfmadd213ps __sA5_FMA(%rax), %zmm12, %zmm15 + vpxord %zmm11, %zmm10, %zmm5 + vmulps %zmm5, %zmm5, %zmm4 + vfmadd213ps __sA3(%rax), %zmm12, %zmm15 + vfmadd213ps %zmm14, %zmm4, %zmm3 + vmulps %zmm12, %zmm15, %zmm14 + vfmadd213ps __sA5_FMA(%rax), %zmm4, %zmm3 + vfmadd213ps %zmm13, %zmm13, %zmm14 + vfmadd213ps __sA3(%rax), %zmm4, %zmm3 + vpxord %zmm0, %zmm14, %zmm0 + vmulps %zmm4, %zmm3, %zmm3 + vfmadd213ps %zmm5, %zmm5, %zmm3 + testl %ecx, %ecx + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + vmovups %zmm0, (%rdi) + vmovups %zmm3, (%rsi) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret + +.LBL_1_3: + cfi_restore_state + vmovups %zmm2, 1152(%rsp) + vmovups %zmm0, 1216(%rsp) + vmovups %zmm3, 1280(%rsp) + je .LBL_1_2 + + xorb %dl, %dl + kmovw %k4, 1048(%rsp) + xorl %eax, %eax + kmovw %k5, 1040(%rsp) + kmovw %k6, 1032(%rsp) + kmovw %k7, 1024(%rsp) + vmovups %zmm16, 960(%rsp) + vmovups %zmm17, 896(%rsp) + vmovups %zmm18, 832(%rsp) + vmovups %zmm19, 768(%rsp) + vmovups %zmm20, 704(%rsp) + vmovups %zmm21, 640(%rsp) + vmovups %zmm22, 576(%rsp) + vmovups %zmm23, 512(%rsp) + vmovups %zmm24, 448(%rsp) + vmovups %zmm25, 384(%rsp) + vmovups %zmm26, 320(%rsp) + vmovups %zmm27, 256(%rsp) + vmovups %zmm28, 192(%rsp) + vmovups %zmm29, 128(%rsp) + vmovups %zmm30, 64(%rsp) + vmovups %zmm31, (%rsp) + movq %rsi, 1056(%rsp) + movq %r12, 1096(%rsp) + cfi_offset_rel_rsp (12, 1096) + movb %dl, %r12b + movq %r13, 1088(%rsp) + cfi_offset_rel_rsp (13, 1088) + movl %eax, %r13d + movq %r14, 1080(%rsp) + cfi_offset_rel_rsp (14, 1080) + movl %ecx, %r14d + movq %r15, 1072(%rsp) + cfi_offset_rel_rsp (15, 1072) + movq %rbx, 1064(%rsp) + movq %rdi, %rbx + cfi_remember_state + +.LBL_1_6: + btl %r13d, %r14d + jc .LBL_1_13 + +.LBL_1_7: + lea 1(%r13), %esi + btl %esi, %r14d + jc .LBL_1_10 + +.LBL_1_8: + addb $1, %r12b + addl $2, %r13d + cmpb $16, %r12b + jb .LBL_1_6 + + movq %rbx, %rdi + kmovw 1048(%rsp), %k4 + movq 1056(%rsp), %rsi + kmovw 1040(%rsp), %k5 + movq 1096(%rsp), %r12 + cfi_restore (%r12) + kmovw 1032(%rsp), %k6 + movq 1088(%rsp), %r13 + cfi_restore (%r13) + kmovw 1024(%rsp), %k7 + vmovups 960(%rsp), %zmm16 + vmovups 896(%rsp), %zmm17 + vmovups 832(%rsp), %zmm18 + vmovups 768(%rsp), %zmm19 + vmovups 704(%rsp), %zmm20 + vmovups 640(%rsp), %zmm21 + vmovups 576(%rsp), %zmm22 + vmovups 512(%rsp), %zmm23 + vmovups 448(%rsp), %zmm24 + vmovups 384(%rsp), %zmm25 + vmovups 320(%rsp), %zmm26 + vmovups 256(%rsp), %zmm27 + vmovups 192(%rsp), %zmm28 + vmovups 128(%rsp), %zmm29 + vmovups 64(%rsp), %zmm30 + vmovups (%rsp), %zmm31 + movq 1080(%rsp), %r14 + cfi_restore (%r14) + movq 1072(%rsp), %r15 + cfi_restore (%r15) + movq 1064(%rsp), %rbx + vmovups 1216(%rsp), %zmm0 + vmovups 1280(%rsp), %zmm3 + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + vmovss 1156(%rsp,%r15,8), %xmm0 + + call sinf@PLT + + vmovss %xmm0, 1220(%rsp,%r15,8) + vmovss 1156(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + vmovss %xmm0, 1284(%rsp,%r15,8) + jmp .LBL_1_8 + +.LBL_1_13: + movzbl %r12b, %r15d + vmovss 1152(%rsp,%r15,8), %xmm0 + + call sinf@PLT + + vmovss %xmm0, 1216(%rsp,%r15,8) + vmovss 1152(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + vmovss %xmm0, 1280(%rsp,%r15,8) + jmp .LBL_1_7 +#endif +END (_ZGVeN16vvv_sincosf_knl) + +ENTRY (_ZGVeN16vvv_sincosf_skx) +#ifndef HAVE_AVX512_ASM_SUPPORT +WRAPPER_IMPL_AVX512_fFF _ZGVdN8vvv_sincosf +#else + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $1344, %rsp + movq __svml_ssincos_data@GOTPCREL(%rip), %rax + vmovaps %zmm0, %zmm4 + vmovups __sAbsMask(%rax), %zmm3 + vmovups __sInvPI(%rax), %zmm5 + vmovups __sRShifter(%rax), %zmm6 + vmovups __sPI1_FMA(%rax), %zmm9 + vmovups __sPI2_FMA(%rax), %zmm10 + vmovups __sSignMask(%rax), %zmm14 + vmovups __sOneHalf(%rax), %zmm7 + vmovups __sPI3_FMA(%rax), %zmm12 + +/* Absolute argument computation */ + vandps %zmm3, %zmm4, %zmm2 + +/* c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value */ + vfmadd213ps %zmm6, %zmm2, %zmm5 + vcmpps $18, __sRangeReductionVal(%rax), %zmm2, %k1 + +/* e) Treat obtained value as integer S for destination sign setting */ + vpslld $31, %zmm5, %zmm0 + +/* g) Subtract "Right Shifter" (0x4B000000) value */ + vsubps %zmm6, %zmm5, %zmm5 + vmovups __sA3(%rax), %zmm6 + +/* h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 3 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3 */ + vmovaps %zmm2, %zmm11 + vfnmadd231ps %zmm5, %zmm9, %zmm11 + vfnmadd231ps %zmm5, %zmm10, %zmm11 + vandps %zmm11, %zmm14, %zmm1 + vxorps %zmm1, %zmm7, %zmm8 + +/* Result sign calculations */ + vpternlogd $150, %zmm0, %zmm14, %zmm1 + vmovups .L_2il0floatpacket.13(%rip), %zmm14 + +/* Add correction term 0.5 for cos() part */ + vaddps %zmm8, %zmm5, %zmm15 + vfnmadd213ps %zmm11, %zmm12, %zmm5 + vandnps %zmm4, %zmm3, %zmm11 + vmovups __sA7_FMA(%rax), %zmm3 + vmovaps %zmm2, %zmm13 + vfnmadd231ps %zmm15, %zmm9, %zmm13 + vxorps %zmm0, %zmm5, %zmm9 + vmovups __sA5_FMA(%rax), %zmm0 + vfnmadd231ps %zmm15, %zmm10, %zmm13 + vmulps %zmm9, %zmm9, %zmm8 + vfnmadd213ps %zmm13, %zmm12, %zmm15 + vmovups __sA9_FMA(%rax), %zmm12 + vxorps %zmm1, %zmm15, %zmm1 + vmulps %zmm1, %zmm1, %zmm13 + +/* 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))) */ + vmovaps %zmm12, %zmm7 + vfmadd213ps %zmm3, %zmm8, %zmm7 + vfmadd213ps %zmm3, %zmm13, %zmm12 + vfmadd213ps %zmm0, %zmm8, %zmm7 + vfmadd213ps %zmm0, %zmm13, %zmm12 + vfmadd213ps %zmm6, %zmm8, %zmm7 + vfmadd213ps %zmm6, %zmm13, %zmm12 + vmulps %zmm8, %zmm7, %zmm10 + vmulps %zmm13, %zmm12, %zmm3 + vfmadd213ps %zmm9, %zmm9, %zmm10 + vfmadd213ps %zmm1, %zmm1, %zmm3 + vxorps %zmm11, %zmm10, %zmm0 + vpandnd %zmm2, %zmm2, %zmm14{%k1} + vptestmd %zmm14, %zmm14, %k0 + kmovw %k0, %ecx + testl %ecx, %ecx + jne .LBL_2_3 + +.LBL_2_2: + cfi_remember_state + vmovups %zmm0, (%rdi) + vmovups %zmm3, (%rsi) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret + +.LBL_2_3: + cfi_restore_state + vmovups %zmm4, 1152(%rsp) + vmovups %zmm0, 1216(%rsp) + vmovups %zmm3, 1280(%rsp) + je .LBL_2_2 + + xorb %dl, %dl + xorl %eax, %eax + kmovw %k4, 1048(%rsp) + kmovw %k5, 1040(%rsp) + kmovw %k6, 1032(%rsp) + kmovw %k7, 1024(%rsp) + vmovups %zmm16, 960(%rsp) + vmovups %zmm17, 896(%rsp) + vmovups %zmm18, 832(%rsp) + vmovups %zmm19, 768(%rsp) + vmovups %zmm20, 704(%rsp) + vmovups %zmm21, 640(%rsp) + vmovups %zmm22, 576(%rsp) + vmovups %zmm23, 512(%rsp) + vmovups %zmm24, 448(%rsp) + vmovups %zmm25, 384(%rsp) + vmovups %zmm26, 320(%rsp) + vmovups %zmm27, 256(%rsp) + vmovups %zmm28, 192(%rsp) + vmovups %zmm29, 128(%rsp) + vmovups %zmm30, 64(%rsp) + vmovups %zmm31, (%rsp) + movq %rsi, 1056(%rsp) + movq %r12, 1096(%rsp) + cfi_offset_rel_rsp (12, 1096) + movb %dl, %r12b + movq %r13, 1088(%rsp) + cfi_offset_rel_rsp (13, 1088) + movl %eax, %r13d + movq %r14, 1080(%rsp) + cfi_offset_rel_rsp (14, 1080) + movl %ecx, %r14d + movq %r15, 1072(%rsp) + cfi_offset_rel_rsp (15, 1072) + movq %rbx, 1064(%rsp) + movq %rdi, %rbx + cfi_remember_state + +.LBL_2_6: + btl %r13d, %r14d + jc .LBL_2_13 + +.LBL_2_7: + lea 1(%r13), %esi + btl %esi, %r14d + jc .LBL_2_10 + +.LBL_2_8: + incb %r12b + addl $2, %r13d + cmpb $16, %r12b + jb .LBL_2_6 + + kmovw 1048(%rsp), %k4 + movq %rbx, %rdi + kmovw 1040(%rsp), %k5 + kmovw 1032(%rsp), %k6 + kmovw 1024(%rsp), %k7 + vmovups 960(%rsp), %zmm16 + vmovups 896(%rsp), %zmm17 + vmovups 832(%rsp), %zmm18 + vmovups 768(%rsp), %zmm19 + vmovups 704(%rsp), %zmm20 + vmovups 640(%rsp), %zmm21 + vmovups 576(%rsp), %zmm22 + vmovups 512(%rsp), %zmm23 + vmovups 448(%rsp), %zmm24 + vmovups 384(%rsp), %zmm25 + vmovups 320(%rsp), %zmm26 + vmovups 256(%rsp), %zmm27 + vmovups 192(%rsp), %zmm28 + vmovups 128(%rsp), %zmm29 + vmovups 64(%rsp), %zmm30 + vmovups (%rsp), %zmm31 + vmovups 1216(%rsp), %zmm0 + vmovups 1280(%rsp), %zmm3 + movq 1056(%rsp), %rsi + movq 1096(%rsp), %r12 + cfi_restore (%r12) + movq 1088(%rsp), %r13 + cfi_restore (%r13) + movq 1080(%rsp), %r14 + cfi_restore (%r14) + movq 1072(%rsp), %r15 + cfi_restore (%r15) + movq 1064(%rsp), %rbx + jmp .LBL_2_2 + +.LBL_2_10: + cfi_restore_state + movzbl %r12b, %r15d + vmovss 1156(%rsp,%r15,8), %xmm0 + vzeroupper + vmovss 1156(%rsp,%r15,8), %xmm0 + + call sinf@PLT + + vmovss %xmm0, 1220(%rsp,%r15,8) + vmovss 1156(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + vmovss %xmm0, 1284(%rsp,%r15,8) + jmp .LBL_2_8 + +.LBL_2_13: + movzbl %r12b, %r15d + vmovss 1152(%rsp,%r15,8), %xmm0 + vzeroupper + vmovss 1152(%rsp,%r15,8), %xmm0 + + call sinf@PLT + + vmovss %xmm0, 1216(%rsp,%r15,8) + vmovss 1152(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + vmovss %xmm0, 1280(%rsp,%r15,8) + jmp .LBL_2_7 +#endif +END (_ZGVeN16vvv_sincosf_skx) + + .section .rodata, "a" +.L_2il0floatpacket.13: + .long 0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff,0xffffffff + .type .L_2il0floatpacket.13,@object diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core.S b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core.S new file mode 100644 index 0000000000..610046b587 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core.S @@ -0,0 +1,38 @@ +/* Multiple versions of vectorized sincosf. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include <init-arch.h> + + .text +ENTRY (_ZGVbN4vvv_sincosf) + .type _ZGVbN4vvv_sincosf, @gnu_indirect_function + cmpl $0, KIND_OFFSET+__cpu_features(%rip) + jne 1f + call __init_cpu_features +1: leaq _ZGVbN4vvv_sincosf_sse4(%rip), %rax + testl $bit_SSE4_1, __cpu_features+CPUID_OFFSET+index_SSE4_1(%rip) + jz 2f + ret +2: leaq _ZGVbN4vvv_sincosf_sse2(%rip), %rax + ret +END (_ZGVbN4vvv_sincosf) +libmvec_hidden_def (_ZGVbN4vvv_sincosf) + +#define _ZGVbN4vvv_sincosf _ZGVbN4vvv_sincosf_sse2 +#include "../svml_s_sincosf4_core.S" diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core_sse4.S new file mode 100644 index 0000000000..8c51e44988 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf4_core_sse4.S @@ -0,0 +1,268 @@ +/* Function sincosf vectorized with SSE4. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_s_sincosf_data.h" + + .text +ENTRY (_ZGVbN4vvv_sincosf_sse4) +/* + ALGORITHM DESCRIPTION: + + 1) Range reduction to [-Pi/4; +Pi/4] interval + a) Grab sign from source argument and save it. + b) Remove sign using AND operation + c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value + e) Treat obtained value as integer S for destination sign setting. + SS = ((S-S&1)&2)<<30; For sin part + SC = ((S+S&1)&2)<<30; For cos part + f) Change destination sign if source sign is negative + using XOR operation. + g) Subtract "Right Shifter" (0x4B000000) value + h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 4 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3 - Y*PI4; + 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))); + c) Swap RS & RC if if first bit of obtained value after + Right Shifting is set to 1. Using And, Andnot & Or operations. + 3) Destination sign setting + a) Set shifted destination sign using XOR operation: + R1 = XOR( RS, SS ); + R2 = XOR( RC, SC ). */ + + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $320, %rsp + movq __svml_ssincos_data@GOTPCREL(%rip), %rax + movups %xmm12, 176(%rsp) + movups %xmm9, 160(%rsp) + movups __sAbsMask(%rax), %xmm12 + +/* Absolute argument computation */ + movaps %xmm12, %xmm5 + andnps %xmm0, %xmm12 + movups __sInvPI(%rax), %xmm7 + andps %xmm0, %xmm5 + +/* c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value. */ + mulps %xmm5, %xmm7 + movups %xmm10, 144(%rsp) + movups __sPI1(%rax), %xmm10 + +/* h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 3 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3. */ + movaps %xmm10, %xmm1 + addps __sRShifter(%rax), %xmm7 + +/* e) Treat obtained value as integer S for destination sign setting */ + movaps %xmm7, %xmm9 + +/* g) Subtract "Right Shifter" (0x4B000000) value */ + subps __sRShifter(%rax), %xmm7 + mulps %xmm7, %xmm1 + pslld $31, %xmm9 + movups __sPI2(%rax), %xmm6 + movups %xmm13, 112(%rsp) + movaps %xmm5, %xmm13 + movaps %xmm6, %xmm2 + subps %xmm1, %xmm13 + mulps %xmm7, %xmm2 + movups __sSignMask(%rax), %xmm3 + movaps %xmm5, %xmm1 + movups __sOneHalf(%rax), %xmm4 + subps %xmm2, %xmm13 + cmpnleps __sRangeReductionVal(%rax), %xmm5 + movaps %xmm3, %xmm2 + andps %xmm13, %xmm2 + xorps %xmm2, %xmm4 + +/* Result sign calculations */ + xorps %xmm2, %xmm3 + xorps %xmm9, %xmm3 + +/* Add correction term 0.5 for cos() part */ + addps %xmm7, %xmm4 + movmskps %xmm5, %ecx + mulps %xmm4, %xmm10 + mulps %xmm4, %xmm6 + subps %xmm10, %xmm1 + movups __sPI3(%rax), %xmm10 + subps %xmm6, %xmm1 + movaps %xmm10, %xmm6 + mulps %xmm7, %xmm6 + mulps %xmm4, %xmm10 + subps %xmm6, %xmm13 + subps %xmm10, %xmm1 + movups __sPI4(%rax), %xmm6 + mulps %xmm6, %xmm7 + mulps %xmm6, %xmm4 + subps %xmm7, %xmm13 + subps %xmm4, %xmm1 + xorps %xmm9, %xmm13 + xorps %xmm3, %xmm1 + movaps %xmm13, %xmm4 + movaps %xmm1, %xmm2 + mulps %xmm13, %xmm4 + mulps %xmm1, %xmm2 + movups __sA9(%rax), %xmm7 + +/* 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))) */ + movaps %xmm7, %xmm3 + mulps %xmm4, %xmm3 + mulps %xmm2, %xmm7 + addps __sA7(%rax), %xmm3 + addps __sA7(%rax), %xmm7 + mulps %xmm4, %xmm3 + mulps %xmm2, %xmm7 + addps __sA5(%rax), %xmm3 + addps __sA5(%rax), %xmm7 + mulps %xmm4, %xmm3 + mulps %xmm2, %xmm7 + addps __sA3(%rax), %xmm3 + addps __sA3(%rax), %xmm7 + mulps %xmm3, %xmm4 + mulps %xmm7, %xmm2 + mulps %xmm13, %xmm4 + mulps %xmm1, %xmm2 + addps %xmm4, %xmm13 + addps %xmm2, %xmm1 + xorps %xmm12, %xmm13 + testl %ecx, %ecx + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + movups 160(%rsp), %xmm9 + movaps %xmm13, (%rdi) + movups 144(%rsp), %xmm10 + movups 176(%rsp), %xmm12 + movups 112(%rsp), %xmm13 + movups %xmm1, (%rsi) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret + +.LBL_1_3: + cfi_restore_state + movups %xmm0, 128(%rsp) + movups %xmm13, 192(%rsp) + movups %xmm1, 256(%rsp) + je .LBL_1_2 + + xorb %dl, %dl + xorl %eax, %eax + movups %xmm8, 48(%rsp) + movups %xmm11, 32(%rsp) + movups %xmm14, 16(%rsp) + movups %xmm15, (%rsp) + movq %rsi, 64(%rsp) + movq %r12, 104(%rsp) + cfi_offset_rel_rsp (12, 104) + movb %dl, %r12b + movq %r13, 96(%rsp) + cfi_offset_rel_rsp (13, 96) + movl %eax, %r13d + movq %r14, 88(%rsp) + cfi_offset_rel_rsp (14, 88) + movl %ecx, %r14d + movq %r15, 80(%rsp) + cfi_offset_rel_rsp (15, 80) + movq %rbx, 72(%rsp) + movq %rdi, %rbx + cfi_remember_state + +.LBL_1_6: + btl %r13d, %r14d + jc .LBL_1_13 + +.LBL_1_7: + lea 1(%r13), %esi + btl %esi, %r14d + jc .LBL_1_10 + +.LBL_1_8: + incb %r12b + addl $2, %r13d + cmpb $16, %r12b + jb .LBL_1_6 + + movups 48(%rsp), %xmm8 + movq %rbx, %rdi + movups 32(%rsp), %xmm11 + movups 16(%rsp), %xmm14 + movups (%rsp), %xmm15 + movq 64(%rsp), %rsi + movq 104(%rsp), %r12 + cfi_restore (%r12) + movq 96(%rsp), %r13 + cfi_restore (%r13) + movq 88(%rsp), %r14 + cfi_restore (%r14) + movq 80(%rsp), %r15 + cfi_restore (%r15) + movq 72(%rsp), %rbx + movups 192(%rsp), %xmm13 + movups 256(%rsp), %xmm1 + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + movss 132(%rsp,%r15,8), %xmm0 + + call sinf@PLT + + movss %xmm0, 196(%rsp,%r15,8) + movss 132(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + movss %xmm0, 260(%rsp,%r15,8) + jmp .LBL_1_8 + +.LBL_1_13: + movzbl %r12b, %r15d + movss 128(%rsp,%r15,8), %xmm0 + + call sinf@PLT + + movss %xmm0, 192(%rsp,%r15,8) + movss 128(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + movss %xmm0, 256(%rsp,%r15,8) + jmp .LBL_1_7 + +END (_ZGVbN4vvv_sincosf_sse4) diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core.S b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core.S new file mode 100644 index 0000000000..9e5be67fc9 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core.S @@ -0,0 +1,38 @@ +/* Multiple versions of vectorized sincosf. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include <init-arch.h> + + .text +ENTRY (_ZGVdN8vvv_sincosf) + .type _ZGVdN8vvv_sincosf, @gnu_indirect_function + cmpl $0, KIND_OFFSET+__cpu_features(%rip) + jne 1f + call __init_cpu_features +1: leaq _ZGVdN8vvv_sincosf_avx2(%rip), %rax + testl $bit_AVX2_Usable, __cpu_features+FEATURE_OFFSET+index_AVX2_Usable(%rip) + jz 2f + ret +2: leaq _ZGVdN8vvv_sincosf_sse_wrapper(%rip), %rax + ret +END (_ZGVdN8vvv_sincosf) +libmvec_hidden_def (_ZGVdN8vvv_sincosf) + +#define _ZGVdN8vvv_sincosf _ZGVdN8vvv_sincosf_sse_wrapper +#include "../svml_s_sincosf8_core.S" diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core_avx2.S new file mode 100644 index 0000000000..153c315799 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_s_sincosf8_core_avx2.S @@ -0,0 +1,241 @@ +/* Function sincosf vectorized with AVX2. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_s_sincosf_data.h" + + .text +ENTRY(_ZGVdN8vvv_sincosf_avx2) +/* + ALGORITHM DESCRIPTION: + + 1) Range reduction to [-Pi/4; +Pi/4] interval + a) Grab sign from source argument and save it. + b) Remove sign using AND operation + c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value + e) Treat obtained value as integer S for destination sign setting. + SS = ((S-S&1)&2)<<30; For sin part + SC = ((S+S&1)&2)<<30; For cos part + f) Change destination sign if source sign is negative + using XOR operation. + g) Subtract "Right Shifter" (0x4B000000) value + h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 4 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3 - Y*PI4; + 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))); + c) Swap RS & RC if if first bit of obtained value after + Right Shifting is set to 1. Using And, Andnot & Or operations. + 3) Destination sign setting + a) Set shifted destination sign using XOR operation: + R1 = XOR( RS, SS ); + R2 = XOR( RC, SC ). */ + + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $448, %rsp + movq __svml_ssincos_data@GOTPCREL(%rip), %rax + vmovdqa %ymm0, %ymm5 + vmovups %ymm13, 352(%rsp) + vmovups __sAbsMask(%rax), %ymm2 + vmovups __sInvPI(%rax), %ymm1 + vmovups __sPI1_FMA(%rax), %ymm13 + vmovups %ymm15, 288(%rsp) + +/* Absolute argument computation */ + vandps %ymm2, %ymm5, %ymm4 + +/* c) Getting octant Y by 2/Pi multiplication + d) Add "Right Shifter" value */ + vfmadd213ps __sRShifter(%rax), %ymm4, %ymm1 + +/* e) Treat obtained value as integer S for destination sign setting */ + vpslld $31, %ymm1, %ymm0 + +/* g) Subtract "Right Shifter" (0x4B000000) value */ + vsubps __sRShifter(%rax), %ymm1, %ymm1 + +/* h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 3 parts: + X = X - Y*PI1 - Y*PI2 - Y*PI3 */ + vmovdqa %ymm4, %ymm7 + vfnmadd231ps %ymm1, %ymm13, %ymm7 + vfnmadd231ps __sPI2_FMA(%rax), %ymm1, %ymm7 + vandps __sSignMask(%rax), %ymm7, %ymm15 + vxorps __sOneHalf(%rax), %ymm15, %ymm6 + +/* Add correction term 0.5 for cos() part */ + vaddps %ymm6, %ymm1, %ymm6 + vmovdqa %ymm4, %ymm3 + vfnmadd231ps %ymm6, %ymm13, %ymm3 + vmovups __sPI3_FMA(%rax), %ymm13 + vcmpnle_uqps __sRangeReductionVal(%rax), %ymm4, %ymm4 + vfnmadd231ps __sPI2_FMA(%rax), %ymm6, %ymm3 + vfnmadd213ps %ymm7, %ymm13, %ymm1 + vfnmadd213ps %ymm3, %ymm13, %ymm6 + +/* Result sign calculations */ + vxorps __sSignMask(%rax), %ymm15, %ymm3 + vxorps %ymm0, %ymm3, %ymm7 + vxorps %ymm7, %ymm6, %ymm3 + vxorps %ymm0, %ymm1, %ymm15 + vandnps %ymm5, %ymm2, %ymm6 + vmovups __sA7_FMA(%rax), %ymm2 + vmulps %ymm15, %ymm15, %ymm13 + vmovups __sA9_FMA(%rax), %ymm7 + vmulps %ymm3, %ymm3, %ymm1 + +/* 2) Polynomial (minimax for sin within [-Pi/4; +Pi/4] interval) + a) Calculate X^2 = X * X + b) Calculate 2 polynomials for sin and cos: + RS = X * ( A0 + X^2 * (A1 + x^2 * (A2 + x^2 * (A3)))); + RC = B0 + X^2 * (B1 + x^2 * (B2 + x^2 * (B3 + x^2 * (B4)))) */ + vmovdqa %ymm2, %ymm0 + vfmadd231ps __sA9_FMA(%rax), %ymm13, %ymm0 + vfmadd213ps %ymm2, %ymm1, %ymm7 + vfmadd213ps __sA5_FMA(%rax), %ymm13, %ymm0 + vfmadd213ps __sA5_FMA(%rax), %ymm1, %ymm7 + vfmadd213ps __sA3(%rax), %ymm13, %ymm0 + vfmadd213ps __sA3(%rax), %ymm1, %ymm7 + vmulps %ymm13, %ymm0, %ymm13 + vmulps %ymm1, %ymm7, %ymm1 + vfmadd213ps %ymm15, %ymm15, %ymm13 + vfmadd213ps %ymm3, %ymm3, %ymm1 + vmovmskps %ymm4, %ecx + vxorps %ymm6, %ymm13, %ymm0 + testl %ecx, %ecx + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + vmovups 352(%rsp), %ymm13 + vmovups 288(%rsp), %ymm15 + vmovups %ymm0, (%rdi) + vmovups %ymm1, (%rsi) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret + +.LBL_1_3: + cfi_restore_state + vmovups %ymm5, 256(%rsp) + vmovups %ymm0, 320(%rsp) + vmovups %ymm1, 384(%rsp) + je .LBL_1_2 + + xorb %dl, %dl + xorl %eax, %eax + vmovups %ymm8, 160(%rsp) + vmovups %ymm9, 128(%rsp) + vmovups %ymm10, 96(%rsp) + vmovups %ymm11, 64(%rsp) + vmovups %ymm12, 32(%rsp) + vmovups %ymm14, (%rsp) + movq %rsi, 192(%rsp) + movq %r12, 232(%rsp) + cfi_offset_rel_rsp (12, 232) + movb %dl, %r12b + movq %r13, 224(%rsp) + cfi_offset_rel_rsp (13, 224) + movl %eax, %r13d + movq %r14, 216(%rsp) + cfi_offset_rel_rsp (14, 216) + movl %ecx, %r14d + movq %r15, 208(%rsp) + cfi_offset_rel_rsp (14, 208) + movq %rbx, 200(%rsp) + movq %rdi, %rbx + cfi_remember_state + +.LBL_1_6: + btl %r13d, %r14d + jc .LBL_1_13 + +.LBL_1_7: + lea 1(%r13), %esi + btl %esi, %r14d + jc .LBL_1_10 + +.LBL_1_8: + incb %r12b + addl $2, %r13d + cmpb $16, %r12b + jb .LBL_1_6 + + vmovups 160(%rsp), %ymm8 + movq %rbx, %rdi + vmovups 128(%rsp), %ymm9 + vmovups 96(%rsp), %ymm10 + vmovups 64(%rsp), %ymm11 + vmovups 32(%rsp), %ymm12 + vmovups (%rsp), %ymm14 + vmovups 320(%rsp), %ymm0 + vmovups 384(%rsp), %ymm1 + movq 192(%rsp), %rsi + movq 232(%rsp), %r12 + cfi_restore (%r12) + movq 224(%rsp), %r13 + cfi_restore (%r13) + movq 216(%rsp), %r14 + cfi_restore (%r14) + movq 208(%rsp), %r15 + cfi_restore (%r15) + movq 200(%rsp), %rbx + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + vmovss 260(%rsp,%r15,8), %xmm0 + vzeroupper + + call sinf@PLT + + vmovss %xmm0, 324(%rsp,%r15,8) + vmovss 260(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + vmovss %xmm0, 388(%rsp,%r15,8) + jmp .LBL_1_8 + +.LBL_1_13: + movzbl %r12b, %r15d + vmovss 256(%rsp,%r15,8), %xmm0 + vzeroupper + + call sinf@PLT + + vmovss %xmm0, 320(%rsp,%r15,8) + vmovss 256(%rsp,%r15,8), %xmm0 + + call cosf@PLT + + vmovss %xmm0, 384(%rsp,%r15,8) + jmp .LBL_1_7 + +END(_ZGVdN8vvv_sincosf_avx2) diff --git a/sysdeps/x86_64/fpu/svml_s_sincosf16_core.S b/sysdeps/x86_64/fpu/svml_s_sincosf16_core.S new file mode 100644 index 0000000000..992f9a91cc --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_s_sincosf16_core.S @@ -0,0 +1,25 @@ +/* Function sincosf vectorized with AVX-512. Wrapper to AVX2 version. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_s_wrapper_impl.h" + + .text +ENTRY (_ZGVeN16vvv_sincosf) +WRAPPER_IMPL_AVX512_fFF _ZGVdN8vvv_sincosf +END (_ZGVeN16vvv_sincosf) diff --git a/sysdeps/x86_64/fpu/svml_s_sincosf4_core.S b/sysdeps/x86_64/fpu/svml_s_sincosf4_core.S new file mode 100644 index 0000000000..d402ffba15 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_s_sincosf4_core.S @@ -0,0 +1,30 @@ +/* Function sincosf vectorized with SSE2. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + + +#include <sysdep.h> +#include "svml_s_wrapper_impl.h" + + .text +ENTRY (_ZGVbN4vvv_sincosf) +WRAPPER_IMPL_SSE2_fFF sincosf +END (_ZGVbN4vvv_sincosf) + +#ifndef USE_MULTIARCH + libmvec_hidden_def (_ZGVbN4vvv_sincosf) +#endif diff --git a/sysdeps/x86_64/fpu/svml_s_sincosf8_core.S b/sysdeps/x86_64/fpu/svml_s_sincosf8_core.S new file mode 100644 index 0000000000..eec7de87d5 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_s_sincosf8_core.S @@ -0,0 +1,29 @@ +/* Function sincosf vectorized with AVX2, wrapper version. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_s_wrapper_impl.h" + + .text +ENTRY (_ZGVdN8vvv_sincosf) +WRAPPER_IMPL_AVX_fFF _ZGVbN4vvv_sincosf +END (_ZGVdN8vvv_sincosf) + +#ifndef USE_MULTIARCH + libmvec_hidden_def (_ZGVdN8vvv_sincosf) +#endif diff --git a/sysdeps/x86_64/fpu/svml_s_sincosf8_core_avx.S b/sysdeps/x86_64/fpu/svml_s_sincosf8_core_avx.S new file mode 100644 index 0000000000..c247444dfc --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_s_sincosf8_core_avx.S @@ -0,0 +1,25 @@ +/* Function sincosf vectorized in AVX ISA as wrapper to SSE4 ISA version. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_s_wrapper_impl.h" + + .text +ENTRY(_ZGVcN8vvv_sincosf) +WRAPPER_IMPL_AVX_fFF _ZGVbN4vvv_sincosf +END(_ZGVcN8vvv_sincosf) diff --git a/sysdeps/x86_64/fpu/svml_s_sincosf_data.S b/sysdeps/x86_64/fpu/svml_s_sincosf_data.S new file mode 100644 index 0000000000..040414d377 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_s_sincosf_data.S @@ -0,0 +1,1140 @@ +/* Data for function sincosf. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include "svml_s_sincosf_data.h" + + .section .rodata, "a" + .align 64 + .align 64 + +/* Data table for vector implementations of function sincosf. + The table may contain polynomial, reduction, lookup coefficients + and other coefficients obtained through different methods of research + and experimental work. */ + + .globl __svml_ssincos_data +__svml_ssincos_data: + +/* Lookup table for high accuracy version (CHL,SHi,SLo,Sigma) */ +.if .-__svml_ssincos_data != __dT +.err +.endif + .long 0x00000000 + .long 0x00000000 + .long 0x00000000 + .long 0x3f800000 + .long 0xb99de7df + .long 0x3cc90ab0 + .long 0xb005c998 + .long 0x3f800000 + .long 0xba9de1c8 + .long 0x3d48fb30 + .long 0xb0ef227f + .long 0x3f800000 + .long 0xbb319298 + .long 0x3d96a905 + .long 0xb1531e61 + .long 0x3f800000 + .long 0xbb9dc971 + .long 0x3dc8bd36 + .long 0xb07592f5 + .long 0x3f800000 + .long 0xbbf66e3c + .long 0x3dfab273 + .long 0xb11568cf + .long 0x3f800000 + .long 0xbc315502 + .long 0x3e164083 + .long 0x31e8e614 + .long 0x3f800000 + .long 0xbc71360b + .long 0x3e2f10a2 + .long 0x311167f9 + .long 0x3f800000 + .long 0xbc9d6830 + .long 0x3e47c5c2 + .long 0xb0e5967d + .long 0x3f800000 + .long 0xbcc70c54 + .long 0x3e605c13 + .long 0x31a7e4f6 + .long 0x3f800000 + .long 0xbcf58104 + .long 0x3e78cfcc + .long 0xb11bd41d + .long 0x3f800000 + .long 0xbd145f8c + .long 0x3e888e93 + .long 0x312c7d9e + .long 0x3f800000 + .long 0xbd305f55 + .long 0x3e94a031 + .long 0x326d59f0 + .long 0x3f800000 + .long 0xbd4ebb8a + .long 0x3ea09ae5 + .long 0xb23e89a0 + .long 0x3f800000 + .long 0xbd6f6f7e + .long 0x3eac7cd4 + .long 0xb2254e02 + .long 0x3f800000 + .long 0xbd893b12 + .long 0x3eb8442a + .long 0xb2705ba6 + .long 0x3f800000 + .long 0xbd9be50c + .long 0x3ec3ef15 + .long 0x31d5d52c + .long 0x3f800000 + .long 0xbdafb2cc + .long 0x3ecf7bca + .long 0x316a3b63 + .long 0x3f800000 + .long 0xbdc4a143 + .long 0x3edae880 + .long 0x321e15cc + .long 0x3f800000 + .long 0xbddaad38 + .long 0x3ee63375 + .long 0xb1d9c774 + .long 0x3f800000 + .long 0xbdf1d344 + .long 0x3ef15aea + .long 0xb1ff2139 + .long 0x3f800000 + .long 0xbe0507ea + .long 0x3efc5d27 + .long 0xb180eca9 + .long 0x3f800000 + .long 0xbe11af97 + .long 0x3f039c3d + .long 0xb25ba002 + .long 0x3f800000 + .long 0xbe1edeb5 + .long 0x3f08f59b + .long 0xb2be4b4e + .long 0x3f800000 + .long 0xbe2c933b + .long 0x3f0e39da + .long 0xb24a32e7 + .long 0x3f800000 + .long 0xbe3acb0c + .long 0x3f13682a + .long 0x32cdd12e + .long 0x3f800000 + .long 0xbe4983f7 + .long 0x3f187fc0 + .long 0xb1c7a3f3 + .long 0x3f800000 + .long 0xbe58bbb7 + .long 0x3f1d7fd1 + .long 0x3292050c + .long 0x3f800000 + .long 0xbe686ff3 + .long 0x3f226799 + .long 0x322123bb + .long 0x3f800000 + .long 0xbe789e3f + .long 0x3f273656 + .long 0xb2038343 + .long 0x3f800000 + .long 0xbe84a20e + .long 0x3f2beb4a + .long 0xb2b73136 + .long 0x3f800000 + .long 0xbe8d2f7d + .long 0x3f3085bb + .long 0xb2ae2d32 + .long 0x3f800000 + .long 0xbe95f61a + .long 0x3f3504f3 + .long 0x324fe77a + .long 0x3f800000 + .long 0x3e4216eb + .long 0x3f396842 + .long 0xb2810007 + .long 0x3f000000 + .long 0x3e2fad27 + .long 0x3f3daef9 + .long 0x319aabec + .long 0x3f000000 + .long 0x3e1cd957 + .long 0x3f41d870 + .long 0x32bff977 + .long 0x3f000000 + .long 0x3e099e65 + .long 0x3f45e403 + .long 0x32b15174 + .long 0x3f000000 + .long 0x3debfe8a + .long 0x3f49d112 + .long 0x32992640 + .long 0x3f000000 + .long 0x3dc3fdff + .long 0x3f4d9f02 + .long 0x327e70e8 + .long 0x3f000000 + .long 0x3d9b4153 + .long 0x3f514d3d + .long 0x300c4f04 + .long 0x3f000000 + .long 0x3d639d9d + .long 0x3f54db31 + .long 0x3290ea1a + .long 0x3f000000 + .long 0x3d0f59aa + .long 0x3f584853 + .long 0xb27d5fc0 + .long 0x3f000000 + .long 0x3c670f32 + .long 0x3f5b941a + .long 0x32232dc8 + .long 0x3f000000 + .long 0xbbe8b648 + .long 0x3f5ebe05 + .long 0x32c6f953 + .long 0x3f000000 + .long 0xbcea5164 + .long 0x3f61c598 + .long 0xb2e7f425 + .long 0x3f000000 + .long 0xbd4e645a + .long 0x3f64aa59 + .long 0x311a08fa + .long 0x3f000000 + .long 0xbd945dff + .long 0x3f676bd8 + .long 0xb2bc3389 + .long 0x3f000000 + .long 0xbdc210d8 + .long 0x3f6a09a7 + .long 0xb2eb236c + .long 0x3f000000 + .long 0xbdf043ab + .long 0x3f6c835e + .long 0x32f328d4 + .long 0x3f000000 + .long 0xbe0f77ad + .long 0x3f6ed89e + .long 0xb29333dc + .long 0x3f000000 + .long 0x3db1f34f + .long 0x3f710908 + .long 0x321ed0dd + .long 0x3e800000 + .long 0x3d826b93 + .long 0x3f731447 + .long 0x32c48e11 + .long 0x3e800000 + .long 0x3d25018c + .long 0x3f74fa0b + .long 0xb2939d22 + .long 0x3e800000 + .long 0x3c88e931 + .long 0x3f76ba07 + .long 0x326d092c + .long 0x3e800000 + .long 0xbbe60685 + .long 0x3f7853f8 + .long 0xb20db9e5 + .long 0x3e800000 + .long 0xbcfd1f65 + .long 0x3f79c79d + .long 0x32c64e59 + .long 0x3e800000 + .long 0xbd60e8f8 + .long 0x3f7b14be + .long 0x32ff75cb + .long 0x3e800000 + .long 0x3d3c4289 + .long 0x3f7c3b28 + .long 0xb231d68b + .long 0x3e000000 + .long 0x3cb2041c + .long 0x3f7d3aac + .long 0xb0f75ae9 + .long 0x3e000000 + .long 0xbb29b1a9 + .long 0x3f7e1324 + .long 0xb2f1e603 + .long 0x3e000000 + .long 0xbcdd0b28 + .long 0x3f7ec46d + .long 0x31f44949 + .long 0x3e000000 + .long 0x3c354825 + .long 0x3f7f4e6d + .long 0x32d01884 + .long 0x3d800000 + .long 0xbc5c1342 + .long 0x3f7fb10f + .long 0x31de5b5f + .long 0x3d800000 + .long 0xbbdbd541 + .long 0x3f7fec43 + .long 0x3084cd0d + .long 0x3d000000 + .long 0x00000000 + .long 0x3f800000 + .long 0x00000000 + .long 0x00000000 + .long 0x3bdbd541 + .long 0x3f7fec43 + .long 0x3084cd0d + .long 0xbd000000 + .long 0x3c5c1342 + .long 0x3f7fb10f + .long 0x31de5b5f + .long 0xbd800000 + .long 0xbc354825 + .long 0x3f7f4e6d + .long 0x32d01884 + .long 0xbd800000 + .long 0x3cdd0b28 + .long 0x3f7ec46d + .long 0x31f44949 + .long 0xbe000000 + .long 0x3b29b1a9 + .long 0x3f7e1324 + .long 0xb2f1e603 + .long 0xbe000000 + .long 0xbcb2041c + .long 0x3f7d3aac + .long 0xb0f75ae9 + .long 0xbe000000 + .long 0xbd3c4289 + .long 0x3f7c3b28 + .long 0xb231d68b + .long 0xbe000000 + .long 0x3d60e8f8 + .long 0x3f7b14be + .long 0x32ff75cb + .long 0xbe800000 + .long 0x3cfd1f65 + .long 0x3f79c79d + .long 0x32c64e59 + .long 0xbe800000 + .long 0x3be60685 + .long 0x3f7853f8 + .long 0xb20db9e5 + .long 0xbe800000 + .long 0xbc88e931 + .long 0x3f76ba07 + .long 0x326d092c + .long 0xbe800000 + .long 0xbd25018c + .long 0x3f74fa0b + .long 0xb2939d22 + .long 0xbe800000 + .long 0xbd826b93 + .long 0x3f731447 + .long 0x32c48e11 + .long 0xbe800000 + .long 0xbdb1f34f + .long 0x3f710908 + .long 0x321ed0dd + .long 0xbe800000 + .long 0x3e0f77ad + .long 0x3f6ed89e + .long 0xb29333dc + .long 0xbf000000 + .long 0x3df043ab + .long 0x3f6c835e + .long 0x32f328d4 + .long 0xbf000000 + .long 0x3dc210d8 + .long 0x3f6a09a7 + .long 0xb2eb236c + .long 0xbf000000 + .long 0x3d945dff + .long 0x3f676bd8 + .long 0xb2bc3389 + .long 0xbf000000 + .long 0x3d4e645a + .long 0x3f64aa59 + .long 0x311a08fa + .long 0xbf000000 + .long 0x3cea5164 + .long 0x3f61c598 + .long 0xb2e7f425 + .long 0xbf000000 + .long 0x3be8b648 + .long 0x3f5ebe05 + .long 0x32c6f953 + .long 0xbf000000 + .long 0xbc670f32 + .long 0x3f5b941a + .long 0x32232dc8 + .long 0xbf000000 + .long 0xbd0f59aa + .long 0x3f584853 + .long 0xb27d5fc0 + .long 0xbf000000 + .long 0xbd639d9d + .long 0x3f54db31 + .long 0x3290ea1a + .long 0xbf000000 + .long 0xbd9b4153 + .long 0x3f514d3d + .long 0x300c4f04 + .long 0xbf000000 + .long 0xbdc3fdff + .long 0x3f4d9f02 + .long 0x327e70e8 + .long 0xbf000000 + .long 0xbdebfe8a + .long 0x3f49d112 + .long 0x32992640 + .long 0xbf000000 + .long 0xbe099e65 + .long 0x3f45e403 + .long 0x32b15174 + .long 0xbf000000 + .long 0xbe1cd957 + .long 0x3f41d870 + .long 0x32bff977 + .long 0xbf000000 + .long 0xbe2fad27 + .long 0x3f3daef9 + .long 0x319aabec + .long 0xbf000000 + .long 0xbe4216eb + .long 0x3f396842 + .long 0xb2810007 + .long 0xbf000000 + .long 0x3e95f61a + .long 0x3f3504f3 + .long 0x324fe77a + .long 0xbf800000 + .long 0x3e8d2f7d + .long 0x3f3085bb + .long 0xb2ae2d32 + .long 0xbf800000 + .long 0x3e84a20e + .long 0x3f2beb4a + .long 0xb2b73136 + .long 0xbf800000 + .long 0x3e789e3f + .long 0x3f273656 + .long 0xb2038343 + .long 0xbf800000 + .long 0x3e686ff3 + .long 0x3f226799 + .long 0x322123bb + .long 0xbf800000 + .long 0x3e58bbb7 + .long 0x3f1d7fd1 + .long 0x3292050c + .long 0xbf800000 + .long 0x3e4983f7 + .long 0x3f187fc0 + .long 0xb1c7a3f3 + .long 0xbf800000 + .long 0x3e3acb0c + .long 0x3f13682a + .long 0x32cdd12e + .long 0xbf800000 + .long 0x3e2c933b + .long 0x3f0e39da + .long 0xb24a32e7 + .long 0xbf800000 + .long 0x3e1edeb5 + .long 0x3f08f59b + .long 0xb2be4b4e + .long 0xbf800000 + .long 0x3e11af97 + .long 0x3f039c3d + .long 0xb25ba002 + .long 0xbf800000 + .long 0x3e0507ea + .long 0x3efc5d27 + .long 0xb180eca9 + .long 0xbf800000 + .long 0x3df1d344 + .long 0x3ef15aea + .long 0xb1ff2139 + .long 0xbf800000 + .long 0x3ddaad38 + .long 0x3ee63375 + .long 0xb1d9c774 + .long 0xbf800000 + .long 0x3dc4a143 + .long 0x3edae880 + .long 0x321e15cc + .long 0xbf800000 + .long 0x3dafb2cc + .long 0x3ecf7bca + .long 0x316a3b63 + .long 0xbf800000 + .long 0x3d9be50c + .long 0x3ec3ef15 + .long 0x31d5d52c + .long 0xbf800000 + .long 0x3d893b12 + .long 0x3eb8442a + .long 0xb2705ba6 + .long 0xbf800000 + .long 0x3d6f6f7e + .long 0x3eac7cd4 + .long 0xb2254e02 + .long 0xbf800000 + .long 0x3d4ebb8a + .long 0x3ea09ae5 + .long 0xb23e89a0 + .long 0xbf800000 + .long 0x3d305f55 + .long 0x3e94a031 + .long 0x326d59f0 + .long 0xbf800000 + .long 0x3d145f8c + .long 0x3e888e93 + .long 0x312c7d9e + .long 0xbf800000 + .long 0x3cf58104 + .long 0x3e78cfcc + .long 0xb11bd41d + .long 0xbf800000 + .long 0x3cc70c54 + .long 0x3e605c13 + .long 0x31a7e4f6 + .long 0xbf800000 + .long 0x3c9d6830 + .long 0x3e47c5c2 + .long 0xb0e5967d + .long 0xbf800000 + .long 0x3c71360b + .long 0x3e2f10a2 + .long 0x311167f9 + .long 0xbf800000 + .long 0x3c315502 + .long 0x3e164083 + .long 0x31e8e614 + .long 0xbf800000 + .long 0x3bf66e3c + .long 0x3dfab273 + .long 0xb11568cf + .long 0xbf800000 + .long 0x3b9dc971 + .long 0x3dc8bd36 + .long 0xb07592f5 + .long 0xbf800000 + .long 0x3b319298 + .long 0x3d96a905 + .long 0xb1531e61 + .long 0xbf800000 + .long 0x3a9de1c8 + .long 0x3d48fb30 + .long 0xb0ef227f + .long 0xbf800000 + .long 0x399de7df + .long 0x3cc90ab0 + .long 0xb005c998 + .long 0xbf800000 + .long 0x00000000 + .long 0x00000000 + .long 0x00000000 + .long 0xbf800000 + .long 0x399de7df + .long 0xbcc90ab0 + .long 0x3005c998 + .long 0xbf800000 + .long 0x3a9de1c8 + .long 0xbd48fb30 + .long 0x30ef227f + .long 0xbf800000 + .long 0x3b319298 + .long 0xbd96a905 + .long 0x31531e61 + .long 0xbf800000 + .long 0x3b9dc971 + .long 0xbdc8bd36 + .long 0x307592f5 + .long 0xbf800000 + .long 0x3bf66e3c + .long 0xbdfab273 + .long 0x311568cf + .long 0xbf800000 + .long 0x3c315502 + .long 0xbe164083 + .long 0xb1e8e614 + .long 0xbf800000 + .long 0x3c71360b + .long 0xbe2f10a2 + .long 0xb11167f9 + .long 0xbf800000 + .long 0x3c9d6830 + .long 0xbe47c5c2 + .long 0x30e5967d + .long 0xbf800000 + .long 0x3cc70c54 + .long 0xbe605c13 + .long 0xb1a7e4f6 + .long 0xbf800000 + .long 0x3cf58104 + .long 0xbe78cfcc + .long 0x311bd41d + .long 0xbf800000 + .long 0x3d145f8c + .long 0xbe888e93 + .long 0xb12c7d9e + .long 0xbf800000 + .long 0x3d305f55 + .long 0xbe94a031 + .long 0xb26d59f0 + .long 0xbf800000 + .long 0x3d4ebb8a + .long 0xbea09ae5 + .long 0x323e89a0 + .long 0xbf800000 + .long 0x3d6f6f7e + .long 0xbeac7cd4 + .long 0x32254e02 + .long 0xbf800000 + .long 0x3d893b12 + .long 0xbeb8442a + .long 0x32705ba6 + .long 0xbf800000 + .long 0x3d9be50c + .long 0xbec3ef15 + .long 0xb1d5d52c + .long 0xbf800000 + .long 0x3dafb2cc + .long 0xbecf7bca + .long 0xb16a3b63 + .long 0xbf800000 + .long 0x3dc4a143 + .long 0xbedae880 + .long 0xb21e15cc + .long 0xbf800000 + .long 0x3ddaad38 + .long 0xbee63375 + .long 0x31d9c774 + .long 0xbf800000 + .long 0x3df1d344 + .long 0xbef15aea + .long 0x31ff2139 + .long 0xbf800000 + .long 0x3e0507ea + .long 0xbefc5d27 + .long 0x3180eca9 + .long 0xbf800000 + .long 0x3e11af97 + .long 0xbf039c3d + .long 0x325ba002 + .long 0xbf800000 + .long 0x3e1edeb5 + .long 0xbf08f59b + .long 0x32be4b4e + .long 0xbf800000 + .long 0x3e2c933b + .long 0xbf0e39da + .long 0x324a32e7 + .long 0xbf800000 + .long 0x3e3acb0c + .long 0xbf13682a + .long 0xb2cdd12e + .long 0xbf800000 + .long 0x3e4983f7 + .long 0xbf187fc0 + .long 0x31c7a3f3 + .long 0xbf800000 + .long 0x3e58bbb7 + .long 0xbf1d7fd1 + .long 0xb292050c + .long 0xbf800000 + .long 0x3e686ff3 + .long 0xbf226799 + .long 0xb22123bb + .long 0xbf800000 + .long 0x3e789e3f + .long 0xbf273656 + .long 0x32038343 + .long 0xbf800000 + .long 0x3e84a20e + .long 0xbf2beb4a + .long 0x32b73136 + .long 0xbf800000 + .long 0x3e8d2f7d + .long 0xbf3085bb + .long 0x32ae2d32 + .long 0xbf800000 + .long 0x3e95f61a + .long 0xbf3504f3 + .long 0xb24fe77a + .long 0xbf800000 + .long 0xbe4216eb + .long 0xbf396842 + .long 0x32810007 + .long 0xbf000000 + .long 0xbe2fad27 + .long 0xbf3daef9 + .long 0xb19aabec + .long 0xbf000000 + .long 0xbe1cd957 + .long 0xbf41d870 + .long 0xb2bff977 + .long 0xbf000000 + .long 0xbe099e65 + .long 0xbf45e403 + .long 0xb2b15174 + .long 0xbf000000 + .long 0xbdebfe8a + .long 0xbf49d112 + .long 0xb2992640 + .long 0xbf000000 + .long 0xbdc3fdff + .long 0xbf4d9f02 + .long 0xb27e70e8 + .long 0xbf000000 + .long 0xbd9b4153 + .long 0xbf514d3d + .long 0xb00c4f04 + .long 0xbf000000 + .long 0xbd639d9d + .long 0xbf54db31 + .long 0xb290ea1a + .long 0xbf000000 + .long 0xbd0f59aa + .long 0xbf584853 + .long 0x327d5fc0 + .long 0xbf000000 + .long 0xbc670f32 + .long 0xbf5b941a + .long 0xb2232dc8 + .long 0xbf000000 + .long 0x3be8b648 + .long 0xbf5ebe05 + .long 0xb2c6f953 + .long 0xbf000000 + .long 0x3cea5164 + .long 0xbf61c598 + .long 0x32e7f425 + .long 0xbf000000 + .long 0x3d4e645a + .long 0xbf64aa59 + .long 0xb11a08fa + .long 0xbf000000 + .long 0x3d945dff + .long 0xbf676bd8 + .long 0x32bc3389 + .long 0xbf000000 + .long 0x3dc210d8 + .long 0xbf6a09a7 + .long 0x32eb236c + .long 0xbf000000 + .long 0x3df043ab + .long 0xbf6c835e + .long 0xb2f328d4 + .long 0xbf000000 + .long 0x3e0f77ad + .long 0xbf6ed89e + .long 0x329333dc + .long 0xbf000000 + .long 0xbdb1f34f + .long 0xbf710908 + .long 0xb21ed0dd + .long 0xbe800000 + .long 0xbd826b93 + .long 0xbf731447 + .long 0xb2c48e11 + .long 0xbe800000 + .long 0xbd25018c + .long 0xbf74fa0b + .long 0x32939d22 + .long 0xbe800000 + .long 0xbc88e931 + .long 0xbf76ba07 + .long 0xb26d092c + .long 0xbe800000 + .long 0x3be60685 + .long 0xbf7853f8 + .long 0x320db9e5 + .long 0xbe800000 + .long 0x3cfd1f65 + .long 0xbf79c79d + .long 0xb2c64e59 + .long 0xbe800000 + .long 0x3d60e8f8 + .long 0xbf7b14be + .long 0xb2ff75cb + .long 0xbe800000 + .long 0xbd3c4289 + .long 0xbf7c3b28 + .long 0x3231d68b + .long 0xbe000000 + .long 0xbcb2041c + .long 0xbf7d3aac + .long 0x30f75ae9 + .long 0xbe000000 + .long 0x3b29b1a9 + .long 0xbf7e1324 + .long 0x32f1e603 + .long 0xbe000000 + .long 0x3cdd0b28 + .long 0xbf7ec46d + .long 0xb1f44949 + .long 0xbe000000 + .long 0xbc354825 + .long 0xbf7f4e6d + .long 0xb2d01884 + .long 0xbd800000 + .long 0x3c5c1342 + .long 0xbf7fb10f + .long 0xb1de5b5f + .long 0xbd800000 + .long 0x3bdbd541 + .long 0xbf7fec43 + .long 0xb084cd0d + .long 0xbd000000 + .long 0x00000000 + .long 0xbf800000 + .long 0x00000000 + .long 0x00000000 + .long 0xbbdbd541 + .long 0xbf7fec43 + .long 0xb084cd0d + .long 0x3d000000 + .long 0xbc5c1342 + .long 0xbf7fb10f + .long 0xb1de5b5f + .long 0x3d800000 + .long 0x3c354825 + .long 0xbf7f4e6d + .long 0xb2d01884 + .long 0x3d800000 + .long 0xbcdd0b28 + .long 0xbf7ec46d + .long 0xb1f44949 + .long 0x3e000000 + .long 0xbb29b1a9 + .long 0xbf7e1324 + .long 0x32f1e603 + .long 0x3e000000 + .long 0x3cb2041c + .long 0xbf7d3aac + .long 0x30f75ae9 + .long 0x3e000000 + .long 0x3d3c4289 + .long 0xbf7c3b28 + .long 0x3231d68b + .long 0x3e000000 + .long 0xbd60e8f8 + .long 0xbf7b14be + .long 0xb2ff75cb + .long 0x3e800000 + .long 0xbcfd1f65 + .long 0xbf79c79d + .long 0xb2c64e59 + .long 0x3e800000 + .long 0xbbe60685 + .long 0xbf7853f8 + .long 0x320db9e5 + .long 0x3e800000 + .long 0x3c88e931 + .long 0xbf76ba07 + .long 0xb26d092c + .long 0x3e800000 + .long 0x3d25018c + .long 0xbf74fa0b + .long 0x32939d22 + .long 0x3e800000 + .long 0x3d826b93 + .long 0xbf731447 + .long 0xb2c48e11 + .long 0x3e800000 + .long 0x3db1f34f + .long 0xbf710908 + .long 0xb21ed0dd + .long 0x3e800000 + .long 0xbe0f77ad + .long 0xbf6ed89e + .long 0x329333dc + .long 0x3f000000 + .long 0xbdf043ab + .long 0xbf6c835e + .long 0xb2f328d4 + .long 0x3f000000 + .long 0xbdc210d8 + .long 0xbf6a09a7 + .long 0x32eb236c + .long 0x3f000000 + .long 0xbd945dff + .long 0xbf676bd8 + .long 0x32bc3389 + .long 0x3f000000 + .long 0xbd4e645a + .long 0xbf64aa59 + .long 0xb11a08fa + .long 0x3f000000 + .long 0xbcea5164 + .long 0xbf61c598 + .long 0x32e7f425 + .long 0x3f000000 + .long 0xbbe8b648 + .long 0xbf5ebe05 + .long 0xb2c6f953 + .long 0x3f000000 + .long 0x3c670f32 + .long 0xbf5b941a + .long 0xb2232dc8 + .long 0x3f000000 + .long 0x3d0f59aa + .long 0xbf584853 + .long 0x327d5fc0 + .long 0x3f000000 + .long 0x3d639d9d + .long 0xbf54db31 + .long 0xb290ea1a + .long 0x3f000000 + .long 0x3d9b4153 + .long 0xbf514d3d + .long 0xb00c4f04 + .long 0x3f000000 + .long 0x3dc3fdff + .long 0xbf4d9f02 + .long 0xb27e70e8 + .long 0x3f000000 + .long 0x3debfe8a + .long 0xbf49d112 + .long 0xb2992640 + .long 0x3f000000 + .long 0x3e099e65 + .long 0xbf45e403 + .long 0xb2b15174 + .long 0x3f000000 + .long 0x3e1cd957 + .long 0xbf41d870 + .long 0xb2bff977 + .long 0x3f000000 + .long 0x3e2fad27 + .long 0xbf3daef9 + .long 0xb19aabec + .long 0x3f000000 + .long 0x3e4216eb + .long 0xbf396842 + .long 0x32810007 + .long 0x3f000000 + .long 0xbe95f61a + .long 0xbf3504f3 + .long 0xb24fe77a + .long 0x3f800000 + .long 0xbe8d2f7d + .long 0xbf3085bb + .long 0x32ae2d32 + .long 0x3f800000 + .long 0xbe84a20e + .long 0xbf2beb4a + .long 0x32b73136 + .long 0x3f800000 + .long 0xbe789e3f + .long 0xbf273656 + .long 0x32038343 + .long 0x3f800000 + .long 0xbe686ff3 + .long 0xbf226799 + .long 0xb22123bb + .long 0x3f800000 + .long 0xbe58bbb7 + .long 0xbf1d7fd1 + .long 0xb292050c + .long 0x3f800000 + .long 0xbe4983f7 + .long 0xbf187fc0 + .long 0x31c7a3f3 + .long 0x3f800000 + .long 0xbe3acb0c + .long 0xbf13682a + .long 0xb2cdd12e + .long 0x3f800000 + .long 0xbe2c933b + .long 0xbf0e39da + .long 0x324a32e7 + .long 0x3f800000 + .long 0xbe1edeb5 + .long 0xbf08f59b + .long 0x32be4b4e + .long 0x3f800000 + .long 0xbe11af97 + .long 0xbf039c3d + .long 0x325ba002 + .long 0x3f800000 + .long 0xbe0507ea + .long 0xbefc5d27 + .long 0x3180eca9 + .long 0x3f800000 + .long 0xbdf1d344 + .long 0xbef15aea + .long 0x31ff2139 + .long 0x3f800000 + .long 0xbddaad38 + .long 0xbee63375 + .long 0x31d9c774 + .long 0x3f800000 + .long 0xbdc4a143 + .long 0xbedae880 + .long 0xb21e15cc + .long 0x3f800000 + .long 0xbdafb2cc + .long 0xbecf7bca + .long 0xb16a3b63 + .long 0x3f800000 + .long 0xbd9be50c + .long 0xbec3ef15 + .long 0xb1d5d52c + .long 0x3f800000 + .long 0xbd893b12 + .long 0xbeb8442a + .long 0x32705ba6 + .long 0x3f800000 + .long 0xbd6f6f7e + .long 0xbeac7cd4 + .long 0x32254e02 + .long 0x3f800000 + .long 0xbd4ebb8a + .long 0xbea09ae5 + .long 0x323e89a0 + .long 0x3f800000 + .long 0xbd305f55 + .long 0xbe94a031 + .long 0xb26d59f0 + .long 0x3f800000 + .long 0xbd145f8c + .long 0xbe888e93 + .long 0xb12c7d9e + .long 0x3f800000 + .long 0xbcf58104 + .long 0xbe78cfcc + .long 0x311bd41d + .long 0x3f800000 + .long 0xbcc70c54 + .long 0xbe605c13 + .long 0xb1a7e4f6 + .long 0x3f800000 + .long 0xbc9d6830 + .long 0xbe47c5c2 + .long 0x30e5967d + .long 0x3f800000 + .long 0xbc71360b + .long 0xbe2f10a2 + .long 0xb11167f9 + .long 0x3f800000 + .long 0xbc315502 + .long 0xbe164083 + .long 0xb1e8e614 + .long 0x3f800000 + .long 0xbbf66e3c + .long 0xbdfab273 + .long 0x311568cf + .long 0x3f800000 + .long 0xbb9dc971 + .long 0xbdc8bd36 + .long 0x307592f5 + .long 0x3f800000 + .long 0xbb319298 + .long 0xbd96a905 + .long 0x31531e61 + .long 0x3f800000 + .long 0xba9de1c8 + .long 0xbd48fb30 + .long 0x30ef227f + .long 0x3f800000 + .long 0xb99de7df + .long 0xbcc90ab0 + .long 0x3005c998 + .long 0x3f800000 + +/* General purpose constants: + absolute value mask */ +float_vector __sAbsMask 0x7fffffff + +/* threshold for out-of-range values */ +float_vector __sRangeReductionVal 0x461c4000 + +/* +INF */ +float_vector __sRangeVal 0x7f800000 + +/* High Accuracy version polynomial coefficients: + S1 = -1.66666666664728165763e-01 */ +float_vector __sS1 0xbe2aaaab + +/* S2 = 8.33329173045453069014e-03 */ +float_vector __sS2 0x3c08885c + +/* C1 = -5.00000000000000000000e-01 */ +float_vector __sC1 0xbf000000 + +/* C2 = 4.16638942914469202550e-02 */ +float_vector __sC2 0x3d2aaa7c + +/* high accuracy table index mask */ +float_vector __iIndexMask 0x000000ff + +/* 2^(k-1) */ +float_vector __i2pK_1 0x00000040 + +/* sign field mask */ +float_vector __sSignMask 0x80000000 + +/* Range reduction PI-based constants: + PI high part */ +float_vector __sPI1 0x40490000 + +/* PI mid part 1 */ +float_vector __sPI2 0x3a7da000 + +/* PI mid part 2 */ +float_vector __sPI3 0x34222000 + +/* PI low part */ +float_vector __sPI4 0x2cb4611a + +/* Range reduction PI-based constants if FMA available: + PI high part (when FMA available) */ +float_vector __sPI1_FMA 0x40490fdb + +/* PI mid part (when FMA available) */ +float_vector __sPI2_FMA 0xb3bbbd2e + +/* PI low part (when FMA available) */ +float_vector __sPI3_FMA 0xa7772ced + +/* Polynomial coefficients: */ +float_vector __sA3 0xbe2aaaa6 +float_vector __sA5 0x3c08876a +float_vector __sA7 0xb94fb7ff +float_vector __sA9 0x362edef8 + +/* Polynomial coefficients (when hardware FMA available) */ +float_vector __sA5_FMA 0x3c088768 +float_vector __sA7_FMA 0xb94fb6cf +float_vector __sA9_FMA 0x362ec335 + +/* 1/PI */ +float_vector __sInvPI 0x3ea2f983 + +/* right-shifter constant */ +float_vector __sRShifter 0x4b400000 + +/* PI/2 */ +float_vector __sHalfPI 0x3fc90fdb + +/* 1/2 */ +float_vector __sOneHalf 0x3f000000 + .type __svml_ssincos_data,@object + .size __svml_ssincos_data,.-__svml_ssincos_data diff --git a/sysdeps/x86_64/fpu/svml_s_sincosf_data.h b/sysdeps/x86_64/fpu/svml_s_sincosf_data.h new file mode 100644 index 0000000000..432511776a --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_s_sincosf_data.h @@ -0,0 +1,61 @@ +/* Offsets for data table for function sincosf. + Copyright (C) 2014-2015 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef S_SINCOSF_DATA_H +#define S_SINCOSF_DATA_H + +#define __dT 0 +#define __sAbsMask 4096 +#define __sRangeReductionVal 4160 +#define __sRangeVal 4224 +#define __sS1 4288 +#define __sS2 4352 +#define __sC1 4416 +#define __sC2 4480 +#define __iIndexMask 4544 +#define __i2pK_1 4608 +#define __sSignMask 4672 +#define __sPI1 4736 +#define __sPI2 4800 +#define __sPI3 4864 +#define __sPI4 4928 +#define __sPI1_FMA 4992 +#define __sPI2_FMA 5056 +#define __sPI3_FMA 5120 +#define __sA3 5184 +#define __sA5 5248 +#define __sA7 5312 +#define __sA9 5376 +#define __sA5_FMA 5440 +#define __sA7_FMA 5504 +#define __sA9_FMA 5568 +#define __sInvPI 5632 +#define __sRShifter 5696 +#define __sHalfPI 5760 +#define __sOneHalf 5824 + +.macro float_vector offset value +.if .-__svml_ssincos_data != \offset +.err +.endif +.rept 16 +.long \value +.endr +.endm + +#endif diff --git a/sysdeps/x86_64/fpu/svml_s_wrapper_impl.h b/sysdeps/x86_64/fpu/svml_s_wrapper_impl.h index f88e30f054..66bb081c9d 100644 --- a/sysdeps/x86_64/fpu/svml_s_wrapper_impl.h +++ b/sysdeps/x86_64/fpu/svml_s_wrapper_impl.h @@ -76,6 +76,67 @@ ret .endm +/* 3 argument SSE2 ISA version as wrapper to scalar. */ +.macro WRAPPER_IMPL_SSE2_fFF callee + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + pushq %rbx + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbx, 0) + movq %rdi, %rbp + movq %rsi, %rbx + subq $40, %rsp + cfi_adjust_cfa_offset(40) + leaq 24(%rsp), %rsi + leaq 28(%rsp), %rdi + movaps %xmm0, (%rsp) + call \callee@PLT + leaq 24(%rsp), %rsi + leaq 28(%rsp), %rdi + movss 28(%rsp), %xmm0 + movss %xmm0, 0(%rbp) + movaps (%rsp), %xmm1 + movss 24(%rsp), %xmm0 + movss %xmm0, (%rbx) + movaps %xmm1, %xmm0 + shufps $85, %xmm1, %xmm0 + call \callee@PLT + movss 28(%rsp), %xmm0 + leaq 24(%rsp), %rsi + movss %xmm0, 4(%rbp) + leaq 28(%rsp), %rdi + movaps (%rsp), %xmm1 + movss 24(%rsp), %xmm0 + movss %xmm0, 4(%rbx) + movaps %xmm1, %xmm0 + unpckhps %xmm1, %xmm0 + call \callee@PLT + movaps (%rsp), %xmm1 + leaq 24(%rsp), %rsi + leaq 28(%rsp), %rdi + movss 28(%rsp), %xmm0 + shufps $255, %xmm1, %xmm1 + movss %xmm0, 8(%rbp) + movss 24(%rsp), %xmm0 + movss %xmm0, 8(%rbx) + movaps %xmm1, %xmm0 + call \callee@PLT + movss 28(%rsp), %xmm0 + movss %xmm0, 12(%rbp) + movss 24(%rsp), %xmm0 + movss %xmm0, 12(%rbx) + addq $40, %rsp + cfi_adjust_cfa_offset(-40) + popq %rbx + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbx) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret +.endm + /* AVX/AVX2 ISA version as wrapper to SSE ISA version. */ .macro WRAPPER_IMPL_AVX callee pushq %rbp @@ -130,6 +191,52 @@ ret .endm +/* 3 argument AVX/AVX2 ISA version as wrapper to SSE ISA version. */ +.macro WRAPPER_IMPL_AVX_fFF callee + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-32, %rsp + pushq %r13 + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%r13, 0) + pushq %r14 + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%r14, 0) + subq $48, %rsp + movq %rsi, %r14 + vmovaps %ymm0, (%rsp) + movq %rdi, %r13 + vmovaps 16(%rsp), %xmm1 + vmovaps %xmm1, 32(%rsp) + vzeroupper + vmovaps (%rsp), %xmm0 + call HIDDEN_JUMPTARGET(\callee) + vmovaps 32(%rsp), %xmm0 + lea (%rsp), %rdi + lea 16(%rsp), %rsi + call HIDDEN_JUMPTARGET(\callee) + vmovaps (%rsp), %xmm0 + vmovaps 16(%rsp), %xmm1 + vmovaps %xmm0, 16(%r13) + vmovaps %xmm1, 16(%r14) + addq $48, %rsp + popq %r14 + cfi_adjust_cfa_offset (-8) + cfi_restore (%r14) + popq %r13 + cfi_adjust_cfa_offset (-8) + cfi_restore (%r13) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret +.endm + /* AVX512 ISA version as wrapper to AVX2 ISA version. */ .macro WRAPPER_IMPL_AVX512 callee pushq %rbp @@ -147,20 +254,9 @@ .byte 0x29 .byte 0x04 .byte 0x24 -/* Below is encoding for vmovaps (%rsp), %ymm0. */ - .byte 0xc5 - .byte 0xfc - .byte 0x28 - .byte 0x04 - .byte 0x24 + vmovaps (%rsp), %ymm0 call HIDDEN_JUMPTARGET(\callee) -/* Below is encoding for vmovaps 32(%rsp), %ymm0. */ - .byte 0xc5 - .byte 0xfc - .byte 0x28 - .byte 0x44 - .byte 0x24 - .byte 0x20 + vmovaps 32(%rsp), %ymm0 call HIDDEN_JUMPTARGET(\callee) movq %rbp, %rsp cfi_def_cfa_register (%rsp) @@ -195,38 +291,57 @@ .byte 0x29 .byte 0x4c .byte 0x24 -/* Below is encoding for vmovaps (%rsp), %ymm0. */ - .byte 0xc5 - .byte 0xfc - .byte 0x28 + vmovaps (%rsp), %ymm0 + vmovaps 64(%rsp), %ymm1 + call HIDDEN_JUMPTARGET(\callee) + vmovaps 32(%rsp), %ymm0 + vmovaps 96(%rsp), %ymm1 + call HIDDEN_JUMPTARGET(\callee) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret +.endm + +/* 3 argument AVX512 ISA version as wrapper to AVX2 ISA version. */ +.macro WRAPPER_IMPL_AVX512_fFF callee + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + pushq %r12 + pushq %r13 + subq $176, %rsp + movq %rsi, %r13 +/* Below is encoding for vmovaps %zmm0, (%rsp). */ + .byte 0x62 + .byte 0xf1 + .byte 0x7c + .byte 0x48 + .byte 0x29 .byte 0x04 .byte 0x24 -/* Below is encoding for vmovaps 64(%rsp), %ymm1. */ - .byte 0xc5 - .byte 0xfc - .byte 0x28 - .byte 0x4c - .byte 0x24 - .byte 0x40 + movq %rdi, %r12 + vmovaps (%rsp), %ymm0 call HIDDEN_JUMPTARGET(\callee) -/* Below is encoding for vmovaps 32(%rsp), %ymm0. */ - .byte 0xc5 - .byte 0xfc - .byte 0x28 - .byte 0x44 - .byte 0x24 - .byte 0x20 -/* Below is encoding for vmovaps 96(%rsp), %ymm1. */ - .byte 0xc5 - .byte 0xfc - .byte 0x28 - .byte 0x4c - .byte 0x24 - .byte 0x60 + vmovaps 32(%rsp), %ymm0 + lea 64(%rsp), %rdi + lea 96(%rsp), %rsi call HIDDEN_JUMPTARGET(\callee) + vmovaps 64(%rsp), %ymm0 + vmovaps 96(%rsp), %ymm1 + vmovaps %ymm0, 32(%r12) + vmovaps %ymm1, 32(%r13) + addq $176, %rsp + popq %r13 + popq %r12 movq %rbp, %rsp cfi_def_cfa_register (%rsp) - popq %rbp + popq %rbp cfi_adjust_cfa_offset (-8) cfi_restore (%rbp) ret diff --git a/sysdeps/x86_64/fpu/test-float-vlen16-wrappers.c b/sysdeps/x86_64/fpu/test-float-vlen16-wrappers.c index 00a1074f2c..6cc6008301 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen16-wrappers.c +++ b/sysdeps/x86_64/fpu/test-float-vlen16-wrappers.c @@ -24,6 +24,7 @@ VECTOR_WRAPPER (WRAPPER_NAME (cosf), _ZGVeN16v_cosf) VECTOR_WRAPPER (WRAPPER_NAME (sinf), _ZGVeN16v_sinf) +VECTOR_WRAPPER_fFF (WRAPPER_NAME (sincosf), _ZGVeN16vvv_sincosf) VECTOR_WRAPPER (WRAPPER_NAME (logf), _ZGVeN16v_logf) VECTOR_WRAPPER (WRAPPER_NAME (expf), _ZGVeN16v_expf) VECTOR_WRAPPER_ff (WRAPPER_NAME (powf), _ZGVeN16vv_powf) diff --git a/sysdeps/x86_64/fpu/test-float-vlen16.c b/sysdeps/x86_64/fpu/test-float-vlen16.c index 86b8c33632..d7f683f09c 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen16.c +++ b/sysdeps/x86_64/fpu/test-float-vlen16.c @@ -20,6 +20,7 @@ #define TEST_VECTOR_cosf 1 #define TEST_VECTOR_sinf 1 +#define TEST_VECTOR_sincosf 1 #define TEST_VECTOR_logf 1 #define TEST_VECTOR_expf 1 #define TEST_VECTOR_powf 1 diff --git a/sysdeps/x86_64/fpu/test-float-vlen4-wrappers.c b/sysdeps/x86_64/fpu/test-float-vlen4-wrappers.c index 7d41e46c4a..ae12a108fc 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen4-wrappers.c +++ b/sysdeps/x86_64/fpu/test-float-vlen4-wrappers.c @@ -24,6 +24,7 @@ VECTOR_WRAPPER (WRAPPER_NAME (cosf), _ZGVbN4v_cosf) VECTOR_WRAPPER (WRAPPER_NAME (sinf), _ZGVbN4v_sinf) +VECTOR_WRAPPER_fFF (WRAPPER_NAME (sincosf), _ZGVbN4vvv_sincosf) VECTOR_WRAPPER (WRAPPER_NAME (logf), _ZGVbN4v_logf) VECTOR_WRAPPER (WRAPPER_NAME (expf), _ZGVbN4v_expf) VECTOR_WRAPPER_ff (WRAPPER_NAME (powf), _ZGVbN4vv_powf) diff --git a/sysdeps/x86_64/fpu/test-float-vlen4.c b/sysdeps/x86_64/fpu/test-float-vlen4.c index 3e74118be0..e56d64260e 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen4.c +++ b/sysdeps/x86_64/fpu/test-float-vlen4.c @@ -20,6 +20,7 @@ #define TEST_VECTOR_cosf 1 #define TEST_VECTOR_sinf 1 +#define TEST_VECTOR_sincosf 1 #define TEST_VECTOR_logf 1 #define TEST_VECTOR_expf 1 #define TEST_VECTOR_powf 1 diff --git a/sysdeps/x86_64/fpu/test-float-vlen8-avx2-wrappers.c b/sysdeps/x86_64/fpu/test-float-vlen8-avx2-wrappers.c index ed1c893157..f0c7d4a55a 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen8-avx2-wrappers.c +++ b/sysdeps/x86_64/fpu/test-float-vlen8-avx2-wrappers.c @@ -27,6 +27,7 @@ VECTOR_WRAPPER (WRAPPER_NAME (cosf), _ZGVdN8v_cosf) VECTOR_WRAPPER (WRAPPER_NAME (sinf), _ZGVdN8v_sinf) +VECTOR_WRAPPER_fFF (WRAPPER_NAME (sincosf), _ZGVdN8vvv_sincosf) VECTOR_WRAPPER (WRAPPER_NAME (logf), _ZGVdN8v_logf) VECTOR_WRAPPER (WRAPPER_NAME (expf), _ZGVdN8v_expf) VECTOR_WRAPPER_ff (WRAPPER_NAME (powf), _ZGVdN8vv_powf) diff --git a/sysdeps/x86_64/fpu/test-float-vlen8-avx2.c b/sysdeps/x86_64/fpu/test-float-vlen8-avx2.c index f0aaec17a5..0012082b8e 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen8-avx2.c +++ b/sysdeps/x86_64/fpu/test-float-vlen8-avx2.c @@ -23,6 +23,7 @@ #define TEST_VECTOR_cosf 1 #define TEST_VECTOR_sinf 1 +#define TEST_VECTOR_sincosf 1 #define TEST_VECTOR_logf 1 #define TEST_VECTOR_expf 1 #define TEST_VECTOR_powf 1 diff --git a/sysdeps/x86_64/fpu/test-float-vlen8-wrappers.c b/sysdeps/x86_64/fpu/test-float-vlen8-wrappers.c index 37bf7020f9..6b267de00c 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen8-wrappers.c +++ b/sysdeps/x86_64/fpu/test-float-vlen8-wrappers.c @@ -24,6 +24,7 @@ VECTOR_WRAPPER (WRAPPER_NAME (cosf), _ZGVcN8v_cosf) VECTOR_WRAPPER (WRAPPER_NAME (sinf), _ZGVcN8v_sinf) +VECTOR_WRAPPER_fFF (WRAPPER_NAME (sincosf), _ZGVcN8vvv_sincosf) VECTOR_WRAPPER (WRAPPER_NAME (logf), _ZGVcN8v_logf) VECTOR_WRAPPER (WRAPPER_NAME (expf), _ZGVcN8v_expf) VECTOR_WRAPPER_ff (WRAPPER_NAME (powf), _ZGVcN8vv_powf) diff --git a/sysdeps/x86_64/fpu/test-float-vlen8.c b/sysdeps/x86_64/fpu/test-float-vlen8.c index ef2aedc845..581cbdec16 100644 --- a/sysdeps/x86_64/fpu/test-float-vlen8.c +++ b/sysdeps/x86_64/fpu/test-float-vlen8.c @@ -20,6 +20,7 @@ #define TEST_VECTOR_cosf 1 #define TEST_VECTOR_sinf 1 +#define TEST_VECTOR_sincosf 1 #define TEST_VECTOR_logf 1 #define TEST_VECTOR_expf 1 #define TEST_VECTOR_powf 1 |