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| author | Andrew Senkevich <andrew.senkevich@intel.com> | 2015-06-17 16:22:26 +0300 |
|---|---|---|
| committer | Andrew Senkevich <andrew.senkevich@intel.com> | 2015-06-17 16:22:26 +0300 |
| commit | c10b9b13f7471b08273effc8cd7e51b119df9348 (patch) | |
| tree | ca058c3446a247a5bccea211bd84a9c0130e1388 /sysdeps/x86_64 | |
| parent | 1663be053d50c06bb0f971c87d41a7b83f96fe15 (diff) | |
| download | glibc-c10b9b13f7471b08273effc8cd7e51b119df9348.tar.gz glibc-c10b9b13f7471b08273effc8cd7e51b119df9348.tar.xz glibc-c10b9b13f7471b08273effc8cd7e51b119df9348.zip | |
Vector pow for x86_64 and tests.
Here is implementation of vectorized pow containing SSE, AVX,
AVX2 and AVX512 versions according to Vector ABI
<https://groups.google.com/forum/#!topic/x86-64-abi/LmppCfN1rZ4>.
* bits/libm-simd-decl-stubs.h: Added stubs for pow.
* math/bits/mathcalls.h: Added pow declaration with __MATHCALL_VEC.
* sysdeps/unix/sysv/linux/x86_64/libmvec.abilist: New versions added.
* sysdeps/x86/fpu/bits/math-vector.h: Added SIMD declaration and asm
redirections for pow.
* 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/svml_d_wrapper_impl.h: Added 2 argument wrappers.
* sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core.S: New file.
* sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S: New file.
* sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core.S: New file.
* sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core_avx2.S: New file.
* sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core.S: New file.
* sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core_avx512.S: New file.
* sysdeps/x86_64/fpu/svml_d_pow2_core.S: New file.
* sysdeps/x86_64/fpu/svml_d_pow4_core.S: New file.
* sysdeps/x86_64/fpu/svml_d_pow4_core_avx.S: New file.
* sysdeps/x86_64/fpu/svml_d_pow8_core.S: New file.
* sysdeps/x86_64/fpu/svml_d_pow_data.S: New file.
* sysdeps/x86_64/fpu/svml_d_pow_data.h: New file.
* sysdeps/x86_64/fpu/test-double-vlen2-wrappers.c: Added vector pow test.
* sysdeps/x86_64/fpu/test-double-vlen2.c: Likewise.
* sysdeps/x86_64/fpu/test-double-vlen4-avx2-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-double-vlen4-avx2.c: Likewise.
* sysdeps/x86_64/fpu/test-double-vlen4-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-double-vlen4.c: Likewise.
* sysdeps/x86_64/fpu/test-double-vlen8-wrappers.c: Likewise.
* sysdeps/x86_64/fpu/test-double-vlen8.c: Likewise.
* NEWS: Mention addition of x86_64 vector pow.
Diffstat (limited to 'sysdeps/x86_64')
25 files changed, 6886 insertions, 2 deletions
diff --git a/sysdeps/x86_64/fpu/Makefile b/sysdeps/x86_64/fpu/Makefile index eab738fb4a..aa9bdea668 100644 --- a/sysdeps/x86_64/fpu/Makefile +++ b/sysdeps/x86_64/fpu/Makefile @@ -13,7 +13,9 @@ libmvec-support += svml_d_cos2_core svml_d_cos4_core_avx \ svml_s_logf_data svml_d_exp2_core svml_d_exp4_core_avx \ svml_d_exp4_core svml_d_exp8_core svml_d_exp_data \ svml_s_expf4_core svml_s_expf8_core_avx svml_s_expf8_core \ - svml_s_expf16_core svml_s_expf_data \ + svml_s_expf16_core svml_s_expf_data svml_d_pow2_core \ + svml_d_pow4_core_avx svml_d_pow4_core svml_d_pow8_core \ + svml_d_pow_data \ init-arch endif diff --git a/sysdeps/x86_64/fpu/Versions b/sysdeps/x86_64/fpu/Versions index 0eaa8e81db..e379c36125 100644 --- a/sysdeps/x86_64/fpu/Versions +++ b/sysdeps/x86_64/fpu/Versions @@ -4,6 +4,7 @@ libmvec { _ZGVbN2v_sin; _ZGVcN4v_sin; _ZGVdN4v_sin; _ZGVeN8v_sin; _ZGVbN2v_log; _ZGVcN4v_log; _ZGVdN4v_log; _ZGVeN8v_log; _ZGVbN2v_exp; _ZGVcN4v_exp; _ZGVdN4v_exp; _ZGVeN8v_exp; + _ZGVbN2vv_pow; _ZGVcN4vv_pow; _ZGVdN4vv_pow; _ZGVeN8vv_pow; _ZGVbN4v_cosf; _ZGVcN8v_cosf; _ZGVdN8v_cosf; _ZGVeN16v_cosf; _ZGVbN4v_sinf; _ZGVcN8v_sinf; _ZGVdN8v_sinf; _ZGVeN16v_sinf; _ZGVbN4v_logf; _ZGVcN8v_logf; _ZGVdN8v_logf; _ZGVeN16v_logf; diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index ba1367f425..718e84c3f9 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -1947,6 +1947,18 @@ ifloat: 4 ildouble: 2 ldouble: 2 +Function: "pow_vlen2": +double: 1 + +Function: "pow_vlen4": +double: 1 + +Function: "pow_vlen4_avx2": +double: 1 + +Function: "pow_vlen8": +double: 1 + Function: "sin": ildouble: 1 ldouble: 1 diff --git a/sysdeps/x86_64/fpu/multiarch/Makefile b/sysdeps/x86_64/fpu/multiarch/Makefile index 9e1025136f..b03b1380c0 100644 --- a/sysdeps/x86_64/fpu/multiarch/Makefile +++ b/sysdeps/x86_64/fpu/multiarch/Makefile @@ -65,5 +65,6 @@ libmvec-sysdep_routines += svml_d_cos2_core_sse4 svml_d_cos4_core_avx2 \ svml_s_logf16_core_avx512 svml_d_exp2_core_sse4 \ svml_d_exp4_core_avx2 svml_d_exp8_core_avx512 \ svml_s_expf4_core_sse4 svml_s_expf8_core_avx2 \ - svml_s_expf16_core_avx512 + svml_s_expf16_core_avx512 svml_d_pow2_core_sse4 \ + svml_d_pow4_core_avx2 svml_d_pow8_core_avx512 endif diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core.S new file mode 100644 index 0000000000..f111388922 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core.S @@ -0,0 +1,38 @@ +/* Multiple versions of vectorized pow. + 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 (_ZGVbN2vv_pow) + .type _ZGVbN2vv_pow, @gnu_indirect_function + cmpl $0, KIND_OFFSET+__cpu_features(%rip) + jne 1f + call __init_cpu_features +1: leaq _ZGVbN2vv_pow_sse4(%rip), %rax + testl $bit_SSE4_1, __cpu_features+CPUID_OFFSET+index_SSE4_1(%rip) + jz 2f + ret +2: leaq _ZGVbN2vv_pow_sse2(%rip), %rax + ret +END (_ZGVbN2vv_pow) +libmvec_hidden_def (_ZGVbN2vv_pow) + +#define _ZGVbN2vv_pow _ZGVbN2vv_pow_sse2 +#include "../svml_d_pow2_core.S" diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S new file mode 100644 index 0000000000..9f6ec29ac5 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S @@ -0,0 +1,432 @@ +/* Function pow 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_d_pow_data.h" + + .text +ENTRY (_ZGVbN2vv_pow_sse4) +/* + ALGORITHM DESCRIPTION: + + 1) Calculating log2|x| + Here we use the following formula. + Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. + Let C ~= 1/ln(2), + Rcp1 ~= 1/X1, X2=Rcp1*X1, + Rcp2 ~= 1/X2, X3=Rcp2*X2, + Rcp3 ~= 1/X3, Rcp3C ~= C/X3. + Then + log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + + log2(X1*Rcp1*Rcp2*Rcp3C/C), + where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. + + The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), + Rcp3C, log2(C/Rcp3C) are taken from tables. + Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C + is exactly represented in target precision. + + log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = + = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = + = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = + = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., + where cq = X1*Rcp1*Rcp2*Rcp3C-C, + a1=1/(C*ln(2))-1 is small, + a2=1/(2*C^2*ln2), + a3=1/(3*C^3*ln2), + ... + We get 3 parts of log2 result: HH+HL+HLL ~= log2|x|. + + 2) Calculation of y*(HH+HL+HLL). + Split y into YHi+YLo. + Get high PH and medium PL parts of y*log2|x|. + Get low PLL part of y*log2|x|. + Now we have PH+PL+PLL ~= y*log2|x|. + + 3) Calculation of 2^(PH+PL+PLL). + Mathematical idea of computing 2^(PH+PL+PLL) is the following. + Let's represent PH+PL+PLL in the form N + j/2^expK + Z, + where expK=7 in this implementation, N and j are integers, + 0<=j<=2^expK-1, |Z|<2^(-expK-1). + Hence 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, + where 2^(j/2^expK) is stored in a table, and + 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. + + We compute 2^(PH+PL+PLL) as follows. + Break PH into PHH + PHL, where PHH = N + j/2^expK. + Z = PHL + PL + PLL + Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 + Get 2^(j/2^expK) from table in the form THI+TLO. + Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). + + Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: + ResHi := THI + ResLo := THI * Exp2Poly + TLO + + Get exponent ERes of the result: + Res := ResHi + ResLo: + Result := ex(Res) + N. */ + + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $256, %rsp + movq __svml_dpow_data@GOTPCREL(%rip), %rdx + movups %xmm14, 80(%rsp) + movups %xmm9, 176(%rsp) + movaps %xmm1, %xmm9 + pshufd $221, %xmm0, %xmm1 + movq _iIndexMask(%rdx), %xmm14 + movq _iIndexAdd(%rdx), %xmm6 + +/* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ + pand %xmm1, %xmm14 + paddd %xmm6, %xmm14 + psrld $10, %xmm14 + movups %xmm13, 96(%rsp) + +/* Index for reciprocal table */ + movdqa %xmm14, %xmm13 + pslld $3, %xmm13 + +/* Index for log2 table */ + pslld $4, %xmm14 + movd %xmm13, %eax + movups %xmm10, 160(%rsp) + movups _iMantissaMask(%rdx), %xmm10 + movslq %eax, %rax + +/* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ + andps %xmm0, %xmm10 + pextrd $1, %xmm13, %ecx + movslq %ecx, %rcx + movups %xmm0, (%rsp) + movdqa %xmm1, %xmm0 + +/* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ + movq _i3fe7fe00(%rdx), %xmm6 + psubd %xmm6, %xmm0 + movups _iHighMask(%rdx), %xmm6 + psrad $20, %xmm0 + movups %xmm15, 48(%rsp) + movups %xmm12, 112(%rsp) + orps _dbOne(%rdx), %xmm10 + movsd 11712(%rdx,%rax), %xmm12 + movd %xmm14, %r8d + movq _i2p20_2p19(%rdx), %xmm15 + movhpd 11712(%rdx,%rcx), %xmm12 + paddd %xmm15, %xmm0 + pextrd $1, %xmm14, %r9d + +/* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ + movaps %xmm6, %xmm14 + andps %xmm10, %xmm14 + movaps %xmm10, %xmm15 + subpd %xmm14, %xmm15 + +/* r1 = x1*rcp1 */ + mulpd %xmm12, %xmm10 + +/* E = -r1+__fence(x1Hi*rcp1) */ + mulpd %xmm12, %xmm14 + +/* E=E+x1Lo*rcp1 */ + mulpd %xmm15, %xmm12 + subpd %xmm10, %xmm14 + pshufd $80, %xmm0, %xmm0 + movslq %r8d, %r8 + andps _iffffffff00000000(%rdx), %xmm0 + subpd _db2p20_2p19(%rdx), %xmm0 + addpd %xmm12, %xmm14 + movslq %r9d, %r9 + +/* T_Rh_Eh = T_Rh + E */ + movaps %xmm14, %xmm15 + movups %xmm8, 208(%rsp) + movups 19968(%rdx,%r8), %xmm8 + movups %xmm11, 144(%rsp) + movaps %xmm8, %xmm11 + +/* cq = c+r1 */ + movups _LHN(%rdx), %xmm13 + movhpd 19968(%rdx,%r9), %xmm11 + addpd %xmm10, %xmm13 + +/* T = k + L1hi */ + addpd %xmm0, %xmm11 + +/* T_Rh = T + cq */ + movaps %xmm13, %xmm12 + addpd %xmm11, %xmm12 + addpd %xmm12, %xmm15 + +/* Rl = T-T_Rh; -> -Rh */ + subpd %xmm12, %xmm11 + +/* HLL = T_Rh - T_Rh_Eh; -> -Eh */ + subpd %xmm15, %xmm12 + +/* Rl=Rl+cq; */ + addpd %xmm13, %xmm11 + +/* cq = cq + E */ + addpd %xmm14, %xmm13 + +/* HLL+=E; -> El */ + addpd %xmm14, %xmm12 + +/* HLL+=Rl */ + addpd %xmm12, %xmm11 + unpckhpd 19968(%rdx,%r9), %xmm8 + +/* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ + movaps %xmm15, %xmm14 + +/* HLL+=L1lo; */ + addpd %xmm11, %xmm8 + movups _clv_2(%rdx), %xmm11 + +/* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ + movaps %xmm6, %xmm12 + +/* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ + mulpd %xmm13, %xmm11 + addpd _clv_3(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_4(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_5(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_6(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_7(%rdx), %xmm11 + mulpd %xmm11, %xmm13 + addpd %xmm13, %xmm8 + addpd %xmm8, %xmm14 + +/* + 2^(y*(HH+HL+HLL)) starts here: + yH = y; Lo(yH)&=0xf8000000 + */ + andps %xmm9, %xmm6 + +/* yL = y-yH; */ + movaps %xmm9, %xmm11 + subpd %xmm6, %xmm11 + andps %xmm14, %xmm12 + +/* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ + movaps %xmm14, %xmm10 + +/* HL = T_Rh_Eh_HLLhi-HH; */ + subpd %xmm12, %xmm14 + subpd %xmm15, %xmm10 + movq _HIDELTA(%rdx), %xmm2 + +/* pH = yH*HH; */ + movaps %xmm6, %xmm13 + movq _LORANGE(%rdx), %xmm3 + paddd %xmm2, %xmm1 + pcmpgtd %xmm1, %xmm3 + +/* pL=yL*HL+yH*HL; pL+=yL*HH; */ + movaps %xmm11, %xmm1 + mulpd %xmm14, %xmm1 + mulpd %xmm14, %xmm6 + mulpd %xmm12, %xmm13 + mulpd %xmm11, %xmm12 + addpd %xmm6, %xmm1 + +/* HLL = HLL - HLLhi */ + subpd %xmm10, %xmm8 + addpd %xmm12, %xmm1 + +/* pLL = y*HLL */ + mulpd %xmm9, %xmm8 + movups _db2p45_2p44(%rdx), %xmm11 + +/* pHH = pH + *(double*)&db2p45_2p44 */ + movaps %xmm11, %xmm12 + addpd %xmm13, %xmm12 + +/* t=pL+pLL; t+=pHL */ + addpd %xmm8, %xmm1 + movq _ABSMASK(%rdx), %xmm5 + pshufd $221, %xmm9, %xmm4 + pand %xmm5, %xmm4 + movq _INF(%rdx), %xmm7 + movdqa %xmm4, %xmm2 + pcmpgtd %xmm7, %xmm2 + pcmpeqd %xmm7, %xmm4 + pshufd $136, %xmm12, %xmm7 + por %xmm4, %xmm2 + +/* pHH = pHH - *(double*)&db2p45_2p44 */ + subpd %xmm11, %xmm12 + pshufd $221, %xmm13, %xmm10 + por %xmm2, %xmm3 + +/* pHL = pH - pHH; */ + subpd %xmm12, %xmm13 + pand %xmm5, %xmm10 + movq _DOMAINRANGE(%rdx), %xmm5 + movdqa %xmm10, %xmm4 + addpd %xmm1, %xmm13 + pcmpgtd %xmm5, %xmm4 + pcmpeqd %xmm5, %xmm10 + por %xmm10, %xmm4 + movq _jIndexMask(%rdx), %xmm6 + por %xmm4, %xmm3 + movmskps %xmm3, %eax + +/* j = Lo(pHH)&0x0000007f */ + pand %xmm7, %xmm6 + movq _iOne(%rdx), %xmm3 + +/* _n = Lo(pHH); + _n = _n & 0xffffff80; + _n = _n >> 7; + Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n + */ + pslld $13, %xmm7 + paddd %xmm3, %xmm7 + pslld $4, %xmm6 + movups _cev_1(%rdx), %xmm3 + movaps %xmm13, %xmm4 + mulpd %xmm13, %xmm3 + +/* T1 = ((double*)exp2_tbl)[ 2*j ] */ + movd %xmm6, %r10d + pshufd $80, %xmm7, %xmm0 + andps _ifff0000000000000(%rdx), %xmm0 + addpd _cev_2(%rdx), %xmm3 + mulpd %xmm13, %xmm3 + addpd _cev_3(%rdx), %xmm3 + mulpd %xmm13, %xmm3 + movslq %r10d, %r10 + andl $3, %eax + pextrd $1, %xmm6, %r11d + movslq %r11d, %r11 + addpd _cev_4(%rdx), %xmm3 + movsd 36416(%rdx,%r10), %xmm2 + movhpd 36416(%rdx,%r11), %xmm2 + mulpd %xmm2, %xmm0 + mulpd %xmm3, %xmm13 + mulpd %xmm0, %xmm4 + addpd _cev_5(%rdx), %xmm13 + mulpd %xmm4, %xmm13 + addpd %xmm13, %xmm0 + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + movups 208(%rsp), %xmm8 + movups 176(%rsp), %xmm9 + movups 160(%rsp), %xmm10 + movups 144(%rsp), %xmm11 + movups 112(%rsp), %xmm12 + movups 96(%rsp), %xmm13 + movups 80(%rsp), %xmm14 + movups 48(%rsp), %xmm15 + 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 (%rsp), %xmm1 + movups %xmm1, 64(%rsp) + movups %xmm9, 128(%rsp) + movups %xmm0, 192(%rsp) + je .LBL_1_2 + + xorb %cl, %cl + xorl %edx, %edx + movq %rsi, 8(%rsp) + movq %rdi, (%rsp) + movq %r12, 40(%rsp) + cfi_offset_rel_rsp (12, 40) + movb %cl, %r12b + movq %r13, 32(%rsp) + cfi_offset_rel_rsp (13, 32) + movl %eax, %r13d + movq %r14, 24(%rsp) + cfi_offset_rel_rsp (14, 24) + movl %edx, %r14d + movq %r15, 16(%rsp) + cfi_offset_rel_rsp (15, 16) + cfi_remember_state + +.LBL_1_6: + btl %r14d, %r13d + jc .LBL_1_12 + +.LBL_1_7: + lea 1(%r14), %esi + btl %esi, %r13d + jc .LBL_1_10 + +.LBL_1_8: + incb %r12b + addl $2, %r14d + cmpb $16, %r12b + jb .LBL_1_6 + + movq 8(%rsp), %rsi + movq (%rsp), %rdi + movq 40(%rsp), %r12 + cfi_restore (%r12) + movq 32(%rsp), %r13 + cfi_restore (%r13) + movq 24(%rsp), %r14 + cfi_restore (%r14) + movq 16(%rsp), %r15 + cfi_restore (%r15) + movups 192(%rsp), %xmm0 + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + shlq $4, %r15 + movsd 72(%rsp,%r15), %xmm0 + movsd 136(%rsp,%r15), %xmm1 + + call pow@PLT + + movsd %xmm0, 200(%rsp,%r15) + jmp .LBL_1_8 + +.LBL_1_12: + movzbl %r12b, %r15d + shlq $4, %r15 + movsd 64(%rsp,%r15), %xmm0 + movsd 128(%rsp,%r15), %xmm1 + + call pow@PLT + + movsd %xmm0, 192(%rsp,%r15) + jmp .LBL_1_7 + +END (_ZGVbN2vv_pow_sse4) diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core.S new file mode 100644 index 0000000000..21e3070a42 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core.S @@ -0,0 +1,38 @@ +/* Multiple versions of vectorized pow. + 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 (_ZGVdN4vv_pow) + .type _ZGVdN4vv_pow, @gnu_indirect_function + cmpl $0, KIND_OFFSET+__cpu_features(%rip) + jne 1f + call __init_cpu_features +1: leaq _ZGVdN4vv_pow_avx2(%rip), %rax + testl $bit_AVX2_Usable, __cpu_features+FEATURE_OFFSET+index_AVX2_Usable(%rip) + jz 2f + ret +2: leaq _ZGVdN4vv_pow_sse_wrapper(%rip), %rax + ret +END (_ZGVdN4vv_pow) +libmvec_hidden_def (_ZGVdN4vv_pow) + +#define _ZGVdN4vv_pow _ZGVdN4vv_pow_sse_wrapper +#include "../svml_d_pow4_core.S" diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core_avx2.S new file mode 100644 index 0000000000..f1f1f35ca2 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core_avx2.S @@ -0,0 +1,387 @@ +/* Function pow 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_d_pow_data.h" + + .text +ENTRY (_ZGVdN4vv_pow_avx2) +/* + ALGORITHM DESCRIPTION: + + 1) Calculating log2|x| + Here we use the following formula. + Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. + Let C ~= 1/ln(2), + Rcp1 ~= 1/X1, X2=Rcp1*X1, + Rcp2 ~= 1/X2, X3=Rcp2*X2, + Rcp3 ~= 1/X3, Rcp3C ~= C/X3. + Then + log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + + log2(X1*Rcp1*Rcp2*Rcp3C/C), + where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. + + The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), + Rcp3C, log2(C/Rcp3C) are taken from tables. + Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C + is exactly represented in target precision. + + log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = + = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = + = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = + = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., + where cq = X1*Rcp1*Rcp2*Rcp3C-C, + a1=1/(C*ln(2))-1 is small, + a2=1/(2*C^2*ln2), + a3=1/(3*C^3*ln2), + ... + We get 3 parts of log2 result: HH+HL+HLL ~= log2|x|. + + 2) Calculation of y*(HH+HL+HLL). + Split y into YHi+YLo. + Get high PH and medium PL parts of y*log2|x|. + Get low PLL part of y*log2|x|. + Now we have PH+PL+PLL ~= y*log2|x|. + + 3) Calculation of 2^(PH+PL+PLL). + Mathematical idea of computing 2^(PH+PL+PLL) is the following. + Let's represent PH+PL+PLL in the form N + j/2^expK + Z, + where expK=7 in this implementation, N and j are integers, + 0<=j<=2^expK-1, |Z|<2^(-expK-1). + Hence 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, + where 2^(j/2^expK) is stored in a table, and + 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. + + We compute 2^(PH+PL+PLL) as follows. + Break PH into PHH + PHL, where PHH = N + j/2^expK. + Z = PHL + PL + PLL + Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 + Get 2^(j/2^expK) from table in the form THI+TLO. + Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). + + Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: + ResHi := THI + ResLo := THI * Exp2Poly + TLO + + Get exponent ERes of the result: + Res := ResHi + ResLo: + Result := ex(Res) + N. */ + + 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_dpow_data@GOTPCREL(%rip), %rax + vmovups %ymm11, 160(%rsp) + vmovups %ymm8, 224(%rsp) + vmovups %ymm10, 352(%rsp) + vmovups %ymm9, 384(%rsp) + vmovups %ymm13, 288(%rsp) + vmovapd %ymm1, %ymm11 + vxorpd %ymm1, %ymm1, %ymm1 + vextracti128 $1, %ymm0, %xmm5 + vshufps $221, %xmm5, %xmm0, %xmm5 + +/* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ + vandps _iIndexMask(%rax), %xmm5, %xmm3 + vpaddd _iIndexAdd(%rax), %xmm3, %xmm6 + vpsrld $10, %xmm6, %xmm8 + +/* Index for reciprocal table */ + vpslld $3, %xmm8, %xmm9 + +/* Index for log2 table */ + vpslld $4, %xmm8, %xmm6 + +/* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ + vandpd _iMantissaMask(%rax), %ymm0, %ymm4 + vorpd _dbOne(%rax), %ymm4, %ymm13 + vpcmpeqd %ymm4, %ymm4, %ymm4 + vpcmpeqd %ymm8, %ymm8, %ymm8 + +/* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ + vpsubd _i3fe7fe00(%rax), %xmm5, %xmm3 + vpaddd _HIDELTA(%rax), %xmm5, %xmm5 + vextracti128 $1, %ymm11, %xmm7 + vshufps $221, %xmm7, %xmm11, %xmm2 + vpand _ABSMASK(%rax), %xmm2, %xmm10 + vpcmpeqd %ymm2, %ymm2, %ymm2 + vgatherdpd %ymm2, 11712(%rax,%xmm9), %ymm1 + vmovups _LORANGE(%rax), %xmm7 + vxorpd %ymm2, %ymm2, %ymm2 + vgatherdpd %ymm4, 19968(%rax,%xmm6), %ymm2 + vxorpd %ymm4, %ymm4, %ymm4 + vgatherdpd %ymm8, 19976(%rax,%xmm6), %ymm4 + vpsrad $20, %xmm3, %xmm6 + vpaddd _i2p20_2p19(%rax), %xmm6, %xmm9 + vpshufd $80, %xmm9, %xmm8 + vpshufd $250, %xmm9, %xmm3 + +/* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ + vandpd _iHighMask(%rax), %ymm13, %ymm9 + vinserti128 $1, %xmm3, %ymm8, %ymm6 + vandpd _iffffffff00000000(%rax), %ymm6, %ymm8 + +/* r1 = x1*rcp1 */ + vmulpd %ymm1, %ymm13, %ymm6 + vsubpd %ymm9, %ymm13, %ymm3 + vsubpd _db2p20_2p19(%rax), %ymm8, %ymm8 + +/* cq = c+r1 */ + vaddpd _LHN(%rax), %ymm6, %ymm13 + +/* E = -r1+__fence(x1Hi*rcp1) */ + vfmsub213pd %ymm6, %ymm1, %ymm9 + +/* E=E+x1Lo*rcp1 */ + vfmadd213pd %ymm9, %ymm1, %ymm3 + +/* T = k + L1hi */ + vaddpd %ymm2, %ymm8, %ymm1 + +/* T_Rh = T + cq */ + vaddpd %ymm13, %ymm1, %ymm8 + +/* Rl = T-T_Rh; -> -Rh */ + vsubpd %ymm8, %ymm1, %ymm6 + +/* Rl=Rl+cq */ + vaddpd %ymm6, %ymm13, %ymm1 + +/* T_Rh_Eh = T_Rh + E */ + vaddpd %ymm3, %ymm8, %ymm6 + +/* cq = cq + E */ + vaddpd %ymm3, %ymm13, %ymm13 + +/* HLL = T_Rh - T_Rh_Eh; -> -Eh */ + vsubpd %ymm6, %ymm8, %ymm9 + +/* HLL+=E; -> El */ + vaddpd %ymm9, %ymm3, %ymm2 + +/* HLL+=Rl */ + vaddpd %ymm1, %ymm2, %ymm8 + +/* HLL+=L1lo */ + vaddpd %ymm4, %ymm8, %ymm4 + vmovupd _clv_2(%rax), %ymm8 + +/* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ + vfmadd213pd _clv_3(%rax), %ymm13, %ymm8 + vfmadd213pd _clv_4(%rax), %ymm13, %ymm8 + vfmadd213pd _clv_5(%rax), %ymm13, %ymm8 + vfmadd213pd _clv_6(%rax), %ymm13, %ymm8 + vfmadd213pd _clv_7(%rax), %ymm13, %ymm8 + vfmadd213pd %ymm4, %ymm13, %ymm8 + +/* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ + vaddpd %ymm8, %ymm6, %ymm9 + +/* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ + vandpd _iHighMask(%rax), %ymm9, %ymm2 + +/* + 2^(y*(HH+HL+HLL)) starts here: + yH = y; Lo(yH)&=0xf8000000; + */ + vandpd _iHighMask(%rax), %ymm11, %ymm1 + +/* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ + vsubpd %ymm6, %ymm9, %ymm13 + +/* HL = T_Rh_Eh_HLLhi-HH */ + vsubpd %ymm2, %ymm9, %ymm4 + +/* pH = yH*HH */ + vmulpd %ymm2, %ymm1, %ymm9 + +/* HLL = HLL - HLLhi */ + vsubpd %ymm13, %ymm8, %ymm6 + +/* yL = y-yH */ + vsubpd %ymm1, %ymm11, %ymm8 + vextracti128 $1, %ymm9, %xmm3 + vshufps $221, %xmm3, %xmm9, %xmm13 + vpand _ABSMASK(%rax), %xmm13, %xmm3 + vpcmpgtd %xmm5, %xmm7, %xmm13 + vpcmpgtd _INF(%rax), %xmm10, %xmm7 + vpcmpeqd _INF(%rax), %xmm10, %xmm10 + vpor %xmm10, %xmm7, %xmm7 + vpor %xmm7, %xmm13, %xmm5 + +/* pL=yL*HL+yH*HL; pL+=yL*HH */ + vmulpd %ymm4, %ymm8, %ymm7 + vpcmpgtd _DOMAINRANGE(%rax), %xmm3, %xmm13 + vpcmpeqd _DOMAINRANGE(%rax), %xmm3, %xmm10 + vpor %xmm10, %xmm13, %xmm3 + vpor %xmm3, %xmm5, %xmm13 + vfmadd213pd %ymm7, %ymm4, %ymm1 + +/* pLL = y*HLL; + pHH = pH + *(double*)&db2p45_2p44 + */ + vaddpd _db2p45_2p44(%rax), %ymm9, %ymm7 + vmovmskps %xmm13, %ecx + vfmadd213pd %ymm1, %ymm2, %ymm8 + +/* t=pL+pLL; t+=pHL */ + vfmadd231pd %ymm11, %ymm6, %ymm8 + vextracti128 $1, %ymm7, %xmm1 + vshufps $136, %xmm1, %xmm7, %xmm10 + +/* _n = Lo(pHH); + _n = _n & 0xffffff80; + _n = _n >> 7; + Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n + */ + vpslld $13, %xmm10, %xmm2 + vpaddd _iOne(%rax), %xmm2, %xmm13 + vpshufd $80, %xmm13, %xmm4 + vpshufd $250, %xmm13, %xmm1 + +/* j = Lo(pHH)&0x0000007f */ + vandps _jIndexMask(%rax), %xmm10, %xmm3 + +/* T1 = ((double*)exp2_tbl)[ 2*j ] */ + vpcmpeqd %ymm10, %ymm10, %ymm10 + vpslld $4, %xmm3, %xmm5 + +/* pHH = pHH - *(double*)&db2p45_2p44 */ + vsubpd _db2p45_2p44(%rax), %ymm7, %ymm7 + +/* pHL = pH - pHH */ + vsubpd %ymm7, %ymm9, %ymm9 + vaddpd %ymm9, %ymm8, %ymm6 + vinserti128 $1, %xmm1, %ymm4, %ymm2 + vxorpd %ymm1, %ymm1, %ymm1 + vgatherdpd %ymm10, 36416(%rax,%xmm5), %ymm1 + vandpd _ifff0000000000000(%rax), %ymm2, %ymm13 + vmovupd _cev_1(%rax), %ymm2 + vmulpd %ymm1, %ymm13, %ymm1 + vfmadd213pd _cev_2(%rax), %ymm6, %ymm2 + vmulpd %ymm6, %ymm1, %ymm8 + vfmadd213pd _cev_3(%rax), %ymm6, %ymm2 + vfmadd213pd _cev_4(%rax), %ymm6, %ymm2 + vfmadd213pd _cev_5(%rax), %ymm6, %ymm2 + vfmadd213pd %ymm1, %ymm8, %ymm2 + testl %ecx, %ecx + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + vmovups 224(%rsp), %ymm8 + vmovups 384(%rsp), %ymm9 + vmovups 352(%rsp), %ymm10 + vmovups 160(%rsp), %ymm11 + vmovups 288(%rsp), %ymm13 + vmovdqa %ymm2, %ymm0 + 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 + vmovupd %ymm0, 192(%rsp) + vmovupd %ymm11, 256(%rsp) + vmovupd %ymm2, 320(%rsp) + je .LBL_1_2 + + xorb %dl, %dl + xorl %eax, %eax + vmovups %ymm12, 64(%rsp) + vmovups %ymm14, 32(%rsp) + vmovups %ymm15, (%rsp) + movq %rsi, 104(%rsp) + movq %rdi, 96(%rsp) + movq %r12, 136(%rsp) + cfi_offset_rel_rsp (12, 136) + movb %dl, %r12b + movq %r13, 128(%rsp) + cfi_offset_rel_rsp (13, 128) + movl %ecx, %r13d + movq %r14, 120(%rsp) + cfi_offset_rel_rsp (14, 120) + movl %eax, %r14d + movq %r15, 112(%rsp) + cfi_offset_rel_rsp (15, 112) + cfi_remember_state + +.LBL_1_6: + btl %r14d, %r13d + jc .LBL_1_12 + +.LBL_1_7: + lea 1(%r14), %esi + btl %esi, %r13d + jc .LBL_1_10 + +.LBL_1_8: + incb %r12b + addl $2, %r14d + cmpb $16, %r12b + jb .LBL_1_6 + + vmovups 64(%rsp), %ymm12 + vmovups 32(%rsp), %ymm14 + vmovups (%rsp), %ymm15 + vmovupd 320(%rsp), %ymm2 + movq 104(%rsp), %rsi + movq 96(%rsp), %rdi + movq 136(%rsp), %r12 + cfi_restore (%r12) + movq 128(%rsp), %r13 + cfi_restore (%r13) + movq 120(%rsp), %r14 + cfi_restore (%r14) + movq 112(%rsp), %r15 + cfi_restore (%r15) + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + shlq $4, %r15 + vmovsd 200(%rsp,%r15), %xmm0 + vmovsd 264(%rsp,%r15), %xmm1 + vzeroupper + + call pow@PLT + + vmovsd %xmm0, 328(%rsp,%r15) + jmp .LBL_1_8 + +.LBL_1_12: + movzbl %r12b, %r15d + shlq $4, %r15 + vmovsd 192(%rsp,%r15), %xmm0 + vmovsd 256(%rsp,%r15), %xmm1 + vzeroupper + + call pow@PLT + + vmovsd %xmm0, 320(%rsp,%r15) + jmp .LBL_1_7 + +END (_ZGVdN4vv_pow_avx2) diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core.S new file mode 100644 index 0000000000..3b11511e51 --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core.S @@ -0,0 +1,39 @@ +/* Multiple versions of vectorized pow. + 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 (_ZGVeN8vv_pow) + .type _ZGVeN8vv_pow, @gnu_indirect_function + cmpl $0, KIND_OFFSET+__cpu_features(%rip) + jne 1 + call __init_cpu_features +1: leaq _ZGVeN8vv_pow_skx(%rip), %rax + testl $bit_AVX512DQ_Usable, __cpu_features+FEATURE_OFFSET+index_AVX512DQ_Usable(%rip) + jnz 3 +2: leaq _ZGVeN8vv_pow_knl(%rip), %rax + testl $bit_AVX512F_Usable, __cpu_features+FEATURE_OFFSET+index_AVX512F_Usable(%rip) + jnz 3 + leaq _ZGVeN8vv_pow_avx2_wrapper(%rip), %rax +3: ret +END (_ZGVeN8vv_pow) + +#define _ZGVeN8vv_pow _ZGVeN8vv_pow_avx2_wrapper +#include "../svml_d_pow8_core.S" diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core_avx512.S new file mode 100644 index 0000000000..8dd89c8ebb --- /dev/null +++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow8_core_avx512.S @@ -0,0 +1,741 @@ +/* Function pow 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_d_pow_data.h" +#include "svml_d_wrapper_impl.h" + +/* ALGORITHM DESCRIPTION: + + 1) Calculating log2|x| + Here we use the following formula. + Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. + Let C ~= 1/ln(2), + Rcp1 ~= 1/X1, X2=Rcp1*X1, + Rcp2 ~= 1/X2, X3=Rcp2*X2, + Rcp3 ~= 1/X3, Rcp3C ~= C/X3. + Then + log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + + log2(X1*Rcp1*Rcp2*Rcp3C/C), + where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. + + The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), + Rcp3C, log2(C/Rcp3C) are taken from tables. + Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C + is exactly represented in target precision. + + log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = + = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = + = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = + = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., + where cq = X1*Rcp1*Rcp2*Rcp3C-C, + a1=1/(C*ln(2))-1 is small, + a2=1/(2*C^2*ln2), + a3=1/(3*C^3*ln2), + ... + We get 3 parts of log2 result: HH+HL+HLL ~= log2|x|. + + 2) Calculation of y*(HH+HL+HLL). + Split y into YHi+YLo. + Get high PH and medium PL parts of y*log2|x|. + Get low PLL part of y*log2|x|. + Now we have PH+PL+PLL ~= y*log2|x|. + + 3) Calculation of 2^(PH+PL+PLL). + Mathematical idea of computing 2^(PH+PL+PLL) is the following. + Let's represent PH+PL+PLL in the form N + j/2^expK + Z, + where expK=7 in this implementation, N and j are integers, + 0<=j<=2^expK-1, |Z|<2^(-expK-1). + Hence 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, + where 2^(j/2^expK) is stored in a table, and + 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. + + We compute 2^(PH+PL+PLL) as follows. + Break PH into PHH + PHL, where PHH = N + j/2^expK. + Z = PHL + PL + PLL + Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 + Get 2^(j/2^expK) from table in the form THI+TLO. + Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). + + Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: + ResHi := THI + ResLo := THI * Exp2Poly + TLO + + Get exponent ERes of the result: + Res := ResHi + ResLo: + Result := ex(Res) + N. */ + + .text +ENTRY (_ZGVeN8vv_pow_knl) +#ifndef HAVE_AVX512_ASM_SUPPORT +WRAPPER_IMPL_AVX512_ff _ZGVdN4vv_pow +#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 + vpsrlq $32, %zmm0, %zmm13 + vmovaps %zmm1, %zmm12 + movq __svml_dpow_data@GOTPCREL(%rip), %rax + movl $255, %edx + vpmovqd %zmm13, %ymm10 + vpsrlq $32, %zmm12, %zmm14 + kmovw %edx, %k1 + movl $-1, %ecx + vpmovqd %zmm14, %ymm15 + +/* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ + vmovups _dbOne(%rax), %zmm6 + +/* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ + vmovaps %zmm10, %zmm5 + +/* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ + vpsubd _i3fe7fe00(%rax), %zmm10, %zmm14{%k1} + vpandd _iIndexMask(%rax), %zmm10, %zmm5{%k1} + vpsrad $20, %zmm14, %zmm14{%k1} + vpxord %zmm9, %zmm9, %zmm9 + vpaddd _HIDELTA(%rax), %zmm10, %zmm3{%k1} + vpaddd _iIndexAdd(%rax), %zmm5, %zmm5{%k1} + vpxord %zmm7, %zmm7, %zmm7 + vpaddd _i2p20_2p19(%rax), %zmm14, %zmm14{%k1} + vpcmpd $1, _LORANGE(%rax), %zmm3, %k2{%k1} + vpsrld $10, %zmm5, %zmm5{%k1} + vpandd _ABSMASK(%rax), %zmm15, %zmm2{%k1} + vpbroadcastd %ecx, %zmm1{%k2}{z} + +/* Index for reciprocal table */ + vpslld $3, %zmm5, %zmm8{%k1} + kxnorw %k2, %k2, %k2 + vgatherdpd 11712(%rax,%ymm8), %zmm9{%k2} + vpmovzxdq %ymm14, %zmm10 + +/* Index for log2 table */ + vpslld $4, %zmm5, %zmm13{%k1} + kxnorw %k2, %k2, %k2 + vpsllq $32, %zmm10, %zmm3 + vpxord %zmm8, %zmm8, %zmm8 + vpcmpd $5, _INF(%rax), %zmm2, %k3{%k1} + vpbroadcastd %ecx, %zmm4{%k3}{z} + vpternlogq $248, _iMantissaMask(%rax), %zmm0, %zmm6 + kxnorw %k3, %k3, %k3 + vpternlogq $168, _iffffffff00000000(%rax), %zmm10, %zmm3 + +/* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ + vpandq _iHighMask(%rax), %zmm6, %zmm2 + vgatherdpd 19976(%rax,%ymm13), %zmm8{%k2} + vpord %zmm4, %zmm1, %zmm11{%k1} + vsubpd _db2p20_2p19(%rax), %zmm3, %zmm1 + vsubpd %zmm2, %zmm6, %zmm5 + +/* r1 = x1*rcp1 */ + vmulpd %zmm9, %zmm6, %zmm6 + vgatherdpd 19968(%rax,%ymm13), %zmm7{%k3} + +/* cq = c+r1 */ + vaddpd _LHN(%rax), %zmm6, %zmm4 + +/* E = -r1+__fence(x1Hi*rcp1) */ + vfmsub213pd %zmm6, %zmm9, %zmm2 + +/* T = k + L1hi */ + vaddpd %zmm7, %zmm1, %zmm7 + +/* E=E+x1Lo*rcp1 */ + vfmadd213pd %zmm2, %zmm9, %zmm5 + +/* T_Rh = T + cq */ + vaddpd %zmm4, %zmm7, %zmm3 + +/* Rl = T-T_Rh; -> -Rh */ + vsubpd %zmm3, %zmm7, %zmm9 + +/* Rl=Rl+cq */ + vaddpd %zmm9, %zmm4, %zmm6 + +/* T_Rh_Eh = T_Rh + E */ + vaddpd %zmm5, %zmm3, %zmm9 + +/* HLL = T_Rh - T_Rh_Eh; -> -Eh */ + vsubpd %zmm9, %zmm3, %zmm2 + +/* cq = cq + E; */ + vaddpd %zmm5, %zmm4, %zmm4 + +/* HLL+=E; -> El */ + vaddpd %zmm2, %zmm5, %zmm1 + vmovups _clv_2(%rax), %zmm5 + +/* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ + vfmadd213pd _clv_3(%rax), %zmm4, %zmm5 + +/* HLL+=Rl */ + vaddpd %zmm6, %zmm1, %zmm7 + +/* 2^(y*(HH+HL+HLL)) starts here: + yH = y; Lo(yH)&=0xf8000000 + */ + vpandq _iHighMask(%rax), %zmm12, %zmm6 + +/* yL = y-yH */ + vsubpd %zmm6, %zmm12, %zmm2 + vfmadd213pd _clv_4(%rax), %zmm4, %zmm5 + +/* HLL+=L1lo */ + vaddpd %zmm8, %zmm7, %zmm8 + vfmadd213pd _clv_5(%rax), %zmm4, %zmm5 + vfmadd213pd _clv_6(%rax), %zmm4, %zmm5 + vfmadd213pd _clv_7(%rax), %zmm4, %zmm5 + vfmadd213pd %zmm8, %zmm4, %zmm5 + +/* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ + vaddpd %zmm5, %zmm9, %zmm13 + +/* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ + vsubpd %zmm9, %zmm13, %zmm10 + +/* HLL = HLL - HLLhi */ + vsubpd %zmm10, %zmm5, %zmm3 + +/* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ + vpandq _iHighMask(%rax), %zmm13, %zmm5 + +/* pH = yH*HH */ + vmulpd %zmm5, %zmm6, %zmm1 + +/* HL = T_Rh_Eh_HLLhi-HH */ + vsubpd %zmm5, %zmm13, %zmm4 + vpsrlq $32, %zmm1, %zmm14 + +/* pLL = y*HLL; + pHH = pH + *(double*)&db2p45_2p44 + */ + vaddpd _db2p45_2p44(%rax), %zmm1, %zmm10 + vpmovqd %zmm14, %ymm15 + vpandd _ABSMASK(%rax), %zmm15, %zmm14{%k1} + vpcmpd $5, _DOMAINRANGE(%rax), %zmm14, %k3{%k1} + +/* T1 = ((double*)exp2_tbl)[ 2*j ] */ + vpxord %zmm14, %zmm14, %zmm14 + vpbroadcastd %ecx, %zmm13{%k3}{z} + vpord %zmm13, %zmm11, %zmm11{%k1} + vptestmd %zmm11, %zmm11, %k0{%k1} + +/* pL=yL*HL+yH*HL; pL+=yL*HH */ + vmulpd %zmm4, %zmm2, %zmm11 + kmovw %k0, %ecx + vfmadd213pd %zmm11, %zmm4, %zmm6 + +/* pHH = pHH - *(double*)&db2p45_2p44 */ + vsubpd _db2p45_2p44(%rax), %zmm10, %zmm11 + vpmovqd %zmm10, %ymm4 + movzbl %cl, %ecx + +/* _n = Lo(pHH); + _n = _n & 0xffffff80; + _n = _n >> 7; + Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n + */ + vpslld $13, %zmm4, %zmm7{%k1} + +/* j = Lo(pHH)&0x0000007f */ + vpandd _jIndexMask(%rax), %zmm4, %zmm9{%k1} + vfmadd213pd %zmm6, %zmm5, %zmm2 + +/* pHL = pH - pHH */ + vsubpd %zmm11, %zmm1, %zmm1 + vpaddd _iOne(%rax), %zmm7, %zmm7{%k1} + +/* t=pL+pLL; t+=pHL */ + vfmadd231pd %zmm12, %zmm3, %zmm2 + vpslld $4, %zmm9, %zmm9{%k1} + kxnorw %k1, %k1, %k1 + vgatherdpd 36416(%rax,%ymm9), %zmm14{%k1} + vpmovzxdq %ymm7, %zmm8 + vaddpd %zmm1, %zmm2, %zmm2 + vmovups _cev_1(%rax), %zmm1 + vpsllq $32, %zmm8, %zmm13 + vpternlogq $168, _ifff0000000000000(%rax), %zmm8, %zmm13 + vfmadd213pd _cev_2(%rax), %zmm2, %zmm1 + vmulpd %zmm14, %zmm13, %zmm15 + vfmadd213pd _cev_3(%rax), %zmm2, %zmm1 + vmulpd %zmm2, %zmm15, %zmm3 + vfmadd213pd _cev_4(%rax), %zmm2, %zmm1 + vfmadd213pd _cev_5(%rax), %zmm2, %zmm1 + vfmadd213pd %zmm15, %zmm3, %zmm1 + testl %ecx, %ecx + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + vmovaps %zmm1, %zmm0 + 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 %zmm0, 1152(%rsp) + vmovups %zmm12, 1216(%rsp) + vmovups %zmm1, 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, 1064(%rsp) + movq %rdi, 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 %ecx, %r13d + movq %r14, 1080(%rsp) + cfi_offset_rel_rsp (14, 1080) + movl %eax, %r14d + movq %r15, 1072(%rsp) + cfi_offset_rel_rsp (15, 1072) + cfi_remember_state + +.LBL_1_6: + btl %r14d, %r13d + jc .LBL_1_12 + +.LBL_1_7: + lea 1(%r14), %esi + btl %esi, %r13d + jc .LBL_1_10 + +.LBL_1_8: + addb $1, %r12b + addl $2, %r14d + cmpb $16, %r12b + jb .LBL_1_6 + + kmovw 1048(%rsp), %k4 + movq 1064(%rsp), %rsi + kmovw 1040(%rsp), %k5 + movq 1056(%rsp), %rdi + kmovw 1032(%rsp), %k6 + movq 1096(%rsp), %r12 + cfi_restore (%r12) + 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) + vmovups 1280(%rsp), %zmm1 + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + shlq $4, %r15 + vmovsd 1160(%rsp,%r15), %xmm0 + vmovsd 1224(%rsp,%r15), %xmm1 + call pow@PLT + vmovsd %xmm0, 1288(%rsp,%r15) + jmp .LBL_1_8 + +.LBL_1_12: + movzbl %r12b, %r15d + shlq $4, %r15 + vmovsd 1152(%rsp,%r15), %xmm0 + vmovsd 1216(%rsp,%r15), %xmm1 + call pow@PLT + vmovsd %xmm0, 1280(%rsp,%r15) + jmp .LBL_1_7 + +#endif +END (_ZGVeN8vv_pow_knl) + +ENTRY (_ZGVeN8vv_pow_skx) +#ifndef HAVE_AVX512_ASM_SUPPORT +WRAPPER_IMPL_AVX512_ff _ZGVdN4vv_pow +#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 + vpsrlq $32, %zmm0, %zmm10 + kxnorw %k1, %k1, %k1 + kxnorw %k2, %k2, %k2 + kxnorw %k3, %k3, %k3 + vpmovqd %zmm10, %ymm7 + movq __svml_dpow_data@GOTPCREL(%rip), %rax + vmovaps %zmm1, %zmm6 + vpsrlq $32, %zmm6, %zmm13 + +/* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ + vpand _iIndexMask(%rax), %ymm7, %ymm15 + vpaddd _HIDELTA(%rax), %ymm7, %ymm2 + +/* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ + vpsubd _i3fe7fe00(%rax), %ymm7, %ymm7 + vmovdqu _ABSMASK(%rax), %ymm4 + vmovdqu _LORANGE(%rax), %ymm3 + +/* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ + vmovups _dbOne(%rax), %zmm11 + vmovdqu _INF(%rax), %ymm5 + vpaddd _iIndexAdd(%rax), %ymm15, %ymm12 + vpmovqd %zmm13, %ymm14 + vpternlogq $248, _iMantissaMask(%rax), %zmm0, %zmm11 + vpsrld $10, %ymm12, %ymm10 + vpsrad $20, %ymm7, %ymm13 + +/* Index for reciprocal table */ + vpslld $3, %ymm10, %ymm8 + +/* Index for log2 table */ + vpslld $4, %ymm10, %ymm1 + vpcmpgtd %ymm2, %ymm3, %ymm3 + vpand %ymm4, %ymm14, %ymm2 + vpaddd _i2p20_2p19(%rax), %ymm13, %ymm14 + vpmovzxdq %ymm14, %zmm15 + vpsllq $32, %zmm15, %zmm7 + vpternlogq $168, _iffffffff00000000(%rax), %zmm15, %zmm7 + vsubpd _db2p20_2p19(%rax), %zmm7, %zmm13 + vpxord %zmm9, %zmm9, %zmm9 + vgatherdpd 11712(%rax,%ymm8), %zmm9{%k1} + +/* T1 = ((double*)exp2_tbl)[ 2*j ] */ + kxnorw %k1, %k1, %k1 + vpxord %zmm12, %zmm12, %zmm12 + vpxord %zmm8, %zmm8, %zmm8 + vgatherdpd 19968(%rax,%ymm1), %zmm12{%k2} + vgatherdpd 19976(%rax,%ymm1), %zmm8{%k3} + vmovups _iHighMask(%rax), %zmm1 + +/* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ + vandpd %zmm1, %zmm11, %zmm10 + vsubpd %zmm10, %zmm11, %zmm15 + +/* r1 = x1*rcp1 */ + vmulpd %zmm9, %zmm11, %zmm11 + +/* E = -r1+__fence(x1Hi*rcp1) */ + vfmsub213pd %zmm11, %zmm9, %zmm10 + +/* cq = c+r1 */ + vaddpd _LHN(%rax), %zmm11, %zmm14 + +/* E=E+x1Lo*rcp1 */ + vfmadd213pd %zmm10, %zmm9, %zmm15 + +/* T = k + L1hi */ + vaddpd %zmm12, %zmm13, %zmm9 + +/* T_Rh = T + cq */ + vaddpd %zmm14, %zmm9, %zmm11 + +/* T_Rh_Eh = T_Rh + E */ + vaddpd %zmm15, %zmm11, %zmm13 + +/* Rl = T-T_Rh; -> -Rh */ + vsubpd %zmm11, %zmm9, %zmm12 + +/* HLL = T_Rh - T_Rh_Eh; -> -Eh */ + vsubpd %zmm13, %zmm11, %zmm9 + +/* Rl=Rl+cq */ + vaddpd %zmm12, %zmm14, %zmm10 + +/* HLL+=E; -> El */ + vaddpd %zmm9, %zmm15, %zmm7 + +/* HLL+=Rl */ + vaddpd %zmm10, %zmm7, %zmm12 + +/* 2^(y*(HH+HL+HLL)) starts here: + yH = y; Lo(yH)&=0xf8000000 + */ + vandpd %zmm1, %zmm6, %zmm7 + +/* HLL+=L1lo */ + vaddpd %zmm8, %zmm12, %zmm12 + +/* cq = cq + E */ + vaddpd %zmm15, %zmm14, %zmm8 + vmovups _clv_2(%rax), %zmm14 + +/* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ + vfmadd213pd _clv_3(%rax), %zmm8, %zmm14 + vfmadd213pd _clv_4(%rax), %zmm8, %zmm14 + vfmadd213pd _clv_5(%rax), %zmm8, %zmm14 + vfmadd213pd _clv_6(%rax), %zmm8, %zmm14 + vfmadd213pd _clv_7(%rax), %zmm8, %zmm14 + vfmadd213pd %zmm12, %zmm8, %zmm14 + +/* yL = y-yH */ + vsubpd %zmm7, %zmm6, %zmm8 + +/* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ + vaddpd %zmm14, %zmm13, %zmm15 + +/* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ + vandpd %zmm1, %zmm15, %zmm11 + +/* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ + vsubpd %zmm13, %zmm15, %zmm13 + +/* pH = yH*HH */ + vmulpd %zmm11, %zmm7, %zmm9 + +/* HLL = HLL - HLLhi */ + vsubpd %zmm13, %zmm14, %zmm12 + +/* HL = T_Rh_Eh_HLLhi-HH */ + vsubpd %zmm11, %zmm15, %zmm10 + vpsrlq $32, %zmm9, %zmm1 + vmovdqu _DOMAINRANGE(%rax), %ymm13 + vpmovqd %zmm1, %ymm1 + vpand %ymm4, %ymm1, %ymm1 + vpcmpgtd %ymm5, %ymm2, %ymm4 + vpcmpeqd %ymm5, %ymm2, %ymm5 + vpternlogd $254, %ymm5, %ymm4, %ymm3 + vpcmpgtd %ymm13, %ymm1, %ymm2 + vpcmpeqd %ymm13, %ymm1, %ymm4 + vpternlogd $254, %ymm4, %ymm2, %ymm3 + +/* pLL = y*HLL */ + vmovups _db2p45_2p44(%rax), %zmm2 + +/* pHH = pH + *(double*)&db2p45_2p44 */ + vaddpd %zmm2, %zmm9, %zmm1 + vpmovqd %zmm1, %ymm5 + +/* j = Lo(pHH)&0x0000007f */ + vpand _jIndexMask(%rax), %ymm5, %ymm14 + vpslld $4, %ymm14, %ymm15 + vmovmskps %ymm3, %ecx + +/* pL=yL*HL+yH*HL; pL+=yL*HH */ + vmulpd %zmm10, %zmm8, %zmm3 + vfmadd213pd %zmm3, %zmm10, %zmm7 + vfmadd213pd %zmm7, %zmm11, %zmm8 + +/* _n = Lo(pHH) + _n = _n & 0xffffff80 + _n = _n >> 7 + Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n + */ + vpslld $13, %ymm5, %ymm7 + +/* t=pL+pLL; t+=pHL */ + vfmadd231pd %zmm6, %zmm12, %zmm8 + vpaddd _iOne(%rax), %ymm7, %ymm10 + vpmovzxdq %ymm10, %zmm11 + vpsllq $32, %zmm11, %zmm3 + vpternlogq $168, _ifff0000000000000(%rax), %zmm11, %zmm3 + +/* pHH = pHH - *(double*)&db2p45_2p44 */ + vsubpd %zmm2, %zmm1, %zmm11 + vmovups _cev_1(%rax), %zmm2 + +/* pHL = pH - pHH */ + vsubpd %zmm11, %zmm9, %zmm9 + vaddpd %zmm9, %zmm8, %zmm8 + vfmadd213pd _cev_2(%rax), %zmm8, %zmm2 + vfmadd213pd _cev_3(%rax), %zmm8, %zmm2 + vfmadd213pd _cev_4(%rax), %zmm8, %zmm2 + vfmadd213pd _cev_5(%rax), %zmm8, %zmm2 + vpxord %zmm4, %zmm4, %zmm4 + vgatherdpd 36416(%rax,%ymm15), %zmm4{%k1} + vmulpd %zmm4, %zmm3, %zmm1 + vmulpd %zmm8, %zmm1, %zmm12 + vfmadd213pd %zmm1, %zmm12, %zmm2 + testl %ecx, %ecx + jne .LBL_2_3 + +.LBL_2_2: + cfi_remember_state + vmovaps %zmm2, %zmm0 + 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 %zmm0, 1152(%rsp) + vmovups %zmm6, 1216(%rsp) + vmovups %zmm2, 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, 1064(%rsp) + movq %rdi, 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 %ecx, %r13d + movq %r14, 1080(%rsp) + cfi_offset_rel_rsp (14, 1080) + movl %eax, %r14d + movq %r15, 1072(%rsp) + cfi_offset_rel_rsp (15, 1072) + cfi_remember_state + +.LBL_2_6: + btl %r14d, %r13d + jc .LBL_2_12 + +.LBL_2_7: + lea 1(%r14), %esi + btl %esi, %r13d + jc .LBL_2_10 + +.LBL_2_8: + incb %r12b + addl $2, %r14d + cmpb $16, %r12b + jb .LBL_2_6 + + kmovw 1048(%rsp), %k4 + 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 1280(%rsp), %zmm2 + movq 1064(%rsp), %rsi + movq 1056(%rsp), %rdi + 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) + jmp .LBL_2_2 + +.LBL_2_10: + cfi_restore_state + movzbl %r12b, %r15d + shlq $4, %r15 + vmovsd 1224(%rsp,%r15), %xmm1 + vzeroupper + vmovsd 1160(%rsp,%r15), %xmm0 + + call pow@PLT + + vmovsd %xmm0, 1288(%rsp,%r15) + jmp .LBL_2_8 + +.LBL_2_12: + movzbl %r12b, %r15d + shlq $4, %r15 + vmovsd 1216(%rsp,%r15), %xmm1 + vzeroupper + vmovsd 1152(%rsp,%r15), %xmm0 + + call pow@PLT + + vmovsd %xmm0, 1280(%rsp,%r15) + jmp .LBL_2_7 + +#endif +END (_ZGVeN8vv_pow_skx) diff --git a/sysdeps/x86_64/fpu/svml_d_pow2_core.S b/sysdeps/x86_64/fpu/svml_d_pow2_core.S new file mode 100644 index 0000000000..0b726a1eaf --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_d_pow2_core.S @@ -0,0 +1,29 @@ +/* Function pow 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_d_wrapper_impl.h" + + .text +ENTRY (_ZGVbN2vv_pow) +WRAPPER_IMPL_SSE2_ff pow +END (_ZGVbN2vv_pow) + +#ifndef USE_MULTIARCH + libmvec_hidden_def (_ZGVbN2vv_pow) +#endif diff --git a/sysdeps/x86_64/fpu/svml_d_pow4_core.S b/sysdeps/x86_64/fpu/svml_d_pow4_core.S new file mode 100644 index 0000000000..9eb47ab8c9 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_d_pow4_core.S @@ -0,0 +1,29 @@ +/* Function pow 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_d_wrapper_impl.h" + + .text +ENTRY (_ZGVdN4vv_pow) +WRAPPER_IMPL_AVX_ff _ZGVbN2vv_pow +END (_ZGVdN4vv_pow) + +#ifndef USE_MULTIARCH + libmvec_hidden_def (_ZGVdN4vv_pow) +#endif diff --git a/sysdeps/x86_64/fpu/svml_d_pow4_core_avx.S b/sysdeps/x86_64/fpu/svml_d_pow4_core_avx.S new file mode 100644 index 0000000000..6c7b59995d --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_d_pow4_core_avx.S @@ -0,0 +1,25 @@ +/* Function pow 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_d_wrapper_impl.h" + + .text +ENTRY (_ZGVcN4vv_pow) +WRAPPER_IMPL_AVX_ff _ZGVbN2vv_pow +END (_ZGVcN4vv_pow) diff --git a/sysdeps/x86_64/fpu/svml_d_pow8_core.S b/sysdeps/x86_64/fpu/svml_d_pow8_core.S new file mode 100644 index 0000000000..cd99457843 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_d_pow8_core.S @@ -0,0 +1,25 @@ +/* Function pow 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_d_wrapper_impl.h" + + .text +ENTRY (_ZGVeN8vv_pow) +WRAPPER_IMPL_AVX512_ff _ZGVdN4vv_pow +END (_ZGVeN8vv_pow) diff --git a/sysdeps/x86_64/fpu/svml_d_pow_data.S b/sysdeps/x86_64/fpu/svml_d_pow_data.S new file mode 100644 index 0000000000..1e0733e0a6 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_d_pow_data.S @@ -0,0 +1,4863 @@ +/* Data for function pow. + 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_d_pow_data.h" + + .section .rodata, "a" + .align 64 + +/* Data table for vector implementations of function pow. + The table may contain polynomial, reduction, lookup coefficients and + other coefficients obtained through different methods of research and + experimental work. */ + + .globl __svml_dpow_data +__svml_dpow_data: + +/* Lookup log(2) table (for HSW): */ +.if .-__svml_dpow_data != _hsw_log2_table +.err +.endif + .quad 0xc08ff00000000000 + .quad 0x0000000000000000 + .quad 0xc08ff005c3e0ffc2 + .quad 0xbd33ab2631d4676d + .quad 0xc08ff00b84e236bc + .quad 0xbd4563ba56cde925 + .quad 0xc08ff01143068126 + .quad 0x3d11790209e88471 + .quad 0xc08ff016fe50b6ee + .quad 0xbd408517f8e37b00 + .quad 0xc08ff01cb6c3abd0 + .quad 0xbd44558b51cada94 + .quad 0xc08ff0226c622f52 + .quad 0xbd3ec312ed069b24 + .quad 0xc08ff0281f2f0cd0 + .quad 0xbd374a4cb0be9e8a + .quad 0xc08ff02dcf2d0b86 + .quad 0x3d26eb3ac8ec0ef7 + .quad 0xc08ff0337c5eee92 + .quad 0xbd45984a60ff3d2f + .quad 0xc08ff03926c7750a + .quad 0xbd0f0cccdd01ee2f + .quad 0xc08ff03ece6959f0 + .quad 0xbd3a5671e1bd4ae8 + .quad 0xc08ff0447347544c + .quad 0xbd3a0976c0a2827d + .quad 0xc08ff04a1564172a + .quad 0x3d1e14ebaf30c95e + .quad 0xc08ff04fb4c251a0 + .quad 0xbd46898809d2dc10 + .quad 0xc08ff0555164aee2 + .quad 0xbd4355e6ecb8e0f1 + .quad 0xc08ff05aeb4dd63c + .quad 0x3cf3c6764fc87b4a + .quad 0xc08ff06082806b1c + .quad 0xbd4532c412ba94db + .quad 0xc08ff06616ff0d24 + .quad 0xbd4465182838ed44 + .quad 0xc08ff06ba8cc5824 + .quad 0xbd47dc6d46384b31 + .quad 0xc08ff07137eae42a + .quad 0xbd35af7a7c7c34f3 + .quad 0xc08ff076c45d4584 + .quad 0x3d18a0e14f76d994 + .quad 0xc08ff07c4e260cc8 + .quad 0xbd44e7e87341aeee + .quad 0xc08ff081d547c6e4 + .quad 0xbd153121e9af5428 + .quad 0xc08ff08759c4fd14 + .quad 0xbd3f9ab3cf74baba + .quad 0xc08ff08cdba034fa + .quad 0xbd3f09941811b2ee + .quad 0xc08ff0925adbf09a + .quad 0xbd3a3c89a2cf3516 + .quad 0xc08ff097d77aae66 + .quad 0x3d291b415eeb24ed + .quad 0xc08ff09d517ee940 + .quad 0x3d2c7a4ff65ddbc9 + .quad 0xc08ff0a2c8eb1886 + .quad 0xbd385a047f97bb3e + .quad 0xc08ff0a83dc1b01a + .quad 0x3d1124ac34b21259 + .quad 0xc08ff0adb005205e + .quad 0xbd34f286d207e2c8 + .quad 0xc08ff0b31fb7d648 + .quad 0xbd33167ccc538261 + .quad 0xc08ff0b88cdc3b5e + .quad 0xbd4542fe4ce30d63 + .quad 0xc08ff0bdf774b5c4 + .quad 0xbd41409e20d7191b + .quad 0xc08ff0c35f83a83c + .quad 0xbd40638b5ff73edf + .quad 0xc08ff0c8c50b7232 + .quad 0x3d294aa31b9b6d65 + .quad 0xc08ff0ce280e6fba + .quad 0xbd38723279ebfab6 + .quad 0xc08ff0d3888ef9a4 + .quad 0xbd124fad116078ef + .quad 0xc08ff0d8e68f6572 + .quad 0xbd437350d69ea580 + .quad 0xc08ff0de4212056c + .quad 0xbd45dd31d962d373 + .quad 0xc08ff0e39b19289e + .quad 0x3d058b34834a501e + .quad 0xc08ff0e8f1a71adc + .quad 0xbd06d26859c7991e + .quad 0xc08ff0ee45be24d0 + .quad 0xbd3ddb7886f88587 + .quad 0xc08ff0f397608bfc + .quad 0xbd42d90e5edaecee + .quad 0xc08ff0f8e69092be + .quad 0xbd40c5eacb577b4a + .quad 0xc08ff0fe33507858 + .quad 0xbce49209a68c72a1 + .quad 0xc08ff1037da278f2 + .quad 0xbd30e0f9c896007d + .quad 0xc08ff108c588cda8 + .quad 0x3d2871a7610e40bd + .quad 0xc08ff10e0b05ac84 + .quad 0xbd31da156756faad + .quad 0xc08ff1134e1b4890 + .quad 0xbd28b7fcd690403e + .quad 0xc08ff1188ecbd1d0 + .quad 0xbd46be4a29c44115 + .quad 0xc08ff11dcd197552 + .quad 0xbd36f6bd48a860f0 + .quad 0xc08ff12309065d28 + .quad 0xbd47913e788c5887 + .quad 0xc08ff1284294b07a + .quad 0xbd28fe35da2ab291 + .quad 0xc08ff12d79c6937e + .quad 0xbd3fb9b1aaf54bcc + .quad 0xc08ff132ae9e278a + .quad 0xbd3c343ea3e580eb + .quad 0xc08ff137e11d8b10 + .quad 0xbd3f1140264356b8 + .quad 0xc08ff13d1146d9a8 + .quad 0xbd34c7e0166e1f56 + .quad 0xc08ff1423f1c2c12 + .quad 0xbd3d449e80431d92 + .quad 0xc08ff1476a9f983e + .quad 0xbd474d3138e94164 + .quad 0xc08ff14c93d33152 + .quad 0x3d2370693afbcdb1 + .quad 0xc08ff151bab907a6 + .quad 0x3d1badba7fbb3d20 + .quad 0xc08ff156df5328d6 + .quad 0x3d2cea9347cb6655 + .quad 0xc08ff15c01a39fbc + .quad 0xbd46879fa00b120a + .quad 0xc08ff16121ac7480 + .quad 0xbd43cf0ff16ff990 + .quad 0xc08ff1663f6fac90 + .quad 0xbd43167ccc538261 + .quad 0xc08ff16b5aef4aae + .quad 0xbd2f7081b8e33aad + .quad 0xc08ff170742d4ef0 + .quad 0xbd13f94e00e7d6bc + .quad 0xc08ff1758b2bb6c8 + .quad 0x3d22280434bda911 + .quad 0xc08ff17a9fec7d06 + .quad 0x3d1108740d92f890 + .quad 0xc08ff17fb27199de + .quad 0xbd416d18135d3266 + .quad 0xc08ff184c2bd02f0 + .quad 0xbd1d97ee9124773b + .quad 0xc08ff189d0d0ab42 + .quad 0xbd40ccd0edd00e4c + .quad 0xc08ff18edcae8352 + .quad 0xbd36d76b9a843329 + .quad 0xc08ff193e6587910 + .quad 0xbd210f7ac89c6f2d + .quad 0xc08ff198edd077e6 + .quad 0xbd40df02face8ca9 + .quad 0xc08ff19df31868c0 + .quad 0xbd41d4cc2f68b868 + .quad 0xc08ff1a2f632320c + .quad 0x3d2e54d71deb636a + .quad 0xc08ff1a7f71fb7ba + .quad 0xbd373af6b5487f35 + .quad 0xc08ff1acf5e2db4e + .quad 0xbd3927dfc23d9780 + .quad 0xc08ff1b1f27d7bd8 + .quad 0x3d2601ccfac2b557 + .quad 0xc08ff1b6ecf175f8 + .quad 0xbd45e96bed8cce30 + .quad 0xc08ff1bbe540a3f0 + .quad 0xbd1b76a46f31880a + .quad 0xc08ff1c0db6cdd94 + .quad 0xbd3bdc81c4db3134 + .quad 0xc08ff1c5cf77f860 + .quad 0xbd304cc6600a133e + .quad 0xc08ff1cac163c770 + .quad 0xbd3b912d8994b162 + .quad 0xc08ff1cfb1321b8c + .quad 0xbd20009770ea1465 + .quad 0xc08ff1d49ee4c326 + .quad 0x3d2a40dc2d2a6bf7 + .quad 0xc08ff1d98a7d8a60 + .quad 0xbd269affffe47644 + .quad 0xc08ff1de73fe3b14 + .quad 0xbd301dc37c84e79a + .quad 0xc08ff1e35b689cd2 + .quad 0xbd2953e61f15bd9b + .quad 0xc08ff1e840be74e6 + .quad 0xbd34998f93e7aa3c + .quad 0xc08ff1ed2401865e + .quad 0x3cf5c14e55f57802 + .quad 0xc08ff1f205339208 + .quad 0xbd3e4e8eea54ce63 + .quad 0xc08ff1f6e4565680 + .quad 0x3d0aaa72ba2c6ba2 + .quad 0xc08ff1fbc16b9026 + .quad 0xbd30144751b3314f + .quad 0xc08ff2009c74f930 + .quad 0x3d2a15a5b343a140 + .quad 0xc08ff205757449a0 + .quad 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0x3ff6a09e667f3bcd + .quad 0x3ff6b052fa75173e + .quad 0x3ff6c012750bdabf + .quad 0x3ff6cfdcddd47645 + .quad 0x3ff6dfb23c651a2f + .quad 0x3ff6ef9298593ae5 + .quad 0x3ff6ff7df9519484 + .quad 0x3ff70f7466f42e87 + .quad 0x3ff71f75e8ec5f74 + .quad 0x3ff72f8286ead08a + .quad 0x3ff73f9a48a58174 + .quad 0x3ff74fbd35d7cbfd + .quad 0x3ff75feb564267c9 + .quad 0x3ff77024b1ab6e09 + .quad 0x3ff780694fde5d3f + .quad 0x3ff790b938ac1cf6 + .quad 0x3ff7a11473eb0187 + .quad 0x3ff7b17b0976cfdb + .quad 0x3ff7c1ed0130c132 + .quad 0x3ff7d26a62ff86f0 + .quad 0x3ff7e2f336cf4e62 + .quad 0x3ff7f3878491c491 + .quad 0x3ff80427543e1a12 + .quad 0x3ff814d2add106d9 + .quad 0x3ff82589994cce13 + .quad 0x3ff8364c1eb941f7 + .quad 0x3ff8471a4623c7ad + .quad 0x3ff857f4179f5b21 + .quad 0x3ff868d99b4492ed + .quad 0x3ff879cad931a436 + .quad 0x3ff88ac7d98a6699 + .quad 0x3ff89bd0a478580f + .quad 0x3ff8ace5422aa0db + .quad 0x3ff8be05bad61778 + .quad 0x3ff8cf3216b5448c + .quad 0x3ff8e06a5e0866d9 + .quad 0x3ff8f1ae99157736 + .quad 0x3ff902fed0282c8a + .quad 0x3ff9145b0b91ffc6 + .quad 0x3ff925c353aa2fe2 + .quad 0x3ff93737b0cdc5e5 + .quad 0x3ff948b82b5f98e5 + .quad 0x3ff95a44cbc8520f + .quad 0x3ff96bdd9a7670b3 + .quad 0x3ff97d829fde4e50 + .quad 0x3ff98f33e47a22a2 + .quad 0x3ff9a0f170ca07ba + .quad 0x3ff9b2bb4d53fe0d + .quad 0x3ff9c49182a3f090 + .quad 0x3ff9d674194bb8d5 + .quad 0x3ff9e86319e32323 + .quad 0x3ff9fa5e8d07f29e + .quad 0x3ffa0c667b5de565 + .quad 0x3ffa1e7aed8eb8bb + .quad 0x3ffa309bec4a2d33 + .quad 0x3ffa42c980460ad8 + .quad 0x3ffa5503b23e255d + .quad 0x3ffa674a8af46052 + .quad 0x3ffa799e1330b358 + .quad 0x3ffa8bfe53c12e59 + .quad 0x3ffa9e6b5579fdbf + .quad 0x3ffab0e521356eba + .quad 0x3ffac36bbfd3f37a + .quad 0x3ffad5ff3a3c2774 + .quad 0x3ffae89f995ad3ad + .quad 0x3ffafb4ce622f2ff + .quad 0x3ffb0e07298db666 + .quad 0x3ffb20ce6c9a8952 + .quad 0x3ffb33a2b84f15fb + .quad 0x3ffb468415b749b1 + .quad 0x3ffb59728de5593a + .quad 0x3ffb6c6e29f1c52a + .quad 0x3ffb7f76f2fb5e47 + .quad 0x3ffb928cf22749e4 + .quad 0x3ffba5b030a1064a + .quad 0x3ffbb8e0b79a6f1f + .quad 0x3ffbcc1e904bc1d2 + .quad 0x3ffbdf69c3f3a207 + .quad 0x3ffbf2c25bd71e09 + .quad 0x3ffc06286141b33d + .quad 0x3ffc199bdd85529c + .quad 0x3ffc2d1cd9fa652c + .quad 0x3ffc40ab5fffd07a + .quad 0x3ffc544778fafb22 + .quad 0x3ffc67f12e57d14b + .quad 0x3ffc7ba88988c933 + .quad 0x3ffc8f6d9406e7b5 + .quad 0x3ffca3405751c4db + .quad 0x3ffcb720dcef9069 + .quad 0x3ffccb0f2e6d1675 + .quad 0x3ffcdf0b555dc3fa + .quad 0x3ffcf3155b5bab74 + .quad 0x3ffd072d4a07897c + .quad 0x3ffd1b532b08c968 + .quad 0x3ffd2f87080d89f2 + .quad 0x3ffd43c8eacaa1d6 + .quad 0x3ffd5818dcfba487 + .quad 0x3ffd6c76e862e6d3 + .quad 0x3ffd80e316c98398 + .quad 0x3ffd955d71ff6075 + .quad 0x3ffda9e603db3285 + .quad 0x3ffdbe7cd63a8315 + .quad 0x3ffdd321f301b460 + .quad 0x3ffde7d5641c0658 + .quad 0x3ffdfc97337b9b5f + .quad 0x3ffe11676b197d17 + .quad 0x3ffe264614f5a129 + .quad 0x3ffe3b333b16ee12 + .quad 0x3ffe502ee78b3ff6 + .quad 0x3ffe653924676d76 + .quad 0x3ffe7a51fbc74c83 + .quad 0x3ffe8f7977cdb740 + .quad 0x3ffea4afa2a490da + .quad 0x3ffeb9f4867cca6e + .quad 0x3ffecf482d8e67f1 + .quad 0x3ffee4aaa2188510 + .quad 0x3ffefa1bee615a27 + .quad 0x3fff0f9c1cb6412a + .quad 0x3fff252b376bba97 + .quad 0x3fff3ac948dd7274 + .quad 0x3fff50765b6e4540 + .quad 0x3fff6632798844f8 + .quad 0x3fff7bfdad9cbe14 + .quad 0x3fff91d802243c89 + .quad 0x3fffa7c1819e90d8 + .quad 0x3fffbdba3692d514 + .quad 0x3fffd3c22b8f71f1 + .quad 0x3fffe9d96b2a23d9 + +/* General purpose constants: + * hsw_dMantMask */ +double_vector _hsw_dMantMask 0x000fffffffffffff + +/* hsw_dOne */ +double_vector _hsw_dOne 0x3ff0000000000000 + +/* hsw_dCvtMask */ +double_vector _hsw_dCvtMask 0x4338000000000000 + +/* hsw_dMinNorm */ +double_vector _hsw_dMinNorm 0x0010000000000000 + +/* hsw_dMaxNorm */ +double_vector _hsw_dMaxNorm 0x7fefffffffffffff + +/* hsw_lRndBit */ +double_vector _hsw_lRndBit 0x0000040000000000 + +/* hsw_lRndMask */ +double_vector _hsw_lRndMask 0xfffff80000000000 + +/* Log polynomial: + * hsw_dc6 */ +double_vector _hsw_dc6 0xbfcec1cfbbc5c90c + +/* hsw_dc5 */ +double_vector _hsw_dc5 0x3fd2776da3d26e6a + +/* hsw_dc4 */ +double_vector _hsw_dc4 0xbfd71547655d37e0 + +/* hsw_dc3 */ +double_vector _hsw_dc3 0x3fdec709dc39fb02 + +/* hsw_dc1 */ +double_vector _hsw_dc1 0x3c777a3a2c24613d + +/* hsw_dc1h */ +double_vector _hsw_dc1h 0x3ff71547652b82fe + +/* hsw_dc2 */ +double_vector _hsw_dc2 0xbfe71547652b82fe + +/* Additional constants: + * hsw_AbsMask */ +double_vector _hsw_dAbsMask 0x7fffffffffffffff + +/* hsw_dDomainRange */ +double_vector _hsw_dDomainRange 0x408fec0000000000 + +/* hsw_dShifter */ +double_vector _hsw_dShifter 0x42b800000003ff00 + +/* hsw_dIndexMask */ +double_vector _hsw_dIndexMask 0x00000000000007f8 + +/* Exp polynomial: + * hsw_dce4 */ +double_vector _hsw_dce4 0x3f83b2ab930f15f9 + +/* hsw_dce3 */ +double_vector _hsw_dce3 0x3fac6b090da1e0a9 + +/* hsw_dce2 */ +double_vector _hsw_dce2 0x3fcebfbdff82c54d + +/* hsw_dce1 */ +double_vector _hsw_dce1 0x3fe62e42fefa39b9 + +/* Reciprocal lookup table for log part (non HSW): */ +.if .-__svml_dpow_data != _rcp_t1 +.err +.endif + .quad 0x3ff7154740000000 + .quad 0x3ff70f8340000000 + .quad 0x3ff709c240000000 + .quad 0x3ff7040440000000 + .quad 0x3ff6fe4900000000 + .quad 0x3ff6f89080000000 + .quad 0x3ff6f2db00000000 + .quad 0x3ff6ed2840000000 + .quad 0x3ff6e77840000000 + .quad 0x3ff6e1cb40000000 + .quad 0x3ff6dc2100000000 + .quad 0x3ff6d67980000000 + .quad 0x3ff6d0d4c0000000 + .quad 0x3ff6cb32c0000000 + .quad 0x3ff6c593c0000000 + .quad 0x3ff6bff780000000 + .quad 0x3ff6ba5dc0000000 + .quad 0x3ff6b4c700000000 + .quad 0x3ff6af32c0000000 + .quad 0x3ff6a9a180000000 + .quad 0x3ff6a41300000000 + .quad 0x3ff69e8700000000 + .quad 0x3ff698fdc0000000 + .quad 0x3ff6937740000000 + .quad 0x3ff68df380000000 + .quad 0x3ff6887280000000 + .quad 0x3ff682f400000000 + .quad 0x3ff67d7840000000 + .quad 0x3ff677ff40000000 + .quad 0x3ff67288c0000000 + .quad 0x3ff66d1540000000 + .quad 0x3ff667a400000000 + .quad 0x3ff6623580000000 + .quad 0x3ff65cc9c0000000 + .quad 0x3ff6576080000000 + .quad 0x3ff651fa00000000 + .quad 0x3ff64c9600000000 + .quad 0x3ff6473480000000 + .quad 0x3ff641d5c0000000 + .quad 0x3ff63c7980000000 + .quad 0x3ff6372000000000 + .quad 0x3ff631c900000000 + .quad 0x3ff62c7480000000 + .quad 0x3ff6272280000000 + .quad 0x3ff621d340000000 + .quad 0x3ff61c8640000000 + .quad 0x3ff6173c00000000 + .quad 0x3ff611f440000000 + .quad 0x3ff60caf00000000 + .quad 0x3ff6076c40000000 + .quad 0x3ff6022c00000000 + .quad 0x3ff5fcee80000000 + .quad 0x3ff5f7b340000000 + .quad 0x3ff5f27a80000000 + .quad 0x3ff5ed4440000000 + .quad 0x3ff5e81040000000 + .quad 0x3ff5e2df00000000 + .quad 0x3ff5ddb040000000 + .quad 0x3ff5d883c0000000 + .quad 0x3ff5d359c0000000 + .quad 0x3ff5ce3240000000 + .quad 0x3ff5c90d40000000 + .quad 0x3ff5c3ea80000000 + .quad 0x3ff5beca40000000 + .quad 0x3ff5b9ac80000000 + .quad 0x3ff5b49100000000 + .quad 0x3ff5af7800000000 + .quad 0x3ff5aa6180000000 + .quad 0x3ff5a54d40000000 + .quad 0x3ff5a03b40000000 + .quad 0x3ff59b2bc0000000 + .quad 0x3ff5961ec0000000 + .quad 0x3ff59113c0000000 + .quad 0x3ff58c0b80000000 + .quad 0x3ff5870540000000 + .quad 0x3ff58201c0000000 + .quad 0x3ff57d0040000000 + .quad 0x3ff5780140000000 + .quad 0x3ff5730480000000 + .quad 0x3ff56e0a00000000 + .quad 0x3ff56911c0000000 + .quad 0x3ff5641c00000000 + .quad 0x3ff55f2880000000 + .quad 0x3ff55a3740000000 + .quad 0x3ff5554840000000 + .quad 0x3ff5505bc0000000 + .quad 0x3ff54b7140000000 + .quad 0x3ff5468900000000 + .quad 0x3ff541a340000000 + .quad 0x3ff53cbf80000000 + .quad 0x3ff537de40000000 + .quad 0x3ff532ff00000000 + .quad 0x3ff52e2240000000 + .quad 0x3ff5294780000000 + .quad 0x3ff5246f00000000 + .quad 0x3ff51f98c0000000 + .quad 0x3ff51ac4c0000000 + .quad 0x3ff515f300000000 + .quad 0x3ff5112340000000 + .quad 0x3ff50c5600000000 + .quad 0x3ff5078ac0000000 + .quad 0x3ff502c1c0000000 + .quad 0x3ff4fdfac0000000 + .quad 0x3ff4f93600000000 + .quad 0x3ff4f47380000000 + .quad 0x3ff4efb340000000 + .quad 0x3ff4eaf500000000 + .quad 0x3ff4e638c0000000 + .quad 0x3ff4e17ec0000000 + .quad 0x3ff4dcc700000000 + .quad 0x3ff4d81180000000 + .quad 0x3ff4d35dc0000000 + .quad 0x3ff4ceac80000000 + .quad 0x3ff4c9fd00000000 + .quad 0x3ff4c54fc0000000 + .quad 0x3ff4c0a4c0000000 + .quad 0x3ff4bbfbc0000000 + .quad 0x3ff4b754c0000000 + .quad 0x3ff4b2b000000000 + .quad 0x3ff4ae0d40000000 + .quad 0x3ff4a96c80000000 + .quad 0x3ff4a4ce00000000 + .quad 0x3ff4a03140000000 + .quad 0x3ff49b9700000000 + .quad 0x3ff496fe80000000 + .quad 0x3ff4926800000000 + .quad 0x3ff48dd3c0000000 + .quad 0x3ff4894180000000 + .quad 0x3ff484b100000000 + .quad 0x3ff48022c0000000 + .quad 0x3ff47b96c0000000 + .quad 0x3ff4770c80000000 + .quad 0x3ff4728440000000 + .quad 0x3ff46dfe00000000 + .quad 0x3ff46979c0000000 + .quad 0x3ff464f780000000 + .quad 0x3ff4607780000000 + .quad 0x3ff45bf940000000 + .quad 0x3ff4577d00000000 + .quad 0x3ff45302c0000000 + .quad 0x3ff44e8a40000000 + .quad 0x3ff44a1400000000 + .quad 0x3ff4459f80000000 + .quad 0x3ff4412d40000000 + .quad 0x3ff43cbcc0000000 + .quad 0x3ff4384e40000000 + .quad 0x3ff433e180000000 + .quad 0x3ff42f7700000000 + .quad 0x3ff42b0e40000000 + .quad 0x3ff426a780000000 + .quad 0x3ff4224280000000 + .quad 0x3ff41ddf80000000 + .quad 0x3ff4197e80000000 + .quad 0x3ff4151f40000000 + .quad 0x3ff410c200000000 + .quad 0x3ff40c66c0000000 + .quad 0x3ff4080d40000000 + .quad 0x3ff403b5c0000000 + .quad 0x3ff3ff6000000000 + .quad 0x3ff3fb0c00000000 + .quad 0x3ff3f6ba40000000 + .quad 0x3ff3f26a00000000 + .quad 0x3ff3ee1bc0000000 + .quad 0x3ff3e9cf80000000 + .quad 0x3ff3e58500000000 + .quad 0x3ff3e13c40000000 + .quad 0x3ff3dcf580000000 + .quad 0x3ff3d8b080000000 + .quad 0x3ff3d46d40000000 + .quad 0x3ff3d02c00000000 + .quad 0x3ff3cbec80000000 + .quad 0x3ff3c7aec0000000 + .quad 0x3ff3c37300000000 + .quad 0x3ff3bf3900000000 + .quad 0x3ff3bb00c0000000 + .quad 0x3ff3b6ca40000000 + .quad 0x3ff3b29580000000 + .quad 0x3ff3ae62c0000000 + .quad 0x3ff3aa3180000000 + .quad 0x3ff3a60240000000 + .quad 0x3ff3a1d4c0000000 + .quad 0x3ff39da900000000 + .quad 0x3ff3997f40000000 + .quad 0x3ff3955700000000 + .quad 0x3ff3913080000000 + .quad 0x3ff38d0bc0000000 + .quad 0x3ff388e900000000 + .quad 0x3ff384c7c0000000 + .quad 0x3ff380a840000000 + .quad 0x3ff37c8ac0000000 + .quad 0x3ff3786ec0000000 + .quad 0x3ff3745480000000 + .quad 0x3ff3703c00000000 + .quad 0x3ff36c2540000000 + .quad 0x3ff3681040000000 + .quad 0x3ff363fcc0000000 + .quad 0x3ff35feb40000000 + .quad 0x3ff35bdb40000000 + .quad 0x3ff357cd00000000 + .quad 0x3ff353c080000000 + .quad 0x3ff34fb5c0000000 + .quad 0x3ff34bac80000000 + .quad 0x3ff347a540000000 + .quad 0x3ff3439f80000000 + .quad 0x3ff33f9b40000000 + .quad 0x3ff33b9900000000 + .quad 0x3ff3379840000000 + .quad 0x3ff3339900000000 + .quad 0x3ff32f9bc0000000 + .quad 0x3ff32b9fc0000000 + .quad 0x3ff327a5c0000000 + .quad 0x3ff323ad40000000 + .quad 0x3ff31fb680000000 + .quad 0x3ff31bc140000000 + .quad 0x3ff317cdc0000000 + .quad 0x3ff313dbc0000000 + .quad 0x3ff30feb80000000 + .quad 0x3ff30bfd00000000 + .quad 0x3ff3080fc0000000 + .quad 0x3ff3042480000000 + .quad 0x3ff3003ac0000000 + .quad 0x3ff2fc5280000000 + .quad 0x3ff2f86bc0000000 + .quad 0x3ff2f48700000000 + .quad 0x3ff2f0a380000000 + .quad 0x3ff2ecc1c0000000 + .quad 0x3ff2e8e180000000 + .quad 0x3ff2e502c0000000 + .quad 0x3ff2e125c0000000 + .quad 0x3ff2dd4a40000000 + .quad 0x3ff2d97080000000 + .quad 0x3ff2d59840000000 + .quad 0x3ff2d1c180000000 + .quad 0x3ff2cdec40000000 + .quad 0x3ff2ca1880000000 + .quad 0x3ff2c64680000000 + .quad 0x3ff2c27600000000 + .quad 0x3ff2bea700000000 + .quad 0x3ff2bad9c0000000 + .quad 0x3ff2b70dc0000000 + .quad 0x3ff2b34380000000 + .quad 0x3ff2af7ac0000000 + .quad 0x3ff2abb340000000 + .quad 0x3ff2a7ed80000000 + .quad 0x3ff2a42980000000 + .quad 0x3ff2a066c0000000 + .quad 0x3ff29ca580000000 + .quad 0x3ff298e5c0000000 + .quad 0x3ff29527c0000000 + .quad 0x3ff2916b00000000 + .quad 0x3ff28dafc0000000 + .quad 0x3ff289f640000000 + .quad 0x3ff2863e00000000 + .quad 0x3ff2828740000000 + .quad 0x3ff27ed240000000 + .quad 0x3ff27b1e80000000 + .quad 0x3ff2776c40000000 + .quad 0x3ff273bb80000000 + .quad 0x3ff2700c40000000 + .quad 0x3ff26c5e80000000 + .quad 0x3ff268b200000000 + .quad 0x3ff2650740000000 + .quad 0x3ff2615dc0000000 + .quad 0x3ff25db5c0000000 + .quad 0x3ff25a0f40000000 + .quad 0x3ff2566a40000000 + .quad 0x3ff252c6c0000000 + .quad 0x3ff24f2480000000 + .quad 0x3ff24b83c0000000 + .quad 0x3ff247e480000000 + .quad 0x3ff24446c0000000 + .quad 0x3ff240aa40000000 + .quad 0x3ff23d0f40000000 + .quad 0x3ff23975c0000000 + .quad 0x3ff235dd80000000 + .quad 0x3ff23246c0000000 + .quad 0x3ff22eb180000000 + .quad 0x3ff22b1d80000000 + .quad 0x3ff2278b00000000 + .quad 0x3ff223fa00000000 + .quad 0x3ff2206a40000000 + .quad 0x3ff21cdc00000000 + .quad 0x3ff2194f00000000 + .quad 0x3ff215c380000000 + .quad 0x3ff2123940000000 + .quad 0x3ff20eb080000000 + .quad 0x3ff20b2940000000 + .quad 0x3ff207a340000000 + .quad 0x3ff2041ec0000000 + .quad 0x3ff2009b80000000 + .quad 0x3ff1fd1980000000 + .quad 0x3ff1f99900000000 + .quad 0x3ff1f619c0000000 + .quad 0x3ff1f29c00000000 + .quad 0x3ff1ef1fc0000000 + .quad 0x3ff1eba480000000 + .quad 0x3ff1e82ac0000000 + .quad 0x3ff1e4b280000000 + .quad 0x3ff1e13b80000000 + .quad 0x3ff1ddc5c0000000 + .quad 0x3ff1da5180000000 + .quad 0x3ff1d6de80000000 + .quad 0x3ff1d36cc0000000 + .quad 0x3ff1cffc40000000 + .quad 0x3ff1cc8d40000000 + .quad 0x3ff1c91f80000000 + .quad 0x3ff1c5b340000000 + .quad 0x3ff1c24840000000 + .quad 0x3ff1bede40000000 + .quad 0x3ff1bb7600000000 + .quad 0x3ff1b80ec0000000 + .quad 0x3ff1b4a900000000 + .quad 0x3ff1b14480000000 + .quad 0x3ff1ade140000000 + .quad 0x3ff1aa7f40000000 + .quad 0x3ff1a71e80000000 + .quad 0x3ff1a3bf40000000 + .quad 0x3ff1a06140000000 + .quad 0x3ff19d0480000000 + .quad 0x3ff199a900000000 + .quad 0x3ff1964ec0000000 + .quad 0x3ff192f5c0000000 + .quad 0x3ff18f9e00000000 + .quad 0x3ff18c47c0000000 + .quad 0x3ff188f280000000 + .quad 0x3ff1859ec0000000 + .quad 0x3ff1824c00000000 + .quad 0x3ff17efac0000000 + .quad 0x3ff17baa80000000 + .quad 0x3ff1785bc0000000 + .quad 0x3ff1750e40000000 + .quad 0x3ff171c1c0000000 + .quad 0x3ff16e76c0000000 + .quad 0x3ff16b2d00000000 + .quad 0x3ff167e440000000 + .quad 0x3ff1649d00000000 + .quad 0x3ff16156c0000000 + .quad 0x3ff15e11c0000000 + .quad 0x3ff15ace40000000 + .quad 0x3ff1578bc0000000 + .quad 0x3ff1544a80000000 + .quad 0x3ff1510a80000000 + .quad 0x3ff14dcbc0000000 + .quad 0x3ff14a8e40000000 + .quad 0x3ff14751c0000000 + .quad 0x3ff14416c0000000 + .quad 0x3ff140dcc0000000 + .quad 0x3ff13da400000000 + .quad 0x3ff13a6c80000000 + .quad 0x3ff1373600000000 + .quad 0x3ff1340100000000 + .quad 0x3ff130cd00000000 + .quad 0x3ff12d9a40000000 + .quad 0x3ff12a68c0000000 + .quad 0x3ff1273840000000 + .quad 0x3ff1240900000000 + .quad 0x3ff120db00000000 + .quad 0x3ff11dae40000000 + .quad 0x3ff11a8280000000 + .quad 0x3ff1175800000000 + .quad 0x3ff1142ec0000000 + .quad 0x3ff11106c0000000 + .quad 0x3ff10ddfc0000000 + .quad 0x3ff10ab9c0000000 + .quad 0x3ff1079540000000 + .quad 0x3ff10471c0000000 + .quad 0x3ff1014f80000000 + .quad 0x3ff0fe2e40000000 + .quad 0x3ff0fb0e40000000 + .quad 0x3ff0f7ef40000000 + .quad 0x3ff0f4d180000000 + .quad 0x3ff0f1b500000000 + .quad 0x3ff0ee9980000000 + .quad 0x3ff0eb7f40000000 + .quad 0x3ff0e86600000000 + .quad 0x3ff0e54e00000000 + .quad 0x3ff0e23700000000 + .quad 0x3ff0df2140000000 + .quad 0x3ff0dc0c80000000 + .quad 0x3ff0d8f900000000 + .quad 0x3ff0d5e6c0000000 + .quad 0x3ff0d2d540000000 + .quad 0x3ff0cfc540000000 + .quad 0x3ff0ccb640000000 + .quad 0x3ff0c9a840000000 + .quad 0x3ff0c69b40000000 + .quad 0x3ff0c38f80000000 + .quad 0x3ff0c08500000000 + .quad 0x3ff0bd7b80000000 + .quad 0x3ff0ba7300000000 + .quad 0x3ff0b76bc0000000 + .quad 0x3ff0b46580000000 + .quad 0x3ff0b16040000000 + .quad 0x3ff0ae5c40000000 + .quad 0x3ff0ab5940000000 + .quad 0x3ff0a85780000000 + .quad 0x3ff0a556c0000000 + .quad 0x3ff0a25700000000 + .quad 0x3ff09f5880000000 + .quad 0x3ff09c5ac0000000 + .quad 0x3ff0995e80000000 + .quad 0x3ff0966300000000 + .quad 0x3ff09368c0000000 + .quad 0x3ff0906f80000000 + .quad 0x3ff08d7740000000 + .quad 0x3ff08a8000000000 + .quad 0x3ff0878a00000000 + .quad 0x3ff0849500000000 + .quad 0x3ff081a100000000 + .quad 0x3ff07eae40000000 + .quad 0x3ff07bbc40000000 + .quad 0x3ff078cb80000000 + .quad 0x3ff075dbc0000000 + .quad 0x3ff072ed00000000 + .quad 0x3ff06fff80000000 + .quad 0x3ff06d12c0000000 + .quad 0x3ff06a2740000000 + .quad 0x3ff0673cc0000000 + .quad 0x3ff0645340000000 + .quad 0x3ff0616ac0000000 + .quad 0x3ff05e8340000000 + .quad 0x3ff05b9d00000000 + .quad 0x3ff058b780000000 + .quad 0x3ff055d340000000 + .quad 0x3ff052f000000000 + .quad 0x3ff0500d80000000 + .quad 0x3ff04d2c40000000 + .quad 0x3ff04a4c00000000 + .quad 0x3ff0476cc0000000 + .quad 0x3ff0448e80000000 + .quad 0x3ff041b140000000 + .quad 0x3ff03ed500000000 + .quad 0x3ff03bf9c0000000 + .quad 0x3ff0391fc0000000 + .quad 0x3ff0364680000000 + .quad 0x3ff0336e40000000 + .quad 0x3ff0309700000000 + .quad 0x3ff02dc0c0000000 + .quad 0x3ff02aeb80000000 + .quad 0x3ff0281740000000 + .quad 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0x3fee03f000000000 + .quad 0x3fedff1000000000 + .quad 0x3fedfa3140000000 + .quad 0x3fedf55440000000 + .quad 0x3fedf07900000000 + .quad 0x3fedeb9f00000000 + .quad 0x3fede6c6c0000000 + .quad 0x3fede1f040000000 + .quad 0x3feddd1b00000000 + .quad 0x3fedd84780000000 + .quad 0x3fedd37580000000 + .quad 0x3fedcea500000000 + .quad 0x3fedc9d600000000 + .quad 0x3fedc508c0000000 + .quad 0x3fedc03d00000000 + .quad 0x3fedbb72c0000000 + .quad 0x3fedb6aa00000000 + .quad 0x3fedb1e2c0000000 + .quad 0x3fedad1d00000000 + .quad 0x3feda85900000000 + .quad 0x3feda39680000000 + .quad 0x3fed9ed540000000 + .quad 0x3fed9a15c0000000 + .quad 0x3fed9557c0000000 + .quad 0x3fed909b40000000 + .quad 0x3fed8be040000000 + .quad 0x3fed8726c0000000 + .quad 0x3fed826f00000000 + .quad 0x3fed7db880000000 + .quad 0x3fed790380000000 + .quad 0x3fed745000000000 + .quad 0x3fed6f9e40000000 + .quad 0x3fed6aedc0000000 + .quad 0x3fed663ec0000000 + .quad 0x3fed619140000000 + .quad 0x3fed5ce540000000 + .quad 0x3fed583ac0000000 + .quad 0x3fed5391c0000000 + .quad 0x3fed4eea40000000 + .quad 0x3fed4a4440000000 + .quad 0x3fed459f80000000 + .quad 0x3fed40fc80000000 + .quad 0x3fed3c5ac0000000 + .quad 0x3fed37bac0000000 + .quad 0x3fed331c00000000 + .quad 0x3fed2e7ec0000000 + .quad 0x3fed29e300000000 + .quad 0x3fed254880000000 + .quad 0x3fed20afc0000000 + .quad 0x3fed1c1840000000 + .quad 0x3fed178240000000 + .quad 0x3fed12edc0000000 + .quad 0x3fed0e5ac0000000 + .quad 0x3fed09c900000000 + .quad 0x3fed0538c0000000 + .quad 0x3fed00aa00000000 + .quad 0x3fecfc1c80000000 + .quad 0x3fecf790c0000000 + .quad 0x3fecf30600000000 + .quad 0x3fecee7d00000000 + .quad 0x3fece9f540000000 + .quad 0x3fece56f00000000 + .quad 0x3fece0ea40000000 + .quad 0x3fecdc66c0000000 + .quad 0x3fecd7e4c0000000 + .quad 0x3fecd36440000000 + .quad 0x3feccee500000000 + .quad 0x3fecca6740000000 + .quad 0x3fecc5eac0000000 + .quad 0x3fecc16fc0000000 + .quad 0x3fecbcf640000000 + .quad 0x3fecb87e00000000 + .quad 0x3fecb40740000000 + .quad 0x3fecaf91c0000000 + .quad 0x3fecab1dc0000000 + .quad 0x3feca6ab00000000 + .quad 0x3feca239c0000000 + .quad 0x3fec9dc9c0000000 + .quad 0x3fec995b40000000 + .quad 0x3fec94ee00000000 + .quad 0x3fec908240000000 + .quad 0x3fec8c17c0000000 + .quad 0x3fec87aec0000000 + .quad 0x3fec834700000000 + .quad 0x3fec7ee0c0000000 + .quad 0x3fec7a7bc0000000 + .quad 0x3fec761800000000 + .quad 0x3fec71b5c0000000 + .quad 0x3fec6d54c0000000 + .quad 0x3fec68f540000000 + .quad 0x3fec649700000000 + .quad 0x3fec603a00000000 + .quad 0x3fec5bde80000000 + .quad 0x3fec578440000000 + .quad 0x3fec532b80000000 + .quad 0x3fec4ed3c0000000 + .quad 0x3fec4a7dc0000000 + .quad 0x3fec4628c0000000 + .quad 0x3fec41d540000000 + .quad 0x3fec3d8300000000 + .quad 0x3fec393200000000 + .quad 0x3fec34e240000000 + .quad 0x3fec309400000000 + .quad 0x3fec2c4700000000 + .quad 0x3fec27fb80000000 + .quad 0x3fec23b100000000 + .quad 0x3fec1f6800000000 + .quad 0x3fec1b2040000000 + .quad 0x3fec16d9c0000000 + .quad 0x3fec1294c0000000 + .quad 0x3fec0e50c0000000 + .quad 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0x3feb6fe9c0000000 + .quad 0x3feb6bd6c0000000 + .quad 0x3feb67c500000000 + .quad 0x3feb63b440000000 + .quad 0x3feb5fa500000000 + .quad 0x3feb5b96c0000000 + .quad 0x3feb5789c0000000 + .quad 0x3feb537e00000000 + .quad 0x3feb4f7380000000 + .quad 0x3feb4b6a00000000 + .quad 0x3feb476200000000 + .quad 0x3feb435b00000000 + .quad 0x3feb3f5540000000 + .quad 0x3feb3b5080000000 + .quad 0x3feb374d00000000 + .quad 0x3feb334ac0000000 + .quad 0x3feb2f49c0000000 + .quad 0x3feb2b49c0000000 + .quad 0x3feb274b40000000 + .quad 0x3feb234d80000000 + .quad 0x3feb1f5140000000 + .quad 0x3feb1b5600000000 + .quad 0x3feb175c00000000 + .quad 0x3feb136300000000 + .quad 0x3feb0f6b80000000 + .quad 0x3feb0b74c0000000 + .quad 0x3feb077f80000000 + .quad 0x3feb038b40000000 + .quad 0x3feaff9840000000 + .quad 0x3feafba640000000 + .quad 0x3feaf7b580000000 + .quad 0x3feaf3c600000000 + .quad 0x3feaefd780000000 + .quad 0x3feaebea40000000 + .quad 0x3feae7fe00000000 + .quad 0x3feae41300000000 + .quad 0x3feae02900000000 + .quad 0x3feadc4040000000 + .quad 0x3fead858c0000000 + .quad 0x3fead47240000000 + .quad 0x3fead08cc0000000 + .quad 0x3feacca8c0000000 + .quad 0x3feac8c580000000 + .quad 0x3feac4e380000000 + .quad 0x3feac102c0000000 + .quad 0x3feabd2300000000 + .quad 0x3feab94480000000 + .quad 0x3feab56700000000 + .quad 0x3feab18a80000000 + .quad 0x3feaadaf80000000 + .quad 0x3feaa9d540000000 + .quad 0x3feaa5fc40000000 + .quad 0x3feaa22440000000 + .quad 0x3fea9e4d80000000 + .quad 0x3fea9a77c0000000 + .quad 0x3fea96a340000000 + .quad 0x3fea92cfc0000000 + .quad 0x3fea8efd80000000 + .quad 0x3fea8b2c40000000 + .quad 0x3fea875c00000000 + .quad 0x3fea838cc0000000 + .quad 0x3fea7fbec0000000 + .quad 0x3fea7bf200000000 + .quad 0x3fea782640000000 + .quad 0x3fea745b80000000 + .quad 0x3fea7091c0000000 + .quad 0x3fea6cc940000000 + .quad 0x3fea6901c0000000 + .quad 0x3fea653b40000000 + .quad 0x3fea617600000000 + .quad 0x3fea5db1c0000000 + .quad 0x3fea59ee80000000 + .quad 0x3fea562c80000000 + .quad 0x3fea526b80000000 + .quad 0x3fea4eab80000000 + .quad 0x3fea4aecc0000000 + .quad 0x3fea472ec0000000 + .quad 0x3fea437200000000 + .quad 0x3fea3fb640000000 + .quad 0x3fea3bfbc0000000 + .quad 0x3fea384240000000 + .quad 0x3fea3489c0000000 + .quad 0x3fea30d240000000 + .quad 0x3fea2d1bc0000000 + .quad 0x3fea296680000000 + .quad 0x3fea25b200000000 + .quad 0x3fea21fec0000000 + .quad 0x3fea1e4cc0000000 + .quad 0x3fea1a9b80000000 + .quad 0x3fea16eb40000000 + .quad 0x3fea133c40000000 + .quad 0x3fea0f8e40000000 + .quad 0x3fea0be140000000 + .quad 0x3fea083540000000 + .quad 0x3fea048a40000000 + .quad 0x3fea00e080000000 + .quad 0x3fe9fd3780000000 + .quad 0x3fe9f98fc0000000 + .quad 0x3fe9f5e900000000 + .quad 0x3fe9f24340000000 + .quad 0x3fe9ee9e80000000 + .quad 0x3fe9eafac0000000 + .quad 0x3fe9e75800000000 + .quad 0x3fe9e3b640000000 + .quad 0x3fe9e01580000000 + .quad 0x3fe9dc7600000000 + .quad 0x3fe9d8d740000000 + .quad 0x3fe9d539c0000000 + .quad 0x3fe9d19d00000000 + .quad 0x3fe9ce0180000000 + .quad 0x3fe9ca66c0000000 + .quad 0x3fe9c6cd40000000 + .quad 0x3fe9c33480000000 + .quad 0x3fe9bf9d00000000 + .quad 0x3fe9bc0680000000 + .quad 0x3fe9b870c0000000 + .quad 0x3fe9b4dc40000000 + .quad 0x3fe9b148c0000000 + .quad 0x3fe9adb600000000 + .quad 0x3fe9aa2480000000 + .quad 0x3fe9a693c0000000 + .quad 0x3fe9a30440000000 + .quad 0x3fe99f7580000000 + .quad 0x3fe99be7c0000000 + .quad 0x3fe9985b40000000 + .quad 0x3fe994cf80000000 + .quad 0x3fe99144c0000000 + .quad 0x3fe98dbb00000000 + .quad 0x3fe98a3240000000 + .quad 0x3fe986aa80000000 + .quad 0x3fe98323c0000000 + .quad 0x3fe97f9e00000000 + .quad 0x3fe97c1900000000 + .quad 0x3fe9789540000000 + .quad 0x3fe9751240000000 + .quad 0x3fe9719080000000 + .quad 0x3fe96e0f80000000 + .quad 0x3fe96a8f80000000 + .quad 0x3fe9671040000000 + .quad 0x3fe9639240000000 + .quad 0x3fe9601540000000 + .quad 0x3fe95c9900000000 + .quad 0x3fe9591dc0000000 + .quad 0x3fe955a380000000 + .quad 0x3fe9522a40000000 + .quad 0x3fe94eb200000000 + .quad 0x3fe94b3a80000000 + .quad 0x3fe947c400000000 + .quad 0x3fe9444e80000000 + .quad 0x3fe940da00000000 + .quad 0x3fe93d6640000000 + .quad 0x3fe939f3c0000000 + .quad 0x3fe9368200000000 + .quad 0x3fe9331140000000 + .quad 0x3fe92fa140000000 + .quad 0x3fe92c3280000000 + .quad 0x3fe928c480000000 + .quad 0x3fe9255780000000 + .quad 0x3fe921eb40000000 + .quad 0x3fe91e8040000000 + .quad 0x3fe91b1600000000 + .quad 0x3fe917ac80000000 + .quad 0x3fe9144440000000 + .quad 0x3fe910dcc0000000 + .quad 0x3fe90d7640000000 + .quad 0x3fe90a1080000000 + .quad 0x3fe906abc0000000 + .quad 0x3fe9034800000000 + .quad 0x3fe8ffe540000000 + .quad 0x3fe8fc8340000000 + .quad 0x3fe8f92240000000 + .quad 0x3fe8f5c200000000 + .quad 0x3fe8f26300000000 + .quad 0x3fe8ef0480000000 + .quad 0x3fe8eba740000000 + .quad 0x3fe8e84ac0000000 + .quad 0x3fe8e4ef40000000 + .quad 0x3fe8e19480000000 + .quad 0x3fe8de3ac0000000 + .quad 0x3fe8dae1c0000000 + .quad 0x3fe8d78a00000000 + .quad 0x3fe8d432c0000000 + .quad 0x3fe8d0dcc0000000 + .quad 0x3fe8cd8780000000 + .quad 0x3fe8ca3300000000 + .quad 0x3fe8c6df80000000 + .quad 0x3fe8c38d00000000 + .quad 0x3fe8c03b40000000 + .quad 0x3fe8bcea80000000 + .quad 0x3fe8b99a80000000 + .quad 0x3fe8b64b80000000 + .quad 0x3fe8b2fd40000000 + .quad 0x3fe8afb000000000 + .quad 0x3fe8ac63c0000000 + .quad 0x3fe8a91840000000 + .quad 0x3fe8a5cd80000000 + .quad 0x3fe8a283c0000000 + .quad 0x3fe89f3b00000000 + .quad 0x3fe89bf300000000 + .quad 0x3fe898abc0000000 + .quad 0x3fe8956580000000 + .quad 0x3fe8922040000000 + .quad 0x3fe88edbc0000000 + .quad 0x3fe88b9800000000 + .quad 0x3fe8885540000000 + .quad 0x3fe8851380000000 + .quad 0x3fe881d240000000 + .quad 0x3fe87e9240000000 + .quad 0x3fe87b52c0000000 + .quad 0x3fe8781480000000 + .quad 0x3fe874d6c0000000 + .quad 0x3fe8719a00000000 + .quad 0x3fe86e5e40000000 + .quad 0x3fe86b2340000000 + .quad 0x3fe867e900000000 + .quad 0x3fe864afc0000000 + .quad 0x3fe8617740000000 + .quad 0x3fe85e3f80000000 + .quad 0x3fe85b08c0000000 + .quad 0x3fe857d300000000 + .quad 0x3fe8549dc0000000 + .quad 0x3fe8516980000000 + .quad 0x3fe84e3640000000 + .quad 0x3fe84b03c0000000 + .quad 0x3fe847d200000000 + .quad 0x3fe844a100000000 + .quad 0x3fe8417100000000 + .quad 0x3fe83e4200000000 + .quad 0x3fe83b1380000000 + .quad 0x3fe837e600000000 + .quad 0x3fe834b940000000 + .quad 0x3fe8318d80000000 + .quad 0x3fe82e6280000000 + .quad 0x3fe82b3840000000 + .quad 0x3fe8280f00000000 + .quad 0x3fe824e640000000 + .quad 0x3fe821bec0000000 + .quad 0x3fe81e97c0000000 + .quad 0x3fe81b71c0000000 + .quad 0x3fe8184c80000000 + .quad 0x3fe8152800000000 + .quad 0x3fe8120480000000 + .quad 0x3fe80ee1c0000000 + .quad 0x3fe80bbfc0000000 + .quad 0x3fe8089e80000000 + .quad 0x3fe8057e40000000 + .quad 0x3fe8025ec0000000 + .quad 0x3fe7ff4000000000 + .quad 0x3fe7fc2200000000 + .quad 0x3fe7f90500000000 + .quad 0x3fe7f5e8c0000000 + .quad 0x3fe7f2cd40000000 + .quad 0x3fe7efb280000000 + .quad 0x3fe7ec9880000000 + .quad 0x3fe7e97f80000000 + .quad 0x3fe7e66740000000 + .quad 0x3fe7e34fc0000000 + .quad 0x3fe7e03940000000 + .quad 0x3fe7dd2340000000 + .quad 0x3fe7da0e40000000 + .quad 0x3fe7d6fa00000000 + .quad 0x3fe7d3e680000000 + .quad 0x3fe7d0d3c0000000 + .quad 0x3fe7cdc1c0000000 + .quad 0x3fe7cab0c0000000 + .quad 0x3fe7c7a080000000 + .quad 0x3fe7c49100000000 + .quad 0x3fe7c18240000000 + .quad 0x3fe7be7440000000 + .quad 0x3fe7bb6700000000 + .quad 0x3fe7b85ac0000000 + .quad 0x3fe7b54f00000000 + .quad 0x3fe7b24440000000 + .quad 0x3fe7af3a40000000 + .quad 0x3fe7ac3100000000 + .quad 0x3fe7a92880000000 + .quad 0x3fe7a620c0000000 + .quad 0x3fe7a319c0000000 + .quad 0x3fe7a013c0000000 + .quad 0x3fe79d0e40000000 + .quad 0x3fe79a09c0000000 + .quad 0x3fe7970600000000 + .quad 0x3fe79402c0000000 + .quad 0x3fe7910080000000 + .quad 0x3fe78dff00000000 + .quad 0x3fe78afe40000000 + .quad 0x3fe787fe40000000 + .quad 0x3fe784ff00000000 + .quad 0x3fe7820080000000 + .quad 0x3fe77f02c0000000 + .quad 0x3fe77c05c0000000 + .quad 0x3fe77909c0000000 + .quad 0x3fe7760e40000000 + .quad 0x3fe7731380000000 + .quad 0x3fe77019c0000000 + .quad 0x3fe76d2080000000 + .quad 0x3fe76a2800000000 + .quad 0x3fe7673080000000 + .quad 0x3fe7643980000000 + .quad 0x3fe7614340000000 + .quad 0x3fe75e4e00000000 + .quad 0x3fe75b5940000000 + .quad 0x3fe7586580000000 + .quad 0x3fe7557240000000 + .quad 0x3fe7527fc0000000 + .quad 0x3fe74f8e40000000 + .quad 0x3fe74c9d40000000 + .quad 0x3fe749ad00000000 + .quad 0x3fe746bd80000000 + .quad 0x3fe743cec0000000 + .quad 0x3fe740e100000000 + .quad 0x3fe73df3c0000000 + .quad 0x3fe73b0740000000 + .quad 0x3fe7381b80000000 + .quad 0x3fe7353080000000 + .quad 0x3fe7324600000000 + .quad 0x3fe72f5c80000000 + .quad 0x3fe72c73c0000000 + .quad 0x3fe7298b80000000 + .quad 0x3fe726a440000000 + .quad 0x3fe723bd80000000 + .quad 0x3fe720d7c0000000 + .quad 0x3fe71df280000000 + .quad 0x3fe71b0e00000000 + .quad 0x3fe7182a40000000 + .quad 0x3fe7154740000000 + .quad 0x0000000000000000 + .rept 48 + .byte 0 + .endr + +/* Log(2) lookup table for log part (non HSW): */ +.if .-__svml_dpow_data != _log2_t1 +.err +.endif + .rept 2 + .quad 0x0000000000000000 + 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0xbe7414ec0c60bad1 + .quad 0xbfc3e0ae00000000 + .quad 0xbe74e9ba984a9a60 + .quad 0xbfc3c6fc00000000 + .quad 0xbe624337ccc1362d + .quad 0xbfc3ad4b00000000 + .quad 0xbe7774b4cc0ec2a8 + .quad 0xbfc393a000000000 + .quad 0xbe732b380b7efc7c + .quad 0xbfc379f700000000 + .quad 0xbe62dac931c2e190 + .quad 0xbfc3605300000000 + .quad 0xbe6b470fa43dc529 + .quad 0xbfc346b100000000 + .quad 0xbe69abf6162bfc32 + .quad 0xbfc32d1300000000 + .quad 0xbe2ba4b334a02879 + .quad 0xbfc3137a00000000 + .quad 0xbe4d8be297e30d03 + .quad 0xbfc2f9e300000000 + .quad 0xbe415bfda1644c22 + .quad 0xbfc2e04f00000000 + .quad 0xbe763bbe948b1ac0 + .quad 0xbfc2c6c000000000 + .quad 0xbe016a3f42b0e0f2 + .quad 0xbfc2ad3400000000 + .quad 0xbe00b500d8b4466e + .quad 0xbfc293ab00000000 + .quad 0xbe767834aad3c38f + .quad 0xbfc27a2700000000 + .quad 0xbe4b3fb7ded60421 + .quad 0xbfc260a600000000 + .quad 0xbe5cc6018f3bcd49 + .quad 0xbfc2472700000000 + .quad 0xbe603b59bc184860 + .quad 0xbfc22dad00000000 + .quad 0xbe7a556695fca0d7 + .quad 0xbfc2143600000000 + .quad 0xbe64434576d52cb7 + .quad 0xbfc1fac400000000 + .quad 0xbe6796ca377ea74e + .quad 0xbfc1e15400000000 + .quad 0xbe66f7798c85559d + .quad 0xbfc1c7e800000000 + .quad 0xbe4bde34965f6984 + .quad 0xbfc1ae7d00000000 + .quad 0xbe79e4ab7003a0e6 + .quad 0xbfc1951900000000 + .quad 0xbe49fd11e39abaac + .quad 0xbfc17bb800000000 + .quad 0xbe56b7b48b95c15b + .quad 0xbfc1625900000000 + .quad 0xbe5cc36d3e3cca65 + .quad 0xbfc148fe00000000 + .quad 0xbe41ce485761f69c + .quad 0xbfc12fa600000000 + .quad 0xbe770a1f05316811 + .quad 0xbfc1165300000000 + .quad 0xbe578d49dc1afe94 + .quad 0xbfc0fd0300000000 + .quad 0xbe6e0dca31cd9e54 + .quad 0xbfc0e3b500000000 + .quad 0xbe784e650e0a2fd5 + .quad 0xbfc0ca6b00000000 + .quad 0xbe7c536d57d9dab9 + .quad 0xbfc0b12500000000 + .quad 0xbe7b57a5578d01fd + .quad 0xbfc097e300000000 + .quad 0xbe759cc0cf3da52a + .quad 0xbfc07ea300000000 + .quad 0xbe70dc7f7c36aab7 + .quad 0xbfc0656900000000 + .quad 0xbe43057726eea6f9 + .quad 0xbfc04c3000000000 + .quad 0xbe75532713b0b555 + .quad 0xbfc032fc00000000 + .quad 0xbe51f736f8234297 + .quad 0xbfc019c900000000 + .quad 0xbe757a9427127e28 + .quad 0xbfc0009c00000000 + .quad 0xbe7dd37909d634e1 + .quad 0xbfbfcee400000000 + .quad 0xbe60e50b92227f37 + .quad 0xbfbf9c9700000000 + .quad 0xbe10744b2bbd5c34 + .quad 0xbfbf6a4d00000000 + .quad 0xbe6576fb1ab66ad7 + .quad 0xbfbf380f00000000 + .quad 0xbe6b5374d31a91ee + .quad 0xbfbf05d600000000 + .quad 0xbe4db610eee1b81b + .quad 0xbfbed3a000000000 + .quad 0xbe6a19b7978e8bb8 + .quad 0xbfbea17600000000 + .quad 0xbe6f4cb6bf56f18e + .quad 0xbfbe6f5100000000 + .quad 0xbe57f67e0bd3b63f + .quad 0xbfbe3d3300000000 + .quad 0xbe666a27d6a83d6c + .quad 0xbfbe0b1a00000000 + .quad 0xbe523cbf0c85fa27 + .quad 0xbfbdd90800000000 + .quad 0xbe6a7ced811f7da6 + .quad 0xbfbda6ff00000000 + .quad 0xbe5615e1bd550182 + .quad 0xbfbd74fd00000000 + .quad 0xbe6b4da043725d03 + .quad 0xbfbd430000000000 + .quad 0xbe658a49aa2dca64 + .quad 0xbfbd110b00000000 + .quad 0xbe6066543ad84ef1 + .quad 0xbfbcdf1a00000000 + .quad 0xbe66073d700e9f19 + .quad 0xbfbcad3500000000 + .quad 0xbe63a29cd758d759 + .quad 0xbfbc7b5100000000 + .quad 0xbe49b8777d6bbc9d + .quad 0xbfbc497800000000 + .quad 0xbe623f87f4487fe4 + .quad 0xbfbc17a400000000 + .quad 0xbe55196cb4c66620 + .quad 0xbfbbe5d800000000 + .quad 0xbe496e785a0317a3 + .quad 0xbfbbb41000000000 + .quad 0xbe5ee49501957b40 + .quad 0xbfbb825000000000 + .quad 0xbe6cf6df4849748b + .quad 0xbfbb509500000000 + .quad 0xbe688f964bd70c8f + .quad 0xbfbb1ee600000000 + .quad 0xbe6072c317519bb4 + .quad 0xbfbaed3800000000 + .quad 0xbe05b3290a662bd0 + .quad 0xbfbabb9500000000 + .quad 0xbe5b246ad0582c09 + .quad 0xbfba89f700000000 + .quad 0xbe55372721811f66 + .quad 0xbfba585d00000000 + .quad 0xbe67c995fe88bce3 + .quad 0xbfba26cc00000000 + .quad 0xbe596605e161e768 + .quad 0xbfb9f54300000000 + .quad 0xbe53bd6ea8cdcabf + .quad 0xbfb9c3be00000000 + .quad 0xbe6873a6488f239e + .quad 0xbfb9924200000000 + .quad 0xbe6038db2539e54e + .quad 0xbfb960ca00000000 + .quad 0xbe6a3576f0eb47ea + .quad 0xbfb92f5b00000000 + .quad 0xbe5ca16578e782d8 + .quad 0xbfb8fdf000000000 + .quad 0xbe6571dd058c9404 + .quad 0xbfb8cc8e00000000 + .quad 0xbe4e8172926b3912 + .quad 0xbfb89b3400000000 + .quad 0xbe458eb8a49a1ed9 + .quad 0xbfb869de00000000 + .quad 0xbe67736434037b3e + .quad 0xbfb8388d00000000 + .quad 0xbe6e2728b7069e85 + .quad 0xbfb8074500000000 + .quad 0xbe61c6bcd5b504de + .quad 0xbfb7d60500000000 + .quad 0xbe62d9f791fd12f7 + .quad 0xbfb7a4ca00000000 + .quad 0xbe53b18b476f88bf + .quad 0xbfb7739300000000 + .quad 0xbe671b2ad71bba2e + .quad 0xbfb7426500000000 + .quad 0xbe6329422bbd68e8 + .quad 0xbfb7113f00000000 + .quad 0xbe6e8b3c2fe4ecae + .quad 0xbfb6e01f00000000 + .quad 0xbe2795edd5ed58e9 + .quad 0xbfb6af0200000000 + .quad 0xbe6c4c07447a13fa + .quad 0xbfb67def00000000 + .quad 0xbe4f2ea58340e81e + .quad 0xbfb64ce400000000 + .quad 0xbe4203398a8ffda4 + .quad 0xbfb61bda00000000 + .quad 0xbe2d4147ad124eaa + .quad 0xbfb5eadc00000000 + .quad 0xbe539c66835b9867 + .quad 0xbfb5b9df00000000 + .quad 0xbe6317f3d15a9860 + .quad 0xbfb588ef00000000 + .quad 0xbe503474104b244e + .quad 0xbfb557ff00000000 + .quad 0xbe6f1dfae0bd2e94 + .quad 0xbfb5271900000000 + .quad 0xbe541889ef09d7c8 + .quad 0xbfb4f63b00000000 + .quad 0xbe52dc76d475d4d1 + .quad 0xbfb4c56200000000 + .quad 0xbe433458770a1735 + .quad 0xbfb4948d00000000 + .quad 0xbe6c8223b5c8b49b + .quad 0xbfb463c200000000 + .quad 0xbe540d91e2302042 + .quad 0xbfb432fb00000000 + .quad 0xbe64b47f064d986f + .quad 0xbfb4023900000000 + .quad 0xbe6ce4d526c81e43 + .quad 0xbfb3d18000000000 + .quad 0xbe6c41714a091d46 + .quad 0xbfb3a0d000000000 + .quad 0xbe63540db8c80703 + .quad 0xbfb3702100000000 + .quad 0xbe5f8cf1a845a25c + .quad 0xbfb33f7b00000000 + .quad 0xbe430a65c7a2686f + .quad 0xbfb30edd00000000 + .quad 0xbe62d26a7215665c + .quad 0xbfb2de4500000000 + .quad 0xbe1bff57e3bab991 + .quad 0xbfb2adb100000000 + .quad 0xbe5e8adfc156e82d + .quad 0xbfb27d2200000000 + .quad 0xbe6e5d041c5f1a05 + .quad 0xbfb24c9d00000000 + .quad 0xbe50a21095df344c + .quad 0xbfb21c2000000000 + .quad 0xbe5b57c218054e22 + .quad 0xbfb1eba400000000 + .quad 0xbe6b1806f4988888 + .quad 0xbfb1bb3200000000 + .quad 0xbe430029dc60a716 + .quad 0xbfb18ac400000000 + .quad 0xbe611e8ed29c4bea + .quad 0xbfb15a5f00000000 + .quad 0xbe6aae4e1e1cd7e9 + .quad 0xbfb12a0000000000 + .quad 0xbe4f2855166a96d5 + .quad 0xbfb0f9a500000000 + .quad 0xbe68ccc743692647 + .quad 0xbfb0c95400000000 + .quad 0xbe50c2b8ff93eea0 + .quad 0xbfb0990400000000 + .quad 0xbe329700306849f4 + .quad 0xbfb068c000000000 + .quad 0xbe661c7597dfa0cf + .quad 0xbfb0387e00000000 + .quad 0xbe64f950c199fdd6 + .quad 0xbfb0084500000000 + .quad 0xbe6434bda55a11e5 + .quad 0xbfafb02300000000 + .quad 0xbe537435dba745c1 + .quad 0xbfaf4fc600000000 + .quad 0xbe4793720209c664 + .quad 0xbfaeef7b00000000 + .quad 0xbe3e845c9d0173b4 + .quad 0xbfae8f3a00000000 + .quad 0xbe527188bd53b8bf + .quad 0xbfae2f0400000000 + .quad 0xbe49e4e1f2d00cb9 + .quad 0xbfadced800000000 + .quad 0xbe57db5b6132809a + .quad 0xbfad6ebf00000000 + .quad 0xbe43c7fbabdf571f + .quad 0xbfad0eb000000000 + .quad 0xbe4c086873f1531f + .quad 0xbfacaeac00000000 + .quad 0xbe33d01264312288 + .quad 0xbfac4eb200000000 + .quad 0xbe4ed73a1b11c287 + .quad 0xbfabeecb00000000 + .quad 0xbe328d5761ea48d2 + .quad 0xbfab8eee00000000 + .quad 0xbe4e2759579ac08a + .quad 0xbfab2f1c00000000 + .quad 0xbe4eea927b8de26e + .quad 0xbfaacf5500000000 + .quad 0xbe3a03ec4341a4ac + .quad 0xbfaa6f9800000000 + .quad 0xbe54efb9656181bf + .quad 0xbfaa0fee00000000 + .quad 0xbe529aa680456564 + .quad 0xbfa9b04f00000000 + .quad 0xbe42b60fbbf05015 + .quad 0xbfa950ba00000000 + .quad 0xbe59ea4d388956ac + .quad 0xbfa8f13800000000 + .quad 0xbe5c820f8ddadcd6 + .quad 0xbfa891ba00000000 + .quad 0xbe27e05a334c58f7 + .quad 0xbfa8324d00000000 + .quad 0xbe5d3229b2ba0376 + .quad 0xbfa7d2ec00000000 + .quad 0xbe545e77c08ed94c + .quad 0xbfa7739600000000 + .quad 0xbe427656b6f95551 + .quad 0xbfa7144a00000000 + .quad 0xbe5c82a193d30405 + .quad 0xbfa6b50a00000000 + .quad 0xbe4ddebd1f3c284a + .quad 0xbfa655dc00000000 + .quad 0xbe599c108199cfd8 + .quad 0xbfa5f6ba00000000 + .quad 0xbe348e1f3828f0d8 + .quad 0xbfa597a200000000 + .quad 0xbe5240beb8df56ca + .quad 0xbfa5389600000000 + .quad 0xbe1aed65370b9099 + .quad 0xbfa4d99400000000 + .quad 0xbe5429166d091c5d + .quad 0xbfa47a9e00000000 + .quad 0xbe44d5db06b75692 + .quad 0xbfa41bba00000000 + .quad 0xbe5e4ff2e670387a + .quad 0xbfa3bcda00000000 + .quad 0xbe5e73df6e675ed2 + .quad 0xbfa35e0d00000000 + .quad 0xbe5df2994af6bbf0 + .quad 0xbfa2ff4c00000000 + .quad 0xbe31a09f65bfdef1 + .quad 0xbfa2a09500000000 + .quad 0xbe5290bafe6a7061 + .quad 0xbfa241ea00000000 + .quad 0xbe425151c43b4181 + .quad 0xbfa1e34a00000000 + .quad 0xbe41d8dbc0646431 + .quad 0xbfa184b500000000 + .quad 0xbe5298ac777c8c9d + .quad 0xbfa1263400000000 + .quad 0xbe10a2f9d7e8035a + .quad 0xbfa0c7b600000000 + .quad 0xbe0bbc4c660fd088 + .quad 0xbfa0694b00000000 + .quad 0xbe3cc374b7950d13 + .quad 0xbfa00aeb00000000 + .quad 0xbe5aa058acdc0265 + .quad 0xbf9f592000000000 + .quad 0xbe149b4d7e5df2c0 + .quad 0xbf9e9c8f00000000 + .quad 0xbe10a7a7e78bdba3 + .quad 0xbf9de01500000000 + .quad 0xbde02a1d978db2f1 + .quad 0xbf9d23b100000000 + .quad 0xbe4e9227a287068e + .quad 0xbf9c676500000000 + .quad 0xbe4e8561096793f8 + .quad 0xbf9bab3100000000 + .quad 0xbe0968e122179f22 + .quad 0xbf9aef1300000000 + .quad 0xbe328465c0dba24f + .quad 0xbf9a330c00000000 + .quad 0xbe47051e31e0d70b + .quad 0xbf99771d00000000 + .quad 0xbe38b8d275ff3a9a + .quad 0xbf98bb5500000000 + .quad 0xbe122bdb89883925 + .quad 0xbf97ff9400000000 + .quad 0xbe36fbf85d50fecb + .quad 0xbf9743eb00000000 + .quad 0xbdf87cba8eccac44 + .quad 0xbf96886800000000 + .quad 0xbe4bd57d800c1470 + .quad 0xbf95ccee00000000 + .quad 0xbe3be2933856d62e + .quad 0xbf95118b00000000 + .quad 0xbe409620e0f1be7b + .quad 0xbf94564f00000000 + .quad 0xbe4e4325cf62b811 + .quad 0xbf939b1c00000000 + .quad 0xbe2adee9af6a25c0 + .quad 0xbf92e00000000000 + .quad 0xbe20ce46d28f63c9 + .quad 0xbf92250b00000000 + .quad 0xbe41f6aa9fb6fe0b + .quad 0xbf916a1e00000000 + .quad 0xbe4e41409957601b + .quad 0xbf90af5900000000 + .quad 0xbe4e53e5a63658ad + .quad 0xbf8fe93900000000 + .quad 0xbe3eded24d629d7d + .quad 0xbf8e73ef00000000 + .quad 0xbe3a29d2ea7d362b + .quad 0xbf8cfef500000000 + .quad 0xbe1e2e79fe4aa765 + .quad 0xbf8b8a0a00000000 + .quad 0xbe3e8785027a216b + .quad 0xbf8a155000000000 + .quad 0xbe37a174d5a8bded + .quad 0xbf88a0c600000000 + .quad 0xbe35dde88f39d7ce + .quad 0xbf872c6c00000000 + .quad 0xbe3c41ea3f44a785 + .quad 0xbf85b86300000000 + .quad 0xbe194c69ffd7f42d + .quad 0xbf84446a00000000 + .quad 0xbe1a5e4e0d24af39 + .quad 0xbf82d0a100000000 + .quad 0xbe381611eb6c3818 + .quad 0xbf815d0900000000 + .quad 0xbe3dd5da9cc5f987 + .quad 0xbf7fd34500000000 + .quad 0xbe25bd80e0b0590e + .quad 0xbf7cec9900000000 + .quad 0xbe1ce47bb0eea510 + .quad 0xbf7a068e00000000 + .quad 0xbe26dbe100877575 + .quad 0xbf7720e600000000 + .quad 0xbd9aa4f614b9e1ac + .quad 0xbf743b5f00000000 + .quad 0xbe271a96b1eb7842 + .quad 0xbf71567b00000000 + .quad 0xbe2318f60005710d + .quad 0xbf6ce37400000000 + .quad 0xbe0c7a4e122b1762 + .quad 0xbf671b3600000000 + .quad 0xbe1c85d1e3d214d1 + .quad 0xbf61533f00000000 + .quad 0xbe0e793b61aa1f54 + .quad 0xbf57181c00000000 + .quad 0xbe01296a4555af78 + .quad 0xbf47168e00000000 + .quad 0xbdf30d6f34ebfa1c + .rept 2 + .quad 0x0000000000000000 + .endr + .rept 48 + .byte 0 + .endr + +/* Exp(2) lookup table for exp part (non HSW) */ +.if .-__svml_dpow_data != _exp2_tbl +.err +.endif + .quad 0x3ff0000000000000 + .quad 0x0000000000000000 + .quad 0x3ff0163da9fb3335 + .quad 0x3c9b61299ab8cdb7 + .quad 0x3ff02c9a3e778061 + .quad 0xbc719083535b085d + .quad 0x3ff04315e86e7f85 + .quad 0xbc90a31c1977c96e + .quad 0x3ff059b0d3158574 + .quad 0x3c8d73e2a475b465 + .quad 0x3ff0706b29ddf6de + .quad 0xbc8c91dfe2b13c26 + .quad 0x3ff0874518759bc8 + .quad 0x3c6186be4bb284ff + .quad 0x3ff09e3ecac6f383 + .quad 0x3c91487818316135 + .quad 0x3ff0b5586cf9890f + .quad 0x3c98a62e4adc610a + .quad 0x3ff0cc922b7247f7 + .quad 0x3c901edc16e24f71 + .quad 0x3ff0e3ec32d3d1a2 + .quad 0x3c403a1727c57b52 + .quad 0x3ff0fb66affed31b + .quad 0xbc6b9bedc44ebd7b + .quad 0x3ff11301d0125b51 + .quad 0xbc96c51039449b39 + .quad 0x3ff12abdc06c31cc + .quad 0xbc51b514b36ca5c7 + .quad 0x3ff1429aaea92de0 + .quad 0xbc932fbf9af1369e + .quad 0x3ff15a98c8a58e51 + .quad 0x3c82406ab9eeab09 + .quad 0x3ff172b83c7d517b + .quad 0xbc819041b9d78a75 + .quad 0x3ff18af9388c8dea + .quad 0xbc911023d1970f6b + .quad 0x3ff1a35beb6fcb75 + .quad 0x3c8e5b4c7b4968e4 + .quad 0x3ff1bbe084045cd4 + .quad 0xbc995386352ef607 + .quad 0x3ff1d4873168b9aa + .quad 0x3c9e016e00a2643c + .quad 0x3ff1ed5022fcd91d + .quad 0xbc91df98027bb78b + .quad 0x3ff2063b88628cd6 + .quad 0x3c8dc775814a8494 + .quad 0x3ff21f49917ddc96 + .quad 0x3c82a97e9494a5ed + .quad 0x3ff2387a6e756238 + .quad 0x3c99b07eb6c70572 + .quad 0x3ff251ce4fb2a63f + .quad 0x3c8ac155bef4f4a4 + .quad 0x3ff26b4565e27cdd + .quad 0x3c82bd339940e9d9 + .quad 0x3ff284dfe1f56381 + .quad 0xbc9a4c3a8c3f0d7d + .quad 0x3ff29e9df51fdee1 + .quad 0x3c8612e8afad1255 + .quad 0x3ff2b87fd0dad990 + .quad 0xbc410adcd6381aa3 + .quad 0x3ff2d285a6e4030b + .quad 0x3c90024754db41d4 + .quad 0x3ff2ecafa93e2f56 + .quad 0x3c71ca0f45d52383 + .quad 0x3ff306fe0a31b715 + .quad 0x3c86f46ad23182e4 + .quad 0x3ff32170fc4cd831 + .quad 0x3c8a9ce78e18047c + .quad 0x3ff33c08b26416ff + .quad 0x3c932721843659a5 + .quad 0x3ff356c55f929ff1 + .quad 0xbc8b5cee5c4e4628 + .quad 0x3ff371a7373aa9cb + .quad 0xbc963aeabf42eae1 + .quad 0x3ff38cae6d05d866 + .quad 0xbc9e958d3c9904bc + .quad 0x3ff3a7db34e59ff7 + .quad 0xbc75e436d661f5e2 + .quad 0x3ff3c32dc313a8e5 + .quad 0xbc9efff8375d29c3 + .quad 0x3ff3dea64c123422 + .quad 0x3c8ada0911f09ebb + .quad 0x3ff3fa4504ac801c + .quad 0xbc97d023f956f9f3 + .quad 0x3ff4160a21f72e2a + .quad 0xbc5ef3691c309278 + .quad 0x3ff431f5d950a897 + .quad 0xbc81c7dde35f7998 + .quad 0x3ff44e086061892d + .quad 0x3c489b7a04ef80cf + .quad 0x3ff46a41ed1d0057 + .quad 0x3c9c944bd1648a76 + .quad 0x3ff486a2b5c13cd0 + .quad 0x3c73c1a3b69062f0 + .quad 0x3ff4a32af0d7d3de + .quad 0x3c99cb62f3d1be56 + .quad 0x3ff4bfdad5362a27 + .quad 0x3c7d4397afec42e2 + .quad 0x3ff4dcb299fddd0d + .quad 0x3c98ecdbbc6a7833 + .quad 0x3ff4f9b2769d2ca7 + .quad 0xbc94b309d25957e3 + .quad 0x3ff516daa2cf6642 + .quad 0xbc8f768569bd93ee + .quad 0x3ff5342b569d4f82 + .quad 0xbc807abe1db13cac + .quad 0x3ff551a4ca5d920f + .quad 0xbc8d689cefede59a + .quad 0x3ff56f4736b527da + .quad 0x3c99bb2c011d93ac + .quad 0x3ff58d12d497c7fd + .quad 0x3c8295e15b9a1de7 + .quad 0x3ff5ab07dd485429 + .quad 0x3c96324c054647ac + .quad 0x3ff5c9268a5946b7 + .quad 0x3c3c4b1b816986a2 + .quad 0x3ff5e76f15ad2148 + .quad 0x3c9ba6f93080e65d + .quad 0x3ff605e1b976dc09 + .quad 0xbc93e2429b56de47 + .quad 0x3ff6247eb03a5585 + .quad 0xbc9383c17e40b496 + .quad 0x3ff6434634ccc320 + .quad 0xbc8c483c759d8932 + .quad 0x3ff6623882552225 + .quad 0xbc9bb60987591c33 + .quad 0x3ff68155d44ca973 + .quad 0x3c6038ae44f73e64 + .quad 0x3ff6a09e667f3bcd + .quad 0xbc9bdd3413b26455 + .quad 0x3ff6c012750bdabf + .quad 0xbc72895667ff0b0c + .quad 0x3ff6dfb23c651a2f + .quad 0xbc6bbe3a683c88aa + .quad 0x3ff6ff7df9519484 + .quad 0xbc883c0f25860ef6 + .quad 0x3ff71f75e8ec5f74 + .quad 0xbc816e4786887a99 + .quad 0x3ff73f9a48a58174 + .quad 0xbc90a8d96c65d53b + .quad 0x3ff75feb564267c9 + .quad 0xbc90245957316dd3 + .quad 0x3ff780694fde5d3f + .quad 0x3c9866b80a02162c + .quad 0x3ff7a11473eb0187 + .quad 0xbc841577ee04992f + .quad 0x3ff7c1ed0130c132 + .quad 0x3c9f124cd1164dd5 + .quad 0x3ff7e2f336cf4e62 + .quad 0x3c705d02ba15797e + .quad 0x3ff80427543e1a12 + .quad 0xbc927c86626d972a + .quad 0x3ff82589994cce13 + .quad 0xbc9d4c1dd41532d7 + .quad 0x3ff8471a4623c7ad + .quad 0xbc88d684a341cdfb + .quad 0x3ff868d99b4492ed + .quad 0xbc9fc6f89bd4f6ba + .quad 0x3ff88ac7d98a6699 + .quad 0x3c9994c2f37cb53a + .quad 0x3ff8ace5422aa0db + .quad 0x3c96e9f156864b26 + .quad 0x3ff8cf3216b5448c + .quad 0xbc70d55e32e9e3aa + .quad 0x3ff8f1ae99157736 + .quad 0x3c85cc13a2e3976c + .quad 0x3ff9145b0b91ffc6 + .quad 0xbc9dd6792e582523 + .quad 0x3ff93737b0cdc5e5 + .quad 0xbc675fc781b57ebb + .quad 0x3ff95a44cbc8520f + .quad 0xbc764b7c96a5f039 + .quad 0x3ff97d829fde4e50 + .quad 0xbc9d185b7c1b85d0 + .quad 0x3ff9a0f170ca07ba + .quad 0xbc9173bd91cee632 + .quad 0x3ff9c49182a3f090 + .quad 0x3c7c7c46b071f2be + .quad 0x3ff9e86319e32323 + .quad 0x3c7824ca78e64c6e + .quad 0x3ffa0c667b5de565 + .quad 0xbc9359495d1cd532 + .quad 0x3ffa309bec4a2d33 + .quad 0x3c96305c7ddc36ab + .quad 0x3ffa5503b23e255d + .quad 0xbc9d2f6edb8d41e1 + .quad 0x3ffa799e1330b358 + .quad 0x3c9bcb7ecac563c6 + .quad 0x3ffa9e6b5579fdbf + .quad 0x3c90fac90ef7fd31 + .quad 0x3ffac36bbfd3f37a + .quad 0xbc8f9234cae76cd0 + .quad 0x3ffae89f995ad3ad + .quad 0x3c97a1cd345dcc81 + .quad 0x3ffb0e07298db666 + .quad 0xbc9bdef54c80e424 + .quad 0x3ffb33a2b84f15fb + .quad 0xbc62805e3084d707 + .quad 0x3ffb59728de5593a + .quad 0xbc9c71dfbbba6de3 + .quad 0x3ffb7f76f2fb5e47 + .quad 0xbc75584f7e54ac3a + .quad 0x3ffba5b030a1064a + .quad 0xbc9efcd30e54292e + .quad 0x3ffbcc1e904bc1d2 + .quad 0x3c823dd07a2d9e84 + .quad 0x3ffbf2c25bd71e09 + .quad 0xbc9efdca3f6b9c72 + .quad 0x3ffc199bdd85529c + .quad 0x3c811065895048dd + .quad 0x3ffc40ab5fffd07a + .quad 0x3c9b4537e083c60a + .quad 0x3ffc67f12e57d14b + .quad 0x3c92884dff483cac + .quad 0x3ffc8f6d9406e7b5 + .quad 0x3c71acbc48805c44 + .quad 0x3ffcb720dcef9069 + .quad 0x3c7503cbd1e949db + .quad 0x3ffcdf0b555dc3fa + .quad 0xbc8dd83b53829d72 + .quad 0x3ffd072d4a07897c + .quad 0xbc9cbc3743797a9c + .quad 0x3ffd2f87080d89f2 + .quad 0xbc9d487b719d8577 + .quad 0x3ffd5818dcfba487 + .quad 0x3c82ed02d75b3706 + .quad 0x3ffd80e316c98398 + .quad 0xbc911ec18beddfe8 + .quad 0x3ffda9e603db3285 + .quad 0x3c9c2300696db532 + .quad 0x3ffdd321f301b460 + .quad 0x3c92da5778f018c2 + .quad 0x3ffdfc97337b9b5f + .quad 0xbc91a5cd4f184b5b + .quad 0x3ffe264614f5a129 + .quad 0xbc97b627817a1496 + .quad 0x3ffe502ee78b3ff6 + .quad 0x3c839e8980a9cc8f + .quad 0x3ffe7a51fbc74c83 + .quad 0x3c92d522ca0c8de1 + .quad 0x3ffea4afa2a490da + .quad 0xbc9e9c23179c2893 + .quad 0x3ffecf482d8e67f1 + .quad 0xbc9c93f3b411ad8c + .quad 0x3ffefa1bee615a27 + .quad 0x3c9dc7f486a4b6b0 + .quad 0x3fff252b376bba97 + .quad 0x3c93a1a5bf0d8e43 + .quad 0x3fff50765b6e4540 + .quad 0x3c99d3e12dd8a18a + .quad 0x3fff7bfdad9cbe14 + .quad 0xbc9dbb12d0063509 + .quad 0x3fffa7c1819e90d8 + .quad 0x3c874853f3a5931e + .quad 0x3fffd3c22b8f71f1 + .quad 0x3c62eb74966579e7 + +/* log2 polynomial coefficients: + * clv7 */ +double_vector _clv_1 0x3f903950cf599c56 + +/* clv6 */ +double_vector _clv_2 0xbf9b4ea0e9419f52 + +/* clv5 */ +double_vector _clv_3 0x3fa7a334ddfc9f86 + +/* clv4 */ +double_vector _clv_4 0xbfb550472a8bb463 + +/* clv3 */ +double_vector _clv_5 0x3fc47fd462b3b816 + +/* clv2 */ +double_vector _clv_6 0xbfd62e4346694107 + +/* clv1 */ +double_vector _clv_7 0x3e79c3a6966457ee + +/* exponential polynomial coefficients: + * cev5 */ +double_vector _cev_1 0x3f55d87fe78a6731 + +/* cev4 */ +double_vector _cev_2 0x3f83b2ab6fba4e77 + +/* cev3 */ +double_vector _cev_3 0x3fac6b08d704a0bf + +/* cev2 */ +double_vector _cev_4 0x3fcebfbdff82c58e + +/* cev1 */ +double_vector _cev_5 0x3fe62e42fefa39ef + +/* General purpose constants: + * iMantissaMask */ +double_vector _iMantissaMask 0x000fffffffffffff + +/* i3fe7fe0000000000 */ +double_vector _i3fe7fe0000000000 0x3fe7fe0000000000 + +/* dbOne */ +double_vector _dbOne 0x3ff0000000000000 + +/* iffffffff00000000 */ +double_vector _iffffffff00000000 0xffffffff00000000 + +/* db2p20_2p19 = 2^20+2^19 */ +double_vector _db2p20_2p19 0x4138000000000000 + +/* iHighMask */ +double_vector _iHighMask 0xfffffffff8000000 + +/* LHN = -log2(e) truncated to 22 bits */ +double_vector _LHN 0xbff7154740000000 + +/* ifff0000000000000 */ +double_vector _ifff0000000000000 0xfff0000000000000 + +/* db2p45_2p44 */ +double_vector _db2p45_2p44 0x42c8000000000000 + +/* NEG_INF */ +double_vector _NEG_INF 0xfff0000000000000 + +/* NEG_ZERO */ +double_vector _NEG_ZERO 0x8000000000000000 + +/* 2pow52 */ +double_vector _d2pow52 0x4330000000000000 + +/* 1div2pow111 */ +double_vector _d1div2pow111 0x3900000000000000 + +/* HIDELTA */ +float_vector _HIDELTA 0x00100000 + +/* LORANGE */ +float_vector _LORANGE 0x00200000 + +/* ABSMASK */ +float_vector _ABSMASK 0x7fffffff + +/* INF */ +float_vector _INF 0x7f800000 + +/* DOMAINRANGE */ +float_vector _DOMAINRANGE 0x408f3fff + +/* iIndexMask */ +float_vector _iIndexMask 0x000ffe00 + +/* iIndexAdd */ +float_vector _iIndexAdd 0x00000200 + +/* i3fe7fe00 */ +float_vector _i3fe7fe00 0x3fe7fe00 + +/* i2p20_2p19 */ +float_vector _i2p20_2p19 0x41380000 + +/* iOne */ +float_vector _iOne 0x3ff00000 + +/* jIndexMask */ +float_vector _jIndexMask 0x0000007f + .type __svml_dpow_data,@object + .size __svml_dpow_data,.-__svml_dpow_data diff --git a/sysdeps/x86_64/fpu/svml_d_pow_data.h b/sysdeps/x86_64/fpu/svml_d_pow_data.h new file mode 100644 index 0000000000..a1b9f9bc46 --- /dev/null +++ b/sysdeps/x86_64/fpu/svml_d_pow_data.h @@ -0,0 +1,104 @@ +/* Offsets for data table for function pow. + 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 D_POW_DATA_H +#define D_POW_DATA_H + +#define _hsw_log2_table 0 +#define _hsw_dTe 8256 +#define _hsw_dMantMask 10304 +#define _hsw_dOne 10368 +#define _hsw_dCvtMask 10432 +#define _hsw_dMinNorm 10496 +#define _hsw_dMaxNorm 10560 +#define _hsw_lRndBit 10624 +#define _hsw_lRndMask 10688 +#define _hsw_dc6 10752 +#define _hsw_dc5 10816 +#define _hsw_dc4 10880 +#define _hsw_dc3 10944 +#define _hsw_dc1 11008 +#define _hsw_dc1h 11072 +#define _hsw_dc2 11136 +#define _hsw_dAbsMask 11200 +#define _hsw_dDomainRange 11264 +#define _hsw_dShifter 11328 +#define _hsw_dIndexMask 11392 +#define _hsw_dce4 11456 +#define _hsw_dce3 11520 +#define _hsw_dce2 11584 +#define _hsw_dce1 11648 +#define _rcp_t1 11712 +#define _log2_t1 19968 +#define _exp2_tbl 36416 +#define _clv_1 38464 +#define _clv_2 38528 +#define _clv_3 38592 +#define _clv_4 38656 +#define _clv_5 38720 +#define _clv_6 38784 +#define _clv_7 38848 +#define _cev_1 38912 +#define _cev_2 38976 +#define _cev_3 39040 +#define _cev_4 39104 +#define _cev_5 39168 +#define _iMantissaMask 39232 +#define _i3fe7fe0000000000 39296 +#define _dbOne 39360 +#define _iffffffff00000000 39424 +#define _db2p20_2p19 39488 +#define _iHighMask 39552 +#define _LHN 39616 +#define _ifff0000000000000 39680 +#define _db2p45_2p44 39744 +#define _NEG_INF 39808 +#define _NEG_ZERO 39872 +#define _d2pow52 39936 +#define _d1div2pow111 40000 +#define _HIDELTA 40064 +#define _LORANGE 40128 +#define _ABSMASK 40192 +#define _INF 40256 +#define _DOMAINRANGE 40320 +#define _iIndexMask 40384 +#define _iIndexAdd 40448 +#define _i3fe7fe00 40512 +#define _i2p20_2p19 40576 +#define _iOne 40640 +#define _jIndexMask 40704 + +.macro double_vector offset value +.if .-__svml_dpow_data != \offset +.err +.endif +.rept 8 +.quad \value +.endr +.endm + +.macro float_vector offset value +.if .-__svml_dpow_data != \offset +.err +.endif +.rept 16 +.long \value +.endr +.endm + +#endif diff --git a/sysdeps/x86_64/fpu/svml_d_wrapper_impl.h b/sysdeps/x86_64/fpu/svml_d_wrapper_impl.h index 4b2e9f5e80..25465cd840 100644 --- a/sysdeps/x86_64/fpu/svml_d_wrapper_impl.h +++ b/sysdeps/x86_64/fpu/svml_d_wrapper_impl.h @@ -34,6 +34,26 @@ ret .endm +/* 2 argument SSE2 ISA version as wrapper to scalar. */ +.macro WRAPPER_IMPL_SSE2_ff callee + subq $56, %rsp + cfi_adjust_cfa_offset(56) + movaps %xmm0, (%rsp) + movaps %xmm1, 16(%rsp) + call \callee@PLT + movsd %xmm0, 32(%rsp) + movsd 8(%rsp), %xmm0 + movsd 24(%rsp), %xmm1 + call \callee@PLT + movsd 32(%rsp), %xmm1 + movsd %xmm0, 40(%rsp) + unpcklpd %xmm0, %xmm1 + movaps %xmm1, %xmm0 + addq $56, %rsp + cfi_adjust_cfa_offset(-56) + ret +.endm + /* AVX/AVX2 ISA version as wrapper to SSE ISA version. */ .macro WRAPPER_IMPL_AVX callee pushq %rbp @@ -60,6 +80,34 @@ ret .endm +/* 2 argument AVX/AVX2 ISA version as wrapper to SSE ISA version. */ +.macro WRAPPER_IMPL_AVX_ff callee + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-32, %rsp + subq $64, %rsp + vextractf128 $1, %ymm0, 16(%rsp) + vextractf128 $1, %ymm1, (%rsp) + vzeroupper + call HIDDEN_JUMPTARGET(\callee) + vmovaps %xmm0, 32(%rsp) + vmovaps 16(%rsp), %xmm0 + vmovaps (%rsp), %xmm1 + call HIDDEN_JUMPTARGET(\callee) + vmovaps %xmm0, %xmm1 + vmovaps 32(%rsp), %xmm0 + vinsertf128 $1, %xmm1, %ymm0, %ymm0 + 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 @@ -99,3 +147,65 @@ cfi_restore (%rbp) ret .endm + +/* 2 argument AVX512 ISA version as wrapper to AVX2 ISA version. */ +.macro WRAPPER_IMPL_AVX512_ff callee + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $128, %rsp +/* 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 %zmm1, 64(%rsp). */ + .byte 0x62 + .byte 0xf1 + .byte 0x7c + .byte 0x48 + .byte 0x29 + .byte 0x4c + .byte 0x24 +/* Below is encoding for vmovapd (%rsp), %ymm0. */ + .byte 0xc5 + .byte 0xfd + .byte 0x28 + .byte 0x04 + .byte 0x24 +/* Below is encoding for vmovapd 64(%rsp), %ymm1. */ + .byte 0xc5 + .byte 0xfd + .byte 0x28 + .byte 0x4c + .byte 0x24 + .byte 0x40 + call HIDDEN_JUMPTARGET(\callee) +/* Below is encoding for vmovapd 32(%rsp), %ymm0. */ + .byte 0xc5 + .byte 0xfd + .byte 0x28 + .byte 0x44 + .byte 0x24 + .byte 0x20 +/* Below is encoding for vmovapd 96(%rsp), %ymm1. */ + .byte 0xc5 + .byte 0xfd + .byte 0x28 + .byte 0x4c + .byte 0x24 + .byte 0x60 + call HIDDEN_JUMPTARGET(\callee) + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret +.endm diff --git a/sysdeps/x86_64/fpu/test-double-vlen2-wrappers.c b/sysdeps/x86_64/fpu/test-double-vlen2-wrappers.c index 946a8f690a..d7897aa874 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen2-wrappers.c +++ b/sysdeps/x86_64/fpu/test-double-vlen2-wrappers.c @@ -26,3 +26,4 @@ VECTOR_WRAPPER (WRAPPER_NAME (cos), _ZGVbN2v_cos) VECTOR_WRAPPER (WRAPPER_NAME (sin), _ZGVbN2v_sin) VECTOR_WRAPPER (WRAPPER_NAME (log), _ZGVbN2v_log) VECTOR_WRAPPER (WRAPPER_NAME (exp), _ZGVbN2v_exp) +VECTOR_WRAPPER_ff (WRAPPER_NAME (pow), _ZGVbN2vv_pow) diff --git a/sysdeps/x86_64/fpu/test-double-vlen2.c b/sysdeps/x86_64/fpu/test-double-vlen2.c index 1b72748a3d..83cab4d443 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen2.c +++ b/sysdeps/x86_64/fpu/test-double-vlen2.c @@ -22,5 +22,6 @@ #define TEST_VECTOR_sin 1 #define TEST_VECTOR_log 1 #define TEST_VECTOR_exp 1 +#define TEST_VECTOR_pow 1 #include "libm-test.c" diff --git a/sysdeps/x86_64/fpu/test-double-vlen4-avx2-wrappers.c b/sysdeps/x86_64/fpu/test-double-vlen4-avx2-wrappers.c index 40c3e25a86..82159ce756 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen4-avx2-wrappers.c +++ b/sysdeps/x86_64/fpu/test-double-vlen4-avx2-wrappers.c @@ -29,3 +29,4 @@ VECTOR_WRAPPER (WRAPPER_NAME (cos), _ZGVdN4v_cos) VECTOR_WRAPPER (WRAPPER_NAME (sin), _ZGVdN4v_sin) VECTOR_WRAPPER (WRAPPER_NAME (log), _ZGVdN4v_log) VECTOR_WRAPPER (WRAPPER_NAME (exp), _ZGVdN4v_exp) +VECTOR_WRAPPER_ff (WRAPPER_NAME (pow), _ZGVdN4vv_pow) diff --git a/sysdeps/x86_64/fpu/test-double-vlen4-avx2.c b/sysdeps/x86_64/fpu/test-double-vlen4-avx2.c index 45d6ed6f43..771dc89e48 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen4-avx2.c +++ b/sysdeps/x86_64/fpu/test-double-vlen4-avx2.c @@ -25,6 +25,7 @@ #define TEST_VECTOR_sin 1 #define TEST_VECTOR_log 1 #define TEST_VECTOR_exp 1 +#define TEST_VECTOR_pow 1 #define REQUIRE_AVX2 diff --git a/sysdeps/x86_64/fpu/test-double-vlen4-wrappers.c b/sysdeps/x86_64/fpu/test-double-vlen4-wrappers.c index 094c9bfb14..9421a59c52 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen4-wrappers.c +++ b/sysdeps/x86_64/fpu/test-double-vlen4-wrappers.c @@ -26,3 +26,4 @@ VECTOR_WRAPPER (WRAPPER_NAME (cos), _ZGVcN4v_cos) VECTOR_WRAPPER (WRAPPER_NAME (sin), _ZGVcN4v_sin) VECTOR_WRAPPER (WRAPPER_NAME (log), _ZGVcN4v_log) VECTOR_WRAPPER (WRAPPER_NAME (exp), _ZGVcN4v_exp) +VECTOR_WRAPPER_ff (WRAPPER_NAME (pow), _ZGVcN4vv_pow) diff --git a/sysdeps/x86_64/fpu/test-double-vlen4.c b/sysdeps/x86_64/fpu/test-double-vlen4.c index b89e77f5f3..8da28c88ac 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen4.c +++ b/sysdeps/x86_64/fpu/test-double-vlen4.c @@ -22,5 +22,6 @@ #define TEST_VECTOR_sin 1 #define TEST_VECTOR_log 1 #define TEST_VECTOR_exp 1 +#define TEST_VECTOR_pow 1 #include "libm-test.c" diff --git a/sysdeps/x86_64/fpu/test-double-vlen8-wrappers.c b/sysdeps/x86_64/fpu/test-double-vlen8-wrappers.c index 0b4398a8c5..4bdcdd4e3a 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen8-wrappers.c +++ b/sysdeps/x86_64/fpu/test-double-vlen8-wrappers.c @@ -26,3 +26,4 @@ VECTOR_WRAPPER (WRAPPER_NAME (cos), _ZGVeN8v_cos) VECTOR_WRAPPER (WRAPPER_NAME (sin), _ZGVeN8v_sin) VECTOR_WRAPPER (WRAPPER_NAME (log), _ZGVeN8v_log) VECTOR_WRAPPER (WRAPPER_NAME (exp), _ZGVeN8v_exp) +VECTOR_WRAPPER_ff (WRAPPER_NAME (pow), _ZGVeN8vv_pow) diff --git a/sysdeps/x86_64/fpu/test-double-vlen8.c b/sysdeps/x86_64/fpu/test-double-vlen8.c index 277b31241f..bf832b194c 100644 --- a/sysdeps/x86_64/fpu/test-double-vlen8.c +++ b/sysdeps/x86_64/fpu/test-double-vlen8.c @@ -22,6 +22,7 @@ #define TEST_VECTOR_sin 1 #define TEST_VECTOR_log 1 #define TEST_VECTOR_exp 1 +#define TEST_VECTOR_pow 1 #define REQUIRE_AVX512F |