diff options
Diffstat (limited to 'sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core_avx2.S')
| -rw-r--r-- | sysdeps/x86_64/fpu/multiarch/svml_d_pow4_core_avx2.S | 387 |
1 files changed, 387 insertions, 0 deletions
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) |