| /* Function pow vectorized with AVX2. |
| Copyright (C) 2014-2018 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 JUMPTARGET(__pow_finite) |
| |
| 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 JUMPTARGET(__pow_finite) |
| |
| vmovsd %xmm0, 320(%rsp,%r15) |
| jmp .LBL_1_7 |
| |
| END (_ZGVdN4vv_pow_avx2) |
