| /* Function powf 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_s_powf_data.h" |
| |
| .text |
| ENTRY(_ZGVdN8vv_powf_avx2) |
| /* |
| ALGORITHM DESCRIPTION: |
| |
| We are using the next identity : pow(x,y) = 2^(y * log2(x)). |
| |
| 1) log2(x) calculation |
| 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), |
| ... |
| Log2 result is split by three parts: HH+HL+HLL |
| |
| 2) Calculation of y*log2(x) |
| 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^(y*log2(x)) |
| 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 |
| lea __VPACK_ODD_ind.6357.0.1(%rip), %rcx |
| vmovups %ymm14, 320(%rsp) |
| |
| /* hi bits */ |
| lea __VPACK_ODD_ind.6358.0.1(%rip), %rax |
| vmovups %ymm12, 256(%rsp) |
| vmovups %ymm9, 96(%rsp) |
| vmovups %ymm13, 224(%rsp) |
| vmovups %ymm15, 352(%rsp) |
| vmovups %ymm11, 384(%rsp) |
| vmovups %ymm10, 288(%rsp) |
| vmovups (%rcx), %ymm10 |
| vmovups %ymm8, 160(%rsp) |
| vmovdqa %ymm1, %ymm9 |
| movq __svml_spow_data@GOTPCREL(%rip), %rdx |
| vextractf128 $1, %ymm0, %xmm7 |
| vcvtps2pd %xmm0, %ymm14 |
| vcvtps2pd %xmm7, %ymm12 |
| vpsubd _NMINNORM(%rdx), %ymm0, %ymm7 |
| |
| /* preserve mantissa, set input exponent to 2^(-10) */ |
| vandpd _ExpMask(%rdx), %ymm14, %ymm3 |
| vandpd _ExpMask(%rdx), %ymm12, %ymm13 |
| |
| /* exponent bits selection */ |
| vpsrlq $20, %ymm12, %ymm12 |
| vpsrlq $20, %ymm14, %ymm14 |
| vextractf128 $1, %ymm9, %xmm2 |
| vcvtps2pd %xmm9, %ymm1 |
| vpand _ABSMASK(%rdx), %ymm9, %ymm8 |
| vcvtps2pd %xmm2, %ymm6 |
| vorpd _Two10(%rdx), %ymm3, %ymm2 |
| vorpd _Two10(%rdx), %ymm13, %ymm3 |
| |
| /* reciprocal approximation good to at least 11 bits */ |
| vcvtpd2ps %ymm2, %xmm5 |
| vcvtpd2ps %ymm3, %xmm15 |
| vrcpps %xmm5, %xmm4 |
| vrcpps %xmm15, %xmm11 |
| vcvtps2pd %xmm4, %ymm13 |
| vcvtps2pd %xmm11, %ymm4 |
| vpermps %ymm12, %ymm10, %ymm11 |
| |
| /* round reciprocal to nearest integer, will have 1+9 mantissa bits */ |
| vroundpd $0, %ymm13, %ymm12 |
| vpermps %ymm14, %ymm10, %ymm5 |
| vroundpd $0, %ymm4, %ymm14 |
| vmovupd _One(%rdx), %ymm4 |
| |
| /* table lookup */ |
| vpsrlq $40, %ymm12, %ymm10 |
| vfmsub213pd %ymm4, %ymm12, %ymm2 |
| vfmsub213pd %ymm4, %ymm14, %ymm3 |
| vcmpgt_oqpd _Threshold(%rdx), %ymm12, %ymm12 |
| vxorpd %ymm4, %ymm4, %ymm4 |
| vandpd _Bias(%rdx), %ymm12, %ymm12 |
| |
| /* biased exponent in DP format */ |
| vcvtdq2pd %xmm11, %ymm13 |
| vpcmpeqd %ymm11, %ymm11, %ymm11 |
| vgatherqpd %ymm11, _Log2Rcp_lookup(%rdx,%ymm10), %ymm4 |
| vpsrlq $40, %ymm14, %ymm10 |
| vcmpgt_oqpd _Threshold(%rdx), %ymm14, %ymm14 |
| vpcmpeqd %ymm11, %ymm11, %ymm11 |
| vandpd _Bias(%rdx), %ymm14, %ymm14 |
| vcvtdq2pd %xmm5, %ymm15 |
| vxorpd %ymm5, %ymm5, %ymm5 |
| vgatherqpd %ymm11, _Log2Rcp_lookup(%rdx,%ymm10), %ymm5 |
| vorpd _Bias1(%rdx), %ymm12, %ymm11 |
| vorpd _Bias1(%rdx), %ymm14, %ymm10 |
| vsubpd %ymm11, %ymm15, %ymm11 |
| vsubpd %ymm10, %ymm13, %ymm14 |
| vmovupd _poly_coeff_4(%rdx), %ymm15 |
| vmovupd _poly_coeff_3(%rdx), %ymm13 |
| vmulpd %ymm3, %ymm3, %ymm10 |
| vfmadd213pd %ymm15, %ymm3, %ymm13 |
| vmovdqa %ymm15, %ymm12 |
| vfmadd231pd _poly_coeff_3(%rdx), %ymm2, %ymm12 |
| vmulpd %ymm2, %ymm2, %ymm15 |
| |
| /* reconstruction */ |
| vfmadd213pd %ymm3, %ymm10, %ymm13 |
| vfmadd213pd %ymm2, %ymm15, %ymm12 |
| vaddpd %ymm5, %ymm13, %ymm13 |
| vaddpd %ymm4, %ymm12, %ymm2 |
| vfmadd231pd _L2(%rdx), %ymm14, %ymm13 |
| vfmadd132pd _L2(%rdx), %ymm2, %ymm11 |
| vmulpd %ymm6, %ymm13, %ymm2 |
| vmulpd %ymm1, %ymm11, %ymm10 |
| vmulpd __dbInvLn2(%rdx), %ymm2, %ymm6 |
| vmulpd __dbInvLn2(%rdx), %ymm10, %ymm15 |
| |
| /* to round down; if dR is an integer we will get R = 1, which is ok */ |
| vsubpd __dbHALF(%rdx), %ymm6, %ymm3 |
| vsubpd __dbHALF(%rdx), %ymm15, %ymm1 |
| vaddpd __dbShifter(%rdx), %ymm3, %ymm13 |
| vaddpd __dbShifter(%rdx), %ymm1, %ymm14 |
| vsubpd __dbShifter(%rdx), %ymm13, %ymm12 |
| vmovups (%rax), %ymm1 |
| vsubpd __dbShifter(%rdx), %ymm14, %ymm11 |
| |
| /* [0..1) */ |
| vsubpd %ymm12, %ymm6, %ymm6 |
| vpermps %ymm10, %ymm1, %ymm3 |
| vpermps %ymm2, %ymm1, %ymm10 |
| vpcmpgtd _NMAXVAL(%rdx), %ymm7, %ymm4 |
| vpcmpgtd _INF(%rdx), %ymm8, %ymm1 |
| vpcmpeqd _NMAXVAL(%rdx), %ymm7, %ymm7 |
| vpcmpeqd _INF(%rdx), %ymm8, %ymm8 |
| vpor %ymm7, %ymm4, %ymm2 |
| vpor %ymm8, %ymm1, %ymm1 |
| vsubpd %ymm11, %ymm15, %ymm7 |
| vinsertf128 $1, %xmm10, %ymm3, %ymm10 |
| vpor %ymm1, %ymm2, %ymm3 |
| |
| /* iAbsX = iAbsX&iAbsMask */ |
| vandps __iAbsMask(%rdx), %ymm10, %ymm10 |
| |
| /* iRangeMask = (iAbsX>iDomainRange) */ |
| vpcmpgtd __iDomainRange(%rdx), %ymm10, %ymm4 |
| vpor %ymm4, %ymm3, %ymm5 |
| vmulpd __dbC1(%rdx), %ymm7, %ymm4 |
| vmovmskps %ymm5, %ecx |
| vmulpd __dbC1(%rdx), %ymm6, %ymm5 |
| |
| /* low K bits */ |
| vandps __lbLOWKBITS(%rdx), %ymm14, %ymm6 |
| |
| /* dpP= _dbT+lJ*T_ITEM_GRAN */ |
| vxorpd %ymm7, %ymm7, %ymm7 |
| vpcmpeqd %ymm1, %ymm1, %ymm1 |
| vandps __lbLOWKBITS(%rdx), %ymm13, %ymm2 |
| vxorpd %ymm10, %ymm10, %ymm10 |
| vpcmpeqd %ymm3, %ymm3, %ymm3 |
| vgatherqpd %ymm1, 13952(%rdx,%ymm6,8), %ymm7 |
| vgatherqpd %ymm3, 13952(%rdx,%ymm2,8), %ymm10 |
| vpsrlq $11, %ymm14, %ymm14 |
| vpsrlq $11, %ymm13, %ymm13 |
| vfmadd213pd %ymm7, %ymm4, %ymm7 |
| vfmadd213pd %ymm10, %ymm5, %ymm10 |
| |
| /* NB : including +/- sign for the exponent!! */ |
| vpsllq $52, %ymm14, %ymm8 |
| vpsllq $52, %ymm13, %ymm11 |
| vpaddq %ymm8, %ymm7, %ymm12 |
| vpaddq %ymm11, %ymm10, %ymm1 |
| vcvtpd2ps %ymm12, %xmm15 |
| vcvtpd2ps %ymm1, %xmm2 |
| vinsertf128 $1, %xmm2, %ymm15, %ymm1 |
| testl %ecx, %ecx |
| jne .LBL_1_3 |
| |
| .LBL_1_2: |
| cfi_remember_state |
| vmovups 160(%rsp), %ymm8 |
| vmovups 96(%rsp), %ymm9 |
| vmovups 288(%rsp), %ymm10 |
| vmovups 384(%rsp), %ymm11 |
| vmovups 256(%rsp), %ymm12 |
| vmovups 224(%rsp), %ymm13 |
| vmovups 320(%rsp), %ymm14 |
| vmovups 352(%rsp), %ymm15 |
| vmovdqa %ymm1, %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 |
| vmovups %ymm0, 64(%rsp) |
| vmovups %ymm9, 128(%rsp) |
| vmovups %ymm1, 192(%rsp) |
| je .LBL_1_2 |
| |
| xorb %dl, %dl |
| xorl %eax, %eax |
| movq %rsi, 8(%rsp) |
| movq %rdi, (%rsp) |
| movq %r12, 40(%rsp) |
| cfi_offset_rel_rsp (12, 40) |
| movb %dl, %r12b |
| movq %r13, 32(%rsp) |
| cfi_offset_rel_rsp (13, 32) |
| movl %ecx, %r13d |
| movq %r14, 24(%rsp) |
| cfi_offset_rel_rsp (14, 24) |
| movl %eax, %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) |
| vmovups 192(%rsp), %ymm1 |
| jmp .LBL_1_2 |
| |
| .LBL_1_10: |
| cfi_restore_state |
| movzbl %r12b, %r15d |
| vmovss 68(%rsp,%r15,8), %xmm0 |
| vmovss 132(%rsp,%r15,8), %xmm1 |
| vzeroupper |
| |
| call JUMPTARGET(__powf_finite) |
| |
| vmovss %xmm0, 196(%rsp,%r15,8) |
| jmp .LBL_1_8 |
| |
| .LBL_1_12: |
| movzbl %r12b, %r15d |
| vmovss 64(%rsp,%r15,8), %xmm0 |
| vmovss 128(%rsp,%r15,8), %xmm1 |
| vzeroupper |
| |
| call JUMPTARGET(__powf_finite) |
| |
| vmovss %xmm0, 192(%rsp,%r15,8) |
| jmp .LBL_1_7 |
| |
| END(_ZGVdN8vv_powf_avx2) |
| |
| .section .rodata, "a" |
| __VPACK_ODD_ind.6357.0.1: |
| .long 1 |
| .long 3 |
| .long 5 |
| .long 7 |
| .long 0 |
| .long 0 |
| .long 0 |
| .long 0 |
| .space 32, 0x00 |
| __VPACK_ODD_ind.6358.0.1: |
| .long 1 |
| .long 3 |
| .long 5 |
| .long 7 |
| .long 0 |
| .long 0 |
| .long 0 |
| .long 0 |
