| /* Function exp vectorized with AVX-512. KNL and SKX versions. |
| 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_exp_data.h" |
| #include "svml_d_wrapper_impl.h" |
| |
| .text |
| ENTRY (_ZGVeN8v_exp_knl) |
| #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
| WRAPPER_IMPL_AVX512 _ZGVdN4v_exp |
| #else |
| /* |
| ALGORITHM DESCRIPTION: |
| |
| Argument representation: |
| N = rint(X*2^k/ln2) = 2^k*M+j |
| X = N*ln2/2^k + r = M*ln2 + ln2*(j/2^k) + r |
| then -ln2/2^(k+1) < r < ln2/2^(k+1) |
| Alternatively: |
| N = trunc(X*2^k/ln2) |
| then 0 < r < ln2/2^k |
| |
| Result calculation: |
| exp(X) = exp(M*ln2 + ln2*(j/2^k) + r) |
| = 2^M * 2^(j/2^k) * exp(r) |
| 2^M is calculated by bit manipulation |
| 2^(j/2^k) is stored in table |
| exp(r) is approximated by polynomial |
| |
| The table lookup is skipped if k = 0. */ |
| |
| pushq %rbp |
| cfi_adjust_cfa_offset (8) |
| cfi_rel_offset (%rbp, 0) |
| movq %rsp, %rbp |
| cfi_def_cfa_register (%rbp) |
| andq $-64, %rsp |
| subq $1280, %rsp |
| movq __svml_dexp_data@GOTPCREL(%rip), %rax |
| |
| /* dR = X - dN*dbLn2hi, dbLn2hi is 52-8-k hi bits of ln2/2^k */ |
| vmovaps %zmm0, %zmm8 |
| |
| /* iAbsX = (int)(lX>>32), lX = *(longlong*)&X */ |
| vpsrlq $32, %zmm0, %zmm1 |
| |
| /* iAbsX = iAbsX&iAbsMask */ |
| movl $255, %edx |
| vpmovqd %zmm1, %ymm2 |
| kmovw %edx, %k2 |
| |
| /* iRangeMask = (iAbsX>iDomainRange) */ |
| movl $-1, %ecx |
| |
| /* table lookup for dT[j] = 2^(j/2^k) */ |
| vpxord %zmm11, %zmm11, %zmm11 |
| vmovups __dbInvLn2(%rax), %zmm5 |
| vmovups __dbLn2hi(%rax), %zmm7 |
| kxnorw %k3, %k3, %k3 |
| |
| /* dM = X*dbInvLn2+dbShifter, dbInvLn2 = 2^k/Ln2 */ |
| vfmadd213pd __dbShifter(%rax), %zmm0, %zmm5 |
| vmovups __dPC2(%rax), %zmm12 |
| |
| /* dN = dM-dbShifter, dN = rint(X*2^k/Ln2) */ |
| vsubpd __dbShifter(%rax), %zmm5, %zmm9 |
| vmovups __lIndexMask(%rax), %zmm4 |
| vfnmadd231pd %zmm9, %zmm7, %zmm8 |
| vpandd __iAbsMask(%rax), %zmm2, %zmm2{%k2} |
| |
| /* lIndex = (*(longlong*)&dM)&lIndexMask, lIndex is the lower K bits of lM */ |
| vpandq %zmm4, %zmm5, %zmm10 |
| vgatherqpd (%rax,%zmm10,8), %zmm11{%k3} |
| vpcmpgtd __iDomainRange(%rax), %zmm2, %k1{%k2} |
| |
| /* lM = (*(longlong*)&dM)&(~lIndexMask) */ |
| vpandnq %zmm5, %zmm4, %zmm6 |
| vpbroadcastd %ecx, %zmm3{%k1}{z} |
| |
| /* lM = lM<<(52-K), 2^M */ |
| vpsllq $42, %zmm6, %zmm14 |
| |
| /* dR = dR - dN*dbLn2lo, dbLn2lo is 40..94 bits of lo part of ln2/2^k */ |
| vfnmadd132pd __dbLn2lo(%rax), %zmm8, %zmm9 |
| |
| /* Mask = iRangeMask?1:0, set mask for overflow/underflow */ |
| vptestmd %zmm3, %zmm3, %k0{%k2} |
| |
| /* exp(r) = b0+r*(b0+r*(b1+r*b2)) */ |
| vfmadd213pd __dPC1(%rax), %zmm9, %zmm12 |
| kmovw %k0, %ecx |
| movzbl %cl, %ecx |
| vfmadd213pd __dPC0(%rax), %zmm9, %zmm12 |
| vfmadd213pd __dPC0(%rax), %zmm9, %zmm12 |
| |
| /* 2^(j/2^k) * exp(r) */ |
| vmulpd %zmm12, %zmm11, %zmm13 |
| |
| /* multiply by 2^M through integer add */ |
| vpaddq %zmm14, %zmm13, %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 %zmm1, 1216(%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 1216(%rsp), %zmm1 |
| jmp .LBL_1_2 |
| |
| .LBL_1_10: |
| cfi_restore_state |
| movzbl %r12b, %r15d |
| shlq $4, %r15 |
| vmovsd 1160(%rsp,%r15), %xmm0 |
| call JUMPTARGET(__exp_finite) |
| vmovsd %xmm0, 1224(%rsp,%r15) |
| jmp .LBL_1_8 |
| |
| .LBL_1_12: |
| movzbl %r12b, %r15d |
| shlq $4, %r15 |
| vmovsd 1152(%rsp,%r15), %xmm0 |
| call JUMPTARGET(__exp_finite) |
| vmovsd %xmm0, 1216(%rsp,%r15) |
| jmp .LBL_1_7 |
| #endif |
| END (_ZGVeN8v_exp_knl) |
| |
| ENTRY (_ZGVeN8v_exp_skx) |
| #ifndef HAVE_AVX512DQ_ASM_SUPPORT |
| WRAPPER_IMPL_AVX512 _ZGVdN4v_exp |
| #else |
| /* |
| ALGORITHM DESCRIPTION: |
| |
| Argument representation: |
| N = rint(X*2^k/ln2) = 2^k*M+j |
| X = N*ln2/2^k + r = M*ln2 + ln2*(j/2^k) + r |
| then -ln2/2^(k+1) < r < ln2/2^(k+1) |
| Alternatively: |
| N = trunc(X*2^k/ln2) |
| then 0 < r < ln2/2^k |
| |
| Result calculation: |
| exp(X) = exp(M*ln2 + ln2*(j/2^k) + r) |
| = 2^M * 2^(j/2^k) * exp(r) |
| 2^M is calculated by bit manipulation |
| 2^(j/2^k) is stored in table |
| exp(r) is approximated by polynomial |
| |
| The table lookup is skipped if k = 0. */ |
| |
| pushq %rbp |
| cfi_adjust_cfa_offset (8) |
| cfi_rel_offset (%rbp, 0) |
| movq %rsp, %rbp |
| cfi_def_cfa_register (%rbp) |
| andq $-64, %rsp |
| subq $1280, %rsp |
| movq __svml_dexp_data@GOTPCREL(%rip), %rax |
| |
| /* table lookup for dT[j] = 2^(j/2^k) */ |
| kxnorw %k1, %k1, %k1 |
| |
| /* iAbsX = (int)(lX>>32), lX = *(longlong*)&X */ |
| vpsrlq $32, %zmm0, %zmm1 |
| vmovups __dbInvLn2(%rax), %zmm7 |
| vmovups __dbShifter(%rax), %zmm5 |
| vmovups __lIndexMask(%rax), %zmm6 |
| vmovups __dbLn2hi(%rax), %zmm9 |
| vmovups __dPC0(%rax), %zmm12 |
| |
| /* dM = X*dbInvLn2+dbShifter, dbInvLn2 = 2^k/Ln2 */ |
| vfmadd213pd %zmm5, %zmm0, %zmm7 |
| vpmovqd %zmm1, %ymm2 |
| |
| /* dN = dM-dbShifter, dN = rint(X*2^k/Ln2) */ |
| vsubpd %zmm5, %zmm7, %zmm11 |
| |
| /* iAbsX = iAbsX&iAbsMask */ |
| vpand __iAbsMask(%rax), %ymm2, %ymm3 |
| |
| /* dR = X - dN*dbLn2hi, dbLn2hi is 52-8-k hi bits of ln2/2^k */ |
| vmovaps %zmm0, %zmm10 |
| vfnmadd231pd %zmm11, %zmm9, %zmm10 |
| vmovups __dPC2(%rax), %zmm9 |
| |
| /* dR = dR - dN*dbLn2lo, dbLn2lo is 40..94 bits of lo part of ln2/2^k */ |
| vfnmadd132pd __dbLn2lo(%rax), %zmm10, %zmm11 |
| |
| /* exp(r) = b0+r*(b0+r*(b1+r*b2)) */ |
| vfmadd213pd __dPC1(%rax), %zmm11, %zmm9 |
| vfmadd213pd %zmm12, %zmm11, %zmm9 |
| vfmadd213pd %zmm12, %zmm11, %zmm9 |
| |
| /* iRangeMask = (iAbsX>iDomainRange) */ |
| vpcmpgtd __iDomainRange(%rax), %ymm3, %ymm4 |
| |
| /* Mask = iRangeMask?1:0, set mask for overflow/underflow */ |
| vmovmskps %ymm4, %ecx |
| |
| /* lIndex = (*(longlong*)&dM)&lIndexMask, lIndex is the lower K bits of lM */ |
| vpandq %zmm6, %zmm7, %zmm13 |
| vpmovqd %zmm13, %ymm14 |
| vpxord %zmm15, %zmm15, %zmm15 |
| vgatherdpd (%rax,%ymm14,8), %zmm15{%k1} |
| |
| /* 2^(j/2^k) * exp(r) */ |
| vmulpd %zmm9, %zmm15, %zmm10 |
| |
| /* lM = (*(longlong*)&dM)&(~lIndexMask) */ |
| vpandnq %zmm7, %zmm6, %zmm8 |
| |
| /* lM = lM<<(52-K), 2^M */ |
| vpsllq $42, %zmm8, %zmm1 |
| |
| /* multiply by 2^M through integer add */ |
| vpaddq %zmm1, %zmm10, %zmm1 |
| testl %ecx, %ecx |
| jne .LBL_2_3 |
| |
| .LBL_2_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_2_3: |
| cfi_restore_state |
| vmovups %zmm0, 1152(%rsp) |
| vmovups %zmm1, 1216(%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 1216(%rsp), %zmm1 |
| 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 1160(%rsp,%r15), %xmm0 |
| vzeroupper |
| vmovsd 1160(%rsp,%r15), %xmm0 |
| call JUMPTARGET(__exp_finite) |
| vmovsd %xmm0, 1224(%rsp,%r15) |
| jmp .LBL_2_8 |
| |
| .LBL_2_12: |
| movzbl %r12b, %r15d |
| shlq $4, %r15 |
| vmovsd 1152(%rsp,%r15), %xmm0 |
| vzeroupper |
| vmovsd 1152(%rsp,%r15), %xmm0 |
| call JUMPTARGET(__exp_finite) |
| vmovsd %xmm0, 1216(%rsp,%r15) |
| jmp .LBL_2_7 |
| |
| #endif |
| END (_ZGVeN8v_exp_skx) |
