/* 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)