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/* Function exp10f vectorized with AVX2.
Copyright (C) 2021-2022 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
https://www.gnu.org/licenses/. */
/*
* ALGORITHM DESCRIPTION:
*
* exp10(x) = 2^x/log10(2) = 2^n * (1 + T[j]) * (1 + P(y))
* where
* x = m*log10(2)/K + y, y in [-log10(2)/K..log10(2)/K]
* m = n*K + j, m, n,j - signed integer, j in [-K/2..K/2]
*
* values of 2^j/K are tabulated
*
* P(y) is a minimax polynomial approximation of exp10(x)-1
* on small interval [-log10(2)/K..log10(2)/K]
*
* Special cases:
*
* exp10(NaN) = NaN
* exp10(+INF) = +INF
* exp10(-INF) = 0
* exp10(x) = 1 for subnormals
* For IEEE float
* if x > 38.5318412780761720 then exp10f(x) overflow
* if x < -45.4555282592773440 then exp10f(x) underflow
*
*/
/* Offsets for data table __svml_sexp10_data_internal
*/
#define _sT 0
#define _sLg2_10 128
#define _sShifter 160
#define _sInvLg2_10hi 192
#define _sInvLg2_10lo 224
#define _sPC0 256
#define _sPC1 288
#define _sPC2 320
#define _iIndexMask 352
#define _iAbsMask 384
#define _iDomainRange 416
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_exp10f_avx2)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-32, %rsp
subq $96, %rsp
lea __svml_sexp10_data_internal(%rip), %rax
vmovups _sShifter+__svml_sexp10_data_internal(%rip), %ymm4
/* Load arument */
vmovups _sLg2_10+__svml_sexp10_data_internal(%rip), %ymm1
vmovups _iIndexMask+__svml_sexp10_data_internal(%rip), %ymm2
vmovaps %ymm0, %ymm3
vfmadd213ps %ymm4, %ymm3, %ymm1
/* Index and lookup */
vandps %ymm2, %ymm1, %ymm7
/* iIndex *= sizeof(S); */
vpslld $2, %ymm7, %ymm10
vsubps %ymm4, %ymm1, %ymm0
/* Check for overflow\underflow */
vandps _iAbsMask+__svml_sexp10_data_internal(%rip), %ymm3, %ymm5
vpcmpgtd _iDomainRange+__svml_sexp10_data_internal(%rip), %ymm5, %ymm6
vmovmskps %ymm6, %edx
vmovd %xmm10, %ecx
vextractf128 $1, %ymm10, %xmm6
vpextrd $1, %xmm10, %esi
vpextrd $2, %xmm10, %edi
vpextrd $3, %xmm10, %r8d
movslq %ecx, %rcx
movslq %esi, %rsi
movslq %edi, %rdi
movslq %r8d, %r8
vmovd (%rax, %rcx), %xmm8
vmovd (%rax, %rsi), %xmm9
vmovd (%rax, %rdi), %xmm11
vmovd (%rax, %r8), %xmm12
vpunpckldq %xmm9, %xmm8, %xmm13
vpunpckldq %xmm12, %xmm11, %xmm14
vpunpcklqdq %xmm14, %xmm13, %xmm15
/* R */
vmovups _sInvLg2_10hi+__svml_sexp10_data_internal(%rip), %ymm13
vmovd %xmm6, %r9d
vfnmadd213ps %ymm3, %ymm0, %ymm13
vpextrd $1, %xmm6, %r10d
movslq %r9d, %r9
movslq %r10d, %r10
vfnmadd132ps _sInvLg2_10lo+__svml_sexp10_data_internal(%rip), %ymm13, %ymm0
vmovd (%rax, %r9), %xmm4
vmovd (%rax, %r10), %xmm5
vpunpckldq %xmm5, %xmm4, %xmm9
/*
* Polynomial
* exp10 = 2^N*(Tj+Tj*poly)
* poly(sN) = {1+later} a0+a1*sR
*/
vmovups _sPC2+__svml_sexp10_data_internal(%rip), %ymm4
vfmadd213ps _sPC1+__svml_sexp10_data_internal(%rip), %ymm0, %ymm4
vpextrd $2, %xmm6, %r11d
vpextrd $3, %xmm6, %ecx
movslq %r11d, %r11
movslq %ecx, %rcx
vfmadd213ps _sPC0+__svml_sexp10_data_internal(%rip), %ymm0, %ymm4
vmovd (%rax, %r11), %xmm7
vmovd (%rax, %rcx), %xmm8
vpunpckldq %xmm8, %xmm7, %xmm11
/* remove index bits */
vpandn %ymm1, %ymm2, %ymm0
vpunpcklqdq %xmm11, %xmm9, %xmm12
/* 2^N */
vpslld $18, %ymm0, %ymm1
vinsertf128 $1, %xmm12, %ymm15, %ymm14
/* Tj_l+Tj_h*poly */
vfmadd213ps %ymm14, %ymm14, %ymm4
/* quick mul 2^N */
vpaddd %ymm1, %ymm4, %ymm0
/* Finish */
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm3
/* Restore registers
* and exit the function
*/
L(EXIT):
movq %rbp, %rsp
popq %rbp
cfi_def_cfa(7, 8)
cfi_restore(6)
ret
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
vmovups %ymm3, 32(%rsp)
vmovups %ymm0, 64(%rsp)
# LOE rbx r12 r13 r14 r15 edx ymm0
xorl %eax, %eax
# LOE rbx r12 r13 r14 r15 eax edx
vzeroupper
movq %r12, 16(%rsp)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
movl %eax, %r12d
movq %r13, 8(%rsp)
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $8, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
vmovups 64(%rsp), %ymm0
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 ymm0
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovss 32(%rsp, %r14, 4), %xmm0
call exp10f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovss %xmm0, 64(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN8v_exp10f_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_sexp10_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 _sT[(1<<5)][1];
__declspec(align(32)) VUINT32 _sLg2_10[8][1];
__declspec(align(32)) VUINT32 _sShifter[8][1];
__declspec(align(32)) VUINT32 _sInvLg2_10hi[8][1];
__declspec(align(32)) VUINT32 _sInvLg2_10lo[8][1];
__declspec(align(32)) VUINT32 _sPC0[8][1];
__declspec(align(32)) VUINT32 _sPC1[8][1];
__declspec(align(32)) VUINT32 _sPC2[8][1];
__declspec(align(32)) VUINT32 _iIndexMask[8][1];
__declspec(align(32)) VUINT32 _iAbsMask[8][1];
__declspec(align(32)) VUINT32 _iDomainRange[8][1];
} __svml_sexp10_data_internal;
#endif
__svml_sexp10_data_internal:
/* _sT */
.long 0x3f800000 // 2^( 0 /32 )
.long 0x3f82cd87 // 2^( 1 /32 )
.long 0x3f85aac3 // 2^( 2 /32 )
.long 0x3f88980f // 2^( 3 /32 )
.long 0x3f8b95c2 // 2^( 4 /32 )
.long 0x3f8ea43a // 2^( 5 /32 )
.long 0x3f91c3d3 // 2^( 6 /32 )
.long 0x3f94f4f0 // 2^( 7 /32 )
.long 0x3f9837f0 // 2^( 8 /32 )
.long 0x3f9b8d3a // 2^( 9 /32 )
.long 0x3f9ef532 // 2^( 10/32 )
.long 0x3fa27043 // 2^( 11/32 )
.long 0x3fa5fed7 // 2^( 12/32 )
.long 0x3fa9a15b // 2^( 13/32 )
.long 0x3fad583f // 2^( 14/32 )
.long 0x3fb123f6 // 2^( 15/32 )
.long 0x3fb504f3 // 2^( 16/32 )
.long 0x3fb8fbaf // 2^( 17/32 )
.long 0x3fbd08a4 // 2^( 18/32 )
.long 0x3fc12c4d // 2^( 19/32 )
.long 0x3fc5672a // 2^( 20/32 )
.long 0x3fc9b9be // 2^( 21/32 )
.long 0x3fce248c // 2^( 22/32 )
.long 0x3fd2a81e // 2^( 23/32 )
.long 0x3fd744fd // 2^( 24/32 )
.long 0x3fdbfbb8 // 2^( 25/32 )
.long 0x3fe0ccdf // 2^( 26/32 )
.long 0x3fe5b907 // 2^( 27/32 )
.long 0x3feac0c7 // 2^( 28/32 )
.long 0x3fefe4ba // 2^( 29/32 )
.long 0x3ff5257d // 2^( 30/32 )
.long 0x3ffa83b3 // 2^( 31/32 )
.align 32
.long 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78, 0x42d49a78 /* _sLg2_10*2^K */
.align 32
.long 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000, 0x4b400000 /* _sShifter) */
.align 32
.long 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000, 0x3c1a2000 /* _sInvLg2_10hi/2^K hi (24-K-7) bits */
.align 32
.long 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc, 0x341a84fc /* _sInvLg2_10lo/2^K lo bits */
// otherwise exp10(0) won't produce exact 1.0
.align 32
.long 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868, 0x2fecc868 /* _sPC0 */
.align 32
.long 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b, 0x40135e1b /* _sPC1 */
.align 32
.long 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2, 0x4029a8d2 /* _sPC2 */
.align 32
.long 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f, 0x0000001f /* _iIndexMask =(2^K-1) */
//common
.align 32
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */
.align 32
.long 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818, 0x4217b818 /* _iDomainRange=-log10(max_denormal=0x007fffff) RZ */
.align 32
.type __svml_sexp10_data_internal, @object
.size __svml_sexp10_data_internal, .-__svml_sexp10_data_internal
|
