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/* Function expm1 vectorized with AVX-512.
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:
* After computing exp(x) in high-low parts, an accurate computation is performed to obtain exp(x)-1
* Typical exp() implementation, except that:
* - tables are small (16 elements), allowing for fast gathers
* - all arguments processed in the main path
* - final VSCALEF assists branch-free design (correct overflow/underflow and special case responses)
* - a VAND is used to ensure the reduced argument |R|<2, even for large inputs
* - RZ mode used to avoid oveflow to +/-Inf for x*log2(e); helps with special case handling
*
*
*/
/* Offsets for data table __svml_dexpm1_data_internal_avx512
*/
#define Exp_tbl_H 0
#define Exp_tbl_L 128
#define L2E 256
#define Shifter 320
#define Threshold 384
#define SgnMask 448
#define L2H 512
#define L2L 576
#define ZThres 640
#define EMask 704
#define poly_coeff7 768
#define poly_coeff6 832
#define poly_coeff5 896
#define poly_coeff4 960
#define poly_coeff3 1024
#define poly_coeff2 1088
#define One 1152
#include <sysdep.h>
.text
.section .text.evex512,"ax",@progbits
ENTRY(_ZGVeN8v_expm1_skx)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-64, %rsp
subq $192, %rsp
vmovups L2E+__svml_dexpm1_data_internal_avx512(%rip), %zmm6
vmovups Shifter+__svml_dexpm1_data_internal_avx512(%rip), %zmm4
vmovups L2H+__svml_dexpm1_data_internal_avx512(%rip), %zmm11
vmovups L2L+__svml_dexpm1_data_internal_avx512(%rip), %zmm5
vmovups Threshold+__svml_dexpm1_data_internal_avx512(%rip), %zmm3
vmovups poly_coeff5+__svml_dexpm1_data_internal_avx512(%rip), %zmm13
vmovups poly_coeff4+__svml_dexpm1_data_internal_avx512(%rip), %zmm15
/* polynomial */
vmovups poly_coeff7+__svml_dexpm1_data_internal_avx512(%rip), %zmm12
/* set Z0=max(Z0, -128.0) */
vmovups ZThres+__svml_dexpm1_data_internal_avx512(%rip), %zmm8
vmovups poly_coeff3+__svml_dexpm1_data_internal_avx512(%rip), %zmm14
vmovups __svml_dexpm1_data_internal_avx512(%rip), %zmm9
vmovaps %zmm0, %zmm2
/* 2^(52-4)*1.5 + x * log2(e) */
vfmadd213pd {rn-sae}, %zmm4, %zmm2, %zmm6
vmovups Exp_tbl_L+__svml_dexpm1_data_internal_avx512(%rip), %zmm0
vcmppd $21, {sae}, %zmm3, %zmm2, %k0
/* Z0 ~ x*log2(e), rounded to 4 fractional bits */
vsubpd {rn-sae}, %zmm4, %zmm6, %zmm7
vpermt2pd Exp_tbl_H+64+__svml_dexpm1_data_internal_avx512(%rip), %zmm6, %zmm9
vpermt2pd Exp_tbl_L+64+__svml_dexpm1_data_internal_avx512(%rip), %zmm6, %zmm0
vandpd SgnMask+__svml_dexpm1_data_internal_avx512(%rip), %zmm2, %zmm1
/* R = x - Z0*log(2) */
vfnmadd213pd {rn-sae}, %zmm2, %zmm7, %zmm11
vmaxpd {sae}, %zmm8, %zmm7, %zmm10
vfnmadd231pd {rn-sae}, %zmm7, %zmm5, %zmm11
kmovw %k0, %edx
/* ensure |R|<2 even for special cases */
vandpd EMask+__svml_dexpm1_data_internal_avx512(%rip), %zmm11, %zmm3
vmovups poly_coeff6+__svml_dexpm1_data_internal_avx512(%rip), %zmm11
/* scale Th */
vscalefpd {rn-sae}, %zmm10, %zmm9, %zmm4
vfmadd231pd {rn-sae}, %zmm3, %zmm13, %zmm15
vfmadd231pd {rn-sae}, %zmm3, %zmm12, %zmm11
vmovups poly_coeff2+__svml_dexpm1_data_internal_avx512(%rip), %zmm12
vmulpd {rn-sae}, %zmm3, %zmm3, %zmm13
vfmadd231pd {rn-sae}, %zmm3, %zmm14, %zmm12
vfmadd213pd {rn-sae}, %zmm15, %zmm13, %zmm11
vfmadd213pd {rn-sae}, %zmm12, %zmm13, %zmm11
/* Tlr + R+ R*Poly */
vfmadd213pd {rn-sae}, %zmm0, %zmm13, %zmm11
/* Th - 1 */
vmovups One+__svml_dexpm1_data_internal_avx512(%rip), %zmm0
vaddpd {rn-sae}, %zmm3, %zmm11, %zmm14
vsubpd {rn-sae}, %zmm0, %zmm4, %zmm15
/* (Th-1)+Th*(Tlr + R+ R*Poly) */
vfmadd213pd {rn-sae}, %zmm15, %zmm14, %zmm4
vorpd %zmm1, %zmm4, %zmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm2
/* 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 %zmm2, 64(%rsp)
vmovups %zmm0, 128(%rsp)
# LOE rbx r12 r13 r14 r15 edx zmm0
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: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 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: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 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 128(%rsp), %zmm0
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 zmm0
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movsd 64(%rsp,%r14,8), %xmm0
call expm1@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movsd %xmm0, 128(%rsp,%r14,8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN8v_expm1_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dexpm1_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Exp_tbl_H[16][2];
__declspec(align(64)) VUINT32 Exp_tbl_L[16][2];
__declspec(align(64)) VUINT32 L2E[8][2];
__declspec(align(64)) VUINT32 Shifter[8][2];
__declspec(align(64)) VUINT32 Threshold[8][2];
__declspec(align(64)) VUINT32 SgnMask[8][2];
__declspec(align(64)) VUINT32 L2H[8][2];
__declspec(align(64)) VUINT32 L2L[8][2];
__declspec(align(64)) VUINT32 ZThres[8][2];
__declspec(align(64)) VUINT32 EMask[8][2];
__declspec(align(64)) VUINT32 poly_coeff7[8][2];
__declspec(align(64)) VUINT32 poly_coeff6[8][2];
__declspec(align(64)) VUINT32 poly_coeff5[8][2];
__declspec(align(64)) VUINT32 poly_coeff4[8][2];
__declspec(align(64)) VUINT32 poly_coeff3[8][2];
__declspec(align(64)) VUINT32 poly_coeff2[8][2];
__declspec(align(64)) VUINT32 One[8][2];
} __svml_dexpm1_data_internal_avx512;
#endif
__svml_dexpm1_data_internal_avx512:
/*== Exp_tbl_H ==*/
.quad 0x3ff0000000000000
.quad 0x3ff0b5586cf9890f
.quad 0x3ff172b83c7d517b
.quad 0x3ff2387a6e756238
.quad 0x3ff306fe0a31b715
.quad 0x3ff3dea64c123422
.quad 0x3ff4bfdad5362a27
.quad 0x3ff5ab07dd485429
.quad 0x3ff6a09e667f3bcd
.quad 0x3ff7a11473eb0187
.quad 0x3ff8ace5422aa0db
.quad 0x3ff9c49182a3f090
.quad 0x3ffae89f995ad3ad
.quad 0x3ffc199bdd85529c
.quad 0x3ffd5818dcfba487
.quad 0x3ffea4afa2a490da
/*== Exp_tbl_L ==*/
.align 64
.quad 0x0000000000000000
.quad 0x3c979aa65d837b6d
.quad 0xbc801b15eaa59348
.quad 0x3c968efde3a8a894
.quad 0x3c834d754db0abb6
.quad 0x3c859f48a72a4c6d
.quad 0x3c7690cebb7aafb0
.quad 0x3c9063e1e21c5409
.quad 0xbc93b3efbf5e2228
.quad 0xbc7b32dcb94da51d
.quad 0x3c8db72fc1f0eab4
.quad 0x3c71affc2b91ce27
.quad 0x3c8c1a7792cb3387
.quad 0x3c736eae30af0cb3
.quad 0x3c74a385a63d07a7
.quad 0xbc8ff7128fd391f0
/*== log2(e) ==*/
.align 64
.quad 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE, 0x3ff71547652B82FE
/*== Shifter=2^(52-4)*1.5 ==*/
.align 64
.quad 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0
/*== Threshold ==*/
.align 64
.quad 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44, 0x40861DA04CBAFE44
/*== Sgn ==*/
.align 64
.quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
/*== L2H = log(2)_high ==*/
.align 64
.quad 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef, 0x3fe62e42fefa39ef
/*== L2L = log(2)_low ==*/
.align 64
.quad 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f, 0x3c7abc9e3b39803f
/*== ZThres ==*/
.align 64
.quad 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000, 0xc060000000000000
/*== EMask ==*/
.align 64
.quad 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff
/*== poly_coeff7 ==*/
.align 64
.quad 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a, 0x3f2a020410303d8a
/*== poly_coeff6 ==*/
.align 64
.quad 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f, 0x3f56c1c38e164a2f
/*== poly_coeff5 ==*/
.align 64
.quad 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214, 0x3f81111110865214
/*== poly_coeff4 ==*/
.align 64
.quad 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06, 0x3fa5555554ad3d06
/*== poly_coeff3 ==*/
.align 64
.quad 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656, 0x3fc5555555555656
/*== poly_coeff2 ==*/
.align 64
.quad 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2, 0x3fe00000000000a2
/*== One ==*/
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
.align 64
.type __svml_dexpm1_data_internal_avx512,@object
.size __svml_dexpm1_data_internal_avx512,.-__svml_dexpm1_data_internal_avx512
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