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/* Function expm1f vectorized with AVX-512.
Copyright (C) 2021-2023 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 (32 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_sexpm1_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 EMask 640
#define poly_coeff3 704
#define poly_coeff2 768
#define One 832
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_expm1f_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_sexpm1_data_internal_avx512(%rip), %zmm5
vmovups Shifter+__svml_sexpm1_data_internal_avx512(%rip), %zmm3
vmovups L2H+__svml_sexpm1_data_internal_avx512(%rip), %zmm8
vmovups L2L+__svml_sexpm1_data_internal_avx512(%rip), %zmm4
vmovups __svml_sexpm1_data_internal_avx512(%rip), %zmm6
/* polynomial */
vmovups poly_coeff3+__svml_sexpm1_data_internal_avx512(%rip), %zmm9
vmovups poly_coeff2+__svml_sexpm1_data_internal_avx512(%rip), %zmm12
vmovups Exp_tbl_L+__svml_sexpm1_data_internal_avx512(%rip), %zmm11
vmovups Threshold+__svml_sexpm1_data_internal_avx512(%rip), %zmm2
/* Th - 1 */
vmovups One+__svml_sexpm1_data_internal_avx512(%rip), %zmm14
vmovaps %zmm0, %zmm1
/* 2^(52-5)*1.5 + x * log2(e) */
vfmadd213ps {rn-sae}, %zmm3, %zmm1, %zmm5
vcmpps $29, {sae}, %zmm2, %zmm1, %k0
/* Z0 ~ x*log2(e), rounded to 5 fractional bits */
vsubps {rn-sae}, %zmm3, %zmm5, %zmm7
vpermt2ps Exp_tbl_H+64+__svml_sexpm1_data_internal_avx512(%rip), %zmm5, %zmm6
vpermt2ps Exp_tbl_L+64+__svml_sexpm1_data_internal_avx512(%rip), %zmm5, %zmm11
vandps SgnMask+__svml_sexpm1_data_internal_avx512(%rip), %zmm1, %zmm0
/* R = x - Z0*log(2) */
vfnmadd213ps {rn-sae}, %zmm1, %zmm7, %zmm8
/* scale Th */
vscalefps {rn-sae}, %zmm7, %zmm6, %zmm2
vfnmadd231ps {rn-sae}, %zmm7, %zmm4, %zmm8
kmovw %k0, %edx
/* ensure |R|<2 even for special cases */
vandps EMask+__svml_sexpm1_data_internal_avx512(%rip), %zmm8, %zmm13
vsubps {rn-sae}, %zmm14, %zmm2, %zmm8
vmulps {rn-sae}, %zmm13, %zmm13, %zmm10
vfmadd231ps {rn-sae}, %zmm13, %zmm9, %zmm12
/* Tlr + R+ R2*Poly */
vfmadd213ps {rn-sae}, %zmm11, %zmm10, %zmm12
vaddps {rn-sae}, %zmm13, %zmm12, %zmm15
/* (Th-1)+Th*(Tlr + R+ R*Poly) */
vfmadd213ps {rn-sae}, %zmm8, %zmm15, %zmm2
vorps %zmm0, %zmm2, %zmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm1
/* 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 %zmm1, 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 $16, %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
vmovss 64(%rsp, %r14, 4), %xmm0
call expm1f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovss %xmm0, 128(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN16v_expm1f_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_sexpm1_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Exp_tbl_H[32][1];
__declspec(align(64)) VUINT32 Exp_tbl_L[32][1];
__declspec(align(64)) VUINT32 L2E[16][1];
__declspec(align(64)) VUINT32 Shifter[16][1];
__declspec(align(64)) VUINT32 Threshold[16][1];
__declspec(align(64)) VUINT32 SgnMask[16][1];
__declspec(align(64)) VUINT32 L2H[16][1];
__declspec(align(64)) VUINT32 L2L[16][1];
__declspec(align(64)) VUINT32 EMask[16][1];
__declspec(align(64)) VUINT32 poly_coeff3[16][1];
__declspec(align(64)) VUINT32 poly_coeff2[16][1];
__declspec(align(64)) VUINT32 One[16][1];
} __svml_sexpm1_data_internal_avx512;
#endif
__svml_sexpm1_data_internal_avx512:
/* Exp_tbl_H */
.long 0x3f800000, 0x3f82cd87, 0x3f85aac3, 0x3f88980f
.long 0x3f8b95c2, 0x3f8ea43a, 0x3f91c3d3, 0x3f94f4f0
.long 0x3f9837f0, 0x3f9b8d3a, 0x3f9ef532, 0x3fa27043
.long 0x3fa5fed7, 0x3fa9a15b, 0x3fad583f, 0x3fb123f6
.long 0x3fb504f3, 0x3fb8fbaf, 0x3fbd08a4, 0x3fc12c4d
.long 0x3fc5672a, 0x3fc9b9be, 0x3fce248c, 0x3fd2a81e
.long 0x3fd744fd, 0x3fdbfbb8, 0x3fe0ccdf, 0x3fe5b907
.long 0x3feac0c7, 0x3fefe4ba, 0x3ff5257d, 0x3ffa83b3
/* Exp_tbl_L */
.align 64
.long 0x00000000, 0xb34a3a0a, 0x3346cb6a, 0xb36ed17e
.long 0xb24e0611, 0xb3517dd9, 0x334b2482, 0xb31586de
.long 0x33092801, 0xb2e6f467, 0x331b85f2, 0x3099b6f1
.long 0xb3051aa8, 0xb2e2a0da, 0xb2006c56, 0xb3365942
.long 0x329302ae, 0x32c595dc, 0xb302e5a2, 0xb28e10a1
.long 0x31b3d0e5, 0xb31a472b, 0x31d1daf2, 0xb305bf64
.long 0xb27ce182, 0xb2f26443, 0xb1b4b0da, 0xb1da8a8f
.long 0xb1d290be, 0xb2d5b899, 0x31b0a147, 0xb2156afc
/* log2(e) */
.align 64
.long 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B, 0x3fB8AA3B
/* Shifter=2^(23-5)*1.5 */
.align 64
.long 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000, 0x48c00000
/* Threshold */
.align 64
.long 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B, 0x42AD496B
/* Sgn */
.align 64
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
/* L2H = log(2)_high */
.align 64
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
/* L2L = log(2)_low */
.align 64
.long 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308, 0xb102e308
/* EMask */
.align 64
.long 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff, 0xbfffffff
/* poly_coeff3 */
.align 64
.long 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3, 0x3e2AABF3
/* poly_coeff2 */
.align 64
.long 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6, 0x3f0000F6
/* One */
.align 64
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
.align 64
.type __svml_sexpm1_data_internal_avx512, @object
.size __svml_sexpm1_data_internal_avx512, .-__svml_sexpm1_data_internal_avx512
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