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/* Function atanhf 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:
*
* Compute atanh(x) as 0.5 * log((1 + x)/(1 - x))
* using small lookup table that map to AVX-512 permute instructions
*
* Special cases:
*
* atanh(0) = 0
* atanh(+1) = +INF
* atanh(-1) = -INF
* atanh(x) = NaN if |x| > 1, or if x is a NaN or INF
*
*/
/* Offsets for data table __svml_satanh_data_internal_avx512
*/
#define Log_tbl_H 0
#define Log_tbl_L 128
#define One 256
#define AbsMask 320
#define AddB5 384
#define RcpBitMask 448
#define poly_coeff3 512
#define poly_coeff2 576
#define poly_coeff1 640
#define poly_coeff0 704
#define Half 768
#define L2H 832
#define L2L 896
#include <sysdep.h>
.text
.section .text.exex512,"ax",@progbits
ENTRY(_ZGVeN16v_atanhf_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 One+__svml_satanh_data_internal_avx512(%rip), %zmm4
/* round reciprocals to 1+5b mantissas */
vmovups AddB5+__svml_satanh_data_internal_avx512(%rip), %zmm14
vmovups RcpBitMask+__svml_satanh_data_internal_avx512(%rip), %zmm1
vmovaps %zmm0, %zmm11
vandps AbsMask+__svml_satanh_data_internal_avx512(%rip), %zmm11, %zmm6
/* 1+y */
vaddps {rn-sae}, %zmm4, %zmm6, %zmm9
/* 1-y */
vsubps {rn-sae}, %zmm6, %zmm4, %zmm8
vxorps %zmm6, %zmm11, %zmm10
/* Yp_high */
vsubps {rn-sae}, %zmm4, %zmm9, %zmm2
/* -Ym_high */
vsubps {rn-sae}, %zmm4, %zmm8, %zmm5
/* RcpP ~ 1/Yp */
vrcp14ps %zmm9, %zmm12
/* RcpM ~ 1/Ym */
vrcp14ps %zmm8, %zmm13
/* input outside (-1, 1) ? */
vcmpps $21, {sae}, %zmm4, %zmm6, %k0
vpaddd %zmm14, %zmm12, %zmm15
vpaddd %zmm14, %zmm13, %zmm0
/* Yp_low */
vsubps {rn-sae}, %zmm2, %zmm6, %zmm3
vandps %zmm1, %zmm15, %zmm7
vandps %zmm1, %zmm0, %zmm12
/* Ym_low */
vaddps {rn-sae}, %zmm5, %zmm6, %zmm5
/* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low */
vfmsub213ps {rn-sae}, %zmm4, %zmm7, %zmm9
/* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low */
vfmsub231ps {rn-sae}, %zmm12, %zmm8, %zmm4
vmovups Log_tbl_L+__svml_satanh_data_internal_avx512(%rip), %zmm8
vmovups Log_tbl_L+64+__svml_satanh_data_internal_avx512(%rip), %zmm13
/* exponents */
vgetexpps {sae}, %zmm7, %zmm15
vfmadd231ps {rn-sae}, %zmm7, %zmm3, %zmm9
/* Table lookups */
vmovups __svml_satanh_data_internal_avx512(%rip), %zmm6
vgetexpps {sae}, %zmm12, %zmm14
vfnmadd231ps {rn-sae}, %zmm12, %zmm5, %zmm4
/* Prepare table index */
vpsrld $18, %zmm7, %zmm3
vpsrld $18, %zmm12, %zmm2
vmovups Log_tbl_H+64+__svml_satanh_data_internal_avx512(%rip), %zmm7
vmovups poly_coeff1+__svml_satanh_data_internal_avx512(%rip), %zmm12
/* Km-Kp */
vsubps {rn-sae}, %zmm15, %zmm14, %zmm1
kmovw %k0, %edx
vmovaps %zmm3, %zmm0
vpermi2ps %zmm13, %zmm8, %zmm3
vpermt2ps %zmm13, %zmm2, %zmm8
vpermi2ps %zmm7, %zmm6, %zmm0
vpermt2ps %zmm7, %zmm2, %zmm6
vsubps {rn-sae}, %zmm3, %zmm8, %zmm5
/* K*L2H + Th */
vmovups L2H+__svml_satanh_data_internal_avx512(%rip), %zmm2
/* K*L2L + Tl */
vmovups L2L+__svml_satanh_data_internal_avx512(%rip), %zmm3
/* polynomials */
vmovups poly_coeff3+__svml_satanh_data_internal_avx512(%rip), %zmm7
vmovups poly_coeff0+__svml_satanh_data_internal_avx512(%rip), %zmm13
/* table values */
vsubps {rn-sae}, %zmm0, %zmm6, %zmm0
vfmadd231ps {rn-sae}, %zmm1, %zmm2, %zmm0
vfmadd213ps {rn-sae}, %zmm5, %zmm3, %zmm1
vmovups poly_coeff2+__svml_satanh_data_internal_avx512(%rip), %zmm3
vmovaps %zmm3, %zmm2
vfmadd231ps {rn-sae}, %zmm9, %zmm7, %zmm2
vfmadd231ps {rn-sae}, %zmm4, %zmm7, %zmm3
vfmadd213ps {rn-sae}, %zmm12, %zmm9, %zmm2
vfmadd213ps {rn-sae}, %zmm12, %zmm4, %zmm3
vfmadd213ps {rn-sae}, %zmm13, %zmm9, %zmm2
vfmadd213ps {rn-sae}, %zmm13, %zmm4, %zmm3
/* (K*L2L + Tl) + Rp*PolyP */
vfmadd213ps {rn-sae}, %zmm1, %zmm9, %zmm2
vorps Half+__svml_satanh_data_internal_avx512(%rip), %zmm10, %zmm9
/* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM */
vfnmadd213ps {rn-sae}, %zmm2, %zmm4, %zmm3
vaddps {rn-sae}, %zmm3, %zmm0, %zmm4
vmulps {rn-sae}, %zmm9, %zmm4, %zmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm11
/* 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 %zmm11, 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
movss 64(%rsp,%r14,4), %xmm0
call atanhf@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movss %xmm0, 128(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN16v_atanhf_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_satanh_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Log_tbl_H[32][1];
__declspec(align(64)) VUINT32 Log_tbl_L[32][1];
__declspec(align(64)) VUINT32 One[16][1];
__declspec(align(64)) VUINT32 AbsMask[16][1];
__declspec(align(64)) VUINT32 AddB5[16][1];
__declspec(align(64)) VUINT32 RcpBitMask[16][1];
__declspec(align(64)) VUINT32 poly_coeff3[16][1];
__declspec(align(64)) VUINT32 poly_coeff2[16][1];
__declspec(align(64)) VUINT32 poly_coeff1[16][1];
__declspec(align(64)) VUINT32 poly_coeff0[16][1];
__declspec(align(64)) VUINT32 Half[16][1];
__declspec(align(64)) VUINT32 L2H[16][1];
__declspec(align(64)) VUINT32 L2L[16][1];
} __svml_satanh_data_internal_avx512;
#endif
__svml_satanh_data_internal_avx512:
/*== Log_tbl_H ==*/
.long 0x00000000
.long 0x3cfc0000
.long 0x3d780000
.long 0x3db78000
.long 0x3df10000
.long 0x3e14c000
.long 0x3e300000
.long 0x3e4a8000
.long 0x3e648000
.long 0x3e7dc000
.long 0x3e8b4000
.long 0x3e974000
.long 0x3ea30000
.long 0x3eae8000
.long 0x3eb9c000
.long 0x3ec4e000
.long 0x3ecfa000
.long 0x3eda2000
.long 0x3ee48000
.long 0x3eeea000
.long 0x3ef8a000
.long 0x3f013000
.long 0x3f05f000
.long 0x3f0aa000
.long 0x3f0f4000
.long 0x3f13d000
.long 0x3f184000
.long 0x3f1ca000
.long 0x3f20f000
.long 0x3f252000
.long 0x3f295000
.long 0x3f2d7000
/*== Log_tbl_L ==*/
.align 64
.long 0x00000000
.long 0x3726c39e
.long 0x38a30c01
.long 0x37528ae5
.long 0x38e0edc5
.long 0xb8ab41f8
.long 0xb7cf8f58
.long 0x3896a73d
.long 0xb5838656
.long 0x380c36af
.long 0xb8235454
.long 0x3862bae1
.long 0x38c5e10e
.long 0x38dedfac
.long 0x38ebfb5e
.long 0xb8e63c9f
.long 0xb85c1340
.long 0x38777bcd
.long 0xb6038656
.long 0x37d40984
.long 0xb8b85028
.long 0xb8ad5a5a
.long 0x3865c84a
.long 0x38c3d2f5
.long 0x383ebce1
.long 0xb8a1ed76
.long 0xb7a332c4
.long 0xb779654f
.long 0xb8602f73
.long 0x38f85db0
.long 0x37b4996f
.long 0xb8bfb3ca
/*== One ==*/
.align 64
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/*== AbsMask ==*/
.align 64
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/*== AddB5 ==*/
.align 64
.long 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000, 0x00020000
/*== RcpBitMask ==*/
.align 64
.long 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000, 0xfffc0000
/*== poly_coeff3 ==*/
.align 64
.long 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810, 0xbe800810
/*== poly_coeff2 ==*/
.align 64
.long 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e, 0x3eaab11e
/*== poly_coeff1 ==*/
.align 64
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000
/*== poly_coeff0 ==*/
.align 64
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/*== Half ==*/
.align 64
.long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000
/*== L2H = log(2)_high ==*/
.align 64
.long 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000, 0x3f317000
/*== L2L = log(2)_low ==*/
.align 64
.long 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4, 0x3805fdf4
.align 64
.type __svml_satanh_data_internal_avx512,@object
.size __svml_satanh_data_internal_avx512,.-__svml_satanh_data_internal_avx512
|
