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/* Function atanh vectorized with AVX-512.
Copyright (C) 2021 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_datanh_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_coeff8 512
#define poly_coeff7 576
#define poly_coeff6 640
#define poly_coeff5 704
#define poly_coeff4 768
#define poly_coeff3 832
#define poly_coeff2 896
#define poly_coeff1 960
#define poly_coeff0 1024
#define Half 1088
#define L2H 1152
#define L2L 1216
#include <sysdep.h>
.text
.section .text.evex512,"ax",@progbits
ENTRY(_ZGVeN8v_atanh_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_datanh_data_internal_avx512(%rip), %zmm15
/* round reciprocals to 1+4b mantissas */
vmovups AddB5+__svml_datanh_data_internal_avx512(%rip), %zmm6
vmovups RcpBitMask+__svml_datanh_data_internal_avx512(%rip), %zmm9
vmovaps %zmm0, %zmm2
vandpd AbsMask+__svml_datanh_data_internal_avx512(%rip), %zmm2, %zmm13
/* 1+y */
vaddpd {rn-sae}, %zmm15, %zmm13, %zmm0
/* 1-y */
vsubpd {rn-sae}, %zmm13, %zmm15, %zmm4
vxorpd %zmm13, %zmm2, %zmm1
/* Yp_high */
vsubpd {rn-sae}, %zmm15, %zmm0, %zmm7
/* -Ym_high */
vsubpd {rn-sae}, %zmm15, %zmm4, %zmm12
/* RcpP ~ 1/Yp */
vrcp14pd %zmm0, %zmm3
/* RcpM ~ 1/Ym */
vrcp14pd %zmm4, %zmm5
/* input outside (-1, 1) ? */
vcmppd $21, {sae}, %zmm15, %zmm13, %k0
vpaddq %zmm6, %zmm3, %zmm11
vpaddq %zmm6, %zmm5, %zmm10
/* Yp_low */
vsubpd {rn-sae}, %zmm7, %zmm13, %zmm8
vandpd %zmm9, %zmm11, %zmm14
vandpd %zmm9, %zmm10, %zmm3
/* Ym_low */
vaddpd {rn-sae}, %zmm12, %zmm13, %zmm12
/* Reduced argument: Rp = (RcpP*Yp - 1)+RcpP*Yp_low */
vfmsub213pd {rn-sae}, %zmm15, %zmm14, %zmm0
/* Reduced argument: Rm = (RcpM*Ym - 1)+RcpM*Ym_low */
vfmsub231pd {rn-sae}, %zmm3, %zmm4, %zmm15
/* exponents */
vgetexppd {sae}, %zmm14, %zmm5
vgetexppd {sae}, %zmm3, %zmm4
/* Table lookups */
vmovups __svml_datanh_data_internal_avx512(%rip), %zmm9
vmovups Log_tbl_H+64+__svml_datanh_data_internal_avx512(%rip), %zmm13
vmovups Log_tbl_L+__svml_datanh_data_internal_avx512(%rip), %zmm7
vfmadd231pd {rn-sae}, %zmm14, %zmm8, %zmm0
vfnmadd231pd {rn-sae}, %zmm3, %zmm12, %zmm15
/* Prepare table index */
vpsrlq $48, %zmm14, %zmm11
vpsrlq $48, %zmm3, %zmm8
vmovups Log_tbl_L+64+__svml_datanh_data_internal_avx512(%rip), %zmm14
/* polynomials */
vmovups poly_coeff8+__svml_datanh_data_internal_avx512(%rip), %zmm3
/* Km-Kp */
vsubpd {rn-sae}, %zmm5, %zmm4, %zmm5
vmovups poly_coeff7+__svml_datanh_data_internal_avx512(%rip), %zmm4
kmovw %k0, %edx
vmovaps %zmm11, %zmm10
vmovaps %zmm4, %zmm6
vpermi2pd %zmm13, %zmm9, %zmm10
vpermi2pd %zmm14, %zmm7, %zmm11
vpermt2pd %zmm13, %zmm8, %zmm9
vpermt2pd %zmm14, %zmm8, %zmm7
vmovups poly_coeff6+__svml_datanh_data_internal_avx512(%rip), %zmm8
vfmadd231pd {rn-sae}, %zmm0, %zmm3, %zmm6
vfmadd231pd {rn-sae}, %zmm15, %zmm3, %zmm4
vmovups poly_coeff3+__svml_datanh_data_internal_avx512(%rip), %zmm13
vmovups poly_coeff2+__svml_datanh_data_internal_avx512(%rip), %zmm14
vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm8, %zmm15, %zmm4
vmovups poly_coeff0+__svml_datanh_data_internal_avx512(%rip), %zmm8
vsubpd {rn-sae}, %zmm11, %zmm7, %zmm12
/* table values */
vsubpd {rn-sae}, %zmm10, %zmm9, %zmm3
vmovups poly_coeff5+__svml_datanh_data_internal_avx512(%rip), %zmm7
vmovups poly_coeff4+__svml_datanh_data_internal_avx512(%rip), %zmm9
/* K*L2H + Th */
vmovups L2H+__svml_datanh_data_internal_avx512(%rip), %zmm10
/* K*L2L + Tl */
vmovups L2L+__svml_datanh_data_internal_avx512(%rip), %zmm11
vfmadd213pd {rn-sae}, %zmm7, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm7, %zmm15, %zmm4
vmovups poly_coeff1+__svml_datanh_data_internal_avx512(%rip), %zmm7
vfmadd231pd {rn-sae}, %zmm5, %zmm10, %zmm3
vfmadd213pd {rn-sae}, %zmm12, %zmm11, %zmm5
vfmadd213pd {rn-sae}, %zmm9, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm9, %zmm15, %zmm4
vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm13, %zmm15, %zmm4
vfmadd213pd {rn-sae}, %zmm14, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm14, %zmm15, %zmm4
vfmadd213pd {rn-sae}, %zmm7, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm7, %zmm15, %zmm4
vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm6
vfmadd213pd {rn-sae}, %zmm8, %zmm15, %zmm4
/* (K*L2L + Tl) + Rp*PolyP */
vfmadd213pd {rn-sae}, %zmm5, %zmm0, %zmm6
vorpd Half+__svml_datanh_data_internal_avx512(%rip), %zmm1, %zmm0
/* (K*L2L + Tl) + Rp*PolyP -Rm*PolyM */
vfnmadd213pd {rn-sae}, %zmm6, %zmm15, %zmm4
vaddpd {rn-sae}, %zmm4, %zmm3, %zmm1
vmulpd {rn-sae}, %zmm0, %zmm1, %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 atanh@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_atanh_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_datanh_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Log_tbl_H[16][2];
__declspec(align(64)) VUINT32 Log_tbl_L[16][2];
__declspec(align(64)) VUINT32 One[8][2];
__declspec(align(64)) VUINT32 AbsMask[8][2];
__declspec(align(64)) VUINT32 AddB5[8][2];
__declspec(align(64)) VUINT32 RcpBitMask[8][2];
__declspec(align(64)) VUINT32 poly_coeff8[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 poly_coeff1[8][2];
__declspec(align(64)) VUINT32 poly_coeff0[8][2];
__declspec(align(64)) VUINT32 Half[8][2];
__declspec(align(64)) VUINT32 L2H[8][2];
__declspec(align(64)) VUINT32 L2L[8][2];
} __svml_datanh_data_internal_avx512;
#endif
__svml_datanh_data_internal_avx512:
/*== Log_tbl_H ==*/
.quad 0x0000000000000000
.quad 0x3faf0a30c0100000
.quad 0x3fbe27076e2a0000
.quad 0x3fc5ff3070a80000
.quad 0x3fcc8ff7c79b0000
.quad 0x3fd1675cabab8000
.quad 0x3fd4618bc21c8000
.quad 0x3fd739d7f6bc0000
.quad 0x3fd9f323ecbf8000
.quad 0x3fdc8ff7c79a8000
.quad 0x3fdf128f5faf0000
.quad 0x3fe0be72e4254000
.quad 0x3fe1e85f5e704000
.quad 0x3fe307d7334f0000
.quad 0x3fe41d8fe8468000
.quad 0x3fe52a2d265bc000
/*== Log_tbl_L ==*/
.align 64
.quad 0x0000000000000000
.quad 0x3d662a6617cc9717
.quad 0x3d6e5cbd3d50fffc
.quad 0xbd6b0b0de3077d7e
.quad 0xbd697794f689f843
.quad 0x3d630701ce63eab9
.quad 0xbd609ec17a426426
.quad 0xbd67fcb18ed9d603
.quad 0x3d584bf2b68d766f
.quad 0x3d5a21ac25d81ef3
.quad 0x3d3bb2cd720ec44c
.quad 0xbd657d49676844cc
.quad 0x3d1a07bd8b34be7c
.quad 0x3d60be1fb590a1f5
.quad 0xbd5aa33736867a17
.quad 0x3d46abb9df22bc57
/*== One ==*/
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
/*== AbsMask ==*/
.align 64
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff
/*== AddB5 ==*/
.align 64
.quad 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000
/*== RcpBitMask ==*/
.align 64
.quad 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000
/*== poly_coeff8 ==*/
.align 64
.quad 0x3fbc81dd40d38142, 0x3fbc81dd40d38142, 0x3fbc81dd40d38142, 0x3fbc81dd40d38142, 0x3fbc81dd40d38142, 0x3fbc81dd40d38142, 0x3fbc81dd40d38142, 0x3fbc81dd40d38142
/*== poly_coeff7 ==*/
.align 64
.quad 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70, 0xbfc0073cb82e8b70
/*== poly_coeff6 ==*/
.align 64
.quad 0x3fc2492298ffdae8, 0x3fc2492298ffdae8, 0x3fc2492298ffdae8, 0x3fc2492298ffdae8, 0x3fc2492298ffdae8, 0x3fc2492298ffdae8, 0x3fc2492298ffdae8, 0x3fc2492298ffdae8
/*== poly_coeff5 ==*/
.align 64
.quad 0xbfc55553f871e5c5, 0xbfc55553f871e5c5, 0xbfc55553f871e5c5, 0xbfc55553f871e5c5, 0xbfc55553f871e5c5, 0xbfc55553f871e5c5, 0xbfc55553f871e5c5, 0xbfc55553f871e5c5
/*== poly_coeff4 ==*/
.align 64
.quad 0x3fc9999999cd394a, 0x3fc9999999cd394a, 0x3fc9999999cd394a, 0x3fc9999999cd394a, 0x3fc9999999cd394a, 0x3fc9999999cd394a, 0x3fc9999999cd394a, 0x3fc9999999cd394a
/*== poly_coeff3 ==*/
.align 64
.quad 0xbfd00000000c2a01, 0xbfd00000000c2a01, 0xbfd00000000c2a01, 0xbfd00000000c2a01, 0xbfd00000000c2a01, 0xbfd00000000c2a01, 0xbfd00000000c2a01, 0xbfd00000000c2a01
/*== poly_coeff2 ==*/
.align 64
.quad 0x3fd5555555555462, 0x3fd5555555555462, 0x3fd5555555555462, 0x3fd5555555555462, 0x3fd5555555555462, 0x3fd5555555555462, 0x3fd5555555555462, 0x3fd5555555555462
/*== poly_coeff1 ==*/
.align 64
.quad 0xbfdfffffffffffc5, 0xbfdfffffffffffc5, 0xbfdfffffffffffc5, 0xbfdfffffffffffc5, 0xbfdfffffffffffc5, 0xbfdfffffffffffc5, 0xbfdfffffffffffc5, 0xbfdfffffffffffc5
/*== poly_coeff0 ==*/
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
/*== Half ==*/
.align 64
.quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
/*== L2H = log(2)_high ==*/
.align 64
.quad 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000
/*== L2L = log(2)_low ==*/
.align 64
.quad 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000
.align 64
.type __svml_datanh_data_internal_avx512,@object
.size __svml_datanh_data_internal_avx512,.-__svml_datanh_data_internal_avx512
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