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/* Function acoshf 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:
*
* Compute acosh(x) as log(x + sqrt(x*x - 1))
* using RSQRT instructions for starting the
* square root approximation, and small table lookups for log
* that map to AVX-512 permute instructions
*
* Special cases:
*
* acosh(NaN) = quiet NaN, and raise invalid exception
* acosh(-INF) = NaN
* acosh(+INF) = +INF
* acosh(x) = NaN if x < 1
* acosh(1) = +0
*
*/
/* Offsets for data table __svml_sacosh_data_internal_avx512
*/
#define Log_tbl_H 0
#define Log_tbl_L 128
#define One 256
#define SmallThreshold 320
#define Threshold 384
#define LargeThreshold 448
#define ca1 512
#define c2s 576
#define c1s 640
#define AddB5 704
#define RcpBitMask 768
#define OneEighth 832
#define Four 896
#define poly_coeff3 960
#define poly_coeff2 1024
#define poly_coeff1 1088
#define L2H 1152
#define L2L 1216
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN16v_acoshf_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_sacosh_data_internal_avx512(%rip), %zmm1
/*
* sqrt(1+x^2) ~ Sh + Sl + Sh*Eh*poly_s
* poly_s = c1+c2*Eh
*/
vmovups c2s+__svml_sacosh_data_internal_avx512(%rip), %zmm13
vmovups c1s+__svml_sacosh_data_internal_avx512(%rip), %zmm15
/* polynomial computation for small inputs */
vmovups ca1+__svml_sacosh_data_internal_avx512(%rip), %zmm9
/* very large inputs ? */
vmovups Threshold+__svml_sacosh_data_internal_avx512(%rip), %zmm10
/* out of range inputs? */
vmovups LargeThreshold+__svml_sacosh_data_internal_avx512(%rip), %zmm11
/* not a very small input ? */
vmovups SmallThreshold+__svml_sacosh_data_internal_avx512(%rip), %zmm6
vmovaps %zmm0, %zmm8
/* x^2 - 1 */
vmovaps %zmm1, %zmm7
vfmsub231ps {rn-sae}, %zmm8, %zmm8, %zmm7
vcmpps $21, {sae}, %zmm10, %zmm8, %k2
vcmpps $22, {sae}, %zmm11, %zmm8, %k0
vcmpps $18, {sae}, %zmm1, %zmm8, %k1
vrsqrt14ps %zmm7, %zmm12
vcmpps $21, {sae}, %zmm6, %zmm7, %k3
vmulps {rn-sae}, %zmm9, %zmm7, %zmm4
/* Sh ~sqrt(-1+x^2) */
vmulps {rn-sae}, %zmm12, %zmm7, %zmm5
/* Sh+x */
vaddps {rn-sae}, %zmm8, %zmm5, %zmm9
/* (Yh*R0)_low */
vmovaps %zmm7, %zmm0
korw %k0, %k1, %k0
/* rel. error term: Eh=1-Sh*R0 */
vmovaps %zmm1, %zmm14
vfmsub213ps {rn-sae}, %zmm5, %zmm12, %zmm0
vfnmadd231ps {rn-sae}, %zmm5, %zmm12, %zmm14
/* rel. error term: Eh=(1-Sh*R0)-Sl*R0 */
vfnmadd231ps {rn-sae}, %zmm0, %zmm12, %zmm14
/* Sh*Eh */
vmulps {rn-sae}, %zmm14, %zmm5, %zmm3
vfmadd231ps {rn-sae}, %zmm14, %zmm13, %zmm15
/* Sl + Sh*Eh*poly_s */
vfmadd213ps {rn-sae}, %zmm0, %zmm15, %zmm3
/* Shh */
vsubps {rn-sae}, %zmm8, %zmm9, %zmm15
/* polynomial computation for small inputs */
vaddps {rn-sae}, %zmm3, %zmm5, %zmm0
/* Xin0+Sl+Sh*Eh*poly_s ~ x+sqrt(1+x^2) */
vaddps {rn-sae}, %zmm3, %zmm9, %zmm2
/* Shl */
vsubps {rn-sae}, %zmm15, %zmm5, %zmm10
vfmadd231ps {rn-sae}, %zmm0, %zmm4, %zmm0
/* fixup for very large inputs */
vmovups OneEighth+__svml_sacosh_data_internal_avx512(%rip), %zmm4
/* Sl_high */
vsubps {rn-sae}, %zmm9, %zmm2, %zmm5
/* polynomial */
vmovups poly_coeff3+__svml_sacosh_data_internal_avx512(%rip), %zmm9
vmulps {rn-sae}, %zmm4, %zmm8, %zmm2{%k2}
/* -K*L2L + Tl */
vmovups L2L+__svml_sacosh_data_internal_avx512(%rip), %zmm4
/* Sl_l */
vsubps {rn-sae}, %zmm5, %zmm3, %zmm3
vrcp14ps %zmm2, %zmm11
vmovups Log_tbl_L+__svml_sacosh_data_internal_avx512(%rip), %zmm5
/* Xin_low */
vaddps {rn-sae}, %zmm10, %zmm3, %zmm13
/* round reciprocal to 1+4b mantissas */
vpaddd AddB5+__svml_sacosh_data_internal_avx512(%rip), %zmm11, %zmm12
vmovups poly_coeff1+__svml_sacosh_data_internal_avx512(%rip), %zmm10
vandps RcpBitMask+__svml_sacosh_data_internal_avx512(%rip), %zmm12, %zmm14
/* fixup for very large inputs */
vxorps %zmm13, %zmm13, %zmm13{%k2}
/* reduced argument for log(): (Rcp*Xin-1)+Rcp*Xin_low */
vfmsub231ps {rn-sae}, %zmm14, %zmm2, %zmm1
/* exponents */
vgetexpps {sae}, %zmm14, %zmm12
vmovups Four+__svml_sacosh_data_internal_avx512(%rip), %zmm2
/* Prepare table index */
vpsrld $18, %zmm14, %zmm3
vfmadd231ps {rn-sae}, %zmm14, %zmm13, %zmm1
vmovups poly_coeff2+__svml_sacosh_data_internal_avx512(%rip), %zmm13
/* Table lookups */
vmovups __svml_sacosh_data_internal_avx512(%rip), %zmm14
vsubps {rn-sae}, %zmm2, %zmm12, %zmm12{%k2}
vpermt2ps Log_tbl_L+64+__svml_sacosh_data_internal_avx512(%rip), %zmm3, %zmm5
vpermt2ps Log_tbl_H+64+__svml_sacosh_data_internal_avx512(%rip), %zmm3, %zmm14
/* R^2 */
vmulps {rn-sae}, %zmm1, %zmm1, %zmm11
/* -K*L2H + Th */
vmovups L2H+__svml_sacosh_data_internal_avx512(%rip), %zmm2
vfmadd231ps {rn-sae}, %zmm1, %zmm9, %zmm13
vfnmadd231ps {rn-sae}, %zmm12, %zmm2, %zmm14
vfnmadd213ps {rn-sae}, %zmm5, %zmm4, %zmm12
vfmadd213ps {rn-sae}, %zmm10, %zmm1, %zmm13
/* Tl + R^2*Poly */
vfmadd213ps {rn-sae}, %zmm12, %zmm11, %zmm13
/* R+Tl + R^2*Poly */
vaddps {rn-sae}, %zmm1, %zmm13, %zmm1
vaddps {rn-sae}, %zmm1, %zmm14, %zmm0{%k3}
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 k0 zmm0 zmm8
/* 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 %zmm8, 64(%rsp)
vmovups %zmm0, 128(%rsp)
# LOE rbx r12 r13 r14 r15 k0 zmm0
xorl %eax, %eax
# LOE rbx r12 r13 r14 r15 eax k0
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
kmovd %k0, %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 function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovss 64(%rsp, %r14, 4), %xmm0
call acoshf@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_acoshf_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_sacosh_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 SmallThreshold[16][1];
__declspec(align(64)) VUINT32 Threshold[16][1];
__declspec(align(64)) VUINT32 LargeThreshold[16][1];
__declspec(align(64)) VUINT32 ca1[16][1];
__declspec(align(64)) VUINT32 c2s[16][1];
__declspec(align(64)) VUINT32 c1s[16][1];
__declspec(align(64)) VUINT32 AddB5[16][1];
__declspec(align(64)) VUINT32 RcpBitMask[16][1];
__declspec(align(64)) VUINT32 OneEighth[16][1];
__declspec(align(64)) VUINT32 Four[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 L2H[16][1];
__declspec(align(64)) VUINT32 L2L[16][1];
} __svml_sacosh_data_internal_avx512;
#endif
__svml_sacosh_data_internal_avx512:
/* Log_tbl_H */
.long 0x00000000
.long 0xbcfc0000
.long 0xbd788000
.long 0xbdb78000
.long 0xbdf14000
.long 0xbe14a000
.long 0xbe300000
.long 0xbe4aa000
.long 0xbe648000
.long 0xbe7dc000
.long 0xbe8b4000
.long 0xbe974000
.long 0xbea31000
.long 0xbeae9000
.long 0xbeb9d000
.long 0xbec4d000
.long 0xbecfa000
.long 0xbeda2000
.long 0xbee48000
.long 0xbeeea000
.long 0xbef89000
.long 0xbf012800
.long 0xbf05f000
.long 0xbf0aa800
.long 0xbf0f4000
.long 0xbf13c800
.long 0xbf184000
.long 0xbf1ca000
.long 0xbf20f000
.long 0xbf252800
.long 0xbf295000
.long 0xbf2d6800
/* Log_tbl_L */
.align 64
.long 0x80000000
.long 0xb726c39e
.long 0x3839e7fe
.long 0xb7528ae5
.long 0x377891d5
.long 0xb8297c10
.long 0x37cf8f58
.long 0x3852b186
.long 0x35838656
.long 0xb80c36af
.long 0x38235454
.long 0xb862bae1
.long 0x37e87bc7
.long 0x37848150
.long 0x37202511
.long 0xb74e1b05
.long 0x385c1340
.long 0xb8777bcd
.long 0x36038656
.long 0xb7d40984
.long 0xb80f5faf
.long 0xb8254b4c
.long 0xb865c84a
.long 0x37f0b42d
.long 0xb83ebce1
.long 0xb83c2513
.long 0x37a332c4
.long 0x3779654f
.long 0x38602f73
.long 0x367449f8
.long 0xb7b4996f
.long 0xb800986b
/* One */
.align 64
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/* SmallThreshold */
.align 64
.long 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000, 0x39800000
/* Threshold */
.align 64
.long 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000, 0x5f000000
/* LargeThreshold */
.align 64
.long 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff, 0x7f7fffff
/* ca1 */
.align 64
.long 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE, 0xbe2AA5DE
/* c2s */
.align 64
.long 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000, 0x3ec00000
/* c1s */
.align 64
.long 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000, 0x3f000000
/* 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
/* OneEighth */
.align 64
.long 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000, 0x3e000000
/* Four */
.align 64
.long 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000, 0x40800000
/* 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
/* 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_sacosh_data_internal_avx512, @object
.size __svml_sacosh_data_internal_avx512, .-__svml_sacosh_data_internal_avx512
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