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/* Function cosh 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 cosh(x) as (exp(x)+exp(-x))/2,
* where exp is calculated as
* exp(M*ln2 + ln2*(j/2^k) + r) = 2^M * 2^(j/2^k) * exp(r)
*
* Special cases:
*
* cosh(NaN) = quiet NaN, and raise invalid exception
* cosh(INF) = that INF
* cosh(0) = 1
* cosh(x) overflows for big x and returns MAXLOG+log(2)
*
*/
/* Offsets for data table __svml_dcosh_data_internal
*/
#define _dTp_h 0
#define _dTn_h 128
#define _dbShifter_UISA 256
#define _dPC2_UISA 320
#define _dPC3_UISA 384
#define _dPC4_UISA 448
#define _dPC5_UISA 512
#define _dPC6_UISA 576
#define _dPC7_UISA 640
#define _dbInvLn2 704
#define _dbLn2hi 768
#define _dbLn2lo 832
#define _dbShifter 896
#define _dPC2 960
#define _dPC3 1024
#define _dPC4 1088
#define _lExpMask 1152
#define _dSign 1216
#define _iDomainRange 1280
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN8v_cosh_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 _dSign+__svml_dcosh_data_internal(%rip), %zmm11
vmovups _dbShifter_UISA+__svml_dcosh_data_internal(%rip), %zmm15
/*
* Load argument
* dM = x*2^K/log(2) + RShifter
*/
vmovups _dbInvLn2+__svml_dcosh_data_internal(%rip), %zmm4
vmovups _dbLn2hi+__svml_dcosh_data_internal(%rip), %zmm2
vmovups _dbLn2lo+__svml_dcosh_data_internal(%rip), %zmm3
vmovups _dPC7_UISA+__svml_dcosh_data_internal(%rip), %zmm8
vmovups _dPC6_UISA+__svml_dcosh_data_internal(%rip), %zmm9
vmovups _dPC2_UISA+__svml_dcosh_data_internal(%rip), %zmm7
vmovups _dPC3_UISA+__svml_dcosh_data_internal(%rip), %zmm6
vmovaps %zmm0, %zmm10
/* Abs argument */
vandnpd %zmm10, %zmm11, %zmm5
/* Index and lookup */
vmovups __svml_dcosh_data_internal(%rip), %zmm11
vmovups _dTn_h+__svml_dcosh_data_internal(%rip), %zmm0
vfmadd213pd {rn-sae}, %zmm15, %zmm5, %zmm4
/*
* Check for overflow\underflow
*
*/
vpsrlq $32, %zmm5, %zmm12
/* dN = dM - RShifter */
vsubpd {rn-sae}, %zmm15, %zmm4, %zmm1
vpmovqd %zmm12, %ymm13
vpermt2pd _dTn_h+64+__svml_dcosh_data_internal(%rip), %zmm4, %zmm0
vpermt2pd _dTp_h+64+__svml_dcosh_data_internal(%rip), %zmm4, %zmm11
/* dR = dX - dN*Log2_hi/2^K */
vfnmadd231pd {rn-sae}, %zmm2, %zmm1, %zmm5
/*
* poly(r) = Gmjp(1 + a2*r^2 + a4*r^4) + Gmjn*(r+ a3*r^3 +a5*r^5) =
* = Gmjp_h +Gmjp_l+ Gmjp*r^2*(a2 + a4*r^2) + Gmjn*(r+ r^3*(a3 +a5*r^2)
*/
vmovups _dPC5_UISA+__svml_dcosh_data_internal(%rip), %zmm12
vpsllq $48, %zmm4, %zmm2
/* dR = dX - dN*Log2_hi/2^K */
vfnmadd231pd {rn-sae}, %zmm3, %zmm1, %zmm5
vmulpd {rn-sae}, %zmm5, %zmm5, %zmm1
vfmadd231pd {rn-sae}, %zmm1, %zmm8, %zmm12
vmovups _dPC4_UISA+__svml_dcosh_data_internal(%rip), %zmm8
vfmadd213pd {rn-sae}, %zmm6, %zmm1, %zmm12
vfmadd231pd {rn-sae}, %zmm1, %zmm9, %zmm8
vfmadd213pd {rn-sae}, %zmm7, %zmm1, %zmm8
vpcmpgtd _iDomainRange+__svml_dcosh_data_internal(%rip), %ymm13, %ymm14
vmovmskps %ymm14, %edx
/* dOut=r^2*(a2 + a4*r^2) */
vmulpd {rn-sae}, %zmm1, %zmm8, %zmm6
/* lM now is an EXP(2^N) */
vpandq _lExpMask+__svml_dcosh_data_internal(%rip), %zmm2, %zmm3
vpaddq %zmm3, %zmm11, %zmm4
vpsubq %zmm3, %zmm0, %zmm0
vsubpd {rn-sae}, %zmm0, %zmm4, %zmm14
vaddpd {rn-sae}, %zmm0, %zmm4, %zmm13
/* dM=r^2*(a3 +a5*r^2) */
vmulpd {rn-sae}, %zmm1, %zmm12, %zmm0
vfmadd213pd {rn-sae}, %zmm13, %zmm13, %zmm6
/* dM= r + r^3*(a3 +a5*r^2) */
vfmadd213pd {rn-sae}, %zmm5, %zmm5, %zmm0
vfmadd213pd {rn-sae}, %zmm6, %zmm14, %zmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm10
/* 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 %zmm10, 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
vmovsd 64(%rsp, %r14, 8), %xmm0
call cosh@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovsd %xmm0, 128(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN8v_cosh_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dcosh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 _dTp_h[(1<<4)][2];
__declspec(align(64)) VUINT32 _dTn_h[(1<<4)][2];
__declspec(align(64)) VUINT32 _dbShifter_UISA[8][2];
__declspec(align(64)) VUINT32 _dPC2_UISA[8][2];
__declspec(align(64)) VUINT32 _dPC3_UISA[8][2];
__declspec(align(64)) VUINT32 _dPC4_UISA[8][2];
__declspec(align(64)) VUINT32 _dPC5_UISA[8][2];
__declspec(align(64)) VUINT32 _dPC6_UISA[8][2];
__declspec(align(64)) VUINT32 _dPC7_UISA[8][2];
__declspec(align(64)) VUINT32 _dbInvLn2[8][2];
__declspec(align(64)) VUINT32 _dbLn2hi[8][2];
__declspec(align(64)) VUINT32 _dbLn2lo[8][2];
__declspec(align(64)) VUINT32 _dbShifter[8][2];
__declspec(align(64)) VUINT32 _dPC2[8][2];
__declspec(align(64)) VUINT32 _dPC3[8][2];
__declspec(align(64)) VUINT32 _dPC4[8][2];
__declspec(align(64)) VUINT32 _lExpMask[8][2];
__declspec(align(64)) VUINT32 _dSign[8][2]; // 0x8000000000000000
__declspec(align(64)) VUINT32 _iDomainRange[16][1];
} __svml_dcosh_data_internal;
#endif
__svml_dcosh_data_internal:
/* _dTp_h */
.quad 0x3fe0000000000000, 0x3fe0b5586cf9890f, 0x3fe172b83c7d517b, 0x3fe2387a6e756238
.quad 0x3fe306fe0a31b715, 0x3fe3dea64c123422, 0x3fe4bfdad5362a27, 0x3fe5ab07dd485429
.quad 0x3fe6a09e667f3bcd, 0x3fe7a11473eb0187, 0x3fe8ace5422aa0db, 0x3fe9c49182a3f090
.quad 0x3feae89f995ad3ad, 0x3fec199bdd85529c, 0x3fed5818dcfba487, 0x3feea4afa2a490da
/* dTn_h */
.align 64
.quad 0x3fe0000000000000, 0x3fdea4afa2a490da, 0x3fdd5818dcfba487, 0x3fdc199bdd85529c
.quad 0x3fdae89f995ad3ad, 0x3fd9c49182a3f090, 0x3fd8ace5422aa0db, 0x3fd7a11473eb0187
.quad 0x3fd6a09e667f3bcd, 0x3fd5ab07dd485429, 0x3fd4bfdad5362a27, 0x3fd3dea64c123422
.quad 0x3fd306fe0a31b715, 0x3fd2387a6e756238, 0x3fd172b83c7d517b, 0x3fd0b5586cf9890f
.align 64
.quad 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000 /* _dbShifter_UISA */
.align 64
.quad 0x3fe0000000000004, 0x3fe0000000000004, 0x3fe0000000000004, 0x3fe0000000000004, 0x3fe0000000000004, 0x3fe0000000000004, 0x3fe0000000000004, 0x3fe0000000000004 /* _dPC2_UISA */
.align 64
.quad 0x3fc5555555555543, 0x3fc5555555555543, 0x3fc5555555555543, 0x3fc5555555555543, 0x3fc5555555555543, 0x3fc5555555555543, 0x3fc5555555555543, 0x3fc5555555555543 /* _dPC3_UISA */
.align 64
.quad 0x3fa5555555484f37, 0x3fa5555555484f37, 0x3fa5555555484f37, 0x3fa5555555484f37, 0x3fa5555555484f37, 0x3fa5555555484f37, 0x3fa5555555484f37, 0x3fa5555555484f37 /* _dPC4_UISA */
.align 64
.quad 0x3f81111111286a0c, 0x3f81111111286a0c, 0x3f81111111286a0c, 0x3f81111111286a0c, 0x3f81111111286a0c, 0x3f81111111286a0c, 0x3f81111111286a0c, 0x3f81111111286a0c /* _dPC5_UISA */
.align 64
.quad 0x3f56c183da08f116, 0x3f56c183da08f116, 0x3f56c183da08f116, 0x3f56c183da08f116, 0x3f56c183da08f116, 0x3f56c183da08f116, 0x3f56c183da08f116, 0x3f56c183da08f116 /* _dPC6_UISA */
.align 64
.quad 0x3f2a018d76da03da, 0x3f2a018d76da03da, 0x3f2a018d76da03da, 0x3f2a018d76da03da, 0x3f2a018d76da03da, 0x3f2a018d76da03da, 0x3f2a018d76da03da, 0x3f2a018d76da03da /* _dPC7_UISA */
/* _dbT */
.align 64
.quad 0x3ff71547652b82fe, 0x3ff71547652b82fe, 0x3ff71547652b82fe, 0x3ff71547652b82fe, 0x3ff71547652b82fe, 0x3ff71547652b82fe, 0x3ff71547652b82fe, 0x3ff71547652b82fe /* _dbInvLn2 = 1/log(2) */
.align 64
.quad 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000, 0x3FE62E42FEFC0000 /* _dbLn2hi = log(2) hi */
.align 64
.quad 0xBDAC610CA86C3899, 0xBDAC610CA86C3899, 0xBDAC610CA86C3899, 0xBDAC610CA86C3899, 0xBDAC610CA86C3899, 0xBDAC610CA86C3899, 0xBDAC610CA86C3899, 0xBDAC610CA86C3899 /* _dbLn2lo = log(2) lo */
.align 64
.quad 0x42B8000000000000, 0x42B8000000000000, 0x42B8000000000000, 0x42B8000000000000, 0x42B8000000000000, 0x42B8000000000000, 0x42B8000000000000, 0x42B8000000000000 /* _dbShifter */
.align 64
.quad 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD /* _dPC2 */
.align 64
.quad 0x3FC5555570813E14, 0x3FC5555570813E14, 0x3FC5555570813E14, 0x3FC5555570813E14, 0x3FC5555570813E14, 0x3FC5555570813E14, 0x3FC5555570813E14, 0x3FC5555570813E14 /* _dPC3 */
.align 64
.quad 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299 /* _dPC4 */
.align 64
.quad 0x7ff0000000000000, 0x7ff0000000000000, 0x7ff0000000000000, 0x7ff0000000000000, 0x7ff0000000000000, 0x7ff0000000000000, 0x7ff0000000000000, 0x7ff0000000000000 /* _lExpMask */
.align 64
.quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 /* _dSign */
.align 64
.long 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99 /* _iDomainRange 0x40861d9ac12a3e85 =(1021*2^K-0.5)*log(2)/2^K -needed for quick exp */
.align 64
.type __svml_dcosh_data_internal, @object
.size __svml_dcosh_data_internal, .-__svml_dcosh_data_internal
|
