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/* Function acos vectorized with AVX2.
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:
*
* SelMask = (|x| >= 0.5) ? 1 : 0;
* R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x|
* acos(|x|) = SelMask ? 2*Poly(R) : (Pi/2 - Poly(R))
* acos(x) = sign(x) ? (Pi - acos(|x|)) : acos(|x|)
*
*/
/* Offsets for data table __svml_dacos_data_internal
*/
#define SgnBit 0
#define OneHalf 32
#define SmallNorm 64
#define MOne 96
#define Two 128
#define sqrt_coeff 160
#define poly_coeff 288
#define PiH 672
#define Pi2H 704
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN4v_acos_avx2)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-32, %rsp
subq $96, %rsp
vmovupd __svml_dacos_data_internal(%rip), %ymm6
vmovupd OneHalf+__svml_dacos_data_internal(%rip), %ymm7
vmovapd %ymm0, %ymm5
/* x = -|arg| */
vorpd %ymm5, %ymm6, %ymm4
/* Y = 0.5 + 0.5*(-x) */
vfmadd231pd %ymm4, %ymm7, %ymm7
/* x^2 */
vmulpd %ymm4, %ymm4, %ymm8
/* S ~ 2*sqrt(Y) */
vmovupd sqrt_coeff+__svml_dacos_data_internal(%rip), %ymm0
vcmplt_oqpd SmallNorm+__svml_dacos_data_internal(%rip), %ymm7, %ymm12
vminpd %ymm7, %ymm8, %ymm2
/* NaN processed in special branch (so wind test passed) */
vcmpnge_uqpd MOne+__svml_dacos_data_internal(%rip), %ymm4, %ymm9
vcvtpd2ps %ymm7, %xmm10
vmovupd poly_coeff+64+__svml_dacos_data_internal(%rip), %ymm8
vcmpnlt_uqpd %ymm7, %ymm2, %ymm1
vrsqrtps %xmm10, %xmm11
vfmadd213pd poly_coeff+96+__svml_dacos_data_internal(%rip), %ymm2, %ymm8
vcvtps2pd %xmm11, %ymm13
vmovupd poly_coeff+128+__svml_dacos_data_internal(%rip), %ymm11
vandnpd %ymm13, %ymm12, %ymm14
vmulpd %ymm14, %ymm14, %ymm15
vfmadd213pd poly_coeff+160+__svml_dacos_data_internal(%rip), %ymm2, %ymm11
vmulpd %ymm2, %ymm2, %ymm13
vmovupd poly_coeff+256+__svml_dacos_data_internal(%rip), %ymm12
vmulpd %ymm13, %ymm13, %ymm10
vfmadd213pd poly_coeff+288+__svml_dacos_data_internal(%rip), %ymm2, %ymm12
vandpd %ymm5, %ymm6, %ymm3
vaddpd %ymm7, %ymm7, %ymm6
vmulpd %ymm6, %ymm14, %ymm7
vfmsub213pd Two+__svml_dacos_data_internal(%rip), %ymm15, %ymm6
vmovupd poly_coeff+320+__svml_dacos_data_internal(%rip), %ymm14
vfmadd213pd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %ymm6, %ymm0
vmulpd %ymm6, %ymm7, %ymm15
vfmadd213pd poly_coeff+352+__svml_dacos_data_internal(%rip), %ymm2, %ymm14
vfmadd213pd sqrt_coeff+64+__svml_dacos_data_internal(%rip), %ymm6, %ymm0
vfmadd213pd sqrt_coeff+96+__svml_dacos_data_internal(%rip), %ymm6, %ymm0
/* polynomial */
vmovupd poly_coeff+__svml_dacos_data_internal(%rip), %ymm6
vfnmadd213pd %ymm7, %ymm15, %ymm0
vfmadd213pd poly_coeff+32+__svml_dacos_data_internal(%rip), %ymm2, %ymm6
vblendvpd %ymm1, %ymm0, %ymm4, %ymm0
vfmadd213pd %ymm8, %ymm13, %ymm6
vmovmskpd %ymm9, %edx
vmovupd poly_coeff+192+__svml_dacos_data_internal(%rip), %ymm9
vfmadd213pd poly_coeff+224+__svml_dacos_data_internal(%rip), %ymm2, %ymm9
vfmadd213pd %ymm9, %ymm13, %ymm11
vfmadd213pd %ymm11, %ymm10, %ymm6
vfmadd213pd %ymm12, %ymm13, %ymm6
vfmadd213pd %ymm14, %ymm13, %ymm6
vmulpd %ymm6, %ymm2, %ymm9
/* X<X^2 iff X<0 */
vcmplt_oqpd %ymm2, %ymm5, %ymm6
vandpd PiH+__svml_dacos_data_internal(%rip), %ymm1, %ymm2
vandnpd Pi2H+__svml_dacos_data_internal(%rip), %ymm1, %ymm7
vxorpd %ymm3, %ymm0, %ymm1
vfmadd213pd %ymm1, %ymm1, %ymm9
vandpd %ymm6, %ymm2, %ymm2
vaddpd %ymm7, %ymm2, %ymm8
vaddpd %ymm9, %ymm8, %ymm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm5
/* 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):
vmovupd %ymm5, 32(%rsp)
vmovupd %ymm0, 64(%rsp)
# LOE rbx r12 r13 r14 r15 edx ymm0
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: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 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: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 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 $4, %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)
vmovupd 64(%rsp), %ymm0
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 ymm0
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovsd 32(%rsp, %r14, 8), %xmm0
call acos@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovsd %xmm0, 64(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN4v_acos_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_dacos_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 SgnBit[4][2];
__declspec(align(32)) VUINT32 OneHalf[4][2];
__declspec(align(32)) VUINT32 SmallNorm[4][2];
__declspec(align(32)) VUINT32 MOne[4][2];
__declspec(align(32)) VUINT32 Two[4][2];
__declspec(align(32)) VUINT32 sqrt_coeff[4][4][2];
__declspec(align(32)) VUINT32 poly_coeff[12][4][2];
__declspec(align(32)) VUINT32 PiH[4][2];
__declspec(align(32)) VUINT32 Pi2H[4][2];
} __svml_dacos_data_internal;
#endif
__svml_dacos_data_internal:
/* SgnBit */
.quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
/* OneHalf */
.align 32
.quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
/* SmallNorm */
.align 32
.quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
/* MOne */
.align 32
.quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000
/* Two */
.align 32
.quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
/* sqrt_coeff[4] */
.align 32
.quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
.quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
.quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
.quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
/* poly_coeff[12] */
.align 32
.quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
.quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
.quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
.quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
.quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
.quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
.quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
.quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
.quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
.quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
.quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
.quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
/* PiH */
.align 32
.quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18
/* Pi2H */
.align 32
.quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
.align 32
.type __svml_dacos_data_internal, @object
.size __svml_dacos_data_internal, .-__svml_dacos_data_internal
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