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/* Function acos vectorized with SSE4.
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 16
#define SmallNorm 32
#define MOne 48
#define Two 64
#define sqrt_coeff 80
#define poly_coeff 144
#define PiH 336
#define Pi2H 352
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN2v_acos_sse4)
subq $72, %rsp
cfi_def_cfa_offset(80)
movaps %xmm0, %xmm5
movups __svml_dacos_data_internal(%rip), %xmm3
movups OneHalf+__svml_dacos_data_internal(%rip), %xmm6
/* x = -|arg| */
movaps %xmm3, %xmm4
orps %xmm5, %xmm4
/* Y = 0.5 + 0.5*(-x) */
movaps %xmm6, %xmm7
mulpd %xmm4, %xmm7
addpd %xmm7, %xmm6
/* S ~ 2*sqrt(Y) */
cvtpd2ps %xmm6, %xmm9
movlhps %xmm9, %xmm9
/* x^2 */
movaps %xmm4, %xmm0
rsqrtps %xmm9, %xmm10
mulpd %xmm4, %xmm0
cvtps2pd %xmm10, %xmm11
minpd %xmm6, %xmm0
movaps %xmm6, %xmm1
movaps %xmm0, %xmm2
cmpltpd SmallNorm+__svml_dacos_data_internal(%rip), %xmm1
cmpnltpd %xmm6, %xmm2
addpd %xmm6, %xmm6
andnps %xmm11, %xmm1
movaps %xmm0, %xmm11
movaps %xmm1, %xmm12
andps %xmm5, %xmm3
mulpd %xmm1, %xmm12
mulpd %xmm6, %xmm1
mulpd %xmm12, %xmm6
mulpd %xmm0, %xmm11
subpd Two+__svml_dacos_data_internal(%rip), %xmm6
movups sqrt_coeff+__svml_dacos_data_internal(%rip), %xmm13
movaps %xmm6, %xmm14
mulpd %xmm6, %xmm13
mulpd %xmm1, %xmm14
addpd sqrt_coeff+16+__svml_dacos_data_internal(%rip), %xmm13
mulpd %xmm6, %xmm13
addpd sqrt_coeff+32+__svml_dacos_data_internal(%rip), %xmm13
mulpd %xmm13, %xmm6
/* polynomial */
movups poly_coeff+__svml_dacos_data_internal(%rip), %xmm15
movaps %xmm11, %xmm7
mulpd %xmm0, %xmm15
addpd sqrt_coeff+48+__svml_dacos_data_internal(%rip), %xmm6
addpd poly_coeff+16+__svml_dacos_data_internal(%rip), %xmm15
mulpd %xmm11, %xmm7
mulpd %xmm6, %xmm14
mulpd %xmm11, %xmm15
subpd %xmm14, %xmm1
movups MOne+__svml_dacos_data_internal(%rip), %xmm8
andps %xmm2, %xmm1
/* NaN processed in special branch (so wind test passed) */
cmpnlepd %xmm4, %xmm8
movmskpd %xmm8, %edx
/* X<X^2 iff X<0 */
movaps %xmm5, %xmm12
movups poly_coeff+32+__svml_dacos_data_internal(%rip), %xmm8
movaps %xmm2, %xmm13
movups poly_coeff+64+__svml_dacos_data_internal(%rip), %xmm6
mulpd %xmm0, %xmm8
mulpd %xmm0, %xmm6
addpd poly_coeff+48+__svml_dacos_data_internal(%rip), %xmm8
addpd poly_coeff+80+__svml_dacos_data_internal(%rip), %xmm6
cmpltpd %xmm0, %xmm12
addpd %xmm15, %xmm8
mulpd %xmm11, %xmm6
mulpd %xmm7, %xmm8
movups poly_coeff+96+__svml_dacos_data_internal(%rip), %xmm9
mulpd %xmm0, %xmm9
addpd poly_coeff+112+__svml_dacos_data_internal(%rip), %xmm9
addpd %xmm6, %xmm9
movups poly_coeff+128+__svml_dacos_data_internal(%rip), %xmm10
movaps %xmm2, %xmm6
mulpd %xmm0, %xmm10
addpd %xmm8, %xmm9
addpd poly_coeff+144+__svml_dacos_data_internal(%rip), %xmm10
mulpd %xmm11, %xmm9
movups poly_coeff+160+__svml_dacos_data_internal(%rip), %xmm14
andnps %xmm4, %xmm6
addpd %xmm9, %xmm10
mulpd %xmm0, %xmm14
mulpd %xmm10, %xmm11
addpd poly_coeff+176+__svml_dacos_data_internal(%rip), %xmm14
addpd %xmm11, %xmm14
mulpd %xmm0, %xmm14
orps %xmm1, %xmm6
pxor %xmm3, %xmm6
mulpd %xmm6, %xmm14
movups PiH+__svml_dacos_data_internal(%rip), %xmm0
andps %xmm2, %xmm0
andnps Pi2H+__svml_dacos_data_internal(%rip), %xmm13
andps %xmm12, %xmm0
addpd %xmm13, %xmm0
addpd %xmm14, %xmm6
addpd %xmm6, %xmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm5
/* Restore registers
* and exit the function
*/
L(EXIT):
addq $72, %rsp
cfi_def_cfa_offset(8)
ret
cfi_def_cfa_offset(80)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
movups %xmm5, 32(%rsp)
movups %xmm0, 48(%rsp)
# LOE rbx rbp r12 r13 r14 r15 edx
xorl %eax, %eax
movq %r12, 16(%rsp)
cfi_offset(12, -64)
movl %eax, %r12d
movq %r13, 8(%rsp)
cfi_offset(13, -72)
movl %edx, %r13d
movq %r14, (%rsp)
cfi_offset(14, -80)
# LOE rbx rbp r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx rbp r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $2, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx rbp r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
movups 48(%rsp), %xmm0
/* Go to exit */
jmp L(EXIT)
cfi_offset(12, -64)
cfi_offset(13, -72)
cfi_offset(14, -80)
# LOE rbx rbp r12 r13 r14 r15 xmm0
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movsd 32(%rsp, %r14, 8), %xmm0
call acos@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movsd %xmm0, 48(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx rbp r15 r12d r13d
END(_ZGVbN2v_acos_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_dacos_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(16)) VUINT32 SgnBit[2][2];
__declspec(align(16)) VUINT32 OneHalf[2][2];
__declspec(align(16)) VUINT32 SmallNorm[2][2];
__declspec(align(16)) VUINT32 MOne[2][2];
__declspec(align(16)) VUINT32 Two[2][2];
__declspec(align(16)) VUINT32 sqrt_coeff[4][2][2];
__declspec(align(16)) VUINT32 poly_coeff[12][2][2];
__declspec(align(16)) VUINT32 PiH[2][2];
__declspec(align(16)) VUINT32 Pi2H[2][2];
} __svml_dacos_data_internal;
#endif
__svml_dacos_data_internal:
/* SgnBit */
.quad 0x8000000000000000, 0x8000000000000000
/* OneHalf */
.align 16
.quad 0x3fe0000000000000, 0x3fe0000000000000
/* SmallNorm */
.align 16
.quad 0x3000000000000000, 0x3000000000000000
/* MOne */
.align 16
.quad 0xbff0000000000000, 0xbff0000000000000
/* Two */
.align 16
.quad 0x4000000000000000, 0x4000000000000000
/* sqrt_coeff[4] */
.align 16
.quad 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
.quad 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
.quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
.quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
/* poly_coeff[12] */
.align 16
.quad 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
.quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
.quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
.quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
.quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
.quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
.quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
.quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
.quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
.quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
.quad 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
.quad 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
/* PiH */
.align 16
.quad 0x400921fb54442d18, 0x400921fb54442d18
/* Pi2H */
.align 16
.quad 0x3ff921fb54442d18, 0x3ff921fb54442d18
.align 16
.type __svml_dacos_data_internal, @object
.size __svml_dacos_data_internal, .-__svml_dacos_data_internal
|
