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/* Function asin 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:
*
* SelMask = (|x| >= 0.5) ? 1 : 0;
* R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x|
* asin(x) = (SelMask ? (Pi/2 - 2*Poly(R)) : Poly(R))*(-1)^sign(x)
*
*/
/* Offsets for data table __svml_dasin_data_internal
*/
#define AbsMask 0
#define OneHalf 64
#define SmallNorm 128
#define One 192
#define Two 256
#define sqrt_coeff_1 320
#define sqrt_coeff_2 384
#define sqrt_coeff_3 448
#define sqrt_coeff_4 512
#define poly_coeff_1 576
#define poly_coeff_2 640
#define poly_coeff_3 704
#define poly_coeff_4 768
#define poly_coeff_5 832
#define poly_coeff_6 896
#define poly_coeff_7 960
#define poly_coeff_8 1024
#define poly_coeff_9 1088
#define poly_coeff_10 1152
#define poly_coeff_11 1216
#define poly_coeff_12 1280
#define Pi2H 1344
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN8v_asin_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 OneHalf+__svml_dasin_data_internal(%rip), %zmm8
/* S ~ -2*sqrt(Y) */
vmovups SmallNorm+__svml_dasin_data_internal(%rip), %zmm10
vmovups Two+__svml_dasin_data_internal(%rip), %zmm14
vmovups sqrt_coeff_1+__svml_dasin_data_internal(%rip), %zmm15
vmovups sqrt_coeff_2+__svml_dasin_data_internal(%rip), %zmm2
vmovups sqrt_coeff_3+__svml_dasin_data_internal(%rip), %zmm1
vmovups One+__svml_dasin_data_internal(%rip), %zmm9
vmovaps %zmm0, %zmm6
/* x = |arg| */
vandpd __svml_dasin_data_internal(%rip), %zmm6, %zmm4
/* Y = 0.5 - 0.5*x */
vmovaps %zmm8, %zmm11
vfnmadd231pd {rn-sae}, %zmm4, %zmm8, %zmm11
/* x^2 */
vmulpd {rn-sae}, %zmm4, %zmm4, %zmm7
vrsqrt14pd %zmm11, %zmm12
vcmppd $17, {sae}, %zmm10, %zmm11, %k1
vcmppd $21, {sae}, %zmm8, %zmm4, %k2
vcmppd $17, {sae}, %zmm4, %zmm9, %k0
vmovups poly_coeff_5+__svml_dasin_data_internal(%rip), %zmm10
/* polynomial */
vmovups poly_coeff_1+__svml_dasin_data_internal(%rip), %zmm8
vmovups poly_coeff_3+__svml_dasin_data_internal(%rip), %zmm9
vminpd {sae}, %zmm11, %zmm7, %zmm3
vxorpd %zmm12, %zmm12, %zmm12{%k1}
vaddpd {rn-sae}, %zmm11, %zmm11, %zmm0
vxorpd %zmm6, %zmm4, %zmm5
vmulpd {rn-sae}, %zmm12, %zmm12, %zmm13
vmulpd {rn-sae}, %zmm12, %zmm0, %zmm7
vmovups poly_coeff_7+__svml_dasin_data_internal(%rip), %zmm11
vmovups poly_coeff_4+__svml_dasin_data_internal(%rip), %zmm12
vfmsub213pd {rn-sae}, %zmm14, %zmm13, %zmm0
vmovups sqrt_coeff_4+__svml_dasin_data_internal(%rip), %zmm13
vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm12
vmovups poly_coeff_11+__svml_dasin_data_internal(%rip), %zmm9
vfmadd231pd {rn-sae}, %zmm0, %zmm15, %zmm2
vmovups poly_coeff_9+__svml_dasin_data_internal(%rip), %zmm15
vmulpd {rn-sae}, %zmm0, %zmm7, %zmm14
vfmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm2
vmovups poly_coeff_2+__svml_dasin_data_internal(%rip), %zmm1
kmovw %k0, %edx
vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm2
vfmadd231pd {rn-sae}, %zmm3, %zmm8, %zmm1
vmovups poly_coeff_10+__svml_dasin_data_internal(%rip), %zmm8
vmulpd {rn-sae}, %zmm3, %zmm3, %zmm0
vfmsub213pd {rn-sae}, %zmm7, %zmm14, %zmm2
vmovups poly_coeff_6+__svml_dasin_data_internal(%rip), %zmm7
vfmadd231pd {rn-sae}, %zmm3, %zmm15, %zmm8
vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm1
vblendmpd %zmm2, %zmm4, %zmm2{%k2}
vfmadd231pd {rn-sae}, %zmm3, %zmm10, %zmm7
vmovups poly_coeff_8+__svml_dasin_data_internal(%rip), %zmm10
vmovups Pi2H+__svml_dasin_data_internal(%rip), %zmm4
vfmadd231pd {rn-sae}, %zmm3, %zmm11, %zmm10
vmovups poly_coeff_12+__svml_dasin_data_internal(%rip), %zmm11
vfmadd213pd {rn-sae}, %zmm10, %zmm0, %zmm7
vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm11
vmulpd {rn-sae}, %zmm0, %zmm0, %zmm10
vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm1
vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm1
vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1
vmulpd {rn-sae}, %zmm3, %zmm1, %zmm3
vfmadd213pd {rn-sae}, %zmm2, %zmm2, %zmm3
vaddpd {rn-sae}, %zmm4, %zmm3, %zmm3{%k2}
vxorpd %zmm5, %zmm3, %zmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm6
/* 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 %zmm6, 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 asin@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_asin_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dasin_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 AbsMask[8][2];
__declspec(align(64)) VUINT32 OneHalf[8][2];
__declspec(align(64)) VUINT32 SmallNorm[8][2];
__declspec(align(64)) VUINT32 One[8][2];
__declspec(align(64)) VUINT32 Two[8][2];
__declspec(align(64)) VUINT32 sqrt_coeff[4][8][2];
__declspec(align(64)) VUINT32 poly_coeff[12][8][2];
__declspec(align(64)) VUINT32 Pi2H[8][2];
} __svml_dasin_data_internal;
#endif
__svml_dasin_data_internal:
/* AbsMask */
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff
/* OneHalf */
.align 64
.quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
/* SmallNorm */
.align 64
.quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
/* One */
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
/* Two */
.align 64
.quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
/* sqrt_coeff[4] */
.align 64
.quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
.quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
.quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
.quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
/* poly_coeff[12] */
.align 64
.quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
.quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
.quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
.quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
.quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
.quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
.quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
.quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
.quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
.quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
.quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
.quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
/* Pi2H */
.align 64
.quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
.align 64
.type __svml_dasin_data_internal, @object
.size __svml_dasin_data_internal, .-__svml_dasin_data_internal
|
