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/* Function atanhf vectorized with AVX2.
Copyright (C) 2021 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 atanh(x) as 0.5 * log((1 + x)/(1 - x))
*
* Special cases:
*
* atanh(0) = 0
* atanh(+1) = +INF
* atanh(-1) = -INF
* atanh(x) = NaN if |x| > 1, or if x is a NaN or INF
*
*/
/* Offsets for data table __svml_satanh_data_internal
*/
#define SgnMask 0
#define sOne 32
#define sPoly 64
#define iBrkValue 320
#define iOffExpoMask 352
#define sHalf 384
#define sSign 416
#define sTopMask12 448
#define TinyRange 480
#define sLn2 512
#include <sysdep.h>
.text
.section .text.avx2,"ax",@progbits
ENTRY(_ZGVdN8v_atanhf_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
/* Load constants including One = 1 */
vmovups sOne+__svml_satanh_data_internal(%rip), %ymm5
vmovups sTopMask12+__svml_satanh_data_internal(%rip), %ymm13
vmovaps %ymm0, %ymm6
/* Strip off the sign, so treat X as positive until right at the end */
vandps SgnMask+__svml_satanh_data_internal(%rip), %ymm6, %ymm10
vsubps %ymm10, %ymm5, %ymm1
/*
* Compute V = 2 * X trivially, and UHi + U_lo = 1 - X in two pieces,
* the upper part UHi being <= 12 bits long. Then we have
* atanh(X) = 1/2 * log((1 + X) / (1 - X)) = 1/2 * log1p(V / (UHi + ULo)).
*/
vaddps %ymm10, %ymm10, %ymm14
/*
* Check whether |X| < 1, in which case we use the main function.
* Otherwise set the rangemask so that the callout will get used.
* Note that this will also use the callout for NaNs since not(NaN < 1).
*/
vcmpnlt_uqps %ymm5, %ymm10, %ymm7
vsubps %ymm1, %ymm5, %ymm9
vcmplt_oqps TinyRange+__svml_satanh_data_internal(%rip), %ymm10, %ymm4
vrcpps %ymm1, %ymm11
vsubps %ymm10, %ymm9, %ymm12
vandps %ymm13, %ymm11, %ymm0
/* No need to split sU when FMA is available */
vfnmadd213ps %ymm5, %ymm0, %ymm1
vmovaps %ymm6, %ymm8
vfmadd213ps %ymm6, %ymm6, %ymm8
vfnmadd231ps %ymm0, %ymm12, %ymm1
/*
* Split V as well into upper 12 bits and lower part, so that we can get
* a preliminary quotient estimate without rounding error.
*/
vandps %ymm13, %ymm14, %ymm15
vmovmskps %ymm7, %edx
vsubps %ymm15, %ymm14, %ymm7
/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
vmulps %ymm15, %ymm0, %ymm10
/* Compute D = E + E^2 */
vfmadd213ps %ymm1, %ymm1, %ymm1
/* Record the sign for eventual reincorporation. */
vandps sSign+__svml_satanh_data_internal(%rip), %ymm6, %ymm3
/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
vorps %ymm3, %ymm8, %ymm2
vmulps %ymm7, %ymm0, %ymm8
/*
* Compute R * (VHi + VLo) * (1 + E + E^2)
* = R * (VHi + VLo) * (1 + D)
* = QHi + (QHi * D + QLo + QLo * D)
*/
vmulps %ymm1, %ymm10, %ymm9
vfmadd213ps %ymm8, %ymm8, %ymm1
vaddps %ymm1, %ymm9, %ymm1
/* reduction: compute r,n */
vmovups iBrkValue+__svml_satanh_data_internal(%rip), %ymm9
/*
* Now finally accumulate the high and low parts of the
* argument to log1p, H + L, with a final compensated summation.
*/
vaddps %ymm1, %ymm10, %ymm12
vsubps %ymm12, %ymm10, %ymm11
/*
* Now we feed into the log1p code, using H in place of _VARG1 and
* later incorporating L into the reduced argument.
* compute 1+x as high, low parts
*/
vmaxps %ymm12, %ymm5, %ymm13
vminps %ymm12, %ymm5, %ymm14
vaddps %ymm11, %ymm1, %ymm0
vaddps %ymm14, %ymm13, %ymm1
vpsubd %ymm9, %ymm1, %ymm7
vsubps %ymm1, %ymm13, %ymm15
vpsrad $23, %ymm7, %ymm10
vpand iOffExpoMask+__svml_satanh_data_internal(%rip), %ymm7, %ymm8
vaddps %ymm15, %ymm14, %ymm13
vpslld $23, %ymm10, %ymm11
vpaddd %ymm9, %ymm8, %ymm15
vaddps %ymm13, %ymm0, %ymm14
vcvtdq2ps %ymm10, %ymm0
vpsubd %ymm11, %ymm5, %ymm12
/* polynomial evaluation */
vsubps %ymm5, %ymm15, %ymm5
vmulps %ymm14, %ymm12, %ymm1
vaddps %ymm5, %ymm1, %ymm5
vmovups sPoly+224+__svml_satanh_data_internal(%rip), %ymm1
vfmadd213ps sPoly+192+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+160+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+128+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+96+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+64+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+32+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vfmadd213ps sPoly+__svml_satanh_data_internal(%rip), %ymm5, %ymm1
vmulps %ymm1, %ymm5, %ymm7
vfmadd213ps %ymm5, %ymm5, %ymm7
/* final reconstruction */
vfmadd132ps sLn2+__svml_satanh_data_internal(%rip), %ymm7, %ymm0
/* Finally, halve the result and reincorporate the sign */
vxorps sHalf+__svml_satanh_data_internal(%rip), %ymm3, %ymm3
vmulps %ymm0, %ymm3, %ymm0
vblendvps %ymm4, %ymm2, %ymm0, %ymm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm6
/* 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 %ymm6, 32(%rsp)
vmovups %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 $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 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 fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 32(%rsp,%r14,4), %xmm0
call atanhf@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movss %xmm0, 64(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN8v_atanhf_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_satanh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 SgnMask[8][1];
__declspec(align(32)) VUINT32 sOne[8][1];
__declspec(align(32)) VUINT32 sPoly[8][8][1];
__declspec(align(32)) VUINT32 iBrkValue[8][1];
__declspec(align(32)) VUINT32 iOffExpoMask[8][1];
__declspec(align(32)) VUINT32 sHalf[8][1];
__declspec(align(32)) VUINT32 sSign[8][1];
__declspec(align(32)) VUINT32 sTopMask12[8][1];
__declspec(align(32)) VUINT32 TinyRange[8][1];
__declspec(align(32)) VUINT32 sLn2[8][1];
} __svml_satanh_data_internal;
#endif
__svml_satanh_data_internal:
/*== SgnMask ==*/
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/*== sOne = SP 1.0 ==*/
.align 32
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/*== sPoly[] = SP polynomial ==*/
.align 32
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
/*== iBrkValue = SP 2/3 ==*/
.align 32
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
/*== iOffExpoMask = SP significand mask ==*/
.align 32
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
/*== sHalf ==*/
.align 32
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
/*== sSign ==*/
.align 32
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
/*== sTopMask12 ==*/
.align 32
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
/*== TinyRange ==*/
.align 32
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
/*== sLn2 = SP ln(2) ==*/
.align 32
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
.align 32
.type __svml_satanh_data_internal,@object
.size __svml_satanh_data_internal,.-__svml_satanh_data_internal
|
