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/* Function atanhf vectorized with SSE4.
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 16
#define sPoly 32
#define iBrkValue 160
#define iOffExpoMask 176
#define sHalf 192
#define sSign 208
#define sTopMask12 224
#define TinyRange 240
#define sLn2 256
#include <sysdep.h>
.text
.section .text.sse4,"ax",@progbits
ENTRY(_ZGVbN4v_atanhf_sse4)
subq $72, %rsp
cfi_def_cfa_offset(80)
movaps %xmm0, %xmm5
/* Load constants including One = 1 */
movups sOne+__svml_satanh_data_internal(%rip), %xmm4
movaps %xmm5, %xmm3
/* Strip off the sign, so treat X as positive until right at the end */
movups SgnMask+__svml_satanh_data_internal(%rip), %xmm7
movaps %xmm4, %xmm8
andps %xmm5, %xmm7
movaps %xmm4, %xmm10
movups sTopMask12+__svml_satanh_data_internal(%rip), %xmm11
movaps %xmm4, %xmm14
movaps %xmm11, %xmm9
/*
* 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)).
*/
movaps %xmm7, %xmm12
/*
* 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).
*/
movaps %xmm7, %xmm6
movaps %xmm7, %xmm2
cmpnltps %xmm4, %xmm6
cmpltps TinyRange+__svml_satanh_data_internal(%rip), %xmm2
mulps %xmm5, %xmm3
subps %xmm7, %xmm8
addps %xmm7, %xmm12
movmskps %xmm6, %edx
subps %xmm8, %xmm10
addps %xmm5, %xmm3
subps %xmm7, %xmm10
andps %xmm8, %xmm9
/*
* 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
*/
movaps %xmm4, %xmm7
/*
* Now compute R = 1/(UHi+ULo) * (1 - E) and the error term E
* The first FMR is exact (we force R to 12 bits just in case it
* isn't already, to make absolutely sure), and since E is ~ 2^-12,
* the rounding error in the other one is acceptable.
*/
rcpps %xmm9, %xmm15
subps %xmm9, %xmm8
andps %xmm11, %xmm15
/*
* Split V as well into upper 12 bits and lower part, so that we can get
* a preliminary quotient estimate without rounding error.
*/
andps %xmm12, %xmm11
mulps %xmm15, %xmm9
addps %xmm8, %xmm10
subps %xmm11, %xmm12
/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
mulps %xmm15, %xmm11
mulps %xmm15, %xmm10
subps %xmm9, %xmm14
mulps %xmm12, %xmm15
subps %xmm10, %xmm14
/* Compute D = E + E^2 */
movaps %xmm14, %xmm13
movaps %xmm4, %xmm8
mulps %xmm14, %xmm13
/* reduction: compute r,n */
movdqu iBrkValue+__svml_satanh_data_internal(%rip), %xmm9
addps %xmm13, %xmm14
/*
* Compute R * (VHi + VLo) * (1 + E + E^2)
* = R * (VHi + VLo) * (1 + D)
* = QHi + (QHi * D + QLo + QLo * D)
*/
movaps %xmm14, %xmm0
mulps %xmm15, %xmm14
mulps %xmm11, %xmm0
addps %xmm14, %xmm15
movdqu iOffExpoMask+__svml_satanh_data_internal(%rip), %xmm12
movaps %xmm4, %xmm14
/* Record the sign for eventual reincorporation. */
movups sSign+__svml_satanh_data_internal(%rip), %xmm1
addps %xmm15, %xmm0
/*
* Now finally accumulate the high and low parts of the
* argument to log1p, H + L, with a final compensated summation.
*/
movaps %xmm0, %xmm6
andps %xmm5, %xmm1
/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
orps %xmm1, %xmm3
addps %xmm11, %xmm6
maxps %xmm6, %xmm7
minps %xmm6, %xmm8
subps %xmm6, %xmm11
movaps %xmm7, %xmm10
andps %xmm2, %xmm3
addps %xmm8, %xmm10
addps %xmm11, %xmm0
subps %xmm10, %xmm7
psubd %xmm9, %xmm10
addps %xmm7, %xmm8
pand %xmm10, %xmm12
psrad $23, %xmm10
cvtdq2ps %xmm10, %xmm13
addps %xmm8, %xmm0
/* final reconstruction */
mulps sLn2+__svml_satanh_data_internal(%rip), %xmm13
pslld $23, %xmm10
paddd %xmm9, %xmm12
psubd %xmm10, %xmm14
/* polynomial evaluation */
subps %xmm4, %xmm12
mulps %xmm0, %xmm14
movups sPoly+112+__svml_satanh_data_internal(%rip), %xmm0
addps %xmm12, %xmm14
mulps %xmm14, %xmm0
/* Finally, halve the result and reincorporate the sign */
movups sHalf+__svml_satanh_data_internal(%rip), %xmm4
pxor %xmm1, %xmm4
addps sPoly+96+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
addps sPoly+80+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
addps sPoly+64+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
addps sPoly+48+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
addps sPoly+32+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
addps sPoly+16+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
addps sPoly+__svml_satanh_data_internal(%rip), %xmm0
mulps %xmm14, %xmm0
mulps %xmm14, %xmm0
addps %xmm0, %xmm14
movaps %xmm2, %xmm0
addps %xmm13, %xmm14
mulps %xmm14, %xmm4
andnps %xmm4, %xmm0
orps %xmm3, %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 $4, %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 fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 32(%rsp,%r14,4), %xmm0
call atanhf@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movss %xmm0, 48(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx rbp r15 r12d r13d
END(_ZGVbN4v_atanhf_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_satanh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(16)) VUINT32 SgnMask[4][1];
__declspec(align(16)) VUINT32 sOne[4][1];
__declspec(align(16)) VUINT32 sPoly[8][4][1];
__declspec(align(16)) VUINT32 iBrkValue[4][1];
__declspec(align(16)) VUINT32 iOffExpoMask[4][1];
__declspec(align(16)) VUINT32 sHalf[4][1];
__declspec(align(16)) VUINT32 sSign[4][1];
__declspec(align(16)) VUINT32 sTopMask12[4][1];
__declspec(align(16)) VUINT32 TinyRange[4][1];
__declspec(align(16)) VUINT32 sLn2[4][1];
} __svml_satanh_data_internal;
#endif
__svml_satanh_data_internal:
/*== SgnMask ==*/
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/*== sOne = SP 1.0 ==*/
.align 16
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/*== sPoly[] = SP polynomial ==*/
.align 16
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
/*== iBrkValue = SP 2/3 ==*/
.align 16
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
/*== iOffExpoMask = SP significand mask ==*/
.align 16
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
/*== sHalf ==*/
.align 16
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
/*== sSign ==*/
.align 16
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000
/*== sTopMask12 ==*/
.align 16
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
/*== TinyRange ==*/
.align 16
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
/*== sLn2 = SP ln(2) ==*/
.align 16
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
.align 16
.type __svml_satanh_data_internal,@object
.size __svml_satanh_data_internal,.-__svml_satanh_data_internal
|
