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/* Function atanhf 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:
*
* 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_avx512. Ordered
by use in the function. On cold-starts this might help the
prefetcher. Possibly a better idea is to interleave start/end so
that the prefetcher is less likely to detect a stream and pull
irrelivant lines into cache. */
#define sOne 0
#define SgnMask 16
#define sTopMask12 32
#define iBrkValue 48
#define iOffExpoMask 64
#define sPoly 80
#define sLn2 208
#define TinyRange 224
#include <sysdep.h>
#define ATANHF_DATA(x) ((x)+__svml_satanh_data_internal)
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN4v_atanhf_sse4)
movaps %xmm0, %xmm5
/* Load constants including One = 1 */
movups ATANHF_DATA(sOne)(%rip), %xmm4
movaps %xmm5, %xmm3
/* Strip off the sign, so treat X as positive until right at the end */
movups ATANHF_DATA(SgnMask)(%rip), %xmm1
movaps %xmm4, %xmm2
andps %xmm1, %xmm0
movaps %xmm4, %xmm10
movups ATANHF_DATA(sTopMask12)(%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 %xmm0, %xmm6
mulps %xmm5, %xmm3
subps %xmm0, %xmm2
addps %xmm0, %xmm6
subps %xmm2, %xmm10
addps %xmm5, %xmm3
subps %xmm0, %xmm10
andps %xmm2, %xmm9
/*
* 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).
*/
rcpps %xmm9, %xmm7
subps %xmm9, %xmm2
andps %xmm11, %xmm7
/*
* Split V as well into upper 12 bits and lower part, so that we can get
* a preliminary quotient estimate without rounding error.
*/
andps %xmm6, %xmm11
mulps %xmm7, %xmm9
addps %xmm2, %xmm10
subps %xmm11, %xmm6
/* Hence get initial quotient estimate QHi + QLo = R * VHi + R * VLo */
mulps %xmm7, %xmm11
mulps %xmm7, %xmm10
subps %xmm9, %xmm14
mulps %xmm6, %xmm7
subps %xmm10, %xmm14
/* Compute D = E + E^2 */
movaps %xmm14, %xmm13
movaps %xmm4, %xmm8
mulps %xmm14, %xmm13
/* reduction: compute r,n */
movdqu ATANHF_DATA(iBrkValue)(%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, %xmm2
mulps %xmm7, %xmm14
mulps %xmm11, %xmm2
addps %xmm14, %xmm7
movdqu ATANHF_DATA(iOffExpoMask)(%rip), %xmm12
movaps %xmm4, %xmm14
/* Record the sign for eventual reincorporation. */
addps %xmm7, %xmm2
/*
* Now finally accumulate the high and low parts of the
* argument to log1p, H + L, with a final compensated summation.
*/
movaps %xmm2, %xmm6
andnps %xmm5, %xmm1
movaps %xmm4, %xmm7
/* Or the sign bit in with the tiny result to handle atanh(-0) correctly */
addps %xmm11, %xmm6
maxps %xmm6, %xmm7
minps %xmm6, %xmm8
subps %xmm6, %xmm11
movaps %xmm7, %xmm10
addps %xmm8, %xmm10
addps %xmm11, %xmm2
subps %xmm10, %xmm7
psubd %xmm9, %xmm10
addps %xmm8, %xmm7
pand %xmm10, %xmm12
psrad $23, %xmm10
cvtdq2ps %xmm10, %xmm13
addps %xmm7, %xmm2
/* final reconstruction */
pslld $23, %xmm10
paddd %xmm9, %xmm12
psubd %xmm10, %xmm14
/* polynomial evaluation */
subps %xmm4, %xmm12
mulps %xmm14, %xmm2
movups ATANHF_DATA(sPoly+0)(%rip), %xmm7
addps %xmm12, %xmm2
mulps %xmm2, %xmm7
/* Finally, halve the result and reincorporate the sign */
addps ATANHF_DATA(sPoly+16)(%rip), %xmm7
mulps %xmm2, %xmm7
addps ATANHF_DATA(sPoly+32)(%rip), %xmm7
mulps %xmm2, %xmm7
addps ATANHF_DATA(sPoly+48)(%rip), %xmm7
mulps %xmm2, %xmm7
addps ATANHF_DATA(sPoly+64)(%rip), %xmm7
mulps %xmm2, %xmm7
addps ATANHF_DATA(sPoly+80)(%rip), %xmm7
mulps %xmm2, %xmm7
addps ATANHF_DATA(sPoly+96)(%rip), %xmm7
mulps %xmm2, %xmm7
movaps ATANHF_DATA(sPoly+112)(%rip), %xmm6
addps %xmm6, %xmm7
mulps %xmm2, %xmm7
mulps %xmm2, %xmm7
mulps ATANHF_DATA(sLn2)(%rip), %xmm13
/* We can build `sHalf` with `sPoly & sOne`. */
andps %xmm4, %xmm6
orps %xmm1, %xmm3
xorps %xmm6, %xmm1
addps %xmm2, %xmm7
addps %xmm13, %xmm7
mulps %xmm7, %xmm1
/* Finish check of NaNs. */
cmpleps %xmm0, %xmm4
movmskps %xmm4, %edx
cmpltps ATANHF_DATA(TinyRange)(%rip), %xmm0
andps %xmm0, %xmm3
andnps %xmm1, %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 xmm0
/* No registers to restore on fast path. */
ret
/* Cold case. edx has 1s where there was a special value that
needs to be handled by a atanhf call. Optimize for code size
more so than speed here. */
L(SPECIAL_VALUES_BRANCH):
# LOE rbx rdx rbp r12 r13 r14 r15 xmm0 xmm5
/* Stack coming in 16-byte aligned. Set 8-byte misaligned so on
call entry will be 16-byte aligned. */
subq $56, %rsp
cfi_def_cfa_offset(64)
movups %xmm0, 24(%rsp)
movups %xmm5, 40(%rsp)
/* Use rbx/rbp for callee save registers as they get short
encoding for many instructions (as compared with r12/r13). */
movq %rbx, (%rsp)
cfi_offset(rbx, -64)
movq %rbp, 8(%rsp)
cfi_offset(rbp, -56)
/* edx has 1s where there was a special value that needs to be handled
by a tanhf call. */
movl %edx, %ebx
L(SPECIAL_VALUES_LOOP):
# LOE rbx rbp r12 r13 r14 r15
/* use rbp as index for special value that is saved across calls to
tanhf. We technically don't need a callee save register here as offset
to rsp is always [0, 12] so we can restore rsp by realigning to 64.
Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
in the loop. */
xorl %ebp, %ebp
bsfl %ebx, %ebp
/* Scalar math function call to process special input. */
movss 40(%rsp, %rbp, 4), %xmm0
call atanhf@PLT
/* No good way to avoid the store-forwarding fault this will cause on
return. `lfence` avoids the SF fault but at greater cost as it
serialized stack/callee save restoration. */
movss %xmm0, 24(%rsp, %rbp, 4)
leal -1(%rbx), %eax
andl %eax, %ebx
jnz L(SPECIAL_VALUES_LOOP)
# LOE r12 r13 r14 r15
/* All results have been written to 24(%rsp). */
movups 24(%rsp), %xmm0
movq (%rsp), %rbx
cfi_restore(rbx)
movq 8(%rsp), %rbp
cfi_restore(rbp)
addq $56, %rsp
cfi_def_cfa_offset(8)
ret
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 sOne[4][1];
__declspec(align(16)) VUINT32 SgnMask[4][1];
__declspec(align(16)) VUINT32 sTopMask12[4][1];
__declspec(align(16)) VUINT32 iBrkValue[4][1];
__declspec(align(16)) VUINT32 iOffExpoMask[4][1];
__declspec(align(16)) VUINT32 sPoly[8][4][1];
__declspec(align(16)) VUINT32 sLn2[4][1];
__declspec(align(16)) VUINT32 TinyRange[4][1];
} __svml_satanh_data_internal;
#endif
__svml_satanh_data_internal:
/* sOne = SP 1.0 */
.align 16
.long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
/* SgnMask */
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
/* sTopMask12 */
.align 16
.long 0xFFFFF000, 0xFFFFF000, 0xFFFFF000, 0xFFFFF000
/* iBrkValue = SP 2/3 */
.align 16
.long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
/* iOffExpoMask = SP significand mask ==*/
.align 16
.long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
/* sPoly[] = SP polynomial */
.align 16
.long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /* 1.3820238411426544189453125e-01 P7 */
.long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
.long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /* 1.4042308926582336425781250e-01 P5 */
.long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
.long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /* 2.0007920265197753906250000e-01 P3 */
.long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
.long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /* 3.3333265781402587890625000e-01 P1 */
.long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
/* sLn2 = SP ln(2) */
.align 16
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
/* TinyRange */
.align 16
.long 0x0C000000, 0x0C000000, 0x0C000000, 0x0C000000
.align 16
.type __svml_satanh_data_internal, @object
.size __svml_satanh_data_internal, .-__svml_satanh_data_internal
|
