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|
/* Function asinhf 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 asinh(x) as log(x + sqrt(x*x + 1))
*
* Special cases:
*
* asinh(NaN) = quiet NaN, and raise invalid exception
* asinh(INF) = that INF
* asinh(0) = that 0
*
*/
/* Offsets for data table __svml_sasinh_data_internal
*/
#define SgnMask 0
#define sOne 16
#define sPoly 32
#define iBrkValue 160
#define iOffExpoMask 176
#define sBigThreshold 192
#define sC2 208
#define sC3 224
#define sHalf 240
#define sLargestFinite 256
#define sLittleThreshold 272
#define sSign 288
#define sThirtyOne 304
#define sTopMask11 320
#define sTopMask8 336
#define XScale 352
#define sLn2 368
#include <sysdep.h>
.text
.section .text.sse4,"ax",@progbits
ENTRY(_ZGVbN4v_asinhf_sse4)
subq $72, %rsp
cfi_def_cfa_offset(80)
movaps %xmm0, %xmm8
/*
* Split X into high and low parts, XHi (<= 11 bits) and XLo (<= 13 bits)
* We could use either X or |X| here, but it doesn't seem to matter
*/
movups sTopMask11+__svml_sasinh_data_internal(%rip), %xmm10
movaps %xmm8, %xmm2
andps %xmm8, %xmm10
/*
* Compute X^2 = (XHi + XLo)^2 = XHi^2 + XLo * (X + XHi)
* The two parts are shifted off by around 11 bits. So even though
* the low bit will not in general be exact, it's near enough
*/
movaps %xmm10, %xmm3
subps %xmm10, %xmm2
mulps %xmm10, %xmm3
addps %xmm8, %xmm10
/* Load the constant 1 and a sign mask */
movups sOne+__svml_sasinh_data_internal(%rip), %xmm7
/*
* Finally, express Y + W = X^2 + 1 accurately where Y has <= 8 bits.
* If |X| <= 1 then |XHi| <= 1 and so |X2Hi| <= 1, so we can treat 1
* as the dominant component in the compensated summation. Otherwise,
* if |X| >= 1, then since X2Hi only has 22 significant bits, the basic
* addition will be exact anyway until we get to |X| >= 2^24. But by
* that time the log function is well-conditioned enough that the
* rounding error doesn't matter. Hence we can treat 1 as dominant even
* if it literally isn't.
*/
movaps %xmm7, %xmm11
movaps %xmm7, %xmm4
movups sTopMask8+__svml_sasinh_data_internal(%rip), %xmm12
addps %xmm3, %xmm11
mulps %xmm10, %xmm2
subps %xmm11, %xmm4
movaps %xmm12, %xmm0
addps %xmm3, %xmm4
/*
* Unfortunately, we can still be in trouble if |X| <= 2^-5, since
* the absolute error 2^-(7+24)-ish in sqrt(1 + X^2) gets scaled up
* by 1/X and comes close to our threshold. Hence if |X| <= 2^-4,
* perform an alternative computation
* sqrt(1 + X^2) - 1 = X^2/2 - X^4/8 + X^6/16
* X2 = X^2
*/
addps %xmm2, %xmm3
addps %xmm2, %xmm4
andps %xmm11, %xmm0
/*
* Compute R = 1/sqrt(Y + W) * (1 + d)
* Force R to <= 8 significant bits.
* This means that R * Y and R^2 * Y are exactly representable.
*/
rsqrtps %xmm0, %xmm14
subps %xmm0, %xmm11
andps %xmm12, %xmm14
addps %xmm11, %xmm4
/*
* Compute S = (Y/sqrt(Y + W)) * (1 + d)
* and T = (W/sqrt(Y + W)) * (1 + d)
* so that S + T = sqrt(Y + W) * (1 + d)
* S is exact, and the rounding error in T is OK.
*/
mulps %xmm14, %xmm0
mulps %xmm14, %xmm4
/*
* Get the absolute value of the input, since we will exploit antisymmetry
* and mostly assume X >= 0 in the core computation
*/
movups SgnMask+__svml_sasinh_data_internal(%rip), %xmm6
/*
* Compute e = -(2 * d + d^2)
* The first FMR is exact, and the rounding error in the other is acceptable
* since d and e are ~ 2^-8
*/
movaps %xmm14, %xmm13
andps %xmm8, %xmm6
/*
* Obtain sqrt(1 + X^2) - 1 in two pieces
* sqrt(1 + X^2) - 1
* = sqrt(Y + W) - 1
* = (S + T) * (1 + Corr) - 1
* = [S - 1] + [T + (S + T) * Corr]
* We need a compensated summation for the last part. We treat S - 1
* as the larger part; it certainly is until about X < 2^-4, and in that
* case, the error is affordable since X dominates over sqrt(1 + X^2) - 1
* Final sum is dTmp5 (hi) + dTmp7 (lo)
*/
movaps %xmm0, %xmm1
/*
* Check whether the input is finite, by checking |X| <= MaxFloat
* Otherwise set the rangemask so that the callout will get used.
* Note that this will also use the callout for NaNs since not(NaN <= MaxFloat)
*/
movaps %xmm6, %xmm9
/*
* The following computation can go wrong for very large X, basically
* because X^2 overflows. But for large X we have
* asinh(X) / log(2 X) - 1 =~= 1/(4 * X^2), so for X >= 2^30
* we can just later stick X back into the log and tweak up the exponent.
* Actually we scale X by 2^-30 and tweak the exponent up by 31,
* to stay in the safe range for the later log computation.
* Compute a flag now telling us when do do this.
*/
movaps %xmm6, %xmm5
cmpnleps sLargestFinite+__svml_sasinh_data_internal(%rip), %xmm9
cmpltps sBigThreshold+__svml_sasinh_data_internal(%rip), %xmm5
mulps %xmm0, %xmm13
addps %xmm4, %xmm1
subps %xmm7, %xmm0
mulps %xmm4, %xmm14
movmskps %xmm9, %edx
movaps %xmm7, %xmm9
/*
* Now 1 / (1 + d)
* = 1 / (1 + (sqrt(1 - e) - 1))
* = 1 / sqrt(1 - e)
* = 1 + 1/2 * e + 3/8 * e^2 + 5/16 * e^3 + 35/128 * e^4 + ...
* So compute the first three nonconstant terms of that, so that
* we have a relative correction (1 + Corr) to apply to S etc.
* C1 = 1/2
* C2 = 3/8
* C3 = 5/16
*/
movups sC3+__svml_sasinh_data_internal(%rip), %xmm15
subps %xmm13, %xmm9
movups sHalf+__svml_sasinh_data_internal(%rip), %xmm10
subps %xmm14, %xmm9
/* sX2over2 = X^2/2 */
mulps %xmm10, %xmm3
mulps %xmm9, %xmm15
/* sX46 = -X^4/4 + X^6/8 */
movaps %xmm3, %xmm2
movaps %xmm3, %xmm12
/*
* Now do another compensated sum to add |X| + [sqrt(1 + X^2) - 1].
* It's always safe to assume |X| is larger.
* This is the final 2-part argument to the log1p function
*/
movaps %xmm6, %xmm14
addps sC2+__svml_sasinh_data_internal(%rip), %xmm15
mulps %xmm9, %xmm15
addps %xmm10, %xmm15
mulps %xmm15, %xmm9
mulps %xmm1, %xmm9
/* Now multiplex to the case X = 2^-30 * input, Xl = sL = 0 in the "big" case. */
movups XScale+__svml_sasinh_data_internal(%rip), %xmm15
addps %xmm9, %xmm4
movaps %xmm4, %xmm11
addps %xmm0, %xmm11
subps %xmm11, %xmm0
addps %xmm0, %xmm4
/* sX4over4 = X^4/4 */
movaps %xmm3, %xmm0
mulps %xmm3, %xmm0
mulps %xmm0, %xmm2
subps %xmm0, %xmm2
/*
* Now we feed into the log1p code, using H in place of _VARG1 and
* also adding L into Xl.
* compute 1+x as high, low parts
*/
movaps %xmm7, %xmm0
/* sX46over2 = -X^4/8 + x^6/16 */
mulps %xmm2, %xmm10
movaps %xmm7, %xmm2
addps %xmm10, %xmm12
subps %xmm12, %xmm3
addps %xmm3, %xmm10
/* Now multiplex the two possible computations */
movaps %xmm6, %xmm3
cmpleps sLittleThreshold+__svml_sasinh_data_internal(%rip), %xmm3
movaps %xmm3, %xmm13
andps %xmm3, %xmm12
andnps %xmm11, %xmm13
movaps %xmm3, %xmm1
orps %xmm12, %xmm13
andnps %xmm4, %xmm1
andps %xmm3, %xmm10
movaps %xmm6, %xmm4
orps %xmm10, %xmm1
addps %xmm13, %xmm14
mulps %xmm15, %xmm6
maxps %xmm14, %xmm0
minps %xmm14, %xmm2
subps %xmm14, %xmm4
movaps %xmm0, %xmm3
addps %xmm4, %xmm13
addps %xmm2, %xmm3
addps %xmm13, %xmm1
subps %xmm3, %xmm0
movaps %xmm5, %xmm4
andps %xmm5, %xmm3
andnps %xmm6, %xmm4
addps %xmm0, %xmm2
/*
* Now resume the main code.
* reduction: compute r,n
*/
movdqu iBrkValue+__svml_sasinh_data_internal(%rip), %xmm6
orps %xmm3, %xmm4
psubd %xmm6, %xmm4
movaps %xmm7, %xmm0
addps %xmm2, %xmm1
movdqu iOffExpoMask+__svml_sasinh_data_internal(%rip), %xmm2
pand %xmm4, %xmm2
psrad $23, %xmm4
cvtdq2ps %xmm4, %xmm3
pslld $23, %xmm4
andps %xmm5, %xmm1
paddd %xmm6, %xmm2
psubd %xmm4, %xmm0
mulps %xmm0, %xmm1
/* polynomial evaluation */
subps %xmm7, %xmm2
movups sPoly+112+__svml_sasinh_data_internal(%rip), %xmm7
addps %xmm2, %xmm1
mulps %xmm1, %xmm7
movaps %xmm5, %xmm2
/* Add 31 to the exponent in the "large" case to get log(2 * input) */
movups sThirtyOne+__svml_sasinh_data_internal(%rip), %xmm0
addps sPoly+96+__svml_sasinh_data_internal(%rip), %xmm7
addps %xmm3, %xmm0
mulps %xmm1, %xmm7
andnps %xmm0, %xmm2
andps %xmm5, %xmm3
orps %xmm3, %xmm2
addps sPoly+80+__svml_sasinh_data_internal(%rip), %xmm7
/* final reconstruction */
mulps sLn2+__svml_sasinh_data_internal(%rip), %xmm2
mulps %xmm1, %xmm7
/* Finally, reincorporate the original sign. */
movups sSign+__svml_sasinh_data_internal(%rip), %xmm0
andps %xmm8, %xmm0
addps sPoly+64+__svml_sasinh_data_internal(%rip), %xmm7
mulps %xmm1, %xmm7
addps sPoly+48+__svml_sasinh_data_internal(%rip), %xmm7
mulps %xmm1, %xmm7
addps sPoly+32+__svml_sasinh_data_internal(%rip), %xmm7
mulps %xmm1, %xmm7
addps sPoly+16+__svml_sasinh_data_internal(%rip), %xmm7
mulps %xmm1, %xmm7
addps sPoly+__svml_sasinh_data_internal(%rip), %xmm7
mulps %xmm1, %xmm7
mulps %xmm1, %xmm7
addps %xmm7, %xmm1
addps %xmm2, %xmm1
pxor %xmm1, %xmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm8
/* 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 %xmm8, 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 asinhf@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_asinhf_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_sasinh_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 sBigThreshold[4][1];
__declspec(align(16)) VUINT32 sC2[4][1];
__declspec(align(16)) VUINT32 sC3[4][1];
__declspec(align(16)) VUINT32 sHalf[4][1];
__declspec(align(16)) VUINT32 sLargestFinite[4][1];
__declspec(align(16)) VUINT32 sLittleThreshold[4][1];
__declspec(align(16)) VUINT32 sSign[4][1];
__declspec(align(16)) VUINT32 sThirtyOne[4][1];
__declspec(align(16)) VUINT32 sTopMask11[4][1];
__declspec(align(16)) VUINT32 sTopMask8[4][1];
__declspec(align(16)) VUINT32 XScale[4][1];
__declspec(align(16)) VUINT32 sLn2[4][1];
} __svml_sasinh_data_internal;
#endif
__svml_sasinh_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
/*== sBigThreshold ==*/
.align 16
.long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000
/*== sC2 ==*/
.align 16
.long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000
/*== sC3 ==*/
.align 16
.long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000
/*== sHalf ==*/
.align 16
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
/*== sLargestFinite ==*/
.align 16
.long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF
/*== sLittleThreshold ==*/
.align 16
.long 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000
/*== sSign ==*/
.align 16
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000
/*== sThirtyOne ==*/
.align 16
.long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000
/*== sTopMask11 ==*/
.align 16
.long 0xFFFFE000, 0xFFFFE000, 0xFFFFE000, 0xFFFFE000
/*== sTopMask8 ==*/
.align 16
.long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000
/*== XScale ==*/
.align 16
.long 0x30800000, 0x30800000, 0x30800000, 0x30800000
/*== sLn2 = SP ln(2) ==*/
.align 16
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
.align 16
.type __svml_sasinh_data_internal,@object
.size __svml_sasinh_data_internal,.-__svml_sasinh_data_internal
|