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/* Function asinhf vectorized with AVX2.
Copyright (C) 2021-2022 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 32
#define sPoly 64
#define iBrkValue 320
#define iOffExpoMask 352
#define sBigThreshold 384
#define sC2 416
#define sC3 448
#define sHalf 480
#define sLargestFinite 512
#define sLittleThreshold 544
#define sSign 576
#define sThirtyOne 608
#define sTopMask8 640
#define XScale 672
#define sLn2 704
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_asinhf_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
vmovaps %ymm0, %ymm9
/* Load the constant 1 and a sign mask */
vmovups sOne+__svml_sasinh_data_internal(%rip), %ymm8
/* No need to split X when FMA is available in hardware. */
vmulps %ymm9, %ymm9, %ymm5
vmovups sTopMask8+__svml_sasinh_data_internal(%rip), %ymm1
/*
* 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.
*/
vaddps %ymm5, %ymm8, %ymm13
vandps %ymm1, %ymm13, %ymm2
vmovaps %ymm9, %ymm4
vsubps %ymm13, %ymm8, %ymm11
vsubps %ymm2, %ymm13, %ymm15
/*
* 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.
*/
vrsqrtps %ymm2, %ymm0
vfmsub213ps %ymm5, %ymm9, %ymm4
vaddps %ymm11, %ymm5, %ymm12
/*
* Get the absolute value of the input, since we will exploit antisymmetry
* and mostly assume X >= 0 in the core computation
*/
vandps SgnMask+__svml_sasinh_data_internal(%rip), %ymm9, %ymm6
/*
* 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)
*/
vcmpnle_uqps sLargestFinite+__svml_sasinh_data_internal(%rip), %ymm6, %ymm10
vaddps %ymm12, %ymm4, %ymm14
/*
* 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
*/
vaddps %ymm4, %ymm5, %ymm4
/*
* 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.
*/
vcmplt_oqps sBigThreshold+__svml_sasinh_data_internal(%rip), %ymm6, %ymm7
vaddps %ymm15, %ymm14, %ymm3
/*
* 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
*/
vmovups sC3+__svml_sasinh_data_internal(%rip), %ymm12
vmovmskps %ymm10, %edx
vandps %ymm1, %ymm0, %ymm10
/*
* 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.
*/
vmulps %ymm10, %ymm2, %ymm15
vmulps %ymm3, %ymm10, %ymm14
vmovups sHalf+__svml_sasinh_data_internal(%rip), %ymm3
vsubps %ymm8, %ymm15, %ymm0
/*
* 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)
*/
vaddps %ymm14, %ymm15, %ymm13
/*
* 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
*/
vmovaps %ymm8, %ymm11
vfnmadd231ps %ymm15, %ymm10, %ymm11
vfnmadd231ps %ymm14, %ymm10, %ymm11
vfmadd213ps sC2+__svml_sasinh_data_internal(%rip), %ymm11, %ymm12
vfmadd213ps %ymm3, %ymm11, %ymm12
vmulps %ymm12, %ymm11, %ymm1
/* Now multiplex the two possible computations */
vcmple_oqps sLittleThreshold+__svml_sasinh_data_internal(%rip), %ymm6, %ymm11
vfmadd213ps %ymm14, %ymm13, %ymm1
vaddps %ymm0, %ymm1, %ymm2
vsubps %ymm2, %ymm0, %ymm10
/* sX2over2 = X^2/2 */
vmulps %ymm4, %ymm3, %ymm0
vaddps %ymm10, %ymm1, %ymm1
/* sX4over4 = X^4/4 */
vmulps %ymm0, %ymm0, %ymm5
/* sX46 = -X^4/4 + X^6/8 */
vfmsub231ps %ymm0, %ymm5, %ymm5
/* sX46over2 = -X^4/8 + x^6/16 */
vmulps %ymm5, %ymm3, %ymm3
vaddps %ymm3, %ymm0, %ymm5
vblendvps %ymm11, %ymm5, %ymm2, %ymm2
vsubps %ymm5, %ymm0, %ymm4
/*
* 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
*/
vaddps %ymm2, %ymm6, %ymm14
/*
* Now resume the main code.
* reduction: compute r, n
*/
vmovups iBrkValue+__svml_sasinh_data_internal(%rip), %ymm5
vaddps %ymm4, %ymm3, %ymm10
/*
* 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
*/
vmaxps %ymm14, %ymm8, %ymm15
vminps %ymm14, %ymm8, %ymm0
vblendvps %ymm11, %ymm10, %ymm1, %ymm12
vsubps %ymm14, %ymm6, %ymm1
vaddps %ymm0, %ymm15, %ymm3
/* Now multiplex to the case X = 2^-30 * input, Xl = sL = 0 in the "big" case. */
vmulps XScale+__svml_sasinh_data_internal(%rip), %ymm6, %ymm6
vaddps %ymm1, %ymm2, %ymm13
vsubps %ymm3, %ymm15, %ymm15
vaddps %ymm13, %ymm12, %ymm1
vaddps %ymm15, %ymm0, %ymm2
vblendvps %ymm7, %ymm3, %ymm6, %ymm0
vaddps %ymm2, %ymm1, %ymm4
vpsubd %ymm5, %ymm0, %ymm1
vpsrad $23, %ymm1, %ymm6
vpand iOffExpoMask+__svml_sasinh_data_internal(%rip), %ymm1, %ymm2
vmovups sPoly+224+__svml_sasinh_data_internal(%rip), %ymm1
vpslld $23, %ymm6, %ymm10
vpaddd %ymm5, %ymm2, %ymm13
vcvtdq2ps %ymm6, %ymm0
vpsubd %ymm10, %ymm8, %ymm12
/* polynomial evaluation */
vsubps %ymm8, %ymm13, %ymm8
/* Add 31 to the exponent in the "large" case to get log(2 * input) */
vaddps sThirtyOne+__svml_sasinh_data_internal(%rip), %ymm0, %ymm3
vandps %ymm7, %ymm4, %ymm11
vmulps %ymm12, %ymm11, %ymm14
vblendvps %ymm7, %ymm0, %ymm3, %ymm0
vaddps %ymm8, %ymm14, %ymm2
vfmadd213ps sPoly+192+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+160+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+128+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+96+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+64+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+32+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vfmadd213ps sPoly+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
vmulps %ymm1, %ymm2, %ymm4
vfmadd213ps %ymm2, %ymm2, %ymm4
/* final reconstruction */
vfmadd132ps sLn2+__svml_sasinh_data_internal(%rip), %ymm4, %ymm0
/* Finally, reincorporate the original sign. */
vandps sSign+__svml_sasinh_data_internal(%rip), %ymm9, %ymm7
vxorps %ymm0, %ymm7, %ymm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm9
/* 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 %ymm9, 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
vmovss 32(%rsp, %r14, 4), %xmm0
call asinhf@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovss %xmm0, 64(%rsp, %r14, 4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN8v_asinhf_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_sasinh_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 sBigThreshold[8][1];
__declspec(align(32)) VUINT32 sC2[8][1];
__declspec(align(32)) VUINT32 sC3[8][1];
__declspec(align(32)) VUINT32 sHalf[8][1];
__declspec(align(32)) VUINT32 sLargestFinite[8][1];
__declspec(align(32)) VUINT32 sLittleThreshold[8][1];
__declspec(align(32)) VUINT32 sSign[8][1];
__declspec(align(32)) VUINT32 sThirtyOne[8][1];
__declspec(align(32)) VUINT32 sTopMask8[8][1];
__declspec(align(32)) VUINT32 XScale[8][1];
__declspec(align(32)) VUINT32 sLn2[8][1];
} __svml_sasinh_data_internal;
#endif
__svml_sasinh_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
/* sBigThreshold */
.align 32
.long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000
/* sC2 */
.align 32
.long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000
/* sC3 */
.align 32
.long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000
/* sHalf */
.align 32
.long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
/* sLargestFinite */
.align 32
.long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF
/* sLittleThreshold */
.align 32
.long 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000
/* sSign */
.align 32
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
/* sThirtyOne */
.align 32
.long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000
/* sTopMask8 */
.align 32
.long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000
/* XScale */
.align 32
.long 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000
/* sLn2 = SP ln(2) */
.align 32
.long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
.align 32
.type __svml_sasinh_data_internal, @object
.size __svml_sasinh_data_internal, .-__svml_sasinh_data_internal
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