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/* Function acoshf vectorized with AVX2.
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 acosh(x) as log(x + sqrt(x*x - 1))
*
* Special cases:
*
* acosh(NaN) = quiet NaN, and raise invalid exception
* acosh(-INF) = NaN
* acosh(+INF) = +INF
* acosh(x) = NaN if x < 1
* acosh(1) = +0
*
*/
/* Offsets for data table __svml_sacosh_data_internal
*/
#define sOne 0
#define sPoly 32
#define iBrkValue 288
#define iOffExpoMask 320
#define sBigThreshold 352
#define sC2 384
#define sC3 416
#define sHalf 448
#define sLargestFinite 480
#define sThirtyOne 512
#define sTopMask8 544
#define XScale 576
#define sLn2 608
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN8v_acoshf_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, always including One = 1 */
vmovups sOne+__svml_sacosh_data_internal(%rip), %ymm2
/* Finally, express Y + W = U * V accurately where Y has <= 8 bits */
vmovups sTopMask8+__svml_sacosh_data_internal(%rip), %ymm9
/*
* 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_sacosh_data_internal(%rip), %ymm14
vmovaps %ymm0, %ymm3
vmovaps %ymm2, %ymm7
vfmsub231ps %ymm3, %ymm3, %ymm7
/*
* Check that 1 < X < +inf; otherwise go to the callout function.
* We need the callout for X = 1 to avoid division by zero below.
* This test ensures that callout handles NaN and either infinity.
*/
vcmpnle_uqps sLargestFinite+__svml_sacosh_data_internal(%rip), %ymm3, %ymm4
vcmpngt_uqps %ymm2, %ymm3, %ymm5
/*
* The following computation can go wrong for very large X, e.g.
* the X^2 - 1 = U * V can overflow. But for large X we have
* acosh(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 to do this.
*/
vcmplt_oqps sBigThreshold+__svml_sacosh_data_internal(%rip), %ymm3, %ymm1
vandps %ymm9, %ymm7, %ymm10
/*
* 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 %ymm10, %ymm8
vsubps %ymm10, %ymm7, %ymm11
vandps %ymm9, %ymm8, %ymm12
/*
* 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 %ymm12, %ymm10, %ymm15
vmulps %ymm11, %ymm12, %ymm0
/* Now multiplex to the case X = 2^-30 * input, Xl = 0 in the "big" case. */
vmulps XScale+__svml_sacosh_data_internal(%rip), %ymm3, %ymm11
/*
* 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 %ymm2, %ymm13
vfnmadd231ps %ymm15, %ymm12, %ymm13
vfnmadd231ps %ymm0, %ymm12, %ymm13
vfmadd213ps sC2+__svml_sacosh_data_internal(%rip), %ymm13, %ymm14
vfmadd213ps sHalf+__svml_sacosh_data_internal(%rip), %ymm13, %ymm14
vmulps %ymm14, %ymm13, %ymm7
vorps %ymm5, %ymm4, %ymm6
/*
* For low-accuracy versions, the computation can be done
* just as U + ((S + T) + (S + T) * Corr)
*/
vaddps %ymm0, %ymm15, %ymm5
/* sU is needed later on */
vsubps %ymm2, %ymm3, %ymm4
vfmadd213ps %ymm5, %ymm7, %ymm5
vmovmskps %ymm6, %edx
vaddps %ymm5, %ymm4, %ymm6
/*
* Now resume the main code.
* reduction: compute r, n
*/
vmovups iBrkValue+__svml_sacosh_data_internal(%rip), %ymm4
/*
* 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 %ymm6, %ymm2, %ymm8
vminps %ymm6, %ymm2, %ymm9
vaddps %ymm9, %ymm8, %ymm12
vblendvps %ymm1, %ymm12, %ymm11, %ymm14
vsubps %ymm12, %ymm8, %ymm10
vpsubd %ymm4, %ymm14, %ymm15
vaddps %ymm10, %ymm9, %ymm13
vpand iOffExpoMask+__svml_sacosh_data_internal(%rip), %ymm15, %ymm14
vpsrad $23, %ymm15, %ymm15
vpaddd %ymm4, %ymm14, %ymm8
vpslld $23, %ymm15, %ymm5
vmovups sPoly+224+__svml_sacosh_data_internal(%rip), %ymm4
vcvtdq2ps %ymm15, %ymm0
vpsubd %ymm5, %ymm2, %ymm7
/* polynomial evaluation */
vsubps %ymm2, %ymm8, %ymm2
/* Add 31 to the exponent in the "large" case to get log(2 * input) */
vaddps sThirtyOne+__svml_sacosh_data_internal(%rip), %ymm0, %ymm5
vandps %ymm1, %ymm13, %ymm6
vmulps %ymm7, %ymm6, %ymm9
vblendvps %ymm1, %ymm0, %ymm5, %ymm0
vaddps %ymm2, %ymm9, %ymm2
vfmadd213ps sPoly+192+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vfmadd213ps sPoly+160+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vfmadd213ps sPoly+128+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vfmadd213ps sPoly+96+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vfmadd213ps sPoly+64+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vfmadd213ps sPoly+32+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vfmadd213ps sPoly+__svml_sacosh_data_internal(%rip), %ymm2, %ymm4
vmulps %ymm4, %ymm2, %ymm6
vfmadd213ps %ymm2, %ymm2, %ymm6
/* final reconstruction */
vfmadd132ps sLn2+__svml_sacosh_data_internal(%rip), %ymm6, %ymm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx ymm0 ymm3
/* 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 %ymm3, 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 function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovss 32(%rsp, %r14, 4), %xmm0
call acoshf@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_acoshf_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_sacosh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__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 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_sacosh_data_internal;
#endif
__svml_sacosh_data_internal:
/* sOne = SP 1.0 */
.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
/* 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_sacosh_data_internal, @object
.size __svml_sacosh_data_internal, .-__svml_sacosh_data_internal
|
