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/* Function exp2f vectorized with AVX-512.
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:
*
* Single precision mantissa represented as: 1.b1b2b3 ... b23
* Constant for single precision: S = 2^19 x 1.5
*
* 2^X = 2^Xo x 2^{X-Xo}
* 2^X = 2^K x 2^fo x 2^{X-Xo}
* 2^X = 2^K x 2^fo x 2^r
*
* 2^K --> Manual scaling
* 2^fo --> Table lookup
* r --> 1 + poly (r = X - Xo)
*
* Xo = K + fo
* Xo = K + 0.x1x2x3x4
*
* r = X - Xo
* = Vreduce(X, imm)
* = X - VRndScale(X, imm), where Xo = VRndScale(X, imm)
*
* Rnd(S + X) = S + Xo, where S is selected as S = 2^19 x 1.5
* S + X = S + floor(X) + 0.x1x2x3x4
* Rnd(S + X) = Rnd(2^19 x 1.5 + X)
* (Note: 2^exp x 1.b1b2b3 ... b23, 2^{exp-23} = 2^-4 for exp=19)
*
* exp2(x) = 2^K x 2^fo x (1 + poly(r)), where 2^r = 1 + poly(r)
*
* Scale back:
* dest = src1 x 2^floor(src2)
*
*
*/
/* Offsets for data table __svml_sexp2_data_internal_avx512
*/
#define Frac_PowerS0 0
#define poly_coeff1 64
#define poly_coeff2 128
#define poly_coeff3 192
#define add_const 256
#define AbsMask 320
#define Threshold 384
#include <sysdep.h>
.text
.section .text.exex512,"ax",@progbits
ENTRY(_ZGVeN16v_exp2f_skx)
pushq %rbp
cfi_def_cfa_offset(16)
movq %rsp, %rbp
cfi_def_cfa(6, 16)
cfi_offset(6, -16)
andq $-64, %rsp
subq $192, %rsp
vmovups add_const+__svml_sexp2_data_internal_avx512(%rip), %zmm3
/*
* Reduced argument
* where VREDUCE is available
*/
vreduceps $65, {sae}, %zmm0, %zmm6
vmovups poly_coeff3+__svml_sexp2_data_internal_avx512(%rip), %zmm5
vmovups poly_coeff2+__svml_sexp2_data_internal_avx512(%rip), %zmm10
vmovups Threshold+__svml_sexp2_data_internal_avx512(%rip), %zmm2
/*
*
* HA
* Variables and constants
* Load constants and vector(s)
*/
vmovups poly_coeff1+__svml_sexp2_data_internal_avx512(%rip), %zmm7
/*
* Integer form of K+0.b1b2b3b4 in lower bits - call K_plus_f0
* Mantisssa of normalized single precision FP: 1.b1b2...b23
*/
vaddps {rd-sae}, %zmm3, %zmm0, %zmm4
vandps AbsMask+__svml_sexp2_data_internal_avx512(%rip), %zmm0, %zmm1
/* c3*r + c2 */
vfmadd231ps {rn-sae}, %zmm6, %zmm5, %zmm10
vcmpps $30, {sae}, %zmm2, %zmm1, %k0
/* c3*r^2 + c2*r + c1 */
vfmadd213ps {rn-sae}, %zmm7, %zmm6, %zmm10
/* Table value: 2^(0.b1b2b3b4) */
vpermps __svml_sexp2_data_internal_avx512(%rip), %zmm4, %zmm9
kmovw %k0, %edx
/* T*r */
vmulps {rn-sae}, %zmm6, %zmm9, %zmm8
/* T + (T*r*(c3*r^2 + c2*r + c1) */
vfmadd213ps {rn-sae}, %zmm9, %zmm8, %zmm10
/* Scaling placed at the end to avoid accuracy loss when T*r*scale underflows */
vscalefps {rn-sae}, %zmm0, %zmm10, %zmm1
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm1
/* Restore registers
* and exit the function
*/
L(EXIT):
vmovaps %zmm1, %zmm0
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 %zmm0, 64(%rsp)
vmovups %zmm1, 128(%rsp)
# LOE rbx r12 r13 r14 r15 edx zmm1
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: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 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: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
movl %edx, %r13d
movq %r14, (%rsp)
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 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 $16, %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 128(%rsp), %zmm1
/* Go to exit */
jmp L(EXIT)
/* DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus) */
.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus) */
.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
/* DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus) */
.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
# LOE rbx r12 r13 r14 r15 zmm1
/* Scalar math fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movss 64(%rsp,%r14,4), %xmm0
call exp2f@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movss %xmm0, 128(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN16v_exp2f_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_sexp2_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Frac_PowerS0[16][1];
__declspec(align(64)) VUINT32 poly_coeff1[16][1];
__declspec(align(64)) VUINT32 poly_coeff2[16][1];
__declspec(align(64)) VUINT32 poly_coeff3[16][1];
__declspec(align(64)) VUINT32 add_const[16][1];
__declspec(align(64)) VUINT32 AbsMask[16][1];
__declspec(align(64)) VUINT32 Threshold[16][1];
} __svml_sexp2_data_internal_avx512;
#endif
__svml_sexp2_data_internal_avx512:
/*== Frac_PowerS0 ==*/
.long 0x3F800000
.long 0x3F85AAC3
.long 0x3F8B95C2
.long 0x3F91C3D3
.long 0x3F9837F0
.long 0x3F9EF532
.long 0x3FA5FED7
.long 0x3FAD583F
.long 0x3FB504F3
.long 0x3FBD08A4
.long 0x3FC5672A
.long 0x3FCE248C
.long 0x3FD744FD
.long 0x3FE0CCDF
.long 0x3FEAC0C7
.long 0x3FF5257D
.align 64
.long 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222, 0x3F317222 /*== poly_coeff1 ==*/
.align 64
.long 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B, 0x3E75F16B /*== poly_coeff2 ==*/
.align 64
.long 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA, 0x3D6854CA /*== poly_coeff3 ==*/
.align 64
.long 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000, 0x49400000 /* add_const */
.align 64
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* AbsMask */
.align 64
.long 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000, 0x42fc0000 /* Threshold=126.0 */
.align 64
.type __svml_sexp2_data_internal_avx512,@object
.size __svml_sexp2_data_internal_avx512,.-__svml_sexp2_data_internal_avx512
|
