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/* Function exp10 vectorized with AVX-512.
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:
* Typical exp10() implementation, except that:
* - tables are small (16 elements), allowing for fast gathers
* - all arguments processed in the main path
* - final VSCALEF assists branch-free design (correct overflow/underflow and special case responses)
* - a VAND is used to ensure the reduced argument |R|<2, even for large inputs
* - RZ mode used to avoid overflow to +/-Inf for x*log2(e); helps with special case handling
* - SAE used to avoid spurious flag settings
*
*/
/* Offsets for data table __svml_dexp10_data_internal_avx512
*/
#define Exp_tbl_H 0
#define L2E 128
#define Shifter 192
#define L2H 256
#define L2L 320
#define EMask 384
#define poly_coeff6 448
#define poly_coeff5 512
#define poly_coeff4 576
#define poly_coeff3 640
#define poly_coeff2 704
#define poly_coeff1 768
#define AbsMask 832
#define Threshold 896
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN8v_exp10_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 L2E+__svml_dexp10_data_internal_avx512(%rip), %zmm4
vmovups Shifter+__svml_dexp10_data_internal_avx512(%rip), %zmm2
vmovups L2H+__svml_dexp10_data_internal_avx512(%rip), %zmm5
vmovups L2L+__svml_dexp10_data_internal_avx512(%rip), %zmm3
/* polynomial */
vmovups poly_coeff6+__svml_dexp10_data_internal_avx512(%rip), %zmm6
vmovups poly_coeff4+__svml_dexp10_data_internal_avx512(%rip), %zmm7
vmovups poly_coeff3+__svml_dexp10_data_internal_avx512(%rip), %zmm9
vmovups poly_coeff2+__svml_dexp10_data_internal_avx512(%rip), %zmm8
vmovups poly_coeff1+__svml_dexp10_data_internal_avx512(%rip), %zmm11
vmovups Threshold+__svml_dexp10_data_internal_avx512(%rip), %zmm14
vmovaps %zmm0, %zmm1
/* 2^(52-4)*1.5 + x * log2(e) */
vfmadd213pd {rz-sae}, %zmm2, %zmm1, %zmm4
vandpd AbsMask+__svml_dexp10_data_internal_avx512(%rip), %zmm1, %zmm13
/* Z0 ~ x*log2(e), rounded down to 4 fractional bits */
vsubpd {rn-sae}, %zmm2, %zmm4, %zmm0
/* Table lookup: Th */
vmovups __svml_dexp10_data_internal_avx512(%rip), %zmm2
vcmppd $29, {sae}, %zmm14, %zmm13, %k0
/* R = x - Z0*log(2) */
vfnmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm5
vpermt2pd Exp_tbl_H+64+__svml_dexp10_data_internal_avx512(%rip), %zmm4, %zmm2
kmovw %k0, %edx
vfnmadd231pd {rn-sae}, %zmm0, %zmm3, %zmm5
vmovups poly_coeff5+__svml_dexp10_data_internal_avx512(%rip), %zmm3
/* ensure |R|<2 even for special cases */
vandpd EMask+__svml_dexp10_data_internal_avx512(%rip), %zmm5, %zmm12
vmulpd {rn-sae}, %zmm12, %zmm12, %zmm10
vmulpd {rn-sae}, %zmm12, %zmm2, %zmm15
vfmadd231pd {rn-sae}, %zmm12, %zmm6, %zmm3
vfmadd231pd {rn-sae}, %zmm12, %zmm7, %zmm9
vfmadd231pd {rn-sae}, %zmm12, %zmm8, %zmm11
vfmadd213pd {rn-sae}, %zmm9, %zmm10, %zmm3
vfmadd213pd {rn-sae}, %zmm11, %zmm10, %zmm3
vfmadd213pd {rn-sae}, %zmm2, %zmm15, %zmm3
vscalefpd {rn-sae}, %zmm0, %zmm3, %zmm0
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):
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 %zmm1, 64(%rsp)
vmovups %zmm0, 128(%rsp)
# LOE rbx r12 r13 r14 r15 edx zmm0
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 $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 128(%rsp), %zmm0
/* 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 zmm0
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovsd 64(%rsp, %r14, 8), %xmm0
call exp10@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovsd %xmm0, 128(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN8v_exp10_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dexp10_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Exp_tbl_H[16][2];
__declspec(align(64)) VUINT32 L2E[8][2];
__declspec(align(64)) VUINT32 Shifter[8][2];
__declspec(align(64)) VUINT32 L2H[8][2];
__declspec(align(64)) VUINT32 L2L[8][2];
__declspec(align(64)) VUINT32 EMask[8][2];
__declspec(align(64)) VUINT32 poly_coeff6[8][2];
__declspec(align(64)) VUINT32 poly_coeff5[8][2];
__declspec(align(64)) VUINT32 poly_coeff4[8][2];
__declspec(align(64)) VUINT32 poly_coeff3[8][2];
__declspec(align(64)) VUINT32 poly_coeff2[8][2];
__declspec(align(64)) VUINT32 poly_coeff1[8][2];
__declspec(align(64)) VUINT32 AbsMask[8][2];
__declspec(align(64)) VUINT32 Threshold[8][2];
} __svml_dexp10_data_internal_avx512;
#endif
__svml_dexp10_data_internal_avx512:
/* Exp_tbl_H */
.quad 0x3ff0000000000000
.quad 0x3ff0b5586cf9890f
.quad 0x3ff172b83c7d517b
.quad 0x3ff2387a6e756238
.quad 0x3ff306fe0a31b715
.quad 0x3ff3dea64c123422
.quad 0x3ff4bfdad5362a27
.quad 0x3ff5ab07dd485429
.quad 0x3ff6a09e667f3bcd
.quad 0x3ff7a11473eb0187
.quad 0x3ff8ace5422aa0db
.quad 0x3ff9c49182a3f090
.quad 0x3ffae89f995ad3ad
.quad 0x3ffc199bdd85529c
.quad 0x3ffd5818dcfba487
.quad 0x3ffea4afa2a490da
/* log2(e) */
.align 64
.quad 0x400A934F0979A371, 0x400A934F0979A371, 0x400A934F0979A371, 0x400A934F0979A371, 0x400A934F0979A371, 0x400A934F0979A371, 0x400A934F0979A371, 0x400A934F0979A371
/* Shifter=2^(52-4)*1.5 */
.align 64
.quad 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0, 0x42f8000000003ff0
/* L2H = log(2)_high */
.align 64
.quad 0x3fd34413509f79ff, 0x3fd34413509f79ff, 0x3fd34413509f79ff, 0x3fd34413509f79ff, 0x3fd34413509f79ff, 0x3fd34413509f79ff, 0x3fd34413509f79ff, 0x3fd34413509f79ff
/* L2L = log(2)_low */
.align 64
.quad 0xbc49dc1da994fd21, 0xbc49dc1da994fd21, 0xbc49dc1da994fd21, 0xbc49dc1da994fd21, 0xbc49dc1da994fd21, 0xbc49dc1da994fd21, 0xbc49dc1da994fd21, 0xbc49dc1da994fd21
/* EMask */
.align 64
.quad 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff, 0xbfffffffffffffff
/* poly_coeff6 */
.align 64
.quad 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020, 0x3fcb137ed8ac2020
/* poly_coeff5 */
.align 64
.quad 0x3fe141a8e24f9424, 0x3fe141a8e24f9424, 0x3fe141a8e24f9424, 0x3fe141a8e24f9424, 0x3fe141a8e24f9424, 0x3fe141a8e24f9424, 0x3fe141a8e24f9424, 0x3fe141a8e24f9424
/* poly_coeff4 */
.align 64
.quad 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d, 0x3ff2bd77a0926c9d
/* poly_coeff3 */
.align 64
.quad 0x40004705908704c8, 0x40004705908704c8, 0x40004705908704c8, 0x40004705908704c8, 0x40004705908704c8, 0x40004705908704c8, 0x40004705908704c8, 0x40004705908704c8
/* poly_coeff2 */
.align 64
.quad 0x40053524c73dfe25, 0x40053524c73dfe25, 0x40053524c73dfe25, 0x40053524c73dfe25, 0x40053524c73dfe25, 0x40053524c73dfe25, 0x40053524c73dfe25, 0x40053524c73dfe25
/* poly_coeff1 */
.align 64
.quad 0x40026bb1bbb554c2, 0x40026bb1bbb554c2, 0x40026bb1bbb554c2, 0x40026bb1bbb554c2, 0x40026bb1bbb554c2, 0x40026bb1bbb554c2, 0x40026bb1bbb554c2, 0x40026bb1bbb554c2
/* AbsMask */
.align 64
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff
/* Threshold */
.align 64
.quad 0x40733A7146F72A41, 0x40733A7146F72A41, 0x40733A7146F72A41, 0x40733A7146F72A41, 0x40733A7146F72A41, 0x40733A7146F72A41, 0x40733A7146F72A41, 0x40733A7146F72A41
.align 64
.type __svml_dexp10_data_internal_avx512, @object
.size __svml_dexp10_data_internal_avx512, .-__svml_dexp10_data_internal_avx512
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