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/* Function log1p 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:
*
* 1+x = 2^k*(xh + xl) is computed in high-low parts; xh in [1,2)
* Get short reciprocal approximation Rcp ~ 1/xh
* R = (Rcp*xh - 1.0) + Rcp*xl
* log1p(x) = k*log(2.0) - log(Rcp) + poly(R)
* log(Rcp) is tabulated
*
*
*/
/* Offsets for data table __svml_dlog1p_data_internal_avx512
*/
#define Log_tbl 0
#define One 128
#define SgnMask 192
#define C075 256
#define poly_coeff9 320
#define poly_coeff8 384
#define poly_coeff7 448
#define poly_coeff6 512
#define poly_coeff5 576
#define poly_coeff4 640
#define poly_coeff3 704
#define poly_coeff2 768
#define L2 832
#include <sysdep.h>
.text
.section .text.evex512,"ax",@progbits
ENTRY(_ZGVeN8v_log1p_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 One+__svml_dlog1p_data_internal_avx512(%rip), %zmm7
vmovups SgnMask+__svml_dlog1p_data_internal_avx512(%rip), %zmm14
vmovaps %zmm0, %zmm9
vaddpd {rn-sae}, %zmm9, %zmm7, %zmm11
vandpd %zmm14, %zmm9, %zmm8
/* compute 1+x as high, low parts */
vmaxpd {sae}, %zmm9, %zmm7, %zmm10
vminpd {sae}, %zmm9, %zmm7, %zmm12
/* GetMant(x), normalized to [1,2) for x>=0, NaN for x<0 */
vgetmantpd $8, {sae}, %zmm11, %zmm6
/* GetExp(x) */
vgetexppd {sae}, %zmm11, %zmm5
vsubpd {rn-sae}, %zmm10, %zmm11, %zmm13
/* DblRcp ~ 1/Mantissa */
vrcp14pd %zmm6, %zmm15
/* Start polynomial evaluation */
vmovups poly_coeff9+__svml_dlog1p_data_internal_avx512(%rip), %zmm10
vmovups poly_coeff7+__svml_dlog1p_data_internal_avx512(%rip), %zmm11
/* Xl */
vsubpd {rn-sae}, %zmm13, %zmm12, %zmm2
vxorpd %zmm14, %zmm5, %zmm3
/* round DblRcp to 4 fractional bits (RN mode, no Precision exception) */
vrndscalepd $88, {sae}, %zmm15, %zmm4
vmovups poly_coeff5+__svml_dlog1p_data_internal_avx512(%rip), %zmm12
vmovups poly_coeff6+__svml_dlog1p_data_internal_avx512(%rip), %zmm14
vmovups poly_coeff3+__svml_dlog1p_data_internal_avx512(%rip), %zmm13
/* Xl*2^(-Expon) */
vscalefpd {rn-sae}, %zmm3, %zmm2, %zmm1
/* Reduced argument: R = DblRcp*(Mantissa+Xl) - 1 */
vfmsub213pd {rn-sae}, %zmm7, %zmm4, %zmm6
vmovups __svml_dlog1p_data_internal_avx512(%rip), %zmm3
/*
* Table lookup
* Prepare exponent correction: DblRcp<0.75?
*/
vmovups C075+__svml_dlog1p_data_internal_avx512(%rip), %zmm2
/* Prepare table index */
vpsrlq $48, %zmm4, %zmm0
vfmadd231pd {rn-sae}, %zmm4, %zmm1, %zmm6
vmovups poly_coeff8+__svml_dlog1p_data_internal_avx512(%rip), %zmm1
vcmppd $17, {sae}, %zmm2, %zmm4, %k1
vcmppd $4, {sae}, %zmm6, %zmm6, %k0
vfmadd231pd {rn-sae}, %zmm6, %zmm10, %zmm1
vmovups poly_coeff4+__svml_dlog1p_data_internal_avx512(%rip), %zmm10
vfmadd231pd {rn-sae}, %zmm6, %zmm11, %zmm14
vmovups L2+__svml_dlog1p_data_internal_avx512(%rip), %zmm4
vpermt2pd Log_tbl+64+__svml_dlog1p_data_internal_avx512(%rip), %zmm0, %zmm3
/* add 1 to Expon if DblRcp<0.75 */
vaddpd {rn-sae}, %zmm7, %zmm5, %zmm5{%k1}
/* R^2 */
vmulpd {rn-sae}, %zmm6, %zmm6, %zmm0
vfmadd231pd {rn-sae}, %zmm6, %zmm12, %zmm10
vmovups poly_coeff2+__svml_dlog1p_data_internal_avx512(%rip), %zmm12
vmulpd {rn-sae}, %zmm0, %zmm0, %zmm15
vfmadd231pd {rn-sae}, %zmm6, %zmm13, %zmm12
vfmadd213pd {rn-sae}, %zmm14, %zmm0, %zmm1
kmovw %k0, %edx
vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm10
/* polynomial */
vfmadd213pd {rn-sae}, %zmm10, %zmm15, %zmm1
vfmadd213pd {rn-sae}, %zmm6, %zmm0, %zmm1
vaddpd {rn-sae}, %zmm1, %zmm3, %zmm6
vfmadd213pd {rn-sae}, %zmm6, %zmm4, %zmm5
vorpd %zmm8, %zmm5, %zmm0
testl %edx, %edx
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 edx zmm0 zmm9
/* 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 %zmm9, 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 fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movsd 64(%rsp,%r14,8), %xmm0
call log1p@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movsd %xmm0, 128(%rsp,%r14,8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN8v_log1p_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dlog1p_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Log_tbl[16][2];
__declspec(align(64)) VUINT32 One[8][2];
__declspec(align(64)) VUINT32 SgnMask[8][2];
__declspec(align(64)) VUINT32 C075[8][2];
__declspec(align(64)) VUINT32 poly_coeff9[8][2];
__declspec(align(64)) VUINT32 poly_coeff8[8][2];
__declspec(align(64)) VUINT32 poly_coeff7[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 L2[8][2];
} __svml_dlog1p_data_internal_avx512;
#endif
__svml_dlog1p_data_internal_avx512:
/*== Log_tbl ==*/
.quad 0x0000000000000000
.quad 0xbfaf0a30c01162a6
.quad 0xbfbe27076e2af2e6
.quad 0xbfc5ff3070a793d4
.quad 0xbfcc8ff7c79a9a22
.quad 0xbfd1675cababa60e
.quad 0xbfd4618bc21c5ec2
.quad 0xbfd739d7f6bbd007
.quad 0x3fd269621134db92
.quad 0x3fcf991c6cb3b379
.quad 0x3fca93ed3c8ad9e3
.quad 0x3fc5bf406b543db2
.quad 0x3fc1178e8227e47c
.quad 0x3fb9335e5d594989
.quad 0x3fb08598b59e3a07
.quad 0x3fa0415d89e74444
/*== One ==*/
.align 64
.quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
/*== SgnMask ==*/
.align 64
.quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
/*== C075 0.75 ==*/
.align 64
.quad 0x3fe8000000000000, 0x3fe8000000000000, 0x3fe8000000000000, 0x3fe8000000000000, 0x3fe8000000000000, 0x3fe8000000000000, 0x3fe8000000000000, 0x3fe8000000000000
/*== poly_coeff9 ==*/
.align 64
.quad 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70, 0x3fbC81CD309D7C70
/*== poly_coeff8 ==*/
.align 64
.quad 0xbfc007357E93AF62, 0xbfc007357E93AF62, 0xbfc007357E93AF62, 0xbfc007357E93AF62, 0xbfc007357E93AF62, 0xbfc007357E93AF62, 0xbfc007357E93AF62, 0xbfc007357E93AF62
/*== poly_coeff7 ==*/
.align 64
.quad 0x3fc249229CEE81EF, 0x3fc249229CEE81EF, 0x3fc249229CEE81EF, 0x3fc249229CEE81EF, 0x3fc249229CEE81EF, 0x3fc249229CEE81EF, 0x3fc249229CEE81EF, 0x3fc249229CEE81EF
/*== poly_coeff6 ==*/
.align 64
.quad 0xbfc55553FB28DB06, 0xbfc55553FB28DB06, 0xbfc55553FB28DB06, 0xbfc55553FB28DB06, 0xbfc55553FB28DB06, 0xbfc55553FB28DB06, 0xbfc55553FB28DB06, 0xbfc55553FB28DB06
/*== poly_coeff5 ==*/
.align 64
.quad 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C, 0x3fc9999999CC9F5C
/*== poly_coeff4 ==*/
.align 64
.quad 0xbfd00000000C05BD, 0xbfd00000000C05BD, 0xbfd00000000C05BD, 0xbfd00000000C05BD, 0xbfd00000000C05BD, 0xbfd00000000C05BD, 0xbfd00000000C05BD, 0xbfd00000000C05BD
/*== poly_coeff3 ==*/
.align 64
.quad 0x3fd5555555555466, 0x3fd5555555555466, 0x3fd5555555555466, 0x3fd5555555555466, 0x3fd5555555555466, 0x3fd5555555555466, 0x3fd5555555555466, 0x3fd5555555555466
/*== poly_coeff2 ==*/
.align 64
.quad 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6, 0xbfdFFFFFFFFFFFC6
/*== L2 = log(2) ==*/
.align 64
.quad 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF, 0x3fe62E42FEFA39EF
.align 64
.type __svml_dlog1p_data_internal_avx512,@object
.size __svml_dlog1p_data_internal_avx512,.-__svml_dlog1p_data_internal_avx512
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