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/* Function exp2 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:
*
* Double precision mantissa represented as: 1.b1b2b3 ... b52
* Constant for double precision: S = 2^48 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(2^48 x 1.5 + X)
* (Note: 2^exp x 1.b1b2b3 ... b52, 2^{exp-52} = 2^-4 for exp=48)
*
* 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_dexp2_data_internal_avx512
*/
#define Frac_PowerD0 0
#define poly_coeff1 128
#define poly_coeff2 192
#define poly_coeff3 256
#define poly_coeff4 320
#define poly_coeff5 384
#define poly_coeff6 448
#define add_const 512
#define AbsMask 576
#define Threshold 640
#define _lIndexMask 704
#include <sysdep.h>
.section .text.evex512, "ax", @progbits
ENTRY(_ZGVeN8v_exp2_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 poly_coeff5+__svml_dexp2_data_internal_avx512(%rip), %zmm14
vmovups poly_coeff6+__svml_dexp2_data_internal_avx512(%rip), %zmm6
/*
* Reduced argument
* where VREDUCE is available
*/
vreducepd $65, {sae}, %zmm0, %zmm10
vmovups poly_coeff4+__svml_dexp2_data_internal_avx512(%rip), %zmm7
vmovups add_const+__svml_dexp2_data_internal_avx512(%rip), %zmm3
vmovups poly_coeff3+__svml_dexp2_data_internal_avx512(%rip), %zmm8
vmovups __svml_dexp2_data_internal_avx512(%rip), %zmm13
/* c6*r + c5 */
vfmadd231pd {rn-sae}, %zmm10, %zmm6, %zmm14
vmovups poly_coeff2+__svml_dexp2_data_internal_avx512(%rip), %zmm9
vmovups Threshold+__svml_dexp2_data_internal_avx512(%rip), %zmm2
/*
*
* HA
* Variables and constants
* Load constants and vector(s)
*/
vmovups poly_coeff1+__svml_dexp2_data_internal_avx512(%rip), %zmm11
/* c6*r^2 + c5*r + c4 */
vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm14
/*
* Integer form of K+0.b1b2b3b4 in lower bits - call K_plus_f0
* Mantisssa of normalized double precision FP: 1.b1b2...b52
*/
vaddpd {rd-sae}, %zmm3, %zmm0, %zmm4
vandpd AbsMask+__svml_dexp2_data_internal_avx512(%rip), %zmm0, %zmm1
/* c6*r^3 + c5*r^2 + c4*r + c3 */
vfmadd213pd {rn-sae}, %zmm8, %zmm10, %zmm14
vcmppd $29, {sae}, %zmm2, %zmm1, %k0
/* c6*r^4 + c5*r^3 + c4*r^2 + c3*r + c2 */
vfmadd213pd {rn-sae}, %zmm9, %zmm10, %zmm14
kmovw %k0, %edx
/* c6*r^5 + c5*r^4 + c4*r^3 + c3*r^2 + c2*r + c1 */
vfmadd213pd {rn-sae}, %zmm11, %zmm10, %zmm14
/* Table value: 2^(0.b1b2b3b4) */
vpandq _lIndexMask+__svml_dexp2_data_internal_avx512(%rip), %zmm4, %zmm5
vpermt2pd Frac_PowerD0+64+__svml_dexp2_data_internal_avx512(%rip), %zmm5, %zmm13
/* T*r */
vmulpd {rn-sae}, %zmm10, %zmm13, %zmm12
/* T + (T*r*(c6*r^5 + c5*r^4 + c4*r^3 + c3*r^2 + c2*r + c1)) */
vfmadd213pd {rn-sae}, %zmm13, %zmm12, %zmm14
/* Scaling placed at the end to avoid accuracy loss when T*r*scale underflows */
vscalefpd {rn-sae}, %zmm0, %zmm14, %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 $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), %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
vmovsd 64(%rsp, %r14, 8), %xmm0
call exp2@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_exp2_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_dexp2_data_internal_avx512_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(64)) VUINT32 Frac_PowerD0[16][2];
__declspec(align(64)) VUINT32 poly_coeff1[8][2];
__declspec(align(64)) VUINT32 poly_coeff2[8][2];
__declspec(align(64)) VUINT32 poly_coeff3[8][2];
__declspec(align(64)) VUINT32 poly_coeff4[8][2];
__declspec(align(64)) VUINT32 poly_coeff5[8][2];
__declspec(align(64)) VUINT32 poly_coeff6[8][2];
__declspec(align(64)) VUINT32 add_const[8][2];
__declspec(align(64)) VUINT32 AbsMask[8][2];
__declspec(align(64)) VUINT32 Threshold[8][2];
__declspec(align(64)) VUINT32 _lIndexMask[8][2];
} __svml_dexp2_data_internal_avx512;
#endif
__svml_dexp2_data_internal_avx512:
/* Frac_PowerD0 */
.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
.align 64
.quad 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B /* == poly_coeff1 == */
.align 64
.quad 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A /* == poly_coeff2 == */
.align 64
.quad 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9 /* == poly_coeff3 == */
.align 64
.quad 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252 /* == poly_coeff4 == */
.align 64
.quad 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19 /* == poly_coeff5 == */
.align 64
.quad 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B /* == poly_coeff6 == */
.align 64
.quad 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000 /* add_const */
.align 64
.quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff /* AbsMask */
.align 64
.quad 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000 /* Threshold */
.align 64
.quad 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F /* _lIndexMask */
.align 64
.type __svml_dexp2_data_internal_avx512, @object
.size __svml_dexp2_data_internal_avx512, .-__svml_dexp2_data_internal_avx512
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