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|
/* Function exp10 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:
*
* exp10(x) = 2^x/log10(2) = 2^n * (1 + T[j]) * (1 + P(y))
* where
* x = m*log10(2)/K + y, y in [-log10(2)/K..log10(2)/K]
* m = n*K + j, m, n,j - signed integer, j in [-K/2..K/2]
*
* values of 2^j/K are tabulated
*
* P(y) is a minimax polynomial approximation of exp10(x)-1
* on small interval [-log10(2)/K..log10(2)/K]
*
* Special cases:
*
* exp10(NaN) = NaN
* exp10(+INF) = +INF
* exp10(-INF) = 0
* exp10(x) = 1 for subnormals
* For IEEE double
* if x > 3.39782712893383973096e+02 then exp10(x) overflow
* if x < -3.45133219101941108420e+02 then exp10(x) underflow
*
*/
/* Offsets for data table __svml_dexp10_data_internal
*/
#define _dbT 0
#define _dbLg2_10 1024
#define _dbShifter 1056
#define _dbInvLg2_10hi 1088
#define _dbInvLg2_10lo 1120
#define _dPC1 1152
#define _dPC2 1184
#define _dPC3 1216
#define _dPC4 1248
#define _dPC5 1280
#define _lExpMask 1312
#define _iIndexMask 1344
#define _iAbsMask 1376
#define _iDomainRange 1408
#include <sysdep.h>
.section .text.avx2, "ax", @progbits
ENTRY(_ZGVdN4v_exp10_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
lea __svml_dexp10_data_internal(%rip), %r8
vmovapd %ymm0, %ymm2
vmovupd _dbShifter+__svml_dexp10_data_internal(%rip), %ymm3
/* Load arument */
vmovupd _dbLg2_10+__svml_dexp10_data_internal(%rip), %ymm0
vfmadd213pd %ymm3, %ymm2, %ymm0
vsubpd %ymm3, %ymm0, %ymm1
/* R */
vmovupd _dbInvLg2_10hi+__svml_dexp10_data_internal(%rip), %ymm3
vfnmadd213pd %ymm2, %ymm1, %ymm3
/* Check for overflow\underflow */
vextractf128 $1, %ymm2, %xmm4
vfnmadd132pd _dbInvLg2_10lo+__svml_dexp10_data_internal(%rip), %ymm3, %ymm1
vshufps $221, %xmm4, %xmm2, %xmm5
vandps _iAbsMask+__svml_dexp10_data_internal(%rip), %xmm5, %xmm6
vpcmpgtd _iDomainRange+__svml_dexp10_data_internal(%rip), %xmm6, %xmm7
/*
* Polynomial
* poly(dN) = a1*dR+...+a5*dR^5
*/
vmovupd _dPC5+__svml_dexp10_data_internal(%rip), %ymm4
vmovmskps %xmm7, %eax
vfmadd213pd _dPC4+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
vfmadd213pd _dPC3+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
vfmadd213pd _dPC2+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
/* a1+...+a5*dR^4 ! */
vfmadd213pd _dPC1+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
/* a1*dR+...+a5*dR^5 */
vmulpd %ymm4, %ymm1, %ymm1
/* Index and lookup */
vextractf128 $1, %ymm0, %xmm8
vshufps $136, %xmm8, %xmm0, %xmm9
vandps _iIndexMask+__svml_dexp10_data_internal(%rip), %xmm9, %xmm10
/* iIndex*=sizeof(D); */
vpslld $3, %xmm10, %xmm13
vmovd %xmm13, %edx
/* 2^N */
vpsllq $45, %ymm0, %ymm0
vpextrd $2, %xmm13, %esi
movslq %edx, %rdx
vpextrd $1, %xmm13, %ecx
movslq %esi, %rsi
vpextrd $3, %xmm13, %edi
movslq %ecx, %rcx
movslq %edi, %rdi
vmovsd (%r8, %rdx), %xmm11
vmovsd (%r8, %rsi), %xmm14
vmovhpd (%r8, %rcx), %xmm11, %xmm12
vmovhpd (%r8, %rdi), %xmm14, %xmm15
/* lM==EXP(2^N) */
vpand _lExpMask+__svml_dexp10_data_internal(%rip), %ymm0, %ymm6
vinsertf128 $1, %xmm15, %ymm12, %ymm5
/* Tj*poly */
vfmadd213pd %ymm5, %ymm5, %ymm1
/* quick 2^N */
vpaddq %ymm6, %ymm1, %ymm0
/* Finish */
testl %eax, %eax
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx r12 r13 r14 r15 eax ymm0 ymm2
/* 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):
vmovupd %ymm2, 32(%rsp)
vmovupd %ymm0, 64(%rsp)
# LOE rbx r12 r13 r14 r15 eax ymm0
xorl %edx, %edx
# 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 %edx, %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 %eax, %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 $4, %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)
vmovupd 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 fucntion call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
vmovsd 32(%rsp, %r14, 8), %xmm0
call exp10@PLT
# LOE rbx r14 r15 r12d r13d xmm0
vmovsd %xmm0, 64(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVdN4v_exp10_avx2)
.section .rodata, "a"
.align 32
#ifdef __svml_dexp10_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(32)) VUINT32 _dbT[(1<<7)][2];
__declspec(align(32)) VUINT32 _dbLg2_10[4][2];
__declspec(align(32)) VUINT32 _dbShifter[4][2];
__declspec(align(32)) VUINT32 _dbInvLg2_10hi[4][2];
__declspec(align(32)) VUINT32 _dbInvLg2_10lo[4][2];
__declspec(align(32)) VUINT32 _dPC1[4][2];
__declspec(align(32)) VUINT32 _dPC2[4][2];
__declspec(align(32)) VUINT32 _dPC3[4][2];
__declspec(align(32)) VUINT32 _dPC4[4][2];
__declspec(align(32)) VUINT32 _dPC5[4][2];
__declspec(align(32)) VUINT32 _lExpMask[4][2];
__declspec(align(32)) VUINT32 _iIndexMask[8][1];
__declspec(align(32)) VUINT32 _iAbsMask[8][1];
__declspec(align(32)) VUINT32 _iDomainRange[8][1];
} __svml_dexp10_data_internal;
#endif
__svml_dexp10_data_internal:
/* _dbT */
.quad 0x3ff0000000000000 /* 2^( 0 /128) */
.quad 0x3ff0163da9fb3335 /* 2^( 1 /128) */
.quad 0x3ff02c9a3e778061 /* 2^( 2 /128) */
.quad 0x3ff04315e86e7f85 /* 2^( 3 /128) */
.quad 0x3ff059b0d3158574 /* 2^( 4 /128) */
.quad 0x3ff0706b29ddf6de /* 2^( 5 /128) */
.quad 0x3ff0874518759bc8 /* 2^( 6 /128) */
.quad 0x3ff09e3ecac6f383 /* 2^( 7 /128) */
.quad 0x3ff0b5586cf9890f /* 2^( 8 /128) */
.quad 0x3ff0cc922b7247f7 /* 2^( 9 /128) */
.quad 0x3ff0e3ec32d3d1a2 /* 2^( 10 /128) */
.quad 0x3ff0fb66affed31b /* 2^( 11 /128) */
.quad 0x3ff11301d0125b51 /* 2^( 12 /128) */
.quad 0x3ff12abdc06c31cc /* 2^( 13 /128) */
.quad 0x3ff1429aaea92de0 /* 2^( 14 /128) */
.quad 0x3ff15a98c8a58e51 /* 2^( 15 /128) */
.quad 0x3ff172b83c7d517b /* 2^( 16 /128) */
.quad 0x3ff18af9388c8dea /* 2^( 17 /128) */
.quad 0x3ff1a35beb6fcb75 /* 2^( 18 /128) */
.quad 0x3ff1bbe084045cd4 /* 2^( 19 /128) */
.quad 0x3ff1d4873168b9aa /* 2^( 20 /128) */
.quad 0x3ff1ed5022fcd91d /* 2^( 21 /128) */
.quad 0x3ff2063b88628cd6 /* 2^( 22 /128) */
.quad 0x3ff21f49917ddc96 /* 2^( 23 /128) */
.quad 0x3ff2387a6e756238 /* 2^( 24 /128) */
.quad 0x3ff251ce4fb2a63f /* 2^( 25 /128) */
.quad 0x3ff26b4565e27cdd /* 2^( 26 /128) */
.quad 0x3ff284dfe1f56381 /* 2^( 27 /128) */
.quad 0x3ff29e9df51fdee1 /* 2^( 28 /128) */
.quad 0x3ff2b87fd0dad990 /* 2^( 29 /128) */
.quad 0x3ff2d285a6e4030b /* 2^( 30 /128) */
.quad 0x3ff2ecafa93e2f56 /* 2^( 31 /128) */
.quad 0x3ff306fe0a31b715 /* 2^( 32 /128) */
.quad 0x3ff32170fc4cd831 /* 2^( 33 /128) */
.quad 0x3ff33c08b26416ff /* 2^( 34 /128) */
.quad 0x3ff356c55f929ff1 /* 2^( 35 /128) */
.quad 0x3ff371a7373aa9cb /* 2^( 36 /128) */
.quad 0x3ff38cae6d05d866 /* 2^( 37 /128) */
.quad 0x3ff3a7db34e59ff7 /* 2^( 38 /128) */
.quad 0x3ff3c32dc313a8e5 /* 2^( 39 /128) */
.quad 0x3ff3dea64c123422 /* 2^( 40 /128) */
.quad 0x3ff3fa4504ac801c /* 2^( 41 /128) */
.quad 0x3ff4160a21f72e2a /* 2^( 42 /128) */
.quad 0x3ff431f5d950a897 /* 2^( 43 /128) */
.quad 0x3ff44e086061892d /* 2^( 44 /128) */
.quad 0x3ff46a41ed1d0057 /* 2^( 45 /128) */
.quad 0x3ff486a2b5c13cd0 /* 2^( 46 /128) */
.quad 0x3ff4a32af0d7d3de /* 2^( 47 /128) */
.quad 0x3ff4bfdad5362a27 /* 2^( 48 /128) */
.quad 0x3ff4dcb299fddd0d /* 2^( 49 /128) */
.quad 0x3ff4f9b2769d2ca7 /* 2^( 50 /128) */
.quad 0x3ff516daa2cf6642 /* 2^( 51 /128) */
.quad 0x3ff5342b569d4f82 /* 2^( 52 /128) */
.quad 0x3ff551a4ca5d920f /* 2^( 53 /128) */
.quad 0x3ff56f4736b527da /* 2^( 54 /128) */
.quad 0x3ff58d12d497c7fd /* 2^( 55 /128) */
.quad 0x3ff5ab07dd485429 /* 2^( 56 /128) */
.quad 0x3ff5c9268a5946b7 /* 2^( 57 /128) */
.quad 0x3ff5e76f15ad2148 /* 2^( 58 /128) */
.quad 0x3ff605e1b976dc09 /* 2^( 59 /128) */
.quad 0x3ff6247eb03a5585 /* 2^( 60 /128) */
.quad 0x3ff6434634ccc320 /* 2^( 61 /128) */
.quad 0x3ff6623882552225 /* 2^( 62 /128) */
.quad 0x3ff68155d44ca973 /* 2^( 63 /128) */
.quad 0x3ff6a09e667f3bcd /* 2^( 64 /128) */
.quad 0x3ff6c012750bdabf /* 2^( 65 /128) */
.quad 0x3ff6dfb23c651a2f /* 2^( 66 /128) */
.quad 0x3ff6ff7df9519484 /* 2^( 67 /128) */
.quad 0x3ff71f75e8ec5f74 /* 2^( 68 /128) */
.quad 0x3ff73f9a48a58174 /* 2^( 69 /128) */
.quad 0x3ff75feb564267c9 /* 2^( 70 /128) */
.quad 0x3ff780694fde5d3f /* 2^( 71 /128) */
.quad 0x3ff7a11473eb0187 /* 2^( 72 /128) */
.quad 0x3ff7c1ed0130c132 /* 2^( 73 /128) */
.quad 0x3ff7e2f336cf4e62 /* 2^( 74 /128) */
.quad 0x3ff80427543e1a12 /* 2^( 75 /128) */
.quad 0x3ff82589994cce13 /* 2^( 76 /128) */
.quad 0x3ff8471a4623c7ad /* 2^( 77 /128) */
.quad 0x3ff868d99b4492ed /* 2^( 78 /128) */
.quad 0x3ff88ac7d98a6699 /* 2^( 79 /128) */
.quad 0x3ff8ace5422aa0db /* 2^( 80 /128) */
.quad 0x3ff8cf3216b5448c /* 2^( 81 /128) */
.quad 0x3ff8f1ae99157736 /* 2^( 82 /128) */
.quad 0x3ff9145b0b91ffc6 /* 2^( 83 /128) */
.quad 0x3ff93737b0cdc5e5 /* 2^( 84 /128) */
.quad 0x3ff95a44cbc8520f /* 2^( 85 /128) */
.quad 0x3ff97d829fde4e50 /* 2^( 86 /128) */
.quad 0x3ff9a0f170ca07ba /* 2^( 87 /128) */
.quad 0x3ff9c49182a3f090 /* 2^( 88 /128) */
.quad 0x3ff9e86319e32323 /* 2^( 89 /128) */
.quad 0x3ffa0c667b5de565 /* 2^( 90 /128) */
.quad 0x3ffa309bec4a2d33 /* 2^( 91 /128) */
.quad 0x3ffa5503b23e255d /* 2^( 92 /128) */
.quad 0x3ffa799e1330b358 /* 2^( 93 /128) */
.quad 0x3ffa9e6b5579fdbf /* 2^( 94 /128) */
.quad 0x3ffac36bbfd3f37a /* 2^( 95 /128) */
.quad 0x3ffae89f995ad3ad /* 2^( 96 /128) */
.quad 0x3ffb0e07298db666 /* 2^( 97 /128) */
.quad 0x3ffb33a2b84f15fb /* 2^( 98 /128) */
.quad 0x3ffb59728de5593a /* 2^( 99 /128) */
.quad 0x3ffb7f76f2fb5e47 /* 2^( 100 /128) */
.quad 0x3ffba5b030a1064a /* 2^( 101 /128) */
.quad 0x3ffbcc1e904bc1d2 /* 2^( 102 /128) */
.quad 0x3ffbf2c25bd71e09 /* 2^( 103 /128) */
.quad 0x3ffc199bdd85529c /* 2^( 104 /128) */
.quad 0x3ffc40ab5fffd07a /* 2^( 105 /128) */
.quad 0x3ffc67f12e57d14b /* 2^( 106 /128) */
.quad 0x3ffc8f6d9406e7b5 /* 2^( 107 /128) */
.quad 0x3ffcb720dcef9069 /* 2^( 108 /128) */
.quad 0x3ffcdf0b555dc3fa /* 2^( 109 /128) */
.quad 0x3ffd072d4a07897c /* 2^( 110 /128) */
.quad 0x3ffd2f87080d89f2 /* 2^( 111 /128) */
.quad 0x3ffd5818dcfba487 /* 2^( 112 /128) */
.quad 0x3ffd80e316c98398 /* 2^( 113 /128) */
.quad 0x3ffda9e603db3285 /* 2^( 114 /128) */
.quad 0x3ffdd321f301b460 /* 2^( 115 /128) */
.quad 0x3ffdfc97337b9b5f /* 2^( 116 /128) */
.quad 0x3ffe264614f5a129 /* 2^( 117 /128) */
.quad 0x3ffe502ee78b3ff6 /* 2^( 118 /128) */
.quad 0x3ffe7a51fbc74c83 /* 2^( 119 /128) */
.quad 0x3ffea4afa2a490da /* 2^( 120 /128) */
.quad 0x3ffecf482d8e67f1 /* 2^( 121 /128) */
.quad 0x3ffefa1bee615a27 /* 2^( 122 /128) */
.quad 0x3fff252b376bba97 /* 2^( 123 /128) */
.quad 0x3fff50765b6e4540 /* 2^( 124 /128) */
.quad 0x3fff7bfdad9cbe14 /* 2^( 125 /128) */
.quad 0x3fffa7c1819e90d8 /* 2^( 126 /128) */
.quad 0x3fffd3c22b8f71f1 /* 2^( 127 /128) */
.align 32
.quad 0x407a934f0979a371, 0x407a934f0979a371, 0x407a934f0979a371, 0x407a934f0979a371 /* _dbLg2_10*2^K */
.align 32
.quad 0x4338800000000000, 0x4338800000000000, 0x4338800000000000, 0x4338800000000000 /* _dbShifter */
.align 32
.quad 0x3f63441350a00000, 0x3f63441350a00000, 0x3f63441350a00000, 0x3f63441350a00000 /* _dbInvLg2_10hi/2^K 53-11-K bits */
.align 32
.quad 0xbd10c0219dc1da99, 0xbd10c0219dc1da99, 0xbd10c0219dc1da99, 0xbd10c0219dc1da99 /* _dbInvLg2_10lo/2^K */
//PC0 = 1.0
.align 32
.quad 0x40026bb1bbb55516, 0x40026bb1bbb55516, 0x40026bb1bbb55516, 0x40026bb1bbb55516 /* _dPC1 */
.align 32
.quad 0x40053524c73ce8e3, 0x40053524c73ce8e3, 0x40053524c73ce8e3, 0x40053524c73ce8e3 /* _dPC2 */
.align 32
.quad 0x4000470591ccea8b, 0x4000470591ccea8b, 0x4000470591ccea8b, 0x4000470591ccea8b /* _dPC3 */
.align 32
.quad 0x3ff2bd767584db59, 0x3ff2bd767584db59, 0x3ff2bd767584db59, 0x3ff2bd767584db59 /* _dPC4 */
.align 32
.quad 0x3fe144c03efafb54, 0x3fe144c03efafb54, 0x3fe144c03efafb54, 0x3fe144c03efafb54 /* _dPC5 */
.align 32
.quad 0xfff0000000000000, 0xfff0000000000000, 0xfff0000000000000, 0xfff0000000000000 /* _lExpMask */
.align 32
.long 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f /* _iIndexMask =(2^K-1) */
//common
.align 32
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */
.align 32
.long 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70 /* _iDomainRange */
.align 32
.type __svml_dexp10_data_internal, @object
.size __svml_dexp10_data_internal, .-__svml_dexp10_data_internal
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