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/* Function exp2 vectorized with SSE4.
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:
*
* exp2(x) = 2^n * T[j] * (1 + P(y))
* where
* x = m*(1/K) + y, y in [-1/K..1/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 exp2(x)-1
* on small interval [-1/K..1/K]
*
* Special cases:
*
* exp2(NaN) = NaN
* exp2(+INF) = +INF
* exp2(-INF) = 0
* exp2(x) = 1 for subnormals
* For IEEE double
* if x >= 1024.0 then exp2(x) overflows
* if x < -1076.0 then exp2(x) underflows
*
*/
/* Offsets for data table __svml_dexp2_data_internal
*/
#define _dbT 0
#define _dbShifter 1024
#define _dPC1 1040
#define _dPC2 1056
#define _dPC3 1072
#define _dPC4 1088
#define _lIndexMask 1104
#define _iAbsMask 1120
#define _iDomainRange 1136
#include <sysdep.h>
.section .text.sse4, "ax", @progbits
ENTRY(_ZGVbN2v_exp2_sse4)
subq $72, %rsp
cfi_def_cfa_offset(80)
/* R */
movaps %xmm0, %xmm7
movups _dbShifter+__svml_dexp2_data_internal(%rip), %xmm1
/* out, basePtr, iIndex, iBaseOfs, iSize, iGran, iOfs */
lea __svml_dexp2_data_internal(%rip), %rsi
/* Load argument */
movaps %xmm1, %xmm10
addpd %xmm0, %xmm10
movaps %xmm10, %xmm6
subpd %xmm1, %xmm6
subpd %xmm6, %xmm7
/*
* Polynomial
* poly(dN) = a1*dR+...+a4*dR^4
*/
movups _dPC4+__svml_dexp2_data_internal(%rip), %xmm8
mulpd %xmm7, %xmm8
addpd _dPC3+__svml_dexp2_data_internal(%rip), %xmm8
mulpd %xmm7, %xmm8
addpd _dPC2+__svml_dexp2_data_internal(%rip), %xmm8
movdqu _lIndexMask+__svml_dexp2_data_internal(%rip), %xmm9
/* Index and lookup */
movdqa %xmm9, %xmm5
pandn %xmm10, %xmm9
pand %xmm10, %xmm5
/* 2^N */
psllq $45, %xmm9
movd %xmm5, %eax
movq _iAbsMask+__svml_dexp2_data_internal(%rip), %xmm2
/* Check for overflow\underflow */
pshufd $221, %xmm0, %xmm4
pextrw $4, %xmm5, %ecx
/* a1+...+a4*dR^3 ! */
mulpd %xmm7, %xmm8
shll $3, %eax
pand %xmm2, %xmm4
shll $3, %ecx
movq (%rsi, %rax), %xmm1
movhpd (%rsi, %rcx), %xmm1
/* dR=dR*dT */
mulpd %xmm1, %xmm7
addpd _dPC1+__svml_dexp2_data_internal(%rip), %xmm8
/*
* Reconstruction
* exp2 = {2^N later}*(Tj+Tj*poly)
* dN = dT+dT*dR*(a1+...+a4*dR^3)
*/
mulpd %xmm7, %xmm8
addpd %xmm8, %xmm1
movq _iDomainRange+__svml_dexp2_data_internal(%rip), %xmm3
pcmpgtd %xmm3, %xmm4
movmskps %xmm4, %edx
/* quick 2^N */
paddq %xmm9, %xmm1
andl $3, %edx
/* Finish */
/* Go to special inputs processing branch */
jne L(SPECIAL_VALUES_BRANCH)
# LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1
/* Restore registers
* and exit the function
*/
L(EXIT):
movaps %xmm1, %xmm0
addq $72, %rsp
cfi_def_cfa_offset(8)
ret
cfi_def_cfa_offset(80)
/* Branch to process
* special inputs
*/
L(SPECIAL_VALUES_BRANCH):
movups %xmm0, 32(%rsp)
movups %xmm1, 48(%rsp)
# LOE rbx rbp r12 r13 r14 r15 edx xmm1
xorl %eax, %eax
movq %r12, 16(%rsp)
cfi_offset(12, -64)
movl %eax, %r12d
movq %r13, 8(%rsp)
cfi_offset(13, -72)
movl %edx, %r13d
movq %r14, (%rsp)
cfi_offset(14, -80)
# LOE rbx rbp r15 r12d r13d
/* Range mask
* bits check
*/
L(RANGEMASK_CHECK):
btl %r12d, %r13d
/* Call scalar math function */
jc L(SCALAR_MATH_CALL)
# LOE rbx rbp r15 r12d r13d
/* Special inputs
* processing loop
*/
L(SPECIAL_VALUES_LOOP):
incl %r12d
cmpl $2, %r12d
/* Check bits in range mask */
jl L(RANGEMASK_CHECK)
# LOE rbx rbp r15 r12d r13d
movq 16(%rsp), %r12
cfi_restore(12)
movq 8(%rsp), %r13
cfi_restore(13)
movq (%rsp), %r14
cfi_restore(14)
movups 48(%rsp), %xmm1
/* Go to exit */
jmp L(EXIT)
cfi_offset(12, -64)
cfi_offset(13, -72)
cfi_offset(14, -80)
# LOE rbx rbp r12 r13 r14 r15 xmm1
/* Scalar math function call
* to process special input
*/
L(SCALAR_MATH_CALL):
movl %r12d, %r14d
movsd 32(%rsp, %r14, 8), %xmm0
call exp2@PLT
# LOE rbx rbp r14 r15 r12d r13d xmm0
movsd %xmm0, 48(%rsp, %r14, 8)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx rbp r15 r12d r13d
END(_ZGVbN2v_exp2_sse4)
.section .rodata, "a"
.align 16
#ifdef __svml_dexp2_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
__declspec(align(16)) VUINT32 _dbT[(1<<7)][2];
__declspec(align(16)) VUINT32 _dbShifter[2][2];
__declspec(align(16)) VUINT32 _dPC1[2][2];
__declspec(align(16)) VUINT32 _dPC2[2][2];
__declspec(align(16)) VUINT32 _dPC3[2][2];
__declspec(align(16)) VUINT32 _dPC4[2][2];
__declspec(align(16)) VUINT32 _lIndexMask[2][2];
__declspec(align(16)) VUINT32 _iAbsMask[4][1];
__declspec(align(16)) VUINT32 _iDomainRange[4][1];
} __svml_dexp2_data_internal;
#endif
__svml_dexp2_data_internal:
/* _dbT */
.quad 0x3ff0000000000000, 0x3ff0163da9fb3335 /* 2^( 0 /128), 2^( 1 /128) */
.quad 0x3ff02c9a3e778061, 0x3ff04315e86e7f85 /* 2^( 2 /128), 2^( 3 /128) */
.quad 0x3ff059b0d3158574, 0x3ff0706b29ddf6de /* 2^( 4 /128), 2^( 5 /128) */
.quad 0x3ff0874518759bc8, 0x3ff09e3ecac6f383 /* 2^( 6 /128), 2^( 7 /128) */
.quad 0x3ff0b5586cf9890f, 0x3ff0cc922b7247f7 /* 2^( 8 /128), 2^( 9 /128) */
.quad 0x3ff0e3ec32d3d1a2, 0x3ff0fb66affed31b /* 2^( 10 /128), 2^( 11 /128) */
.quad 0x3ff11301d0125b51, 0x3ff12abdc06c31cc /* 2^( 12 /128), 2^( 13 /128) */
.quad 0x3ff1429aaea92de0, 0x3ff15a98c8a58e51 /* 2^( 14 /128), 2^( 15 /128) */
.quad 0x3ff172b83c7d517b, 0x3ff18af9388c8dea /* 2^( 16 /128), 2^( 17 /128) */
.quad 0x3ff1a35beb6fcb75, 0x3ff1bbe084045cd4 /* 2^( 18 /128), 2^( 19 /128) */
.quad 0x3ff1d4873168b9aa, 0x3ff1ed5022fcd91d /* 2^( 20 /128), 2^( 21 /128) */
.quad 0x3ff2063b88628cd6, 0x3ff21f49917ddc96 /* 2^( 22 /128), 2^( 23 /128) */
.quad 0x3ff2387a6e756238, 0x3ff251ce4fb2a63f /* 2^( 24 /128), 2^( 25 /128) */
.quad 0x3ff26b4565e27cdd, 0x3ff284dfe1f56381 /* 2^( 26 /128), 2^( 27 /128) */
.quad 0x3ff29e9df51fdee1, 0x3ff2b87fd0dad990 /* 2^( 28 /128), 2^( 29 /128) */
.quad 0x3ff2d285a6e4030b, 0x3ff2ecafa93e2f56 /* 2^( 30 /128), 2^( 31 /128) */
.quad 0x3ff306fe0a31b715, 0x3ff32170fc4cd831 /* 2^( 32 /128), 2^( 33 /128) */
.quad 0x3ff33c08b26416ff, 0x3ff356c55f929ff1 /* 2^( 34 /128), 2^( 35 /128) */
.quad 0x3ff371a7373aa9cb, 0x3ff38cae6d05d866 /* 2^( 36 /128), 2^( 37 /128) */
.quad 0x3ff3a7db34e59ff7, 0x3ff3c32dc313a8e5 /* 2^( 38 /128), 2^( 39 /128) */
.quad 0x3ff3dea64c123422, 0x3ff3fa4504ac801c /* 2^( 40 /128), 2^( 41 /128) */
.quad 0x3ff4160a21f72e2a, 0x3ff431f5d950a897 /* 2^( 42 /128), 2^( 43 /128) */
.quad 0x3ff44e086061892d, 0x3ff46a41ed1d0057 /* 2^( 44 /128), 2^( 45 /128) */
.quad 0x3ff486a2b5c13cd0, 0x3ff4a32af0d7d3de /* 2^( 46 /128), 2^( 47 /128) */
.quad 0x3ff4bfdad5362a27, 0x3ff4dcb299fddd0d /* 2^( 48 /128), 2^( 49 /128) */
.quad 0x3ff4f9b2769d2ca7, 0x3ff516daa2cf6642 /* 2^( 50 /128), 2^( 51 /128) */
.quad 0x3ff5342b569d4f82, 0x3ff551a4ca5d920f /* 2^( 52 /128), 2^( 53 /128) */
.quad 0x3ff56f4736b527da, 0x3ff58d12d497c7fd /* 2^( 54 /128), 2^( 55 /128) */
.quad 0x3ff5ab07dd485429, 0x3ff5c9268a5946b7 /* 2^( 56 /128), 2^( 57 /128) */
.quad 0x3ff5e76f15ad2148, 0x3ff605e1b976dc09 /* 2^( 58 /128), 2^( 59 /128) */
.quad 0x3ff6247eb03a5585, 0x3ff6434634ccc320 /* 2^( 60 /128), 2^( 61 /128) */
.quad 0x3ff6623882552225, 0x3ff68155d44ca973 /* 2^( 62 /128), 2^( 63 /128) */
.quad 0x3ff6a09e667f3bcd, 0x3ff6c012750bdabf /* 2^( 64 /128), 2^( 65 /128) */
.quad 0x3ff6dfb23c651a2f, 0x3ff6ff7df9519484 /* 2^( 66 /128), 2^( 67 /128) */
.quad 0x3ff71f75e8ec5f74, 0x3ff73f9a48a58174 /* 2^( 68 /128), 2^( 69 /128) */
.quad 0x3ff75feb564267c9, 0x3ff780694fde5d3f /* 2^( 70 /128), 2^( 71 /128) */
.quad 0x3ff7a11473eb0187, 0x3ff7c1ed0130c132 /* 2^( 72 /128), 2^( 73 /128) */
.quad 0x3ff7e2f336cf4e62, 0x3ff80427543e1a12 /* 2^( 74 /128), 2^( 75 /128) */
.quad 0x3ff82589994cce13, 0x3ff8471a4623c7ad /* 2^( 76 /128), 2^( 77 /128) */
.quad 0x3ff868d99b4492ed, 0x3ff88ac7d98a6699 /* 2^( 78 /128), 2^( 79 /128) */
.quad 0x3ff8ace5422aa0db, 0x3ff8cf3216b5448c /* 2^( 80 /128), 2^( 81 /128) */
.quad 0x3ff8f1ae99157736, 0x3ff9145b0b91ffc6 /* 2^( 82 /128), 2^( 83 /128) */
.quad 0x3ff93737b0cdc5e5, 0x3ff95a44cbc8520f /* 2^( 84 /128), 2^( 85 /128) */
.quad 0x3ff97d829fde4e50, 0x3ff9a0f170ca07ba /* 2^( 86 /128), 2^( 87 /128) */
.quad 0x3ff9c49182a3f090, 0x3ff9e86319e32323 /* 2^( 88 /128), 2^( 89 /128) */
.quad 0x3ffa0c667b5de565, 0x3ffa309bec4a2d33 /* 2^( 90 /128), 2^( 91 /128) */
.quad 0x3ffa5503b23e255d, 0x3ffa799e1330b358 /* 2^( 92 /128), 2^( 93 /128) */
.quad 0x3ffa9e6b5579fdbf, 0x3ffac36bbfd3f37a /* 2^( 94 /128), 2^( 95 /128) */
.quad 0x3ffae89f995ad3ad, 0x3ffb0e07298db666 /* 2^( 96 /128), 2^( 97 /128) */
.quad 0x3ffb33a2b84f15fb, 0x3ffb59728de5593a /* 2^( 98 /128), 2^( 99 /128) */
.quad 0x3ffb7f76f2fb5e47, 0x3ffba5b030a1064a /* 2^( 100 /128), 2^( 101 /128) */
.quad 0x3ffbcc1e904bc1d2, 0x3ffbf2c25bd71e09 /* 2^( 102 /128), 2^( 103 /128) */
.quad 0x3ffc199bdd85529c, 0x3ffc40ab5fffd07a /* 2^( 104 /128), 2^( 105 /128) */
.quad 0x3ffc67f12e57d14b, 0x3ffc8f6d9406e7b5 /* 2^( 106 /128), 2^( 107 /128) */
.quad 0x3ffcb720dcef9069, 0x3ffcdf0b555dc3fa /* 2^( 108 /128), 2^( 109 /128) */
.quad 0x3ffd072d4a07897c, 0x3ffd2f87080d89f2 /* 2^( 110 /128), 2^( 111 /128) */
.quad 0x3ffd5818dcfba487, 0x3ffd80e316c98398 /* 2^( 112 /128), 2^( 113 /128) */
.quad 0x3ffda9e603db3285, 0x3ffdd321f301b460 /* 2^( 114 /128), 2^( 115 /128) */
.quad 0x3ffdfc97337b9b5f, 0x3ffe264614f5a129 /* 2^( 116 /128), 2^( 117 /128) */
.quad 0x3ffe502ee78b3ff6, 0x3ffe7a51fbc74c83 /* 2^( 118 /128), 2^( 119 /128) */
.quad 0x3ffea4afa2a490da, 0x3ffecf482d8e67f1 /* 2^( 120 /128), 2^( 121 /128) */
.quad 0x3ffefa1bee615a27, 0x3fff252b376bba97 /* 2^( 122 /128), 2^( 123 /128) */
.quad 0x3fff50765b6e4540, 0x3fff7bfdad9cbe14 /* 2^( 124 /128), 2^( 125 /128) */
.quad 0x3fffa7c1819e90d8, 0x3fffd3c22b8f71f1 /* 2^( 126 /128), 2^( 127 /128) */
.align 16
.quad 0x42c8000000000000, 0x42c8000000000000 /* _dbShifter - 0x433-7=0x42c shifted right on K! */
//log2(relerr) = -53.547756365162
.align 16
.quad 0x3fe62e42fefa3685, 0x3fe62e42fefa3685 /* _dPC1 */
.align 16
.quad 0x3fcebfbdff82ca48, 0x3fcebfbdff82ca48 /* _dPC2 */
.align 16
.quad 0x3fac6b09b180f045, 0x3fac6b09b180f045 /* _dPC3 */
.align 16
.quad 0x3f83b2ab5bb1268f, 0x3f83b2ab5bb1268f /* _dPC4 */
.align 16
.quad 0x000000000000007f, 0x000000000000007f /* _lIndexMask =(2^K-1) */
.align 16
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _iAbsMask */
.align 16
.long 0x408fefff, 0x408fefff, 0x408fefff, 0x408fefff /* _iDomainRange */
.align 16
.type __svml_dexp2_data_internal, @object
.size __svml_dexp2_data_internal, .-__svml_dexp2_data_internal
|
