2
* Copyright (c) 2016, 2021, Intel Corporation. All rights reserved.
3
* Intel Math Library (LIBM) Source Code
5
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
7
* This code is free software; you can redistribute it and/or modify it
8
* under the terms of the GNU General Public License version 2 only, as
9
* published by the Free Software Foundation.
11
* This code is distributed in the hope that it will be useful, but WITHOUT
12
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14
* version 2 for more details (a copy is included in the LICENSE file that
15
* accompanied this code).
17
* You should have received a copy of the GNU General Public License version
18
* 2 along with this work; if not, write to the Free Software Foundation,
19
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
21
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22
* or visit www.oracle.com if you need additional information or have any
27
#include "precompiled.hpp"
28
#include "asm/assembler.hpp"
29
#include "asm/assembler.inline.hpp"
30
#include "macroAssembler_x86.hpp"
31
#include "runtime/stubRoutines.hpp"
32
#include "utilities/globalDefinitions.hpp"
34
/******************************************************************************/
35
// ALGORITHM DESCRIPTION - LOG10()
36
// ---------------------
38
// Let x=2^k * mx, mx in [1,2)
40
// Get B~1/mx based on the output of rcpss instruction (B0)
41
// B = int((B0*LH*2^7+0.5))/2^7
42
// LH is a short approximation for log10(e)
44
// Reduced argument: r=B*mx-LH (computed accurately in high and low parts)
46
// Result: k*log10(2) - log(B) + p(r)
47
// p(r) is a degree 7 polynomial
48
// -log(B) read from data table (high, low parts)
49
// Result is formed from high and low parts
52
// log10(0) = -INF with divide-by-zero exception raised
54
// log10(x) = NaN with invalid exception raised if x < -0, including -INF
57
/******************************************************************************/
59
// The 32 bit code is at most SSE2 compliant
61
ATTRIBUTE_ALIGNED(16) static const juint _static_const_table_log10[] =
63
0x509f7800UL, 0x3fd34413UL, 0x1f12b358UL, 0x3d1fef31UL, 0x80333400UL,
64
0x3fd32418UL, 0xc671d9d0UL, 0xbcf542bfUL, 0x51195000UL, 0x3fd30442UL,
65
0x78a4b0c3UL, 0x3d18216aUL, 0x6fc79400UL, 0x3fd2e490UL, 0x80fa389dUL,
66
0xbc902869UL, 0x89d04000UL, 0x3fd2c502UL, 0x75c2f564UL, 0x3d040754UL,
67
0x4ddd1c00UL, 0x3fd2a598UL, 0xd219b2c3UL, 0xbcfa1d84UL, 0x6baa7c00UL,
68
0x3fd28651UL, 0xfd9abec1UL, 0x3d1be6d3UL, 0x94028800UL, 0x3fd2672dUL,
69
0xe289a455UL, 0xbd1ede5eUL, 0x78b86400UL, 0x3fd2482cUL, 0x6734d179UL,
70
0x3d1fe79bUL, 0xcca3c800UL, 0x3fd2294dUL, 0x981a40b8UL, 0xbced34eaUL,
71
0x439c5000UL, 0x3fd20a91UL, 0xcc392737UL, 0xbd1a9cc3UL, 0x92752c00UL,
72
0x3fd1ebf6UL, 0x03c9afe7UL, 0x3d1e98f8UL, 0x6ef8dc00UL, 0x3fd1cd7dUL,
73
0x71dae7f4UL, 0x3d08a86cUL, 0x8fe4dc00UL, 0x3fd1af25UL, 0xee9185a1UL,
74
0xbcff3412UL, 0xace59400UL, 0x3fd190eeUL, 0xc2cab353UL, 0x3cf17ed9UL,
75
0x7e925000UL, 0x3fd172d8UL, 0x6952c1b2UL, 0x3cf1521cUL, 0xbe694400UL,
76
0x3fd154e2UL, 0xcacb79caUL, 0xbd0bdc78UL, 0x26cbac00UL, 0x3fd1370dUL,
77
0xf71f4de1UL, 0xbd01f8beUL, 0x72fa0800UL, 0x3fd11957UL, 0x55bf910bUL,
78
0x3c946e2bUL, 0x5f106000UL, 0x3fd0fbc1UL, 0x39e639c1UL, 0x3d14a84bUL,
79
0xa802a800UL, 0x3fd0de4aUL, 0xd3f31d5dUL, 0xbd178385UL, 0x0b992000UL,
80
0x3fd0c0f3UL, 0x3843106fUL, 0xbd1f602fUL, 0x486ce800UL, 0x3fd0a3baUL,
81
0x8819497cUL, 0x3cef987aUL, 0x1de49400UL, 0x3fd086a0UL, 0x1caa0467UL,
82
0x3d0faec7UL, 0x4c30cc00UL, 0x3fd069a4UL, 0xa4424372UL, 0xbd1618fcUL,
83
0x94490000UL, 0x3fd04cc6UL, 0x946517d2UL, 0xbd18384bUL, 0xb7e84000UL,
84
0x3fd03006UL, 0xe0109c37UL, 0xbd19a6acUL, 0x798a0c00UL, 0x3fd01364UL,
85
0x5121e864UL, 0xbd164cf7UL, 0x38ce8000UL, 0x3fcfedbfUL, 0x46214d1aUL,
86
0xbcbbc402UL, 0xc8e62000UL, 0x3fcfb4efUL, 0xdab93203UL, 0x3d1e0176UL,
87
0x2cb02800UL, 0x3fcf7c5aUL, 0x2a2ea8e4UL, 0xbcfec86aUL, 0xeeeaa000UL,
88
0x3fcf43fdUL, 0xc18e49a4UL, 0x3cf110a8UL, 0x9bb6e800UL, 0x3fcf0bdaUL,
89
0x923cc9c0UL, 0xbd15ce99UL, 0xc093f000UL, 0x3fced3efUL, 0x4d4b51e9UL,
90
0x3d1a04c7UL, 0xec58f800UL, 0x3fce9c3cUL, 0x163cad59UL, 0x3cac8260UL,
91
0x9a907000UL, 0x3fce2d7dUL, 0x3fa93646UL, 0x3ce4a1c0UL, 0x37311000UL,
92
0x3fcdbf99UL, 0x32abd1fdUL, 0x3d07ea9dUL, 0x6744b800UL, 0x3fcd528cUL,
93
0x4dcbdfd4UL, 0xbd1b08e2UL, 0xe36de800UL, 0x3fcce653UL, 0x0b7b7f7fUL,
94
0xbd1b8f03UL, 0x77506800UL, 0x3fcc7aecUL, 0xa821c9fbUL, 0x3d13c163UL,
95
0x00ff8800UL, 0x3fcc1053UL, 0x536bca76UL, 0xbd074ee5UL, 0x70719800UL,
96
0x3fcba684UL, 0xd7da9b6bUL, 0xbd1fbf16UL, 0xc6f8d800UL, 0x3fcb3d7dUL,
97
0xe2220bb3UL, 0x3d1a295dUL, 0x16c15800UL, 0x3fcad53cUL, 0xe724911eUL,
98
0xbcf55822UL, 0x82533800UL, 0x3fca6dbcUL, 0x6d982371UL, 0x3cac567cUL,
99
0x3c19e800UL, 0x3fca06fcUL, 0x84d17d80UL, 0x3d1da204UL, 0x85ef8000UL,
100
0x3fc9a0f8UL, 0x54466a6aUL, 0xbd002204UL, 0xb0ac2000UL, 0x3fc93baeUL,
101
0xd601fd65UL, 0x3d18840cUL, 0x1bb9b000UL, 0x3fc8d71cUL, 0x7bf58766UL,
102
0xbd14f897UL, 0x34aae800UL, 0x3fc8733eUL, 0x3af6ac24UL, 0xbd0f5c45UL,
103
0x76d68000UL, 0x3fc81012UL, 0x4303e1a1UL, 0xbd1f9a80UL, 0x6af57800UL,
104
0x3fc7ad96UL, 0x43fbcb46UL, 0x3cf4c33eUL, 0xa6c51000UL, 0x3fc74bc7UL,
105
0x70f0eac5UL, 0xbd192e3bUL, 0xccab9800UL, 0x3fc6eaa3UL, 0xc0093dfeUL,
106
0xbd0faf15UL, 0x8b60b800UL, 0x3fc68a28UL, 0xde78d5fdUL, 0xbc9ea4eeUL,
107
0x9d987000UL, 0x3fc62a53UL, 0x962bea6eUL, 0xbd194084UL, 0xc9b0e800UL,
108
0x3fc5cb22UL, 0x888dd999UL, 0x3d1fe201UL, 0xe1634800UL, 0x3fc56c93UL,
109
0x16ada7adUL, 0x3d1b1188UL, 0xc176c000UL, 0x3fc50ea4UL, 0x4159b5b5UL,
110
0xbcf09c08UL, 0x51766000UL, 0x3fc4b153UL, 0x84393d23UL, 0xbcf6a89cUL,
111
0x83695000UL, 0x3fc4549dUL, 0x9f0b8bbbUL, 0x3d1c4b8cUL, 0x538d5800UL,
112
0x3fc3f881UL, 0xf49df747UL, 0x3cf89b99UL, 0xc8138000UL, 0x3fc39cfcUL,
113
0xd503b834UL, 0xbd13b99fUL, 0xf0df0800UL, 0x3fc3420dUL, 0xf011b386UL,
114
0xbd05d8beUL, 0xe7466800UL, 0x3fc2e7b2UL, 0xf39c7bc2UL, 0xbd1bb94eUL,
115
0xcdd62800UL, 0x3fc28de9UL, 0x05e6d69bUL, 0xbd10ed05UL, 0xd015d800UL,
116
0x3fc234b0UL, 0xe29b6c9dUL, 0xbd1ff967UL, 0x224ea800UL, 0x3fc1dc06UL,
117
0x727711fcUL, 0xbcffb30dUL, 0x01540000UL, 0x3fc183e8UL, 0x39786c5aUL,
118
0x3cc23f57UL, 0xb24d9800UL, 0x3fc12c54UL, 0xc905a342UL, 0x3d003a1dUL,
119
0x82835800UL, 0x3fc0d54aUL, 0x9b9920c0UL, 0x3d03b25aUL, 0xc72ac000UL,
120
0x3fc07ec7UL, 0x46f26a24UL, 0x3cf0fa41UL, 0xdd35d800UL, 0x3fc028caUL,
121
0x41d9d6dcUL, 0x3d034a65UL, 0x52474000UL, 0x3fbfa6a4UL, 0x44f66449UL,
122
0x3d19cad3UL, 0x2da3d000UL, 0x3fbefcb8UL, 0x67832999UL, 0x3d18400fUL,
123
0x32a10000UL, 0x3fbe53ceUL, 0x9c0e3b1aUL, 0xbcff62fdUL, 0x556b7000UL,
124
0x3fbdabe3UL, 0x02976913UL, 0xbcf8243bUL, 0x97e88000UL, 0x3fbd04f4UL,
125
0xec793797UL, 0x3d1c0578UL, 0x09647000UL, 0x3fbc5effUL, 0x05fc0565UL,
126
0xbd1d799eUL, 0xc6426000UL, 0x3fbbb9ffUL, 0x4625f5edUL, 0x3d1f5723UL,
127
0xf7afd000UL, 0x3fbb15f3UL, 0xdd5aae61UL, 0xbd1a7e1eUL, 0xd358b000UL,
128
0x3fba72d8UL, 0x3314e4d3UL, 0x3d17bc91UL, 0x9b1f5000UL, 0x3fb9d0abUL,
129
0x9a4d514bUL, 0x3cf18c9bUL, 0x9cd4e000UL, 0x3fb92f69UL, 0x7e4496abUL,
130
0x3cf1f96dUL, 0x31f4f000UL, 0x3fb88f10UL, 0xf56479e7UL, 0x3d165818UL,
131
0xbf628000UL, 0x3fb7ef9cUL, 0x26bf486dUL, 0xbd1113a6UL, 0xb526b000UL,
132
0x3fb7510cUL, 0x1a1c3384UL, 0x3ca9898dUL, 0x8e31e000UL, 0x3fb6b35dUL,
133
0xb3875361UL, 0xbd0661acUL, 0xd01de000UL, 0x3fb6168cUL, 0x2a7cacfaUL,
134
0xbd1bdf10UL, 0x0af23000UL, 0x3fb57a98UL, 0xff868816UL, 0x3cf046d0UL,
135
0xd8ea0000UL, 0x3fb4df7cUL, 0x1515fbe7UL, 0xbd1fd529UL, 0xde3b2000UL,
136
0x3fb44538UL, 0x6e59a132UL, 0x3d1faeeeUL, 0xc8df9000UL, 0x3fb3abc9UL,
137
0xf1322361UL, 0xbd198807UL, 0x505f1000UL, 0x3fb3132dUL, 0x0888e6abUL,
138
0x3d1e5380UL, 0x359bd000UL, 0x3fb27b61UL, 0xdfbcbb22UL, 0xbcfe2724UL,
139
0x429ee000UL, 0x3fb1e463UL, 0x6eb4c58cUL, 0xbcfe4dd6UL, 0x4a673000UL,
140
0x3fb14e31UL, 0x4ce1ac9bUL, 0x3d1ba691UL, 0x28b96000UL, 0x3fb0b8c9UL,
141
0x8c7813b8UL, 0xbd0b3872UL, 0xc1f08000UL, 0x3fb02428UL, 0xc2bc8c2cUL,
142
0x3cb5ea6bUL, 0x05a1a000UL, 0x3faf209cUL, 0x72e8f18eUL, 0xbce8df84UL,
143
0xc0b5e000UL, 0x3fadfa6dUL, 0x9fdef436UL, 0x3d087364UL, 0xaf416000UL,
144
0x3facd5c2UL, 0x1068c3a9UL, 0x3d0827e7UL, 0xdb356000UL, 0x3fabb296UL,
145
0x120a34d3UL, 0x3d101a9fUL, 0x5dfea000UL, 0x3faa90e6UL, 0xdaded264UL,
146
0xbd14c392UL, 0x6034c000UL, 0x3fa970adUL, 0x1c9d06a9UL, 0xbd1b705eUL,
147
0x194c6000UL, 0x3fa851e8UL, 0x83996ad9UL, 0xbd0117bcUL, 0xcf4ac000UL,
148
0x3fa73492UL, 0xb1a94a62UL, 0xbca5ea42UL, 0xd67b4000UL, 0x3fa618a9UL,
149
0x75aed8caUL, 0xbd07119bUL, 0x9126c000UL, 0x3fa4fe29UL, 0x5291d533UL,
150
0x3d12658fUL, 0x6f4d4000UL, 0x3fa3e50eUL, 0xcd2c5cd9UL, 0x3d1d5c70UL,
151
0xee608000UL, 0x3fa2cd54UL, 0xd1008489UL, 0x3d1a4802UL, 0x9900e000UL,
152
0x3fa1b6f9UL, 0x54fb5598UL, 0xbd16593fUL, 0x06bb6000UL, 0x3fa0a1f9UL,
153
0x64ef57b4UL, 0xbd17636bUL, 0xb7940000UL, 0x3f9f1c9fUL, 0xee6a4737UL,
154
0x3cb5d479UL, 0x91aa0000UL, 0x3f9cf7f5UL, 0x3a16373cUL, 0x3d087114UL,
155
0x156b8000UL, 0x3f9ad5edUL, 0x836c554aUL, 0x3c6900b0UL, 0xd4764000UL,
156
0x3f98b67fUL, 0xed12f17bUL, 0xbcffc974UL, 0x77dec000UL, 0x3f9699a7UL,
157
0x232ce7eaUL, 0x3d1e35bbUL, 0xbfbf4000UL, 0x3f947f5dUL, 0xd84ffa6eUL,
158
0x3d0e0a49UL, 0x82c7c000UL, 0x3f92679cUL, 0x8d170e90UL, 0xbd14d9f2UL,
159
0xadd20000UL, 0x3f90525dUL, 0x86d9f88eUL, 0x3cdeb986UL, 0x86f10000UL,
160
0x3f8c7f36UL, 0xb9e0a517UL, 0x3ce29faaUL, 0xb75c8000UL, 0x3f885e9eUL,
161
0x542568cbUL, 0xbd1f7bdbUL, 0x46b30000UL, 0x3f8442e8UL, 0xb954e7d9UL,
162
0x3d1e5287UL, 0xb7e60000UL, 0x3f802c07UL, 0x22da0b17UL, 0xbd19fb27UL,
163
0x6c8b0000UL, 0x3f7833e3UL, 0x821271efUL, 0xbd190f96UL, 0x29910000UL,
164
0x3f701936UL, 0xbc3491a5UL, 0xbd1bcf45UL, 0x354a0000UL, 0x3f600fe3UL,
165
0xc0ff520aUL, 0xbd19d71cUL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
166
0x00000000UL, 0x509f7800UL, 0x3f934413UL, 0x1f12b358UL, 0x3cdfef31UL,
167
0xc1a5f12eUL, 0x40358874UL, 0x64d4ef0dUL, 0xc0089309UL, 0x385593b1UL,
168
0xc025c917UL, 0xdc963467UL, 0x3ffc6a02UL, 0x7f9d3aa1UL, 0x4016ab9fUL,
169
0xdc77b115UL, 0xbff27af2UL, 0xf8000000UL, 0xffffffffUL, 0x00000000UL,
170
0xffffe000UL, 0x00000000UL, 0x3fdbc000UL, 0xbf2e4108UL, 0x3f5a7a6cUL
174
// scratch: xmm1, xmm2, xmm3, xmm4, xmm5, xmm6, xmm7
175
// rax, rdx, rcx, rbx (tmp)
177
void MacroAssembler::fast_log10(XMMRegister xmm0, XMMRegister xmm1, XMMRegister xmm2, XMMRegister xmm3,
178
XMMRegister xmm4, XMMRegister xmm5, XMMRegister xmm6, XMMRegister xmm7,
179
Register eax, Register ecx, Register edx, Register tmp) {
181
Label L_2TAG_PACKET_0_0_2, L_2TAG_PACKET_1_0_2, L_2TAG_PACKET_2_0_2, L_2TAG_PACKET_3_0_2;
182
Label L_2TAG_PACKET_4_0_2, L_2TAG_PACKET_5_0_2, L_2TAG_PACKET_6_0_2, L_2TAG_PACKET_7_0_2;
183
Label L_2TAG_PACKET_8_0_2, L_2TAG_PACKET_9_0_2, L_2TAG_PACKET_10_0_2;
185
assert_different_registers(tmp, eax, ecx, edx);
187
address static_const_table_log10 = (address)_static_const_table_log10;
190
movl(Address(rsp, 40), tmp);
191
lea(tmp, ExternalAddress(static_const_table_log10));
194
pinsrw(xmm2, eax, 3);
195
movl(ecx, 1054736384);
199
pinsrw(xmm3, edx, 3);
200
movsd(xmm0, Address(rsp, 112));
204
movdqu(xmm5, Address(tmp, 2128)); //0x3ffc6a02UL, 0x7f9d3aa1UL, 0x4016ab9fUL, 0xdc77b115UL
205
pextrw(eax, xmm0, 3);
209
movsd(xmm2, Address(tmp, 2144)); //0xbff27af2UL, 0xf8000000UL, 0xffffffffUL, 0x00000000UL
213
pshufd(xmm6, xmm5, 78);
217
jcc(Assembler::aboveEqual, L_2TAG_PACKET_0_0_2);
219
bind(L_2TAG_PACKET_1_0_2);
230
cvtsi2sdl(xmm7, eax);
233
movsd(xmm6, Address(tmp, 2064)); //0xbd19d71cUL, 0x00000000UL, 0x00000000UL, 0x00000000UL
234
movdqu(xmm3, Address(tmp, 2080)); //0x00000000UL, 0x509f7800UL, 0x3f934413UL, 0x1f12b358UL
238
movdqu(xmm0, Address(tmp, edx, Address::times_1, -1504));
239
movdqu(xmm4, Address(tmp, 2096)); //0x3cdfef31UL, 0xc1a5f12eUL, 0x40358874UL, 0x64d4ef0dUL
241
movdqu(xmm2, Address(tmp, 2112)); //0xc0089309UL, 0x385593b1UL, 0xc025c917UL, 0xdc963467UL
243
pshufd(xmm5, xmm1, 68);
244
mulsd(xmm7, Address(tmp, 2072)); //0x00000000UL, 0x00000000UL, 0x00000000UL, 0x509f7800UL
248
movsd(xmm6, Address(tmp, 2152)); //0xffffffffUL, 0x00000000UL, 0xffffe000UL, 0x00000000UL
252
pshufd(xmm2, xmm0, 228);
258
pshufd(xmm2, xmm0, 238);
266
pshufd(xmm5, xmm4, 238);
269
jmp(L_2TAG_PACKET_2_0_2);
271
bind(L_2TAG_PACKET_0_0_2);
272
movsd(xmm0, Address(rsp, 112)); //0xbcfa1d84UL, 0x6baa7c00UL, 0x3fd28651UL, 0xfd9abec1UL
276
jcc(Assembler::aboveEqual, L_2TAG_PACKET_3_0_2);
278
jcc(Assembler::below, L_2TAG_PACKET_4_0_2);
280
bind(L_2TAG_PACKET_5_0_2);
282
jmp(L_2TAG_PACKET_2_0_2);
284
bind(L_2TAG_PACKET_6_0_2);
285
jcc(Assembler::above, L_2TAG_PACKET_5_0_2);
287
jcc(Assembler::above, L_2TAG_PACKET_5_0_2);
288
jmp(L_2TAG_PACKET_7_0_2);
290
bind(L_2TAG_PACKET_3_0_2);
296
jcc(Assembler::aboveEqual, L_2TAG_PACKET_6_0_2);
299
jcc(Assembler::equal, L_2TAG_PACKET_8_0_2);
301
bind(L_2TAG_PACKET_7_0_2);
305
pinsrw(xmm1, eax, 3);
309
bind(L_2TAG_PACKET_9_0_2);
310
movsd(Address(rsp, 0), xmm0);
311
movsd(xmm0, Address(rsp, 112)); //0xbcfa1d84UL, 0x6baa7c00UL, 0x3fd28651UL, 0xfd9abec1UL
312
fld_d(Address(rsp, 0));
313
jmp(L_2TAG_PACKET_10_0_2);
315
bind(L_2TAG_PACKET_8_0_2);
319
pinsrw(xmm0, eax, 3);
322
jmp(L_2TAG_PACKET_9_0_2);
324
bind(L_2TAG_PACKET_4_0_2);
330
jcc(Assembler::equal, L_2TAG_PACKET_8_0_2);
333
pinsrw(xmm1, eax, 3);
337
pinsrw(xmm2, eax, 3);
339
pextrw(eax, xmm0, 3);
343
movsd(xmm2, Address(tmp, 2144)); //0xbff27af2UL, 0xf8000000UL, 0xffffffffUL, 0x00000000UL
347
pshufd(xmm6, xmm5, 78);
349
jmp(L_2TAG_PACKET_1_0_2);
351
bind(L_2TAG_PACKET_2_0_2);
352
movsd(Address(rsp, 24), xmm0);
353
fld_d(Address(rsp, 24));
355
bind(L_2TAG_PACKET_10_0_2);
356
movl(tmp, Address(rsp, 40));