1 /*
2 * Copyright (c) 2015, Intel Corporation.
3 * Intel Math Library (LIBM) Source Code
4 *
5 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
6 *
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.
10 *
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).
16 *
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.
20 *
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
23 * questions.
24 *
25 */
26
27 /******************************************************************************/
28 // ALGORITHM DESCRIPTION
29 // ---------------------
30 //
31 // Description:
32 // Let K = 64 (table size).
33 // x x/log(2) n
34 // e = 2 = 2 * T[j] * (1 + P(y))
35 // where
36 // x = m*log(2)/K + y, y in [-log(2)/K..log(2)/K]
37 // m = n*K + j, m,n,j - signed integer, j in [-K/2..K/2]
38 // j/K
39 // values of 2 are tabulated as T[j] = T_hi[j] ( 1 + T_lo[j]).
40 //
41 // P(y) is a minimax polynomial approximation of exp(x)-1
42 // on small interval [-log(2)/K..log(2)/K] (were calculated by Maple V).
43 //
44 // To avoid problems with arithmetic overflow and underflow,
45 // n n1 n2
46 // value of 2 is safely computed as 2 * 2 where n1 in [-BIAS/2..BIAS/2]
47 // where BIAS is a value of exponent bias.
48 //
49 // Special cases:
50 // exp(NaN) = NaN
51 // exp(+INF) = +INF
52 // exp(-INF) = 0
53 // exp(x) = 1 for subnormals
54 // for finite argument, only exp(0)=1 is exact
55 // For IEEE double
56 // if x > 709.782712893383973096 then exp(x) overflow
57 // if x < -745.133219101941108420 then exp(x) underflow
58 //
59 /******************************************************************************/
60
61
62 #include "precompiled.hpp"
63 #include "asm/assembler.hpp"
64 #include "asm/assembler.inline.hpp"
65 #include "macroAssembler_x86.hpp"
66
67 #ifdef _MSC_VER
68 #define ALIGNED_(x) __declspec(align(x))
69 #else
70 #define ALIGNED_(x) __attribute__ ((aligned(x)))
71 #endif
72
73 #ifdef _LP64
74
75 ALIGNED_(16) juint _cv[] =
76 {
77 0x652b82feUL, 0x40571547UL, 0x652b82feUL, 0x40571547UL, 0xfefa0000UL,
78 0x3f862e42UL, 0xfefa0000UL, 0x3f862e42UL, 0xbc9e3b3aUL, 0x3d1cf79aUL,
79 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xfffffffeUL, 0x3fdfffffUL, 0xfffffffeUL,
80 0x3fdfffffUL, 0xe3289860UL, 0x3f56c15cUL, 0x555b9e25UL, 0x3fa55555UL,
81 0xc090cf0fUL, 0x3f811115UL, 0x55548ba1UL, 0x3fc55555UL
82 };
83
84 ALIGNED_(16) juint _shifter[] =
85 {
86 0x00000000UL, 0x43380000UL, 0x00000000UL, 0x43380000UL
87 };
88
89 ALIGNED_(16) juint _mmask[] =
90 {
91 0xffffffc0UL, 0x00000000UL, 0xffffffc0UL, 0x00000000UL
92 };
93
94 ALIGNED_(16) juint _bias[] =
95 {
96 0x0000ffc0UL, 0x00000000UL, 0x0000ffc0UL, 0x00000000UL
97 };
98
99 ALIGNED_(16) juint _Tbl_addr[] =
100 {
101 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0e03754dUL,
102 0x3cad7bbfUL, 0x3e778060UL, 0x00002c9aUL, 0x3567f613UL, 0x3c8cd252UL,
103 0xd3158574UL, 0x000059b0UL, 0x61e6c861UL, 0x3c60f74eUL, 0x18759bc8UL,
104 0x00008745UL, 0x5d837b6cUL, 0x3c979aa6UL, 0x6cf9890fUL, 0x0000b558UL,
105 0x702f9cd1UL, 0x3c3ebe3dUL, 0x32d3d1a2UL, 0x0000e3ecUL, 0x1e63bcd8UL,
106 0x3ca3516eUL, 0xd0125b50UL, 0x00011301UL, 0x26f0387bUL, 0x3ca4c554UL,
107 0xaea92ddfUL, 0x0001429aUL, 0x62523fb6UL, 0x3ca95153UL, 0x3c7d517aUL,
108 0x000172b8UL, 0x3f1353bfUL, 0x3c8b898cUL, 0xeb6fcb75UL, 0x0001a35bUL,
109 0x3e3a2f5fUL, 0x3c9aecf7UL, 0x3168b9aaUL, 0x0001d487UL, 0x44a6c38dUL,
110 0x3c8a6f41UL, 0x88628cd6UL, 0x0002063bUL, 0xe3a8a894UL, 0x3c968efdUL,
111 0x6e756238UL, 0x0002387aUL, 0x981fe7f2UL, 0x3c80472bUL, 0x65e27cddUL,
112 0x00026b45UL, 0x6d09ab31UL, 0x3c82f7e1UL, 0xf51fdee1UL, 0x00029e9dUL,
113 0x720c0ab3UL, 0x3c8b3782UL, 0xa6e4030bUL, 0x0002d285UL, 0x4db0abb6UL,
114 0x3c834d75UL, 0x0a31b715UL, 0x000306feUL, 0x5dd3f84aUL, 0x3c8fdd39UL,
115 0xb26416ffUL, 0x00033c08UL, 0xcc187d29UL, 0x3ca12f8cUL, 0x373aa9caUL,
116 0x000371a7UL, 0x738b5e8bUL, 0x3ca7d229UL, 0x34e59ff6UL, 0x0003a7dbUL,
117 0xa72a4c6dUL, 0x3c859f48UL, 0x4c123422UL, 0x0003dea6UL, 0x259d9205UL,
118 0x3ca8b846UL, 0x21f72e29UL, 0x0004160aUL, 0x60c2ac12UL, 0x3c4363edUL,
119 0x6061892dUL, 0x00044e08UL, 0xdaa10379UL, 0x3c6ecce1UL, 0xb5c13cd0UL,
120 0x000486a2UL, 0xbb7aafb0UL, 0x3c7690ceUL, 0xd5362a27UL, 0x0004bfdaUL,
121 0x9b282a09UL, 0x3ca083ccUL, 0x769d2ca6UL, 0x0004f9b2UL, 0xc1aae707UL,
122 0x3ca509b0UL, 0x569d4f81UL, 0x0005342bUL, 0x18fdd78eUL, 0x3c933505UL,
123 0x36b527daUL, 0x00056f47UL, 0xe21c5409UL, 0x3c9063e1UL, 0xdd485429UL,
124 0x0005ab07UL, 0x2b64c035UL, 0x3c9432e6UL, 0x15ad2148UL, 0x0005e76fUL,
125 0x99f08c0aUL, 0x3ca01284UL, 0xb03a5584UL, 0x0006247eUL, 0x0073dc06UL,
126 0x3c99f087UL, 0x82552224UL, 0x00066238UL, 0x0da05571UL, 0x3c998d4dUL,
127 0x667f3bccUL, 0x0006a09eUL, 0x86ce4786UL, 0x3ca52bb9UL, 0x3c651a2eUL,
128 0x0006dfb2UL, 0x206f0dabUL, 0x3ca32092UL, 0xe8ec5f73UL, 0x00071f75UL,
129 0x8e17a7a6UL, 0x3ca06122UL, 0x564267c8UL, 0x00075febUL, 0x461e9f86UL,
130 0x3ca244acUL, 0x73eb0186UL, 0x0007a114UL, 0xabd66c55UL, 0x3c65ebe1UL,
131 0x36cf4e62UL, 0x0007e2f3UL, 0xbbff67d0UL, 0x3c96fe9fUL, 0x994cce12UL,
132 0x00082589UL, 0x14c801dfUL, 0x3c951f14UL, 0x9b4492ecUL, 0x000868d9UL,
133 0xc1f0eab4UL, 0x3c8db72fUL, 0x422aa0dbUL, 0x0008ace5UL, 0x59f35f44UL,
134 0x3c7bf683UL, 0x99157736UL, 0x0008f1aeUL, 0x9c06283cUL, 0x3ca360baUL,
135 0xb0cdc5e4UL, 0x00093737UL, 0x20f962aaUL, 0x3c95e8d1UL, 0x9fde4e4fUL,
136 0x00097d82UL, 0x2b91ce27UL, 0x3c71affcUL, 0x82a3f090UL, 0x0009c491UL,
137 0x589a2ebdUL, 0x3c9b6d34UL, 0x7b5de564UL, 0x000a0c66UL, 0x9ab89880UL,
138 0x3c95277cUL, 0xb23e255cUL, 0x000a5503UL, 0x6e735ab3UL, 0x3c846984UL,
139 0x5579fdbfUL, 0x000a9e6bUL, 0x92cb3387UL, 0x3c8c1a77UL, 0x995ad3adUL,
140 0x000ae89fUL, 0xdc2d1d96UL, 0x3ca22466UL, 0xb84f15faUL, 0x000b33a2UL,
141 0xb19505aeUL, 0x3ca1112eUL, 0xf2fb5e46UL, 0x000b7f76UL, 0x0a5fddcdUL,
142 0x3c74ffd7UL, 0x904bc1d2UL, 0x000bcc1eUL, 0x30af0cb3UL, 0x3c736eaeUL,
143 0xdd85529cUL, 0x000c199bUL, 0xd10959acUL, 0x3c84e08fUL, 0x2e57d14bUL,
144 0x000c67f1UL, 0x6c921968UL, 0x3c676b2cUL, 0xdcef9069UL, 0x000cb720UL,
145 0x36df99b3UL, 0x3c937009UL, 0x4a07897bUL, 0x000d072dUL, 0xa63d07a7UL,
146 0x3c74a385UL, 0xdcfba487UL, 0x000d5818UL, 0xd5c192acUL, 0x3c8e5a50UL,
147 0x03db3285UL, 0x000da9e6UL, 0x1c4a9792UL, 0x3c98bb73UL, 0x337b9b5eUL,
148 0x000dfc97UL, 0x603a88d3UL, 0x3c74b604UL, 0xe78b3ff6UL, 0x000e502eUL,
149 0x92094926UL, 0x3c916f27UL, 0xa2a490d9UL, 0x000ea4afUL, 0x41aa2008UL,
150 0x3c8ec3bcUL, 0xee615a27UL, 0x000efa1bUL, 0x31d185eeUL, 0x3c8a64a9UL,
151 0x5b6e4540UL, 0x000f5076UL, 0x4d91cd9dUL, 0x3c77893bUL, 0x819e90d8UL,
152 0x000fa7c1UL
153 };
154
155 ALIGNED_(16) juint _ALLONES[] =
156 {
157 0xffffffffUL, 0xffffffffUL, 0xffffffffUL, 0xffffffffUL
158 };
159
160 ALIGNED_(16) juint _ebias[] =
161 {
162 0x00000000UL, 0x3ff00000UL, 0x00000000UL, 0x3ff00000UL
163 };
164
165 ALIGNED_(4) juint _XMAX[] =
166 {
167 0xffffffffUL, 0x7fefffffUL
168 };
169
170 ALIGNED_(4) juint _XMIN[] =
171 {
172 0x00000000UL, 0x00100000UL
173 };
174
175 ALIGNED_(4) juint _INF[] =
176 {
177 0x00000000UL, 0x7ff00000UL
178 };
179
180 ALIGNED_(4) juint _ZERO[] =
181 {
182 0x00000000UL, 0x00000000UL
183 };
184
185 ALIGNED_(4) juint _ONE_val[] =
186 {
187 0x00000000UL, 0x3ff00000UL
188 };
189
190
191 // Registers:
192 // input: xmm0
193 // scratch: xmm1, xmm2, xmm3, xmm4, xmm5, xmm6, xmm7
194 // rax, rdx, rcx, tmp - r11
195
196 // Code generated by Intel C compiler for LIBM library
197
198 void MacroAssembler::fast_exp(XMMRegister xmm0, XMMRegister xmm1, XMMRegister xmm2, XMMRegister xmm3, XMMRegister xmm4, XMMRegister xmm5, XMMRegister xmm6, XMMRegister xmm7, Register eax, Register ecx, Register edx, Register tmp) {
199 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;
200 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;
201 Label L_2TAG_PACKET_8_0_2, L_2TAG_PACKET_9_0_2, L_2TAG_PACKET_10_0_2, L_2TAG_PACKET_11_0_2;
202 Label L_2TAG_PACKET_12_0_2, B1_3, B1_5, start;
203
204 assert_different_registers(tmp, eax, ecx, edx);
205 jmp(start);
206 address cv = (address)_cv;
207 address Shifter = (address)_shifter;
208 address mmask = (address)_mmask;
209 address bias = (address)_bias;
210 address Tbl_addr = (address)_Tbl_addr;
211 address ALLONES = (address)_ALLONES;
212 address ebias = (address)_ebias;
213 address XMAX = (address)_XMAX;
214 address XMIN = (address)_XMIN;
215 address INF = (address)_INF;
216 address ZERO = (address)_ZERO;
217 address ONE_val = (address)_ONE_val;
218
219 bind(start);
220 subq(rsp, 24);
221 movsd(Address(rsp, 8), xmm0);
222 unpcklpd(xmm0, xmm0);
223 movdqu(xmm1, ExternalAddress(cv)); // 0x652b82feUL, 0x40571547UL, 0x652b82feUL, 0x40571547UL
224 movdqu(xmm6, ExternalAddress(Shifter)); // 0x00000000UL, 0x43380000UL, 0x00000000UL, 0x43380000UL
225 movdqu(xmm2, ExternalAddress(16+cv)); // 0xfefa0000UL, 0x3f862e42UL, 0xfefa0000UL, 0x3f862e42UL
226 movdqu(xmm3, ExternalAddress(32+cv)); // 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xbc9e3b3aUL, 0x3d1cf79aUL
227 pextrw(eax, xmm0, 3);
228 andl(eax, 32767);
229 movl(edx, 16527);
230 subl(edx, eax);
231 subl(eax, 15504);
232 orl(edx, eax);
233 cmpl(edx, INT_MIN);
234 jcc(Assembler::aboveEqual, L_2TAG_PACKET_0_0_2);
235 mulpd(xmm1, xmm0);
236 addpd(xmm1, xmm6);
237 movapd(xmm7, xmm1);
238 subpd(xmm1, xmm6);
239 mulpd(xmm2, xmm1);
240 movdqu(xmm4, ExternalAddress(64+cv)); // 0xe3289860UL, 0x3f56c15cUL, 0x555b9e25UL, 0x3fa55555UL
241 mulpd(xmm3, xmm1);
242 movdqu(xmm5, ExternalAddress(80+cv)); // 0xc090cf0fUL, 0x3f811115UL, 0x55548ba1UL, 0x3fc55555UL
243 subpd(xmm0, xmm2);
244 movdl(eax, xmm7);
245 movl(ecx, eax);
246 andl(ecx, 63);
247 shll(ecx, 4);
248 sarl(eax, 6);
249 movl(edx, eax);
250 movdqu(xmm6, ExternalAddress(mmask)); // 0xffffffc0UL, 0x00000000UL, 0xffffffc0UL, 0x00000000UL
251 pand(xmm7, xmm6);
252 movdqu(xmm6, ExternalAddress(bias)); // 0x0000ffc0UL, 0x00000000UL, 0x0000ffc0UL, 0x00000000UL
253 paddq(xmm7, xmm6);
254 psllq(xmm7, 46);
255 subpd(xmm0, xmm3);
256 lea(tmp, ExternalAddress(Tbl_addr));
257 movdqu(xmm2, Address(ecx,tmp));
258 mulpd(xmm4, xmm0);
259 movapd(xmm6, xmm0);
260 movapd(xmm1, xmm0);
261 mulpd(xmm6, xmm6);
262 mulpd(xmm0, xmm6);
263 addpd(xmm5, xmm4);
264 mulsd(xmm0, xmm6);
265 mulpd(xmm6, ExternalAddress(48+cv)); // 0xfffffffeUL, 0x3fdfffffUL, 0xfffffffeUL, 0x3fdfffffUL
266 addsd(xmm1, xmm2);
267 unpckhpd(xmm2, xmm2);
268 mulpd(xmm0, xmm5);
269 addsd(xmm1, xmm0);
270 por(xmm2, xmm7);
271 unpckhpd(xmm0, xmm0);
272 addsd(xmm0, xmm1);
273 addsd(xmm0, xmm6);
274 addl(edx, 894);
275 cmpl(edx, 1916);
276 jcc (Assembler::above, L_2TAG_PACKET_1_0_2);
277 mulsd(xmm0, xmm2);
278 addsd(xmm0, xmm2);
279 jmp (B1_5);
280
281 bind(L_2TAG_PACKET_1_0_2);
282 xorpd(xmm3, xmm3);
283 movdqu(xmm4, ExternalAddress(ALLONES)); // 0xffffffffUL, 0xffffffffUL, 0xffffffffUL, 0xffffffffUL
284 movl(edx, -1022);
285 subl(edx, eax);
286 movdl(xmm5, edx);
287 psllq(xmm4, xmm5);
288 movl(ecx, eax);
289 sarl(eax, 1);
290 pinsrw(xmm3, eax, 3);
291 movdqu(xmm6, ExternalAddress(ebias)); // 0x00000000UL, 0x3ff00000UL, 0x00000000UL, 0x3ff00000UL
292 psllq(xmm3, 4);
293 psubd(xmm2, xmm3);
294 mulsd(xmm0, xmm2);
295 cmpl(edx, 52);
296 jcc(Assembler::greater, L_2TAG_PACKET_2_0_2);
297 pand(xmm4, xmm2);
298 paddd(xmm3, xmm6);
299 subsd(xmm2, xmm4);
300 addsd(xmm0, xmm2);
301 cmpl(ecx, 1023);
302 jcc(Assembler::greaterEqual, L_2TAG_PACKET_3_0_2);
303 pextrw(ecx, xmm0, 3);
304 andl(ecx, 32768);
305 orl(edx, ecx);
306 cmpl(edx, 0);
307 jcc(Assembler::equal, L_2TAG_PACKET_4_0_2);
308 movapd(xmm6, xmm0);
309 addsd(xmm0, xmm4);
310 mulsd(xmm0, xmm3);
311 pextrw(ecx, xmm0, 3);
312 andl(ecx, 32752);
313 cmpl(ecx, 0);
314 jcc(Assembler::equal, L_2TAG_PACKET_5_0_2);
315 jmp(B1_5);
316
317 bind(L_2TAG_PACKET_5_0_2);
318 mulsd(xmm6, xmm3);
319 mulsd(xmm4, xmm3);
320 movdqu(xmm0, xmm6);
321 pxor(xmm6, xmm4);
322 psrad(xmm6, 31);
323 pshufd(xmm6, xmm6, 85);
324 psllq(xmm0, 1);
325 psrlq(xmm0, 1);
326 pxor(xmm0, xmm6);
327 psrlq(xmm6, 63);
328 paddq(xmm0, xmm6);
329 paddq(xmm0, xmm4);
330 movl(Address(rsp,0), 15);
331 jmp(L_2TAG_PACKET_6_0_2);
332
333 bind(L_2TAG_PACKET_4_0_2);
334 addsd(xmm0, xmm4);
335 mulsd(xmm0, xmm3);
336 jmp(B1_5);
337
338 bind(L_2TAG_PACKET_3_0_2);
339 addsd(xmm0, xmm4);
340 mulsd(xmm0, xmm3);
341 pextrw(ecx, xmm0, 3);
342 andl(ecx, 32752);
343 cmpl(ecx, 32752);
344 jcc(Assembler::aboveEqual, L_2TAG_PACKET_7_0_2);
345 jmp(B1_5);
346
347 bind(L_2TAG_PACKET_2_0_2);
348 paddd(xmm3, xmm6);
349 addpd(xmm0, xmm2);
350 mulsd(xmm0, xmm3);
351 movl(Address(rsp,0), 15);
352 jmp(L_2TAG_PACKET_6_0_2);
353
354 bind(L_2TAG_PACKET_8_0_2);
355 cmpl(eax, 2146435072);
356 jcc(Assembler::aboveEqual, L_2TAG_PACKET_9_0_2);
357 movl(eax, Address(rsp,12));
358 cmpl(eax, INT_MIN);
359 jcc(Assembler::aboveEqual, L_2TAG_PACKET_10_0_2);
360 movsd(xmm0, ExternalAddress(XMAX)); // 0xffffffffUL, 0x7fefffffUL
361 mulsd(xmm0, xmm0);
362
363 bind(L_2TAG_PACKET_7_0_2);
364 movl(Address(rsp,0), 14);
365 jmp(L_2TAG_PACKET_6_0_2);
366
367 bind(L_2TAG_PACKET_10_0_2);
368 movsd(xmm0, ExternalAddress(XMIN)); // 0x00000000UL, 0x00100000UL
369 mulsd(xmm0, xmm0);
370 movl(Address(rsp,0), 15);
371 jmp(L_2TAG_PACKET_6_0_2);
372
373 bind(L_2TAG_PACKET_9_0_2);
374 movl(edx, Address(rsp,8));
375 cmpl(eax, 2146435072);
376 jcc(Assembler::above, L_2TAG_PACKET_11_0_2);
377 cmpl(edx, 0);
378 jcc(Assembler::notEqual, L_2TAG_PACKET_11_0_2);
379 movl(eax, Address(rsp,12));
380 cmpl(eax, 2146435072);
381 jcc(Assembler::notEqual, L_2TAG_PACKET_12_0_2);
382 movsd(xmm0, ExternalAddress(INF)); // 0x00000000UL, 0x7ff00000UL
383 jmp(B1_5);
384
385 bind(L_2TAG_PACKET_12_0_2);
386 movsd(xmm0, ExternalAddress(ZERO)); // 0x00000000UL, 0x00000000UL
387 jmp(B1_5);
388
389 bind(L_2TAG_PACKET_11_0_2);
390 movsd(xmm0, Address(rsp, 8));
391 addsd(xmm0, xmm0);
392 jmp(B1_5);
393
394 bind(L_2TAG_PACKET_0_0_2);
395 movl(eax, Address(rsp, 12));
396 andl(eax, 2147483647);
397 cmpl(eax, 1083179008);
398 jcc(Assembler::aboveEqual, L_2TAG_PACKET_8_0_2);
399 movsd(Address(rsp, 8), xmm0);
400 addsd(xmm0, ExternalAddress(ONE_val)); // 0x00000000UL, 0x3ff00000UL
401 jmp(B1_5);
402
403 bind(L_2TAG_PACKET_6_0_2);
404 movq(Address(rsp, 16), xmm0);
405
406 bind(B1_3);
407 movq(xmm0, Address(rsp, 16));
408
409 bind(B1_5);
410 addq(rsp, 24);
411 }
412 #endif
413
414 #ifndef _LP64
415
416 ALIGNED_(16) juint _static_const_table[] =
417 {
418 0x00000000UL, 0xfff00000UL, 0x00000000UL, 0xfff00000UL, 0xffffffc0UL,
419 0x00000000UL, 0xffffffc0UL, 0x00000000UL, 0x0000ffc0UL, 0x00000000UL,
420 0x0000ffc0UL, 0x00000000UL, 0x00000000UL, 0x43380000UL, 0x00000000UL,
421 0x43380000UL, 0x652b82feUL, 0x40571547UL, 0x652b82feUL, 0x40571547UL,
422 0xfefa0000UL, 0x3f862e42UL, 0xfefa0000UL, 0x3f862e42UL, 0xbc9e3b3aUL,
423 0x3d1cf79aUL, 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xfffffffeUL, 0x3fdfffffUL,
424 0xfffffffeUL, 0x3fdfffffUL, 0xe3289860UL, 0x3f56c15cUL, 0x555b9e25UL,
425 0x3fa55555UL, 0xc090cf0fUL, 0x3f811115UL, 0x55548ba1UL, 0x3fc55555UL,
426 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0e03754dUL,
427 0x3cad7bbfUL, 0x3e778060UL, 0x00002c9aUL, 0x3567f613UL, 0x3c8cd252UL,
428 0xd3158574UL, 0x000059b0UL, 0x61e6c861UL, 0x3c60f74eUL, 0x18759bc8UL,
429 0x00008745UL, 0x5d837b6cUL, 0x3c979aa6UL, 0x6cf9890fUL, 0x0000b558UL,
430 0x702f9cd1UL, 0x3c3ebe3dUL, 0x32d3d1a2UL, 0x0000e3ecUL, 0x1e63bcd8UL,
431 0x3ca3516eUL, 0xd0125b50UL, 0x00011301UL, 0x26f0387bUL, 0x3ca4c554UL,
432 0xaea92ddfUL, 0x0001429aUL, 0x62523fb6UL, 0x3ca95153UL, 0x3c7d517aUL,
433 0x000172b8UL, 0x3f1353bfUL, 0x3c8b898cUL, 0xeb6fcb75UL, 0x0001a35bUL,
434 0x3e3a2f5fUL, 0x3c9aecf7UL, 0x3168b9aaUL, 0x0001d487UL, 0x44a6c38dUL,
435 0x3c8a6f41UL, 0x88628cd6UL, 0x0002063bUL, 0xe3a8a894UL, 0x3c968efdUL,
436 0x6e756238UL, 0x0002387aUL, 0x981fe7f2UL, 0x3c80472bUL, 0x65e27cddUL,
437 0x00026b45UL, 0x6d09ab31UL, 0x3c82f7e1UL, 0xf51fdee1UL, 0x00029e9dUL,
438 0x720c0ab3UL, 0x3c8b3782UL, 0xa6e4030bUL, 0x0002d285UL, 0x4db0abb6UL,
439 0x3c834d75UL, 0x0a31b715UL, 0x000306feUL, 0x5dd3f84aUL, 0x3c8fdd39UL,
440 0xb26416ffUL, 0x00033c08UL, 0xcc187d29UL, 0x3ca12f8cUL, 0x373aa9caUL,
441 0x000371a7UL, 0x738b5e8bUL, 0x3ca7d229UL, 0x34e59ff6UL, 0x0003a7dbUL,
442 0xa72a4c6dUL, 0x3c859f48UL, 0x4c123422UL, 0x0003dea6UL, 0x259d9205UL,
443 0x3ca8b846UL, 0x21f72e29UL, 0x0004160aUL, 0x60c2ac12UL, 0x3c4363edUL,
444 0x6061892dUL, 0x00044e08UL, 0xdaa10379UL, 0x3c6ecce1UL, 0xb5c13cd0UL,
445 0x000486a2UL, 0xbb7aafb0UL, 0x3c7690ceUL, 0xd5362a27UL, 0x0004bfdaUL,
446 0x9b282a09UL, 0x3ca083ccUL, 0x769d2ca6UL, 0x0004f9b2UL, 0xc1aae707UL,
447 0x3ca509b0UL, 0x569d4f81UL, 0x0005342bUL, 0x18fdd78eUL, 0x3c933505UL,
448 0x36b527daUL, 0x00056f47UL, 0xe21c5409UL, 0x3c9063e1UL, 0xdd485429UL,
449 0x0005ab07UL, 0x2b64c035UL, 0x3c9432e6UL, 0x15ad2148UL, 0x0005e76fUL,
450 0x99f08c0aUL, 0x3ca01284UL, 0xb03a5584UL, 0x0006247eUL, 0x0073dc06UL,
451 0x3c99f087UL, 0x82552224UL, 0x00066238UL, 0x0da05571UL, 0x3c998d4dUL,
452 0x667f3bccUL, 0x0006a09eUL, 0x86ce4786UL, 0x3ca52bb9UL, 0x3c651a2eUL,
453 0x0006dfb2UL, 0x206f0dabUL, 0x3ca32092UL, 0xe8ec5f73UL, 0x00071f75UL,
454 0x8e17a7a6UL, 0x3ca06122UL, 0x564267c8UL, 0x00075febUL, 0x461e9f86UL,
455 0x3ca244acUL, 0x73eb0186UL, 0x0007a114UL, 0xabd66c55UL, 0x3c65ebe1UL,
456 0x36cf4e62UL, 0x0007e2f3UL, 0xbbff67d0UL, 0x3c96fe9fUL, 0x994cce12UL,
457 0x00082589UL, 0x14c801dfUL, 0x3c951f14UL, 0x9b4492ecUL, 0x000868d9UL,
458 0xc1f0eab4UL, 0x3c8db72fUL, 0x422aa0dbUL, 0x0008ace5UL, 0x59f35f44UL,
459 0x3c7bf683UL, 0x99157736UL, 0x0008f1aeUL, 0x9c06283cUL, 0x3ca360baUL,
460 0xb0cdc5e4UL, 0x00093737UL, 0x20f962aaUL, 0x3c95e8d1UL, 0x9fde4e4fUL,
461 0x00097d82UL, 0x2b91ce27UL, 0x3c71affcUL, 0x82a3f090UL, 0x0009c491UL,
462 0x589a2ebdUL, 0x3c9b6d34UL, 0x7b5de564UL, 0x000a0c66UL, 0x9ab89880UL,
463 0x3c95277cUL, 0xb23e255cUL, 0x000a5503UL, 0x6e735ab3UL, 0x3c846984UL,
464 0x5579fdbfUL, 0x000a9e6bUL, 0x92cb3387UL, 0x3c8c1a77UL, 0x995ad3adUL,
465 0x000ae89fUL, 0xdc2d1d96UL, 0x3ca22466UL, 0xb84f15faUL, 0x000b33a2UL,
466 0xb19505aeUL, 0x3ca1112eUL, 0xf2fb5e46UL, 0x000b7f76UL, 0x0a5fddcdUL,
467 0x3c74ffd7UL, 0x904bc1d2UL, 0x000bcc1eUL, 0x30af0cb3UL, 0x3c736eaeUL,
468 0xdd85529cUL, 0x000c199bUL, 0xd10959acUL, 0x3c84e08fUL, 0x2e57d14bUL,
469 0x000c67f1UL, 0x6c921968UL, 0x3c676b2cUL, 0xdcef9069UL, 0x000cb720UL,
470 0x36df99b3UL, 0x3c937009UL, 0x4a07897bUL, 0x000d072dUL, 0xa63d07a7UL,
471 0x3c74a385UL, 0xdcfba487UL, 0x000d5818UL, 0xd5c192acUL, 0x3c8e5a50UL,
472 0x03db3285UL, 0x000da9e6UL, 0x1c4a9792UL, 0x3c98bb73UL, 0x337b9b5eUL,
473 0x000dfc97UL, 0x603a88d3UL, 0x3c74b604UL, 0xe78b3ff6UL, 0x000e502eUL,
474 0x92094926UL, 0x3c916f27UL, 0xa2a490d9UL, 0x000ea4afUL, 0x41aa2008UL,
475 0x3c8ec3bcUL, 0xee615a27UL, 0x000efa1bUL, 0x31d185eeUL, 0x3c8a64a9UL,
476 0x5b6e4540UL, 0x000f5076UL, 0x4d91cd9dUL, 0x3c77893bUL, 0x819e90d8UL,
477 0x000fa7c1UL, 0x00000000UL, 0x3ff00000UL, 0x00000000UL, 0x7ff00000UL,
478 0x00000000UL, 0x00000000UL, 0xffffffffUL, 0x7fefffffUL, 0x00000000UL,
479 0x00100000UL
480 };
481
482 //registers,
483 // input: (rbp + 8)
484 // scratch: xmm1, xmm2, xmm3, xmm4, xmm5, xmm6, xmm7
485 // rax, rdx, rcx, rbx (tmp)
486
487 // Code generated by Intel C compiler for LIBM library
488
489 void MacroAssembler::fast_exp(XMMRegister xmm0, XMMRegister xmm1, XMMRegister xmm2, XMMRegister xmm3, XMMRegister xmm4, XMMRegister xmm5, XMMRegister xmm6, XMMRegister xmm7, Register eax, Register ecx, Register edx, Register tmp) {
490 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;
491 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;
492 Label L_2TAG_PACKET_8_0_2, L_2TAG_PACKET_9_0_2, L_2TAG_PACKET_10_0_2, L_2TAG_PACKET_11_0_2;
493 Label L_2TAG_PACKET_12_0_2, L_2TAG_PACKET_13_0_2, B1_3, B1_5, start;
494
495 assert_different_registers(tmp, eax, ecx, edx);
496 jmp(start);
497 address static_const_table = (address)_static_const_table;
498
499 bind(start);
500 subl(rsp, 120);
501 movl(Address(rsp, 64), tmp);
502 lea(tmp, ExternalAddress(static_const_table));
503 movdqu(xmm0, Address(rsp, 128));
504 unpcklpd(xmm0, xmm0);
505 movdqu(xmm1, Address(tmp, 64)); // 0x652b82feUL, 0x40571547UL, 0x652b82feUL, 0x40571547UL
506 movdqu(xmm6, Address(tmp, 48)); // 0x00000000UL, 0x43380000UL, 0x00000000UL, 0x43380000UL
507 movdqu(xmm2, Address(tmp, 80)); // 0xfefa0000UL, 0x3f862e42UL, 0xfefa0000UL, 0x3f862e42UL
508 movdqu(xmm3, Address(tmp, 96)); // 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xbc9e3b3aUL, 0x3d1cf79aUL
509 pextrw(eax, xmm0, 3);
510 andl(eax, 32767);
511 movl(edx, 16527);
512 subl(edx, eax);
513 subl(eax, 15504);
514 orl(edx, eax);
515 cmpl(edx, INT_MIN);
516 jcc(Assembler::aboveEqual, L_2TAG_PACKET_0_0_2);
517 mulpd(xmm1, xmm0);
518 addpd(xmm1, xmm6);
519 movapd(xmm7, xmm1);
520 subpd(xmm1, xmm6);
521 mulpd(xmm2, xmm1);
522 movdqu(xmm4, Address(tmp, 128)); // 0xe3289860UL, 0x3f56c15cUL, 0x555b9e25UL, 0x3fa55555UL
523 mulpd(xmm3, xmm1);
524 movdqu(xmm5, Address(tmp, 144)); // 0xc090cf0fUL, 0x3f811115UL, 0x55548ba1UL, 0x3fc55555UL
525 subpd(xmm0, xmm2);
526 movdl(eax, xmm7);
527 movl(ecx, eax);
528 andl(ecx, 63);
529 shll(ecx, 4);
530 sarl(eax, 6);
531 movl(edx, eax);
532 movdqu(xmm6, Address(tmp, 16)); // 0xffffffc0UL, 0x00000000UL, 0xffffffc0UL, 0x00000000UL
533 pand(xmm7, xmm6);
534 movdqu(xmm6, Address(tmp, 32)); // 0x0000ffc0UL, 0x00000000UL, 0x0000ffc0UL, 0x00000000UL
535 paddq(xmm7, xmm6);
536 psllq(xmm7, 46);
537 subpd(xmm0, xmm3);
538 movdqu(xmm2, Address(tmp, ecx, Address::times_1, 160));
539 mulpd(xmm4, xmm0);
540 movapd(xmm6, xmm0);
541 movapd(xmm1, xmm0);
542 mulpd(xmm6, xmm6);
543 mulpd(xmm0, xmm6);
544 addpd(xmm5, xmm4);
545 mulsd(xmm0, xmm6);
546 mulpd(xmm6, Address(tmp, 112)); // 0xfffffffeUL, 0x3fdfffffUL, 0xfffffffeUL, 0x3fdfffffUL
547 addsd(xmm1, xmm2);
548 unpckhpd(xmm2, xmm2);
549 mulpd(xmm0, xmm5);
550 addsd(xmm1, xmm0);
551 por(xmm2, xmm7);
552 unpckhpd(xmm0, xmm0);
553 addsd(xmm0, xmm1);
554 addsd(xmm0, xmm6);
555 addl(edx, 894);
556 cmpl(edx, 1916);
557 jcc (Assembler::above, L_2TAG_PACKET_1_0_2);
558 mulsd(xmm0, xmm2);
559 addsd(xmm0, xmm2);
560 jmp(L_2TAG_PACKET_2_0_2);
561
562 bind(L_2TAG_PACKET_1_0_2);
563 fnstcw(Address(rsp, 24));
564 movzwl(edx, Address(rsp, 24));
565 orl(edx, 768);
566 movw(Address(rsp, 28), edx);
567 fldcw(Address(rsp, 28));
568 movl(edx, eax);
569 sarl(eax, 1);
570 subl(edx, eax);
571 movdqu(xmm6, Address(tmp, 0)); // 0x00000000UL, 0xfff00000UL, 0x00000000UL, 0xfff00000UL
572 pandn(xmm6, xmm2);
573 addl(eax, 1023);
574 movdl(xmm3, eax);
575 psllq(xmm3, 52);
576 por(xmm6, xmm3);
577 addl(edx, 1023);
578 movdl(xmm4, edx);
579 psllq(xmm4, 52);
580 movsd(Address(rsp, 8), xmm0);
581 fld_d(Address(rsp, 8));
582 movsd(Address(rsp, 16), xmm6);
583 fld_d(Address(rsp, 16));
584 fmula(1);
585 faddp(1);
586 movsd(Address(rsp, 8), xmm4);
587 fld_d(Address(rsp, 8));
588 fmulp(1);
589 fstp_d(Address(rsp, 8));
590 movsd(xmm0,Address(rsp, 8));
591 fldcw(Address(rsp, 24));
592 pextrw(ecx, xmm0, 3);
593 andl(ecx, 32752);
594 cmpl(ecx, 32752);
595 jcc(Assembler::greaterEqual, L_2TAG_PACKET_3_0_2);
596 cmpl(ecx, 0);
597 jcc(Assembler::equal, L_2TAG_PACKET_4_0_2);
598 jmp(L_2TAG_PACKET_2_0_2);
599 cmpl(ecx, INT_MIN);
600 jcc(Assembler::less, L_2TAG_PACKET_3_0_2);
601 cmpl(ecx, -1064950997);
602 jcc(Assembler::less, L_2TAG_PACKET_2_0_2);
603 jcc(Assembler::greater, L_2TAG_PACKET_4_0_2);
604 movl(edx, Address(rsp, 128));
605 cmpl(edx ,-17155601);
606 jcc(Assembler::less, L_2TAG_PACKET_2_0_2);
607 jmp(L_2TAG_PACKET_4_0_2);
608
609 bind(L_2TAG_PACKET_3_0_2);
610 movl(edx, 14);
611 jmp(L_2TAG_PACKET_5_0_2);
612
613 bind(L_2TAG_PACKET_4_0_2);
614 movl(edx, 15);
615
616 bind(L_2TAG_PACKET_5_0_2);
617 movsd(Address(rsp, 0), xmm0);
618 movsd(xmm0, Address(rsp, 128));
619 fld_d(Address(rsp, 0));
620 jmp(L_2TAG_PACKET_6_0_2);
621
622 bind(L_2TAG_PACKET_7_0_2);
623 cmpl(eax, 2146435072);
624 jcc(Assembler::greaterEqual, L_2TAG_PACKET_8_0_2);
625 movl(eax, Address(rsp, 132));
626 cmpl(eax, INT_MIN);
627 jcc(Assembler::greaterEqual, L_2TAG_PACKET_9_0_2);
628 movsd(xmm0, Address(tmp, 1208)); // 0xffffffffUL, 0x7fefffffUL
629 mulsd(xmm0, xmm0);
630 movl(edx, 14);
631 jmp(L_2TAG_PACKET_5_0_2);
632
633 bind(L_2TAG_PACKET_9_0_2);
634 movsd(xmm0, Address(tmp, 1216));
635 mulsd(xmm0, xmm0);
636 movl(edx, 15);
637 jmp(L_2TAG_PACKET_5_0_2);
638
639 bind(L_2TAG_PACKET_8_0_2);
640 movl(edx, Address(rsp, 128));
641 cmpl(eax, 2146435072);
642 jcc(Assembler::above, L_2TAG_PACKET_10_0_2);
643 cmpl(edx, 0);
644 jcc(Assembler::notEqual, L_2TAG_PACKET_10_0_2);
645 movl(eax, Address(rsp, 132));
646 cmpl(eax, 2146435072);
647 jcc(Assembler::notEqual, L_2TAG_PACKET_11_0_2);
648 movsd(xmm0, Address(tmp, 1192)); // 0x00000000UL, 0x7ff00000UL
649 jmp(L_2TAG_PACKET_2_0_2);
650
651 bind(L_2TAG_PACKET_11_0_2);
652 movsd(xmm0, Address(tmp, 1200)); // 0x00000000UL, 0x00000000UL
653 jmp(L_2TAG_PACKET_2_0_2);
654
655 bind(L_2TAG_PACKET_10_0_2);
656 movsd(xmm0, Address(rsp, 128));
657 addsd(xmm0, xmm0);
658 jmp(L_2TAG_PACKET_2_0_2);
659
660 bind(L_2TAG_PACKET_0_0_2);
661 movl(eax, Address(rsp, 132));
662 andl(eax, 2147483647);
663 cmpl(eax, 1083179008);
664 jcc(Assembler::aboveEqual, L_2TAG_PACKET_7_0_2);
665 movsd(xmm0, Address(rsp, 128));
666 addsd(xmm0, Address(tmp, 1184)); // 0x00000000UL, 0x3ff00000UL
667 jmp(L_2TAG_PACKET_2_0_2);
668
669 bind(L_2TAG_PACKET_2_0_2);
670 movsd(Address(rsp, 48), xmm0);
671 fld_d(Address(rsp, 48));
672
673 bind(L_2TAG_PACKET_6_0_2);
674 movl(tmp, Address(rsp, 64));
675 }
676
677 #endif