1 /* 2 Copyright (c) 2014, Intel Corporation 3 All rights reserved. 4 5 Redistribution and use in source and binary forms, with or without 6 modification, are permitted provided that the following conditions are met: 7 8 * Redistributions of source code must retain the above copyright notice, 9 * this list of conditions and the following disclaimer. 10 11 * Redistributions in binary form must reproduce the above copyright notice, 12 * this list of conditions and the following disclaimer in the documentation 13 * and/or other materials provided with the distribution. 14 15 * Neither the name of Intel Corporation nor the names of its contributors 16 * may be used to endorse or promote products derived from this software 17 * without specific prior written permission. 18 19 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 20 ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 21 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 22 DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR 23 ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 24 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 25 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON 26 ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 27 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 28 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 29 */ 30 31 /******************************************************************************/ 32 // ALGORITHM DESCRIPTION 33 // --------------------- 34 // 35 // Description: 36 // Let K = 64 (table size). 37 // x x/log(2) n 38 // e = 2 = 2 * T[j] * (1 + P(y)) 39 // where 40 // x = m*log(2)/K + y, y in [-log(2)/K..log(2)/K] 41 // m = n*K + j, m,n,j - signed integer, j in [-K/2..K/2] 42 // j/K 43 // values of 2 are tabulated as T[j] = T_hi[j] ( 1 + T_lo[j]). 44 // 45 // P(y) is a minimax polynomial approximation of exp(x)-1 46 // on small interval [-log(2)/K..log(2)/K] (were calculated by Maple V). 47 // 48 // To avoid problems with arithmetic overflow and underflow, 49 // n n1 n2 50 // value of 2 is safely computed as 2 * 2 where n1 in [-BIAS/2..BIAS/2] 51 // where BIAS is a value of exponent bias. 52 // 53 // Special cases: 54 // exp(NaN) = NaN 55 // exp(+INF) = +INF 56 // exp(-INF) = 0 57 // exp(x) = 1 for subnormals 58 // for finite argument, only exp(0)=1 is exact 59 // For IEEE double 60 // if x > 709.782712893383973096 then exp(x) overflow 61 // if x < -745.133219101941108420 then exp(x) underflow 62 // 63 /******************************************************************************/ 64 65 #include <private/bionic_asm.h> 66 # -- Begin static_func 67 .text 68 .align __bionic_asm_align 69 .type static_func, @function 70 static_func: 71 ..B1.1: 72 call ..L2 73 ..L2: 74 popl %eax 75 lea _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax 76 lea static_const_table@GOTOFF(%eax), %eax 77 ret 78 .size static_func,.-static_func 79 # -- End static_func 80 81 # -- Begin exp 82 ENTRY(exp) 83 # parameter 1: 8 + %ebp 84 ..B2.1: 85 ..B2.2: 86 pushl %ebp 87 movl %esp, %ebp 88 subl $120, %esp 89 movl %ebx, 64(%esp) 90 call static_func 91 movl %eax, %ebx 92 movsd 128(%esp), %xmm0 93 unpcklpd %xmm0, %xmm0 94 movapd 64(%ebx), %xmm1 95 movapd 48(%ebx), %xmm6 96 movapd 80(%ebx), %xmm2 97 movapd 96(%ebx), %xmm3 98 pextrw $3, %xmm0, %eax 99 andl $32767, %eax 100 movl $16527, %edx 101 subl %eax, %edx 102 subl $15504, %eax 103 orl %eax, %edx 104 cmpl $-2147483648, %edx 105 jae .L_2TAG_PACKET_0.0.2 106 mulpd %xmm0, %xmm1 107 addpd %xmm6, %xmm1 108 movapd %xmm1, %xmm7 109 subpd %xmm6, %xmm1 110 mulpd %xmm1, %xmm2 111 movapd 128(%ebx), %xmm4 112 mulpd %xmm1, %xmm3 113 movapd 144(%ebx), %xmm5 114 subpd %xmm2, %xmm0 115 movd %xmm7, %eax 116 movl %eax, %ecx 117 andl $63, %ecx 118 shll $4, %ecx 119 sarl $6, %eax 120 movl %eax, %edx 121 movdqa 16(%ebx), %xmm6 122 pand %xmm6, %xmm7 123 movdqa 32(%ebx), %xmm6 124 paddq %xmm6, %xmm7 125 psllq $46, %xmm7 126 subpd %xmm3, %xmm0 127 movapd 160(%ebx,%ecx), %xmm2 128 mulpd %xmm0, %xmm4 129 movapd %xmm0, %xmm6 130 movapd %xmm0, %xmm1 131 mulpd %xmm6, %xmm6 132 mulpd %xmm6, %xmm0 133 addpd %xmm4, %xmm5 134 mulsd %xmm6, %xmm0 135 mulpd 112(%ebx), %xmm6 136 addsd %xmm2, %xmm1 137 unpckhpd %xmm2, %xmm2 138 mulpd %xmm5, %xmm0 139 addsd %xmm0, %xmm1 140 orpd %xmm7, %xmm2 141 unpckhpd %xmm0, %xmm0 142 addsd %xmm1, %xmm0 143 addsd %xmm6, %xmm0 144 addl $894, %edx 145 cmpl $1916, %edx 146 ja .L_2TAG_PACKET_1.0.2 147 mulsd %xmm2, %xmm0 148 addsd %xmm2, %xmm0 149 jmp .L_2TAG_PACKET_2.0.2 150 .L_2TAG_PACKET_1.0.2: 151 fstcw 24(%esp) 152 movzwl 24(%esp), %edx 153 orl $768, %edx 154 movw %dx, 28(%esp) 155 fldcw 28(%esp) 156 movl %eax, %edx 157 sarl $1, %eax 158 subl %eax, %edx 159 movdqa (%ebx), %xmm6 160 pandn %xmm2, %xmm6 161 addl $1023, %eax 162 movd %eax, %xmm3 163 psllq $52, %xmm3 164 orpd %xmm3, %xmm6 165 addl $1023, %edx 166 movd %edx, %xmm4 167 psllq $52, %xmm4 168 movsd %xmm0, 8(%esp) 169 fldl 8(%esp) 170 movsd %xmm6, 16(%esp) 171 fldl 16(%esp) 172 fmul %st, %st(1) 173 faddp %st, %st(1) 174 movsd %xmm4, 8(%esp) 175 fldl 8(%esp) 176 fmulp %st, %st(1) 177 fstpl 8(%esp) 178 movsd 8(%esp), %xmm0 179 fldcw 24(%esp) 180 pextrw $3, %xmm0, %ecx 181 andl $32752, %ecx 182 cmpl $32752, %ecx 183 jae .L_2TAG_PACKET_3.0.2 184 cmpl $0, %ecx 185 je .L_2TAG_PACKET_4.0.2 186 jmp .L_2TAG_PACKET_2.0.2 187 cmpl $-2147483648, %ecx 188 jb .L_2TAG_PACKET_3.0.2 189 cmpl $-1064950997, %ecx 190 jb .L_2TAG_PACKET_2.0.2 191 ja .L_2TAG_PACKET_4.0.2 192 movl 128(%esp), %edx 193 cmpl $-17155601, %edx 194 jb .L_2TAG_PACKET_2.0.2 195 jmp .L_2TAG_PACKET_4.0.2 196 .L_2TAG_PACKET_3.0.2: 197 movl $14, %edx 198 jmp .L_2TAG_PACKET_5.0.2 199 .L_2TAG_PACKET_4.0.2: 200 movl $15, %edx 201 .L_2TAG_PACKET_5.0.2: 202 movsd %xmm0, (%esp) 203 movsd 128(%esp), %xmm0 204 fldl (%esp) 205 jmp .L_2TAG_PACKET_6.0.2 206 .L_2TAG_PACKET_7.0.2: 207 cmpl $2146435072, %eax 208 jae .L_2TAG_PACKET_8.0.2 209 movl 132(%esp), %eax 210 cmpl $-2147483648, %eax 211 jae .L_2TAG_PACKET_9.0.2 212 movsd 1208(%ebx), %xmm0 213 mulsd %xmm0, %xmm0 214 movl $14, %edx 215 jmp .L_2TAG_PACKET_5.0.2 216 .L_2TAG_PACKET_9.0.2: 217 movsd 1216(%ebx), %xmm0 218 mulsd %xmm0, %xmm0 219 movl $15, %edx 220 jmp .L_2TAG_PACKET_5.0.2 221 .L_2TAG_PACKET_8.0.2: 222 movl 128(%esp), %edx 223 cmpl $2146435072, %eax 224 ja .L_2TAG_PACKET_10.0.2 225 cmpl $0, %edx 226 jne .L_2TAG_PACKET_10.0.2 227 movl 132(%esp), %eax 228 cmpl $2146435072, %eax 229 jne .L_2TAG_PACKET_11.0.2 230 movsd 1192(%ebx), %xmm0 231 jmp .L_2TAG_PACKET_2.0.2 232 .L_2TAG_PACKET_11.0.2: 233 movsd 1200(%ebx), %xmm0 234 jmp .L_2TAG_PACKET_2.0.2 235 .L_2TAG_PACKET_10.0.2: 236 movsd 128(%esp), %xmm0 237 addsd %xmm0, %xmm0 238 jmp .L_2TAG_PACKET_2.0.2 239 .L_2TAG_PACKET_0.0.2: 240 movl 132(%esp), %eax 241 andl $2147483647, %eax 242 cmpl $1083179008, %eax 243 jae .L_2TAG_PACKET_7.0.2 244 movsd 128(%esp), %xmm0 245 addsd 1184(%ebx), %xmm0 246 jmp .L_2TAG_PACKET_2.0.2 247 .L_2TAG_PACKET_2.0.2: 248 movsd %xmm0, 48(%esp) 249 fldl 48(%esp) 250 .L_2TAG_PACKET_6.0.2: 251 movl 64(%esp), %ebx 252 movl %ebp, %esp 253 popl %ebp 254 ret 255 ..B2.3: 256 END(exp) 257 # -- End exp 258 259 # Start file scope ASM 260 ALIAS_SYMBOL(expl, exp); 261 # End file scope ASM 262 .section .rodata, "a" 263 .align 16 264 .align 16 265 static_const_table: 266 .long 0 267 .long 4293918720 268 .long 0 269 .long 4293918720 270 .long 4294967232 271 .long 0 272 .long 4294967232 273 .long 0 274 .long 65472 275 .long 0 276 .long 65472 277 .long 0 278 .long 0 279 .long 1127743488 280 .long 0 281 .long 1127743488 282 .long 1697350398 283 .long 1079448903 284 .long 1697350398 285 .long 1079448903 286 .long 4277796864 287 .long 1065758274 288 .long 4277796864 289 .long 1065758274 290 .long 3164486458 291 .long 1025308570 292 .long 3164486458 293 .long 1025308570 294 .long 4294967294 295 .long 1071644671 296 .long 4294967294 297 .long 1071644671 298 .long 3811088480 299 .long 1062650204 300 .long 1432067621 301 .long 1067799893 302 .long 3230715663 303 .long 1065423125 304 .long 1431604129 305 .long 1069897045 306 .long 0 307 .long 0 308 .long 0 309 .long 0 310 .long 235107661 311 .long 1018002367 312 .long 1048019040 313 .long 11418 314 .long 896005651 315 .long 1015861842 316 .long 3541402996 317 .long 22960 318 .long 1642514529 319 .long 1012987726 320 .long 410360776 321 .long 34629 322 .long 1568897900 323 .long 1016568486 324 .long 1828292879 325 .long 46424 326 .long 1882168529 327 .long 1010744893 328 .long 852742562 329 .long 58348 330 .long 509852888 331 .long 1017336174 332 .long 3490863952 333 .long 70401 334 .long 653277307 335 .long 1017431380 336 .long 2930322911 337 .long 82586 338 .long 1649557430 339 .long 1017729363 340 .long 1014845818 341 .long 94904 342 .long 1058231231 343 .long 1015777676 344 .long 3949972341 345 .long 107355 346 .long 1044000607 347 .long 1016786167 348 .long 828946858 349 .long 119943 350 .long 1151779725 351 .long 1015705409 352 .long 2288159958 353 .long 132667 354 .long 3819481236 355 .long 1016499965 356 .long 1853186616 357 .long 145530 358 .long 2552227826 359 .long 1015039787 360 .long 1709341917 361 .long 158533 362 .long 1829350193 363 .long 1015216097 364 .long 4112506593 365 .long 171677 366 .long 1913391795 367 .long 1015756674 368 .long 2799960843 369 .long 184965 370 .long 1303423926 371 .long 1015238005 372 .long 171030293 373 .long 198398 374 .long 1574172746 375 .long 1016061241 376 .long 2992903935 377 .long 211976 378 .long 3424156969 379 .long 1017196428 380 .long 926591434 381 .long 225703 382 .long 1938513547 383 .long 1017631273 384 .long 887463926 385 .long 239579 386 .long 2804567149 387 .long 1015390024 388 .long 1276261410 389 .long 253606 390 .long 631083525 391 .long 1017690182 392 .long 569847337 393 .long 267786 394 .long 1623370770 395 .long 1011049453 396 .long 1617004845 397 .long 282120 398 .long 3667985273 399 .long 1013894369 400 .long 3049340112 401 .long 296610 402 .long 3145379760 403 .long 1014403278 404 .long 3577096743 405 .long 311258 406 .long 2603100681 407 .long 1017152460 408 .long 1990012070 409 .long 326066 410 .long 3249202951 411 .long 1017448880 412 .long 1453150081 413 .long 341035 414 .long 419288974 415 .long 1016280325 416 .long 917841882 417 .long 356167 418 .long 3793507337 419 .long 1016095713 420 .long 3712504873 421 .long 371463 422 .long 728023093 423 .long 1016345318 424 .long 363667784 425 .long 386927 426 .long 2582678538 427 .long 1017123460 428 .long 2956612996 429 .long 402558 430 .long 7592966 431 .long 1016721543 432 .long 2186617380 433 .long 418360 434 .long 228611441 435 .long 1016696141 436 .long 1719614412 437 .long 434334 438 .long 2261665670 439 .long 1017457593 440 .long 1013258798 441 .long 450482 442 .long 544148907 443 .long 1017323666 444 .long 3907805043 445 .long 466805 446 .long 2383914918 447 .long 1017143586 448 .long 1447192520 449 .long 483307 450 .long 1176412038 451 .long 1017267372 452 .long 1944781190 453 .long 499988 454 .long 2882956373 455 .long 1013312481 456 .long 919555682 457 .long 516851 458 .long 3154077648 459 .long 1016528543 460 .long 2571947538 461 .long 533897 462 .long 348651999 463 .long 1016405780 464 .long 2604962540 465 .long 551129 466 .long 3253791412 467 .long 1015920431 468 .long 1110089947 469 .long 568549 470 .long 1509121860 471 .long 1014756995 472 .long 2568320822 473 .long 586158 474 .long 2617649212 475 .long 1017340090 476 .long 2966275556 477 .long 603959 478 .long 553214634 479 .long 1016457425 480 .long 2682146383 481 .long 621954 482 .long 730975783 483 .long 1014083580 484 .long 2191782032 485 .long 640145 486 .long 1486499517 487 .long 1016818996 488 .long 2069751140 489 .long 658534 490 .long 2595788928 491 .long 1016407932 492 .long 2990417244 493 .long 677123 494 .long 1853053619 495 .long 1015310724 496 .long 1434058175 497 .long 695915 498 .long 2462790535 499 .long 1015814775 500 .long 2572866477 501 .long 714911 502 .long 3693944214 503 .long 1017259110 504 .long 3092190714 505 .long 734114 506 .long 2979333550 507 .long 1017188654 508 .long 4076559942 509 .long 753526 510 .long 174054861 511 .long 1014300631 512 .long 2420883922 513 .long 773150 514 .long 816778419 515 .long 1014197934 516 .long 3716502172 517 .long 792987 518 .long 3507050924 519 .long 1015341199 520 .long 777507147 521 .long 813041 522 .long 1821514088 523 .long 1013410604 524 .long 3706687593 525 .long 833312 526 .long 920623539 527 .long 1016295433 528 .long 1242007931 529 .long 853805 530 .long 2789017511 531 .long 1014276997 532 .long 3707479175 533 .long 874520 534 .long 3586233004 535 .long 1015962192 536 .long 64696965 537 .long 895462 538 .long 474650514 539 .long 1016642419 540 .long 863738718 541 .long 916631 542 .long 1614448851 543 .long 1014281732 544 .long 3884662774 545 .long 938030 546 .long 2450082086 547 .long 1016164135 548 .long 2728693977 549 .long 959663 550 .long 1101668360 551 .long 1015989180 552 .long 3999357479 553 .long 981531 554 .long 835814894 555 .long 1015702697 556 .long 1533953344 557 .long 1003638 558 .long 1301400989 559 .long 1014466875 560 .long 2174652632 561 .long 1025985 562 .long 0 563 .long 1072693248 564 .long 0 565 .long 2146435072 566 .long 0 567 .long 0 568 .long 4294967295 569 .long 2146435071 570 .long 0 571 .long 1048576 572 .type static_const_table,@object 573 .size static_const_table,1224 574 .data 575 .section .note.GNU-stack, "" 576 # End 577
