File size: 31,073 Bytes
6e5c708 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 |
"""
Random kit 1.3
Copyright (c) 2003-2005, Jean-Sebastien Roy (js@jeannot.org)
The rk_random and rk_seed functions algorithms and the original design of
the Mersenne Twister RNG:
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The names of its contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Original algorithm for the implementation of rk_interval function from
Richard J. Wagner's implementation of the Mersenne Twister RNG, optimised by
Magnus Jonsson.
Constants used in the rk_double implementation by Isaku Wada.
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
""" # NOQA
from cupy import _core
rk_use_binominal = '''
#define CUPY_USE_BINOMIAL
'''
rk_basic_definition = '''
typedef struct {
unsigned int xor128[4];
double gauss;
int has_gauss; // !=0: gauss contains a gaussian deviate
#ifdef CUPY_USE_BINOMIAL
int has_binomial; // !=0: following parameters initialized for binomial
/* The rk_state structure has been extended to store the following
* information for the binomial generator. If the input values of n or p
* are different than nsave and psave, then the other parameters will be
* recomputed. RTK 2005-09-02 */
int nsave, m;
double psave, r, q, fm, p1, xm, xl, xr, c, laml, lamr, p2, p3, p4;
#endif
} rk_state;
__device__ void rk_seed(unsigned long long s, rk_state *state) {
for (int i = 1; i <= 4; i++) {
s = 1812433253U * (s ^ (s >> 30)) + i;
state->xor128[i - 1] = s;
}
state->has_gauss = 0;
#ifdef CUPY_USE_BINOMIAL
state->has_binomial = 0;
#endif
}
__device__ unsigned long rk_random(rk_state *state) {
unsigned int *xor128 = state->xor128;
unsigned int t = xor128[0] ^ (xor128[0] << 11);
xor128[0] = xor128[1];
xor128[1] = xor128[2];
xor128[2] = xor128[3];
return xor128[3] ^= (xor128[3] >> 19) ^ t ^ (t >> 8);
}
__device__ double rk_double(rk_state *state) {
/* shifts : 67108864 = 0x4000000, 9007199254740992 = 0x20000000000000 */
int a = rk_random(state) >> 5, b = rk_random(state) >> 6;
return (a * 67108864.0 + b) / 9007199254740992.0;
}
'''
# The kernels for distributions are based on
# numpy/random/mtrand/distributions.c
# with the following licenses:
"""
/* Copyright 2005 Robert Kern (robert.kern@gmail.com)
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
/* The implementations of rk_hypergeometric_hyp(), rk_hypergeometric_hrua(),
* and rk_triangular() were adapted from Ivan Frohne's rv.py which has this
* license:
*
* Copyright 1998 by Ivan Frohne; Wasilla, Alaska, U.S.A.
* All Rights Reserved
*
* Permission to use, copy, modify and distribute this software and its
* documentation for any purpose, free of charge, is granted subject to the
* following conditions:
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the software.
*
* THE SOFTWARE AND DOCUMENTATION IS PROVIDED WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHOR
* OR COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM OR DAMAGES IN A CONTRACT
* ACTION, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR ITS DOCUMENTATION.
*/
""" # NOQA
loggam_definition = '''
/*
* log-gamma function to support some of these distributions. The
* algorithm comes from SPECFUN by Shanjie Zhang and Jianming Jin and their
* book "Computation of Special Functions", 1996, John Wiley & Sons, Inc.
*/
static __device__ double loggam(double x) {
double x0, x2, xp, gl, gl0;
long k, n;
double a[10] = {8.333333333333333e-02,-2.777777777777778e-03,
7.936507936507937e-04,-5.952380952380952e-04,
8.417508417508418e-04,-1.917526917526918e-03,
6.410256410256410e-03,-2.955065359477124e-02,
1.796443723688307e-01,-1.39243221690590e+00};
x0 = x;
n = 0;
if ((x == 1.0) || (x == 2.0)) {
return 0.0;
} else if (x <= 7.0) {
n = (long)(7 - x);
x0 = x + n;
}
x2 = 1.0/(x0*x0);
xp = 2*M_PI;
gl0 = a[9];
for (k=8; k>=0; k--) {
gl0 *= x2;
gl0 += a[k];
}
gl = gl0/x0 + 0.5*log(xp) + (x0-0.5)*log(x0) - x0;
if (x <= 7.0) {
for (k=1; k<=n; k++) {
gl -= log(x0-1.0);
x0 -= 1.0;
}
}
return gl;
}
'''
rk_standard_exponential_definition = '''
__device__ double rk_standard_exponential(rk_state *state) {
/* We use -log(1-U) since U is [0, 1) */
return -log(1.0 - rk_double(state));
}
'''
rk_standard_gamma_definition = '''
__device__ double rk_standard_gamma(rk_state *state, double shape) {
double b, c;
double U, V, X, Y;
if (shape == 1.0) {
return rk_standard_exponential(state);
} else if (shape < 1.0) {
for (;;) {
U = rk_double(state);
V = rk_standard_exponential(state);
if (U <= 1.0 - shape) {
X = pow(U, 1./shape);
if (X <= V) {
return X;
}
} else {
Y = -log((1-U)/shape);
X = pow(1.0 - shape + shape*Y, 1./shape);
if (X <= (V + Y)) {
return X;
}
}
}
} else {
b = shape - 1./3.;
c = 1./sqrt(9*b);
for (;;) {
do {
X = rk_gauss(state);
V = 1.0 + c*X;
} while (V <= 0.0);
V = V*V*V;
U = rk_double(state);
if (U < 1.0 - 0.0331*(X*X)*(X*X)) return (b*V);
if (log(U) < 0.5*X*X + b*(1. - V + log(V))) return (b*V);
}
}
}
'''
rk_beta_definition = '''
__device__ double rk_beta(rk_state *state, double a, double b) {
double Ga, Gb;
if ((a <= 1.0) && (b <= 1.0)) {
double U, V, X, Y;
/* Use Johnk's algorithm */
while (1) {
U = rk_double(state);
V = rk_double(state);
X = pow(U, 1.0/a);
Y = pow(V, 1.0/b);
if ((X + Y) <= 1.0) {
if (X +Y > 0) {
return X / (X + Y);
} else {
double logX = log(U) / a;
double logY = log(V) / b;
double logM = logX > logY ? logX : logY;
logX -= logM;
logY -= logM;
return exp(logX - log(exp(logX) + exp(logY)));
}
}
}
} else {
Ga = rk_standard_gamma(state, a);
Gb = rk_standard_gamma(state, b);
return Ga/(Ga + Gb);
}
}
'''
rk_chisquare_definition = '''
__device__ double rk_chisquare(rk_state *state, double df) {
return 2.0*rk_standard_gamma(state, df/2.0);
}
'''
rk_noncentral_chisquare_definition = '''
__device__ double rk_noncentral_chisquare(
rk_state *state, double df, double nonc)
{
if (nonc == 0){
return rk_chisquare(state, df);
}
if(1 < df)
{
const double Chi2 = rk_chisquare(state, df - 1);
const double N = rk_gauss(state) + sqrt(nonc);
return Chi2 + N*N;
}
else
{
const long i = rk_poisson(state, nonc / 2.0);
return rk_chisquare(state, df + 2 * i);
}
}
'''
rk_f_definition = '''
__device__ double rk_f(rk_state *state, double dfnum, double dfden) {
return ((rk_chisquare(state, dfnum) * dfden) /
(rk_chisquare(state, dfden) * dfnum));
}
'''
rk_noncentral_f_definition = '''
__device__ double rk_noncentral_f(
rk_state *state, double dfnum, double dfden, double nonc)
{
double t = rk_noncentral_chisquare(state, dfnum, nonc) * dfden;
return t / (rk_chisquare(state, dfden) * dfnum);
}
'''
rk_binomial_definition = '''
__device__ long rk_binomial_btpe(rk_state *state, long n, double p) {
double r,q,fm,p1,xm,xl,xr,c,laml,lamr,p2,p3,p4;
double a,u,v,s,F,rho,t,A,nrq,x1,x2,f1,f2,z,z2,w,w2,x;
int m,y,k,i;
if (!(state->has_binomial) ||
(state->nsave != n) ||
(state->psave != p)) {
/* initialize */
state->nsave = n;
state->psave = p;
state->has_binomial = 1;
state->r = r = min(p, 1.0-p);
state->q = q = 1.0 - r;
state->fm = fm = n*r+r;
state->m = m = (long)floor(state->fm);
state->p1 = p1 = floor(2.195*sqrt(n*r*q)-4.6*q) + 0.5;
state->xm = xm = m + 0.5;
state->xl = xl = xm - p1;
state->xr = xr = xm + p1;
state->c = c = 0.134 + 20.5/(15.3 + m);
a = (fm - xl)/(fm-xl*r);
state->laml = laml = a*(1.0 + a/2.0);
a = (xr - fm)/(xr*q);
state->lamr = lamr = a*(1.0 + a/2.0);
state->p2 = p2 = p1*(1.0 + 2.0*c);
state->p3 = p3 = p2 + c/laml;
state->p4 = p4 = p3 + c/lamr;
} else {
r = state->r;
q = state->q;
fm = state->fm;
m = state->m;
p1 = state->p1;
xm = state->xm;
xl = state->xl;
xr = state->xr;
c = state->c;
laml = state->laml;
lamr = state->lamr;
p2 = state->p2;
p3 = state->p3;
p4 = state->p4;
}
/* sigh ... */
Step10:
nrq = n*r*q;
u = rk_double(state)*p4;
v = rk_double(state);
if (u > p1) goto Step20;
y = (long)floor(xm - p1*v + u);
goto Step60;
Step20:
if (u > p2) goto Step30;
x = xl + (u - p1)/c;
v = v*c + 1.0 - fabs(m - x + 0.5)/p1;
if (v > 1.0) goto Step10;
y = (long)floor(x);
goto Step50;
Step30:
if (u > p3) goto Step40;
y = (long)floor(xl + log(v)/laml);
if (y < 0) goto Step10;
v = v*(u-p2)*laml;
goto Step50;
Step40:
y = (long)floor(xr - log(v)/lamr);
if (y > n) goto Step10;
v = v*(u-p3)*lamr;
Step50:
k = labs(y - m);
if ((k > 20) && (k < ((nrq)/2.0 - 1))) goto Step52;
s = r/q;
a = s*(n+1);
F = 1.0;
if (m < y) {
for (i=m+1; i<=y; i++) {
F *= (a/i - s);
}
} else if (m > y) {
for (i=y+1; i<=m; i++) {
F /= (a/i - s);
}
}
if (v > F) goto Step10;
goto Step60;
Step52:
rho = (k/(nrq))*((k*(k/3.0 + 0.625) + 0.16666666666666666)/nrq + 0.5);
t = -k*k/(2*nrq);
A = log(v);
if (A < (t - rho)) goto Step60;
if (A > (t + rho)) goto Step10;
x1 = y+1;
f1 = m+1;
z = n+1-m;
w = n-y+1;
x2 = x1*x1;
f2 = f1*f1;
z2 = z*z;
w2 = w*w;
if (A > (xm*log(f1/x1)
+ (n-m+0.5)*log(z/w)
+ (y-m)*log(w*r/(x1*q))
+ (13680.-(462.-(132.-(99.-140./f2)/f2)/f2)/f2)/f1/166320.
+ (13680.-(462.-(132.-(99.-140./z2)/z2)/z2)/z2)/z/166320.
+ (13680.-(462.-(132.-(99.-140./x2)/x2)/x2)/x2)/x1/166320.
+ (13680.-(462.-(132.-(99.-140./w2)/w2)/w2)/w2)/w/166320.)) {
goto Step10;
}
Step60:
if (p > 0.5) {
y = n - y;
}
return y;
}
__device__ long rk_binomial_inversion(rk_state *state, int n, double p) {
double q, qn, np, px, U;
int X, bound;
if (!(state->has_binomial) ||
(state->nsave != n) ||
(state->psave != p)) {
state->nsave = n;
state->psave = p;
state->has_binomial = 1;
state->q = q = 1.0 - p;
state->r = qn = exp(n * log(q));
state->c = np = n*p;
state->m = bound = min((double)n, np + 10.0*sqrt(np*q + 1));
} else {
q = state->q;
qn = state->r;
np = state->c;
bound = state->m;
}
X = 0;
px = qn;
U = rk_double(state);
while (U > px) {
X++;
if (X > bound) {
X = 0;
px = qn;
U = rk_double(state);
} else {
U -= px;
px = ((n-X+1) * p * px)/(X*q);
}
}
return X;
}
__device__ long rk_binomial(rk_state *state, int n, double p) {
double q;
if (p <= 0.5) {
if (p*n <= 30.0) {
return rk_binomial_inversion(state, n, p);
} else {
return rk_binomial_btpe(state, n, p);
}
} else {
q = 1.0-p;
if (q*n <= 30.0) {
return n - rk_binomial_inversion(state, n, q);
} else {
return n - rk_binomial_btpe(state, n, q);
}
}
}
'''
rk_poisson_mult_definition = '''
__device__ long rk_poisson_mult(rk_state *state, double lam) {
long X;
double prod, U, enlam;
enlam = exp(-lam);
X = 0;
prod = 1.0;
while (1) {
U = rk_double(state);
prod *= U;
if (prod > enlam) {
X += 1;
} else {
return X;
}
}
}
'''
rk_poisson_ptrs_definition = '''
/*
* The transformed rejection method for generating Poisson random variables
* W. Hoermann
* Insurance: Mathematics and Economics 12, 39-45 (1993)
*/
#define LS2PI 0.91893853320467267
#define TWELFTH 0.083333333333333333333333
__device__ long rk_poisson_ptrs(rk_state *state, double lam) {
long k;
double U, V, slam, loglam, a, b, invalpha, vr, us;
slam = sqrt(lam);
loglam = log(lam);
b = 0.931 + 2.53*slam;
a = -0.059 + 0.02483*b;
invalpha = 1.1239 + 1.1328/(b-3.4);
vr = 0.9277 - 3.6224/(b-2);
while (1) {
U = rk_double(state) - 0.5;
V = rk_double(state);
us = 0.5 - fabs(U);
k = (long)floor((2*a/us + b)*U + lam + 0.43);
if ((us >= 0.07) && (V <= vr)) {
return k;
}
if ((k < 0) ||
((us < 0.013) && (V > us))) {
continue;
}
if ((log(V) + log(invalpha) - log(a/(us*us)+b)) <=
(-lam + k*loglam - loggam(k+1))) {
return k;
}
}
}
'''
rk_poisson_definition = '''
__device__ long rk_poisson(rk_state *state, double lam) {
if (lam >= 10) {
return rk_poisson_ptrs(state, lam);
} else if (lam == 0) {
return 0;
} else {
return rk_poisson_mult(state, lam);
}
}
'''
rk_standard_t_definition = '''
__device__ double rk_standard_t(rk_state *state, double df) {
return sqrt(df/2)*rk_gauss(state)/sqrt(rk_standard_gamma(state, df/2));
}
'''
rk_vonmises_definition = '''
__device__ double rk_vonmises(rk_state *state, double mu, double kappa)
{
double s;
double U, V, W, Y, Z;
double result, mod;
int neg;
if (kappa < 1e-8)
{
return M_PI * (2*rk_double(state)-1);
}
else
{
/* with double precision rho is zero until 1.4e-8 */
if (kappa < 1e-5) {
/*
* second order taylor expansion around kappa = 0
* precise until relatively large kappas as second order is 0
*/
s = (1./kappa + kappa);
}
else {
double r = 1 + sqrt(1 + 4*kappa*kappa);
double rho = (r - sqrt(2*r)) / (2*kappa);
s = (1 + rho*rho)/(2*rho);
}
while (1)
{
U = rk_double(state);
Z = cos(M_PI*U);
W = (1 + s*Z)/(s + Z);
Y = kappa * (s - W);
V = rk_double(state);
if ((Y*(2-Y) - V >= 0) || (log(Y/V)+1 - Y >= 0))
{
break;
}
}
U = rk_double(state);
result = acos(W);
if (U < 0.5)
{
result = -result;
}
result += mu;
neg = (result < 0);
mod = fabs(result);
mod = (fmod(mod+M_PI, 2*M_PI)-M_PI);
if (neg)
{
mod *= -1;
}
return mod;
}
}
'''
rk_zipf_definition = '''
__device__ long rk_zipf(rk_state *state, double a)
{
double am1, b;
am1 = a - 1.0;
b = pow(2.0, am1);
while (1) {
double T, U, V, X;
U = 1.0 - rk_double(state);
V = rk_double(state);
X = floor(pow(U, -1.0/am1));
if (X < 1.0) {
continue;
}
T = pow(1.0 + 1.0/X, am1);
if (V*X*(T - 1.0)/(b - 1.0) <= T/b) {
return (long)X;
}
}
}
'''
rk_geometric_definition = '''
__device__ long rk_geometric_search(rk_state *state, double p) {
double U;
long X;
double sum, prod, q;
X = 1;
sum = prod = p;
q = 1.0 - p;
U = rk_double(state);
while (U > sum) {
prod *= q;
sum += prod;
X++;
}
return X;
}
__device__ long rk_geometric_inversion(rk_state *state, double p) {
return (long)ceil(log(1.0-rk_double(state))/log(1.0-p));
}
__device__ long rk_geometric(rk_state *state, double p) {
if (p >= 0.333333333333333333333333) {
return rk_geometric_search(state, p);
} else {
return rk_geometric_inversion(state, p);
}
}
'''
# min and max for the long type are not defined in cuda90 but in cuda75.
long_min_max_definition = '''
__device__ long long_min(long a, long b)
{
return a < b ? a : b;
}
__device__ long long_max(long a, long b)
{
return a > b ? a : b;
}
'''
rk_hypergeometric_definition = '''
__device__ long rk_hypergeometric_hyp(
rk_state *state, long good, long bad, long sample)
{
long d1, K, Z;
double d2, U, Y;
d1 = bad + good - sample;
d2 = (double)long_min(bad, good);
Y = d2;
K = sample;
while (Y > 0.0)
{
U = rk_double(state);
Y -= (long)floor(U + Y/(d1 + K));
K--;
if (K == 0) break;
}
Z = (long)(d2 - Y);
if (good > bad) Z = sample - Z;
return Z;
}
/* D1 = 2*sqrt(2/e) */
/* D2 = 3 - 2*sqrt(3/e) */
#define D1 1.7155277699214135
#define D2 0.8989161620588988
__device__ long rk_hypergeometric_hrua(
rk_state *state, long good, long bad, long sample)
{
long mingoodbad, maxgoodbad, popsize, m, d9;
double d4, d5, d6, d7, d8, d10, d11;
long Z;
double T, W, X, Y;
mingoodbad = long_min(good, bad);
popsize = good + bad;
maxgoodbad = long_max(good, bad);
m = long_min(sample, popsize - sample);
d4 = ((double)mingoodbad) / popsize;
d5 = 1.0 - d4;
d6 = m*d4 + 0.5;
d7 = sqrt((double)(popsize - m) * sample * d4 * d5 / (popsize - 1) + 0.5);
d8 = D1*d7 + D2;
d9 = (long)floor((double)(m + 1) * (mingoodbad + 1) / (popsize + 2));
d10 = (loggam(d9+1) + loggam(mingoodbad-d9+1) + loggam(m-d9+1) +
loggam(maxgoodbad-m+d9+1));
d11 = min(long_min(m, mingoodbad)+1.0, floor(d6+16*d7));
/* 16 for 16-decimal-digit precision in D1 and D2 */
while (1)
{
X = rk_double(state);
Y = rk_double(state);
W = d6 + d8*(Y- 0.5)/X;
/* fast rejection: */
if ((W < 0.0) || (W >= d11)) continue;
Z = (long)floor(W);
T = d10 - (loggam(Z+1) + loggam(mingoodbad-Z+1) + loggam(m-Z+1) +
loggam(maxgoodbad-m+Z+1));
/* fast acceptance: */
if ((X*(4.0-X)-3.0) <= T) break;
/* fast rejection: */
if (X*(X-T) >= 1) continue;
if (2.0*log(X) <= T) break; /* acceptance */
}
/* this is a correction to HRUA* by Ivan Frohne in rv.py */
if (good > bad) Z = m - Z;
/* another fix from rv.py to allow sample to exceed popsize/2 */
if (m < sample) Z = good - Z;
return Z;
}
#undef D1
#undef D2
__device__ long rk_hypergeometric(
rk_state *state, long good, long bad, long sample)
{
if (sample > 10)
{
return rk_hypergeometric_hrua(state, good, bad, sample);
} else
{
return rk_hypergeometric_hyp(state, good, bad, sample);
}
}
'''
rk_logseries_definition = '''
__device__ long rk_logseries(rk_state *state, double p)
{
double q, r, U, V;
long result;
r = log(1.0 - p);
while (1) {
V = rk_double(state);
if (V >= p) {
return 1;
}
U = rk_double(state);
q = 1.0 - exp(r*U);
if (V <= q*q) {
result = (long)floor(1 + log(V)/log(q));
if (result < 1) {
continue;
}
else {
return result;
}
}
if (V >= q) {
return 1;
}
return 2;
}
}
'''
rk_gauss_definition = '''
__device__ double rk_gauss(rk_state *state) {
if (state->has_gauss) {
const double tmp = state->gauss;
state->gauss = 0;
state->has_gauss = 0;
return tmp;
} else {
double f, x1, x2, r2;
do {
x1 = 2.0*rk_double(state) - 1.0;
x2 = 2.0*rk_double(state) - 1.0;
r2 = x1*x1 + x2*x2;
}
while (r2 >= 1.0 || r2 == 0.0);
/* Box-Muller transform */
f = sqrt(-2.0*log(r2)/r2);
/* Keep for next call */
state->gauss = f*x1;
state->has_gauss = 1;
return f*x2;
}
}
'''
open_uniform_definition = '''
__device__ void open_uniform(rk_state *state, double *U) {
do {
*U = rk_double(state);
} while (*U <= 0.0 || *U >= 1.0);
}
__device__ void open_uniform(rk_state *state, float *U) {
do {
*U = rk_double(state);
} while (*U <= 0.0 || *U >= 1.0);
}
'''
definitions = [
rk_basic_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition,
rk_beta_definition]
beta_kernel = _core.ElementwiseKernel(
'S a, T b, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_beta(&internal_state, a, b);
''',
'cupy_beta_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_use_binominal, rk_basic_definition, rk_binomial_definition]
binomial_kernel = _core.ElementwiseKernel(
'S n, T p, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_binomial(&internal_state, n, p);
''',
'cupy_binomial_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition,
rk_standard_t_definition]
standard_t_kernel = _core.ElementwiseKernel(
'S df, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_standard_t(&internal_state, df);
''',
'cupy_standard_t_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition,
rk_chisquare_definition]
chisquare_kernel = _core.ElementwiseKernel(
'T df, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_chisquare(&internal_state, df);
''',
'cupy_chisquare_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition,
rk_chisquare_definition, rk_f_definition]
f_kernel = _core.ElementwiseKernel(
'S dfnum, T dfden, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_f(&internal_state, dfnum, dfden);
''',
'cupy_f_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, rk_geometric_definition]
geometric_kernel = _core.ElementwiseKernel(
'T p, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_geometric(&internal_state, p);
''',
'cupy_geometric_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, loggam_definition, long_min_max_definition,
rk_hypergeometric_definition]
hypergeometric_kernel = _core.ElementwiseKernel(
'S good, T bad, U sample, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_hypergeometric(&internal_state, good, bad, sample);
''',
'cupy_hypergeometric_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, rk_logseries_definition]
logseries_kernel = _core.ElementwiseKernel(
'T p, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_logseries(&internal_state, p);
''',
'cupy_logseries_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_basic_definition, loggam_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition,
rk_chisquare_definition, rk_poisson_mult_definition,
rk_poisson_ptrs_definition, rk_poisson_definition,
rk_noncentral_chisquare_definition]
noncentral_chisquare_kernel = _core.ElementwiseKernel(
'S df, T nonc, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_noncentral_chisquare(&internal_state, df, nonc);
''',
'cupy_noncentral_chisquare_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_basic_definition, loggam_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition,
rk_chisquare_definition, rk_poisson_mult_definition,
rk_poisson_ptrs_definition, rk_poisson_definition,
rk_noncentral_chisquare_definition, rk_noncentral_f_definition]
noncentral_f_kernel = _core.ElementwiseKernel(
'S dfnum, T dfden, U nonc, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_noncentral_f(&internal_state, dfnum, dfden, nonc);
''',
'cupy_noncentral_f_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = \
[rk_basic_definition, loggam_definition,
rk_poisson_mult_definition, rk_poisson_ptrs_definition,
rk_poisson_definition]
poisson_kernel = _core.ElementwiseKernel(
'T lam, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_poisson(&internal_state, lam);
''',
'cupy_poisson_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_basic_definition, rk_gauss_definition,
rk_standard_exponential_definition, rk_standard_gamma_definition]
standard_gamma_kernel = _core.ElementwiseKernel(
'T shape, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_standard_gamma(&internal_state, shape);
''',
'cupy_standard_gamma_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_basic_definition, rk_vonmises_definition]
vonmises_kernel = _core.ElementwiseKernel(
'S mu, T kappa, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_vonmises(&internal_state, mu, kappa);
''',
'cupy_vonmises_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_basic_definition, rk_zipf_definition]
zipf_kernel = _core.ElementwiseKernel(
'T a, uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
y = rk_zipf(&internal_state, a);
''',
'cupy_zipf_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
definitions = [
rk_basic_definition, open_uniform_definition]
open_uniform_kernel = _core.ElementwiseKernel(
'uint64 seed', 'Y y',
'''
rk_seed(seed + i, &internal_state);
open_uniform(&internal_state, &y);
''',
'cupy_open_uniform_kernel',
preamble=''.join(definitions),
loop_prep='rk_state internal_state;'
)
|