Mercurial > octave-nkf
changeset 5742:2cd0af543e7a
[project @ 2006-04-06 08:15:49 by jwe]
| author | jwe |
|---|---|
| date | Thu, 06 Apr 2006 08:15:49 +0000 |
| parents | 07421c4e0312 |
| children | a527e0f77aa5 |
| files | liboctave/randgamma.c liboctave/randgamma.h liboctave/randmtzig.c liboctave/randmtzig.h liboctave/randpoisson.c liboctave/randpoisson.h |
| diffstat | 6 files changed, 1410 insertions(+), 0 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/randgamma.c Thu Apr 06 08:15:49 2006 +0000 @@ -0,0 +1,126 @@ +/* This code is in the public domain */ + +/* + +double randg(a) +void fill_randg(a,n,x) + +Generate a series of standard gamma distributions. + +See: Marsaglia G and Tsang W (2000), "A simple method for generating +gamma variables", ACM Transactions on Mathematical Software 26(3) 363-372 + +Needs the following defines: +* NAN: value to return for Not-A-Number +* RUNI: uniform generator on (0,1) +* RNOR: normal generator +* REXP: exponential generator, or -log(RUNI) if one isn't available +* INFINITE: function to test whether a value is infinite + +Test using: + mean = a + variance = a + skewness = 2/sqrt(a) + kurtosis = 3 + 6/sqrt(a) + +Note that randg can be used to generate many distributions: + +gamma(a,b) for a>0, b>0 (from R) + r = b*randg(a) +beta(a,b) for a>0, b>0 + r1 = randg(a,1) + r = r1 / (r1 + randg(b,1)) +Erlang(a,n) + r = a*randg(n) +chisq(df) for df>0 + r = 2*randg(df/2) +t(df) for 0<df<inf (use randn if df is infinite) + r = randn() / sqrt(2*randg(df/2)/df) +F(n1,n2) for 0<n1, 0<n2 + r1 = 2*randg(n1/2)/n1 or 1 if n1 is infinite + r2 = 2*randg(n2/2)/n2 or 1 if n2 is infinite + r = r1 / r2 +negative binonial (n, p) for n>0, 0<p<=1 + r = randp((1-p)/p * randg(n)) + (from R, citing Devroye(1986), Non-Uniform Random Variate Generation) +non-central chisq(df,L), for df>=0 and L>0 (use chisq if L=0) + r = randp(L/2) + r(r>0) = 2*randg(r(r>0)) + r(df>0) += 2*randg(df(df>0)/2) + (from R, citing formula 29.5b-c in Johnson, Kotz, Balkrishnan(1995)) +Dirichlet(a1,...,ak) for ai > 0 + r = (randg(a1),...,randg(ak)) + r = r / sum(r) + (from GSL, citing Law & Kelton(1991), Simulation Modeling and Analysis) +*/ + +#if defined (HAVE_CONFIG_H) +#include <config.h> +#endif + +#include <math.h> +#include <stdio.h> + +#include "lo-ieee.h" +#include "randmtzig.h" +#include "randgamma.h" + +#undef NAN +#define NAN octave_NaN +#define INFINITE lo_ieee_isinf +#define RUNI oct_randu() +#define RNOR oct_randn() +#define REXP oct_rande() + +void +oct_fill_randg (double a, octave_idx_type n, double *r) +{ + octave_idx_type i; + /* If a < 1, start by generating gamma(1+a) */ + const double d = (a < 1. ? 1.+a : a) - 1./3.; + const double c = 1./sqrt(9.*d); + + /* Handle invalid cases */ + if (a <= 0 || INFINITE(a)) + { + for (i=0; i < n; i++) + r[i] = NAN; + return; + } + + for (i=0; i < n; i++) + { + double x, xsq, v, u; + restart: + x = RNOR; + v = (1+c*x); + v *= v*v; + if (v <= 0) + goto restart; /* rare, so don't bother moving up */ + u = RUNI; + xsq = x*x; + if (u >= 1.-0.0331*xsq*xsq && log(u) >= 0.5*xsq + d*(1-v+log(v))) + goto restart; + r[i] = d*v; + } + if (a < 1) + { /* Use gamma(a) = gamma(1+a)*U^(1/a) */ + /* Given REXP = -log(U) then U^(1/a) = exp(-REXP/a) */ + for (i = 0; i < n; i++) + r[i] *= exp(-REXP/a); + } +} + +double +oct_randg (double a) +{ + double ret; + oct_fill_randg(a,1,&ret); + return ret; +} + +/* +;;; Local Variables: *** +;;; mode: C *** +;;; End: *** +*/
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/randgamma.h Thu Apr 06 08:15:49 2006 +0000 @@ -0,0 +1,24 @@ +/* This code is in the public domain */ + +#ifndef _RANDGAMMA_H + +#include "oct-types.h" + +#ifdef __cplusplus +extern "C" { +#endif + +extern double oct_randg (double a); +extern void oct_fill_randg (double a, octave_idx_type n, double *p); + +#ifdef __cplusplus +} +#endif +#endif + +/* +;;; Local Variables: *** +;;; mode: C *** +;;; End: *** +*/ +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/randmtzig.c Thu Apr 06 08:15:49 2006 +0000 @@ -0,0 +1,686 @@ +/* + A C-program for MT19937, with initialization improved 2002/2/10. + Coded by Takuji Nishimura and Makoto Matsumoto. + This is a faster version by taking Shawn Cokus's optimization, + Matthe Bellew's simplification, Isaku Wada's real version. + David Bateman added normal and exponential distributions following + Marsaglia and Tang's Ziggurat algorithm. + + Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, + Copyright (C) 2004, David Bateman + 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. + + + Any feedback is very welcome. + http://www.math.keio.ac.jp/matumoto/emt.html + email: matumoto@math.keio.ac.jp + + * 2006-04-01 David Bateman + * * convert for use in octave, declaring static functions only used + * here and adding oct_ to functions visible externally + * * inverse sense of ALLBITS + * 2004-01-19 Paul Kienzle + * * comment out main + * add init_by_entropy, get_state, set_state + * * converted to allow compiling by C++ compiler + * + * 2004-01-25 David Bateman + * * Add Marsaglia and Tsang Ziggurat code + * + * 2004-07-13 Paul Kienzle + * * make into an independent library with some docs. + * * introduce new main and test code. + * + * 2004-07-28 Paul Kienzle & David Bateman + * * add -DALLBITS flag for 32 vs. 53 bits of randomness in mantissa + * * make the naming scheme more uniform + * * add -DHAVE_X86 for faster support of 53 bit mantissa on x86 arch. + * + * 2005-02-23 Paul Kienzle + * * fix -DHAVE_X86_32 flag and add -DUSE_X86_32=0|1 for explicit control + */ + +/* + === Build instructions === + + Compile with -DHAVE_GETTIMEOFDAY if the gettimeofday function is + available. This is not necessary if your architecture has + /dev/urandom defined. + + Compile with -DALLBITS to disable 53-bit random numbers. This is about + 50% slower than using 32-bit random numbers. + + Uses implicit -Di386 or explicit -DHAVE_X86_32 to determine if CPU=x86. + You can force X86 behaviour with -DUSE_X86_32=1, or suppress it with + -DUSE_X86_32=0. You should also consider -march=i686 or similar for + extra performance. Check whether -DUSE_X86_32=0 is faster on 64-bit + x86 architectures. + + If you want to replace the Mersenne Twister with another + generator then redefine randi32 appropriately. + + === Usage instructions === + Before using any of the generators, initialize the state with one of + oct_init_by_int, oct_init_by_array or oct_init_by_entropy. + + All generators share the same state vector. + + === Mersenne Twister === + void oct_init_by_int(uint32_t s) 32-bit initial state + void oct_init_by_array(uint32_t k[],int m) m*32-bit initial state + void oct_init_by_entropy(void) random initial state + void oct_get_state(uint32_t save[MT_N+1]) saves state in array + void oct_set_state(uint32_t save[MT_N+1]) restores state from array + static inline uint32_t randmt(void) returns 32-bit unsigned int + + === inline generators === + static inline uint32_t randi32(void) returns 32-bit unsigned int + static inline uint64_t randi53(void) returns 53-bit unsigned int + static inline uint64_t randi54(void) returns 54-bit unsigned int + static inline uint64_t randi64(void) returns 64-bit unsigned int + static inline double randu32(void) returns 32-bit uniform in (0,1) + static inline double randu53(void) returns 53-bit uniform in (0,1) + + double oct_randu(void) returns M-bit uniform in (0,1) + double oct_randn(void) returns M-bit standard normal + double oct_rande(void) returns N-bit standard exponential + + === Array generators === + void oct_fill_randi32(octave_idx_type, uint32_t []) + void oct_fill_randi64(octave_idx_type, uint64_t []) + void oct_fill_randu(octave_idx_type, double []) + void oct_fill_randn(octave_idx_type, double []) + void oct_fill_rande(octave_idx_type, double []) + +*/ + +#if defined (HAVE_CONFIG_H) +#include <config.h> +#endif + +#include <math.h> +#include <stdio.h> +#include <time.h> + +#ifdef HAVE_GETTIMEOFDAY +#include <sys/time.h> +#endif + +#include "randmtzig.h" + +/* XXX FIXME XXX may want to suppress X86 if sizeof(long)>4 */ +#if !defined(USE_X86_32) +# if defined(i386) || defined(HAVE_X86_32) +# define USE_X86_32 1 +# else +# define USE_X86_32 0 +# endif +#endif + +/* ===== Mersenne Twister 32-bit generator ===== */ + +#define MT_M 397 +#define MATRIX_A 0x9908b0dfUL /* constant vector a */ +#define UMASK 0x80000000UL /* most significant w-r bits */ +#define LMASK 0x7fffffffUL /* least significant r bits */ +#define MIXBITS(u,v) ( ((u) & UMASK) | ((v) & LMASK) ) +#define TWIST(u,v) ((MIXBITS(u,v) >> 1) ^ ((v)&1UL ? MATRIX_A : 0UL)) + +static uint32_t *next; +static uint32_t state[MT_N]; /* the array for the state vector */ +static int left = 1; +static int initf = 0; +static int initt = 1; + +/* initializes state[MT_N] with a seed */ +void +oct_init_by_int (uint32_t s) +{ + int j; + state[0] = s & 0xffffffffUL; + for (j = 1; j < MT_N; j++) { + state[j] = (1812433253UL * (state[j-1] ^ (state[j-1] >> 30)) + j); + /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */ + /* In the previous versions, MSBs of the seed affect */ + /* only MSBs of the array state[]. */ + /* 2002/01/09 modified by Makoto Matsumoto */ + state[j] &= 0xffffffffUL; /* for >32 bit machines */ + } + left = 1; + initf = 1; +} + +/* initialize by an array with array-length */ +/* init_key is the array for initializing keys */ +/* key_length is its length */ +void +oct_init_by_array (uint32_t init_key[], int key_length) +{ + int i, j, k; + oct_init_by_int (19650218UL); + i = 1; + j = 0; + k = (MT_N > key_length ? MT_N : key_length); + for (; k; k--) + { + state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1664525UL)) + + init_key[j] + j; /* non linear */ + state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ + i++; + j++; + if (i >= MT_N) + { + state[0] = state[MT_N-1]; + i = 1; + } + if (j >= key_length) + j = 0; + } + for (k = MT_N - 1; k; k--) + { + state[i] = (state[i] ^ ((state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL)) + - i; /* non linear */ + state[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ + i++; + if (i >= MT_N) + { + state[0] = state[MT_N-1]; + i = 1; + } + } + + state[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ + left = 1; + initf = 1; +} + +void +oct_init_by_entropy (void) +{ + uint32_t entropy[MT_N]; + int n = 0; + + /* Look for entropy in /dev/urandom */ + FILE* urandom =fopen("/dev/urandom", "rb"); + if (urandom) + { + while (n < MT_N) + { + unsigned char word[4]; + if (fread(word, 4, 1, urandom) != 1) + break; + entropy[n++] = word[0]+(word[1]<<8)+(word[2]<<16)+(word[3]<<24); + } + fclose(urandom); + } + + /* If there isn't enough entropy, gather some from various sources */ + if (n < MT_N) + entropy[n++] = time(NULL); /* Current time in seconds */ + if (n < MT_N) + entropy[n++] = clock(); /* CPU time used (usec) */ +#ifdef HAVE_GETTIMEOFDAY + if (n < MT_N) + { + struct timeval tv; + if (gettimeofday(&tv, NULL) != -1) + entropy[n++] = tv.tv_usec; /* Fractional part of current time */ + } +#endif + /* Send all the entropy into the initial state vector */ + oct_init_by_array(entropy,n); +} + +void +oct_set_state (uint32_t save[]) +{ + int i; + for (i=0; i < MT_N; i++) + state[i] = save[i]; + left = save[MT_N]; + next = state + (MT_N - left + 1); +} + +void +oct_get_state (uint32_t save[]) +{ + int i; + for (i = 0; i < MT_N; i++) + save[i] = state[i]; + save[MT_N] = left; +} + +static void +next_state (void) +{ + uint32_t *p = state; + int j; + + /* if init_by_int() has not been called, */ + /* a default initial seed is used */ + /* if (initf==0) init_by_int(5489UL); */ + /* Or better yet, a random seed! */ + if (initf == 0) + oct_init_by_entropy(); + + left = MT_N; + next = state; + + for (j = MT_N - MT_M + 1; --j; p++) + *p = p[MT_M] ^ TWIST(p[0], p[1]); + + for (j = MT_M; --j; p++) + *p = p[MT_M-MT_N] ^ TWIST(p[0], p[1]); + + *p = p[MT_M-MT_N] ^ TWIST(p[0], state[0]); +} + +/* generates a random number on [0,0xffffffff]-interval */ +static inline uint32_t +randmt (void) +{ + register uint32_t y; + + if (--left == 0) + next_state(); + y = *next++; + + /* Tempering */ + y ^= (y >> 11); + y ^= (y << 7) & 0x9d2c5680UL; + y ^= (y << 15) & 0xefc60000UL; + return (y ^ (y >> 18)); +} + +/* ===== Uniform generators ===== */ + +/* Select which 32 bit generator to use */ +#define randi32 randmt + +static inline uint64_t +randi53 (void) +{ + const uint32_t lo = randi32(); + const uint32_t hi = randi32()&0x1FFFFF; +#if HAVE_X86_32 + uint64_t u; + uint32_t *p = (uint32_t *)&u; + p[0] = lo; + p[1] = hi; + return u; +#else + return (((uint64_t)hi<<32)|lo); +#endif +} + +static inline uint64_t +randi54 (void) +{ + const uint32_t lo = randi32(); + const uint32_t hi = randi32()&0x3FFFFF; +#if HAVE_X86_32 + uint64_t u; + uint32_t *p = (uint32_t *)&u; + p[0] = lo; + p[1] = hi; + return u; +#else + return (((uint64_t)hi<<32)|lo); +#endif +} + +static inline uint64_t +randi64 (void) +{ + const uint32_t lo = randi32(); + const uint32_t hi = randi32(); +#if HAVE_X86_32 + uint64_t u; + uint32_t *p = (uint32_t *)&u; + p[0] = lo; + p[1] = hi; + return u; +#else + return (((uint64_t)hi<<32)|lo); +#endif +} + +/* generates a random number on (0,1)-real-interval */ +static inline double +randu32 (void) +{ + return ((double)randi32() + 0.5) * (1.0/4294967296.0); + /* divided by 2^32 */ +} + +/* generates a random number on (0,1) with 53-bit resolution */ +static inline double +randu53 (void) +{ + const uint32_t a=randi32()>>5; + const uint32_t b=randi32()>>6; + return(a*67108864.0+b+0.4) * (1.0/9007199254740992.0); +} + +/* Determine mantissa for uniform doubles */ +#ifdef ALLBITS +double +oct_randu (void) +{ + return randu32(); +} +#else +double +oct_randu (void) +{ + return randu53(); +} +#endif + +/* ===== Ziggurat normal and exponential generators ===== */ +#ifdef ALLBITS +# define ZIGINT uint32_t +# define EMANTISSA 4294967296.0 /* 32 bit mantissa */ +# define ERANDI randi32() /* 32 bits for mantissa */ +# define NMANTISSA 2147483648.0 /* 31 bit mantissa */ +# define NRANDI randi32() /* 31 bits for mantissa + 1 bit sign */ +# define RANDU randu32() +#else +# define ZIGINT uint64_t +# define EMANTISSA 9007199254740992.0 /* 53 bit mantissa */ +# define ERANDI randi53() /* 53 bits for mantissa */ +# define NMANTISSA EMANTISSA +# define NRANDI randi54() /* 53 bits for mantissa + 1 bit sign */ +# define RANDU randu53() +#endif + +#define ZIGGURAT_TABLE_SIZE 256 + +#define ZIGGURAT_NOR_R 3.6541528853610088 +#define ZIGGURAT_NOR_INV_R 0.27366123732975828 +#define NOR_SECTION_AREA 0.00492867323399 + +#define ZIGGURAT_EXP_R 7.69711747013104972 +#define ZIGGURAT_EXP_INV_R 0.129918765548341586 +#define EXP_SECTION_AREA 0.0039496598225815571993 + +static ZIGINT ki[ZIGGURAT_TABLE_SIZE]; +static double wi[ZIGGURAT_TABLE_SIZE], fi[ZIGGURAT_TABLE_SIZE]; +static ZIGINT ke[ZIGGURAT_TABLE_SIZE]; +static double we[ZIGGURAT_TABLE_SIZE], fe[ZIGGURAT_TABLE_SIZE]; + +/* +This code is based on the paper Marsaglia and Tsang, "The ziggurat method +for generating random variables", Journ. Statistical Software. Code was +presented in this paper for a Ziggurat of 127 levels and using a 32 bit +integer random number generator. This version of the code, uses the +Mersenne Twister as the integer generator and uses 256 levels in the +Ziggurat. This has several advantages. + + 1) As Marsaglia and Tsang themselves states, the more levels the few + times the expensive tail algorithm must be called + 2) The cycle time of the generator is determined by the integer + generator, thus the use of a Mersenne Twister for the core random + generator makes this cycle extremely long. + 3) The license on the original code was unclear, thus rewriting the code + from the article means we are free of copyright issues. + 4) Compile flag for full 53-bit random mantissa. + +It should be stated that the authors made my life easier, by the fact that +the algorithm developed in the text of the article is for a 256 level +ziggurat, even if the code itself isn't... + +One modification to the algorithm developed in the article, is that it is +assumed that 0 <= x < Inf, and "unsigned long"s are used, thus resulting in +terms like 2^32 in the code. As the normal distribution is defined between +-Inf < x < Inf, we effectively only have 31 bit integers plus a sign. Thus +in Marsaglia and Tsang, terms like 2^32 become 2^31. We use NMANTISSA for +this term. The exponential distribution is one sided so we use the +full 32 bits. We use EMANTISSA for this term. + +It appears that I'm slightly slower than the code in the article, this +is partially due to a better generator of random integers than they +use. But might also be that the case of rapid return was optimized by +inlining the relevant code with a #define. As the basic Mersenne +Twister is only 25% faster than this code I suspect that the main +reason is just the use of the Mersenne Twister and not the inlining, +so I'm not going to try and optimize further. +*/ + +static void +create_ziggurat_tables (void) +{ + int i; + double x, x1; + + /* Ziggurat tables for the normal distribution */ + x1 = ZIGGURAT_NOR_R; + wi[255] = x1 / NMANTISSA; + fi[255] = exp (-0.5 * x1 * x1); + + /* Index zero is special for tail strip, where Marsaglia and Tsang + * defines this as + * k_0 = 2^31 * r * f(r) / v, w_0 = 0.5^31 * v / f(r), f_0 = 1, + * where v is the area of each strip of the ziggurat. + */ + ki[0] = (ZIGINT) (x1 * fi[255] / NOR_SECTION_AREA * NMANTISSA); + wi[0] = NOR_SECTION_AREA / fi[255] / NMANTISSA; + fi[0] = 1.; + + for (i = 254; i > 0; i--) + { + /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus + * need inverse operator of y = exp(-0.5*x*x) -> x = sqrt(-2*ln(y)) + */ + x = sqrt(-2. * log(NOR_SECTION_AREA / x1 + fi[i+1])); + ki[i+1] = (ZIGINT)(x / x1 * NMANTISSA); + wi[i] = x / NMANTISSA; + fi[i] = exp (-0.5 * x * x); + x1 = x; + } + + ki[1] = 0; + + /* Zigurrat tables for the exponential distribution */ + x1 = ZIGGURAT_EXP_R; + we[255] = x1 / EMANTISSA; + fe[255] = exp (-x1); + + /* Index zero is special for tail strip, where Marsaglia and Tsang + * defines this as + * k_0 = 2^32 * r * f(r) / v, w_0 = 0.5^32 * v / f(r), f_0 = 1, + * where v is the area of each strip of the ziggurat. + */ + ke[0] = (ZIGINT) (x1 * fe[255] / EXP_SECTION_AREA * EMANTISSA); + we[0] = EXP_SECTION_AREA / fe[255] / EMANTISSA; + fe[0] = 1.; + + for (i = 254; i > 0; i--) + { + /* New x is given by x = f^{-1}(v/x_{i+1} + f(x_{i+1})), thus + * need inverse operator of y = exp(-x) -> x = -ln(y) + */ + x = - log(EXP_SECTION_AREA / x1 + fe[i+1]); + ke[i+1] = (ZIGINT)(x / x1 * EMANTISSA); + we[i] = x / EMANTISSA; + fe[i] = exp (-x); + x1 = x; + } + ke[1] = 0; + + initt = 0; +} + +/* + * Here is the guts of the algorithm. As Marsaglia and Tsang state the + * algorithm in their paper + * + * 1) Calculate a random signed integer j and let i be the index + * provided by the rightmost 8-bits of j + * 2) Set x = j * w_i. If j < k_i return x + * 3) If i = 0, then return x from the tail + * 4) If [f(x_{i-1}) - f(x_i)] * U < f(x) - f(x_i), return x + * 5) goto step 1 + * + * Where f is the functional form of the distribution, which for a normal + * distribution is exp(-0.5*x*x) + */ + +double +oct_randn (void) +{ + if (initt) + create_ziggurat_tables(); + + while (1) + { + /* The following code is specialized for 32-bit mantissa. + * Compared to the arbitrary mantissa code, there is a performance + * gain for 32-bits: PPC: 2%, MIPS: 8%, x86: 40% + * There is a bigger performance gain compared to using a full + * 53-bit mantissa: PPC: 60%, MIPS: 65%, x86: 240% + * Of course, different compilers and operating systems may + * have something to do with this. + */ +#if !defined(ALLBITS) +# if HAVE_X86_32 + /* 53-bit mantissa, 1-bit sign, x86 32-bit architecture */ + double x; + int si,idx; + register uint32_t lo, hi; + int64_t rabs; + uint32_t *p = (uint32_t *)&rabs; + lo = randi32(); + idx = lo&0xFF; + hi = randi32(); + si = hi&UMASK; + p[0] = lo; + p[1] = hi&0x1FFFFF; + x = ( si ? -rabs : rabs ) * wi[idx]; +# else /* !HAVE_X86_32 */ + /* arbitrary mantissa (selected by NRANDI, with 1 bit for sign) */ + const uint64_t r = NRANDI; + const int64_t rabs=r>>1; + const int idx = (int)(rabs&0xFF); + const double x = ( r&1 ? -rabs : rabs) * wi[idx]; +# endif /* !HAVE_X86_32 */ + if (rabs < (int64_t)ki[idx]) +#else /* ALLBITS */ + /* 32-bit mantissa */ + const uint32_t r = randi32(); + const uint32_t rabs = r&LMASK; + const int idx = (int)(r&0xFF); + const double x = ((int32_t)r) * wi[idx]; + if (rabs < ki[idx]) +#endif /* ALLBITS */ + return x; /* 99.3% of the time we return here 1st try */ + else if (idx == 0) + { + /* As stated in Marsaglia and Tsang + * + * For the normal tail, the method of Marsaglia[5] provides: + * generate x = -ln(U_1)/r, y = -ln(U_2), until y+y > x*x, + * then return r+x. Except that r+x is always in the positive + * tail!!!! Any thing random might be used to determine the + * sign, but as we already have r we might as well use it + * + * [PAK] but not the bottom 8 bits, since they are all 0 here! + */ + double xx, yy; + do + { + xx = - ZIGGURAT_NOR_INV_R * log (RANDU); + yy = - log (RANDU); + } + while ( yy+yy <= xx*xx); + return (rabs&0x100 ? -ZIGGURAT_NOR_R-xx : ZIGGURAT_NOR_R+xx); + } + else if ((fi[idx-1] - fi[idx]) * RANDU + fi[idx] < exp(-0.5*x*x)) + return x; + } +} + +double +oct_rande (void) +{ + if (initt) + create_ziggurat_tables(); + + while (1) + { + ZIGINT ri = ERANDI; + const int idx = (int)(ri & 0xFF); + const double x = ri * we[idx]; + if (ri < ke[idx]) + return x; // 98.9% of the time we return here 1st try + else if (idx == 0) + { + /* As stated in Marsaglia and Tsang + * + * For the exponential tail, the method of Marsaglia[5] provides: + * x = r - ln(U); + */ + return ZIGGURAT_EXP_R - log(RANDU); + } + else if ((fe[idx-1] - fe[idx]) * RANDU + fe[idx] < exp(-x)) + return x; + } +} + +/* Array generators */ +void +oct_fill_randu (octave_idx_type n, double *p) +{ + octave_idx_type i; + for (i = 0; i < n; i++) + p[i] = oct_randu(); +} + +void +oct_fill_randn (octave_idx_type n, double *p) +{ + octave_idx_type i; + for (i = 0; i < n; i++) + p[i] = oct_randn(); +} + +void +oct_fill_rande (octave_idx_type n, double *p) +{ + octave_idx_type i; + for (i = 0; i < n; i++) + p[i] = oct_rande(); +} + +/* +;;; Local Variables: *** +;;; mode: C *** +;;; End: *** +*/
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/randmtzig.h Thu Apr 06 08:15:49 2006 +0000 @@ -0,0 +1,104 @@ +/* + A C-program for MT19937, with initialization improved 2002/2/10. + Coded by Takuji Nishimura and Makoto Matsumoto. + This is a faster version by taking Shawn Cokus's optimization, + Matthe Bellew's simplification, Isaku Wada's real version. + David Bateman added normal and exponential distributions following + Marsaglia and Tang's Ziggurat algorithm. + + Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, + Copyright (C) 2004, David Bateman + 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. + +*/ + +#ifndef _RANDMTZIG_H +#define _RANDMTZIG_H + +#ifdef HAVE_CONFIG_H +#include <config.h> +#endif + +#include "oct-types.h" + +#define MT_N 624 + +#ifdef __cplusplus +extern "C" { +#endif + +#ifdef HAVE_INTTYPES_H +#include <inttypes.h> +#else +#if SIZEOF_INT == 4 +typedef unsigned int uint32_t; +#elif SIZEOF_LONG == 4 +typedef unsigned long uint32_t; +#else +#error "No 4 byte integer type found!" +#endif + +#if SIZEOF_LONG == 8 +typedef unsigned long uint64_t; +#else +#if SIZEOF_LONG_LONG == 8 +typedef unsigned long long uint64_t; +#endif +#endif +#endif + +/* === Mersenne Twister === */ +extern void oct_init_by_int (uint32_t s); +extern void oct_init_by_array (uint32_t init_key[], int key_length); +extern void oct_init_by_entropy (void); +extern void oct_set_state (uint32_t save[]); +extern void oct_get_state (uint32_t save[]); + +/* === Array generators === */ +extern double oct_randu (void); +extern double oct_randn (void); +extern double oct_rande (void); + +/* === Array generators === */ +extern void oct_fill_randu (octave_idx_type n, double *p); +extern void oct_fill_randn (octave_idx_type n, double *p); +extern void oct_fill_rande (octave_idx_type n, double *p); + +#ifdef __cplusplus +} +#endif +#endif + +/* +;;; Local Variables: *** +;;; mode: C *** +;;; End: *** +*/ +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/randpoisson.c Thu Apr 06 08:15:49 2006 +0000 @@ -0,0 +1,446 @@ +/* This code is in the public domain */ + +/* Needs the following defines: + * NAN: value to return for Not-A-Number + * RUNI: uniform generator on (0,1) + * RNOR: normal generator + * LGAMMA: log gamma function + * INFINITE: function to test whether a value is infinite + */ + +#if defined (HAVE_CONFIG_H) +#include <config.h> +#endif + +#include <math.h> +#include <stdio.h> + +#include "f77-fcn.h" +#include "lo-ieee.h" +#include "lo-error.h" +#include "randmtzig.h" +#include "randpoisson.h" + +#undef NAN +#define NAN octave_NaN +#define INFINITE lo_ieee_isinf +#define RUNI oct_randu() +#define RNOR oct_randn() +#define LGAMMA xlgamma + +F77_RET_T +F77_FUNC (dlgams, DLGAMS) (const double *, double *, double *); + +static double +xlgamma (double x) +{ + double result; + double sgngam; + + if (lo_ieee_isnan (x)) + result = x; + else if (x <= 0 || lo_ieee_isinf (x)) + result = octave_Inf; + else + F77_XFCN (dlgams, DLGAMS, (&x, &result, &sgngam)); + + return result; +} + +/* ---- pprsc.c from Stadloeber's winrand --- */ + +#include <math.h> + +/* flogfak(k) = ln(k!) */ +static double +flogfak (double k) +{ +#define C0 9.18938533204672742e-01 +#define C1 8.33333333333333333e-02 +#define C3 -2.77777777777777778e-03 +#define C5 7.93650793650793651e-04 +#define C7 -5.95238095238095238e-04 + + static double logfak[30L] = { + 0.00000000000000000, 0.00000000000000000, 0.69314718055994531, + 1.79175946922805500, 3.17805383034794562, 4.78749174278204599, + 6.57925121201010100, 8.52516136106541430, 10.60460290274525023, + 12.80182748008146961, 15.10441257307551530, 17.50230784587388584, + 19.98721449566188615, 22.55216385312342289, 25.19122118273868150, + 27.89927138384089157, 30.67186010608067280, 33.50507345013688888, + 36.39544520803305358, 39.33988418719949404, 42.33561646075348503, + 45.38013889847690803, 48.47118135183522388, 51.60667556776437357, + 54.78472939811231919, 58.00360522298051994, 61.26170176100200198, + 64.55753862700633106, 67.88974313718153498, 71.25703896716800901 + }; + + double r, rr; + + if (k >= 30.0) + { + r = 1.0 / k; + rr = r * r; + return ((k + 0.5)*log(k) - k + C0 + r*(C1 + rr*(C3 + rr*(C5 + rr*C7)))); + } + else + return (logfak[(int)k]); +} + + +/****************************************************************** + * * + * Poisson Distribution - Patchwork Rejection/Inversion * + * * + ****************************************************************** + * * + * For parameter my < 10 Tabulated Inversion is applied. * + * For my >= 10 Patchwork Rejection is employed: * + * The area below the histogram function f(x) is rearranged in * + * its body by certain point reflections. Within a large center * + * interval variates are sampled efficiently by rejection from * + * uniform hats. Rectangular immediate acceptance regions speed * + * up the generation. The remaining tails are covered by * + * exponential functions. * + * * + ****************************************************************** + * * + * FUNCTION : - pprsc samples a random number from the Poisson * + * distribution with parameter my > 0. * + * REFERENCE : - H. Zechner (1994): Efficient sampling from * + * continuous and discrete unimodal distributions, * + * Doctoral Dissertation, 156 pp., Technical * + * University Graz, Austria. * + * SUBPROGRAM : - drand(seed) ... (0,1)-Uniform generator with * + * unsigned long integer *seed. * + * * + * Implemented by H. Zechner, January 1994 * + * Revised by F. Niederl, July 1994 * + * * + ******************************************************************/ + +static double +f (double k, double l_nu, double c_pm) +{ + return exp(k * l_nu - flogfak(k) - c_pm); +} + +static double +pprsc (double my) +{ + static double my_last = -1.0; + static double m, k2, k4, k1, k5; + static double dl, dr, r1, r2, r4, r5, ll, lr, l_my, c_pm, + f1, f2, f4, f5, p1, p2, p3, p4, p5, p6; + double Dk, X, Y; + double Ds, U, V, W; + + if (my != my_last) + { /* set-up */ + my_last = my; + /* approximate deviation of reflection points k2, k4 from my - 1/2 */ + Ds = sqrt(my + 0.25); + + /* mode m, reflection points k2 and k4, and points k1 and k5, */ + /* which delimit the centre region of h(x) */ + m = floor(my); + k2 = ceil(my - 0.5 - Ds); + k4 = floor(my - 0.5 + Ds); + k1 = k2 + k2 - m + 1L; + k5 = k4 + k4 - m; + + /* range width of the critical left and right centre region */ + dl = (k2 - k1); + dr = (k5 - k4); + + /* recurrence constants r(k)=p(k)/p(k-1) at k = k1, k2, k4+1, k5+1 */ + r1 = my / k1; + r2 = my / k2; + r4 = my / (k4 + 1.0); + r5 = my / (k5 + 1.0); + + /* reciprocal values of the scale parameters of exp. tail envelope */ + ll = log(r1); /* expon. tail left */ + lr = -log(r5); /* expon. tail right*/ + + /* Poisson constants, necessary for computing function values f(k) */ + l_my = log(my); + c_pm = m * l_my - flogfak(m); + + /* function values f(k) = p(k)/p(m) at k = k2, k4, k1, k5 */ + f2 = f(k2, l_my, c_pm); + f4 = f(k4, l_my, c_pm); + f1 = f(k1, l_my, c_pm); + f5 = f(k5, l_my, c_pm); + + /* area of the two centre and the two exponential tail regions */ + /* area of the two immediate acceptance regions between k2, k4 */ + p1 = f2 * (dl + 1.0); /* immed. left */ + p2 = f2 * dl + p1; /* centre left */ + p3 = f4 * (dr + 1.0) + p2; /* immed. right */ + p4 = f4 * dr + p3; /* centre right */ + p5 = f1 / ll + p4; /* exp. tail left */ + p6 = f5 / lr + p5; /* exp. tail right*/ + } + + for (;;) + { + /* generate uniform number U -- U(0, p6) */ + /* case distinction corresponding to U */ + if ((U = RUNI * p6) < p2) + { /* centre left */ + + /* immediate acceptance region + R2 = [k2, m) *[0, f2), X = k2, ... m -1 */ + if ((V = U - p1) < 0.0) return(k2 + floor(U/f2)); + /* immediate acceptance region + R1 = [k1, k2)*[0, f1), X = k1, ... k2-1 */ + if ((W = V / dl) < f1 ) return(k1 + floor(V/f1)); + + /* computation of candidate X < k2, and its counterpart Y > k2 */ + /* either squeeze-acceptance of X or acceptance-rejection of Y */ + Dk = floor(dl * RUNI) + 1.0; + if (W <= f2 - Dk * (f2 - f2/r2)) + { /* quick accept of */ + return(k2 - Dk); /* X = k2 - Dk */ + } + if ((V = f2 + f2 - W) < 1.0) + { /* quick reject of Y*/ + Y = k2 + Dk; + if (V <= f2 + Dk * (1.0 - f2)/(dl + 1.0)) + { /* quick accept of */ + return(Y); /* Y = k2 + Dk */ + } + if (V <= f(Y, l_my, c_pm)) return(Y); /* final accept of Y*/ + } + X = k2 - Dk; + } + else if (U < p4) + { /* centre right */ + /* immediate acceptance region + R3 = [m, k4+1)*[0, f4), X = m, ... k4 */ + if ((V = U - p3) < 0.0) return(k4 - floor((U - p2)/f4)); + /* immediate acceptance region + R4 = [k4+1, k5+1)*[0, f5) */ + if ((W = V / dr) < f5 ) return(k5 - floor(V/f5)); + + /* computation of candidate X > k4, and its counterpart Y < k4 */ + /* either squeeze-acceptance of X or acceptance-rejection of Y */ + Dk = floor(dr * RUNI) + 1.0; + if (W <= f4 - Dk * (f4 - f4*r4)) + { /* quick accept of */ + return(k4 + Dk); /* X = k4 + Dk */ + } + if ((V = f4 + f4 - W) < 1.0) + { /* quick reject of Y*/ + Y = k4 - Dk; + if (V <= f4 + Dk * (1.0 - f4)/ dr) + { /* quick accept of */ + return(Y); /* Y = k4 - Dk */ + } + if (V <= f(Y, l_my, c_pm)) return(Y); /* final accept of Y*/ + } + X = k4 + Dk; + } + else + { + W = RUNI; + if (U < p5) + { /* expon. tail left */ + Dk = floor(1.0 - log(W)/ll); + if ((X = k1 - Dk) < 0L) continue; /* 0 <= X <= k1 - 1 */ + W *= (U - p4) * ll; /* W -- U(0, h(x)) */ + if (W <= f1 - Dk * (f1 - f1/r1)) + return(X); /* quick accept of X*/ + } + else + { /* expon. tail right*/ + Dk = floor(1.0 - log(W)/lr); + X = k5 + Dk; /* X >= k5 + 1 */ + W *= (U - p5) * lr; /* W -- U(0, h(x)) */ + if (W <= f5 - Dk * (f5 - f5*r5)) + return(X); /* quick accept of X*/ + } + } + + /* acceptance-rejection test of candidate X from the original area */ + /* test, whether W <= f(k), with W = U*h(x) and U -- U(0, 1)*/ + /* log f(X) = (X - m)*log(my) - log X! + log m! */ + if (log(W) <= X * l_my - flogfak(X) - c_pm) return(X); + } +} +/* ---- pprsc.c end ------ */ + + +/* The remainder of the file is by Paul Kienzle */ + +/* Given uniform u, find x such that CDF(L,x)==u. Return x. */ +static void +poisson_cdf_lookup(double lambda, double *p, size_t n) +{ + /* Table size is predicated on the maximum value of lambda + * we want to store in the table, and the maximum value of + * returned by the uniform random number generator on [0,1). + * With lambda==10 and u_max = 1 - 1/(2^32+1), we + * have poisson_pdf(lambda,36) < 1-u_max. If instead our + * generator uses more bits of mantissa or returns a value + * in the range [0,1], then for lambda==10 we need a table + * size of 46 instead. For long doubles, the table size + * will need to be longer still. */ +#define TABLESIZE 46 + double t[TABLESIZE]; + + /* Precompute the table for the u up to and including 0.458. + * We will almost certainly need it. */ + int intlambda = (int)floor(lambda); + double P; + int tableidx; + size_t i = n; + + t[0] = P = exp(-lambda); + for (tableidx = 1; tableidx <= intlambda; tableidx++) { + P = P*lambda/(double)tableidx; + t[tableidx] = t[tableidx-1] + P; + } + + while (i-- > 0) { + double u = RUNI; + + /* If u > 0.458 we know we can jump to floor(lambda) before + * comparing (this observation is based on Stadlober's winrand + * code). For lambda >= 1, this will be a win. Lambda < 1 + * is already fast, so adding an extra comparison is not a + * problem. */ + int k = (u > 0.458 ? intlambda : 0); + + /* We aren't using a for loop here because when we find the + * right k we want to jump to the next iteration of the + * outer loop, and the continue statement will only work for + * the inner loop. */ + nextk: + if ( u <= t[k] ) { + p[i] = (double) k; + continue; + } + if (++k < tableidx) goto nextk; + + /* We only need high values of the table very rarely so we + * don't automatically compute the entire table. */ + while (tableidx < TABLESIZE) { + P = P*lambda/(double)tableidx; + t[tableidx] = t[tableidx-1] + P; + /* Make sure we converge to 1.0 just in case u is uniform + * on [0,1] rather than [0,1). */ + if (t[tableidx] == t[tableidx-1]) t[tableidx] = 1.0; + tableidx++; + if (u <= t[tableidx-1]) break; + } + + /* We are assuming that the table size is big enough here. + * This should be true even if RUNI is returning values in + * the range [0,1] rather than [0,1). + */ + p[i] = (double)(tableidx-1); + } +} + +/* From Press, et al., Numerical Recipes */ +static void +poisson_rejection (double lambda, double *p, size_t n) +{ + double sq = sqrt(2.0*lambda); + double alxm = log(lambda); + double g = lambda*alxm - LGAMMA(lambda+1.0); + size_t i; + + for (i = 0; i < n; i++) + { + double y, em, t; + do { + do { + y = tan(M_PI*RUNI); + em = sq * y + lambda; + } while (em < 0.0); + em = floor(em); + t = 0.9*(1.0+y*y)*exp(em*alxm-flogfak(em)-g); + } while (RUNI > t); + p[i] = em; + } +} + +/* The cutoff of L <= 1e8 in the following two functions before using + * the normal approximation is based on: + * > L=1e8; x=floor(linspace(0,2*L,1000)); + * > max(abs(normal_pdf(x,L,L)-poisson_pdf(x,L))) + * ans = 1.1376e-28 + * For L=1e7, the max is around 1e-9, which is within the step size of RUNI. + * For L>1e10 the pprsc function breaks down, as I saw from the histogram + * of a large sample, so 1e8 is both small enough and large enough. */ + +/* Generate a set of poisson numbers with the same distribution */ +void +oct_fill_randp (double L, octave_idx_type n, double *p) +{ + octave_idx_type i; + if (L < 0.0 || INFINITE(L)) + { + for (i=0; i<n; i++) + p[i] = NAN; + } + else if (L <= 10.0) + { + poisson_cdf_lookup(L, p, n); + } + else if (L <= 1e8) + { + for (i=0; i<n; i++) + p[i] = pprsc(L); + } + else + { + /* normal approximation: from Phys. Rev. D (1994) v50 p1284 */ + const double sqrtL = sqrt(L); + for (i = 0; i < L; i++) + { + p[i] = floor(RNOR*sqrtL + L + 0.5); + if (p[i] < 0.0) + p[i] = 0.0; /* will probably never happen */ + } + } +} + +/* Generate one poisson variate */ +double +oct_randp (double L) +{ + double ret; + if (L < 0.0) ret = NAN; + else if (L <= 12.0) { + /* From Press, et al. Numerical recipes */ + double g = exp(-L); + int em = -1; + double t = 1.0; + do { + ++em; + t *= RUNI; + } while (t > g); + ret = em; + } else if (L <= 1e8) { + /* numerical recipes */ + poisson_rejection(L, &ret, 1); + } else if (INFINITE(L)) { + /* XXX FIXME XXX R uses NaN, but the normal approx. suggests that as + * limit should be inf. Which is correct? */ + ret = NAN; + } else { + /* normal approximation: from Phys. Rev. D (1994) v50 p1284 */ + ret = floor(RNOR*sqrt(L) + L + 0.5); + if (ret < 0.0) ret = 0.0; /* will probably never happen */ + } + return ret; +} + +/* +;;; Local Variables: *** +;;; mode: C *** +;;; End: *** +*/
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/randpoisson.h Thu Apr 06 08:15:49 2006 +0000 @@ -0,0 +1,24 @@ +/* This code is in the public domain */ + +#ifndef _RANDPOISSON_H + +#include "oct-types.h" + +#ifdef __cplusplus +extern "C" { +#endif + +extern double oct_randp (double L); +extern void oct_fill_randp (double L, octave_idx_type n, double *p); + +#ifdef __cplusplus +} +#endif +#endif + +/* +;;; Local Variables: *** +;;; mode: C *** +;;; End: *** +*/ +