1 /* Copyright (C) 1999,2000,2001, 2003, 2005, 2006, 2009 Free Software Foundation, Inc.
2 * This library is free software; you can redistribute it and/or
3 * modify it under the terms of the GNU Lesser General Public License
4 * as published by the Free Software Foundation; either version 3 of
5 * the License, or (at your option) any later version.
7 * This library is distributed in the hope that it will be useful, but
8 * WITHOUT ANY WARRANTY; without even the implied warranty of
9 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
10 * Lesser General Public License for more details.
12 * You should have received a copy of the GNU Lesser General Public
13 * License along with this library; if not, write to the Free Software
14 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
20 /* Author: Mikael Djurfeldt <djurfeldt@nada.kth.se> */
26 #include "libguile/_scm.h"
32 #include "libguile/smob.h"
33 #include "libguile/numbers.h"
34 #include "libguile/feature.h"
35 #include "libguile/strings.h"
36 #include "libguile/arrays.h"
37 #include "libguile/srfi-4.h"
38 #include "libguile/vectors.h"
39 #include "libguile/generalized-vectors.h"
41 #include "libguile/validate.h"
42 #include "libguile/random.h"
46 * A plugin interface for RNGs
48 * Using this interface, it is possible for the application to tell
49 * libguile to use a different RNG. This is desirable if it is
50 * necessary to use the same RNG everywhere in the application in
51 * order to prevent interference, if the application uses RNG
52 * hardware, or if the application has special demands on the RNG.
54 * Look in random.h and how the default generator is "plugged in" in
58 scm_t_rng scm_the_rng
;
64 * This is the MWC (Multiply With Carry) random number generator
65 * described by George Marsaglia at the Department of Statistics and
66 * Supercomputer Computations Research Institute, The Florida State
67 * University (http://stat.fsu.edu/~geo).
69 * It uses 64 bits, has a period of 4578426017172946943 (4.6e18), and
70 * passes all tests in the DIEHARD test suite
71 * (http://stat.fsu.edu/~geo/diehard.html)
74 #define A 2131995753UL
77 #define M_PI 3.14159265359
83 scm_i_uniform32 (scm_t_i_rstate
*state
)
85 scm_t_uint64 x
= (scm_t_uint64
) A
* state
->w
+ state
->c
;
86 scm_t_uint32 w
= x
& 0xffffffffUL
;
94 /* ww This is a portable version of the same RNG without 64 bit
97 * xx It is only intended to provide identical behaviour on
98 * xx platforms without 8 byte longs or long longs until
99 * xx someone has implemented the routine in assembler code.
105 #define L(x) ((x) & 0xffff)
106 #define H(x) ((x) >> 16)
109 scm_i_uniform32 (scm_t_i_rstate
*state
)
111 scm_t_uint32 x1
= L (A
) * L (state
->w
);
112 scm_t_uint32 x2
= L (A
) * H (state
->w
);
113 scm_t_uint32 x3
= H (A
) * L (state
->w
);
114 scm_t_uint32 w
= L (x1
) + L (state
->c
);
115 scm_t_uint32 m
= H (x1
) + L (x2
) + L (x3
) + H (state
->c
) + H (w
);
116 scm_t_uint32 x4
= H (A
) * H (state
->w
);
117 state
->w
= w
= (L (m
) << 16) + L (w
);
118 state
->c
= H (x2
) + H (x3
) + x4
+ H (m
);
125 scm_i_init_rstate (scm_t_i_rstate
*state
, const char *seed
, int n
)
130 for (i
= 0; i
< n
; ++i
)
134 w
+= seed
[i
] << (8 * m
);
136 c
+= seed
[i
] << (8 * (m
- 4));
138 if ((w
== 0 && c
== 0) || (w
== -1 && c
== A
- 1))
145 scm_i_copy_rstate (scm_t_i_rstate
*state
)
147 scm_t_rstate
*new_state
;
149 new_state
= scm_gc_malloc_pointerless (scm_the_rng
.rstate_size
,
151 return memcpy (new_state
, state
, scm_the_rng
.rstate_size
);
156 * Random number library functions
160 scm_c_make_rstate (const char *seed
, int n
)
164 state
= scm_gc_malloc_pointerless (scm_the_rng
.rstate_size
,
166 state
->reserved0
= 0;
167 scm_the_rng
.init_rstate (state
, seed
, n
);
173 scm_c_default_rstate ()
174 #define FUNC_NAME "scm_c_default_rstate"
176 SCM state
= SCM_VARIABLE_REF (scm_var_random_state
);
177 if (!SCM_RSTATEP (state
))
178 SCM_MISC_ERROR ("*random-state* contains bogus random state", SCM_EOL
);
179 return SCM_RSTATE (state
);
185 scm_c_uniform01 (scm_t_rstate
*state
)
187 double x
= (double) scm_the_rng
.random_bits (state
) / (double) 0xffffffffUL
;
188 return ((x
+ (double) scm_the_rng
.random_bits (state
))
189 / (double) 0xffffffffUL
);
193 scm_c_normal01 (scm_t_rstate
*state
)
195 if (state
->reserved0
)
197 state
->reserved0
= 0;
198 return state
->reserved1
;
204 r
= sqrt (-2.0 * log (scm_c_uniform01 (state
)));
205 a
= 2.0 * M_PI
* scm_c_uniform01 (state
);
208 state
->reserved1
= r
* cos (a
);
209 state
->reserved0
= 1;
216 scm_c_exp1 (scm_t_rstate
*state
)
218 return - log (scm_c_uniform01 (state
));
221 unsigned char scm_masktab
[256];
224 scm_c_random (scm_t_rstate
*state
, unsigned long m
)
226 unsigned long r
, mask
;
227 #if SCM_SIZEOF_UNSIGNED_LONG == 4
231 ? scm_masktab
[m
>> 8] << 8 | 0xff
233 ? scm_masktab
[m
>> 16] << 16 | 0xffff
234 : scm_masktab
[m
>> 24] << 24 | 0xffffff)));
235 while ((r
= scm_the_rng
.random_bits (state
) & mask
) >= m
);
236 #elif SCM_SIZEOF_UNSIGNED_LONG == 8
240 ? scm_masktab
[m
>> 8] << 8 | 0xff
242 ? scm_masktab
[m
>> 16] << 16 | 0xffff
244 ? scm_masktab
[m
>> 24] << 24 | 0xffffff
246 ? ((unsigned long) scm_masktab
[m
>> 32] << 32
249 ? ((unsigned long) scm_masktab
[m
>> 40] << 40
252 ? ((unsigned long) scm_masktab
[m
>> 48] << 48
254 : ((unsigned long) scm_masktab
[m
>> 56] << 56
255 | 0xffffffffffffffUL
))))))));
256 while ((r
= ((scm_the_rng
.random_bits (state
) << 32
257 | scm_the_rng
.random_bits (state
))) & mask
) >= m
);
259 #error "Cannot deal with this platform's unsigned long size"
265 SCM scm_c_random_bignum (scm_t_rstate *state, SCM m)
267 Takes a random state (source of random bits) and a bignum m.
268 Returns a bignum b, 0 <= b < m.
270 It does this by allocating a bignum b with as many base 65536 digits
271 as m, filling b with random bits (in 32 bit chunks) up to the most
272 significant 1 in m, and, finally checking if the resultant b is too
273 large (>= m). If too large, we simply repeat the process again. (It
274 is important to throw away all generated random bits if b >= m,
275 otherwise we'll end up with a distorted distribution.)
280 scm_c_random_bignum (scm_t_rstate
*state
, SCM m
)
282 SCM result
= scm_i_mkbig ();
283 const size_t m_bits
= mpz_sizeinbase (SCM_I_BIG_MPZ (m
), 2);
284 /* how many bits would only partially fill the last unsigned long? */
285 const size_t end_bits
= m_bits
% (sizeof (unsigned long) * SCM_CHAR_BIT
);
286 unsigned long *random_chunks
= NULL
;
287 const unsigned long num_full_chunks
=
288 m_bits
/ (sizeof (unsigned long) * SCM_CHAR_BIT
);
289 const unsigned long num_chunks
= num_full_chunks
+ ((end_bits
) ? 1 : 0);
291 /* we know the result will be this big */
292 mpz_realloc2 (SCM_I_BIG_MPZ (result
), m_bits
);
295 (unsigned long *) scm_gc_calloc (num_chunks
* sizeof (unsigned long),
296 "random bignum chunks");
300 unsigned long *current_chunk
= random_chunks
+ (num_chunks
- 1);
301 unsigned long chunks_left
= num_chunks
;
303 mpz_set_ui (SCM_I_BIG_MPZ (result
), 0);
307 /* generate a mask with ones in the end_bits position, i.e. if
308 end_bits is 3, then we'd have a mask of ...0000000111 */
309 const unsigned long rndbits
= scm_the_rng
.random_bits (state
);
310 int rshift
= (sizeof (unsigned long) * SCM_CHAR_BIT
) - end_bits
;
311 unsigned long mask
= ((unsigned long) ULONG_MAX
) >> rshift
;
312 unsigned long highest_bits
= rndbits
& mask
;
313 *current_chunk
-- = highest_bits
;
319 /* now fill in the remaining unsigned long sized chunks */
320 *current_chunk
-- = scm_the_rng
.random_bits (state
);
323 mpz_import (SCM_I_BIG_MPZ (result
),
326 sizeof (unsigned long),
330 /* if result >= m, regenerate it (it is important to regenerate
331 all bits in order not to get a distorted distribution) */
332 } while (mpz_cmp (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (m
)) >= 0);
333 scm_gc_free (random_chunks
,
334 num_chunks
* sizeof (unsigned long),
335 "random bignum chunks");
336 return scm_i_normbig (result
);
340 * Scheme level representation of random states.
343 scm_t_bits scm_tc16_rstate
;
346 make_rstate (scm_t_rstate
*state
)
348 SCM_RETURN_NEWSMOB (scm_tc16_rstate
, state
);
353 * Scheme level interface.
356 SCM_GLOBAL_VARIABLE_INIT (scm_var_random_state
, "*random-state*", scm_seed_to_random_state (scm_from_locale_string ("URL:http://stat.fsu.edu/~geo/diehard.html")));
358 SCM_DEFINE (scm_random
, "random", 1, 1, 0,
360 "Return a number in [0, N).\n"
362 "Accepts a positive integer or real n and returns a\n"
363 "number of the same type between zero (inclusive) and\n"
364 "N (exclusive). The values returned have a uniform\n"
367 "The optional argument @var{state} must be of the type produced\n"
368 "by @code{seed->random-state}. It defaults to the value of the\n"
369 "variable @var{*random-state*}. This object is used to maintain\n"
370 "the state of the pseudo-random-number generator and is altered\n"
371 "as a side effect of the random operation.")
372 #define FUNC_NAME s_scm_random
374 if (SCM_UNBNDP (state
))
375 state
= SCM_VARIABLE_REF (scm_var_random_state
);
376 SCM_VALIDATE_RSTATE (2, state
);
379 unsigned long m
= SCM_I_INUM (n
);
380 SCM_ASSERT_RANGE (1, n
, m
> 0);
381 return scm_from_ulong (scm_c_random (SCM_RSTATE (state
), m
));
383 SCM_VALIDATE_NIM (1, n
);
385 return scm_from_double (SCM_REAL_VALUE (n
)
386 * scm_c_uniform01 (SCM_RSTATE (state
)));
389 SCM_WRONG_TYPE_ARG (1, n
);
390 return scm_c_random_bignum (SCM_RSTATE (state
), n
);
394 SCM_DEFINE (scm_copy_random_state
, "copy-random-state", 0, 1, 0,
396 "Return a copy of the random state @var{state}.")
397 #define FUNC_NAME s_scm_copy_random_state
399 if (SCM_UNBNDP (state
))
400 state
= SCM_VARIABLE_REF (scm_var_random_state
);
401 SCM_VALIDATE_RSTATE (1, state
);
402 return make_rstate (scm_the_rng
.copy_rstate (SCM_RSTATE (state
)));
406 SCM_DEFINE (scm_seed_to_random_state
, "seed->random-state", 1, 0, 0,
408 "Return a new random state using @var{seed}.")
409 #define FUNC_NAME s_scm_seed_to_random_state
412 if (SCM_NUMBERP (seed
))
413 seed
= scm_number_to_string (seed
, SCM_UNDEFINED
);
414 SCM_VALIDATE_STRING (1, seed
);
415 res
= make_rstate (scm_c_make_rstate (scm_i_string_chars (seed
),
416 scm_i_string_length (seed
)));
417 scm_remember_upto_here_1 (seed
);
423 SCM_DEFINE (scm_random_uniform
, "random:uniform", 0, 1, 0,
425 "Return a uniformly distributed inexact real random number in\n"
427 #define FUNC_NAME s_scm_random_uniform
429 if (SCM_UNBNDP (state
))
430 state
= SCM_VARIABLE_REF (scm_var_random_state
);
431 SCM_VALIDATE_RSTATE (1, state
);
432 return scm_from_double (scm_c_uniform01 (SCM_RSTATE (state
)));
436 SCM_DEFINE (scm_random_normal
, "random:normal", 0, 1, 0,
438 "Return an inexact real in a normal distribution. The\n"
439 "distribution used has mean 0 and standard deviation 1. For a\n"
440 "normal distribution with mean m and standard deviation d use\n"
441 "@code{(+ m (* d (random:normal)))}.")
442 #define FUNC_NAME s_scm_random_normal
444 if (SCM_UNBNDP (state
))
445 state
= SCM_VARIABLE_REF (scm_var_random_state
);
446 SCM_VALIDATE_RSTATE (1, state
);
447 return scm_from_double (scm_c_normal01 (SCM_RSTATE (state
)));
452 vector_scale_x (SCM v
, double c
)
455 if (scm_is_simple_vector (v
))
457 n
= SCM_SIMPLE_VECTOR_LENGTH (v
);
459 SCM_REAL_VALUE (SCM_SIMPLE_VECTOR_REF (v
, n
)) *= c
;
463 /* must be a f64vector. */
464 scm_t_array_handle handle
;
469 elts
= scm_f64vector_writable_elements (v
, &handle
, &len
, &inc
);
471 for (i
= 0; i
< len
; i
++, elts
+= inc
)
474 scm_array_handle_release (&handle
);
479 vector_sum_squares (SCM v
)
483 if (scm_is_simple_vector (v
))
485 n
= SCM_SIMPLE_VECTOR_LENGTH (v
);
488 x
= SCM_REAL_VALUE (SCM_SIMPLE_VECTOR_REF (v
, n
));
494 /* must be a f64vector. */
495 scm_t_array_handle handle
;
500 elts
= scm_f64vector_elements (v
, &handle
, &len
, &inc
);
502 for (i
= 0; i
< len
; i
++, elts
+= inc
)
508 scm_array_handle_release (&handle
);
513 /* For the uniform distribution on the solid sphere, note that in
514 * this distribution the length r of the vector has cumulative
515 * distribution r^n; i.e., u=r^n is uniform [0,1], so r can be
516 * generated as r=u^(1/n).
518 SCM_DEFINE (scm_random_solid_sphere_x
, "random:solid-sphere!", 1, 1, 0,
520 "Fills @var{vect} with inexact real random numbers the sum of\n"
521 "whose squares is less than 1.0. Thinking of @var{vect} as\n"
522 "coordinates in space of dimension @var{n} @math{=}\n"
523 "@code{(vector-length @var{vect})}, the coordinates are\n"
524 "uniformly distributed within the unit @var{n}-sphere.")
525 #define FUNC_NAME s_scm_random_solid_sphere_x
527 if (SCM_UNBNDP (state
))
528 state
= SCM_VARIABLE_REF (scm_var_random_state
);
529 SCM_VALIDATE_RSTATE (2, state
);
530 scm_random_normal_vector_x (v
, state
);
532 pow (scm_c_uniform01 (SCM_RSTATE (state
)),
533 1.0 / scm_c_generalized_vector_length (v
))
534 / sqrt (vector_sum_squares (v
)));
535 return SCM_UNSPECIFIED
;
539 SCM_DEFINE (scm_random_hollow_sphere_x
, "random:hollow-sphere!", 1, 1, 0,
541 "Fills vect with inexact real random numbers\n"
542 "the sum of whose squares is equal to 1.0.\n"
543 "Thinking of vect as coordinates in space of\n"
544 "dimension n = (vector-length vect), the coordinates\n"
545 "are uniformly distributed over the surface of the\n"
547 #define FUNC_NAME s_scm_random_hollow_sphere_x
549 if (SCM_UNBNDP (state
))
550 state
= SCM_VARIABLE_REF (scm_var_random_state
);
551 SCM_VALIDATE_RSTATE (2, state
);
552 scm_random_normal_vector_x (v
, state
);
553 vector_scale_x (v
, 1 / sqrt (vector_sum_squares (v
)));
554 return SCM_UNSPECIFIED
;
559 SCM_DEFINE (scm_random_normal_vector_x
, "random:normal-vector!", 1, 1, 0,
561 "Fills vect with inexact real random numbers that are\n"
562 "independent and standard normally distributed\n"
563 "(i.e., with mean 0 and variance 1).")
564 #define FUNC_NAME s_scm_random_normal_vector_x
567 scm_t_array_handle handle
;
568 scm_t_array_dim
*dim
;
570 if (SCM_UNBNDP (state
))
571 state
= SCM_VARIABLE_REF (scm_var_random_state
);
572 SCM_VALIDATE_RSTATE (2, state
);
574 scm_generalized_vector_get_handle (v
, &handle
);
575 dim
= scm_array_handle_dims (&handle
);
577 if (scm_is_vector (v
))
579 SCM
*elts
= scm_array_handle_writable_elements (&handle
);
580 for (i
= dim
->lbnd
; i
<= dim
->ubnd
; i
++, elts
+= dim
->inc
)
581 *elts
= scm_from_double (scm_c_normal01 (SCM_RSTATE (state
)));
585 /* must be a f64vector. */
586 double *elts
= scm_array_handle_f64_writable_elements (&handle
);
587 for (i
= dim
->lbnd
; i
<= dim
->ubnd
; i
++, elts
+= dim
->inc
)
588 *elts
= scm_c_normal01 (SCM_RSTATE (state
));
591 scm_array_handle_release (&handle
);
593 return SCM_UNSPECIFIED
;
597 SCM_DEFINE (scm_random_exp
, "random:exp", 0, 1, 0,
599 "Return an inexact real in an exponential distribution with mean\n"
600 "1. For an exponential distribution with mean u use (* u\n"
602 #define FUNC_NAME s_scm_random_exp
604 if (SCM_UNBNDP (state
))
605 state
= SCM_VARIABLE_REF (scm_var_random_state
);
606 SCM_VALIDATE_RSTATE (1, state
);
607 return scm_from_double (scm_c_exp1 (SCM_RSTATE (state
)));
615 /* plug in default RNG */
618 sizeof (scm_t_i_rstate
),
619 (unsigned long (*)()) scm_i_uniform32
,
620 (void (*)()) scm_i_init_rstate
,
621 (scm_t_rstate
*(*)()) scm_i_copy_rstate
625 scm_tc16_rstate
= scm_make_smob_type ("random-state", 0);
627 for (m
= 1; m
<= 0x100; m
<<= 1)
628 for (i
= m
>> 1; i
< m
; ++i
)
629 scm_masktab
[i
] = m
- 1;
631 #include "libguile/random.x"
633 scm_add_feature ("random");