1 /* Copyright (C) 1999,2000,2001, 2003, 2005, 2006, 2009, 2010 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
81 scm_i_uniform32 (scm_t_i_rstate
*state
)
83 scm_t_uint64 x
= (scm_t_uint64
) A
* state
->w
+ state
->c
;
84 scm_t_uint32 w
= x
& 0xffffffffUL
;
91 scm_i_init_rstate (scm_t_i_rstate
*state
, const char *seed
, int n
)
96 for (i
= 0; i
< n
; ++i
)
100 w
+= seed
[i
] << (8 * m
);
102 c
+= seed
[i
] << (8 * (m
- 4));
104 if ((w
== 0 && c
== 0) || (w
== -1 && c
== A
- 1))
111 scm_i_copy_rstate (scm_t_i_rstate
*state
)
113 scm_t_rstate
*new_state
;
115 new_state
= scm_gc_malloc_pointerless (scm_the_rng
.rstate_size
,
117 return memcpy (new_state
, state
, scm_the_rng
.rstate_size
);
120 SCM_SYMBOL(scm_i_rstate_tag
, "multiply-with-carry");
123 scm_i_init_rstate_scm (scm_t_i_rstate
*state
, SCM value
)
124 #define FUNC_NAME "scm_i_init_rstate_scm"
129 SCM_VALIDATE_LIST_COPYLEN (SCM_ARG1
, value
, length
);
130 SCM_ASSERT (length
== 3, value
, SCM_ARG1
, FUNC_NAME
);
131 SCM_ASSERT (scm_is_eq (SCM_CAR (value
), scm_i_rstate_tag
),
132 value
, SCM_ARG1
, FUNC_NAME
);
133 SCM_VALIDATE_UINT_COPY (SCM_ARG1
, SCM_CADR (value
), w
);
134 SCM_VALIDATE_UINT_COPY (SCM_ARG1
, SCM_CADDR (value
), c
);
142 scm_i_expose_rstate (scm_t_i_rstate
*state
)
144 return scm_list_3 (scm_i_rstate_tag
,
145 scm_from_uint32 (state
->w
),
146 scm_from_uint32 (state
->c
));
151 * Random number library functions
155 scm_c_make_rstate (const char *seed
, int n
)
159 state
= scm_gc_malloc_pointerless (scm_the_rng
.rstate_size
,
161 state
->reserved0
= 0;
162 scm_the_rng
.init_rstate (state
, seed
, n
);
167 scm_c_make_rstate_scm (SCM external
)
171 state
= scm_gc_malloc_pointerless (scm_the_rng
.rstate_size
,
173 state
->reserved0
= 0;
174 scm_the_rng
.init_rstate_scm (state
, external
);
179 scm_c_default_rstate ()
180 #define FUNC_NAME "scm_c_default_rstate"
182 SCM state
= SCM_VARIABLE_REF (scm_var_random_state
);
183 if (!SCM_RSTATEP (state
))
184 SCM_MISC_ERROR ("*random-state* contains bogus random state", SCM_EOL
);
185 return SCM_RSTATE (state
);
191 scm_c_uniform01 (scm_t_rstate
*state
)
193 double x
= (double) scm_the_rng
.random_bits (state
) / (double) 0xffffffffUL
;
194 return ((x
+ (double) scm_the_rng
.random_bits (state
))
195 / (double) 0xffffffffUL
);
199 scm_c_normal01 (scm_t_rstate
*state
)
201 if (state
->reserved0
)
203 state
->reserved0
= 0;
204 return state
->reserved1
;
210 r
= sqrt (-2.0 * log (scm_c_uniform01 (state
)));
211 a
= 2.0 * M_PI
* scm_c_uniform01 (state
);
214 state
->reserved1
= r
* cos (a
);
215 state
->reserved0
= 1;
222 scm_c_exp1 (scm_t_rstate
*state
)
224 return - log (scm_c_uniform01 (state
));
227 unsigned char scm_masktab
[256];
230 scm_c_random (scm_t_rstate
*state
, scm_t_uint32 m
)
232 scm_t_uint32 r
, mask
;
236 ? scm_masktab
[m
>> 8] << 8 | 0xff
238 ? scm_masktab
[m
>> 16] << 16 | 0xffff
239 : scm_masktab
[m
>> 24] << 24 | 0xffffff)));
240 while ((r
= scm_the_rng
.random_bits (state
) & mask
) >= m
);
245 SCM scm_c_random_bignum (scm_t_rstate *state, SCM m)
247 Takes a random state (source of random bits) and a bignum m.
248 Returns a bignum b, 0 <= b < m.
250 It does this by allocating a bignum b with as many base 65536 digits
251 as m, filling b with random bits (in 32 bit chunks) up to the most
252 significant 1 in m, and, finally checking if the resultant b is too
253 large (>= m). If too large, we simply repeat the process again. (It
254 is important to throw away all generated random bits if b >= m,
255 otherwise we'll end up with a distorted distribution.)
260 scm_c_random_bignum (scm_t_rstate
*state
, SCM m
)
262 SCM result
= scm_i_mkbig ();
263 const size_t m_bits
= mpz_sizeinbase (SCM_I_BIG_MPZ (m
), 2);
264 /* how many bits would only partially fill the last scm_t_uint32? */
265 const size_t end_bits
= m_bits
% (sizeof (scm_t_uint32
) * SCM_CHAR_BIT
);
266 scm_t_uint32
*random_chunks
= NULL
;
267 const scm_t_uint32 num_full_chunks
=
268 m_bits
/ (sizeof (scm_t_uint32
) * SCM_CHAR_BIT
);
269 const scm_t_uint32 num_chunks
= num_full_chunks
+ ((end_bits
) ? 1 : 0);
271 /* we know the result will be this big */
272 mpz_realloc2 (SCM_I_BIG_MPZ (result
), m_bits
);
275 (scm_t_uint32
*) scm_gc_calloc (num_chunks
* sizeof (scm_t_uint32
),
276 "random bignum chunks");
280 scm_t_uint32
*current_chunk
= random_chunks
+ (num_chunks
- 1);
281 scm_t_uint32 chunks_left
= num_chunks
;
283 mpz_set_ui (SCM_I_BIG_MPZ (result
), 0);
287 /* generate a mask with ones in the end_bits position, i.e. if
288 end_bits is 3, then we'd have a mask of ...0000000111 */
289 const scm_t_uint32 rndbits
= scm_the_rng
.random_bits (state
);
290 int rshift
= (sizeof (scm_t_uint32
) * SCM_CHAR_BIT
) - end_bits
;
291 scm_t_uint32 mask
= ((scm_t_uint32
)-1) >> rshift
;
292 scm_t_uint32 highest_bits
= rndbits
& mask
;
293 *current_chunk
-- = highest_bits
;
299 /* now fill in the remaining scm_t_uint32 sized chunks */
300 *current_chunk
-- = scm_the_rng
.random_bits (state
);
303 mpz_import (SCM_I_BIG_MPZ (result
),
306 sizeof (scm_t_uint32
),
310 /* if result >= m, regenerate it (it is important to regenerate
311 all bits in order not to get a distorted distribution) */
312 } while (mpz_cmp (SCM_I_BIG_MPZ (result
), SCM_I_BIG_MPZ (m
)) >= 0);
313 scm_gc_free (random_chunks
,
314 num_chunks
* sizeof (scm_t_uint32
),
315 "random bignum chunks");
316 return scm_i_normbig (result
);
320 * Scheme level representation of random states.
323 scm_t_bits scm_tc16_rstate
;
326 make_rstate (scm_t_rstate
*state
)
328 SCM_RETURN_NEWSMOB (scm_tc16_rstate
, state
);
333 * Scheme level interface.
336 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")));
338 SCM_DEFINE (scm_random
, "random", 1, 1, 0,
340 "Return a number in [0, N).\n"
342 "Accepts a positive integer or real n and returns a\n"
343 "number of the same type between zero (inclusive) and\n"
344 "N (exclusive). The values returned have a uniform\n"
347 "The optional argument @var{state} must be of the type produced\n"
348 "by @code{seed->random-state}. It defaults to the value of the\n"
349 "variable @var{*random-state*}. This object is used to maintain\n"
350 "the state of the pseudo-random-number generator and is altered\n"
351 "as a side effect of the random operation.")
352 #define FUNC_NAME s_scm_random
354 if (SCM_UNBNDP (state
))
355 state
= SCM_VARIABLE_REF (scm_var_random_state
);
356 SCM_VALIDATE_RSTATE (2, state
);
359 scm_t_uint32 m
= SCM_I_INUM (n
);
360 SCM_ASSERT_RANGE (1, n
, m
> 0);
361 return scm_from_uint32 (scm_c_random (SCM_RSTATE (state
), m
));
363 SCM_VALIDATE_NIM (1, n
);
365 return scm_from_double (SCM_REAL_VALUE (n
)
366 * scm_c_uniform01 (SCM_RSTATE (state
)));
369 SCM_WRONG_TYPE_ARG (1, n
);
370 return scm_c_random_bignum (SCM_RSTATE (state
), n
);
374 SCM_DEFINE (scm_copy_random_state
, "copy-random-state", 0, 1, 0,
376 "Return a copy of the random state @var{state}.")
377 #define FUNC_NAME s_scm_copy_random_state
379 if (SCM_UNBNDP (state
))
380 state
= SCM_VARIABLE_REF (scm_var_random_state
);
381 SCM_VALIDATE_RSTATE (1, state
);
382 return make_rstate (scm_the_rng
.copy_rstate (SCM_RSTATE (state
)));
386 SCM_DEFINE (scm_seed_to_random_state
, "seed->random-state", 1, 0, 0,
388 "Return a new random state using @var{seed}.")
389 #define FUNC_NAME s_scm_seed_to_random_state
392 if (SCM_NUMBERP (seed
))
393 seed
= scm_number_to_string (seed
, SCM_UNDEFINED
);
394 SCM_VALIDATE_STRING (1, seed
);
395 res
= make_rstate (scm_c_make_rstate (scm_i_string_chars (seed
),
396 scm_i_string_length (seed
)));
397 scm_remember_upto_here_1 (seed
);
403 SCM_DEFINE (scm_external_to_random_state
, "external->random-state", 1, 0, 0,
405 "Return a new random state using @var{external}.\n"
407 "@var{external} must be an external state representation obtained\n"
408 "from @code{random-state->external}.")
409 #define FUNC_NAME s_scm_external_to_random_state
411 return make_rstate (scm_c_make_rstate_scm (external
));
415 SCM_DEFINE (scm_random_state_to_external
, "random-state->external", 1, 0, 0,
417 "Return an external representation of @var{state}.")
418 #define FUNC_NAME s_scm_random_state_to_external
420 SCM_VALIDATE_RSTATE (1, state
);
421 return scm_the_rng
.expose_rstate (SCM_RSTATE (state
));
425 SCM_DEFINE (scm_random_uniform
, "random:uniform", 0, 1, 0,
427 "Return a uniformly distributed inexact real random number in\n"
429 #define FUNC_NAME s_scm_random_uniform
431 if (SCM_UNBNDP (state
))
432 state
= SCM_VARIABLE_REF (scm_var_random_state
);
433 SCM_VALIDATE_RSTATE (1, state
);
434 return scm_from_double (scm_c_uniform01 (SCM_RSTATE (state
)));
438 SCM_DEFINE (scm_random_normal
, "random:normal", 0, 1, 0,
440 "Return an inexact real in a normal distribution. The\n"
441 "distribution used has mean 0 and standard deviation 1. For a\n"
442 "normal distribution with mean m and standard deviation d use\n"
443 "@code{(+ m (* d (random:normal)))}.")
444 #define FUNC_NAME s_scm_random_normal
446 if (SCM_UNBNDP (state
))
447 state
= SCM_VARIABLE_REF (scm_var_random_state
);
448 SCM_VALIDATE_RSTATE (1, state
);
449 return scm_from_double (scm_c_normal01 (SCM_RSTATE (state
)));
454 vector_scale_x (SCM v
, double c
)
457 if (scm_is_simple_vector (v
))
459 n
= SCM_SIMPLE_VECTOR_LENGTH (v
);
461 SCM_REAL_VALUE (SCM_SIMPLE_VECTOR_REF (v
, n
)) *= c
;
465 /* must be a f64vector. */
466 scm_t_array_handle handle
;
471 elts
= scm_f64vector_writable_elements (v
, &handle
, &len
, &inc
);
473 for (i
= 0; i
< len
; i
++, elts
+= inc
)
476 scm_array_handle_release (&handle
);
481 vector_sum_squares (SCM v
)
485 if (scm_is_simple_vector (v
))
487 n
= SCM_SIMPLE_VECTOR_LENGTH (v
);
490 x
= SCM_REAL_VALUE (SCM_SIMPLE_VECTOR_REF (v
, n
));
496 /* must be a f64vector. */
497 scm_t_array_handle handle
;
502 elts
= scm_f64vector_elements (v
, &handle
, &len
, &inc
);
504 for (i
= 0; i
< len
; i
++, elts
+= inc
)
510 scm_array_handle_release (&handle
);
515 /* For the uniform distribution on the solid sphere, note that in
516 * this distribution the length r of the vector has cumulative
517 * distribution r^n; i.e., u=r^n is uniform [0,1], so r can be
518 * generated as r=u^(1/n).
520 SCM_DEFINE (scm_random_solid_sphere_x
, "random:solid-sphere!", 1, 1, 0,
522 "Fills @var{vect} with inexact real random numbers the sum of\n"
523 "whose squares is less than 1.0. Thinking of @var{vect} as\n"
524 "coordinates in space of dimension @var{n} @math{=}\n"
525 "@code{(vector-length @var{vect})}, the coordinates are\n"
526 "uniformly distributed within the unit @var{n}-sphere.")
527 #define FUNC_NAME s_scm_random_solid_sphere_x
529 if (SCM_UNBNDP (state
))
530 state
= SCM_VARIABLE_REF (scm_var_random_state
);
531 SCM_VALIDATE_RSTATE (2, state
);
532 scm_random_normal_vector_x (v
, state
);
534 pow (scm_c_uniform01 (SCM_RSTATE (state
)),
535 1.0 / scm_c_generalized_vector_length (v
))
536 / sqrt (vector_sum_squares (v
)));
537 return SCM_UNSPECIFIED
;
541 SCM_DEFINE (scm_random_hollow_sphere_x
, "random:hollow-sphere!", 1, 1, 0,
543 "Fills vect with inexact real random numbers\n"
544 "the sum of whose squares is equal to 1.0.\n"
545 "Thinking of vect as coordinates in space of\n"
546 "dimension n = (vector-length vect), the coordinates\n"
547 "are uniformly distributed over the surface of the\n"
549 #define FUNC_NAME s_scm_random_hollow_sphere_x
551 if (SCM_UNBNDP (state
))
552 state
= SCM_VARIABLE_REF (scm_var_random_state
);
553 SCM_VALIDATE_RSTATE (2, state
);
554 scm_random_normal_vector_x (v
, state
);
555 vector_scale_x (v
, 1 / sqrt (vector_sum_squares (v
)));
556 return SCM_UNSPECIFIED
;
561 SCM_DEFINE (scm_random_normal_vector_x
, "random:normal-vector!", 1, 1, 0,
563 "Fills vect with inexact real random numbers that are\n"
564 "independent and standard normally distributed\n"
565 "(i.e., with mean 0 and variance 1).")
566 #define FUNC_NAME s_scm_random_normal_vector_x
569 scm_t_array_handle handle
;
570 scm_t_array_dim
*dim
;
572 if (SCM_UNBNDP (state
))
573 state
= SCM_VARIABLE_REF (scm_var_random_state
);
574 SCM_VALIDATE_RSTATE (2, state
);
576 scm_generalized_vector_get_handle (v
, &handle
);
577 dim
= scm_array_handle_dims (&handle
);
579 if (scm_is_vector (v
))
581 SCM
*elts
= scm_array_handle_writable_elements (&handle
);
582 for (i
= dim
->lbnd
; i
<= dim
->ubnd
; i
++, elts
+= dim
->inc
)
583 *elts
= scm_from_double (scm_c_normal01 (SCM_RSTATE (state
)));
587 /* must be a f64vector. */
588 double *elts
= scm_array_handle_f64_writable_elements (&handle
);
589 for (i
= dim
->lbnd
; i
<= dim
->ubnd
; i
++, elts
+= dim
->inc
)
590 *elts
= scm_c_normal01 (SCM_RSTATE (state
));
593 scm_array_handle_release (&handle
);
595 return SCM_UNSPECIFIED
;
599 SCM_DEFINE (scm_random_exp
, "random:exp", 0, 1, 0,
601 "Return an inexact real in an exponential distribution with mean\n"
602 "1. For an exponential distribution with mean u use (* u\n"
604 #define FUNC_NAME s_scm_random_exp
606 if (SCM_UNBNDP (state
))
607 state
= SCM_VARIABLE_REF (scm_var_random_state
);
608 SCM_VALIDATE_RSTATE (1, state
);
609 return scm_from_double (scm_c_exp1 (SCM_RSTATE (state
)));
617 /* plug in default RNG */
620 sizeof (scm_t_i_rstate
),
621 (scm_t_uint32 (*)()) scm_i_uniform32
,
622 (void (*)()) scm_i_init_rstate
,
623 (scm_t_rstate
*(*)()) scm_i_copy_rstate
,
624 (void (*)(scm_t_rstate
*, SCM
)) scm_i_init_rstate_scm
,
625 (SCM (*)(scm_t_rstate
*)) scm_i_expose_rstate
629 scm_tc16_rstate
= scm_make_smob_type ("random-state", 0);
631 for (m
= 1; m
<= 0x100; m
<<= 1)
632 for (i
= m
>> 1; i
< m
; ++i
)
633 scm_masktab
[i
] = m
- 1;
635 #include "libguile/random.x"
637 scm_add_feature ("random");