1/*  Part of SWI-Prolog
    2
    3    Author:        R.A. O'Keefe, V.S. Costa, L. Damas, Jan Wielemaker
    4    E-mail:        J.Wielemaker@vu.nl
    5    WWW:           http://www.swi-prolog.org
    6    Copyright (c)  2011-2016, Universidade do Porto, University of Amsterdam,
    7                              VU University Amsterdam.
    8    All rights reserved.
    9
   10    Redistribution and use in source and binary forms, with or without
   11    modification, are permitted provided that the following conditions
   12    are met:
   13
   14    1. Redistributions of source code must retain the above copyright
   15       notice, this list of conditions and the following disclaimer.
   16
   17    2. Redistributions in binary form must reproduce the above copyright
   18       notice, this list of conditions and the following disclaimer in
   19       the documentation and/or other materials provided with the
   20       distribution.
   21
   22    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   23    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   24    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
   25    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
   26    COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
   27    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
   28    BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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   30    CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   31    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
   32    ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
   33    POSSIBILITY OF SUCH DAMAGE.
   34*/
   35
   36:- module(random,
   37          [ random/1,                   % -Float (0,1)
   38            random_between/3,           % +Low, +High, -Random
   39
   40            getrand/1,                  % -State
   41            setrand/1,                  % +State
   42
   43            maybe/0,
   44            maybe/1,                    % +P
   45            maybe/2,                    % +K, +N
   46
   47            random_perm2/4,             % A,B, X,Y
   48
   49            random_member/2,            % -Element, +List
   50            random_select/3,            % ?Element, +List, -Rest
   51
   52            randseq/3,                  % +Size, +Max, -Set
   53            randset/3,                  % +Size, +Max, -List
   54            random_permutation/2,       % ?List, ?Permutation
   55
   56                                        % deprecated interface
   57            random/3                    % +Low, +High, -Random
   58          ]).   59:- use_module(library(pairs)).   60:- use_module(library(error)).   61:- use_module(library(lists)).

   74check_gmp :-
   75    current_arithmetic_function(random_float),
   76    !.
   77check_gmp :-
   78    print_message(warning, random(no_gmp)).
   79
   80:- initialization check_gmp.   81
   82
   83                 /*******************************
   84                 *         PRIMITIVES           *
   85                 *******************************/

 random(-R:float) is det

Binds R to a new random float in the open interval (0.0,1.0).

See also

- setrand/1, getrand/1 may be used to fetch/set the state.

- In SWI-Prolog, random/1 is implemented by the function random_float/0.

   95random(R) :-
   96    R is random_float.

 random_between(+L:int, +U:int, -R:int) is semidet

Binds R to a random integer in [L,U] (i.e., including both L and U). Fails silently if U<L.

  103random_between(L, U, R) :-
  104    integer(L), integer(U),
  105    !,
  106    U >= L,
  107    R is L+random((U+1)-L).
  108random_between(L, U, _) :-
  109    must_be(integer, L),
  110    must_be(integer, U).

 random(+L:int, +U:int, -R:int) is det

random(+L:float, +U:float, -R:float) is det

Generate a random integer or float in a range. If L and U are both integers, R is a random integer in the half open interval [L,U). If L and U are both floats, R is a float in the open interval (L,U).

deprecated

- Please use random/1 for generating a random float and random_between/3 for generating a random integer. Note that random_between/3 includes the upper bound, while this predicate excludes it.

  126random(L, U, R) :-
  127    integer(L), integer(U),
  128    !,
  129    R is L+random(U-L).
  130random(L, U, R) :-
  131    number(L), number(U),
  132    !,
  133    R is L+((U-L)*random_float).
  134random(L, U, _) :-
  135    must_be(number, L),
  136    must_be(number, U).
  137
  138
  139                 /*******************************
  140                 *             STATE            *
  141                 *******************************/

 setrand(+State) is det

 getrand(-State) is det

Query/set the state of the random generator. This is intended for restarting the generator at a known state only. The predicate setrand/1 accepts an opaque term returned by getrand/1. This term may be asserted, written and read. The application may not make other assumptions about this term.

For compatibility reasons with older versions of this library, setrand/1 also accepts a term rand(A,B,C), where A, B and C are integers in the range 1..30,000. This argument is used to seed the random generator. Deprecated.

Errors

- existence_error(random_state, _) is raised if the underlying infrastructure cannot fetch the random state. This is currently the case if SWI-Prolog is not compiled with the GMP library.

See also

- set_random/1 and random_property/1 provide the SWI-Prolog native implementation.

  164setrand(rand(A,B,C)) :-
  165    !,
  166    Seed is A<<30+B<<15+C,
  167    set_random(seed(Seed)).
  168setrand(State) :-
  169    set_random(state(State)).
  170
  171:- if(current_predicate(random_property/1)).  172getrand(State) :-
  173    random_property(state(State)).
  174:- else.  175getrand(State) :-
  176    existence_error(random_state, State).
  177:- endif.  178
  179
  180                 /*******************************
  181                 *            MAYBE             *
  182                 *******************************/

 maybe is semidet

Succeed/fail with equal probability (variant of maybe/1).

  188maybe :-
  189    random(2) =:= 0.

 maybe(+P) is semidet

Succeed with probability P, fail with probability 1-P

  195maybe(P) :-
  196    must_be(between(0.0,1.0), P),
  197    random_float < P.

 maybe(+K, +N) is semidet

Succeed with probability K/N (variant of maybe/1)

  203maybe(K, N) :-
  204    integer(K), integer(N),
  205    between(0, N, K),
  206    !,
  207    random(N) < K.
  208maybe(K, N) :-
  209    must_be(nonneg, K),
  210    must_be(nonneg, N),
  211    domain_error(not_less_than_zero,N-K).
  212
  213
  214                 /*******************************
  215                 *          PERMUTATION         *
  216                 *******************************/

 random_perm2(?A, ?B, ?X, ?Y) is semidet

Does X=A,Y=B or X=B,Y=A with equal probability.

  222random_perm2(A,B, X,Y) :-
  223    (   maybe
  224    ->  X = A, Y = B
  225    ;   X = B, Y = A
  226    ).
  227
  228
  229                 /*******************************
  230                 *    SET AND LIST OPERATIONS   *
  231                 *******************************/

 random_member(-X, +List:list) is semidet

X is a random member of List. Equivalent to random_between(1, |List|), followed by nth1/3. Fails of List is the empty list.

Compatibility

- Quintus and SICStus libraries.

  240random_member(X, List) :-
  241    must_be(list, List),
  242    length(List, Len),
  243    Len > 0,
  244    N is random(Len),
  245    nth0(N, List, X).

 random_select(-X, +List, -Rest) is semidet

random_select(+X, -List, +Rest) is det

Randomly select or insert an element. Either List or Rest must be a list. Fails if List is the empty list.

Compatibility

- Quintus and SICStus libraries.

  255random_select(X, List, Rest) :-
  256    (   '$skip_list'(Len, List, Tail),
  257        Tail == []
  258    ->  true
  259    ;   '$skip_list'(RLen, Rest, Tail),
  260        Tail == []
  261    ->  Len is RLen+1
  262    ),
  263    !,
  264    Len > 0,
  265    N is random(Len),
  266    nth0(N, List, X, Rest).
  267random_select(_, List, Rest) :-
  268    partial_list(List), partial_list(Rest),
  269    instantiation_error(List+Rest).
  270random_select(_, List, Rest) :-
  271    must_be(list, List),
  272    must_be(list, Rest).

 randset(+K:int, +N:int, -S:list(int)) is det

S is a sorted list of K unique random integers in the range 1..N. Implemented by enumerating 1..N and deciding whether or not the number should be part of the set. For example:

?- randset(5, 5, S).
S = [1, 2, 3, 4, 5].          (always)
?- randset(5, 20, S).
S = [2, 7, 10, 19, 20].

See also

- randseq/3.

bug

- Slow if N is large and K is small.

  290randset(K, N, S) :-
  291    must_be(nonneg, K),
  292    K =< N,
  293    randset(K, N, [], S).
  294
  295randset(0, _, S, S) :- !.
  296randset(K, N, Si, So) :-
  297    random(N) < K,
  298    !,
  299    J is K-1,
  300    M is N-1,
  301    randset(J, M, [N|Si], So).
  302randset(K, N, Si, So) :-
  303    M is N-1,
  304    randset(K, M, Si, So).

 randseq(+K:int, +N:int, -List:list(int)) is det

S is a list of K unique random integers in the range 1..N. The order is random. Works as if defined by the following code.

randseq(K, N, List) :-
      randset(K, N, Set),
      random_permutation(Set, List).

See also

- randset/3.

  321randseq(K, N, S) :-
  322    randseq(K, N, L, []),
  323    keysort(L, R),
  324    pairs_values(R, S).
  325
  326randseq(0, _, S, S) :- !.
  327randseq(K, N, [Y-N|Si], So) :-
  328    random(N) < K,
  329    !,
  330    random(Y),
  331    J is K-1,
  332    M is N-1,
  333    randseq(J, M, Si, So).
  334randseq(K, N, Si, So) :-
  335    M is N-1,
  336    randseq(K, M, Si, So).

 random_permutation(+List, -Permutation) is det

random_permutation(-List, +Permutation) is det

Permutation is a random permutation of List. This is intended to process the elements of List in random order. The predicate is symmetric.

Errors

- instantiation_error, type_error(list, _).

  347random_permutation(List1, List2) :-
  348    is_list(List1),
  349    !,
  350    random_permutation_(List1, List2).
  351random_permutation(List1, List2) :-
  352    is_list(List2),
  353    !,
  354    random_permutation_(List2, List1).
  355random_permutation(List1, List2) :-
  356    partial_list(List1), partial_list(List2),
  357    !,
  358    instantiation_error(List1+List2).
  359random_permutation(List1, List2) :-
  360    must_be(list, List1),
  361    must_be(list, List2).
  362
  363random_permutation_(List, RandomPermutation) :-
  364    key_random(List, Keyed),
  365    keysort(Keyed, Sorted),
  366    pairs_values(Sorted, RandomPermutation).
  367
  368key_random([], []).
  369key_random([H|T0], [K-H|T]) :-
  370    random(K),
  371    key_random(T0, T).

 partial_list(@Term) is semidet

True if Term is a partial list.

  377partial_list(List) :-
  378    '$skip_list'(_, List, Tail),
  379    var(Tail).
  380
  381:- multifile
  382    prolog:message//1.  383
  384prolog:message(random(no_gmp)) -->
  385    [ 'This version of SWI-Prolog is not compiled with GMP support.'-[], nl,
  386      'Floating point random operations are not supported.'-[]
  387    ]