/* Part of SWI-Prolog Author: R.A. O'Keefe, V.S. Costa, L. Damas, Jan Wielemaker E-mail: J.Wielemaker@vu.nl WWW: http://www.swi-prolog.org Copyright (c) 2011-2016, Universidade do Porto, University of Amsterdam, VU University Amsterdam. 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. 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. */ :- module(random, [ random/1, % -Float (0,1) random_between/3, % +Low, +High, -Random getrand/1, % -State setrand/1, % +State maybe/0, maybe/1, % +P maybe/2, % +K, +N random_perm2/4, % A,B, X,Y random_member/2, % -Element, +List random_select/3, % ?Element, +List, -Rest random_subseq/3, % ?List, ?Subseq, ?Complement randseq/3, % +Size, +Max, -Set randset/3, % +Size, +Max, -List random_permutation/2, % ?List, ?Permutation random_numlist/4, % +P, +L, +U, -List % deprecated interface random/3 % +Low, +High, -Random ]). :- autoload(library(apply),[maplist/2]). :- autoload(library(error), [must_be/2,domain_error/2,instantiation_error/1]). :- autoload(library(lists),[nth0/3,nth0/4,append/3]). :- autoload(library(pairs),[pairs_values/2]). /** Random numbers This library is derived from the DEC10 library random. Later, the core random generator was moved to C. The current version uses the SWI-Prolog arithmetic functions to realise this library. These functions are based on the GMP library. @author R.A. O'Keefe, V.S. Costa, L. Damas, Jan Wielemaker @see Built-in function random/1: A is random(10) */ check_gmp :- current_arithmetic_function(random_float), !. check_gmp :- print_message(warning, random(no_gmp)). :- initialization check_gmp. /******************************* * PRIMITIVES * *******************************/ %! random(-R:float) is det. % % Binds R to a new random float in the _open_ interval (0.0,1.0). % % @see setrand/1, getrand/1 may be used to fetch/set the state. % @see In SWI-Prolog, random/1 is implemented by the function % random_float/0. random(R) :- 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, R is L+random((U+1)-L). random_between(L, U, _) :- must_be(integer, L), 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. random(L, U, R) :- integer(L), integer(U), !, R is L+random(U-L). random(L, U, R) :- number(L), number(U), !, R is L+((U-L)*random_float). random(L, U, _) :- must_be(number, L), must_be(number, U). /******************************* * STATE * *******************************/ %! 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. % % @see set_random/1 and random_property/1 provide the SWI-Prolog % native implementation. % @error 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. setrand(rand(A,B,C)) :- !, Seed is A<<30+B<<15+C, set_random(seed(Seed)). setrand(State) :- set_random(state(State)). :- if(current_predicate(random_property/1)). getrand(State) :- random_property(state(State)). :- else. getrand(State) :- existence_error(random_state, State). :- endif. /******************************* * MAYBE * *******************************/ %! maybe is semidet. % % Succeed/fail with equal probability (variant of maybe/1). maybe :- random(2) =:= 0. %! maybe(+P) is semidet. % % Succeed with probability P, fail with probability 1-P maybe(P) :- must_be(between(0.0,1.0), P), random_float < P. %! maybe(+K, +N) is semidet. % % Succeed with probability K/N (variant of maybe/1) maybe(K, N) :- integer(K), integer(N), between(0, N, K), !, random(N) < K. maybe(K, N) :- must_be(nonneg, K), must_be(nonneg, N), domain_error(not_less_than_zero,N-K). /******************************* * PERMUTATION * *******************************/ %! random_perm2(?A, ?B, ?X, ?Y) is semidet. % % Does X=A,Y=B or X=B,Y=A with equal probability. random_perm2(A,B, X,Y) :- ( maybe -> X = A, Y = B ; X = B, Y = A ). /******************************* * SET AND LIST OPERATIONS * *******************************/ %! 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. % % @compat Quintus and SICStus libraries. random_member(X, List) :- must_be(list, List), length(List, Len), Len > 0, N is random(Len), 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. % % @compat Quintus and SICStus libraries. random_select(X, List, Rest) :- ( '$skip_list'(Len, List, Tail), Tail == [] -> true ; '$skip_list'(RLen, Rest, Tail), Tail == [] -> Len is RLen+1 ), !, Len > 0, N is random(Len), nth0(N, List, X, Rest). random_select(_, List, Rest) :- partial_list(List), partial_list(Rest), instantiation_error(List+Rest). random_select(_, List, Rest) :- must_be(list, List), must_be(list, Rest). %! random_subseq(+List, -Subseq, -Complement) is det. %! random_subseq(-List, +Subseq, +Complement) is semidet. % % Selects a random subsequence Subseq of List, with Complement % containing all elements of List that were not selected. Each element % of List is included with equal probability in either Subseq or % Complement. % % random_subseq/3 may also be called with Subseq and Complement bound % and List unbound, which will recreate List by randomly interleaving % Subseq and Complement. This mode may fail randomly, matching SICStus % behavior. The failure probability corresponds to the probability of % the "forward" mode selecting a Subseq/Complement combination with % different lengths. % % @compat SICStus 4 random_subseq([], [], []). random_subseq([Head|Tail], Subseq, Complement) :- ( maybe -> Subseq = [Head|SubTail], Complement = CompTail ; Subseq = SubTail, Complement = [Head|CompTail] ), random_subseq(Tail, SubTail, CompTail). %! 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. % The implementation uses different techniques depending on the ratio % K/N. For small K/N it generates a set of K random numbers, removes % the duplicates and adds more numbers until |S| is K. For a large K/N % it enumerates 1..N and decides randomly to include the number or % not. For example: % % == % ?- randset(5, 5, S). % S = [1, 2, 3, 4, 5]. (always) % ?- randset(5, 20, S). % S = [2, 7, 10, 19, 20]. % == % % @see randseq/3. randset(K, N, S) :- must_be(nonneg, K), K =< N, ( K < N//7 -> randsetn(K, N, [], S) ; randset(K, N, [], S) ). randset(0, _, S, S) :- !. randset(K, N, Si, So) :- random(N) < K, !, J is K-1, M is N-1, randset(J, M, [N|Si], So). randset(K, N, Si, So) :- M is N-1, randset(K, M, Si, So). randsetn(K, N, Sofar, S) :- length(Sofar, Len), ( Len =:= K -> S = Sofar ; Needed is K-Len, length(New, Needed), maplist(srand(N), New), ( Sofar == [] -> sort(New, Sorted) ; append(New, Sofar, Sofar2), sort(Sofar2, Sorted) ), randsetn(K, N, Sorted, S) ). srand(N, E) :- E is random(N)+1. %! 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. Defined as % % ``` % randseq(K, N, List) :- % randset(K, N, Set), % random_permutation(Set, List). % ``` % % @see randset/3. randseq(K, N, Seq) :- randset(K, N, Set), random_permutation_(Set, Seq). %! 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. % % @error instantiation_error, type_error(list, _). random_permutation(List1, List2) :- is_list(List1), !, random_permutation_(List1, List2). random_permutation(List1, List2) :- is_list(List2), !, random_permutation_(List2, List1). random_permutation(List1, List2) :- partial_list(List1), partial_list(List2), !, instantiation_error(List1+List2). random_permutation(List1, List2) :- must_be(list, List1), must_be(list, List2). random_permutation_(List, RandomPermutation) :- key_random(List, Keyed), keysort(Keyed, Sorted), pairs_values(Sorted, RandomPermutation). key_random([], []). key_random([H|T0], [K-H|T]) :- random(K), key_random(T0, T). %! random_numlist(+P, +L, +U, -List) is det. % % Unify List with an ascending list of integers between L and U % (inclusive). Each integer in the range L..U is included with % probability P. % % @compat SICStus 4 random_numlist(P, L, U, List) :- must_be(between(0.0, 1.0), P), must_be(integer, L), must_be(integer, U), random_numlist_(P, L, U, List). random_numlist_(_P, L, U, List) :- L > U, !, List = []. random_numlist_(P, L, U, List) :- ( maybe(P) -> List = [L|Tail] ; List = Tail ), L1 is L + 1, random_numlist_(P, L1, U, Tail). %! partial_list(@Term) is semidet. % % True if Term is a partial list. partial_list(List) :- '$skip_list'(_, List, Tail), var(Tail). :- multifile prolog:message//1. prolog:message(random(no_gmp)) --> [ 'This version of SWI-Prolog is not compiled with GMP support.'-[], nl, 'Floating point random operations are not supported.'-[] ].