189 lines
6.1 KiB
OCaml
189 lines
6.1 KiB
OCaml
(***********************************************************************)
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(* *)
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(* Objective Caml *)
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(* *)
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(* Damien Doligez, projet Para, INRIA Rocquencourt *)
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(* *)
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(* Copyright 1996 Institut National de Recherche en Informatique et *)
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(* en Automatique. All rights reserved. This file is distributed *)
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(* under the terms of the GNU Library General Public License. *)
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(* *)
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(***********************************************************************)
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(* $Id$ *)
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(* "Linear feedback shift register" random number generator. *)
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(* References: Robert Sedgewick, "Algorithms", Addison-Wesley *)
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(* The PRNG is a linear feedback shift register.
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It is seeded by a MD5-based PRNG.
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*)
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(* This is the state you get with [init 27182818] on a 32-bit machine. *)
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let state = [|
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561073064; 1051173471; 764306064; 9858203; 1023641486; 615350359;
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552627506; 486882977; 147054819; 951240904; 869261341; 71648846; 848741663;
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337696531; 66770770; 473370118; 998499212; 477485839; 814302728; 281896889;
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206134737; 796925167; 762624501; 971004788; 878960411; 233350272;
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965168955; 933858406; 572927557; 708896334; 32881167; 462134267; 868098973;
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768795410; 567327260; 4136554; 268309077; 804670393; 854580894; 781847598;
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310632349; 22990936; 187230644; 714526560; 146577263; 979459837; 514922558;
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414383108; 21528564; 896816596; 33747835; 180326017; 414576093; 124177607;
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440266690
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|]
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let j = ref 0
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(* Returns 30 random bits as an integer 0 <= x < 1073741824 *)
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let bits () =
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j := (!j + 1) mod 55;
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let newval =
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Array.unsafe_get state ((!j+24) mod 55) + Array.unsafe_get state !j in
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Array.unsafe_set state !j newval;
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newval land 0x3FFFFFFF
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(* Returns a float 0 <= x < 1 with at most 90 bits of precision. *)
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let rawfloat () =
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let scale = 1073741824.0
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and r0 = float (bits ())
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and r1 = float (bits ())
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and r2 = float (bits ())
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in ((r0 /. scale +. r1) /. scale +. r2) /. scale
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let rec intaux n =
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let r = bits () in
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if r >= n then intaux n else r
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let int bound =
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if bound > 0x3FFFFFFF || bound <= 0
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then invalid_arg "Random.int"
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else (intaux (0x3FFFFFFF / bound * bound)) mod bound
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let float bound = rawfloat () *. bound
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(* Simple initialisation. The seed is an integer.
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Two seeds that are close enough will not produce uncorrelated
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pseudo-random sequences.
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*)
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let init seed =
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let st = ref seed in
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let mdg () =
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st := !st + 1;
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let d = Digest.string (string_of_int !st) in
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(Char.code d.[0] + (Char.code d.[1] lsl 8) + (Char.code d.[2] lsl 16))
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lxor (Char.code d.[3] lsl 22)
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in
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for i = 0 to 54 do
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Array.unsafe_set state i (mdg ())
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done;
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j := 0
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(* Full initialisation. The seed is an array of integers. *)
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let full_init seed =
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init 27182818;
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for i = 0 to Array.length (seed) - 1 do
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let j = i mod 55 in
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Array.unsafe_set state j
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(Array.unsafe_get state j + Array.unsafe_get seed i)
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done
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(* Low-entropy system-dependent initialisation. *)
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external random_seed: unit -> int = "sys_random_seed";;
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let self_init () = init (random_seed());;
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(********************
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(* Test functions. Not included in the library.
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The [chisquare] function should be called with n > 10r.
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It returns a triple (low, actual, high).
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If low <= actual <= high, the [g] function passed the test,
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otherwise it failed.
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Some results:
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Random.init 27182818; chisquare Random.int 100000 1000;;
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Random.init 27182818; chisquare Random.int 100000 100;;
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Random.init 27182818; chisquare Random.int 100000 5000;;
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Random.init 27182818; chisquare Random.int 1000000 1000;;
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Random.init 27182818; chisquare Random.int 100000 1024;;
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Random.init 299792643; chisquare Random.int 100000 1024;;
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Random.init 14142136; chisquare Random.int 100000 1024;;
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Random.init 27182818; init_diff 1024; chisquare diff 100000 1024;;
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Random.init 27182818; init_diff 100; chisquare diff 100000 100;;
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Random.init 27182818; init_diff2 1024; chisquare diff2 100000 1024;;
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Random.init 27182818; init_diff2 100; chisquare diff2 100000 100;;
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Random.init 14142136; init_diff2 100; chisquare diff2 100000 100;;
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Random.init 299792643; init_diff2 100; chisquare diff2 100000 100;;
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- : float * float * float = 936.754446797, 948.8, 1063.2455532
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#- : float * float * float = 80, 80.076, 120
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#- : float * float * float = 4858.57864376, 4767.5, 5141.42135624 <==
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#- : float * float * float = 936.754446797, 951.2, 1063.2455532
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#- : float * float * float = 960, 1028.31104, 1088
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#- : float * float * float = 960, 1012.64384, 1088
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#- : float * float * float = 960, 970.25024, 1088
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#- : float * float * float = 960, 982.29248, 1088
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#- : float * float * float = 80, 110.418, 120
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#- : float * float * float = 960, 1022.76096, 1088
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#- : float * float * float = 80, 96.894, 120
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#- : float * float * float = 80, 83.864, 120
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#- : float * float * float = 80, 89.956, 120
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*)
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(* Return the sum of the squares of v[i0,i1[ *)
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let rec sumsq v i0 i1 =
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if i0 >= i1 then 0.0
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else if i1 = i0 + 1 then float v.(i0) *. float v.(i0)
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else sumsq v i0 ((i0+i1)/2) +. sumsq v ((i0+i1)/2) i1
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;;
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let chisquare g n r =
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if n <= 10 * r then invalid_arg "chisquare";
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let f = Array.make r 0 in
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for i = 1 to n do
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let t = g r in
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f.(t) <- f.(t) + 1
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done;
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let t = sumsq f 0 r
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and r = float r
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and n = float n in
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let sr = 2.0 *. sqrt r in
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(r -. sr, (r *. t /. n) -. n, r +. sr)
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;;
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(* This is to test for linear dependencies between successive random numbers.
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*)
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let st = ref 0;;
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let init_diff r = st := Random.int r;;
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let diff r =
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let x1 = !st
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and x2 = Random.int r
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in
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st := x2;
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if x1 >= x2 then
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x1 - x2
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else
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r + x1 - x2
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;;
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let st1 = ref 0
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and st2 = ref 0
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;;
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(* This is to test for quadratic dependencies between successive random
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numbers.
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*)
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let init_diff2 r = st1 := Random.int r; st2 := Random.int r;;
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let diff2 r =
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let x1 = !st1
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and x2 = !st2
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and x3 = Random.int r
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in
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st1 := x2;
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st2 := x3;
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(x3 - x2 - x2 + x1 + 2*r) mod r
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;;
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********************)
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