tasks a-s

Task/Random-numbers/0DESCRIPTION

@@ -0,0 +1,3 @@
+The goal of this task is to generate a collection filled with 1000 normally distributed random (or pseudorandom)  numbers with a mean of 1.0 and a [[wp:Standard_deviation|standard deviation]] of 0.5
+
+Many libraries only generate uniformly distributed random numbers. If so, use [[wp:Normal_distribution#Generating_values_from_normal_distribution|this formula]] to convert them to a normal distribution.

Task/Random-numbers/1META.yaml

@@ -0,0 +1,4 @@
+---
+category:
+- Probability and statistics
+note: Basic language learning

Task/Random-numbers/ALGOL-68/random-numbers.alg

@@ -0,0 +1,13 @@
+PROC random normal = REAL:  # normal distribution, centered on 0, std dev 1 #
+(
+  sqrt(-2*log(random)) * cos(2*pi*random)
+);
+
+test:(
+  [1000]REAL rands;
+  FOR i TO UPB rands DO
+    rands[i] := 1 + random normal/2
+  OD;
+  INT limit=10;
+  printf(($"("n(limit-1)(-d.6d",")-d.5d" ... )"$, rands[:limit]))
+)

Task/Random-numbers/AWK/random-numbers.awk

@@ -0,0 +1 @@
+$ awk 'func r(){return sqrt(-2*log(rand()))*cos(6.2831853*rand())}BEGIN{for(i=0;i<1000;i++)s=s" "1+0.5*r();print s}'

Task/Random-numbers/Ada/random-numbers.ada

@@ -0,0 +1,23 @@
+with Ada.Numerics;                       use Ada.Numerics;
+with Ada.Numerics.Float_Random;          use Ada.Numerics.Float_Random;
+with Ada.Numerics.Elementary_Functions;  use Ada.Numerics.Elementary_Functions;
+
+procedure Normal_Random is
+   function Normal_Distribution
+            (  Seed  : Generator;
+               Mu    : Float := 1.0;
+               Sigma : Float := 0.5
+            )  return Float is
+   begin
+      return
+         Mu + (Sigma * Sqrt (-2.0 * Log (Random (Seed), 10.0)) * Cos (2.0 * Pi * Random (Seed)));
+   end Normal_Distribution;
+
+   Seed         : Generator;
+   Distribution : array (1..1_000) of Float;
+begin
+   Reset (Seed);
+   for I in Distribution'Range loop
+      Distribution (I) := Normal_Distribution (Seed);
+   end loop;
+end Normal_Random;

Task/Random-numbers/AutoHotkey/random-numbers.ahk

@@ -0,0 +1,15 @@
+Loop 40
+   R .= RandN(1,0.5) "`n"  ; mean = 1.0, standard deviation = 0.5
+MsgBox %R%
+
+RandN(m,s) { ; Normally distributed random numbers of mean = m, std.dev = s by Box-Muller method
+   Static i, Y
+   If (i := !i) { ; every other call
+      Random U, 0, 1.0
+      Random V, 0, 6.2831853071795862
+      U := sqrt(-2*ln(U))*s
+      Y := m + U*sin(V)
+      Return m + U*cos(V)
+   }
+   Return Y
+}

Task/Random-numbers/BBC-BASIC/random-numbers.bbc

@@ -0,0 +1,11 @@
+      DIM array(999)
+      FOR number% = 0 TO 999
+        array(number%) = 1.0 + 0.5 * SQR(-2*LN(RND(1))) * COS(2*PI*RND(1))
+      NEXT
+
+      mean = SUM(array()) / (DIM(array(),1) + 1)
+      array() -= mean
+      stdev = MOD(array()) / SQR(DIM(array(),1) + 1)
+
+      PRINT "Mean = " ; mean
+      PRINT "Standard deviation = " ; stdev

Task/Random-numbers/C++/random-numbers-1.cpp

@@ -0,0 +1,27 @@
+#include <cstdlib>   // for rand
+#include <cmath>     // for atan, sqrt, log, cos
+#include <algorithm> // for generate_n
+
+double const pi = 4*std::atan(1.0);
+
+// simple functor for normal distribution
+class normal_distribution
+{
+public:
+  normal_distribution(double m, double s): mu(m), sigma(s) {}
+  double operator() const // returns a single normally distributed number
+  {
+    double r1 = (std::rand() + 1.0)/(RAND_MAX + 1.0); // gives equal distribution in (0, 1]
+    double r2 = (std::rand() + 1.0)/(RAND_MAX + 1.0);
+    return mu + sigma * std::sqrt(-2*std::log(r1))*std::cos(2*pi*r2);
+  }
+private:
+  const double mu, sigma;
+};
+
+int main()
+{
+  double array[1000];
+  std::generate_n(array, 1000, normal_distribution(1.0, 0.5));
+  return 0;
+}

Task/Random-numbers/C++/random-numbers-2.cpp

@@ -0,0 +1,20 @@
+#include <vector>
+#include "boost/random.hpp"
+#include "boost/generator_iterator.hpp"
+#include <boost/random/normal_distribution.hpp>
+#include <algorithm>
+
+typedef boost::mt19937 RNGType; ///< mersenne twister generator
+
+int main() {
+    RNGType rng;
+    boost::normal_distribution<> rdist(1.0,0.5); /**< normal distribution
+                           with mean of 1.0 and standard deviation of 0.5 */
+
+    boost::variate_generator< RNGType, boost::normal_distribution<> >
+                    get_rand(rng, rdist);
+
+    std::vector<double> v(1000);
+    generate(v.begin(),v.end(),get_rand);
+    return 0;
+}

Task/Random-numbers/C++/random-numbers-3.cpp

@@ -0,0 +1,17 @@
+#include <random>
+#include <functional>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+int main()
+{
+  random_device seed;
+  mt19937 engine(seed());
+  normal_distribution<> dist(1.0, 0.5);
+  auto rnd = bind(dist, engine);
+
+  vector<double> v(1000);
+  generate(v.begin(), v.end(), rnd);
+  return 0;
+}

Task/Random-numbers/C-sharp/random-numbers-1.cs

@@ -0,0 +1,4 @@
+private static double randomNormal()
+{
+	return Math.Cos(2 * Math.PI * tRand.NextDouble()) * Math.Sqrt(-2 * Math.Log(tRand.NextDouble()));
+}

Task/Random-numbers/C-sharp/random-numbers-2.cs

@@ -0,0 +1,27 @@
+static Random tRand = new Random();
+
+static void Main(string[] args)
+{
+	double[] a = new double[1000];
+
+	double tAvg = 0;
+	for (int x = 0; x < a.Length; x++)
+	{
+		a[x] = randomNormal() / 2 + 1;
+		tAvg += a[x];
+	}
+
+	tAvg /= a.Length;
+	Console.WriteLine("Average: " + tAvg.ToString());
+
+	double s = 0;
+	for (int x = 0; x < a.Length; x++)
+	{
+		s += Math.Pow((a[x] - tAvg), 2);
+	}
+	s = Math.Sqrt(s / 1000);
+
+	Console.WriteLine("Standard Deviation: " + s.ToString());
+
+	Console.ReadLine();
+}

Task/Random-numbers/C/random-numbers.c

@@ -0,0 +1,22 @@
+#include <stdlib.h>
+#include <math.h>
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+double drand()   /* uniform distribution, (0..1] */
+{
+  return (rand()+1.0)/(RAND_MAX+1.0);
+}
+double random_normal()  /* normal distribution, centered on 0, std dev 1 */
+{
+  return sqrt(-2*log(drand())) * cos(2*M_PI*drand());
+}
+int main()
+{
+  int i;
+  double rands[1000];
+  for (i=0; i<1000; i++)
+    rands[i] = 1.0 + 0.5*random_normal();
+  return 0;
+}

Task/Random-numbers/Clojure/random-numbers.clj

@@ -0,0 +1,4 @@
+(import '(java.util Random))
+(def normals
+  (let [r (Random.)]
+    (take 1000 (repeatedly #(-> r .nextGaussian (* 0.5) (+ 1.0))))))

Task/Random-numbers/Common-Lisp/random-numbers.lisp

@@ -0,0 +1,2 @@
+(loop for i from 1 to 1000
+      collect (1+ (* (sqrt (* -2 (log (random 1.0)))) (cos (* 2 pi (random 1.0))) 0.5)))

Task/Random-numbers/D/random-numbers-1.d

@@ -0,0 +1,24 @@
+import std.stdio, std.random, std.math;
+
+struct NormalRandom {
+    double mean, stdDev;
+
+    // needed because it also defines an opCall
+    this(in double mean_, in double stdDev_) pure nothrow {
+        this.mean = mean_;
+        this.stdDev = stdDev_;
+    }
+
+    double opCall() const /*nothrow*/ {
+        immutable double r1 = uniform(0.0, 1.0);
+        immutable double r2 = uniform(0.0, 1.0);
+        return mean + stdDev * sqrt(-2 * log(r1)) * cos(2 * PI * r2);
+    }
+}
+
+void main() {
+    double[1000] array;
+    auto nrnd = NormalRandom(1.0, 0.5);
+    foreach (ref x; array)
+        x = nrnd();
+}

Task/Random-numbers/D/random-numbers-2.d

@@ -0,0 +1,10 @@
+import tango.math.random.Random;
+
+void main() {
+    double[1000] list;
+    auto r = new Random();
+    foreach (ref l; list) {
+        r.normalSource!(double)()(l);
+        l = 1.0 + 0.5 * l;
+    }
+}

Task/Random-numbers/DWScript/random-numbers.dwscript

@@ -0,0 +1,5 @@
+var values : array [0..999] of Float;
+var i : Integer;
+
+for i := values.Low to values.High do
+   values := RandG(1, 0.5);

Task/Random-numbers/Delphi/random-numbers.delphi

@@ -0,0 +1,19 @@
+program Randoms;
+
+{$APPTYPE CONSOLE}
+
+uses
+  Math;
+
+var
+  Values: array[0..999] of Double;
+  I: Integer;
+
+begin
+//  Randomize;   Commented to obtain reproducible results
+  for I:= Low(Values) to High(Values) do
+    Values[I]:= RandG(1.0, 0.5);  // Mean = 1.0, StdDev = 0.5
+  Writeln('Mean          = ', Mean(Values):6:4);
+  Writeln('Std Deviation = ', StdDev(Values):6:4);
+  Readln;
+end.

Task/Random-numbers/E/random-numbers.e

@@ -0,0 +1 @@
+accum [] for _ in 1..1000 { _.with(entropy.nextGaussian()) }

Task/Random-numbers/Eiffel/random-numbers.e

@@ -0,0 +1,95 @@
+class
+	APPLICATION
+
+inherit
+	ARGUMENTS
+
+create
+	make
+
+feature {NONE} -- Initialization
+
+	l_time: TIME
+	l_seed: INTEGER
+	math:DOUBLE_MATH
+	rnd:RANDOM
+	Size:INTEGER
+		once
+			Result:= 1000
+		end
+
+	make
+			-- Run application.
+		local
+			ergebnis:ARRAY[DOUBLE]
+			tavg: DOUBLE
+			x: INTEGER
+			tmp: DOUBLE
+			text : STRING
+
+		do
+			-- initialize random generator
+			create l_time.make_now
+     		        l_seed := l_time.hour
+      		        l_seed := l_seed * 60 + l_time.minute
+      		        l_seed := l_seed * 60 + l_time.second
+      		        l_seed := l_seed * 1000 + l_time.milli_second
+      		        create rnd.set_seed (l_seed)
+
+			-- initialize random number container and math
+			create ergebnis.make_filled (0.0, 1, size)
+			tavg := 0;
+			create math
+
+			from
+				x := 1
+			until
+				x > ergebnis.count
+			loop
+				tmp := randomNormal / 2 + 1
+				tavg := tavg + tmp
+				ergebnis.enter (tmp , x)
+				x := x + 1
+			end
+
+			tavg := tavg / ergebnis.count
+			text := "Average: "
+			text.append_double (tavg)
+			text.append ("%N")
+			print(text)
+
+			tmp := 0
+			from
+				x:= 1
+			until
+				x > ergebnis.count
+			loop
+				tmp := tmp + (ergebnis.item (x) - tavg)^2
+				x := x + 1
+			end
+
+			tmp := math.sqrt (tmp / ergebnis.count)
+			text := "Standard Deviation: "
+			text.append_double (tmp)
+			text.append ("%N")
+			print(text)
+
+		end
+
+	randomNormal:DOUBLE
+
+		local
+
+      		        first: DOUBLE
+      		        second: DOUBLE
+
+		do
+                        rnd.forth
+                        first := rnd.double_item
+                        rnd.forth
+                        second := rnd.double_item
+
+                        Result := math.cosine (2 * math.pi * first) * math.sqrt (-2 * math.log (second))
+
+		end
+end

Task/Random-numbers/Erlang/random-numbers.erl

@@ -0,0 +1,31 @@
+mean(Values) ->
+    mean(tl(Values), hd(Values), 1).
+
+mean([], Acc, Length) ->
+    Acc / Length;
+mean(Values, Acc, Length) ->
+    mean(tl(Values), hd(Values)+Acc, Length+1).
+
+variance(Values) ->
+    Mean = mean(Values),
+    variance(Values, Mean, 0) / length(Values).
+
+variance([], _, Acc) ->
+    Acc;
+variance(Values, Mean, Acc) ->
+    Diff = hd(Values) - Mean,
+    DiffSqr = Diff * Diff,
+    variance(tl(Values), Mean, Acc + DiffSqr).
+
+stddev(Values) ->
+    math:sqrt(variance(Values)).
+
+normal(Mean, StdDev) ->
+    U = random:uniform(),
+    V = random:uniform(),
+    Mean + StdDev * ( math:sqrt(-2 * math:log(U)) * math:cos(2 * math:pi() * V) ).  % Erlang's math:log is the natural logarithm.
+
+main(_) ->
+    X = [ normal(1.0, 0.5) || _ <- lists:seq(1, 1000) ],
+    io:format("mean = ~w\n", [mean(X)]),
+    io:format("stddev = ~w\n", [stddev(X)]).

Task/Random-numbers/Euler-Math-Toolbox/random-numbers.euler

@@ -0,0 +1,4 @@
+>v=normal(1,1000)*0.5+1;
+>mean(v), dev(v)
+ 1.00291801071
+ 0.498226876528

Task/Random-numbers/Euphoria/random-numbers.euphoria

@@ -0,0 +1,15 @@
+include misc.e
+
+function RandomNormal()
+    atom x1, x2
+    x1 = rand(999999) / 1000000
+    x2 = rand(999999) / 1000000
+    return sqrt(-2*log(x1)) * cos(2*PI*x2)
+end function
+
+constant n = 1000
+sequence s
+s = repeat(0,n)
+for i = 1 to n do
+    s[i] = 1 + 0.5 * RandomNormal()
+end for

Task/Random-numbers/Factor/random-numbers.factor

@@ -0,0 +1 @@
+1000 [ 1.0 0.5 normal-random-float ] replicate

Task/Random-numbers/Fantom/random-numbers-1.fantom

@@ -0,0 +1,17 @@
+class Main
+{
+  static const Float PI := 0.0f.acos * 2  // we need to precompute PI
+
+  static Float randomNormal ()
+  {
+    return (Float.random * PI * 2).cos * (Float.random.log * -2).sqrt
+  }
+
+  public static Void main ()
+  {
+    mean := 1.0f
+    sd := 0.5f
+    Float[] values := [,] // this is the collection to fill with random numbers
+    1000.times { values.add (randomNormal * sd + mean) }
+  }
+}

Task/Random-numbers/Fantom/random-numbers-2.fantom

@@ -0,0 +1,20 @@
+using [java] java.util::Random
+
+class Main
+{
+  Random generator := Random()
+
+  Float randomNormal ()
+  {
+    return generator.nextGaussian
+  }
+
+  public static Void main ()
+  {
+    rnd := Main()  // create an instance of Main class, which holds the generator
+    mean := 1.0f
+    sd := 0.5f
+    Float[] values := [,] // this is the collection to fill with random numbers
+    1000.times { values.add (rnd.randomNormal * sd + mean) }
+  }
+}

Task/Random-numbers/Forth/random-numbers.fth

@@ -0,0 +1,16 @@
+require random.fs
+here to seed
+
+-1. 1 rshift 2constant MAX-D	\ or s" MAX-D" ENVIRONMENT? drop
+
+: frnd ( -- f )			\ uniform distribution 0..1
+  rnd rnd dabs d>f MAX-D d>f f/ ;
+
+: frnd-normal ( -- f )		\ centered on 0, std dev 1
+  frnd pi f* 2e f* fcos
+  frnd fln -2e f* fsqrt f* ;
+
+: ,normals ( n -- )		\ store many, centered on 1, std dev 0.5
+  0 do frnd-normal 0.5e f* 1e f+ f, loop ;
+
+create rnd-array 1000 ,normals

Task/Random-numbers/Fortran/random-numbers.f

@@ -0,0 +1,24 @@
+PROGRAM Random
+
+  INTEGER, PARAMETER :: n = 1000
+  INTEGER :: i
+  REAL :: array(n), pi, temp, mean = 1.0, sd = 0.5
+
+  pi = 4.0*ATAN(1.0)
+  CALL RANDOM_NUMBER(array) ! Uniform distribution
+
+! Now convert to normal distribution
+  DO i = 1, n-1, 2
+    temp = sd * SQRT(-2.0*LOG(array(i))) * COS(2*pi*array(i+1)) + mean
+    array(i+1) = sd * SQRT(-2.0*LOG(array(i))) * SIN(2*pi*array(i+1)) + mean
+    array(i) = temp
+  END DO
+
+! Check mean and standard deviation
+  mean = SUM(array)/n
+  sd = SQRT(SUM((array - mean)**2)/n)
+
+  WRITE(*, "(A,F8.6)") "Mean = ", mean
+  WRITE(*, "(A,F8.6)") "Standard Deviation = ", sd
+
+END PROGRAM Random

Task/Random-numbers/Go/random-numbers.go

@@ -0,0 +1,17 @@
+package main
+
+import (
+    "math/rand"
+    "time"
+)
+
+const mean = 1.0
+const stdv = .5
+
+func main() {
+    var list [1000]float64
+    rand.Seed(time.Now().UnixNano())
+    for i := range list {
+        list[i] = mean + stdv*rand.NormFloat64()
+    }
+}

Task/Random-numbers/Groovy/random-numbers.groovy

@@ -0,0 +1,2 @@
+rnd = new Random()
+result = (1..1000).inject([]) { r, i -> r << rnd.nextGaussian() }

Task/Random-numbers/Haskell/random-numbers.hs

@@ -0,0 +1,14 @@
+import System.Random
+
+pairs :: [a] -> [(a,a)]
+pairs (x:y:zs) = (x,y):pairs zs
+pairs _        = []
+
+gauss mu sigma (r1,r2) =
+  mu + sigma * sqrt (-2 * log r1) * cos (2 * pi * r2)
+
+gaussians :: (RandomGen g, Random a, Floating a) => Int -> g -> [a]
+gaussians n g = take n $ map (gauss 1.0 0.5) $ pairs $ randoms g
+
+result :: IO [Double]
+result = getStdGen >>= \g -> return $ gaussians 1000 g

Task/Random-numbers/HicEst/random-numbers.hicest

@@ -0,0 +1,4 @@
+REAL :: n=1000, m=1, s=0.5, array(n)
+
+pi = 4 * ATAN(1)
+array = s * (-2*LOG(RAN(1)))^0.5  * COS(2*pi*RAN(1)) + m

Task/Random-numbers/IDL/random-numbers.idl

@@ -0,0 +1 @@
+result = 1.0 + 0.5*randomn(seed,1000)

Task/Random-numbers/Icon/random-numbers.icon

@@ -0,0 +1,7 @@
+procedure main()
+    local L
+    L := list(1000)
+    every L[1 to 1000] := 1.0 + 0.5 * sqrt(-2.0 * log(?0)) * cos(2.0 * &pi * ?0)
+
+    every write(!L)
+end

Task/Random-numbers/J/random-numbers-1.j

@@ -0,0 +1,4 @@
+urand=: ?@$ 0:
+zrand=: (2 o. 2p1 * urand) * [: %: _2 * [: ^. urand
+
+1 + 0.5 * zrand 100

Task/Random-numbers/J/random-numbers-2.j

@@ -0,0 +1,3 @@
+   require 'stats/distribs/normal'
+   1 0.5 rnorm 1000
+1.44868803 1.21548637 0.812460657 1.54295452 1.2470606 ...

Task/Random-numbers/Java/random-numbers.java

@@ -0,0 +1,6 @@
+double[] list = new double[1000];
+double mean = 1.0, std = 0.5;
+Random rng = new Random();
+for(int i = 0;i<list.length;i++) {
+  list[i] = mean + std * rng.nextGaussian();
+}

Task/Random-numbers/JavaScript/random-numbers.js

@@ -0,0 +1,8 @@
+function randomNormal() {
+  return Math.cos(2 * Math.PI * Math.random()) * Math.sqrt(-2 * Math.log(Math.random()))
+}
+
+var a = []
+for (var i=0; i < 1000; i++){
+  a[i] = randomNormal() / 2 + 1
+}

Task/Random-numbers/Liberty-BASIC/random-numbers.liberty

@@ -0,0 +1,6 @@
+dim a(1000)
+mean =1
+sd =0.5
+for i = 1 to 1000   '   throw 1000 normal variates
+   a( i)  =mean +sd *( sqr( -2 * log( rnd( 0))) * cos( 2 * pi * rnd( 0)))
+next i

Task/Random-numbers/Logo/random-numbers.logo

@@ -0,0 +1,10 @@
+to random.float   ; 0..1
+  localmake "max.int lshift -1 -1
+  output quotient random :max.int :max.int
+end
+
+to random.gaussian
+  output product cos random 360  sqrt -2 / ln random.float
+end
+
+make "randoms cascade 1000 [fput random.gaussian / 2 + 1 ?] []

Task/Random-numbers/MATLAB/random-numbers-1.m

@@ -0,0 +1,2 @@
+    mu = 1; sd = 0.5;
+    x = randn(1000,1) * sd + mu;

Task/Random-numbers/MATLAB/random-numbers-2.m

@@ -0,0 +1 @@
+   x = normrnd(mu, sd, [1000,1]);

Task/Random-numbers/MATLAB/random-numbers-3.m

@@ -0,0 +1,15 @@
+function randNum = randNorm(mu0,chi2, sz)
+
+    radiusSquared = +Inf;
+
+    while (radiusSquared >= 1)
+        u = ( 2 * rand(sz) ) - 1;
+        v = ( 2 * rand(sz) ) - 1;
+
+        radiusSquared = u.^2 + v.^2;
+    end
+
+    scaleFactor = sqrt( ( -2*log(radiusSquared) )./ radiusSquared );
+    randNum = (v .* scaleFactor .* chi2) + mu0;
+
+end

Task/Random-numbers/MATLAB/random-numbers-4.m

@@ -0,0 +1,5 @@
+>> randNorm(1,.5, [1000,1])
+
+ans =
+
+   0.693984121077029

Task/Random-numbers/MAXScript/random-numbers.maxscript

@@ -0,0 +1,8 @@
+arr = #()
+for i in 1 to 1000 do
+(
+    a = random 0.0 1.0
+    b = random 0.0 1.0
+    c = 1.0 + 0.5 * sqrt (-2*log a) * cos (360*b) -- Maxscript cos takes degrees
+    append arr c
+)

Task/Random-numbers/Mathematica/random-numbers.math

@@ -0,0 +1 @@
+RandomReal[NormalDistribution[1, 1/2], 1000]

Task/Random-numbers/Maxima/random-numbers.maxima

@@ -0,0 +1,3 @@
+load(distrib)$
+
+random_normal(1.0, 0.5, 1000);

Task/Random-numbers/Metafont/random-numbers.metafont

@@ -0,0 +1,19 @@
+numeric col[];
+
+m := 0;               % m holds the mean, for testing purposes
+for i = 1 upto 1000:
+  col[i] := 1 + .5normaldeviate;
+  m := m + col[i];
+endfor
+
+% testing
+m := m / 1000;       % finalize the computation of the mean
+
+s := 0;              % in s we compute the standard deviation
+for i = 1 upto 1000:
+  s := s + (col[i] - m)**2;
+endfor
+s := sqrt(s / 1000);
+
+show m, s;    % and let's show that really they get what we wanted
+end

Task/Random-numbers/Mirah/random-numbers.mirah

@@ -0,0 +1,9 @@
+import java.util.Random
+
+list = double[999]
+mean = 1.0
+std = 0.5
+rng = Random.new
+0.upto(998) do | i |
+    list[i] = mean + std * rng.nextGaussian
+end

Task/Random-numbers/Modula-3/random-numbers.mod3

@@ -0,0 +1,21 @@
+MODULE Rand EXPORTS Main;
+
+IMPORT Random;
+FROM Math IMPORT log, cos, sqrt, Pi;
+
+VAR rands: ARRAY [1..1000] OF LONGREAL;
+
+(* Normal distribution. *)
+PROCEDURE RandNorm(): LONGREAL =
+  BEGIN
+    WITH rand = NEW(Random.Default).init() DO
+      RETURN
+        sqrt(-2.0D0 * log(rand.longreal())) * cos(2.0D0 * Pi * rand.longreal());
+    END;
+  END RandNorm;
+
+BEGIN
+  FOR i := FIRST(rands) TO LAST(rands) DO
+    rands[i] := 1.0D0 + 0.5D0 * RandNorm();
+  END;
+END Rand.

Task/Random-numbers/NetRexx/random-numbers.netrexx

@@ -0,0 +1,55 @@
+/* NetRexx */
+options replace format comments java crossref symbols nobinary
+
+import java.math.BigDecimal
+import java.math.MathContext
+
+-- prologue
+numeric digits 20
+
+-- get input, set defaults
+parse arg dp mu sigma ec .
+if mu    = '' | mu    = '.' then mean             =  1.0; else mean             = mu
+if sigma = '' | sigma = '.' then stdDeviation     =  0.5; else stdDeviation     = sigma
+if dp    = '' | dp    = '.' then displayPrecision =    1; else displayPrecision = dp
+if ec    = '' | ec    = '.' then elements         = 1000; else elements         = ec
+
+-- set up
+RNG = Random()
+numberList = java.util.List
+numberList = ArrayList()
+
+-- generate list of random numbers
+loop for elements
+  rn = mean + stdDeviation * RNG.nextGaussian()
+  numberList.add(BigDecimal(rn, MathContext.DECIMAL128))
+  end
+
+-- report
+say "Mean:              " mean
+say "Standard Deviation:" stdDeviation
+say "Precision:         " displayPrecision
+say
+drawBellCurve(numberList, displayPrecision)
+
+return
+
+-- -----------------------------------------------------------------------------
+method drawBellCurve(numberList = java.util.List, precision) static
+  Collections.sort(numberList)
+  val = BigDecimal
+  lastN = ''
+  nextN = ''
+  loop val over numberList
+    nextN = Rexx(val.toPlainString()).format(5, precision)
+    select
+      when lastN = '' then nop
+      when lastN \= nextN then say lastN
+      otherwise nop
+      end
+    say '*\-'
+    lastN = nextN
+    end val
+  say lastN
+
+  return

Task/Random-numbers/NewLISP/random-numbers.newlisp

@@ -0,0 +1 @@
+(normal 1 .5 1000)

Task/Random-numbers/OCaml/random-numbers.ocaml

@@ -0,0 +1,4 @@
+let pi = 4. *. atan 1.;;
+let random_gaussian () =
+  1. +. sqrt (-2. *. log (Random.float 1.)) *. cos (2. *. pi *. Random.float 1.);;
+let a = Array.init 1000 (fun _ -> random_gaussian ());;

Task/Random-numbers/Objeck/random-numbers.objeck

@@ -0,0 +1,18 @@
+bundle Default {
+  class RandomNumbers {
+    function : Main(args : String[]) ~ Nil {
+      rands := Float->New[1000];
+      for(i := 0; i < rands->Size(); i += 1;) {
+        rands[i] := 1.0 + 0.5 * RandomNormal();
+      };
+
+      each(i : rands) {
+        rands[i]->PrintLine();
+      };
+    }
+
+    function : native : RandomNormal() ~ Float {
+      return (2 * Float->Pi() * Float->Random())->Cos() * (-2 * (Float->Random()->Log()))->SquareRoot();
+    }
+  }
+}

Task/Random-numbers/Octave/random-numbers.octave

@@ -0,0 +1,3 @@
+p = normrnd(1.0, 0.5, 1000, 1);
+disp(mean(p));
+disp(sqrt(sum((p - mean(p)).^2)/numel(p)));

Task/Random-numbers/PARI-GP/random-numbers.pari

@@ -0,0 +1,6 @@
+rnormal()={
+	my(pr=32*ceil(default(realprecision)*log(10)/log(4294967296)),u1=random(2^pr)*1.>>pr,u2=random(2^pr)*1.>>pr);
+	sqrt(-2*log(u1))*cos(2*Pi*u1)
+	\\ Could easily be extended with a second normal at very little cost.
+};
+vector(1000,unused,rnormal()/2+1)

Task/Random-numbers/PHP/random-numbers.php

@@ -0,0 +1,11 @@
+function random() {
+    return mt_rand() / mt_getrandmax();
+}
+
+$pi 	= pi();          // Set PI
+
+$a = array();
+for ($i = 0; $i < 1000; $i++) {
+    $a[$i] = 1.0 + ((sqrt(-2 * log(random())) * cos(2 * $pi * random())) * 0.5);
+
+}

Task/Random-numbers/PL-I/random-numbers.pli

@@ -0,0 +1,21 @@
+/* CONVERTED FROM WIKI FORTRAN */
+Normal_Random: procedure options (main);
+   declare (array(1000), pi, temp,
+            mean initial (1.0), sd initial (0.5)) float (18);
+   declare (i, n) fixed binary;
+
+   n = hbound(array, 1);
+   pi = 4.0*ATAN(1.0);
+   array = random(); /* Uniform distribution */
+   /* Now convert to normal distribution */
+   DO i = 1 to n-1 by 2;
+      temp = sd * SQRT(-2.0*LOG(array(i))) * COS(2*pi*array(i+1)) + mean;
+      array(i+1) = sd * SQRT(-2.0*LOG(array(i))) * SIN(2*pi*array(i+1)) + mean;
+      array(i) = temp;
+   END;
+   /* Check mean and standard deviation */
+   mean = SUM(array)/n;
+   sd = SQRT(SUM((array - mean)**2)/n);
+   put skip edit ( "Mean = ", mean ) (a, F(18,16) );
+   put skip edit ( "Standard Deviation = ", sd) (a, F(18,16));
+END Normal_Random;

Task/Random-numbers/PL-SQL/random-numbers.sql

@@ -0,0 +1,24 @@
+create or replace
+PROCEDURE PROCEDURE1 AS
+    TYPE numsColl is TABLE OF NUMBER;
+    nums numsColl;
+
+    FUNCTION GenNums(n IN NUMBER) RETURN numsColl AS
+        PI NUMBER := ACOS (-1);
+    BEGIN
+        nums := numsColl();
+        nums.extend(n);
+
+        FOR i in 1 .. n LOOP
+            nums(i) := 1 + .5 * (sqrt(-2 * log(dbms_random.value, 10)) * cos(2 * PI * dbms_random.value));
+        END LOOP;
+
+        RETURN nums;
+    END GenNums;
+
+BEGIN
+    nums := GenNums(10);
+    FOR i in 1 .. 10 LOOP
+        DBMS_OUTPUT.PUT_LINE(nums(i));
+    END LOOP;
+END PROCEDURE1;

Task/Random-numbers/Perl-6/random-numbers.pl6

@@ -0,0 +1,5 @@
+sub randnorm ($mean, $stddev) {
+    $mean + $stddev * sqrt(-2 * log rand) * cos(2 * pi * rand)
+}
+
+my @nums = map { randnorm 1, 0.5 }, ^1000;

Task/Random-numbers/Perl/random-numbers.pl

@@ -0,0 +1,5 @@
+my $PI = 2 * atan2 1, 0;
+
+my @nums = map {
+    1 + 0.5 * sqrt(-2 * log rand) * cos(2 * $PI * rand)
+} 1..1000;

Task/Random-numbers/PicoLisp/random-numbers.l

@@ -0,0 +1,16 @@
+(load "@lib/math.l")
+
+(de randomNormal ()  # Normal distribution, centered on 0, std dev 1
+   (*/
+      (sqrt (* -2.0 (log (rand 0 1.0))))
+      (cos (*/ 2.0 pi (rand 0 1.0) `(* 1.0 1.0)))
+      1.0 ) )
+
+(seed (time))                                      # Randomize
+
+(let Result
+   (make                                           # Build list
+      (do 1000                                     # of 1000 elements
+         (link (+ 1.0 (/ (randomNormal) 2))) ) )
+   (for N (head 7 Result)                          # Print first 7 results
+      (prin (format N *Scl) " ") ) )

Task/Random-numbers/Pop11/random-numbers.pop11

@@ -0,0 +1,15 @@
+;;; Choose radians as arguments to trigonometic functions
+true -> popradians;
+
+;;; procedure generating standard normal distribution
+define random_normal() -> result;
+lvars r1 = random0(1.0), r2 = random0(1.0);
+     cos(2*pi*r1)*sqrt(-2*log(r2)) -> result
+enddefine;
+
+lvars array, i;
+
+;;; Put numbers on the stack
+for i from 1 to 1000 do 1.0+0.5*random_normal() endfor;
+;;; collect them into array
+consvector(1000) -> array;

Task/Random-numbers/PureBasic/random-numbers.purebasic

@@ -0,0 +1,18 @@
+Procedure.f RandomNormal()
+   ; This procedure can return any real number.
+   Protected.f x1, x2
+
+   ; random numbers from the open interval ]0, 1[
+   x1 = (Random(999998)+1) / 1000000       ; must be > 0 because of Log(x1)
+   x2 = (Random(999998)+1) / 1000000
+
+   ProcedureReturn Sqr(-2*Log(x1)) * Cos(2*#PI*x2)
+EndProcedure
+
+
+Define i, n=1000
+
+Dim a.q(n-1)
+For i = 0 To n-1
+   a(i) = 1 + 0.5 * RandomNormal()
+Next

Task/Random-numbers/Python/random-numbers-1.py

@@ -0,0 +1,3 @@
+import random
+values = [random.gauss(1, .5) for i in range(1000)]
+# or [ random.normalvariate(1, 0.5) for i in range(1000)]

Task/Random-numbers/Python/random-numbers-2.py

@@ -0,0 +1,4 @@
+>>> mean = sum(values)/1000
+>>> sdeviation = (sum((i - mean)**2 for i in values)/1000)**0.5
+>>> mean, sdeviation
+(1.0127861555468178, 0.5006682783828207)

Task/Random-numbers/R/random-numbers.r

@@ -0,0 +1 @@
+result <- rnorm(1000, mean=1, sd=0.5)

Task/Random-numbers/REXX/random-numbers.rexx

@@ -0,0 +1,41 @@
+/*REXX pgm gens 1,000 normally distributed #s: mean=1, standard dev.=½. */
+call pi                                /*call subroutine to define  pi. */
+parse arg n seed .                     /*allow specification of N | seed*/
+if n=='' | n==','  then n=1000         /*  N  is the size of the array. */
+if seed\=='' then call random ,,seed   /*use seed for repeatable RANDOM#*/
+mean=1                                 /*desired new mean (arith. avg.) */
+sd=1/2                                 /*desired new standard deviation.*/
+          do g=1  for n                /*generate N uniform random nums.*/
+          #.g=random(0,1e5)/1e5        /*REXX gens uniform rand integers*/
+          end   /*g*/
+
+say '              old mean=' mean()
+say 'old standard deviation=' stddev()
+say
+      do j=1  to n-1  by 2
+      m=j+1
+        _=sd*sqrt(-2*ln(#.j))*cos(2*pi*#.m)+mean /*use Box-Muller method*/
+      #.m=sd*sqrt(-2*ln(#.j))*sin(2*pi*#.m)+mean /*rand # must be 0──<E29480>1.*/
+      #.j=_
+      end    /*j*/
+say '              new mean=' mean()
+say 'new standard deviation=' stddev()
+exit                                   /*stick a fork in it, we're done.*/
+/*──────────────────────────────────subroutines─────────────────────────*/
+mean:   _=0; do k=1 for n; _=_+#.k; end; return _/n
+stddev: _avg=mean(); _=0; do k=1 for n; _=_+(#.k-_avg)**2; end; return sqrt(_/n)
+e:      e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535;  return e
+pi:     pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi
+r2r:    return arg(1)//(2*pi())
+sqrt:   procedure;parse arg x; if x=0 then return 0; d=digits(); numeric digits 11; g=.sqrtGuess()
+        do j=0 while p>9; m.j=p; p=p%2+1; end; do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k
+        g=.5*(g+x/g); end; numeric digits d; return g/1
+.sqrtGuess: numeric form;  m.=11;  p=d+d%4+2
+        parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
+cos:    procedure; arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9); if a=pi() then return -1
+        if a=pi()/2|a=2*pi() then return 0;if a=pi()/3 then return .5;if a=2*pi()/3 then return -.5;return .sincos(1,1,-1)
+sin:    procedure; arg x; x=r2r(x); numeric fuzz min(5,digits()-3); if abs(x)=pi() then return 0; return .sincos(x,x,1)
+.sincos:parse arg z,_,i; x=x*x; p=z; do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z
+ln:     procedure; parse arg x,f; call e; ig=x>1.5; is=1-2*(ig\==1); ii=0; xx=x; return .ln_comp()
+.ln_comp: do while ig&xx>1.5|\ig&xx<.5;_=e;do k=-1;iz=xx*_**-is;if k>=0&(ig&iz<1|\ig&iz>.5) then leave;_=_*_;izz=iz;end
+        xx=izz;ii=ii+is*2**k;end;x=x*e**-ii-1;z=0;_=-1;p=z;do k=1;_=-_*x;z=z+_/k;if z=p then leave;p=z;end;return z+ii

Task/Random-numbers/Ruby/random-numbers.rb

@@ -0,0 +1 @@
+Array.new(1000) { 1 + Math.sqrt(-2 * Math.log(rand)) * Math.cos(2 * Math::PI * rand) }

Task/Random-numbers/Run-BASIC/random-numbers.run

@@ -0,0 +1,5 @@
+dim a(1000)
+pi = 22/7
+for i = 1 to 1000
+   a( i)  = 1 + .5 * (sqr(-2 * log(rnd(0))) * cos(2 * pi * rnd(0)))
+next i

Task/Random-numbers/Sather/random-numbers.sa

@@ -0,0 +1,19 @@
+class MAIN is
+  main is
+    a:ARRAY{FLTD} := #(1000);
+    i:INT;
+
+    RND::seed(2010);
+    loop i := 1.upto!(1000) - 1;
+      a[i] := 1.0d + 0.5d * RND::standard_normal;
+    end;
+
+    -- testing the distribution
+    mean ::= a.reduce(bind(_.plus(_))) / a.size.fltd;
+    #OUT + "mean " + mean + "\n";
+    a.map(bind(_.minus(mean)));
+    a.map(bind(_.pow(2.0d)));
+    dev ::= (a.reduce(bind(_.plus(_))) / a.size.fltd).sqrt;
+    #OUT + "dev  " + dev + "\n";
+  end;
+end;

Task/Random-numbers/Scala/random-numbers.scala

@@ -0,0 +1 @@
+List.fill(1000)(1.0 + 0.5 * scala.util.Random.nextGaussian)

Task/Random-numbers/Scheme/random-numbers.ss

@@ -0,0 +1,47 @@
+; linear congruential generator given in C99 section 7.20.2.1
+(define ((c-rand seed)) (set! seed (remainder (+ (* 1103515245 seed) 12345) 2147483648)) (quotient seed 65536))
+
+; uniform real numbers in open interval (0, 1)
+(define (unif-rand seed) (let ((r (c-rand seed))) (lambda () (/ (+ (r) 1) 32769.0))))
+
+; Box-Muller method to generate normal distribution
+(define (normal-rand unif m s)
+(let ((? #t) (! 0.0) (twopi (* 2.0 (acos -1.0))))
+(lambda ()
+   (set! ? (not ?))
+   (if ? !
+         (let ((a (sqrt (* -2.0 (log (unif))))) (b (* twopi (unif))))
+              (set! ! (+ m (* s a (sin b))))
+              (+ m (* s a (cos b))))))))
+
+(define rnorm (normal-rand (unif-rand 0) 1.0 0.5))
+
+; auxiliary function to get a list of 'n random numbers from generator 'r
+(define (rand-list r n) = (if (zero? n) '() (cons (r) (rand-list r (- n 1)))))
+
+(define v (rand-list rnorm 1000))
+
+v
+#|
+(-0.27965824722565835
+ -0.8870860825789542
+ 0.6499618744638194
+ 0.31336141955110863
+ ...
+ 0.5648743998193049
+ 0.8282656735558756
+ 0.6399951934564637
+ 0.7699535302478072)
+|#
+
+; check mean and standard deviation
+(define (mean-sdev v)
+(let loop ((v v) (a 0) (b 0) (n 0))
+(if (null? v)
+    (let ((mean (/ a n)))
+         (list mean (sqrt (/ (- b (* n mean mean)) (- n 1)))))
+    (let ((x (car v)))
+         (loop (cdr v) (+ a x) (+ b (* x x)) (+ n 1))))))
+
+(mean-sdev v)
+; (0.9562156817697293 0.5097087109575911)

Task/Random-numbers/Seed7/random-numbers.seed7

@@ -0,0 +1,25 @@
+$ include "seed7_05.s7i";
+  include "float.s7i";
+  include "math.s7i";
+
+const func float: frand is func  # Uniform distribution, (0..1]
+  result
+    var float: frand is 0.0;
+  begin
+    repeat
+      frand := rand(0.0, 1.0);
+    until frand <> 0.0;
+  end func;
+
+const func float: randomNormal is  # Normal distribution, centered on 0, std dev 1
+  return sqrt(-2.0 * log(frand)) * cos(2.0 * PI * frand);
+
+const proc: main is func
+  local
+    var integer: i is 0;
+    var array float: rands is 1000 times 0.0;
+  begin
+    for i range 1 to length(rands) do
+      rands[i] := 1.0 + 0.5 * randomNormal;
+    end for;
+  end func;

Task/Random-numbers/Standard-ML/random-numbers-1.ml

@@ -0,0 +1,5 @@
+val seed = 0w42;
+val gen = Rand.mkRandom seed;
+fun random_gaussian () =
+  1.0 + Math.sqrt (~2.0 * Math.ln (Rand.norm (gen ()))) * Math.cos (2.0 * Math.pi * Rand.norm (gen ()));
+val a = List.tabulate (1000, fn _ => random_gaussian ());

Task/Random-numbers/Standard-ML/random-numbers-2.ml

@@ -0,0 +1,5 @@
+val seed = (47,42);
+val gen = Random.rand seed;
+fun random_gaussian () =
+  1.0 + Math.sqrt (~2.0 * Math.ln (Random.randReal gen)) * Math.cos (2.0 * Math.pi * Random.randReal gen);
+val a = List.tabulate (1000, fn _ => random_gaussian ());

Task/Random-numbers/Tcl/random-numbers.tcl

@@ -0,0 +1,11 @@
+package require Tcl 8.5
+variable ::pi [expr acos(0)]
+proc ::tcl::mathfunc::nrand {} {
+    expr {sqrt(-2*log(rand())) * cos(2*$::pi*rand())}
+}
+
+set mean 1.0
+set stddev 0.5
+for {set i 0} {$i < 1000} {incr i} {
+    lappend result [expr {$mean + $stddev*nrand()}]
+}

Task/Random-numbers/Ursala/random-numbers.ursala

@@ -0,0 +1,14 @@
+#import nat
+#import flo
+
+pop_stats("mu","sigma") = plus/*"mu"+ times/*"sigma"+ Z*+ iota
+
+sample_stats("mu","sigma") = plus^*D(minus/"mu"+ mean,~&)+ vid^*D(div\"sigma"+ stdev,~&)+ Z*+ iota
+
+#cast %eWL
+
+test =
+
+^(mean,stdev)* <
+   pop_stats(1.,0.5) 1000,
+   sample_stats(1.,0.5) 1000>

Task/Random-numbers/Yorick/random-numbers.yorick

@@ -0,0 +1,3 @@
+func random_normal(count) {
+   return sqrt(-2*log(random(count))) * cos(2*pi*random(count));
+}

Task/Random-numbers/ZX-Spectrum-Basic/random-numbers.zx

@@ -0,0 +1,6 @@
+10 RANDOMIZE 0 : REM seeds random number generator based on uptime
+20 DIM a(1000)
+30 CLS
+40 FOR i = 1 TO 1000
+50 LET a(i) = 1 + SQR(-2 * LN(RND)) * COS(2 * PI * RND)
+60 NEXT i