⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

{{task|Basic language learning}} [[Category:Probability and statistics]] [[Category:Randomness]] {{omit from|GUISS}} {{omit from|UNIX Shell|From the shell, we simply invoke the awk solution}}

;Task: Generate a collection filled with '''1000''' normally distributed random (or pseudo-random) 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.

;Related task:

  • [[Standard deviation]]

Ada

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;

ALGOL 68

{{trans|C}}

{{works with|ALGOL 68|Revision 1 - no extensions to language used}}

{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of FORMATted transput}}

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]))
)

{{out}}


( 0.693461, 0.948424, 0.482261, 1.045939, 0.890818, 1.467935, 0.604153, 0.804811, 0.690227, 0.83462 ... )

AutoHotkey

contributed by Laszlo on the ahk [http://www.autohotkey.com/forum/post-276261.html#276261 forum]

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
}

AWK

'''One-liner:'''

$ 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}'

'''Readable version:'''


function r() {
  return sqrt( -2*log( rand() ) ) * cos(6.2831853*rand() )
}

BEGIN {
  n=1000
  for(i=0;i<n;i++) {
    x = 1 + 0.5*r()
    s = s" "x
  }
  print s
}

{{out}} first few values only


0.783753 1.16682 1.17989 1.14975 1.34784 0.29296 0.979227 1.04402 0.567835 1.58812 0.465559 1.27186 0.324533 0.725827 -0.0626549 0.632273 1.0145 1.3387 0.861667 1.04147 1.2576 1.02497 0.58453 0.9619 1.26902 0.851048 -0.126259 0.863256

...

BASIC

{{works with|QuickBasic|4.5}} RANDOMIZE TIMER 'seeds random number generator with the system time pi = 3.141592653589793# DIM a(1 TO 1000) AS DOUBLE CLS FOR i = 1 TO 1000 a(i) = 1 + SQR(-2 * LOG(RND)) * COS(2 * pi * RND) NEXT i

BBC BASIC

      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

{{out}}

Mean = 1.01848064
Standard deviation = 0.503551814

C

#include <iostream>
#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;
}

C#

{{trans|JavaScript}}


private static double randomNormal()
{
	return Math.Cos(2 * Math.PI * tRand.NextDouble()) * Math.Sqrt(-2 * Math.Log(tRand.NextDouble()));
}

Then the methods in [[Random numbers#Metafont]] are used to calculate the average and the Standard Deviation:


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();
}

An example result:


Average: 1,00510073053613
Standard Deviation: 0,502540443430955

C++

{{works with|C++11}}

The new C++ standard looks very similar to the Boost library example below.

#include <random>
#include <functional>
#include <vector>
#include <algorithm>
using namespace std;

int main()
{
  random_device seed;
  mt19937 engine(seed());
  normal_distribution<double> dist(1.0, 0.5);
  auto rnd = bind(dist, engine);

  vector<double> v(1000);
  generate(v.begin(), v.end(), rnd);
  return 0;
}

{{works with|C++03}}

#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;
}

{{libheader|Boost}}

This example used Mersenne Twister generator. It can be changed by changing the typedef.


#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;
}

Clojure

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

Common Lisp

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

D

import std.stdio, std.random, std.math;

struct NormalRandom {
    double mean, stdDev;

    // Necessary 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 r1 = uniform01, r2 = uniform01; // Not nothrow.
        return mean + stdDev * sqrt(-2 * r1.log) * cos(2 * PI * r2);
    }
}

void main() {
    double[1000] array;
    auto nRnd = NormalRandom(1.0, 0.5);
    foreach (ref x; array)
        //x = nRnd;
        x = nRnd();
}

Alternative Version

(Untested) {{libheader|tango}}

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;
    }
}

Delphi

Delphi has RandG function which generates random numbers with normal distribution using Marsaglia-Bray algorithm:

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.

{{out}}

Mean          = 1.0098
Std deviation = 0.5016

DWScript

var values : array [0..999] of Float;
var i : Integer;

for i := values.Low to values.High do
   values[i] := RandG(1, 0.5);

E

accum [] for _ in 1..1000 { _.with(entropy.nextGaussian()) }

EasyLang

floatvars len a[] 1000 for i% range len a[] a[i%] = 1 + 0.5 * sqrt (-2 * logn randomf) * cos (360 * randomf) .




## Eiffel


```eiffel

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

Example Result


Average: 1.0079398405028137
Standard Deviation: 0.49042787564453988

Elena

{{trans|C#}} ELENA 4.1 :

import extensions;
import extensions'math;

randomNormal()
{
    ^ cos(2 * Pi_value * randomGenerator.nextReal())
                      * sqrt(-2 * ln(randomGenerator.nextReal()))
}

public program()
{
    real[] a := new real[](1000);

    real tAvg := 0;
    for (int x := 0, x < a.Length, x += 1)
    {
        a[x] := (randomNormal()) / 2 + 1;
        tAvg += a[x]
    };

    tAvg /= a.Length;
    console.printLine("Average: ", tAvg);

    real s := 0;
    for (int x := 0, x < a.Length, x += 1)
    {
        s += power(a[x] - tAvg, 2)
    };

    s := sqrt(s / 1000);

    console.printLine("Standard Deviation: ", s);

    console.readChar()
}

{{out}}


Average: 0.9842420481571
Standard Deviation: 0.5109070975558

Elixir

defmodule Random do
  def normal(mean, sd) do
    {a, b} = {:rand.uniform, :rand.uniform}
    mean + sd * (:math.sqrt(-2 * :math.log(a)) * :math.cos(2 * :math.pi * b))
  end
end

std_dev = fn (list) ->
            mean = Enum.sum(list) / length(list)
            sd = Enum.reduce(list, 0, fn x,acc -> acc + (x-mean)*(x-mean) end) / length(list)
                 |> :math.sqrt
            IO.puts "Mean: #{mean},\tStdDev: #{sd}"
          end

xs = for _ <- 1..1000, do: Random.normal(1.0, 0.5)
std_dev.(xs)

{{out}}


Mean: 1.009079383094275,        StdDev: 0.4991894476975088

used Erlang function :rand.normal

xs = for _ <- 1..1000, do: 1.0 + :rand.normal * 0.5
std_dev.(xs)

{{out}}


Mean: 0.9955701150615597,       StdDev: 0.5036412260426065

Erlang

{{works with|Erlang}}


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)]).

{{out}}


mean = 1.0118289913718608
stddev = 0.5021636849524854

ERRE

PROGRAM DISTRIBUTION

! ! for rosettacode.org !

! formulas taken from TI-59 Master Library manual

CONST NUM_ITEM=1000

!VAR SUMX#,SUMX2#,R1#,R2#,Z#,I%

DIM A#[1000]

BEGIN ! seeds random number generator with system time RANDOMIZE(TIMER)

PRINT(CHR$(12);) !CLS SUMX#=0 SUMX2#=0

FOR I%=1 TO NUM_ITEM DO R1#=RND(1) R2#=RND(1) Z#=SQR(-2LOG(R1#))COS(2πR2#) A#[I%]=Z#/2+1 ! I want a normal distribution with ! mean=1 and std.dev=0.5 SUMX#+=A#[I%] SUMX2#+=A#[I%]*A#[I%] END FOR

Z#=SUMX#/NUM_ITEM

PRINT("Average is";Z#) PRINT("Standard dev. is";SQR(SUMX2#/NUM_ITEM-Z#*Z#))

END PROGRAM




## Euler Math Toolbox



```Euler Math Toolbox

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

Euphoria

{{trans|PureBasic}}

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

=={{header|F_Sharp|F#}}==


let n = MathNet.Numerics.Distributions.Normal(1.0,0.5)
List.init 1000 (fun _->n.Sample())

{{out}}


  [0.734433576; 1.54225304; 0.4407528678; 1.177675412; 0.4318617021;
   0.6026656337; 0.769764924; 1.104693934; 0.6297500925; 0.9594598077;
   1.684736389; 1.160376323; 0.883354356; 0.9513968363; 0.9727698268;
   0.5315570949; 0.9599239266; 1.564976755; 0.7232002879; 1.084139442;
   1.220914517; 0.3553085946; 1.112549824; 1.989443553; 0.5752307543;
   1.156682549; 0.7886670467; 0.02050745923; 1.532060208; 1.18789591;
   1.408946777; 1.038812004; 1.724679503; 1.671565045; 1.266831442;
   1.363611654; 1.705819067; 0.5772366328; 0.4503488498; 1.496891481;
   0.9831877282; 0.3845460366; 0.8253240671; 1.298969969; 0.4265904553;
   0.9303696876; 0.445003361; 0.753175816; 0.6143534043; 1.059982235;
   0.7143206784; 0.2233328038; 1.005178481; 0.7697392436; 0.5904948577;
   0.5127953044; 0.6467346747; 0.7929387604; -0.1501790761; 0.8750780903;
   0.941704369; 1.37941579; 0.4739006145; 1.998886344; 1.219428519;
   0.06270791476; 1.097739804; 0.7584232803; 1.042177217; 1.166561247;
   1.502357164; 1.171525776; 0.1528807432; 0.2289389756; 1.36208422;
   0.3714421124; 1.299571092; 1.171553369; 1.317807265; 1.616662281;
   1.724223246; 1.059580642; 1.270520918; -0.1827677907; 1.938593232;
   1.420362143; 1.888357595; 0.7851629936; 0.7080554899; 0.7747215818;
   1.403719877; 0.5765950249; 1.275206565; 0.6292054813; 1.525562798;
   0.6224640457; 0.8524078517; 0.7646595627; 0.6799834691; 0.773111053; ...]

Factor

USING: random ;
1000 [ 1.0 0.5 normal-random-float ] replicate

=={{header|Falcon|}}==

a = []
for i in [0:1000] : a+= norm_rand_num()

function norm_rand_num()
   pi = 2*acos(0)
   return 1 + (cos(2 * pi * random()) * pow(-2 * log(random()) ,1/2)) /2
end

Fantom

Two solutions. The first uses Fantom's random-number generator, which produces a uniform distribution. So, convert to a normal distribution using a formula:


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) }
  }
}

The second calls out to Java's Gaussian random-number generator:


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) }
  }
}

Forth

{{works with|gforth|0.6.2}}

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

For newer versions of gforth (tested on 0.7.3), it seems you need to use HERE SEED ! instead of HERE TO SEED, because SEED has been made a variable instead of a value.

Fortran

{{works with|Fortran|90 and later}}

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

{{out}}


 Mean = 0.995112
 Standard Deviation = 0.503373

FreeBASIC

' FB 1.05.0 Win64

Const pi As Double = 3.141592653589793
Randomize

' Generates normally distributed random numbers with mean 0 and standard deviation 1
Function randomNormal() As Double
  Return Cos(2.0 * pi * Rnd) * Sqr(-2.0 * Log(Rnd))
End Function

Dim r(0 To 999) As Double
Dim sum As Double = 0.0

' Generate 1000 normally distributed random numbers
' with mean 1 and standard deviation 0.5
' and calculate their sum
For i As Integer = 0 To 999
   r(i) = 1.0 + randomNormal/2.0
   sum += r(i)
Next

Dim mean As Double = sum / 1000.0

Dim sd As Double
sum = 0.0
' Now calculate their standard deviation
For i As Integer = 0 To 999
  sum += (r(i) - mean) ^ 2.0
Next
sd  = Sqr(sum/1000.0)

Print "Mean is              "; mean
Print "Standard Deviation is"; sd
Print
Print "Press any key to quit"
Sleep

Sample result: {{out}}


Mean is               1.000763573902885
Standard Deviation is 0.500653063426955

Free Pascal

Free Pascal provides the '''randg''' function in the RTL math unit that produces Gaussian-distributed random numbers with the Box-Müller algorithm.


function randg(mean,stddev: float): float;

=={{header|F_Sharp|F#}}==

let gaussianRand count =
    let o = new System.Random()
    let pi = System.Math.PI
    let gaussrnd =
        (fun _ -> 1. + 0.5 * sqrt(-2. * log(o.NextDouble())) * cos(2. * pi * o.NextDouble()))
    [ for i in {0 .. (int count)} -> gaussrnd() ]

Go

This solution uses math/rand package in the standard library. See also though the subrepository rand package at https://godoc.org/golang.org/x/exp/rand, which also has a NormFloat64 and has a rand source with a number of advantages over the one in standard library.

package main

import (
    "fmt"
    "math"
    "math/rand"
    "strings"
    "time"
)

const mean = 1.0
const stdv = .5
const n = 1000

func main() {
    var list [n]float64
    rand.Seed(time.Now().UnixNano())
    for i := range list {
        list[i] = mean + stdv*rand.NormFloat64()
    }
    // show computed mean and stdv of list
    var s, sq float64
    for _, v := range list {
        s += v
    }
    cm := s / n
    for _, v := range list {
        d := v - cm
        sq += d * d
    }
    fmt.Printf("mean %.3f, stdv %.3f\n", cm, math.Sqrt(sq/(n-1)))
    // show histogram by hdiv divisions per stdv over +/-hrange stdv
    const hdiv = 3
    const hrange = 2
    var h [1 + 2*hrange*hdiv]int
    for _, v := range list {
        bin := hrange*hdiv + int(math.Floor((v-mean)/stdv*hdiv+.5))
        if bin >= 0 && bin < len(h) {
            h[bin]++
        }
    }
    const hscale = 10
    for _, c := range h {
        fmt.Println(strings.Repeat("*", (c+hscale/2)/hscale))
    }
}

{{out}}


mean 0.995, stdv 0.503
**
****
******
********
************
************
*************
************
**********
********
*****
***
**

FutureBasic

Note: To generate the random number, rather than using FB's native "rnd" function, this code wraps C code into the RandomZeroToOne function.


include "ConsoleWindow"

local fn RandomZeroToOne as double
dim as double result
BeginCCode
  result = (double)( (rand() % 100000 ) * 0.00001 );
EndC
end fn = result

local fn RandomGaussian as double
dim as double r

r = fn RandomZeroToOne
end fn = 1 + .5 * ( sqr( -2 * log(r) ) * cos( 2 * pi * r ) )

dim as long i
dim as double mean, std, a(1000)

for i = 1 to 1000
  a(i) = fn RandomGaussian
  mean += a(i)
next
mean = mean / 1000

for i = 1 to 1000
  std += ( a(i) - mean )^2
next
std = std / 1000

print "           Average:"; mean
print "Standard Deviation:"; std

Output:


           Average: 1.0258434498
Standard Deviation: 0.2771047023

Groovy

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

Haskell

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

Or using Data.Random from random-fu package:

replicateM 1000 $ normal 1 0.5

To print them:

import  Data.Random
import Control.Monad

thousandRandomNumbers :: RVar [Double]
thousandRandomNumbers =  replicateM 1000 $ normal 1 0.5

main = do
   x <- sample thousandRandomNumbers
   print x

HicEst

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

=={{header|Icon}} and {{header|Unicon}}== The seed '''&random''' may be assigned in either language; either to randomly seed or to pick a fixed starting point. ?i is the random number generator, returning an integer from 0 to i - 1 for non-zero integer i. As a special case, ?0 yields a random floating point number from 0.0 <= r < 1.0

Note that Unicon randomly seeds it's generator.


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

IDL

result = 1.0 + 0.5*randomn(seed,1000)

J

'''Solution:'''

urand=: ?@$ 0:
zrand=: (2 o. 2p1 * urand) * [: %: _2 * [: ^. urand

1 + 0.5 * zrand 100

'''Alternative Solution:'''

Using the normal script from the [[j:Addons/stats/distribs|stats/distribs addon]].

   require 'stats/distribs/normal'
   1 0.5 rnorm 1000
1.44868803 1.21548637 0.812460657 1.54295452 1.2470606 ...

Java

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();
}

JavaScript

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
}

jq

{{works with|jq|1.4}}

Since jq is a purely functional language, it is convenient to define the pseudo-random number generator functions as filters whose inputs and outputs are arrays containing a "seed".

The following uses the same pseudo-random number generator as the Microsoft C Runtime (see [[Linear congruential generator]]).

''''A Pseudo-Random Number Generator''''

# 15-bit integers generated using the same formula as rand() from the Microsoft C Runtime.
# The random numbers are in [0 -- 32767] inclusive.
# Input: an array of length at least 2 interpreted as [count, state, ...]
# Output: [count+1, newstate, r] where r is the next pseudo-random number.
def next_rand_Microsoft:
  .[0] as $count | .[1] as $state
  | ( (214013 * $state) + 2531011) % 2147483648 # mod 2^31
  | [$count+1 , ., (. / 65536 | floor) ] ;

''''Box-Muller Method''''

# Generate a single number following the normal distribution with mean 0, variance 1,
# using the Box-Muller method: X = sqrt(-2 ln U) * cos(2 pi V) where U and V are uniform on [0,1].
# Input: [n, state]
# Output [n+1, nextstate, r]
def next_rand_normal:
  def u: next_rand_Microsoft | .[2] /= 32767;
  u as $u1
  | ($u1 | u) as $u2
  | ((( (8*(1|atan)) * $u1[2]) | cos)
     * ((-2 * (($u2[2]) | log)) | sqrt)) as $r
  | [ (.[0]+1), $u2[1], $r] ;

# Generate "count" arrays, each containing a random normal variate with the given mean and standard deviation.
# Input: [count, state]
# Output: [updatedcount, updatedstate, rnv]
# where "state" is a seed and "updatedstate" can be used as a seed.
def random_normal_variate(mean; sd; count):
  next_rand_normal
  | recurse( if .[0] < count then next_rand_normal else empty end)
  | .[2] = (.[2] * sd) + mean;

'''Example''' The task can be completed using: [0,1] | random_normal_variate(1; 0.5; 1000) | .[2]

We show just the sample average and standard deviation:

def summary:
  length as $l | add as $sum | ($sum/$l) as $a
  | reduce .[] as $x (0; . + ( ($x - $a) | .*. ))
  | [ $a, (./$l | sqrt)] ;

[ [0,1] | random_normal_variate(1; 0.5; 1000) | .[2] ] | summary

{{out}} $ jq -n -c -f Random_numbers.jq [0.9932830741018853,0.4977760644490579]

Julia

Julia's standard library provides a randn function to generate normally distributed random numbers (with mean 0 and standard deviation 0.5, which can be easily rescaled to any desired values):

randn(1000) * 0.5 + 1

Kotlin

// version 1.0.6

import java.util.Random

fun main(args: Array<String>) {
    val r = Random()
    val da = DoubleArray(1000)
    for (i in 0 until 1000)  da[i] = 1.0 + 0.5 * r.nextGaussian()
    // now check actual mean and SD
    val mean = da.average()
    val sd = Math.sqrt(da.map { (it - mean) * (it - mean) }.average())
    println("Mean is $mean")
    println("S.D. is $sd")
}

Sample output: {{out}}


Mean is 1.0071784073168768
S.D. is 0.48567118114896807

LabVIEW

{{works with|LabVIEW|8.6}} [[File:LV_array_of_randoms_with_given_mean_and_stdev.png]]

Liberty BASIC

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

{{works with|UCB Logo}} The earliest Logos only have a RANDOM function for picking a random non-negative integer. Many modern Logos have floating point random generators built-in.

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 ?] []

Lingo

-- Returns a random float value in range 0..1
on randf ()
    n = random(the maxinteger)-1
    return n / float(the maxinteger-1)
end
normal = []
repeat with i = 1 to 1000
    normal.add(1 + sqrt(-2 * log(randf())) * cos(2 * PI * randf()) / 2)
end repeat

Lua

local list = {}
for i = 1, 1000 do
  list[i] = 1 + math.sqrt(-2 * math.log(math.random())) * math.cos(2 * math.pi * math.random()) / 2
end

M2000 Interpreter

M2000 use a Wichmann - Hill Pseudo Random Number Generator.


Module CheckIt {
      Function StdDev (A()) {
          \\ A()  has a copy of values
            N=Len(A())
            if N<1 then Error "Empty Array"
            M=Each(A())
            k=0
            \\ make sum, dev same type as A(k)
            sum=A(k)-A(k)
            dev=sum
            \\ find mean
            While M {
                  sum+=Array(M)
            }
            Mean=sum/N
            \\ make a pointet to A()
            P=A()
            \\ subtruct from each item
            P-=Mean

            M=Each(P)
            While M {
                  dev+=Array(M)*Array(M)
            }
            \\ as pointer to arrray
             =(if(dev>0->Sqrt(dev/N), 0), Mean)
      }
      Function randomNormal {
            \\ by default all numbers are double
            \\ cos() get degrees
          =1+Cos(360 * rnd) * Sqrt(-2 * Ln(rnd)) /2
      }
      \\ fill array calling  randomNormal() for each item
      Dim A(1000)<<randomNormal()
      \\ we can pass a pointer to array and place it to stack of values
      DisplayMeanAndStdDeviation(A())  ' mean ~ 1 std deviation ~0.5
      \\ check M2000 rnd only
      Dim B(1000)<<rnd
      DisplayMeanAndStdDeviation(B())  ' mean ~ 0.5 std deviation ~0.28


      DisplayMeanAndStdDeviation((0,0,14,14))  ' mean = 7 std deviation = 7
      DisplayMeanAndStdDeviation((0,6,8,14))  ' mean = 7 std deviation = 5
      DisplayMeanAndStdDeviation((6,6,8,8))  ' mean = 7 std deviation = 1

      Sub DisplayMeanAndStdDeviation(A)
            \\ push to stack all items of an array (need an array pointer)
            Push  ! StdDev(A)
            \\ read from strack two numbers
            Print "Mean is               "; Number
            Print "Standard Deviation is "; Number
      End Sub
}
Checkit

Maple

with(Statistics):
Sample(Normal(1, 0.5), 1000);

Mathematica

Built-in function RandomReal with built-in distribution NormalDistribution as an argument:

RandomReal[NormalDistribution[1, 1/2], 1000]

MATLAB

Native support :

    mu = 1; sd = 0.5;
    x = randn(1000,1) * sd + mu;

The statistics toolbox provides this function

   x = normrnd(mu, sd, [1000,1]);

This script uses the Box-Mueller Transform to transform a number from the uniform distribution to a normal distribution of mean = mu0 and standard deviation = chi2.

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

Output:

 randNorm(1,.5, [1000,1])

ans =

   0.693984121077029

Maxima

load(distrib)$

random_normal(1.0, 0.5, 1000);

MAXScript

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
)

Metafont

Metafont has normaldeviate which produces pseudorandom normal distributed numbers with mean 0 and variance one. So the following complete the task:

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

A run gave

>> 0.99947
>> 0.50533

Assigning a value to the special variable '''randomseed''' will allow to have always the same sequence of pseudorandom numbers

Mirah

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

=={{header|МК-61/52}}== П7 <-> П8 1/x П6 ИП6 П9 СЧ П6 1/x ln ИП8 * 2 * КвКор ИП9 2 * пи

  • sin * ИП7 + С/П БП 05


''Input'': РY - variance, РX - expectation.

Or:

<lang>3	10^x	П0	ПП	13	2	/	1	+	С/П	L0	03	С/П
СЧ	lg	2	/-/	*	КвКор	2	пи	^	СЧ	*	*	cos	*	В/О

to generate 1000 numbers with a mean of 1.0 and a standard deviation of 0.5.

=={{header|Modula-3}}== {{trans|C}}

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.

NetRexx

/* 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

{{out}}


Mean:               1.0
Standard Deviation: 0.5
Precision:          1

*    2.7
**    2.5
*    2.4
***    2.3
*****    2.2
*******    2.1
*************    2.0
*************    1.9
*****************************    1.8
*************************    1.7
*************************************    1.6
******************************************************    1.5
********************************************    1.4
********************************************************************    1.3
*****************************************************************    1.2
**************************************************************************    1.1
*********************************************************************************************    1.0
*************************************************************    0.9
**********************************************************************    0.8
**************************************************************    0.7
***********************************************************************    0.6
**************************************************************    0.5
******************************************    0.4
*******************************    0.3
***************************    0.2
***************    0.1
*********    0.0
******   -0.1
***   -0.2
***   -0.3
*   -0.4
*   -0.6
**   -0.7

NewLISP

(normal 1 .5 1000)

Nim

import math, strutils

const  precisn = 5
var rs: TRunningStat

proc normGauss: float {.inline.} = 1 + 0.76 * cos(2*PI*random(1.0)) * sqrt(-2*log10(random(1.0)))

randomize()

for j in 0..5:
   for i in 0..1000:
      rs.push(normGauss())
   echo("mean: ", $formatFloat(rs.mean,ffDecimal,precisn),
        " stdDev: ", $formatFloat(rs.standardDeviation(),ffDecimal,precisn))

{{out}}

mean: 1.01703 stdDev: 0.50324
mean: 1.01187 stdDev: 0.50060
mean: 1.00216 stdDev: 0.49969
mean: 1.00335 stdDev: 0.50184
mean: 1.00120 stdDev: 0.49830
mean: 1.00217 stdDev: 0.49911

Objeck

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();
    }
  }
}

OCaml

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 ());;

Octave

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

{{out}}

1.0209
0.51048

ooRexx

{{trans|REXX}}

version 1

/*REXX pgm gens 1,000 normally distributed #s: mean=1, standard dev.=0.5*/
  pi=RxCalcPi()                     /* get value of 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.*/
    n.g=random(0,1e5)/1e5           /* REXX gens uniform rand integers*/
    End

  Say '              old mean=' mean()
  Say 'old standard deviation=' stddev()
  Say
  Do j=1 To n-1 By 2
    m=j+1
                                    /*use Box-Muller method           */
    _=sd*RxCalcPower(-2*RxCalcLog(n.j),.5)*RxCalcCos(2*pi*n.m,,'R')+mean
    n.m=sd*RxCalcpower(-2*RxCalcLog(n.j),.5)*RxCalcSin(2*pi*n.m,,'R')+,
  mean                              /* rand # must be 0???1.          */
    n.j=_
    End                             /* j                              */
  Say '              new mean=' mean()
  Say 'new standard deviation=' stddev()
  Exit
mean:
  _=0
  Do k=1 For n
    _=_+n.k
    End
  Return _/n
stddev:
  _avg=mean()
  _=0
  Do k=1 For n
    _=_+(n.k-_avg)**2
    End
  Return RxCalcPower(_/n,.5)

:: requires rxmath library

{{out}}

              old mean= 0.49830002
old standard deviation= 0.283199568

              new mean= 1.00377404
new standard deviation= 0.501444536

version 2

Using the nice function names in the algorithm.

/*REXX pgm gens 1,000 normally distributed #s: mean=1, standard dev.=0.5*/
  pi=RxCalcPi()                     /* get value of 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.*/
    n.g=random(0,1e5)/1e5           /* REXX gens uniform rand integers*/
    End

  Say '              old mean=' mean()
  Say 'old standard deviation=' stddev()
  Say
  Do j=1 To n-1 By 2
    m=j+1
                                    /*use Box-Muller method           */
    _=sd*sqrt(-2*ln(n.j))*cos(2*pi*n.m)+mean
    n.m=sd*sqrt(-2*ln(n.j))*sin(2*pi*n.m)+mean
    n.j=_
    End
  Say '              new mean=' mean()
  Say 'new standard deviation=' stddev()
  Exit
mean:
  _=0
  Do k=1 For n
    _=_+n.k
    End
  Return _/n
stddev:
  _avg=mean()
  _=0
  Do k=1 For n
    _=_+(n.k-_avg)**2
    End
  Return sqrt(_/n)

sqrt: Return RxCalcSqrt(arg(1))
ln:   Return RxCalcLog(arg(1))
cos:  Return RxCalcCos(arg(1),,'R')
sin:  Return RxCalcSin(arg(1),,'R')

:: requires rxmath library

PARI/GP

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)

Pascal

The following function calculates Gaussian-distributed random numbers with the Box-Müller algorithm:


function rnorm (mean, sd: real): real;
 {Calculates Gaussian random numbers according to the Box-Müller approach}
var
  u1, u2: real;
begin
  u1 := random;
  u2 := random;
  rnorm := mean * abs(1 + sqrt(-2 * (ln(u1))) * cos(2 * pi * u2) * sd);
end;

[[#Delphi | Delphi]] and [[#Free Pascal|Free Pascal]] support implement a '''randg''' function that delivers Gaussian-distributed random numbers.

Perl

my $PI = 2 * atan2 1, 0;

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

Perl 6

{{works with|Rakudo|#22 "Thousand Oaks"}}

sub randnorm ($mean, $stddev) {
    $mean + $stddev * sqrt(-2 * log rand) * cos(2 * pi * rand)
}

my @nums = randnorm(1, 0.5) xx 1000;

# Checking
say my $mean = @nums R/ [+] @nums;
say my $stddev = sqrt $mean**2 R- @nums R/ [+] @nums X** 2;

Phix

{{Trans|Euphoria}}

function RandomNormal()
    return sqrt(-2*log(rnd())) * cos(2*PI*rnd())
end function

sequence s = repeat(0,1000)
for i=1 to length(s) do
    s[i] = 1 + 0.5 * RandomNormal()
end for

PHP

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);

}

PicoLisp

{{trans|C}}

(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) " ") ) )

{{out}}

1.500334 1.212931 1.095283 0.433122 0.459116 1.302446 0.402477

PL/I


/* 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;

{{out}}


Mean = 1.0125630677913652  Standard Deviation = 0.5067289784535284
3 runs with different seeds to random():
Mean = 1.0008390411168471  Standard Deviation = 0.5095810511317908
Mean = 0.9754351286894838  Standard Deviation = 0.4804376530558166
Mean = 1.0177411222687990  Standard Deviation = 0.5165899662493400

PL/SQL


DECLARE
  --The desired collection
  type t_coll is table of number index by binary_integer;
  l_coll t_coll;

  c_max pls_integer := 1000;
BEGIN
   FOR l_counter IN 1 .. c_max
   LOOP
      -- dbms_random.normal delivers normal distributed random numbers with a mean of 0 and a variance of 1
      -- We just adjust the values and get the desired result:
      l_coll(l_counter) := DBMS_RANDOM.normal * 0.5 + 1;
      DBMS_OUTPUT.put_line (l_coll(l_counter));
   END LOOP;
END;

Pop11

;;; 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;

PowerShell

Equation adapted from Liberty BASIC

function Get-RandomNormal
    {
    [CmdletBinding()]
    Param ( [double]$Mean, [double]$StandardDeviation )

    $RandomNormal = $Mean + $StandardDeviation * [math]::Sqrt( -2 * [math]::Log( ( Get-Random -Minimum 0.0 -Maximum 1.0 ) ) ) * [math]::Cos( 2 * [math]::PI * ( Get-Random -Minimum 0.0 -Maximum 1.0 ) )

    return $RandomNormal
    }

#  Standard deviation function for testing
function Get-StandardDeviation
    {
    [CmdletBinding()]
    param ( [double[]]$Numbers )

    $Measure = $Numbers | Measure-Object -Average
    $PopulationDeviation = 0
    ForEach ($Number in $Numbers) { $PopulationDeviation += [math]::Pow( ( $Number - $Measure.Average ), 2 ) }
    $StandardDeviation = [math]::Sqrt( $PopulationDeviation / ( $Measure.Count - 1 ) )
    return $StandardDeviation
    }

#  Test
$RandomNormalNumbers = 1..1000 | ForEach { Get-RandomNormal -Mean 1 -StandardDeviation 0.5 }

$Measure = $RandomNormalNumbers | Measure-Object -Average

$Stats = [PSCustomObject]@{
    Count             = $Measure.Count
    Average           = $Measure.Average
    StandardDeviation = Get-StandardDeviation -Numbers $RandomNormalNumbers
}

$Stats | Format-List

{{out}}


Count             : 1000
Average           : 1.01206560135809
StandardDeviation : 0.489099623426272

PureBasic

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

Python

;Using random.gauss:

 import random
>>> values = [random.gauss(1, .5) for i in range(1000)]
>>>

;Quick check of distribution:

 def quick_check(numbers):
    count = len(numbers)
    mean = sum(numbers) / count
    sdeviation = (sum((i - mean)**2 for i in numbers) / count)**0.5
    return mean, sdeviation

>>> quick_check(values)
(1.0140373306786599, 0.49943411329234066)
>>>

Note that the ''random'' module in the Python standard library supports a number of statistical distribution methods.

;Alternatively using random.normalvariate:

 values = [ random.normalvariate(1, 0.5) for i in range(1000)]
>>> quick_check(values)
(0.990099111944864, 0.5029847005836282)
>>>

R

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

Racket


#lang racket
(for/list ([i 1000])
  (add1 (* (sqrt (* -2 (log (random)))) (cos (* 2 pi (random))) 0.5)))

Raven

define PI
   -1 acos

define rand1
   9999999 choose 1 + 10000000.0 /

define randNormal
   rand1 PI * 2 * cos
   rand1 log -2 * sqrt
   *
   2 / 1 +

1000 each drop randNormal "%f\n" print

Quick Check (on linux with code in file rand.rv)

raven rand.rv | awk '{sum+=$1; sumsq+=$1*$1;} END {print "stdev = " sqrt(sumsq/NR - (sum/NR)**2); print "mean = " sum/NR}'
stdev = 0.497773
mean = 1.01497

REXX

The REXX language doesn't have any "higher math" functions like SQRT/SIN/COS/LN/LOG/EXP/POW/etc.,

so we ''hoi polloi'' REXX programmers have to roll our own.

Programming note: note the range of the random numbers: (0,1]

(that is, random numbers from zero──►unity, excluding zero, including unity).

/*REXX pgm generates 1,000 normally distributed numbers:  mean=1,  standard deviation=½.*/
numeric digits 20                                /*the default decimal digit precision=9*/
parse arg n seed .                               /*allow specification of N and the seed*/
if n==''  |  n==","    then n=1000               /*N:    is the size of the array.      */
if datatype(seed,'W')  then call random ,,seed   /*SEED: for repeatable random numbers. */
newMean=1                                        /*the desired new mean (arithmetic avg)*/
sd=1/2                                           /*the desired new standard deviation.  */
       do g=1  for n                             /*generate  N uniform random #'s (0,1].*/
       #.g = random(1, 1e5)  /  1e5              /*REXX's RANDOM BIF generates integers.*/
       end   /*g*/                               /* [↑]  random integers ──► fractions. */
say '              old mean='   mean()
say 'old standard deviation='   stdDev()
call pi;       pi2=pi * 2                        /*define   pi    and also    2 * pi.   */
say
       do j=1  to n-1  by 2;    m=j+1            /*step through the iterations by two.  */
           _=sd *  sqrt(ln(#.j) * -2)            /*calculate the  used-twice expression.*/
       #.j=_ * cos(pi2 * #.m)  +  newMean        /*utilize the  Box─Muller method.      */
       #.m=_ * sin(pi2 * #.m)  +  newMean        /*random number must be:      (0,1]    */
       end   /*j*/
say '              new mean='     mean()
say 'new standard deviation='     stdDev()
exit                                             /*stick a fork in it,  we're all done. */
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
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   /*digs overkill*/
pi:     pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi  /*  "      "   */
r2r:    return arg(1)  //  (pi() * 2)                                                                 /*normalize ang*/
sin:    procedure; parse 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
          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
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
cos:    procedure; parse arg x;       x=r2r(x);        a=abs(x);               hpi=pi * .5
            numeric fuzz min(6, digits() - 3);      if a=pi    then return -1
            if a=hpi | a=hpi*3  then return 0;      if a=pi/3  then return .5
            if a=pi * 2/3       then return -.5;                    return .sinCos(1,1,-1)
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
sqrt:   procedure; parse arg x; if x=0  then return 0;  d=digits();  numeric digits; h=d+6
        numeric form; parse value format(x,2,1,,0) 'E0'  with  g 'E' _ .;  g=g * .5'e'_ %2
        m.=9;     do j=0  while h>9;       m.j=h;                h=h%2 + 1;      end /*j*/
                  do k=j+5  to 0  by -1;   numeric digits m.k;   g=(g+x/g)*.5;   end /*k*/
        numeric digits d;     return g/1

'''output''' when using the default inputs:


              old mean= 0.5015724
old standard deviation= 0.28652466389342471402

              new mean= 0.98807025356443262689
new standard deviation= 0.50002924192766720838

Ring


for i = 1 to 10
    see random(i) + nl
next i

Ruby

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

Run BASIC

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

Rust

{{libheader|rand}} '''Using a for-loop:'''

extern crate rand;
use rand::distributions::{Normal, IndependentSample};

fn main() {
    let mut rands = [0.0; 1000];
    let normal = Normal::new(1.0, 0.5);
    let mut rng = rand::thread_rng();
    for num in rands.iter_mut() {
        *num = normal.ind_sample(&mut rng);
    }
}

'''Using iterators:'''

extern crate rand;
use rand::distributions::{Normal, IndependentSample};

fn main() {
    let rands: Vec<_> = {
        let normal = Normal::new(1.0, 0.5);
        let mut rng = rand::thread_rng();
        (0..1000).map(|_| normal.ind_sample(&mut rng)).collect()
    };
}

SAS


/* Generate 1000 random numbers with mean 1 and standard deviation 0.5.
  SAS version 9.2 was used to create this code.*/

data norm1000;
  call streaminit(123456);
/* Set the starting point, so we can replicate results.
   If you want different results each time, comment the above line. */
  do i=1 to 1000;
    r=rand('normal',1,0.5);
    output;
  end;
run;

Results:


 The MEANS Procedure

                     Analysis Variable : r

                          Mean         Std Dev
                  ----------------------------
                     0.9907408       0.4844051
                  ----------------------------

Sather

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;

Scala

One liner

List.fill(1000)(1.0 + 0.5 * scala.util.Random.nextGaussian)

Academic

val distrubution = {
  def randomNormal = 1.0 + 0.5 * scala.util.Random.nextGaussian

  def normalDistribution(a: Double): Stream[Double] = a #:: normalDistribution(randomNormal)

  normalDistribution(randomNormal)
}

/*
 * Let's test it
 */
  def calcAvgAndStddev[T](ts: Iterable[T])(implicit num: Fractional[T]): (T, Double) = {
    val mean: T =
      num.div(ts.sum, num.fromInt(ts.size)) // Leaving with type of function T

    // Root of mean diffs
    val stdDev = sqrt(ts.map { x =>
      val diff = num.toDouble(num.minus(x, mean))
      diff * diff
    }.sum / ts.size)

    (mean, stdDev)
  }

println(calcAvgAndStddev(distrubution.take(1000))) // e.g. (1.0061433267806525,0.5291834867560893)

Scheme

; 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)

Seed7

$ 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;

Sidef

var arr = 1000.of { 1 + (0.5 * sqrt(-2 * 1.rand.log) * cos(Num.tau * 1.rand)) }
arr.each { .say }

Standard ML

{{works with|SML/NJ}} SML/NJ has two structures for random numbers:

  1. Rand (a linear congruential generator). You create the generator by calling Rand.mkRandom with a seed (of word type). You can call the generator with () repeatedly to get a word in the range [Rand.randMin, Rand.randMax]. You can use the Rand.norm function to transform the output into a real from 0 to 1, or use the Rand.range (i,j) function to transform the output into an int of the given range.
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 ());
  1. Random (a subtract-with-borrow generator). You create the generator by calling Random.rand with a seed (of a pair of ints). You can use the Random.randInt function to generate a random int over its whole range; Random.randNat to generate a non-negative random int; Random.randReal to generate a real between 0 and 1; or Random.randRange (i,j) to generate an int in the given range.
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 ());

Other implementations of Standard ML have their own random number generators. For example, Moscow ML has a Random structure that is different from the one from SML/NJ. {{works with|PolyML}} The SML Basis Library does not provide a routine for uniform deviate generation, and PolyML does not have one. Using a routine from "Monte Carlo" by Fishman (Springer), in the function uniformdeviate, and avoiding the slow IntInf's:


val urandomlist =  fn seed => fn n =>
let
	val uniformdeviate = fn seed =>
	let
	  val in31m = (Real.fromInt o Int32.toInt ) (getOpt (Int32.maxInt,0) );
	  val in31 = in31m +1.0;
	  val s1 = 41160.0;
	  val s2 = 950665216.0;
	  val v = Real.realFloor seed;
	  val val1 = v*s1;
	  val val2 = v*s2;
	  val next1 = Real.fromLargeInt (Real.toLargeInt IEEEReal.TO_NEGINF (val1/in31)) ;
	  val next2 = Real.rem(Real.realFloor(val2/in31) , in31m );
	  val valt = val1+val2 - (next1+next2)*in31m;
	  val nextt = Real.realFloor(valt/in31m);
	  val valt = valt - nextt*in31m;
	in
	  (valt/in31m,valt)
	end;
val store =  ref (0.0,0.0);
val rec u =  fn S => fn 0 => [] | n=> (store:=uniformdeviate S; (#1 (!store)):: (u (#2 (!store)) (n-1))) ;
in
	u seed n
end;

local
	open Math
in
	val bmconv = fn urand => fn vrand => 1.0+0.5*(sqrt(~2.0*ln urand)*cos (2.0*pi*vrand) )
end;

val rec makeNormals = fn once => fn u::v::[] => [once u v] |
	u::v::rm => (once u v )::(makeNormals once rm );

val anyrealseed=1009.0 ;
makeNormals bmconv (urandomlist anyrealseed 2000);

Stata

clear all
set obs 1000
gen x=rnormal(1,0.5)

Mata

a = rnormal(1000,1,1,0.5)

Tcl

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()}]
}

=={{header|TI-83 BASIC}}== Builtin function: randNorm() randNorm(1,.5)

Or by a program:

Calculator symbol translations:

"STO" arrow: →

Square root sign: √

ClrList L1 Radian For(A,1,1000) √(-2ln(rand))cos(2πA)→L1(A) End

TorqueScript

for (%i = 0; %i < 1000; %i++)
	%list[%i] = 1 + mSqrt(-2 * mLog(getRandom())) * mCos(2 * $pi * getRandom());

Ursala

There are two ways of interpreting the task, either to simulate sampling a population described by the given statistics, or to construct a sample exhibiting the given statistics. Both are illustrated below. The functions parameterized by the mean and standard deviation take a sample size and return a sample of that size, represented as a list of floating point numbers. The Z library function simulates a draw from a standard normal distribution. Mean and standard deviation library functions are also used in this example.

#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>

The output shows the mean and standard deviation for both sample vectors, the latter being exact by construction.

<
   (1.004504e+00,4.915525e-01),
   (1.000000e+00,5.000000e-01)>

Visual FoxPro


LOCAL i As Integer, m As Double, n As Integer, sd As Double
py = PI()
SET TALK OFF
SET DECIMALS TO 6
CREATE CURSOR gdev (deviate B(6))
RAND(-1)
n = 1000
m = 1
sd = 0.5
CLEAR
FOR i = 1 TO n
	INSERT INTO gdev VALUES (GaussDev(m, 1/sd))
ENDFOR
CALCULATE AVG(deviate), STD(deviate) TO m, sd
? "Mean", m, "Std Dev", sd
SET TALK ON
SET DECIMALS TO

FUNCTION GaussDev(mean As Double, sdev As Double) As Double
LOCAL z As Double
z = SQRT(-2*LOG(RAND()))*COS(py*RAND())
IF sdev # 0
	z = mean + z/sdev
ENDIF
RETURN z
ENDFUNC

Yorick

Returns array of ''count'' random numbers with mean 0 and standard deviation 1.

func random_normal(count) {
   return sqrt(-2*log(random(count))) * cos(2*pi*random(count));
}

Example of basic use:

> nums = random_normal(1000); // create an array 1000 random numbers
> nums(avg); // show the mean
0.00901216
> nums(rms); // show the standard deviation
0.990265

Example with a mean of 1.0 and a standard deviation of 0.5:

> nums = random_normal(1000) * 0.5 + 1;
> nums(avg);
1.00612
> nums(rms);
0.496853

zkl

fcn mkRand(mean,sd){ //normally distributed random w/mean & standard deviation
   pi:=(0.0).pi;    // using the Box–Muller transform
   rz1:=fcn{1.0-(0.0).random(1)}  // from [0,1) to (0,1]
   return('wrap(){((-2.0*rz1().log()).sqrt() * (2.0*pi*rz1()).cos())*sd + mean })
}

This creates a new random number generator, now to use it:

var g=mkRand(1,0.5);
ns:=(0).pump(1000,List,g); // 1000 rands with mean==1 & sd==1/2
mean:=(ns.sum(0.0)/1000);  //-->1.00379
   // calc sd of list of numbers:
(ns.reduce('wrap(p,n){p+(n-mean).pow(2)},0.0)/1000).sqrt() //-->0.494844

ZX Spectrum Basic

Here we have converted the QBasic code to suit the ZX Spectrum:

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