Random numbers

From Rosetta Code
Task
Random numbers
You are encouraged to solve this task according to the task description, using any language you may know.

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 standard deviation of 0.5

Many libraries only generate uniformly distributed random numbers.

If so, use this formula to convert them to a normal distribution.

See also

Ada[edit]

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[edit]

Translation of: C
Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
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]))
)
Output:
( 0.693461, 0.948424, 0.482261, 1.045939, 0.890818, 1.467935, 0.604153, 0.804811, 0.690227, 0.83462 ... )

AutoHotkey[edit]

contributed by Laszlo on the ahk 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[edit]

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
}
 
Output:
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[edit]

Works with: QuickBasic version 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[edit]

      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
Output:
Mean = 1.01848064
Standard deviation = 0.503551814

C[edit]

#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;
}

C#[edit]

Translation of: 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++[edit]

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;
}
Library: 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[edit]

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

Common Lisp[edit]

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

D[edit]

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[edit]

(Untested)

Library: 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[edit]

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.
Output:
Mean          = 1.0098
Std deviation = 0.5016

DWScript[edit]

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[edit]

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

Eiffel[edit]

 
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

Elixir[edit]

 
defmodule Random do
def init() do
 :random.seed(:erlang.now())
end
def normal(mean, sd) do
{a, b} = {:random.uniform(), :random.uniform()}
mean + sd * (:math.sqrt(-2 * :math.log(a)) * :math.cos(2 * :math.pi * b))
end
end
 
Random.init()
xs = for _ <- 1..1000, do: Random.normal(1.0, 0.5)
 

Erlang[edit]

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)]).
 
Output:
mean = 1.0118289913718608
stddev = 0.5021636849524854

ERRE[edit]

 
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(-2*LOG(R1#))*COS(2*π*R2#)
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[edit]

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

Euphoria[edit]

Translation of: 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

Factor[edit]

1000 [ 1.0 0.5 normal-random-float ] replicate

Falcon[edit]

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[edit]

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[edit]

Works with: gforth version 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

Fortran[edit]

Works with: Fortran version 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
Output:
 Mean = 0.995112
 Standard Deviation = 0.503373

Free Pascal[edit]

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;
 

F#[edit]

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[edit]

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()
}
}

Groovy[edit]

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

Haskell[edit]

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

HicEst[edit]

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

Icon and Unicon[edit]

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[edit]

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

J[edit]

Solution:

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

Alternative Solution:
Using the normal script from the stats/distribs addon.

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

Java[edit]

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[edit]

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[edit]

Works with: jq version 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
Output:
$ jq -n -c -f Random_numbers.jq
[0.9932830741018853,0.4977760644490579]

Julia[edit]

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

LabVIEW[edit]

Works with: LabVIEW version 8.6

LV array of randoms with given mean and stdev.png

Liberty BASIC[edit]

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

[edit]

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 ?] []


lua[edit]

 
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
 

Mathematica[edit]

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

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

MATLAB[edit]

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[edit]

load(distrib)$
 
random_normal(1.0, 0.5, 1000);

MAXScript[edit]

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[edit]

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[edit]

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
 

МК-61/52[edit]

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:

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.

Modula-3[edit]

Translation of: 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[edit]

/* 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
 
Output:
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[edit]

(normal 1 .5 1000)

Nim[edit]

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))
Output:
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[edit]

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[edit]

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[edit]

p = normrnd(1.0, 0.5, 1000, 1);
disp(mean(p));
disp(sqrt(sum((p - mean(p)).^2)/numel(p)));
Output:
1.0209
0.51048

ooRexx[edit]

Translation of: REXX

version 1[edit]

/*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
Output:
              old mean= 0.49830002
old standard deviation= 0.283199568

              new mean= 1.00377404
new standard deviation= 0.501444536  

version 2[edit]

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[edit]

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[edit]

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 and Free Pascal support implement a randg function that delivers Gaussian-distributed random numbers.

Perl[edit]

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

Perl 6[edit]

Works with: Rakudo version #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[edit]

Translation of: 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[edit]

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[edit]

Translation of: 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) " ") ) )
Output:
1.500334 1.212931 1.095283 0.433122 0.459116 1.302446 0.402477

PL/I[edit]

 
/* 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;
 
Output:
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[edit]

 
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[edit]

;;; 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[edit]

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
 
"Count: " + $Measure.Count
"Average: " + $Measure.Average
"Standard deviation: " + ( Get-StandardDeviation -Numbers $RandomNormalNumbers )
Output:
Count:    1000
Average:  0.99601224493548
Standard deviation:  0.480629257616293

PureBasic[edit]

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[edit]

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[edit]

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

Racket[edit]

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

Raven[edit]

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[edit]

The REXX language doesn't have any "higher math" functions like SQRT/SIN/COS/LN/LOG/EXP/POW/etc.,
so we hoi polloi programmers have 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 gens 1,000 normally distributed #s:  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 seed\=='' 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*/ /* [↑] rand integers ──► fractions. */
say ' old mean=' mean()
say 'old standard deviation=' stdDev()
call pi; pi2=pi+pi /*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. */
/*──────────────────────────────────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 /*digs overkill*/
pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi /* " " */
r2r: return arg(1) // (2*pi()) /*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; 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
 
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(); i=; m.=9
numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
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)i /*make complex if X < 0.*/

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[edit]

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

Ruby[edit]

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

Run BASIC[edit]

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[edit]

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[edit]

 
/* 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[edit]

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[edit]

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

Scheme[edit]

; 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[edit]

$ 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[edit]

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

Standard ML[edit]

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 ());

2) 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.

Tcl[edit]

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()}]
}

TI-83 BASIC[edit]

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)
√(-2*ln(rand))*cos(2*π*A)→L1(A)
End

TorqueScript[edit]

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

Ursala[edit]

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[edit]

 
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[edit]

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[edit]

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[edit]

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