```Contributor: RANDALL ELTON DING

(*
From: randyd@alpha2.csd.uwm.edu (Randall Elton Ding)

>I a program I'm currently struggeling with, I need to get a random number
>from a Gaussian distribution. Anybody got any ideas or anybody able to point
>to something which does the job.

This does a pretty good job of generating a gaussian random variable
with mean `a` and standard deviation `d`.
This program also does a graphic plot to demonstrate the function.

First, here is the origional C source if the gaussian function
which I transcribed to beloved pascal..

/* ------------------------------------------------ *
* gaussian -- generates a gaussian random variable *
*             with mean a and standard deviation d *
* ------------------------------------------------ */
double gaussian(a,d)
double a,d;
{
static double t = 0.0;
double x,v1,v2,r;
if (t == 0) {
do {
v1 = 2.0 * rnd() - 1.0;
v2 = 2.0 * rnd() - 1.0;
r = v1 * v1 + v2 * v2;
} while (r>=1.0);
r = sqrt((-2.0*log(r))/r);
t = v2*r;
return(a+v1*r*d);
}
else {
x = t;
t = 0.0;
return(a+x*d);
}
}

* ----------------------------------------------------------------------
* now, the same thing in pascal
* ----------------------------------------------------------------------
*)

{\$N+}
program testgaussian;

uses graph,crt;

const
bgipath = 'e:\bp\bgi';

procedure initbgi;
var
errcode,grdriver,grmode: integer;

begin
grdriver:= detect;
grmode:= 0;
initgraph (grdriver,grmode,bgipath);
errcode:= graphresult;
if errcode <> grok then begin
writeln ('Graphics error: ',grapherrormsg (errcode));
halt (1);
end;
end;

function rnd: double;   { this isn't the best, but it works }
var                   { returns a random number between 0 and 1 }
i: integer;
r: double;

begin
r:= 0;
for i:= 1 to 15 do begin
r:= r + random(10);
r:= r/10;
end;
rnd:= r;
end;

function gaussian(a,d: double): double;      { a is mean }
const                                      { d is standard deviation }
t: double = 0;   { pascal's equivalent to C's static variable }

var
x,v1,v2,r: double;

begin
if t=0 then begin
repeat
v1:= 2*rnd-1;
v2:= 2*rnd-1;
r:= v1*v1+v2*v2
until r<1;
r:= sqrt((-2*ln(r))/r);
t:= v2*r;
gaussian:= a+v1*r*d;
end
else begin
x:= t;
t:= 0;
gaussian:= a+x*d;
end;
end;

procedure testplot;
var
x,mx,my,y1: word;
y: array[1..999] of word;
{ ^^^ make this bigger if you have incredible graphics }
begin
initbgi;
mx:= getmaxx+1;
my:= getmaxy;
fillchar(y,sizeof(y),#0);
repeat
x:= trunc(gaussian(mx/2,50));
y1:= y[x];
putpixel(x,my-y1,white);
y[x]:= y1+1;
until keypressed;
closegraph;
end;

begin
randomize;
testplot;
end.

```