From: "Earl F. Glynn"
Subject: Re: Delphi's Random Number Generator
Date: Friday, October 06, 2000 8:50 AM

John:

> We are using Borland's Random Number Generator for Statistical
> Sampling.  Our Auditors need to know about the
> Random number formula the Random Procedure uses to generate
> random numbers.  Can you tell us the name of the formula used,
> and what the formula is?

The Random function uses "compiler magic" to decide whether it
returns an integer or floating-point extended result.  For an
integer result, _RandInt in System.PAS is called.  For an extended
result, _RandExt in System.PAS is called.

Here are the assembly language routines from System.PAS:

procedure       _RandInt;
asm
{     ->EAX     Range   }
{     <-EAX     Result  }
        IMUL    EDX,RandSeed,08088405H
        INC     EDX
        MOV     RandSeed,EDX
        MUL     EDX
        MOV     EAX,EDX
end;

procedure       _RandExt;
const two2neg32: double = ((1.0/$10000) / $10000);  // 2^-32
asm
{       FUNCTION _RandExt: Extended;    }

        IMUL    EDX,RandSeed,08088405H
        INC     EDX
        MOV     RandSeed,EDX

        FLD     two2neg32
        PUSH    0
        PUSH    EDX
        FILD    qword ptr [ESP]
        ADD     ESP,8
        FMULP  ST(1), ST(0)
end;


RandSeed can be set directly or through a call to Randomize.

In Ray Lishner's "Delphi in a NutShell" he says:
"Delphi uses a pseudorandom number generator (PRNG) with a cycle of
2^32.  Although adequate for simple simulations, it is not suitable for use
in encrption or other areas where you need a high-quality PRNG."
I don't know whether your auditors will like that statement or not.

For alternative random number generators, try:

- Fast BASM implementation of the "Mother-of-all Pseudo Random Number Generators" as proposed by
well-known random number guru, Dr. George Marsaglia of the Department of Statistics, Florida State
University. Freeware with source code.
www.mindspring.com/~efd/tools.htm
(Perhaps your auditors would like a Florida professor's work!)

Ultimate Random Number Suite
http://www.engineeringobjects.com/URNS.htm

I keep info about Random number generators in Delphi in the Probability and Links sections of this
page:
http://www.efg2.com/Lab/Library/Delphi/MathFunctions/StatisticsAndProbability.htm