# The mt19937 Reference Manual

Next: , Previous: , Up: (dir)   [Contents][Index]

# The mt19937 Reference Manual

This is the mt19937 Reference Manual, version 1.1, generated automatically by Declt version 2.4 "Will Decker" on Wed Jun 20 12:18:50 2018 GMT+0.

Next: , Previous: , Up: Top   [Contents][Index]

## 1 Introduction

```Introduction
============

MT19937 is a portable Mersenne Twister random number generator. It
is mainly a modification of CMUCL's random number generator with all
the CMUCL-specific parts taken out.

It is faster than the JMT Mersenne Twister implementation, but
significantly slower than native random number generators provided by
major Common Lisp implementations. For light use this shouldn't be a
problem, since it is still very fast.

It should be very stable, since it's based on stable CMUCL code. It
has been tested on CMUCL, SBCL, LispWorks, Allegro CL, GCL, CLISP, and
Corman Lisp.

What's the point?
=================

Why, you might ask, would you want to use a portable, slower random
number generator? The answer is consistancy. The portable version of
this code was originally created for Maxima, a computer algebra
system. They wanted the results of the random number generator to be
portable across several implementations and platforms, so that if you
used a certain seed on CMUCL the numbers generated would be the same
as you would get with the same seed on GCL or CLISP. This was more
important than achieving the maximum possible speed. You may have
similar problems.

Usage
=====

MT19937 is a plug-in replacement for the Common Lisp random-number
generator. The MT19937 package exports all the Common Lisp symbols
related to random number generation, so you just need to load MT19937
and call its functions instead of the built-in ones. For example:

;; Make random numbers with your implementation's random
;; number generator.
(random 1234567)
(random 42.56)
(random 3.1415d0)

;; Make random numbers using MT19937
(mt19937:random 1234567)
(mt19937:random 42.56)
(mt19937:random 3.1415d0)

;; MT19937 has its own random state
(eq *random-state*
mt19937:*random-state*)  => nil

=======

MT19937 is in the public domain.
```

Next: , Previous: , Up: Top   [Contents][Index]

## 2 Systems

The main system appears first, followed by any subsystem dependency.

Previous: , Up: Systems   [Contents][Index]

### 2.1 mt19937

Author

Douglas T. Crosher and Raymond Toy

Public domain

Description

Portable MT19937 Mersenne Twister random number generator

Version

1.1

Source

mt19937.asd (file)

Component

mt19937.lisp (file)

Next: , Previous: , Up: Top   [Contents][Index]

## 3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

Previous: , Up: Files   [Contents][Index]

### 3.1 Lisp

Next: , Previous: , Up: Lisp files   [Contents][Index]

#### 3.1.1 mt19937.asd

Location

mt19937.asd

Systems

mt19937 (system)

Packages

Previous: , Up: Lisp files   [Contents][Index]

#### 3.1.2 mt19937/mt19937.lisp

Parent

mt19937 (system)

Location

mt19937.lisp

Packages
Exported Definitions
Internal Definitions

Next: , Previous: , Up: Top   [Contents][Index]

## 4 Packages

Packages are listed by definition order.

Next: , Previous: , Up: Packages   [Contents][Index]

### 4.1 mt19937-system

Source

mt19937.asd

Use List
• asdf/interface
• common-lisp

Previous: , Up: Packages   [Contents][Index]

### 4.2 mt19937

Source

mt19937.lisp (file)

Use List

common-lisp

Exported Definitions
Internal Definitions

Next: , Previous: , Up: Top   [Contents][Index]

## 5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

Next: , Previous: , Up: Definitions   [Contents][Index]

### 5.1 Exported definitions

Next: , Previous: , Up: Exported definitions   [Contents][Index]

#### 5.1.1 Special variables

Special Variable: *random-state*
Package
Source

mt19937.lisp (file)

Next: , Previous: , Up: Exported definitions   [Contents][Index]

#### 5.1.2 Compiler macros

Compiler Macro: random ARG &optional STATE
Package
Source

mt19937.lisp (file)

Next: , Previous: , Up: Exported definitions   [Contents][Index]

#### 5.1.3 Functions

Function: %random-double-float ARG STATE

Handle the single or double float case of RANDOM. We generate a float
in [0d0, 1d0) by clobbering the mantissa of 1d0 with random bits (52 bits); this yields a number in [1d0, 2d0). Then 1d0 is subtracted.

Package
Source

mt19937.lisp (file)

Function: %random-single-float ARG STATE

Handle the single or double float case of RANDOM. We generate a float
in [0f0, 1f0) by clobbering the mantissa of 1f0 with random bits (23 bits); this yields a number in [1f0, 2f0). Then 1f0 is subtracted.

Package
Source

mt19937.lisp (file)

Function: init-random-state &optional SEED STATE

Generate an random state vector from the given SEED. The seed can be either an integer or a vector of (unsigned-byte 32)

Package
Source

mt19937.lisp (file)

Function: make-random-state &optional STATE

Make a random state object. If STATE is not supplied, return a copy of the default random state. If STATE is a random state, then return a copy of STATE. If STATE is T then return a random state generated from the universal time. To make a random state from an integer seed, try “(make-random-object :state (init-random-state <seed>))”.

Package
Source

mt19937.lisp (file)

Function: random ARG &optional STATE

Generates a uniformly distributed pseudo-random number greater than or equal to zero and less than Arg. State, if supplied, is the random state to use.

Package
Source

mt19937.lisp (file)

Function: random-chunk STATE
Package
Source

mt19937.lisp (file)

Function: random-state-p OBJECT
Package
Source

mt19937.lisp (file)

Previous: , Up: Exported definitions   [Contents][Index]

#### 5.1.4 Structures

Structure: random-state ()
Package
Source

mt19937.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots
Slot: state
Type

(simple-array (unsigned-byte 32) (627))

Initform

(mt19937:init-random-state)

random-state-state (function)

Writers

(setf random-state-state) (function)

Previous: , Up: Definitions   [Contents][Index]

### 5.2 Internal definitions

Next: , Previous: , Up: Internal definitions   [Contents][Index]

#### 5.2.1 Constants

Constant: mt19937-b
Package
Source

mt19937.lisp (file)

Constant: mt19937-c
Package
Source

mt19937.lisp (file)

Package
Source

mt19937.lisp (file)

Constant: mt19937-m
Package
Source

mt19937.lisp (file)

Constant: mt19937-n
Package
Source

mt19937.lisp (file)

Package
Source

mt19937.lisp (file)

Constant: random-chunk-length
Package
Source

mt19937.lisp (file)

Previous: , Up: Internal definitions   [Contents][Index]

#### 5.2.2 Functions

Function: %random-integer ARG STATE

Generates an integer greater than or equal to zero and less than Arg. Successive chunks are concatenated without overlap to construct integers larger than a single chunk. The return value has this property:
If two integers are generated from the same state with Arg equal to 2^m and 2^n, respectively, then bit k is the same in both integers for 0 <= k < min(m,n). Each call to %RANDOM-INTEGER consumes at least one chunk; bits left over from previous chunks are not re-used.

Package
Source

mt19937.lisp (file)

Function: copy-random-state INSTANCE
Package
Source

mt19937.lisp (file)

Function: generate-seed ()
Package
Source

mt19937.lisp (file)

Function: int-init-random-state &optional SEED STATE
Package
Source

mt19937.lisp (file)

Function: make-random-object &key (STATE STATE)
Package
Source

mt19937.lisp (file)

Function: random-mt19937-update STATE
Package
Source

mt19937.lisp (file)

Function: random-state-state INSTANCE
Function: (setf random-state-state) VALUE INSTANCE
Package
Source

mt19937.lisp (file)

Function: vec-init-random-state KEY &optional STATE
Package
Source

mt19937.lisp (file)

Previous: , Up: Top   [Contents][Index]

## Appendix A Indexes

Next: , Previous: , Up: Indexes   [Contents][Index]

### A.1 Concepts

Next: , Previous: , Up: Indexes   [Contents][Index]

### A.2 Functions

Next: , Previous: , Up: Indexes   [Contents][Index]