This is a Mersenne Twister pseudorandom number generator
with period 2^19937-1 with improved initialization scheme,
modified on 2002/2/10 by Takuji Nishimura and Makoto Matsumoto. 
This is a faster version by taking Shawn Cokus's optimization, 
Matthe Bellew's simplification, Isaku Wada's real version.

Contents of this tar ball:
readme-mt.txt	  this file
mt19937ar-cok.c	  the C source (ar: initialize by ARray)
mt19937ar-cok.out Test outputs of six types generators. 1000 for each

1. Initialization
  The initialization scheme for the previous versions of MT
(e.g. 1999/10/28 version or earlier) has a tiny problem, that
the most significant bits of the seed is not well reflected 
to the state vector of MT.

This version (2002/2/10) has two initialization schemes:
init_genrand(seed) and init_by_array(init_key, key_length).

init_genrand(seed) initializes the state vector by using
one unsigned 32-bit integer "seed", which may be zero.

init_by_array(init_key, key_length) initializes the state vector 
by using an array init_key[] of unsigned 32-bit integers
of length key_kength. If key_length is smaller than 624,
then each array of 32-bit integers gives distinct initial
state vector. This is useful if you want a larger seed space
than 32-bit word.

2. Generation
After initialization, the following type of pseudorandom numbers
are available. 

genrand_int32() generates unsigned 32-bit integers.
genrand_int31() generates unsigned 31-bit integers.
genrand_real1() generates uniform real in [0,1] (32-bit resolution). 
genrand_real2() generates uniform real in [0,1) (32-bit resolution). 
genrand_real3() generates uniform real in (0,1) (32-bit resolution).
genrand_res53() generates uniform real in [0,1) with 53-bit resolution.

Note: the last five functions call the first one. 
if you need more speed for these five functions, you may
suppress the function call by copying genrand_int32() and
replacing the last return(), following to these five functions.

3. main()
main() is an example to initialize with an array of length 4,
then 1000 outputs of unsigned 32-bit integers, 
then 1000 outputs of real [0,1) numbers. 

4. The outputs
The output of the mt19937ar-cok.c is in the file mt19937ar-cok.out.
If you revise or translate the code, check the output
by using this file. 

5. Cryptography
This generator is not cryptoraphically secure. 
You need to use a one-way (or hash) function to obtain 
a secure random sequence.

6. Correspondence
See:
URL http://www.math.keio.ac.jp/matumoto/emt.html
email matumoto@math.keio.ac.jp, nisimura@sci.kj.yamagata-u.ac.jp

7. Reference
M. Matsumoto and T. Nishimura,
"Mersenne Twister: A 623-Dimensionally Equidistributed Uniform  
Pseudo-Random Number Generator",
ACM Transactions on Modeling and Computer Simulation,
Vol. 8, No. 1, January 1998, pp 3--30.

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Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.