Uniform XOR4096-based RNG. More...

Public Member Functions
subroutine	xor4096s_0d (seed, singleintegerrn, save_state)

subroutine	xor4096s_1d (seed, singleintegerrn, save_state)

subroutine	xor4096f_0d (seed, singlerealrn, save_state)

subroutine	xor4096f_1d (seed, singlerealrn, save_state)

subroutine	xor4096l_0d (seed, doubleintegerrn, save_state)

subroutine	xor4096l_1d (seed, doubleintegerrn, save_state)

subroutine	xor4096d_0d (seed, doublerealrn, save_state)

subroutine	xor4096d_1d (seed, doublerealrn, save_state)

Detailed Description

Uniform XOR4096-based RNG.

Generates a uniform distributed random number based on xor4096 algorithm proposed by Brent et.al (2006).

The original version of this source code (without multiple streams and optional arguments) is under GNU General Public Licence xorgens.c Copyright (C) 2004 R. P. Brent. This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License, version 2, June 1991, as published by the Free Software Foundation. For details see http://www.gnu.org/copyleft/gpl.html . Author: Richard P. Brent (rando.nosp@m.m@rp.nosp@m.brent.nosp@m..co..nosp@m.uk)

The period of the generator is
(2^4096 - 1)*2^32 for single precision version and (2^4096 - 1)*2^64 for double precision version.
The generator is based on bitwise XOR compositions of left- and right-shifted numbers.
The generator has to be called once with a non-zero seed value which initializes a new random number stream. The subsequent calls are with seed=0 which returns the following numbers within the beforehand initialized stream. Since the random numbers are based on the initial seed, the precison of the seed (sp/dp) determines the precision of the returned random number (sp/dp).
If one initialize the generator with an array of seeds, one initializes n independent streams of random numbers. Lets assume that the streams with seed: 1_sp is 10, 20, 30 ...
2_sp is 40, 50, 60 ...
3_sp is 70, 80, 90 ...
What you get is:
1st call

call xor( (/ 1_SP, 2_SP, 3_SP /), RN ) --> RN = (/ 10, 40, 70 /)

2nd call

call xor( (/ 0_SP, 0_SP, 0_SP /), RN ) --> RN = (/ 20, 50, 80 /)

3rd call

call xor( (/ 0_SP, 0_SP, 0_SP /), RN ) --> RN = (/ 30, 60, 90 /)

Since after every initialization one looses the old stream of random numbers, it might be necessary to switch between different streams. Therefore, one needs the optional save_state argument. What you get is: 1st call of 1st stream

call xor( 1_SP, RN, save_state=save_stream_1 ) RN = 10

2nd call of 1st stream

call xor( 0_SP, RN, save_state=save_stream_1 ) RN = 20

1st call of 2nd stream

call xor( 2_SP, RN, save_state=save_stream_2 ) RN = 40

3rd call of 1st stream

call xor( 0_SP, RN, save_state=save_stream_1 ) RN = 30

Note: If you would have called 4 times without optional argument, you would have get 50 in the 4th call.

Example

I4 seeds are generating I4 or SP random numbers, I8 seeds are generating I8 or DP random numbers.

Initializing:

real(SP) :: RN(3)
seed = (/ 1_i4, 100_i4, 2_i4 /)
call xor4096(seed,rn)
print*, rn --> (/ 0.1_sp, 0.2_sp, 0.6_sp /)

After initializing

seed = (/ 0_i4, 0_i4, 0_i4 /)
call xor4096(seed,rn)
print*, rn --> (/ 0.3_sp, 0.1_sp, 0.5_sp /)

Literature

Brent RP. Some long-period random number generators using shifts and xors, 2010
Brent RP. From Mersenne Primes to Rndom Number Generators, 2006
L''Ecuyer P & Simard R. ACM: TestU01: A C Library for Empirical Testing of Random Number Generators, 2007

Parameters

[in]	integer(i4/i8) :: seed/seed(:)	Value or 1D-array with non-zero seeds for initialization or zero for subsequent callsyy
[out]	integer(i4/i8)/real(sp/dp) :: RN/RN(size(seed))	uniform distributed random number with interval: i4: (-2^31,2^31-1) i8: (-2^63,2^63-1) sp: (0.0_sp, 1.0_sp) dp: (0.0_dp, 1.0_dp)
[in,out]	integer(i4/i8), dimension(size(seed), n_save_state), opional :: save_state	Array carrying state of random number stream this should be used if several streams are used, i.e. each stream has its own save_state.

Author: Juliane Mai

Date: Nov 2011

Definition at line 200 of file mo_xor4096.f90.

Member Function/Subroutine Documentation

◆ xor4096d_0d()

subroutine mo_xor4096::xor4096::xor4096d_0d	(	integer(i8), intent(in)	seed,
		real(dp), intent(out)	doublerealrn,
		integer(i8), dimension(n_save_state), intent(inout), optional	save_state
	)

Definition at line 1126 of file mo_xor4096.f90.

◆ xor4096d_1d()

subroutine mo_xor4096::xor4096::xor4096d_1d	(	integer(i8), dimension(:), intent(in)	seed,
		real(dp), dimension(size(seed, 1)), intent(out)	doublerealrn,
		integer(i8), dimension(size(seed, 1), n_save_state), intent(inout), optional	save_state
	)

Definition at line 1237 of file mo_xor4096.f90.

◆ xor4096f_0d()

subroutine mo_xor4096::xor4096::xor4096f_0d	(	integer(i4), intent(in)	seed,
		real(sp), intent(out)	singlerealrn,
		integer(i4), dimension(n_save_state), intent(inout), optional	save_state
	)

Definition at line 622 of file mo_xor4096.f90.

◆ xor4096f_1d()

subroutine mo_xor4096::xor4096::xor4096f_1d	(	integer(i4), dimension(:), intent(in)	seed,
		real(sp), dimension(size(seed)), intent(out)	singlerealrn,
		integer(i4), dimension(size(seed, 1), n_save_state), intent(inout), optional	save_state
	)

Definition at line 737 of file mo_xor4096.f90.

◆ xor4096l_0d()

subroutine mo_xor4096::xor4096::xor4096l_0d	(	integer(i8), intent(in)	seed,
		integer(i8), intent(out)	doubleintegerrn,
		integer(i8), dimension(n_save_state), intent(inout), optional	save_state
	)

Definition at line 886 of file mo_xor4096.f90.

◆ xor4096l_1d()

subroutine mo_xor4096::xor4096::xor4096l_1d	(	integer(i8), dimension(:), intent(in)	seed,
		integer(i8), dimension(size(seed, 1)), intent(out)	doubleintegerrn,
		integer(i8), dimension(size(seed, 1), n_save_state), intent(inout), optional	save_state
	)

Definition at line 987 of file mo_xor4096.f90.

◆ xor4096s_0d()

subroutine mo_xor4096::xor4096::xor4096s_0d	(	integer(i4), intent(in)	seed,
		integer(i4), intent(out)	singleintegerrn,
		integer(i4), dimension(n_save_state), intent(inout), optional	save_state
	)

Definition at line 382 of file mo_xor4096.f90.

◆ xor4096s_1d()

subroutine mo_xor4096::xor4096::xor4096s_1d	(	integer(i4), dimension(:), intent(in)	seed,
		integer(i4), dimension(size(seed, 1)), intent(out)	singleintegerrn,
		integer(i4), dimension(size(seed, 1), n_save_state), intent(inout), optional	save_state
	)

Definition at line 483 of file mo_xor4096.f90.

The documentation for this interface was generated from the following file:

src/mo_xor4096.f90

Public Member Functions