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sja
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Posts: 29
Joined: Sun Jan 22, 2012 6:26 pm
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Pseudo Random Number Generator Script (xorshift64* )

Tue Sep 29, 2015 9:11 am

Sometime ago I needed a reasonably efficient pseudo random number generator to run on ROS. After some research the most efficient and acceptable script that I found was xorshift64* from http://xorshift.di.unimi.it/.

This is how I implemented it. The script contains comments, test vectors and debug instructions. The actual code is quite simple.

I hope that this is useful to someone.
:global getRandom64 do={
	# Parameters:
	#		none
	# Return value:
	#		A 64 bit pseudo random number obtained from the xorshift64* prng. 
	#      The number lies in the range [1, 2**64).  Note that it will NEVER be 0.
	#		The number is returned as a ROS array of integers { t=top_32_bits; b=bottom_32_bits }
	#
	#	xorshift64* is defined in http://xorshift.di.unimi.it/
	# It is the smallest state 64bit prng that is recommended especially for memory limited devices.
	# As well as passing all the statistical tests (except MatrixRank test) it has the property that even on the first iteration it 
	# produces numbers with each bit =1  has 0.5 probability (see 
	# chapter 7.2 "Escaping Zeroland" in http://vigna.di.unimi.it/ftp/papers/xorshift.pdf )
	# End chapter 5 (page 14) "suggests that for these generators it is better to extract the lower bits,
	# rather than the high bits, when just a subsequence is needed."
	#
	# The algorithm is (from the above references):
	#		uint64_t x; /* The state must be seeded with a nonzero value. */
	#		uint64_t next() {
	#			x ^= x >> 12; // a
	#			x ^= x << 25; // b
	#			x ^= x >> 27; // c
	#			return x * 2685821657736338717LL;
	#		}
	# http://www.javascripter.net/math/calculators/primefactorscalculator.htm
	#
	# ROS does not have 64 bit unsigned integers so we need to emulate using a pair of 
	# 32bit unsigned integers which are contained in the lower 32 bits of two ROS 64 bit signed integers.
	# Care must be taken when doing addition and multiplication to avoid hitting the sign bit in the 64bit ROS variable.
	# Fortunately, the xorshift64* algorithm only requires multiplication by the constant 2685821657736338717LL which has 
	# a hex representation of 2545f491 4f6cdd1d where the space indicates the 32 bit boundary. This means that the largest multiplication 
	# result within a "32bit half" is 4f6cdd1d * (2**32 -1 ) < 4f6cdd1d00000000. Thus overflow will never occur.
	# Note that additions are done only using 32-bit halves thus overflow can never occur.
	# The following test vectors were obtained from an independent implementation 
	#  Initial seed (t, b)									xorshift64* result
	#	0,0													0
	#	0,1													0x47e4ce4b896cdd1d
	#	0,2													0x8fc99c9712d9ba3a
	#	1,1													0x84e9495afd4c80bd
	#	0x21212121,0x32323232					0xff3ddfa115d6198d
	# 	0xfefefefe,0xcacacaca						0xc67bafe0b4bc30cf
	# 
	# In this implementation a 64 bit unsigned variable x is represented as the pair xt ("x top") and xb ("x bottom"). The 
	# most significant 32 bits of x are in xt whilst the least significant are in xb
	:global Random64Statet
	:global Random64Stateb	
	# Uncomment following two lines to debug
	#:set Random64Statet [:tonum $1]
	#:set Random64Stateb [:tonum $2]
	# Define the multiplier 2685821657736338717LL:
	:local ct 0x2545F491
	:local cb 0x4F6CDD1D
	# Define the multiplier used for calculating modulo 2**32
	:local mask32 0xFFFFFFFF
	#  Do x ^= x >> 12
	:set Random64Stateb ($Random64Stateb ^ ((($Random64Stateb >> 12) | ($Random64Statet << 20)) & $mask32))
	:set Random64Statet ($Random64Statet ^ ($Random64Statet >> 12))
	# Do x ^= x << 25
	:set Random64Statet ($Random64Statet ^ ((($Random64Statet << 25) | ($Random64Stateb >> 7)) & $mask32))
	:set Random64Stateb ($Random64Stateb ^ (($Random64Stateb << 25) & $mask32))
	# Do x ^= x >> 27
	:set Random64Stateb ($Random64Stateb ^ ((($Random64Stateb >> 27) | ($Random64Statet << 5)) & $mask32))
	:set Random64Statet ($Random64Statet ^ ($Random64Statet >> 27))
	#	Calculate result = x * 2685821657736338717LL
	#  Use the formulae (we work mod 2**64):
	# x * c	= (xt * 2**32 + xb) * (ct * 2**32 + cb)
	#			= xt * ct * 2**64 + (xt * cb + xb * ct) * 2**32 + xb * cb
	#			=                         (xt * cb + xb * ct) * 2**32 + xb * cb  # because we are working mod 2**64
	# Note that the top half of xb * cb must be carried to the top half of the result
	# and the top half of  (xt * cb + xb * ct)  can be discarded.
	:local resultt (((($Random64Statet * $cb) & $mask32) + (($Random64Stateb * $ct) & $mask32) +  (($Random64Stateb * $cb) >> 32)) & $mask32)
	:local resultb (($Random64Stateb * $cb) & $mask32) 
	# Uncomment following line to debug
	#:global convertToHex
	#:put "$[$convertToHex  $resultt] $[$convertToHex $resultb]"
	:return { t=$resultt; b=$resultb}
}

 
alisc
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Posts: 59
Joined: Thu Dec 01, 2011 10:51 am

Re: Pseudo Random Number Generator Script (xorshift64* )

Fri Feb 03, 2017 10:44 am

hi
thanks a lot

how to send ( show ) result on log ?

exmaple :
:log warning $resultt
I'm not English
my english not so good , excuse me

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