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Re: counting bits [message #34140 is a reply to message #34107]

Tue, 25 February 2003 15:17

condor
Messages: 35
Registered: January 2002

Member

JD Smith <jdsmith@as.arizona.edu> wrote in message news:<pan.2003.02.20.15.43.26.137656.2731@as.arizona.edu>...

> One thing I did notice when creating "random" arrays:
>
> IDL> print,FORMAT='(F5.2,A)',total(ulong(randomu(sd,100)*2.^31) mod 2 eq 1),$
> '% odd'
>
> Try this a few times. That lowest bit just does not get set. Some
> floating-point representation expert must have an explanation.

Dunno that this needs an expert: give a /double to the call to rendomu
and it works as expected -- otherwise randomu will return a float
array, floats have 4 byte representation and thus the graininess at
which floats can be represented cannot possibly be better than 1 bit
in 32 (and in reality it's a good bit less).

In other words: you're multiplying floats 0<f<1 with 2.^31 which means
for them to be distinguishable in the last bit the original floats
would have had to have a spacing of 1/2^30 :

m = machar()
print,m.eps
1.19209e-07
print,1/(2^31.)
4.65661e-10

So you have numbers that are at most about 10^7 apart from each other
(the machine precision) and you multiply them with almost 10^10 and
thus will not get numbers that are 'one' apart from each other.

You want weird? Check for all the bits OTHER than the last one:

print,FORMAT='(F5.2,A)',total(ulong(randomu(sd,100)*2.^31) and $
2ul eq 2ul),'% set'

print,FORMAT='(F5.2,A)',total(ulong(randomu(sd,100)*2.^31) and $
4ul eq 4ul),'% set'

print,FORMAT='(F5.2,A)',total(ulong(randomu(sd,100)*2.^31) and $
8ul eq 8ul),'% set'

etc ...

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[Message index]

		counting bits By: Joe Foose on Mon, 17 February 2003 11:50
		Re: counting bits By: thompson on Wed, 26 February 2003 12:15
		Re: counting bits By: JD Smith on Wed, 26 February 2003 10:29
		Re: counting bits By: condor on Tue, 25 February 2003 15:17
		Re: counting bits By: Dick Jackson on Thu, 20 February 2003 14:53

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