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Re: Commutativity of multiplication [message #50978 is a reply to message #50968]

Wed, 25 October 2006 16:09

JD Smith
Messages: 850
Registered: December 1999

Senior Member

On Wed, 25 Oct 2006 14:54:59 -0700, Sven Geier wrote:

> David Fanning wrote:
> [...]
>> It also explains this:
>>
>> IDL> f = 500L
>> IDL> g = 1UL
>> IDL> help, g*(-f)
>> <Expression> ULONG = 4294966796
>> IDL> help, (-f)*g
>
> Wow. This is ... uhm ... "more interesting than I thought". There's whole
> realms of oddity here that I never knew existed:
>
> IDL> help,f,g
> F LONG = -500
> G ULONG = 1
> IDL> print,f*g
> -500
> IDL> print,g*f
> 4294966796
> IDL> if f*g eq g*f then print,f*g," equals ",g*f
> -500 equals 4294966796

The bit pattern for these two numbers is *exactly* the same. The only
difference is the "type" that IDL assigns them, which affects how the
numbers are printed (and only how they are printed). That type (for
IDL) is determined by the "left-most" variable or constant in the
expression, with the exception that if anything to the right has a
larger range, it will be used as the type (e.g. promotion to float,
double, ULONG64, etc.), hence:

IDL> f=1.0
IDL> l=100UL
IDL> help,l+f
<Expression> FLOAT = 101.000

When the range is the same, e.g. UL and L, leftmost always wins.

Commutation hasn't been broken, only "type commutation", which doesn't
really exist. For all purposes, given the limitations of integer
representation in computers, -500 and 4294966796 *are* the same. I
could just as easily claim that "adding and subtracting 1 is broken":

IDL> print, 4294967295UL + 1UL
0

IDL> print,0b - 1b
255

JD

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[Message index]

		Re: Commutativity of multiplication By: JD Smith on Thu, 26 October 2006 10:47
		Re: Commutativity of multiplication By: JD Smith on Thu, 26 October 2006 10:37
		Re: Commutativity of multiplication By: Braedley on Thu, 26 October 2006 10:24
		Re: Commutativity of multiplication By: Foldy Lajos on Thu, 26 October 2006 01:26
		Re: Commutativity of multiplication By: JD Smith on Wed, 25 October 2006 16:09
		Re: Commutativity of multiplication By: David Fanning on Wed, 25 October 2006 15:33
		Re: Commutativity of multiplication By: Sven Geier on Wed, 25 October 2006 14:54
		Re: Commutativity of multiplication By: K. Bowman on Wed, 25 October 2006 13:42
		Re: Commutativity of multiplication By: David Fanning on Wed, 25 October 2006 13:54

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