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Re: Commutativity of multiplication [message #50958]

Thu, 26 October 2006 10:47

JD Smith
Messages: 850
Registered: December 1999

Senior Member

On Thu, 26 Oct 2006 10:24:32 -0700, Braedley wrote:
>> IDL> print, 4294967295UL + 1UL
>> 0
>>
>> IDL> print,0b - 1b
>> 255
>>
>> JD
>
> IDL must make a choice as to which type to use, since the length of ranges
> of LONG and ULONG are exactly the same, but there is only 50% overlap.
> The result from the multiplication may be within the range of both, in
> which case everything is fine. However, if the result is negative, the
> result will be outside the range of ULONG. Likewise, if the two numbers
> are sufficiently large, the result will be outside the range of LONG. IDL
> doesn't know beforehand what the result will be, and therefore assigns the
> type of the leftmost variable.

It's actually much simpler than that, with no real "decision" involved.
The result of multiplying two integers is exactly the same whether they
are interpreted as signed or unsigned, including if you overflow the size
of the integer (this is the chief reason the two-complement system is so
prevalent). It is up to you (or, in this case, IDL) to decide how to
interpret the resulting number.

IDL> print,2L^30 * 2L
-2147483648
IDL> print,2UL^30 * 2UL
2147483648
IDL> print,long(2UL^30 * 2UL)
-2147483648

The only case where this isn't so is up-conversion to non-equivalent
types (like floating point), but that's a separate matter, and it is
up to the environment (C compiler, IDL, etc.) as to how to handle
that.

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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