[M3devel] integer division/mod questions?

[Tony Hosking]

On 17 Jan 2010, at 05:50, Jay K wrote:

> I think I missed a sign.
> 
> -2147483648 - 2147483647  * -2
>  actually -2147483648 + 2 * 2147483647
>   actually 2147483646
> 
> which agrees.
> 
> so 
> 
> -2147483648 div 2147483647 = -2 
> -2147483648 mod 2147483647 = 2147483646 
> 
> -2 * 2147483647 + 2147483646  = -2147483648
> 
> I'll make sure m3_mod works this way if it doesn't already.
> Presumably we are stuck with these rules.

Yep.  I seem to remember reading some rationale somewhere sometime somehow, but I forget where when how.  Anyone?

> 
>  - Jay
> 
> From: jay.krell at cornell.edu
> To: m3devel at elegosoft.com
> Subject: integer division/mod questions?
> Date: Sun, 17 Jan 2010 10:44:53 +0000
> 
> -2147483648 div 2147483647 ?
> -2147483648 mod 2147483647 ?
> 
> quotient = -1, remainer = -1 seems reasonable.
> 2147483647 * -1 + -1 == -2147483648
> 
> 
> However, Modula-3 specifies div as rounding down, so
> 
> -2147483648 div 2147483647  == -2
> 
> and then
> 
> http://www.modula3.com/cm3/doc/reference/arithmetic.html
> 
> The value x DIV y is the floor of the quotient of x and y; that is, the maximum integer not exceeding the real number z such that z * y = x. For integers x and y, the value of x MOD y is defined to be x - y * (x DIV y). This means that for positive y, the value of x MOD y lies in the interval [0 .. y-1], regardless of the sign of x. For negative y, the value of x MOD y lies in the interval [y+1 .. 0], regardless of the sign of x. 
> 
> -2147483648 - 2147483647  * -2
> -2147483648 +2  (due to overflow)
> -2147483646
> 
> which contradicts the second part.
> 
> Maybe I'm confused? I should work this all through again?
> 
>  - Jay

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