Re: Modulo operator produces incorrect results with negative operand(s).
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- Subject: Re: Modulo operator produces incorrect results with negative operand(s).
- From: Martin <eden_martin_fuhrspam@...>
- Date: Thu, 9 Feb 2017 03:18:40 -0800
On 02/08/2017 02:40 PM, chris beck wrote:
>> Hmmm... So why does my programmers calculator, Go, JavaScript, etc,
> etc all return -3 in this case?
>>
>> Personally I think it's a bug, as "2" is not the correct result for
> that expression (in any language but Lua it seems).
>
> For what it's worth, among anyone who was a math major or took a course
> in algebra in college, the congruence class of -2 mod 5 is 3
[snip]
It depends on additional restrictions of mod() results.
Gerenally
mod(n, m) is some function like
: get x, y such that
: x * m + y == n,
: int(x), int(y), abs(y) < abs(m)
: return y
And further restrictions possible:
: x = min(possible x) // x leftmost from zero
=> mod(-2, -5): 0 * -5 + -2 => -2 (1)
=> mod( 2, -5): -1 * -5 + -3 => -3
=> mod(-2, 5): -1 * 5 + 3 => 3
=> mod( 2, 5): 0 * 5 + 2 => 2
: x = max(possible x) // x rightmost from zero
=> mod(-2, -5): 1 * -5 + 3 => 3 (2)
=> mod( 2, -5): 0 * -5 + 2 => 2
=> mod(-2, 5): 0 * 5 + -2 => -2
=> mod( 2, 5): 1 * 5 + -3 => -3
: y = min(possible y) // y leftmost from zero
=> mod(-2, -5): 0 * -5 + -2 => -2 (3)
=> mod( 2, -5): -1 * -5 + -3 => -3
=> mod(-2, 5): 0 * 5 + -2 => -2
=> mod( 2, 5): 1 * 5 + -3 => -3
: y = max(possible y) // y rightmost from zero
=> mod(-2, -5): 1 * -5 + 3 => 3 (4)
=> mod( 2, -5): 0 * -5 + 2 => 2
=> mod(-2, 5): -1 * 5 + 3 => 3
=> mod( 2, 5): 0 * 5 + 2 => 2
And even more:
: x = min(abs(possible x)) // x towards zero
=> mod(-2, -5): 0 * -5 + -2 => -2 (5)
=> mod( 2, -5): 0 * -5 + 2 => 2
=> mod(-2, 5): 0 * 5 + -2 => -2
=> mod( 2, 5): 0 * 5 + 2 => 2
: x = max(abs(possible x)) // x away zero
=> mod(-2, -5): 1 * -5 + 3 => 3 (6)
=> mod( 2, -5): -1 * -5 + -3 => -3
=> mod(-2, 5): -1 * 5 + 3 => 3
=> mod( 2, 5): 1 * 5 + -3 => -3
: y = min(abs(possible y)) // y towards zero
=> mod(-2, -5): 0 * -5 + -2 => -2 (7)
=> mod( 2, -5): 0 * -5 + 2 => 2
=> mod(-2, 5): 0 * 5 + -2 => -2
=> mod( 2, 5): 0 * 5 + 2 => 2
: y = max(abs(possible y)) // y away zero
=> mod(-2, -5): 1 * -5 + 3 => 3 (8)
=> mod( 2, -5): -1 * -5 + -3 => -3
=> mod(-2, 5): -1 * 5 + 3 => 3
=> mod( 2, 5): 1 * 5 + -3 => -3
/*
Due some reason results of (5) and (7) are equal.
Same for results (6) and (8).
*/
So at least six different variants possible. Which one you prefer and why?
-- Martin