[Python-ideas] division oddness

[Terry Reedy]

On 5/6/2010 9:09 PM, MRAB wrote:
> Mathias Panzenböck wrote:
>> Shouldn't by by mathematical definition -x // y
be the same as -(x // y)?

When defining division of counts, which have no signs, quotient and 
remainder cannot be negative. So division both rounds down and rounds 
toward zero. It both truncates and floors.

When defining division on integers (signed counts), one can either 
define it to round down or to round toward zero, but obviously not both. 
As mentioned in the article Chris linked to,
http://en.wikipedia.org/wiki/Modulo_operation
one can also round down or up depending on the sign of the divisor.

The above definition is 'round toward zero' truncation. It has the 
anomaly that 0 then is the rounded value (and representative) of all 
ratios in the doubly open length-2 range (-1, 1) while all other 
quotients represent a half-open length-1 range. The is because -0 == 0 
whereas -n != n for all other ints. For 'round down', every quotient, 
including 0, represents a half-open length-1 range.

> It's so that:
> y == (y // x) * x + (y % x)
> is always True (assuming x != 0).

No, this is true for any definition of y//x if you *define* y % x to be 
y - (y//x)*x. But for truncation, this mean that the sign of y%x depends 
on the sign of y rather than the sign of x, as with floor division. The 
latter is probably more useful more of the time. For instance, y % 2 has 
only 2 possible values (0,1) with flooring rather than three (-1, 0, 1) 
as with truncation.

Terry Jan Reedy