Floating point modulus - the "why not"

Floating point modulus - the "why not"

[Bart Schaefer]

I think we did the right thing, but just as a counter-point:

torch% print $(( 91 % 13 ))                 
0
torch% print $(( 9.1 % 1.3 ))    
1.2999999999999994

Re: Floating point modulus - the "why not"

[Peter Stephenson]

On Mon, 12 Jan 2015 21:38:52 -0800
Bart Schaefer <schaefer@brasslantern.com> wrote:
> I think we did the right thing, but just as a counter-point:
> 
> torch% print $(( 91 % 13 ))                 
> 0
> torch% print $(( 9.1 % 1.3 ))    
> 1.2999999999999994

That's the same problem with floating point division as everywhere else;
if you need to round it, you need to decide what you're rounding to and
add half of that before you truncate downwards.  I don't think that's a
fundamentally new effect in this one case.

pws

Re: Floating point modulus - the "why not"

[Vincent Lefevre]

On 2015-01-13 10:10:16 +0000, Peter Stephenson wrote:
> On Mon, 12 Jan 2015 21:38:52 -0800
> Bart Schaefer <schaefer@brasslantern.com> wrote:
> > I think we did the right thing, but just as a counter-point:
> > 
> > torch% print $(( 91 % 13 ))                 
> > 0
> > torch% print $(( 9.1 % 1.3 ))    
> > 1.2999999999999994
> 
> That's the same problem with floating point division as everywhere else;
> if you need to round it, you need to decide what you're rounding to and
> add half of that before you truncate downwards.  I don't think that's a
> fundamentally new effect in this one case.

The problem actually comes from the decimal to binary conversions,
not with the division (or modulo) itself: 9.1 and 1.3 are not exactly
representable. While 91 is a multiple of 13, 9.1 converted to binary
is not a multiple of 1.3 converted to binary.

-- 
Vincent Lefèvre <vincent@vinc17.net> - Web: <https://www.vinc17.net/>
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Re: Floating point modulus - the "why not"

[Bart Schaefer]

On Jan 13,  5:18pm, Vincent Lefevre wrote:
} Subject: Re: Floating point modulus - the "why not"
}
} On 2015-01-13 10:10:16 +0000, Peter Stephenson wrote:
} > On Mon, 12 Jan 2015 21:38:52 -0800
} > Bart Schaefer <schaefer@brasslantern.com> wrote:
} > > torch% print $(( 9.1 % 1.3 ))    
} > > 1.2999999999999994
} 
} The problem actually comes from the decimal to binary conversions,

Yes, I know; the point is that you can't guarantee a consistent result
from floating-point division, and this is particularly significant for
modulus because the error may be (almost) as large as the divisor; so
it's easy to see why that operation may have been left unimplemented.

(Compare division

torch% print $(( 9.1 / 1.3 ))     
6.9999999999999991

where the error is a tiny fraction of the result.)