Re: [Caml-list] truncated division, remainder and arithmetics

[Xavier Leroy <Xavier.Leroy@inria.fr>]

On 27/01/16 01:34, peio wrote:

> while doing some modular arithmetic I discovered that OCaml uses the
> 'truncated division' convention for the `/` (quotient) operator.
> Actually this convention may seem innocent but it greatly affects the
> `mod` (remainder) operator: the sign of the result is the same as
> dividend.
> 
> After some research I realized that lots of people (D.Knuth!)
> criticized this convention in favor of floored division (sign of
> remainder same as divisor) or euclidean division (remainder always
> positive). I know such a key component of the language isn't likely to
> be changed but I would like to get some of the rationals behind this
> decision.

All contemporary microprocessors that implement division in hardware
implement what you call truncated division.  The other forms of
division and modulus (there are at least two others) can be
implemented on top of that.  See this excellent summary:

Daan Leijen, Division and Modulus for Computer Scientists , July 2003.
http://research.microsoft.com/apps/pubs/default.aspx?id=151917

> At last another thing that (slightly) bugs me: why don't `ceil` and
> `floor` have the type `float -> int`? Because the inherent definitions
> of these functions talks about integers, not floats

Yes, but with the type you propose they would overflow easily for
large enough FP arguments.  In FP computations involving ceil and
floor, it is often possible to do the computation entirely in
floating-point, avoiding catastrophic overflow cases.

> Maybe even more subtle is that `truncate`
> has type `float -> int`. In my opinion the type `float -> float` would
> be more appropriate here because the truncation operation is about
> approximating a real number with a decimal (we already got
> `int_of_float` for rough converting).

"truncate" and "int_of_float" are (currently) the same function.

- Xavier Leroy