Re: integer exponentiation with negative exponent

[Peng Zhicheng <pengzhicheng1986@...>]

On 04/12/2014 01:02 PM, Coda Highland wrote:
> On Fri, Apr 11, 2014 at 9:05 PM, Peng Zhicheng
> <pengzhicheng1986@gmail.com> wrote:
> > It may be faster. but it is the semantic difference that I was concerned.
> > I suppose the pow function would quite usually overflow a integer(even
> > 64-bit long),
> > do we really need a dedicated `pow' for integers?
> Consider (this is Lua 5.1):
>
> > x = 2^56
> > y = x + 1
> > =x
> 7.2057594037928e+16
> > =y
> 7.2057594037928e+16
> > =x == y
> true
>
> The actual value is 72057594037927936. This is an exact number, with
> no precision loss, but the float version gets it wrong.
>
> Now, I don't have 5.3work installed, but I do have Python, which uses
> integer exponentiation:

I can't agree.

double precision floating point number has 56 precision bits, while long long has 64.
there is not much difference.
if you need more than 56, double is not enough.
what if you need more than 64? long long is not enough either.

speaking of correctness,  that `x == x+1' is of course incorrect.
so is 'x ^ y == 0' where x is not zero.

I am personally concerned about overflow more than losing precision.