• Subject: Re: Should not integer exponentiation work when it works?
• From: Coda Highland <chighland@...>
• Date: Thu, 9 Jun 2016 10:02:08 -0700

```On Thu, Jun 9, 2016 at 6:19 AM, Egor Skriptunoff
<egor.skriptunoff@gmail.com> wrote:
> On Thu, Jun 9, 2016 at 11:45 AM, Dirk Laurie <dirk.laurie@gmail.com> wrote:
>>
>> I know I am reopening an old can of worms.
>
>
> I like the worms from this can.
>
>>
>> so there must have been an overflow, but is there a cheap,
>> elegant way to detect it?
>
>
> if log(37)*12 < log(2^63) then integer_operation else float_operation end
>
>
> Is log(x) cheap?
>
> The idea to use approximation for log() may be attractive:
> log2((1+m)*2^e) ~ m+e  (m and e are extracted from float using bit-fiddling)
> Or more exact approximation:
> http://www.machinedlearnings.com/2011/06/fast-approximate-logarithm-exponential.html
> But, unfortunately, approximated log() is not sensitive enough to feel the
> difference:
> 2^63 > 3037000499^2
> 2^63 < 3037000500^2
>
>
> More straightforward solution:
> Calculation of a^b (both a and b are integers, b is non-negative)
>
> If a is non-negative:
> 1) Do float calculation, as usual: result = a^b
> 2) If result is less that 2^53, then convert it to integer and return
> integer result
> 3) If result is above 2^63, then return float result
> 4) Recalculate the result using integer multiplication and return it
>
> If a is negative, then we calculate (-1)^b*(-a)^b,
> but instead of returning float on step 3 we raise an error.