Re: A missing (?) function: exponentfp(x)

[Ilya Zakharevich <nospam-abuse@ilyaz.org>]

On Sat, Sep 14, 2024 at 12:31:57PM +0200, Loïc Grenié wrote:
>      In gp you can cheat
> 
> ? install(dbllog2,lG);
> ? install(dbltor,L);
> ? flog2(x)=dbltor(dbllog2(x));
> ? my(il2=1/log(2));setrand(1);for(i=1,10^6,log(random(1.)<<4)*il2)
> cpu time = 3,868 ms, real time = 3,868 ms.
> ? setrand(1);for(i=1,10^6,flog2(random(1.)<<4))
> cpu time = 655 ms, real time = 656 ms.

Moreover, on my CPU, exponent() is 400 times quicker than
log()/log(2).  So your 5x speedup is still “more or less negligible”!

  (A partial aside:

   In my vita, for a smooth user experience, there is an important
   aspect which is almost universally overlooked.  I prefer to call it
   “gradual degradation”.

   For example, people often advocate as the preferred target to aim at:
     • It should be possible to be able to code the “required things”.
     • It should be simple to code the simple “required things”.
   With “gradual degradation”, one (or ≥1) more requirements appears:
     • It should be only moderately hard to code “required things”
       which are moderately hard.

   Without this, what usually happens is an almost insurmountable
   obstacle:
     ∘ as a test, you code something simple.  It works!
     ∘ then you want to do more — but the amount of extra work to make
       even a small step forward is formidable.  You give up!

   I would say that for a smooth progression, the coefficient should
   be about 3: the next step in the ladder should not require “more
   than 3x the effort” of the previous one.)

Following this, I would think that having a flavor of exponent() which
is at most 3x slower (but gives a continuous/or/C¹/or/piecewise-quadratic
approximation to log2()) may be beneficial in many situations.

Hope this helps,
Ilya