Re: Inaccurate results from numeric ln(), log(), exp() and pow()

Dean Rasheed <dean(dot)a(dot)rasheed(at)gmail(dot)com> writes:
> On 13 November 2015 at 18:36, Tom Lane <tgl(at)sss(dot)pgh(dot)pa(dot)us> wrote:
>> Seems like we arguably should do this whenever the weight isn't zero,
>> so as to minimize the number of sqrt() steps.

> It's a bit arbitrary. There is a tradeoff here -- computing ln(10) is
> more expensive than doing a sqrt() since the Babylonian algorithm used
> for sqrt() is quadratically convergent, whereas the Taylor series for
> ln() converges more slowly. At the default precision, ln(10) is around
> 7 times slower than sqrt() on my machine, although that will vary with
> precision, and the sqrt()s increase the local rscale and so they will
> get slower. Anyway, it seemed reasonable to not do the extra ln()
> unless it was going to save at least a couple of sqrt()s.

OK --- I think I miscounted how many sqrt's we could expect to save.

One more thing: the approach you used in power_var() of doing a whole
separate exp * ln(base) calculation to approximate the result weight
seems mighty expensive, even if it is done at minimal precision.
Couldn't we get a good-enough approximation using basically
numericvar_to_double_no_overflow(exp) * estimate_ln_weight(base) ?

regards, tom lane