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

On 13 November 2015 at 23:10, Tom Lane <tgl@sss.pgh.pa.us> wrote:
> 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) ?
>

I can't see a way to make that work reliably. It would need to be
10^estimate_ln_weight(base) and the problem is that both exp and
ln_weight could be too big to fit in double variables, and become
HUGE_VAL, losing all precision.

An interesting example is the limit of (1+1/x)^x as x approaches
infinity which is e (the base of natural logarithms), so in that case
both the exponent and ln_weight could be arbitrarily big (well too big
for doubles anyway). For example (1+1/1.2e+500)^(1.2e500) =
2.7182818284...

Regards,
Dean