Re: More efficient "dbl_raise"

[Daniel J S. <dan...@ie...>]

Ethan A Merritt wrote:

> Note that 2147483648.0, although a large number in absolute terms, corresponds
> to an error in the 15th decimal place of the decimal representation of 10^25.
> More to the point, that corresponds to about 50 bits of precision.
> Since double-precision IEEE format only provides 52 bits of precision in the
> mantissa, this is within one bit of the expected rounding error.
> (And that one bit may be my mistake; I'm doing this on my fingers, as it were).

Right, the example

powint(base,power) = power==0 ? 1.0 : base * powint(base,power - 1)
powdiff(base,power) = (base**power / powint(base,power)) - 1.0
set samples 61 ; plot [0:60] powdiff(10,x)

suggests that.  I guess my feeling is to not discount the pow() function off 
hand, unless someone has seen some awful implementations out there.  It is a 
standard library function, you'd think designers would put effort into its 
accuracy and users would complain otherwise.

Dan