Re: [Mingw-users] expm1()

[Danny S. <dan...@cl...>]

Greg Chicares wrote:
> log1p() would be much more useful if its companion expm1()
> [C99 7.12.6.3] were provided as well. Is there a reason not
> to have expm1(), other than "no one has contributed it yet"?
>
> For instance, Conklin, credited as the original author of
>    /mingw/runtime/mingwex/math/log1pl.S?rev=1.1&view=markup
> said in an earlier version
>    http://www.klid.dk/pub/gnu/gnu-utils/src/libm/src/s_log1p.s
>
>    /*
>     * Since the fyl2xp1 instruction has such a limited range:
>     * -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1
>     * it's not worth trying to use it.
>     */
>
> but apparently later realized its worth. Did something like
> that happen for expm1()? Hmm...I find Conklin's log1p() in the
> netbsd src/lib/libm sources, but no corresponding expm1().
>
> I realize expm1() will be an intrinsic in gcc-4.0
>    http://www.gnu.org/software/gcc/gcc-4.0/changes.html
> but apparently only with '-ffast-math', so there's still
> a use for an expm1() that conforms to the language and
> numeric standards.
>

Off top of head, it would be quite easy to do

if (x < small_value)
{
  /* Taylor series expansion
  return y such that additional term is smaller than  machine eps  */
}
else
 return exp(x) - 1;

Not very fast,  but I'll bet I can find a good old Fortran IV routine that has
been tested as accurate.

Danny
>
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