Re: Unexpected overflow in acosh and asinh

[Raymond T. <toy...@gm...>]

One more thing I just noticed.  (acosh 1d50) gives a division by 0.  But
asinh gives the expected answer.

On Mon, Jan 10, 2022 at 8:59 AM Raymond Toy <toy...@gm...> wrote:

> While working on some maxima stuff, I found out that clisp can't compute
> acosh(most-positive-double-float).  I get an overflow.  Same happens with
> asinh.  The actual answer should be about 710.475.
>
> I'm guessing this happens because clisp is using the log definition for
> these functions.  For example, asinh(x) = log(x+sqrt(x^2+1)).
>
> So for any value above sqrt(most-positive), there's an overflow.
>
> In this case, for large enough x, sqrt(x^2+1) = x so the final answer is
> log(2*x).  However, that would overflow if x is greater than
> most-positive/2.  In that case, we can use log(x)+log(x).
>
> This will allow clisp to compute acosh and asinh for the entire range of
> floats as expected.
>
> Oh, just noticed that clisp also fails to compute sinh(710.475d0).  This
> probably happens because sinh(x) is probably computed using
> (exp(x)-exp(-x))/2.  exp(710.475) overflows.  One possible way to avoid
> this is to compute exp(x/2)/sqrt(2).  This won't overflow.  Then square the
> result to get the final answer.
>
> --
> Ray
>


-- 
Ray