Use of C99 extra long double math functions after r236148

[Stephen Montgomery-Smith]

On 07/19/2012 09:19 PM, Bruce Evans wrote:
> On Thu, 19 Jul 2012, Stephen Montgomery-Smith wrote:

>
>> I can now see that the separate cases of the real part and imaginary
>> parts of casinh being zero is going to be hard.
>
> I won't ask for that and will measure errors relative to the absolute value
> of the result.

But the algorithm in the paper by Hull et al (the paper recommended by 
Jeremy) manages to do this very effectively.  So I will abandon my 
algorithm, and use Hull et al's algorithms.

The real part of casinh(z) is zero only if z=I*y, |y|<=1, and the 
imaginary part of casinh(z) is zero only if z is real.  This is much 
easier to quantify in floating point terms than the condition for 
clog(z) to be pure imaginary (|z|=1).  Once you realize this, you see 
that it makes sense to compute casinh(z) by considering the real and 
imaginary parts separately.  And this is exactly what Hull et al does.