Re: no tests for trigonometric functions? need help / hints how to adapt tests for gnumeric 'long' version,

[Steven D'Aprano <steve pearwood info>]

On Sat, May 28, 2022 at 12:43:45AM -0700, John Denker via gnumeric-list wrote:

> In any serious application it would be better to use tanpi(0.5)
> which produces #NUM! which is IMHO the right answer. Note that
> cospi(0.5) is exactly zero, as it should be.

Can you point me at the source code for cospi please?


> OTOH if for some reason we can't do that, the value of pi()/2
> is 1.5707963267948966192313217 (to high accuracy). However an
> IEEE double cannot represent that; the closest it can come is
> 1.5707963267948965579989817
>
> If you take the tangent of that (to high accuracy) you get
> 16331239353195369.755 for which the closest IEEE double is
> 16331239353195370. So I don't consider that a failure.

Using Python 3.10 on Linux, I get tan(pi/2) as

1.633123935319537e+16

which matches your result.

> tan() produces an output that is grossly
> nonlinear (indeed wildly non-monotonic).

Why is that? The mathematical function tan is monotonically increasing 
in the range [0, π/2). Shouldn't tan() be the same?

Using Python (as above), and starting at pi/2 and working backwards, I 
was unable to find any non-monotonic behaviour in tan() in the range
1.5707963260321207 through pi/2. (That's 3435237 doubles.)

Obviously this result can depend on the quality of your platform's maths 
library. Do you have any examples of where it fails?


Thanks,


-- 
Steve