Re: Ada.Numerics, Accuracy of trigonometric functions

[Brian Drummond <brian@shapes.demon.co.uk>]

On Fri, 07 Oct 2016 12:13:48 +0200, Markus Schöpflin wrote:

> The following tests have been performed using GNAT 7.4 on a 64bit Linux
> system.
> 
> I'm puzzled by the seemingly bad accuracy of calling COS on a large
> value of type Short_Float.
> 
> ---%<---
> Size of SHORT_FLOAT =  32 Maximum relative error of COS =  2.38419E-07
> Angle threshold =  12 X = 4294967296.00000; COS(X) =  1.00000      <--
> WHAT?
> --->%---
> 
> The corresponding C program:
> 
> ---%<---
> 
> gives:
> 
> ---%<---
> sizeof(float) = 4 x = 4294967296.000000; cos(x) = -0.886887    <--- OK
> --->%---
> 
> Now, why is the error on cos(2**32) so large in this case? I am aware
> that I'm way beyond the required angle threshold mentioned in G.2.4(12),
> so it's up to the compiler to decide on the accuracy.

C tends to silently coerce "float" to "double" any time you pass a float 
argument to a function unless you jump through hoops to make such 
coercion impossible. 

So my suspicion is simply that the C program is giving you double 
precision.

-- Brian