[fpc-devel]MATH.PP

[Jonas Maebe]

On maandag, oktober 15, 2001, at 09:25 , Michael Van Canneyt wrote:

>> const Epsilon = 1.0e-9;
>> ....
>> if (x-1)<=Epsilon then x:=1;
>> if (x+1)<=Epsilon then x:=-1;
>>
>> I made these changes because of InvalidArgument exception when arcsin
>> parameter (displayed by GDB) is 1 (but, I think, it was near 1, but
>> not 1).
>
> But if it is larger than 1, arcsin is not defined ?
> You deliberately introduce an error in the calculation in this way ?

The problem is that floats on computers are inherently inexact and if 
you perform a number of calculations the results becomes more inexact 
after every operation (I had a lot of trouble with this while 
implementing the str_real() routine). You should indeed work with a 
small epsilon to compensate for this, but the size of this epsilon 
depends on the size of the best real type available (for extended = 10 
bytes, it could be 1.0e-9, but for extended = 8 bytes, it will be 
bigger).

> Because then reals are used for the comparision, since in the case
> of abs(X) > 1 the '1' will probably be interpreted as an integer.

No, if one operand in an expression is a float, everything will be 
converted to a float.


Jonas