Teluhiko HILANO on Wed, 2 Aug 2000 11:29:44 +0900

 Re:(BUG?) Erroneous I+R overflow in GP/PARI Version 2.0.18 (beta)

```>
> This "overflow" looks like a bug to me.
>
>   parisize = 4000000, primelimit = 500000
>   ?  exp(2*Pi*I*((9/2)/(3/35 + 3/35*I)))-1
>     ***   overflow in I+R
>   ?  exp(2*Pi*I*((9/2)/(3/35 + 3/35*I)))
>   %1 = 0.0000000000000000000000000000 +
> 4.263424501275723583926909456 E71*I

I checked the following

? exp(2*Pi*I*((9/2)/(3/35+3/35*I)))-1.0
%3 = 0.0000000000000000000000000000 +
4.263424501275723583926909456 E71*I
I agree you, because both real part are equal.
It seems that this bug appears in calcurate the real part.

I have changed the precision to 100 digits and
have the following result

? exp(2*Pi*I*(105-105*I)/4)
%1 = 0.0000000000000000000000000000 +
4.263424501275723583926909456 E71*I
? exp(2*Pi*I*(105-105*I)/4)-1
***   overflow in I+R
? exp(2*Pi*I*(105-105*I)/4)-1.0
%2 = 0.0000000000000000000000000000 +
4.263424501275723583926909456 E71*I
? default(realprecision,100)
realprecision = 105 significant digits (100 digits displayed)
? exp(2*Pi*I*(105-105*I)/4)-1
%3 = -0.99999999999999999999999999999998810292859218243763
15778112806134582485529029689024016459308767990225 +
42634245012757235839269094622528336838340048084665
0532478826897906943814.1042587459518788730331359099*I
? exp(2*Pi*I*(105-105*I)/4)-1.0
%4 = -0.99999999999999999999999999999998810292859218243763
15778112806134582485529029689024016459308767990225 +
42634245012757235839269094622528336838340048084665
0532478826897906943814.1042587459518788730331359099*I
? %3-%4
%5 = 1.09003771 E-106 + 0.E-34*I

The final result looks a little curious.
-------------------------------------------------
Teluhiko HILANO(hilano@bekkoame.ne.jp)
(hilano@gen.kanagawa-it.ac.jp)
(RXF13157@nifty.ne.jp)
------------------------------------------
```