Complex arg-trig functions

[Stephen Montgomery-Smith]

On 08/13/2012 05:16 PM, Stephen Montgomery-Smith wrote:
> On 08/13/2012 04:45 PM, Bruce Evans wrote:
>
>> y can have any sign I think.  But the problem only seemed to happen with
>> denormals and/or NaNs.  There might be a problem with NaNs not giving one
>> of the canceling negatives.
>
> OK.
>
>>>> @ --- 408,420 ----
>>>> @ @       if (ISFINITE(bx) && ISFINITE(by) && (x >
>>>> RECIP_SQRT_EPSILON_100 || y > RECIP_SQRT_EPSILON_100)) {
>>>> @ !         /* XXX following can also raise overflow */
>>>
>>> I don't see how the code could raise an overflow.  The output of clog
>>> should always be very much less than DBL_MAX.  (Originally I had
>>> clog(2*z), and that could raise an unwarranted overflow.)
>>
>> @       if (ISFINITE(bx) && ISFINITE(by) && (x > RECIP_SQRT_EPSILON_100
>> || y > RECIP_SQRT_EPSILON_100)) {
>> @ !         /* XXX following can also raise overflow */
>> @ !         if (huge+x+y>one) { /* raise inexact */
>> @ !             w = clog_for_large_values(z);
>> @ !             /* Can't add M_LN2 to w since it should clobber -0*I. */
>> @ !             rx = fabs(cimag(w));
>> @ !             ry = creal(w) + M_LN2;
>> @               if (sy == 0)
>> @ !                 ry = -ry;
>> @ !             return (cpack(rx, ry));
>> @           }
>> @       }
>>
>> clog() won't overflow spuriously, but huge+x+y might.
>
> Yes, I didn't think of that!
>
>> ((int)x == 0)' is a safer method of raising inexact for certain x.
>
> But this only works if x is less than 1.
>
> OK, how about this:
>
> sqrt_huge = 1e150;
> if (sqrt_huge+x>one || sqrt_huge+y>one) ...

Oops

if (sqrt_huge+x>one && sqrt_huge+y>one)