Date: Mon, 13 Aug 2012 17:22:59 -0500 From: Stephen Montgomery-Smith <stephen@missouri.edu> To: freebsd-numerics@freebsd.org Subject: Re: Complex arg-trig functions Message-ID: <50297E43.7090309@missouri.edu> In-Reply-To: <50297CA5.5010900@missouri.edu> References: <5017111E.6060003@missouri.edu> <501C361D.4010807@missouri.edu> <20120804165555.X1231@besplex.bde.org> <501D51D7.1020101@missouri.edu> <20120805030609.R3101@besplex.bde.org> <501D9C36.2040207@missouri.edu> <20120805175106.X3574@besplex.bde.org> <501EC015.3000808@missouri.edu> <20120805191954.GA50379@troutmask.apl.washington.edu> <20120807205725.GA10572@server.rulingia.com> <20120809025220.N4114@besplex.bde.org> <5027F07E.9060409@missouri.edu> <20120814003614.H3692@besplex.bde.org> <50295F5C.6010800@missouri.edu> <20120814072946.S5260@besplex.bde.org> <50297CA5.5010900@missouri.edu>
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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)
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