Results of cos(pi/2) tests are dependent on error rounding pi/2 to a type.

Results of cos(pi/2) tests are dependent on error rounding pi/2 to a type.

[Carlos O'Donell]

Community,

I've recently fixed the cos(pi/2) tests to expect the correct
result from the rounding of pi/2. The tests previously expected
cos(M_PI_2l) to return 0.0, but this is naive. The actual answer
is a non-zero value almost equal to the error in rounding pi/2
to the floating point representation.

The first derivitive of cos(pi/2) is ~1, therefore any error
in pi/2 has a direct and linear effect on the result of the answer
either causing it to be slightly more than 0 or slightly less than
zero. The exact answer to cos(pi/2) is highly dependent on the type
used.

I've tried to take into account all of the types, but in the event
that I've made a mistake please come to me and I'll help fix it.

Cheers,
Carlos.

Re: Results of cos(pi/2) tests are dependent on error rounding pi/2 to a type.

[Andreas Schwab]

I'm getting this result on ppc for long double:

Failure: Test: cos (pi/2) == 1.082856673921913968223746169860580e-32
Result:
 is:          1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
 should be:   1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
 difference:  5.71253355584909492648e-62   0x1.78000000000000000000p-204
 ulp       :  376.0000
 max.ulp   :  0.0000
Maximal error of `cos'
 is      : 376 ulp
 accepted: 1 ulp
Failure: Test: sincos (pi/2, &sin_res, &cos_res) puts 1.082856673921913968223746169860580e-32 in cos_res
Result:
 is:          1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
 should be:   1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
 difference:  5.71253355584909492648e-62   0x1.78000000000000000000p-204
 ulp       :  376.0000
 max.ulp   :  0.0000
Maximal error of `sincos'
 is      : 376 ulp
 accepted: 1 ulp

Filed as PR15359.

Andreas.

-- 
Andreas Schwab, schwab@linux-m68k.org
GPG Key fingerprint = 58CA 54C7 6D53 942B 1756  01D3 44D5 214B 8276 4ED5
"And now for something completely different."

Re: Results of cos(pi/2) tests are dependent on error rounding pi/2 to a type.

[Carlos O'Donell]

On 04/11/2013 01:44 PM, Andreas Schwab wrote:
> I'm getting this result on ppc for long double:
> 
> Failure: Test: cos (pi/2) == 1.082856673921913968223746169860580e-32
> Result:
>  is:          1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
>  should be:   1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
>  difference:  5.71253355584909492648e-62   0x1.78000000000000000000p-204
>  ulp       :  376.0000
>  max.ulp   :  0.0000
> Maximal error of `cos'
>  is      : 376 ulp
>  accepted: 1 ulp
> Failure: Test: sincos (pi/2, &sin_res, &cos_res) puts 1.082856673921913968223746169860580e-32 in cos_res
> Result:
>  is:          1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
>  should be:   1.08285667392191396822e-32   0x1.c1cd129024e088a67cc7p-107
>  difference:  5.71253355584909492648e-62   0x1.78000000000000000000p-204
>  ulp       :  376.0000
>  max.ulp   :  0.0000
> Maximal error of `sincos'
>  is      : 376 ulp
>  accepted: 1 ulp
> 
> Filed as PR15359.

Could you print the following for me?

printf ("%.100000g\n", (long double)(M_PIl/2.0L));

The most likely scenario is that I lost digits of precision when using only %.100Le.

I'm trying to get my hands on a fast ppc box to test stuff on.

Cheers,
Carlos.