tgamma and y{0,1,n} test failures

[staticfloat]

These 18 test failures occur on both OSX and Linux in test-double:

$ ./test-double                                                                                              
testing double (without inline functions)
Failure: tgamma (0) == NaN plus invalid exception: Exception "Divide by zero" set
Failure: tgamma (0) == NaN plus invalid exception: Exception "Invalid operation" not set
Failure: Test: tgamma (0) == NaN plus invalid exception
Result:
 is:          inf   inf
 should be:  -nan  -nan
Failure: tgamma (-0) == NaN plus invalid exception: Exception "Divide by zero" set
Failure: tgamma (-0) == NaN plus invalid exception: Exception "Invalid operation" not set
Failure: Test: tgamma (-0) == NaN plus invalid exception
Result:
 is:         -inf  -inf
 should be:  -nan  -nan
Failure: y0 (-1.0) == -inf: Exception "Invalid operation" set
Failure: Test: y0 (-1.0) == -inf
Result:
 is:         -nan  -nan
 should be:  -inf  -inf
Failure: y0 (0.0) == -inf: Exception "Divide by zero" set
Failure: y1 (-1.0) == -inf: Exception "Invalid operation" set
Failure: Test: y1 (-1.0) == -inf
Result:
 is:         -nan  -nan
 should be:  -inf  -inf
Failure: y1 (0.0) == -inf: Exception "Divide by zero" set
Failure: yn (0, -1.0) == -inf: Exception "Invalid operation" set
Failure: Test: yn (0, -1.0) == -inf
Result:
 is:         -nan  -nan
 should be:  -inf  -inf
Failure: yn (0, 0.0) == -inf: Exception "Divide by zero" set
Failure: yn (1, -1.0) == -inf: Exception "Invalid operation" set
Failure: Test: yn (1, -1.0) == -inf
Result:
 is:         -nan  -nan
 should be:  -inf  -inf
Failure: yn (1, 0.0) == -inf: Exception "Divide by zero" set

Test suite completed:
  1129 test cases plus 944 tests for exception flags executed.
  18 errors occurred.

test-float has two more errors:

Failure: Test: yn (3, 0.7) == -15.819479052819633505
Result:
 is:         -1.58194799423217773438e+01  -0x1.fa392e00000000000000p+3
 should be:  -1.58194789886474609375e+01  -0x1.fa392c00000000000000p+3
 difference:  9.53674316406250000000e-07   0x1.00000000000000000000p-20
 ulp       :  1.0000
 max.ulp   :  0.0000

A lot of these look like really simple things like returning nan instead of inf. I may submit a pull request to fix these easy ones up, since I'm in the openlibm sources anyway right now.

[Keno]

Are we sure the tests are correct? @ViralBShah

[ViralBShah]

Although the libm is from BSD, the tests are from glibc or Apple, I forget. I have not checked if the tests are indeed correct. I generally like looking at the apple libm for correctness, etc. It is the best and fastest of the open source ones, but the license may be incompatible.

[staticfloat]

Looking at the Darwin libm implementation of tgamma, and our implementation of tgamma, it looks like we just have a conflict of definitions. Our tgamma is defined to be inf and raise divide by zero when passed +-0, however Apple's tests expect nan and "invalid" to be raised. I don't know which one is more "correct", so I figure I'll just change the tests to match the documentation of our functions. If we should go the other way, e.g. massage our tgamma function to match Apple's tests, let's just reject my pull request.

[staticfloat]

I also took a look at an erfc test that fails on test-float for me on Linux, but that one is a little trickier; especially since our erfc implementation is identical to that of Darwin's, as is our test. It's possible the apple test would fail as well, I don't think I have that source on my mac.

[ViralBShah]

On Darwin, the test-double gives 34 failures. All of them are minor and not worrisome, but it would be good to dig deeper and resolve.