Message9285

I've noticed that our implementation of the (real) math module is at the root of many of our cmath problems. sinh(x) = (exp(x) - exp(-x)) / 2 in theory, but it's not accurate to compute this way for small x. For abs(x) < 2**-53, it just evaluates to zero.

Yet Jython math passes the tests in test_math.py . Why?

I decided to look at the range of x (not counting 0, 1, inf and nan) over which these methods are actually tested. Test values come from the same file cmath_testcases.txt as is used for cmath. test_math.MathTests.test_testfile() reads the file, then uses only the cases where the argument is real. The resultant coverage is this:

test_testfile (__main__.TestCaseCoverage) ... 
acos       5e-324                   <= x <= 0.9999999999999999      
acosh      1.0000000000000002       <= x <= 1.5653640340214026e+308 
asin       1e-323                   <= x <= 0.9999999999999999      
asinh      5e-324                   <= x <= 1.6025136110019349e+308 
atan       1.0516056964171069e+308  <= x <= 1.440812624377215e+308  
atanh      1e-323                   <= x <= 0.9999999999999999      
cos        None                     <= x <= None                    
cosh       None                     <= x <= None                    
exp        745.0                    <= x <= 745.0                   
log        1e-323                   <= x <= 1.440860577601428e+308  
log10      1e-323                   <= x <= 1.440860577601428e+308  
sin        None                     <= x <= None                    
sinh       None                     <= x <= None                    
sqrt       1e-323                   <= x <= 1e+299                  
tan        None                     <= x <= None                    
tanh       None                     <= x <= None                    

None means they aren't tested at all. This happens when all the non-trivial examples use a complex argument. In addition, test_math.py only requires the library to get within 1e-5 of the reference answer, quite unlike the more demanding test_cmath.py .

So that's why we pass. I'll add to our cmath_testcases.txt, some examples I generate to address that.

But this also implies CPython (real) math is not tested properly, except to the extent cmath relies on it. I think improved rigour here is something we could give back.