Message9287

New issue to separate this from related #2237.

The Jython implementation of a few math functions has been inaccurate in parts of their domain, and this has gone unnoticed by test_math.

In test.test_math, class MathTests tests each of the methods in math at various special values, such as sin(pi/2) and exp(1). The success criterion, applied in MathTests.ftest, is that the absolute difference from the expected value be at most 1e-5.

In addition, MathTests.test_testfile takes examples from cmath_testcases.txt (which test_cmath also uses), and using only those cases where the argument and the result are both real, once more uses ftest and a 1e-5 tolerance.

This is not a very tight criterion, and for several functions the cases provided, if there are any at all, do not explore interesting parts of the domain. In contrast, test.test_cmath finds a more interesting set of test cases and tolerates much smaller errors.

The number of positive and negative arguments with which each function is tested, and their range, is listed here:

acos      16 +ve 1e-323                   <= x <= 0.9999999999999999      
          18 -ve -1.0                     <= x <= -5e-324                 
acosh     16 +ve 1.0000000000000002       <= x <= 1.5653640340214026e+308 
asin      14 +ve 1e-323                   <= x <= 0.9999999999999999      
          16 -ve -1.0                     <= x <= -1e-323                 
asinh      4 +ve 3.38339e-318             <= x <= 1.6025136110019349e+308 
           4 -ve -1.2775271979042634e+308 <= x <= -5e-324                 
atan       2 +ve 1.2956339389525244e+308  <= x <= 1.440812624377215e+308  
           2 -ve -1.0631786461936417e+308 <= x <= -1.0516056964171069e+308
atanh     16 +ve 1e-323                   <= x <= 0.9999999999999999      
          16 -ve -0.9999999999999999      <= x <= -1e-323                 
cos        0 +ve None                     <= x <= None                    
           0 -ve None                     <= x <= None                    
cosh       0 +ve None                     <= x <= None                    
           0 -ve None                     <= x <= None                    
exp        0 +ve None                     <= x <= None                    
           1 -ve -745.0                   <= x <= -745.0                  
log       32 +ve 1e-323                   <= x <= 1.440860577601428e+308  
log10     32 +ve 1e-323                   <= x <= 1.440860577601428e+308  
sin        0 +ve None                     <= x <= None                    
           0 -ve None                     <= x <= None                    
sinh       0 +ve None                     <= x <= None                    
           0 -ve None                     <= x <= None                    
sqrt      30 +ve 1e-323                   <= x <= 1e+299                  
tan        0 +ve None                     <= x <= None                    
           0 -ve None                     <= x <= None                    
tanh       0 +ve None                     <= x <= None                    
           0 -ve None                     <= x <= None                    

The original approach may be satisfactory for CPython math because it is little more than a facade on the C math library, and must also tolerate platform variations. The java.lang.Math class underlying Jython's math makes strong guarantees about accuracy.

I propose to augment cmath_testcases.txt with real-valued cases to cover the domain of each of these functions, and apply a tighter acceptance criterion.