Few coverage nitpicks for the cmath module (python#102067)

- partial tests for cosh/sinh overflows (L535 and L771).  I doubt
  both ||-ed conditions could be tested.
- removed inaccessible case in sqrt (L832): ax=ay=0 is handled
  above (L823) because fabs() is exact.  Also added test (checked
  with mpmath and gmpy2) for second condition on that line.
- some trivial tests for isclose (cover all conditions on L1217-1218)
- add comment for uncovered L1018

Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

Lib/test/cmath_testcases.txt

@@ -1536,6 +1536,7 @@ sqrt0141 sqrt -1.797e+308 -9.9999999999999999e+306 -> 3.7284476432057307e+152 -1
 sqrt0150 sqrt 1.7976931348623157e+308 0.0 -> 1.3407807929942596355e+154 0.0
 sqrt0151 sqrt 2.2250738585072014e-308 0.0 -> 1.4916681462400413487e-154 0.0
 sqrt0152 sqrt 5e-324 0.0 -> 2.2227587494850774834e-162 0.0
+sqrt0153 sqrt 5e-324 1.0 -> 0.7071067811865476 0.7071067811865476
 
 -- special values
 sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0
@@ -1744,6 +1745,7 @@ cosh0023 cosh 2.218885944363501 2.0015727395883687 -> -1.94294321081968 4.129026
 -- large real part
 cosh0030 cosh 710.5 2.3519999999999999 -> -1.2967465239355998e+308 1.3076707908857333e+308
 cosh0031 cosh -710.5 0.69999999999999996 -> 1.4085466381392499e+308 -1.1864024666450239e+308
+cosh0032 cosh 720.0 0.0 -> inf 0.0 overflow
 
 -- Additional real values (mpmath)
 cosh0050 cosh 1e-150 0.0 -> 1.0 0.0
@@ -1853,6 +1855,7 @@ sinh0023 sinh 0.043713693678420068 0.22512549887532657 -> 0.042624198673416713 0
 -- large real part
 sinh0030 sinh 710.5 -2.3999999999999999 -> -1.3579970564885919e+308 -1.24394470907798e+308
 sinh0031 sinh -710.5 0.80000000000000004 -> -1.2830671601735164e+308 1.3210954193997678e+308
+sinh0032 sinh 720.0 0.0 -> inf 0.0 overflow
 
 -- Additional real values (mpmath)
 sinh0050 sinh 1e-100 0.0 -> 1.00000000000000002e-100 0.0

Lib/test/test_cmath.py

@@ -607,6 +607,14 @@ def test_complex_near_zero(self):
         self.assertIsClose(0.001-0.001j, 0.001+0.001j, abs_tol=2e-03)
         self.assertIsNotClose(0.001-0.001j, 0.001+0.001j, abs_tol=1e-03)
 
+    def test_complex_special(self):
+        self.assertIsNotClose(INF, INF*1j)
+        self.assertIsNotClose(INF*1j, INF)
+        self.assertIsNotClose(INF, -INF)
+        self.assertIsNotClose(-INF, INF)
+        self.assertIsNotClose(0, INF)
+        self.assertIsNotClose(0, INF*1j)
+
 
 if __name__ == "__main__":
     unittest.main()

Modules/cmathmodule.c

@@ -829,7 +829,7 @@ cmath_sqrt_impl(PyObject *module, Py_complex z)
     ax = fabs(z.real);
     ay = fabs(z.imag);
 
-    if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
+    if (ax < DBL_MIN && ay < DBL_MIN) {
         /* here we catch cases where hypot(ax, ay) is subnormal */
         ax = ldexp(ax, CM_SCALE_UP);
         s = ldexp(sqrt(ax + hypot(ax, ldexp(ay, CM_SCALE_UP))),
@@ -1013,7 +1013,7 @@ cmath_phase_impl(PyObject *module, Py_complex z)
     double phi;
 
     errno = 0;
-    phi = c_atan2(z);
+    phi = c_atan2(z); /* should not cause any exception */
     if (errno != 0)
         return math_error();
     else