Patch #1675423: PyComplex_AsCComplex() now tries to convert an object

to complex using its __complex__() method before falling back to the
__float__() method. Therefore, the functions in the cmath module now
can operate on objects that define a __complex__() method.
 (backport)

Doc/api/concrete.tex

@@ -443,7 +443,9 @@ booleans.  The following macros are available, however.
 
 \begin{cfuncdesc}{double}{PyFloat_AsDouble}{PyObject *pyfloat}
   Return a C \ctype{double} representation of the contents of
-  \var{pyfloat}.
+  \var{pyfloat}.  If \var{pyfloat} is not a Python floating point
+  object but has a \method{__float__} method, this method will first
+  be called to convert \var{pyfloat} into a float.
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{double}{PyFloat_AS_DOUBLE}{PyObject *pyfloat}
@@ -558,8 +560,11 @@ typedef struct {
 \end{cfuncdesc}
 
 \begin{cfuncdesc}{Py_complex}{PyComplex_AsCComplex}{PyObject *op}
-  Return the \ctype{Py_complex} value of the complex number
+  Return the \ctype{Py_complex} value of the complex number \var{op}.
-  \var{op}.
+  \versionchanged[If \var{op} is not a Python complex number object
+                  but has a \method{__complex__} method, this method
+		  will first be called to convert \var{op} to a Python
+		  complex number object]{2.6}
 \end{cfuncdesc}
 
 

Doc/lib/libcmath.tex

@@ -5,7 +5,14 @@
 \modulesynopsis{Mathematical functions for complex numbers.}
 
 This module is always available.  It provides access to mathematical
-functions for complex numbers.  The functions are:
+functions for complex numbers.  The functions in this module accept
+integers, floating-point numbers or complex numbers as arguments.
+They will also accept any Python object that has either a
+\method{__complex__} or a \method{__float__} method: these methods are
+used to convert the object to a complex or floating-point number, respectively, and
+the function is then applied to the result of the conversion.
+
+The functions are:
 
 \begin{funcdesc}{acos}{x}
 Return the arc cosine of \var{x}.

Lib/test/test_cmath.py

@@ -1,52 +1,196 @@
-#! /usr/bin/env python
+from test.test_support import run_unittest
-""" Simple test script for cmathmodule.c
+import unittest
-    Roger E. Masse
-"""
 import cmath, math
-from test.test_support import verbose, verify, TestFailed
 
-verify(abs(cmath.log(10) - math.log(10)) < 1e-9)
+class CMathTests(unittest.TestCase):
-verify(abs(cmath.log(10,2) - math.log(10,2)) < 1e-9)
+    # list of all functions in cmath
-try:
+    test_functions = [getattr(cmath, fname) for fname in [
-    cmath.log('a')
+            'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
-except TypeError:
+            'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
-    pass
+            'sqrt', 'tan', 'tanh']]
-else:
+    # test first and second arguments independently for 2-argument log
-    raise TestFailed
+    test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
+    test_functions.append(lambda x : cmath.log(14.-27j, x))
 
-try:
+    def cAssertAlmostEqual(self, a, b, rel_eps = 1e-10, abs_eps = 1e-100):
-    cmath.log(10, 'a')
+        """Check that two complex numbers are almost equal."""
-except TypeError:
+        # the two complex numbers are considered almost equal if
-    pass
+        # either the relative error is <= rel_eps or the absolute error
-else:
+        # is tiny, <= abs_eps.
-    raise TestFailed
+        if a == b == 0:
+            return
+        absolute_error = abs(a-b)
+        relative_error = absolute_error/max(abs(a), abs(b))
+        if relative_error > rel_eps and absolute_error > abs_eps:
+            self.fail("%s and %s are not almost equal" % (a, b))
 
+    def test_constants(self):
+        e_expected = 2.71828182845904523536
+        pi_expected = 3.14159265358979323846
+        self.assertAlmostEqual(cmath.pi, pi_expected, 9,
+            "cmath.pi is %s; should be %s" % (cmath.pi, pi_expected))
+        self.assertAlmostEqual(cmath.e,  e_expected, 9,
+            "cmath.e is %s; should be %s" % (cmath.e, e_expected))
 
-testdict = {'acos' : 1.0,
+    def test_user_object(self):
-            'acosh' : 1.0,
+        # Test automatic calling of __complex__ and __float__ by cmath
-            'asin' : 1.0,
+        # functions
-            'asinh' : 1.0,
-            'atan' : 0.2,
-            'atanh' : 0.2,
-            'cos' : 1.0,
-            'cosh' : 1.0,
-            'exp' : 1.0,
-            'log' : 1.0,
-            'log10' : 1.0,
-            'sin' : 1.0,
-            'sinh' : 1.0,
-            'sqrt' : 1.0,
-            'tan' : 1.0,
-            'tanh' : 1.0}
 
-for func in testdict.keys():
+        # some random values to use as test values; we avoid values
-    f = getattr(cmath, func)
+        # for which any of the functions in cmath is undefined
-    r = f(testdict[func])
+        # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
-    if verbose:
+        cx_arg = 4.419414439 + 1.497100113j
-        print 'Calling %s(%f) = %f' % (func, testdict[func], abs(r))
+        flt_arg = -6.131677725
 
-p = cmath.pi
+        # a variety of non-complex numbers, used to check that
-e = cmath.e
+        # non-complex return values from __complex__ give an error
-if verbose:
+        non_complexes = ["not complex", 1, 5L, 2., None,
-    print 'PI = ', abs(p)
+                         object(), NotImplemented]
-    print 'E = ', abs(e)
+
+        # Now we introduce a variety of classes whose instances might
+        # end up being passed to the cmath functions
+
+        # usual case: new-style class implementing __complex__
+        class MyComplex(object):
+            def __init__(self, value):
+                self.value = value
+            def __complex__(self):
+                return self.value
+
+        # old-style class implementing __complex__
+        class MyComplexOS:
+            def __init__(self, value):
+                self.value = value
+            def __complex__(self):
+                return self.value
+
+        # classes for which __complex__ raises an exception
+        class SomeException(Exception):
+            pass
+        class MyComplexException(object):
+            def __complex__(self):
+                raise SomeException
+        class MyComplexExceptionOS:
+            def __complex__(self):
+                raise SomeException
+
+        # some classes not providing __float__ or __complex__
+        class NeitherComplexNorFloat(object):
+            pass
+        class NeitherComplexNorFloatOS:
+            pass
+        class MyInt(object):
+            def __int__(self): return 2
+            def __long__(self): return 2L
+            def __index__(self): return 2
+        class MyIntOS:
+            def __int__(self): return 2
+            def __long__(self): return 2L
+            def __index__(self): return 2
+
+        # other possible combinations of __float__ and __complex__
+        # that should work
+        class FloatAndComplex(object):
+            def __float__(self):
+                return flt_arg
+            def __complex__(self):
+                return cx_arg
+        class FloatAndComplexOS:
+            def __float__(self):
+                return flt_arg
+            def __complex__(self):
+                return cx_arg
+        class JustFloat(object):
+            def __float__(self):
+                return flt_arg
+        class JustFloatOS:
+            def __float__(self):
+                return flt_arg
+
+        for f in self.test_functions:
+            # usual usage
+            self.cAssertAlmostEqual(f(MyComplex(cx_arg)), f(cx_arg))
+            self.cAssertAlmostEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
+            # other combinations of __float__ and __complex__
+            self.cAssertAlmostEqual(f(FloatAndComplex()), f(cx_arg))
+            self.cAssertAlmostEqual(f(FloatAndComplexOS()), f(cx_arg))
+            self.cAssertAlmostEqual(f(JustFloat()), f(flt_arg))
+            self.cAssertAlmostEqual(f(JustFloatOS()), f(flt_arg))
+            # TypeError should be raised for classes not providing
+            # either __complex__ or __float__, even if they provide
+            # __int__, __long__ or __index__.  An old-style class
+            # currently raises AttributeError instead of a TypeError;
+            # this could be considered a bug.
+            self.assertRaises(TypeError, f, NeitherComplexNorFloat())
+            self.assertRaises(TypeError, f, MyInt())
+            self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
+            self.assertRaises(Exception, f, MyIntOS())
+            # non-complex return value from __complex__ -> TypeError
+            for bad_complex in non_complexes:
+                self.assertRaises(TypeError, f, MyComplex(bad_complex))
+                self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
+            # exceptions in __complex__ should be propagated correctly
+            self.assertRaises(SomeException, f, MyComplexException())
+            self.assertRaises(SomeException, f, MyComplexExceptionOS())
+
+    def test_input_type(self):
+        # ints and longs should be acceptable inputs to all cmath
+        # functions, by virtue of providing a __float__ method
+        for f in self.test_functions:
+            for arg in [2, 2L, 2.]:
+                self.cAssertAlmostEqual(f(arg), f(arg.__float__()))
+
+        # but strings should give a TypeError
+        for f in self.test_functions:
+            for arg in ["a", "long_string", "0", "1j", ""]:
+                self.assertRaises(TypeError, f, arg)
+
+    def test_cmath_matches_math(self):
+        # check that corresponding cmath and math functions are equal
+        # for floats in the appropriate range
+
+        # test_values in (0, 1)
+        test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]
+
+        # test_values for functions defined on [-1., 1.]
+        unit_interval = test_values + [-x for x in test_values] + \
+            [0., 1., -1.]
+
+        # test_values for log, log10, sqrt
+        positive = test_values + [1.] + [1./x for x in test_values]
+        nonnegative = [0.] + positive
+
+        # test_values for functions defined on the whole real line
+        real_line = [0.] + positive + [-x for x in positive]
+
+        test_functions = {
+            'acos' : unit_interval,
+            'asin' : unit_interval,
+            'atan' : real_line,
+            'cos' : real_line,
+            'cosh' : real_line,
+            'exp' : real_line,
+            'log' : positive,
+            'log10' : positive,
+            'sin' : real_line,
+            'sinh' : real_line,
+            'sqrt' : nonnegative,
+            'tan' : real_line,
+            'tanh' : real_line}
+
+        for fn, values in test_functions.items():
+            float_fn = getattr(math, fn)
+            complex_fn = getattr(cmath, fn)
+            for v in values:
+                self.cAssertAlmostEqual(float_fn(v), complex_fn(v))
+
+        # test two-argument version of log with various bases
+        for base in [0.5, 2., 10.]:
+            for v in positive:
+                self.cAssertAlmostEqual(cmath.log(v, base), math.log(v, base))
+
+def test_main():
+    run_unittest(CMathTests)
+
+if __name__ == "__main__":
+    test_main()

Misc/NEWS

@@ -12,6 +12,11 @@ What's New in Python 2.6 alpha 1?
 Core and builtins
 -----------------
 
+- Patch #1675423: PyComplex_AsCComplex() now tries to convert an object
+  to complex using its __complex__() method before falling back to the
+  __float__() method. Therefore, the functions in the cmath module now
+  can operate on objects that define a __complex__() method.
+
 - Patch #1623563: allow __class__ assignment for classes with __slots__.
   The old and the new class are still required to have the same slot names.
 

Objects/complexobject.c

@@ -252,12 +252,59 @@ Py_complex
 PyComplex_AsCComplex(PyObject *op)
 {
 	Py_complex cv;
+	PyObject *newop = NULL;
+	static PyObject *complex_str = NULL;
+
+	assert(op);
+	/* If op is already of type PyComplex_Type, return its value */
 	if (PyComplex_Check(op)) {
 		return ((PyComplexObject *)op)->cval;
 	}
+	/* If not, use op's __complex__  method, if it exists */
+	
+	/* return -1 on failure */
+	cv.real = -1.;
+	cv.imag = 0.;
+	
+	if (PyInstance_Check(op)) {
+		/* this can go away in python 3000 */
+		if (PyObject_HasAttrString(op, "__complex__")) {
+			newop = PyObject_CallMethod(op, "__complex__", NULL);
+			if (!newop)
+				return cv;
+		}
+		/* else try __float__ */
+	} else {
+		PyObject *complexfunc;
+		if (!complex_str) {
+			if (!(complex_str = PyString_FromString("__complex__")))
+				return cv;
+		}
+		complexfunc = _PyType_Lookup(op->ob_type, complex_str);
+		/* complexfunc is a borrowed reference */
+		if (complexfunc) {
+			newop = PyObject_CallFunctionObjArgs(complexfunc, op, NULL);
+			if (!newop)
+				return cv;
+		}
+	}
+
+	if (newop) {
+		if (!PyComplex_Check(newop)) {
+			PyErr_SetString(PyExc_TypeError,
+				"__complex__ should return a complex object");
+			Py_DECREF(newop);
+			return cv;
+		}
+		cv = ((PyComplexObject *)newop)->cval;
+		Py_DECREF(newop);
+		return cv;
+	}
+	/* If neither of the above works, interpret op as a float giving the
+	   real part of the result, and fill in the imaginary part as 0. */
 	else {
+		/* PyFloat_AsDouble will return -1 on failure */
 		cv.real = PyFloat_AsDouble(op);
-		cv.imag = 0.;
 		return cv;
 	}
 }