Index: Objects/complexobject.c
===================================================================
--- Objects/complexobject.c	(revision 71809)
+++ Objects/complexobject.c	(working copy)
@@ -756,12 +756,8 @@
 {
 	const char *s, *start;
 	char *end;
-	double x=0.0, y=0.0, z;
-	int got_re=0, got_im=0, got_bracket=0, done=0;
-	int digit_or_dot;
-	int sw_error=0;
-	int sign;
-	char buffer[256]; /* For errors */
+	double x, y;
+	int got_bracket=0;
 	char s_buffer[256];
 	Py_ssize_t len;
 
@@ -785,16 +781,13 @@
 		return NULL;
 	}
 
+	errno = 0;
+
 	/* position on first nonblank */
 	start = s;
 	while (*s && isspace(Py_CHARMASK(*s)))
 		s++;
-	if (s[0] == '\0') {
-		PyErr_SetString(PyExc_ValueError,
-				"complex() arg is an empty string");
-		return NULL;
-	}
-	if (s[0] == '(') {
+	if (*s == '(') {
 		/* Skip over possible bracket from repr(). */
 		got_bracket = 1;
 		s++;
@@ -802,120 +795,51 @@
 			s++;
 	}
 
-	z = -1.0;
-	sign = 1;
-	do {
+	/* get float */
+	x = PyOS_ascii_strtod(s, &end);
+	if (end == s)
+		goto error;
+	s = end;
+	if (*s == '+' || *s == '-') {
+		/* we've got a real part *and* an imaginary part */
+		y = PyOS_ascii_strtod(s, &end);
+		if (end == s || !(*end == 'j' || *end == 'J'))
+			goto error;
+		s = ++end;
+	}
+	else if (*s == 'j' || *s == 'J') {
+		/* no real part; x is the imaginary part; swap around */
+		s++;
+		y = x;
+		x = 0.0;
+	}
+	else
+		/* no imaginary part */
+		y = 0.0;
 
-		switch (*s) {
-
-		case '\0':
-			if (s-start != len) {
-				PyErr_SetString(
-					PyExc_ValueError,
-					"complex() arg contains a null byte");
-				return NULL;
-			}
-			if(!done) sw_error=1;
-			break;
-
-		case ')':
-			if (!got_bracket || !(got_re || got_im)) {
-				sw_error=1;
-				break;
-			}
-			got_bracket=0;
-			done=1;
-			s++;
-			while (*s && isspace(Py_CHARMASK(*s)))
-				s++;
-			if (*s) sw_error=1;
-			break;
-
-		case '-':
-			sign = -1;
-				/* Fallthrough */
-		case '+':
-			if (done)  sw_error=1;
-			s++;
-			if  (  *s=='\0'||*s=='+'||*s=='-'||*s==')'||
-			       isspace(Py_CHARMASK(*s))  )  sw_error=1;
-			break;
-
-		case 'J':
-		case 'j':
-			if (got_im || done) {
-				sw_error = 1;
-				break;
-			}
-			if  (z<0.0) {
-				y=sign;
-			}
-			else{
-				y=sign*z;
-			}
-			got_im=1;
-			s++;
-			if  (*s!='+' && *s!='-' )
-				done=1;
-			break;
-
-		default:
-			if (isspace(Py_CHARMASK(*s))) {
-				while (*s && isspace(Py_CHARMASK(*s)))
-					s++;
-				if (*s && *s != ')')
-					sw_error=1;
-				else
-					done = 1;
-				break;
-			}
-			digit_or_dot =
-				(*s=='.' || isdigit(Py_CHARMASK(*s)));
-			if  (done||!digit_or_dot) {
-				sw_error=1;
-				break;
-			}
-			errno = 0;
-			PyFPE_START_PROTECT("strtod", return 0)
-				z = PyOS_ascii_strtod(s, &end) ;
-			PyFPE_END_PROTECT(z)
-				if (errno != 0) {
-					PyOS_snprintf(buffer, sizeof(buffer),
-					  "float() out of range: %.150s", s);
-					PyErr_SetString(
-						PyExc_ValueError,
-						buffer);
-					return NULL;
-				}
-			s=end;
-			if  (*s=='J' || *s=='j') {
-
-				break;
-			}
-			if  (got_re) {
-				sw_error=1;
-				break;
-			}
-
-				/* accept a real part */
-			x=sign*z;
-			got_re=1;
-			if  (got_im)  done=1;
-			z = -1.0;
-			sign = 1;
-			break;
-
-		}  /* end of switch  */
-
-	} while (s - start < len && !sw_error);
-
-	if (sw_error || got_bracket) {
-		PyErr_SetString(PyExc_ValueError,
-				"complex() arg is a malformed string");
-		return NULL;
+	/* trailing whitespace and closing bracket */
+	while (*s && isspace(Py_CHARMASK(*s)))
+		s++;
+	if (got_bracket && *s == ')') {
+		got_bracket = 0;
+		s++;
+		while (*s && isspace(Py_CHARMASK(*s)))
+		       s++;
 	}
+	/* we should now be at the end of the string */
+	if (*s != '\0' || s-start != len || got_bracket)
+		goto error;
 
 	return complex_subtype_from_doubles(type, x, y);
+
+  error:
+	/* check for PyOS_ascii_strtod failure due to lack of memory */
+	if (errno == ENOMEM)
+		return PyErr_NoMemory();
+	PyErr_SetString(PyExc_ValueError,
+			"complex() arg is a malformed string");
+	return NULL;
+
 }
 
 static PyObject *
Index: Misc/NEWS
===================================================================
--- Misc/NEWS	(revision 71809)
+++ Misc/NEWS	(working copy)
@@ -12,6 +12,9 @@
 Core and Builtins
 -----------------
 
+- The complex constructor now accepts strings involving nans and infs,
+  to match float('nan') and float('inf').
+
 - Issue #3166: Make long -> float (and int -> float) conversions
   correctly rounded.
 
Index: Lib/test/test_complex.py
===================================================================
--- Lib/test/test_complex.py	(revision 71809)
+++ Lib/test/test_complex.py	(working copy)
@@ -202,6 +202,8 @@
         self.assertAlmostEqual(complex("+1"), +1)
         self.assertAlmostEqual(complex("(1+2j)"), 1+2j)
         self.assertAlmostEqual(complex("(1.3+2.2j)"), 1.3+2.2j)
+        self.assertAlmostEqual(complex("3.14+1J"), 3.14+1j)
+        self.assertAlmostEqual(complex(" ( +3.14-6J )"), 3.14-6j)
 
         class complex2(complex): pass
         self.assertAlmostEqual(complex(complex2(1+1j)), 1+1j)
@@ -229,8 +231,6 @@
         self.assertRaises(TypeError, complex, "1", "1")
         self.assertRaises(TypeError, complex, 1, "1")
 
-        self.assertEqual(complex("  3.14+J  "), 3.14+1j)
-
         # SF bug 543840:  complex(string) accepts strings with \0
         # Fixed in 2.3.
         self.assertRaises(ValueError, complex, '1+1j\0j')
@@ -254,6 +254,11 @@
         self.assertRaises(ValueError, complex, "(1+2j)123")
         self.assertRaises(ValueError, complex, "1"*500)
         self.assertRaises(ValueError, complex, "x")
+        self.assertRaises(ValueError, complex, "J")
+        self.assertRaises(ValueError, complex, "1j+2")
+        self.assertRaises(ValueError, complex, "1e1ej")
+        self.assertRaises(ValueError, complex, "1e++1ej")
+        self.assertRaises(ValueError, complex, ")1+2j(")
 
         class EvilExc(Exception):
             pass