Merged revisions 62380,62382-62383 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r62380 | christian.heimes | 2008-04-19 01:13:07 +0200 (Sat, 19 Apr 2008) | 3 lines

  I finally got the time to update and merge Mark's and my trunk-math branch. The patch is collaborated work of Mark Dickinson and me. It was mostly done a few months ago. The patch fixes a lot of loose ends and edge cases related to operations with NaN, INF, very small values and complex math.

  The patch also adds acosh, asinh, atanh, log1p and copysign to all platforms. Finally it fixes differences between platforms like different results or exceptions for edge cases. Have fun :)
........
  r62382 | christian.heimes | 2008-04-19 01:40:40 +0200 (Sat, 19 Apr 2008) | 2 lines

  Added new files to Windows project files
  More Windows related fixes are coming soon
........
  r62383 | christian.heimes | 2008-04-19 01:49:11 +0200 (Sat, 19 Apr 2008) | 1 line

  Stupid me. Py_RETURN_NAN should actually return something ...
........

2 files changed, 1235 insertions, 233 deletions

diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index ec48ce8..8e3c31e 100644
--- a/Modules/cmathmodule.c
+++ b/Modules/cmathmodule.c
@@ -3,31 +3,172 @@
 /* much code borrowed from mathmodule.c */
 
 #include "Python.h"
+/* we need DBL_MAX, DBL_MIN, DBL_EPSILON, DBL_MANT_DIG and FLT_RADIX from
+   float.h.  We assume that FLT_RADIX is either 2 or 16. */
+#include <float.h>
 
-#ifndef M_PI
-#define M_PI (3.141592653589793239)
+#if (FLT_RADIX != 2 && FLT_RADIX != 16)
+#error "Modules/cmathmodule.c expects FLT_RADIX to be 2 or 16"
 #endif
 
-/* First, the C functions that do the real work */
+#ifndef M_LN2
+#define M_LN2 (0.6931471805599453094) /* natural log of 2 */
+#endif
+
+#ifndef M_LN10
+#define M_LN10 (2.302585092994045684) /* natural log of 10 */
+#endif
 
-/* constants */
-static Py_complex c_one = {1., 0.};
-static Py_complex c_half = {0.5, 0.};
-static Py_complex c_i = {0., 1.};
-static Py_complex c_halfi = {0., 0.5};
+/*
+   CM_LARGE_DOUBLE is used to avoid spurious overflow in the sqrt, log,
+   inverse trig and inverse hyperbolic trig functions.  Its log is used in the
+   evaluation of exp, cos, cosh, sin, sinh, tan, and tanh to avoid unecessary
+   overflow.
+ */
+
+#define CM_LARGE_DOUBLE (DBL_MAX/4.)
+#define CM_SQRT_LARGE_DOUBLE (sqrt(CM_LARGE_DOUBLE))
+#define CM_LOG_LARGE_DOUBLE (log(CM_LARGE_DOUBLE))
+#define CM_SQRT_DBL_MIN (sqrt(DBL_MIN))
+
+/* 
+   CM_SCALE_UP is an odd integer chosen such that multiplication by
+   2**CM_SCALE_UP is sufficient to turn a subnormal into a normal.
+   CM_SCALE_DOWN is (-(CM_SCALE_UP+1)/2).  These scalings are used to compute
+   square roots accurately when the real and imaginary parts of the argument
+   are subnormal.
+*/
+
+#if FLT_RADIX==2
+#define CM_SCALE_UP (2*(DBL_MANT_DIG/2) + 1)
+#elif FLT_RADIX==16
+#define CM_SCALE_UP (4*DBL_MANT_DIG+1)
+#endif
+#define CM_SCALE_DOWN (-(CM_SCALE_UP+1)/2)
 
 /* forward declarations */
-static Py_complex c_log(Py_complex);
-static Py_complex c_prodi(Py_complex);
+static Py_complex c_asinh(Py_complex);
+static Py_complex c_atanh(Py_complex);
+static Py_complex c_cosh(Py_complex);
+static Py_complex c_sinh(Py_complex);
 static Py_complex c_sqrt(Py_complex);
+static Py_complex c_tanh(Py_complex);
 static PyObject * math_error(void);
 
+/* Code to deal with special values (infinities, NaNs, etc.). */
+
+/* special_type takes a double and returns an integer code indicating
+   the type of the double as follows:
+*/
+
+enum special_types {
+	ST_NINF,	/* 0, negative infinity */
+	ST_NEG,		/* 1, negative finite number (nonzero) */
+	ST_NZERO,	/* 2, -0. */
+	ST_PZERO,	/* 3, +0. */
+	ST_POS,		/* 4, positive finite number (nonzero) */
+	ST_PINF,	/* 5, positive infinity */
+	ST_NAN,		/* 6, Not a Number */
+};
+
+static enum special_types
+special_type(double d)
+{
+	if (Py_IS_FINITE(d)) {
+		if (d != 0) {
+			if (copysign(1., d) == 1.)
+				return ST_POS;
+			else
+				return ST_NEG;
+		}
+		else {
+			if (copysign(1., d) == 1.)
+				return ST_PZERO;
+			else
+				return ST_NZERO;
+		}
+	}
+	if (Py_IS_NAN(d))
+		return ST_NAN;
+	if (copysign(1., d) == 1.)
+		return ST_PINF;
+	else
+		return ST_NINF;
+}
+
+#define SPECIAL_VALUE(z, table)						\
+	if (!Py_IS_FINITE((z).real) || !Py_IS_FINITE((z).imag)) {	\
+		errno = 0;                                              \
+		return table[special_type((z).real)]	                \
+			    [special_type((z).imag)];			\
+	}
+
+#define P Py_MATH_PI
+#define P14 0.25*Py_MATH_PI
+#define P12 0.5*Py_MATH_PI
+#define P34 0.75*Py_MATH_PI
+#ifdef MS_WINDOWS
+/* On Windows HUGE_VAL is an extern variable and not a constant. Since the
+   special value arrays need a constant we have to roll our own infinity
+   and nan. */
+#  define INF (DBL_MAX*DBL_MAX)
+#  define N (INF*0.)
+#else
+#  define INF Py_HUGE_VAL
+#  define N Py_NAN
+#endif /* MS_WINDOWS */
+#define U -9.5426319407711027e33 /* unlikely value, used as placeholder */
+
+/* First, the C functions that do the real work.  Each of the c_*
+   functions computes and returns the C99 Annex G recommended result
+   and also sets errno as follows: errno = 0 if no floating-point
+   exception is associated with the result; errno = EDOM if C99 Annex
+   G recommends raising divide-by-zero or invalid for this result; and
+   errno = ERANGE where the overflow floating-point signal should be
+   raised.
+*/
+
+static Py_complex acos_special_values[7][7] = {
+  {{P34,INF},{P,INF}, {P,INF}, {P,-INF}, {P,-INF}, {P34,-INF},{N,INF}},
+  {{P12,INF},{U,U},   {U,U},   {U,U},    {U,U},    {P12,-INF},{N,N}},
+  {{P12,INF},{U,U},   {P12,0.},{P12,-0.},{U,U},    {P12,-INF},{P12,N}},
+  {{P12,INF},{U,U},   {P12,0.},{P12,-0.},{U,U},    {P12,-INF},{P12,N}},
+  {{P12,INF},{U,U},   {U,U},   {U,U},    {U,U},    {P12,-INF},{N,N}},
+  {{P14,INF},{0.,INF},{0.,INF},{0.,-INF},{0.,-INF},{P14,-INF},{N,INF}},
+  {{N,INF},  {N,N},   {N,N},   {N,N},    {N,N},    {N,-INF},  {N,N}}
+};
 
 static Py_complex
-c_acos(Py_complex x)
+c_acos(Py_complex z)
 {
-	return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
-		    c_sqrt(c_diff(c_one,c_prod(x,x))))))));
+	Py_complex s1, s2, r;
+
+	SPECIAL_VALUE(z, acos_special_values);
+
+	if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
+		/* avoid unnecessary overflow for large arguments */
+		r.real = atan2(fabs(z.imag), z.real);
+		/* split into cases to make sure that the branch cut has the
+		   correct continuity on systems with unsigned zeros */
+		if (z.real < 0.) {
+			r.imag = -copysign(log(hypot(z.real/2., z.imag/2.)) +
+					   M_LN2*2., z.imag);
+		} else {
+			r.imag = copysign(log(hypot(z.real/2., z.imag/2.)) +
+					  M_LN2*2., -z.imag);
+		}
+	} else {
+		s1.real = 1.-z.real;
+		s1.imag = -z.imag;
+		s1 = c_sqrt(s1);
+		s2.real = 1.+z.real;
+		s2.imag = z.imag;
+		s2 = c_sqrt(s2);
+		r.real = 2.*atan2(s1.real, s2.real);
+		r.imag = asinh(s2.real*s1.imag - s2.imag*s1.real);
+	}
+	errno = 0;
+	return r;
 }
 
 PyDoc_STRVAR(c_acos_doc,
@@ -36,14 +177,39 @@ PyDoc_STRVAR(c_acos_doc,
 "Return the arc cosine of x.");
 
 
+static Py_complex acosh_special_values[7][7] = {
+  {{INF,-P34},{INF,-P}, {INF,-P}, {INF,P}, {INF,P}, {INF,P34},{INF,N}},
+  {{INF,-P12},{U,U},    {U,U},    {U,U},   {U,U},   {INF,P12},{N,N}},
+  {{INF,-P12},{U,U},    {0.,-P12},{0.,P12},{U,U},   {INF,P12},{N,N}},
+  {{INF,-P12},{U,U},    {0.,-P12},{0.,P12},{U,U},   {INF,P12},{N,N}},
+  {{INF,-P12},{U,U},    {U,U},    {U,U},   {U,U},   {INF,P12},{N,N}},
+  {{INF,-P14},{INF,-0.},{INF,-0.},{INF,0.},{INF,0.},{INF,P14},{INF,N}},
+  {{INF,N},   {N,N},    {N,N},    {N,N},   {N,N},   {INF,N},  {N,N}}
+};
+
 static Py_complex
-c_acosh(Py_complex x)
+c_acosh(Py_complex z)
 {
-	Py_complex z;
-	z = c_sqrt(c_half);
-	z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_one)),
-				  c_sqrt(c_diff(x,c_one)))));
-	return c_sum(z, z);
+	Py_complex s1, s2, r;
+
+	SPECIAL_VALUE(z, acosh_special_values);
+
+	if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
+		/* avoid unnecessary overflow for large arguments */
+		r.real = log(hypot(z.real/2., z.imag/2.)) + M_LN2*2.;
+		r.imag = atan2(z.imag, z.real);
+	} else {
+		s1.real = z.real - 1.;
+		s1.imag = z.imag;
+		s1 = c_sqrt(s1);
+		s2.real = z.real + 1.;
+		s2.imag = z.imag;
+		s2 = c_sqrt(s2);
+		r.real = asinh(s1.real*s2.real + s1.imag*s2.imag);
+		r.imag = 2.*atan2(s1.imag, s2.real);
+	}
+	errno = 0;
+	return r;
 }
 
 PyDoc_STRVAR(c_acosh_doc,
@@ -53,14 +219,16 @@ PyDoc_STRVAR(c_acosh_doc,
 
 
 static Py_complex
-c_asin(Py_complex x)
+c_asin(Py_complex z)
 {
-	/* -i * log[(sqrt(1-x**2) + i*x] */
-	const Py_complex squared = c_prod(x, x);
-	const Py_complex sqrt_1_minus_x_sq = c_sqrt(c_diff(c_one, squared));
-        return c_neg(c_prodi(c_log(
-        		c_sum(sqrt_1_minus_x_sq, c_prodi(x))
-		    )       )     );
+	/* asin(z) = -i asinh(iz) */
+	Py_complex s, r;
+	s.real = -z.imag;
+	s.imag = z.real;
+	s = c_asinh(s);
+	r.real = s.imag;
+	r.imag = -s.real;
+	return r;
 }
 
 PyDoc_STRVAR(c_asin_doc,
@@ -69,14 +237,44 @@ PyDoc_STRVAR(c_asin_doc,
 "Return the arc sine of x.");
 
 
+static Py_complex asinh_special_values[7][7] = {
+  {{-INF,-P14},{-INF,-0.},{-INF,-0.},{-INF,0.},{-INF,0.},{-INF,P14},{-INF,N}},
+  {{-INF,-P12},{U,U},     {U,U},     {U,U},    {U,U},    {-INF,P12},{N,N}},
+  {{-INF,-P12},{U,U},     {-0.,-0.}, {-0.,0.}, {U,U},    {-INF,P12},{N,N}},
+  {{INF,-P12}, {U,U},     {0.,-0.},  {0.,0.},  {U,U},    {INF,P12}, {N,N}},
+  {{INF,-P12}, {U,U},     {U,U},     {U,U},    {U,U},    {INF,P12}, {N,N}},
+  {{INF,-P14}, {INF,-0.}, {INF,-0.}, {INF,0.}, {INF,0.}, {INF,P14}, {INF,N}},
+  {{INF,N},    {N,N},     {N,-0.},   {N,0.},   {N,N},    {INF,N},   {N,N}}
+};
+
 static Py_complex
-c_asinh(Py_complex x)
+c_asinh(Py_complex z)
 {
-	Py_complex z;
-	z = c_sqrt(c_half);
-	z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)),
-				  c_sqrt(c_diff(x, c_i)))));
-	return c_sum(z, z);
+	Py_complex s1, s2, r;
+
+	SPECIAL_VALUE(z, asinh_special_values);
+
+	if (fabs(z.real) > CM_LARGE_DOUBLE || fabs(z.imag) > CM_LARGE_DOUBLE) {
+		if (z.imag >= 0.) {
+			r.real = copysign(log(hypot(z.real/2., z.imag/2.)) +
+					  M_LN2*2., z.real);
+		} else {
+			r.real = -copysign(log(hypot(z.real/2., z.imag/2.)) +
+					   M_LN2*2., -z.real);
+		}
+		r.imag = atan2(z.imag, fabs(z.real));
+	} else {
+		s1.real = 1.+z.imag;
+		s1.imag = -z.real;
+		s1 = c_sqrt(s1);
+		s2.real = 1.-z.imag;
+		s2.imag = z.real;
+		s2 = c_sqrt(s2);
+		r.real = asinh(s1.real*s2.imag-s2.real*s1.imag);
+		r.imag = atan2(z.imag, s1.real*s2.real-s1.imag*s2.imag);
+	}
+	errno = 0;
+	return r;
 }
 
 PyDoc_STRVAR(c_asinh_doc,
@@ -86,9 +284,37 @@ PyDoc_STRVAR(c_asinh_doc,
 
 
 static Py_complex
-c_atan(Py_complex x)
+c_atan(Py_complex z)
 {
-	return c_prod(c_halfi,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
+	/* atan(z) = -i atanh(iz) */
+	Py_complex s, r;
+	s.real = -z.imag;
+	s.imag = z.real;
+	s = c_atanh(s);
+	r.real = s.imag;
+	r.imag = -s.real;
+	return r;
+}
+
+/* Windows screws up atan2 for inf and nan */
+static double
+c_atan2(Py_complex z)
+{
+	if (Py_IS_NAN(z.real) || Py_IS_NAN(z.imag))
+		return Py_NAN;
+	if (Py_IS_INFINITY(z.imag)) {
+		if (Py_IS_INFINITY(z.real)) {
+			if (copysign(1., z.real) == 1.)
+				/* atan2(+-inf, +inf) == +-pi/4 */
+				return copysign(0.25*Py_MATH_PI, z.imag);
+			else
+				/* atan2(+-inf, -inf) == +-pi*3/4 */
+				return copysign(0.75*Py_MATH_PI, z.imag);
+		}
+		/* atan2(+-inf, x) == +-pi/2 for finite x */
+		return copysign(0.5*Py_MATH_PI, z.imag);
+	}
+	return atan2(z.imag, z.real);
 }
 
 PyDoc_STRVAR(c_atan_doc,
@@ -97,10 +323,61 @@ PyDoc_STRVAR(c_atan_doc,
 "Return the arc tangent of x.");
 
 
+static Py_complex atanh_special_values[7][7] = {
+  {{-0.,-P12},{-0.,-P12},{-0.,-P12},{-0.,P12},{-0.,P12},{-0.,P12},{-0.,N}},
+  {{-0.,-P12},{U,U},     {U,U},     {U,U},    {U,U},    {-0.,P12},{N,N}},
+  {{-0.,-P12},{U,U},     {-0.,-0.}, {-0.,0.}, {U,U},    {-0.,P12},{-0.,N}},
+  {{0.,-P12}, {U,U},     {0.,-0.},  {0.,0.},  {U,U},    {0.,P12}, {0.,N}},
+  {{0.,-P12}, {U,U},     {U,U},     {U,U},    {U,U},    {0.,P12}, {N,N}},
+  {{0.,-P12}, {0.,-P12}, {0.,-P12}, {0.,P12}, {0.,P12}, {0.,P12}, {0.,N}},
+  {{0.,-P12}, {N,N},     {N,N},     {N,N},    {N,N},    {0.,P12}, {N,N}}
+};
+
 static Py_complex
-c_atanh(Py_complex x)
+c_atanh(Py_complex z)
 {
-	return c_prod(c_half,c_log(c_quot(c_sum(c_one,x),c_diff(c_one,x))));
+	Py_complex r;
+	double ay, h;
+
+	SPECIAL_VALUE(z, atanh_special_values);
+
+	/* Reduce to case where z.real >= 0., using atanh(z) = -atanh(-z). */
+	if (z.real < 0.) {
+		return c_neg(c_atanh(c_neg(z)));
+	}
+
+	ay = fabs(z.imag);
+	if (z.real > CM_SQRT_LARGE_DOUBLE || ay > CM_SQRT_LARGE_DOUBLE) {
+		/*
+		   if abs(z) is large then we use the approximation
+		   atanh(z) ~ 1/z +/- i*pi/2 (+/- depending on the sign
+		   of z.imag)
+		*/
+		h = hypot(z.real/2., z.imag/2.);  /* safe from overflow */
+		r.real = z.real/4./h/h;
+		/* the two negations in the next line cancel each other out
+		   except when working with unsigned zeros: they're there to
+		   ensure that the branch cut has the correct continuity on
+		   systems that don't support signed zeros */
+		r.imag = -copysign(Py_MATH_PI/2., -z.imag);
+		errno = 0;
+	} else if (z.real == 1. && ay < CM_SQRT_DBL_MIN) {
+		/* C99 standard says:  atanh(1+/-0.) should be inf +/- 0i */
+		if (ay == 0.) {
+			r.real = INF;
+			r.imag = z.imag;
+			errno = EDOM;
+		} else {
+			r.real = -log(sqrt(ay)/sqrt(hypot(ay, 2.)));
+			r.imag = copysign(atan2(2., -ay)/2, z.imag);
+			errno = 0;
+		}
+	} else {
+		r.real = log1p(4.*z.real/((1-z.real)*(1-z.real) + ay*ay))/4.;
+		r.imag = -atan2(-2.*z.imag, (1-z.real)*(1+z.real) - ay*ay)/2.;
+		errno = 0;
+	}
+	return r;
 }
 
 PyDoc_STRVAR(c_atanh_doc,
@@ -110,11 +387,13 @@ PyDoc_STRVAR(c_atanh_doc,
 
 
 static Py_complex
-c_cos(Py_complex x)
+c_cos(Py_complex z)
 {
+	/* cos(z) = cosh(iz) */
 	Py_complex r;
-	r.real = cos(x.real)*cosh(x.imag);
-	r.imag = -sin(x.real)*sinh(x.imag);
+	r.real = -z.imag;
+	r.imag = z.real;
+	r = c_cosh(r);
 	return r;
 }
 
@@ -124,12 +403,64 @@ PyDoc_STRVAR(c_cos_doc,
 "Return the cosine of x.");
 
 
+/* cosh(infinity + i*y) needs to be dealt with specially */
+static Py_complex cosh_special_values[7][7] = {
+  {{INF,N},{U,U},{INF,0.}, {INF,-0.},{U,U},{INF,N},{INF,N}},
+  {{N,N},  {U,U},{U,U},    {U,U},    {U,U},{N,N},  {N,N}},
+  {{N,0.}, {U,U},{1.,0.},  {1.,-0.}, {U,U},{N,0.}, {N,0.}},
+  {{N,0.}, {U,U},{1.,-0.}, {1.,0.},  {U,U},{N,0.}, {N,0.}},
+  {{N,N},  {U,U},{U,U},    {U,U},    {U,U},{N,N},  {N,N}},
+  {{INF,N},{U,U},{INF,-0.},{INF,0.}, {U,U},{INF,N},{INF,N}},
+  {{N,N},  {N,N},{N,0.},   {N,0.},   {N,N},{N,N},  {N,N}}
+};
+
 static Py_complex
-c_cosh(Py_complex x)
+c_cosh(Py_complex z)
 {
 	Py_complex r;
-	r.real = cos(x.imag)*cosh(x.real);
-	r.imag = sin(x.imag)*sinh(x.real);
+	double x_minus_one;
+
+	/* special treatment for cosh(+/-inf + iy) if y is not a NaN */
+	if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+		if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag) &&
+		    (z.imag != 0.)) {
+			if (z.real > 0) {
+				r.real = copysign(INF, cos(z.imag));
+				r.imag = copysign(INF, sin(z.imag));
+			}
+			else {
+				r.real = copysign(INF, cos(z.imag));
+				r.imag = -copysign(INF, sin(z.imag));
+			}
+		}
+		else {
+			r = cosh_special_values[special_type(z.real)]
+				               [special_type(z.imag)];
+		}
+		/* need to set errno = EDOM if y is +/- infinity and x is not
+		   a NaN */
+		if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
+			errno = EDOM;
+		else
+			errno = 0;
+		return r;
+	}
+
+	if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
+		/* deal correctly with cases where cosh(z.real) overflows but
+		   cosh(z) does not. */
+		x_minus_one = z.real - copysign(1., z.real);
+		r.real = cos(z.imag) * cosh(x_minus_one) * Py_MATH_E;
+		r.imag = sin(z.imag) * sinh(x_minus_one) * Py_MATH_E;
+	} else {
+		r.real = cos(z.imag) * cosh(z.real);
+		r.imag = sin(z.imag) * sinh(z.real);
+	}
+	/* detect overflow, and set errno accordingly */
+	if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
+		errno = ERANGE;
+	else
+		errno = 0;
 	return r;
 }
 
@@ -139,13 +470,65 @@ PyDoc_STRVAR(c_cosh_doc,
 "Return the hyperbolic cosine of x.");
 
 
+/* exp(infinity + i*y) and exp(-infinity + i*y) need special treatment for
+   finite y */
+static Py_complex exp_special_values[7][7] = {
+  {{0.,0.},{U,U},{0.,-0.}, {0.,0.}, {U,U},{0.,0.},{0.,0.}},
+  {{N,N},  {U,U},{U,U},    {U,U},   {U,U},{N,N},  {N,N}},
+  {{N,N},  {U,U},{1.,-0.}, {1.,0.}, {U,U},{N,N},  {N,N}},
+  {{N,N},  {U,U},{1.,-0.}, {1.,0.}, {U,U},{N,N},  {N,N}},
+  {{N,N},  {U,U},{U,U},    {U,U},   {U,U},{N,N},  {N,N}},
+  {{INF,N},{U,U},{INF,-0.},{INF,0.},{U,U},{INF,N},{INF,N}},
+  {{N,N},  {N,N},{N,-0.},  {N,0.},  {N,N},{N,N},  {N,N}}
+};
+
 static Py_complex
-c_exp(Py_complex x)
+c_exp(Py_complex z)
 {
 	Py_complex r;
-	double l = exp(x.real);
-	r.real = l*cos(x.imag);
-	r.imag = l*sin(x.imag);
+	double l;
+
+	if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+		if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
+		    && (z.imag != 0.)) {
+			if (z.real > 0) {
+				r.real = copysign(INF, cos(z.imag));
+				r.imag = copysign(INF, sin(z.imag));
+			}
+			else {
+				r.real = copysign(0., cos(z.imag));
+				r.imag = copysign(0., sin(z.imag));
+			}
+		}
+		else {
+			r = exp_special_values[special_type(z.real)]
+				              [special_type(z.imag)];
+		}
+		/* need to set errno = EDOM if y is +/- infinity and x is not
+		   a NaN and not -infinity */
+		if (Py_IS_INFINITY(z.imag) &&
+		    (Py_IS_FINITE(z.real) ||
+		     (Py_IS_INFINITY(z.real) && z.real > 0)))
+			errno = EDOM;
+		else
+			errno = 0;
+		return r;
+	}
+
+	if (z.real > CM_LOG_LARGE_DOUBLE) {
+		l = exp(z.real-1.);
+		r.real = l*cos(z.imag)*Py_MATH_E;
+		r.imag = l*sin(z.imag)*Py_MATH_E;
+	} else {
+		l = exp(z.real);
+		r.real = l*cos(z.imag);
+		r.imag = l*sin(z.imag);
+	}
+	/* detect overflow, and set errno accordingly */
+	if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
+		errno = ERANGE;
+	else
+		errno = 0;
 	return r;
 }
 
@@ -155,24 +538,97 @@ PyDoc_STRVAR(c_exp_doc,
 "Return the exponential value e**x.");
 
 
+static Py_complex log_special_values[7][7] = {
+  {{INF,-P34},{INF,-P}, {INF,-P},  {INF,P},  {INF,P}, {INF,P34}, {INF,N}},
+  {{INF,-P12},{U,U},    {U,U},     {U,U},    {U,U},   {INF,P12}, {N,N}},
+  {{INF,-P12},{U,U},    {-INF,-P}, {-INF,P}, {U,U},   {INF,P12}, {N,N}},
+  {{INF,-P12},{U,U},    {-INF,-0.},{-INF,0.},{U,U},   {INF,P12}, {N,N}},
+  {{INF,-P12},{U,U},    {U,U},     {U,U},    {U,U},   {INF,P12}, {N,N}},
+  {{INF,-P14},{INF,-0.},{INF,-0.}, {INF,0.}, {INF,0.},{INF,P14}, {INF,N}},
+  {{INF,N},   {N,N},    {N,N},     {N,N},    {N,N},   {INF,N},   {N,N}}
+};
+
 static Py_complex
-c_log(Py_complex x)
+c_log(Py_complex z)
 {
+	/*
+	   The usual formula for the real part is log(hypot(z.real, z.imag)).
+	   There are four situations where this formula is potentially
+	   problematic:
+
+	   (1) the absolute value of z is subnormal.  Then hypot is subnormal,
+	   so has fewer than the usual number of bits of accuracy, hence may
+	   have large relative error.  This then gives a large absolute error
+	   in the log.  This can be solved by rescaling z by a suitable power
+	   of 2.
+
+	   (2) the absolute value of z is greater than DBL_MAX (e.g. when both
+	   z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
+	   Again, rescaling solves this.
+
+	   (3) the absolute value of z is close to 1.  In this case it's
+	   difficult to achieve good accuracy, at least in part because a
+	   change of 1ulp in the real or imaginary part of z can result in a
+	   change of billions of ulps in the correctly rounded answer.
+
+	   (4) z = 0.  The simplest thing to do here is to call the
+	   floating-point log with an argument of 0, and let its behaviour
+	   (returning -infinity, signaling a floating-point exception, setting
+	   errno, or whatever) determine that of c_log.  So the usual formula
+	   is fine here.
+
+	 */
+
 	Py_complex r;
-	double l = hypot(x.real,x.imag);
-	r.imag = atan2(x.imag, x.real);
-	r.real = log(l);
+	double ax, ay, am, an, h;
+
+	SPECIAL_VALUE(z, log_special_values);
+
+	ax = fabs(z.real);
+	ay = fabs(z.imag);
+
+	if (ax > CM_LARGE_DOUBLE || ay > CM_LARGE_DOUBLE) {
+		r.real = log(hypot(ax/2., ay/2.)) + M_LN2;
+	} else if (ax < DBL_MIN && ay < DBL_MIN) {
+		if (ax > 0. || ay > 0.) {
+			/* catch cases where hypot(ax, ay) is subnormal */
+			r.real = log(hypot(ldexp(ax, DBL_MANT_DIG),
+				 ldexp(ay, DBL_MANT_DIG))) - DBL_MANT_DIG*M_LN2;
+		}
+		else {
+			/* log(+/-0. +/- 0i) */
+			r.real = -INF;
+			r.imag = atan2(z.imag, z.real);
+			errno = EDOM;
+			return r;
+		}
+	} else {
+		h = hypot(ax, ay);
+		if (0.71 <= h && h <= 1.73) {
+			am = ax > ay ? ax : ay;  /* max(ax, ay) */
+			an = ax > ay ? ay : ax;  /* min(ax, ay) */
+			r.real = log1p((am-1)*(am+1)+an*an)/2.;
+		} else {
+			r.real = log(h);
+		}
+	}
+	r.imag = atan2(z.imag, z.real);
+	errno = 0;
 	return r;
 }
 
 
 static Py_complex
-c_log10(Py_complex x)
+c_log10(Py_complex z)
 {
 	Py_complex r;
-	double l = hypot(x.real,x.imag);
-	r.imag = atan2(x.imag, x.real)/log(10.);
-	r.real = log10(l);
+	int errno_save;
+
+	r = c_log(z);
+	errno_save = errno; /* just in case the divisions affect errno */
+	r.real = r.real / M_LN10;
+	r.imag = r.imag / M_LN10;
+	errno = errno_save;
 	return r;
 }
 
@@ -182,23 +638,16 @@ PyDoc_STRVAR(c_log10_doc,
 "Return the base-10 logarithm of x.");
 
 
-/* internal function not available from Python */
-static Py_complex
-c_prodi(Py_complex x)
-{
-	Py_complex r;
-	r.real = -x.imag;
-	r.imag = x.real;
-	return r;
-}
-
-
 static Py_complex
-c_sin(Py_complex x)
+c_sin(Py_complex z)
 {
-	Py_complex r;
-	r.real = sin(x.real) * cosh(x.imag);
-	r.imag = cos(x.real) * sinh(x.imag);
+	/* sin(z) = -i sin(iz) */
+	Py_complex s, r;
+	s.real = -z.imag;
+	s.imag = z.real;
+	s = c_sinh(s);
+	r.real = s.imag;
+	r.imag = -s.real;
 	return r;
 }
 
@@ -208,12 +657,63 @@ PyDoc_STRVAR(c_sin_doc,
 "Return the sine of x.");
 
 
+/* sinh(infinity + i*y) needs to be dealt with specially */
+static Py_complex sinh_special_values[7][7] = {
+  {{INF,N},{U,U},{-INF,-0.},{-INF,0.},{U,U},{INF,N},{INF,N}},
+  {{N,N},  {U,U},{U,U},     {U,U},    {U,U},{N,N},  {N,N}},
+  {{0.,N}, {U,U},{-0.,-0.}, {-0.,0.}, {U,U},{0.,N}, {0.,N}},
+  {{0.,N}, {U,U},{0.,-0.},  {0.,0.},  {U,U},{0.,N}, {0.,N}},
+  {{N,N},  {U,U},{U,U},     {U,U},    {U,U},{N,N},  {N,N}},
+  {{INF,N},{U,U},{INF,-0.}, {INF,0.}, {U,U},{INF,N},{INF,N}},
+  {{N,N},  {N,N},{N,-0.},   {N,0.},   {N,N},{N,N},  {N,N}}
+};
+
 static Py_complex
-c_sinh(Py_complex x)
+c_sinh(Py_complex z)
 {
 	Py_complex r;
-	r.real = cos(x.imag) * sinh(x.real);
-	r.imag = sin(x.imag) * cosh(x.real);
+	double x_minus_one;
+
+	/* special treatment for sinh(+/-inf + iy) if y is finite and
+	   nonzero */
+	if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+		if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
+		    && (z.imag != 0.)) {
+			if (z.real > 0) {
+				r.real = copysign(INF, cos(z.imag));
+				r.imag = copysign(INF, sin(z.imag));
+			}
+			else {
+				r.real = -copysign(INF, cos(z.imag));
+				r.imag = copysign(INF, sin(z.imag));
+			}
+		}
+		else {
+			r = sinh_special_values[special_type(z.real)]
+				               [special_type(z.imag)];
+		}
+		/* need to set errno = EDOM if y is +/- infinity and x is not
+		   a NaN */
+		if (Py_IS_INFINITY(z.imag) && !Py_IS_NAN(z.real))
+			errno = EDOM;
+		else
+			errno = 0;
+		return r;
+	}
+
+	if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
+		x_minus_one = z.real - copysign(1., z.real);
+		r.real = cos(z.imag) * sinh(x_minus_one) * Py_MATH_E;
+		r.imag = sin(z.imag) * cosh(x_minus_one) * Py_MATH_E;
+	} else {
+		r.real = cos(z.imag) * sinh(z.real);
+		r.imag = sin(z.imag) * cosh(z.real);
+	}
+	/* detect overflow, and set errno accordingly */
+	if (Py_IS_INFINITY(r.real) || Py_IS_INFINITY(r.imag))
+		errno = ERANGE;
+	else
+		errno = 0;
 	return r;
 }
 
@@ -223,29 +723,80 @@ PyDoc_STRVAR(c_sinh_doc,
 "Return the hyperbolic sine of x.");
 
 
+static Py_complex sqrt_special_values[7][7] = {
+  {{INF,-INF},{0.,-INF},{0.,-INF},{0.,INF},{0.,INF},{INF,INF},{N,INF}},
+  {{INF,-INF},{U,U},    {U,U},    {U,U},   {U,U},   {INF,INF},{N,N}},
+  {{INF,-INF},{U,U},    {0.,-0.}, {0.,0.}, {U,U},   {INF,INF},{N,N}},
+  {{INF,-INF},{U,U},    {0.,-0.}, {0.,0.}, {U,U},   {INF,INF},{N,N}},
+  {{INF,-INF},{U,U},    {U,U},    {U,U},   {U,U},   {INF,INF},{N,N}},
+  {{INF,-INF},{INF,-0.},{INF,-0.},{INF,0.},{INF,0.},{INF,INF},{INF,N}},
+  {{INF,-INF},{N,N},    {N,N},    {N,N},   {N,N},   {INF,INF},{N,N}}
+};
+
 static Py_complex
-c_sqrt(Py_complex x)
+c_sqrt(Py_complex z)
 {
+	/*
+	   Method: use symmetries to reduce to the case when x = z.real and y
+	   = z.imag are nonnegative.  Then the real part of the result is
+	   given by
+
+	     s = sqrt((x + hypot(x, y))/2)
+
+	   and the imaginary part is
+
+	     d = (y/2)/s
+
+	   If either x or y is very large then there's a risk of overflow in
+	   computation of the expression x + hypot(x, y).  We can avoid this
+	   by rewriting the formula for s as:
+
+	     s = 2*sqrt(x/8 + hypot(x/8, y/8))
+
+	   This costs us two extra multiplications/divisions, but avoids the
+	   overhead of checking for x and y large.
+
+	   If both x and y are subnormal then hypot(x, y) may also be
+	   subnormal, so will lack full precision.  We solve this by rescaling
+	   x and y by a sufficiently large power of 2 to ensure that x and y
+	   are normal.
+	*/
+
+
 	Py_complex r;
 	double s,d;
-	if (x.real == 0. && x.imag == 0.)
-		r = x;
-	else {
-		s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));
-		d = 0.5*x.imag/s;
-		if (x.real > 0.) {
-			r.real = s;
-			r.imag = d;
-		}
-		else if (x.imag >= 0.) {
-			r.real = d;
-			r.imag = s;
-		}
-		else {
-			r.real = -d;
-			r.imag = -s;
-		}
+	double ax, ay;
+
+	SPECIAL_VALUE(z, sqrt_special_values);
+
+	if (z.real == 0. && z.imag == 0.) {
+		r.real = 0.;
+		r.imag = z.imag;
+		return r;
+	}
+
+	ax = fabs(z.real);
+	ay = fabs(z.imag);
+
+	if (ax < DBL_MIN && ay < DBL_MIN && (ax > 0. || ay > 0.)) {
+		/* 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))),
+			  CM_SCALE_DOWN);
+	} else {
+		ax /= 8.;
+		s = 2.*sqrt(ax + hypot(ax, ay/8.));
+	}
+	d = ay/(2.*s);
+
+	if (z.real >= 0.) {
+		r.real = s;
+		r.imag = copysign(d, z.imag);
+	} else {
+		r.real = d;
+		r.imag = copysign(s, z.imag);
 	}
+	errno = 0;
 	return r;
 }
 
@@ -256,23 +807,15 @@ PyDoc_STRVAR(c_sqrt_doc,
 
 
 static Py_complex
-c_tan(Py_complex x)
+c_tan(Py_complex z)
 {
-	Py_complex r;
-	double sr,cr,shi,chi;
-	double rs,is,rc,ic;
-	double d;
-	sr = sin(x.real);
-	cr = cos(x.real);
-	shi = sinh(x.imag);
-	chi = cosh(x.imag);
-	rs = sr * chi;
-	is = cr * shi;
-	rc = cr * chi;
-	ic = -sr * shi;
-	d = rc*rc + ic * ic;
-	r.real = (rs*rc + is*ic) / d;
-	r.imag = (is*rc - rs*ic) / d;
+	/* tan(z) = -i tanh(iz) */
+	Py_complex s, r;
+	s.real = -z.imag;
+	s.imag = z.real;
+	s = c_tanh(s);
+	r.real = s.imag;
+	r.imag = -s.real;
 	return r;
 }
 
@@ -282,24 +825,78 @@ PyDoc_STRVAR(c_tan_doc,
 "Return the tangent of x.");
 
 
+/* tanh(infinity + i*y) needs to be dealt with specially */
+static Py_complex tanh_special_values[7][7] = {
+  {{-1.,0.},{U,U},{-1.,-0.},{-1.,0.},{U,U},{-1.,0.},{-1.,0.}},
+  {{N,N},   {U,U},{U,U},    {U,U},   {U,U},{N,N},   {N,N}},
+  {{N,N},   {U,U},{-0.,-0.},{-0.,0.},{U,U},{N,N},   {N,N}},
+  {{N,N},   {U,U},{0.,-0.}, {0.,0.}, {U,U},{N,N},   {N,N}},
+  {{N,N},   {U,U},{U,U},    {U,U},   {U,U},{N,N},   {N,N}},
+  {{1.,0.}, {U,U},{1.,-0.}, {1.,0.}, {U,U},{1.,0.}, {1.,0.}},
+  {{N,N},   {N,N},{N,-0.},  {N,0.},  {N,N},{N,N},   {N,N}}
+};
+
 static Py_complex
-c_tanh(Py_complex x)
+c_tanh(Py_complex z)
 {
+	/* Formula:
+
+	   tanh(x+iy) = (tanh(x)(1+tan(y)^2) + i tan(y)(1-tanh(x))^2) /
+	   (1+tan(y)^2 tanh(x)^2)
+
+	   To avoid excessive roundoff error, 1-tanh(x)^2 is better computed
+	   as 1/cosh(x)^2.  When abs(x) is large, we approximate 1-tanh(x)^2
+	   by 4 exp(-2*x) instead, to avoid possible overflow in the
+	   computation of cosh(x).
+
+	*/
+
 	Py_complex r;
-	double si,ci,shr,chr;
-	double rs,is,rc,ic;
-	double d;
-	si = sin(x.imag);
-	ci = cos(x.imag);
-	shr = sinh(x.real);
-	chr = cosh(x.real);
-	rs = ci * shr;
-	is = si * chr;
-	rc = ci * chr;
-	ic = si * shr;
-	d = rc*rc + ic*ic;
-	r.real = (rs*rc + is*ic) / d;
-	r.imag = (is*rc - rs*ic) / d;
+	double tx, ty, cx, txty, denom;
+
+	/* special treatment for tanh(+/-inf + iy) if y is finite and
+	   nonzero */
+	if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+		if (Py_IS_INFINITY(z.real) && Py_IS_FINITE(z.imag)
+		    && (z.imag != 0.)) {
+			if (z.real > 0) {
+				r.real = 1.0;
+				r.imag = copysign(0.,
+						  2.*sin(z.imag)*cos(z.imag));
+			}
+			else {
+				r.real = -1.0;
+				r.imag = copysign(0.,
+						  2.*sin(z.imag)*cos(z.imag));
+			}
+		}
+		else {
+			r = tanh_special_values[special_type(z.real)]
+				               [special_type(z.imag)];
+		}
+		/* need to set errno = EDOM if z.imag is +/-infinity and
+		   z.real is finite */
+		if (Py_IS_INFINITY(z.imag) && Py_IS_FINITE(z.real))
+			errno = EDOM;
+		else
+			errno = 0;
+		return r;
+	}
+
+	/* danger of overflow in 2.*z.imag !*/
+	if (fabs(z.real) > CM_LOG_LARGE_DOUBLE) {
+		r.real = copysign(1., z.real);
+		r.imag = 4.*sin(z.imag)*cos(z.imag)*exp(-2.*fabs(z.real));
+	} else {
+		tx = tanh(z.real);
+		ty = tan(z.imag);
+		cx = 1./cosh(z.real);
+		txty = tx*ty;
+		denom = 1. + txty*txty;
+		r.real = tx*(1.+ty*ty)/denom;
+		r.imag = ((ty/denom)*cx)*cx;
+	}
+	errno = 0;
 	return r;
 }
 
@@ -308,6 +905,7 @@ PyDoc_STRVAR(c_tanh_doc,
 "\n"
 "Return the hyperbolic tangent of x.");
 
+
 static PyObject *
 cmath_log(PyObject *self, PyObject *args)
 {
@@ -325,7 +923,6 @@ cmath_log(PyObject *self, PyObject *args)
 	PyFPE_END_PROTECT(x)
 	if (errno != 0)
 		return math_error();
-	Py_ADJUST_ERANGE2(x.real, x.imag);
 	return PyComplex_FromCComplex(x);
 }
 
@@ -351,18 +948,24 @@ math_error(void)
 static PyObject *
 math_1(PyObject *args, Py_complex (*func)(Py_complex))
 {
-	Py_complex x;
+	Py_complex x,r ;
 	if (!PyArg_ParseTuple(args, "D", &x))
 		return NULL;
 	errno = 0;
-	PyFPE_START_PROTECT("complex function", return 0)
-	x = (*func)(x);
-	PyFPE_END_PROTECT(x)
-	Py_ADJUST_ERANGE2(x.real, x.imag);
-	if (errno != 0)
-		return math_error();
-	else
-		return PyComplex_FromCComplex(x);
+	PyFPE_START_PROTECT("complex function", return 0);
+	r = (*func)(x);
+	PyFPE_END_PROTECT(r);
+	if (errno == EDOM) {
+		PyErr_SetString(PyExc_ValueError, "math domain error");
+		return NULL;
+	}
+	else if (errno == ERANGE) {
+		PyErr_SetString(PyExc_OverflowError, "math range error");
+		return NULL;
+	}
+	else {
+		return PyComplex_FromCComplex(r);
+	}
 }
 
 #define FUNC1(stubname, func) \
@@ -386,6 +989,151 @@ FUNC1(cmath_sqrt, c_sqrt)
 FUNC1(cmath_tan, c_tan)
 FUNC1(cmath_tanh, c_tanh)
 
+static PyObject *
+cmath_phase(PyObject *self, PyObject *args)
+{
+	Py_complex z;
+	double phi;
+	if (!PyArg_ParseTuple(args, "D:phase", &z))
+		return NULL;
+	errno = 0;
+	PyFPE_START_PROTECT("arg function", return 0)
+	phi = c_atan2(z);
+	PyFPE_END_PROTECT(r)
+	if (errno != 0)
+		return math_error();
+	else
+		return PyFloat_FromDouble(phi);
+}
+
+PyDoc_STRVAR(cmath_phase_doc,
+"phase(z) -> float\n\n\
+Return argument, also known as the phase angle, of a complex.");
+
+static PyObject *
+cmath_polar(PyObject *self, PyObject *args)
+{
+	Py_complex z;
+	double r, phi;
+	if (!PyArg_ParseTuple(args, "D:polar", &z))
+		return NULL;
+	PyFPE_START_PROTECT("polar function", return 0)
+	phi = c_atan2(z); /* should not cause any exception */
+	r = c_abs(z); /* sets errno to ERANGE on overflow;  otherwise 0 */
+	PyFPE_END_PROTECT(r)
+	if (errno != 0)
+		return math_error();
+	else
+		return Py_BuildValue("dd", r, phi);
+}
+
+PyDoc_STRVAR(cmath_polar_doc,
+"polar(z) -> r: float, phi: float\n\n\
+Convert a complex from rectangular coordinates to polar coordinates. r is\n\
+the distance from 0 and phi the phase angle.");
+
+/*
+  rect() isn't covered by the C99 standard, but it's not too hard to
+  figure out 'spirit of C99' rules for special value handing:
+
+    rect(x, t) should behave like exp(log(x) + it) for positive-signed x
+    rect(x, t) should behave like -exp(log(-x) + it) for negative-signed x
+    rect(nan, t) should behave like exp(nan + it), except that rect(nan, 0)
+      gives nan +- i0 with the sign of the imaginary part unspecified.
+
+*/
+
+static Py_complex rect_special_values[7][7] = {
+  {{INF,N},{U,U},{-INF,0.},{-INF,-0.},{U,U},{INF,N},{INF,N}},
+  {{N,N},  {U,U},{U,U},    {U,U},     {U,U},{N,N},  {N,N}},
+  {{0.,0.},{U,U},{-0.,0.}, {-0.,-0.}, {U,U},{0.,0.},{0.,0.}},
+  {{0.,0.},{U,U},{0.,-0.}, {0.,0.},   {U,U},{0.,0.},{0.,0.}},
+  {{N,N},  {U,U},{U,U},    {U,U},     {U,U},{N,N},  {N,N}},
+  {{INF,N},{U,U},{INF,-0.},{INF,0.},  {U,U},{INF,N},{INF,N}},
+  {{N,N},  {N,N},{N,0.},   {N,0.},    {N,N},{N,N},  {N,N}}
+};
+
+static PyObject *
+cmath_rect(PyObject *self, PyObject *args)
+{
+	Py_complex z;
+	double r, phi;
+	if (!PyArg_ParseTuple(args, "dd:rect", &r, &phi))
+		return NULL;
+	errno = 0;
+	PyFPE_START_PROTECT("rect function", return 0)
+
+	/* deal with special values */
+	if (!Py_IS_FINITE(r) || !Py_IS_FINITE(phi)) {
+		/* if r is +/-infinity and phi is finite but nonzero then
+		   result is (+-INF +-INF i), but we need to compute cos(phi)
+		   and sin(phi) to figure out the signs. */
+		if (Py_IS_INFINITY(r) && (Py_IS_FINITE(phi)
+					  && (phi != 0.))) {
+			if (r > 0) {
+				z.real = copysign(INF, cos(phi));
+				z.imag = copysign(INF, sin(phi));
+			}
+			else {
+				z.real = -copysign(INF, cos(phi));
+				z.imag = -copysign(INF, sin(phi));
+			}
+		}
+		else {
+			z = rect_special_values[special_type(r)]
+				               [special_type(phi)];
+		}
+		/* need to set errno = EDOM if r is a nonzero number and phi
+		   is infinite */
+		if (r != 0. && !Py_IS_NAN(r) && Py_IS_INFINITY(phi))
+			errno = EDOM;
+		else
+			errno = 0;
+	}
+	else {
+		z.real = r * cos(phi);
+		z.imag = r * sin(phi);
+		errno = 0;
+	}
+
+	PyFPE_END_PROTECT(z)
+	if (errno != 0)
+		return math_error();
+	else
+		return PyComplex_FromCComplex(z);
+}
+
+PyDoc_STRVAR(cmath_rect_doc,
+"rect(r, phi) -> z: complex\n\n\
+Convert from polar coordinates to rectangular coordinates.");
+
+static PyObject *
+cmath_isnan(PyObject *self, PyObject *args)
+{
+	Py_complex z;
+	if (!PyArg_ParseTuple(args, "D:isnan", &z))
+		return NULL;
+	return PyBool_FromLong(Py_IS_NAN(z.real) || Py_IS_NAN(z.imag));
+}
+
+PyDoc_STRVAR(cmath_isnan_doc,
+"isnan(z) -> bool\n\
+Checks if the real or imaginary part of z not a number (NaN)");
+
+static PyObject *
+cmath_isinf(PyObject *self, PyObject *args)
+{
+	Py_complex z;
+	if (!PyArg_ParseTuple(args, "D:isnan", &z))
+		return NULL;
+	return PyBool_FromLong(Py_IS_INFINITY(z.real) ||
+			       Py_IS_INFINITY(z.imag));
+}
+
+PyDoc_STRVAR(cmath_isinf_doc,
+"isinf(z) -> bool\n\
+Checks if the real or imaginary part of z is infinite.");
+
 
 PyDoc_STRVAR(module_doc,
 "This module is always available. It provides access to mathematical\n"
@@ -401,8 +1149,13 @@ static PyMethodDef cmath_methods[] = {
 	{"cos",    cmath_cos,   METH_VARARGS, c_cos_doc},
 	{"cosh",   cmath_cosh,  METH_VARARGS, c_cosh_doc},
 	{"exp",    cmath_exp,   METH_VARARGS, c_exp_doc},
+	{"isinf",  cmath_isinf, METH_VARARGS, cmath_isinf_doc},
+	{"isnan",  cmath_isnan, METH_VARARGS, cmath_isnan_doc},
 	{"log",    cmath_log,   METH_VARARGS, cmath_log_doc},
 	{"log10",  cmath_log10, METH_VARARGS, c_log10_doc},
+	{"phase",  cmath_phase, METH_VARARGS, cmath_phase_doc},
+	{"polar",  cmath_polar, METH_VARARGS, cmath_polar_doc},
+	{"rect",   cmath_rect,  METH_VARARGS, cmath_rect_doc},
 	{"sin",    cmath_sin,   METH_VARARGS, c_sin_doc},
 	{"sinh",   cmath_sinh,  METH_VARARGS, c_sinh_doc},
 	{"sqrt",   cmath_sqrt,  METH_VARARGS, c_sqrt_doc},
@@ -421,6 +1174,6 @@ initcmath(void)
 		return;
 
 	PyModule_AddObject(m, "pi",
-                           PyFloat_FromDouble(atan(1.0) * 4.0));
-	PyModule_AddObject(m, "e", PyFloat_FromDouble(exp(1.0)));
+                           PyFloat_FromDouble(Py_MATH_PI));
+	PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
 }
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index cf2bf64..8c48316 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -1,17 +1,60 @@
 /* Math module -- standard C math library functions, pi and e */
 
+/* Here are some comments from Tim Peters, extracted from the
+   discussion attached to http://bugs.python.org/issue1640.  They
+   describe the general aims of the math module with respect to
+   special values, IEEE-754 floating-point exceptions, and Python
+   exceptions.
+
+These are the "spirit of 754" rules:
+
+1. If the mathematical result is a real number, but of magnitude too
+large to approximate by a machine float, overflow is signaled and the
+result is an infinity (with the appropriate sign).
+
+2. If the mathematical result is a real number, but of magnitude too
+small to approximate by a machine float, underflow is signaled and the
+result is a zero (with the appropriate sign).
+
+3. At a singularity (a value x such that the limit of f(y) as y
+approaches x exists and is an infinity), "divide by zero" is signaled
+and the result is an infinity (with the appropriate sign).  This is
+complicated a little by that the left-side and right-side limits may
+not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
+from the positive or negative directions.  In that specific case, the
+sign of the zero determines the result of 1/0.
+
+4. At a point where a function has no defined result in the extended
+reals (i.e., the reals plus an infinity or two), invalid operation is
+signaled and a NaN is returned.
+
+And these are what Python has historically /tried/ to do (but not
+always successfully, as platform libm behavior varies a lot):
+
+For #1, raise OverflowError.
+
+For #2, return a zero (with the appropriate sign if that happens by
+accident ;-)).
+
+For #3 and #4, raise ValueError.  It may have made sense to raise
+Python's ZeroDivisionError in #3, but historically that's only been
+raised for division by zero and mod by zero.
+
+*/
+
+/*
+   In general, on an IEEE-754 platform the aim is to follow the C99
+   standard, including Annex 'F', whenever possible.  Where the
+   standard recommends raising the 'divide-by-zero' or 'invalid'
+   floating-point exceptions, Python should raise a ValueError.  Where
+   the standard recommends raising 'overflow', Python should raise an
+   OverflowError.  In all other circumstances a value should be
+   returned.
+ */
+
 #include "Python.h"
 #include "longintrepr.h" /* just for SHIFT */
 
-#ifndef _MSC_VER
-#ifndef __STDC__
-extern double fmod (double, double);
-extern double frexp (double, int *);
-extern double ldexp (double, int);
-extern double modf (double, double *);
-#endif /* __STDC__ */
-#endif /* _MSC_VER */
-
 #ifdef _OSF_SOURCE
 /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
 extern double copysign(double, double);
@@ -52,41 +95,111 @@ is_error(double x)
 	return result;
 }
 
+/*
+   math_1 is used to wrap a libm function f that takes a double
+   arguments and returns a double.
+
+   The error reporting follows these rules, which are designed to do
+   the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
+   platforms.
+
+   - a NaN result from non-NaN inputs causes ValueError to be raised
+   - an infinite result from finite inputs causes OverflowError to be
+     raised if can_overflow is 1, or raises ValueError if can_overflow
+     is 0.
+   - if the result is finite and errno == EDOM then ValueError is
+     raised
+   - if the result is finite and nonzero and errno == ERANGE then
+     OverflowError is raised
+
+   The last rule is used to catch overflow on platforms which follow
+   C89 but for which HUGE_VAL is not an infinity.
+
+   For the majority of one-argument functions these rules are enough
+   to ensure that Python's functions behave as specified in 'Annex F'
+   of the C99 standard, with the 'invalid' and 'divide-by-zero'
+   floating-point exceptions mapping to Python's ValueError and the
+   'overflow' floating-point exception mapping to OverflowError.
+   math_1 only works for functions that don't have singularities *and*
+   the possibility of overflow; fortunately, that covers everything we
+   care about right now.
+*/
+
 static PyObject *
 math_1_to_whatever(PyObject *arg, double (*func) (double),
-                   PyObject *(*from_double_func) (double))
+                   PyObject *(*from_double_func) (double),
+                   int can_overflow)
 {
-	double x = PyFloat_AsDouble(arg);
+	double x, r;
+	x = PyFloat_AsDouble(arg);
 	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	errno = 0;
-	PyFPE_START_PROTECT("in math_1", return 0)
-	x = (*func)(x);
-	PyFPE_END_PROTECT(x)
-	Py_SET_ERRNO_ON_MATH_ERROR(x);
-	if (errno && is_error(x))
+	PyFPE_START_PROTECT("in math_1", return 0);
+	r = (*func)(x);
+	PyFPE_END_PROTECT(r);
+	if (Py_IS_NAN(r)) {
+		if (!Py_IS_NAN(x))
+			errno = EDOM;
+		else
+			errno = 0;
+	}
+	else if (Py_IS_INFINITY(r)) {
+		if (Py_IS_FINITE(x))
+			errno = can_overflow ? ERANGE : EDOM;
+		else
+			errno = 0;
+	}
+	if (errno && is_error(r))
 		return NULL;
 	else
-        	return (*from_double_func)(x);
+        	return (*from_double_func)(r);
 }
 
+/*
+   math_2 is used to wrap a libm function f that takes two double
+   arguments and returns a double.
+
+   The error reporting follows these rules, which are designed to do
+   the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
+   platforms.
+
+   - a NaN result from non-NaN inputs causes ValueError to be raised
+   - an infinite result from finite inputs causes OverflowError to be
+     raised.
+   - if the result is finite and errno == EDOM then ValueError is
+     raised
+   - if the result is finite and nonzero and errno == ERANGE then
+     OverflowError is raised
+
+   The last rule is used to catch overflow on platforms which follow
+   C89 but for which HUGE_VAL is not an infinity.
+
+   For most two-argument functions (copysign, fmod, hypot, atan2)
+   these rules are enough to ensure that Python's functions behave as
+   specified in 'Annex F' of the C99 standard, with the 'invalid' and
+   'divide-by-zero' floating-point exceptions mapping to Python's
+   ValueError and the 'overflow' floating-point exception mapping to
+   OverflowError.
+*/
+
 static PyObject *
-math_1(PyObject *arg, double (*func) (double))
+math_1(PyObject *arg, double (*func) (double), int can_overflow)
 {
-	return math_1_to_whatever(arg, func, PyFloat_FromDouble);
+	return math_1_to_whatever(arg, func, PyFloat_FromDouble, can_overflow);
 }
 
 static PyObject *
-math_1_to_int(PyObject *arg, double (*func) (double))
+math_1_to_int(PyObject *arg, double (*func) (double), int can_overflow)
 {
-	return math_1_to_whatever(arg, func, PyLong_FromDouble);
+	return math_1_to_whatever(arg, func, PyLong_FromDouble, can_overflow);
 }
 
 static PyObject *
 math_2(PyObject *args, double (*func) (double, double), char *funcname)
 {
 	PyObject *ox, *oy;
-	double x, y;
+	double x, y, r;
 	if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
 		return NULL;
 	x = PyFloat_AsDouble(ox);
@@ -94,19 +207,30 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname)
 	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
 		return NULL;
 	errno = 0;
-	PyFPE_START_PROTECT("in math_2", return 0)
-	x = (*func)(x, y);
-	PyFPE_END_PROTECT(x)
-	Py_SET_ERRNO_ON_MATH_ERROR(x);
-	if (errno && is_error(x))
+	PyFPE_START_PROTECT("in math_2", return 0);
+	r = (*func)(x, y);
+	PyFPE_END_PROTECT(r);
+	if (Py_IS_NAN(r)) {
+		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+			errno = EDOM;
+		else
+			errno = 0;
+	}
+	else if (Py_IS_INFINITY(r)) {
+		if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
+			errno = ERANGE;
+		else
+			errno = 0;
+	}
+	if (errno && is_error(r))
 		return NULL;
 	else
-		return PyFloat_FromDouble(x);
+		return PyFloat_FromDouble(r);
 }
 
-#define FUNC1(funcname, func, docstring) \
+#define FUNC1(funcname, func, can_overflow, docstring)			\
 	static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
-		return math_1(args, func); \
+		return math_1(args, func, can_overflow);		    \
 	}\
         PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
@@ -116,15 +240,21 @@ math_2(PyObject *args, double (*func) (double, double), char *funcname)
 	}\
         PyDoc_STRVAR(math_##funcname##_doc, docstring);
 
-FUNC1(acos, acos,
+FUNC1(acos, acos, 0,
       "acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
-FUNC1(asin, asin,
+FUNC1(acosh, acosh, 0,
+      "acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
+FUNC1(asin, asin, 0,
       "asin(x)\n\nReturn the arc sine (measured in radians) of x.")
-FUNC1(atan, atan,
+FUNC1(asinh, asinh, 0,
+      "asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
+FUNC1(atan, atan, 0,
       "atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
 FUNC2(atan2, atan2,
       "atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
       "Unlike atan(y/x), the signs of both x and y are considered.")
+FUNC1(atanh, atanh, 0,
+      "atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
 
 static PyObject * math_ceil(PyObject *self, PyObject *number) {
 	static PyObject *ceil_str = NULL;
@@ -138,7 +268,7 @@ static PyObject * math_ceil(PyObject *self, PyObject *number) {
 
 	method = _PyType_Lookup(Py_TYPE(number), ceil_str);
 	if (method == NULL)
-		return math_1_to_int(number, ceil);
+		return math_1_to_int(number, ceil, 0);
 	else
 		return PyObject_CallFunction(method, "O", number);
 }
@@ -147,23 +277,15 @@ PyDoc_STRVAR(math_ceil_doc,
 	     "ceil(x)\n\nReturn the ceiling of x as an int.\n"
 	     "This is the smallest integral value >= x.");
 
-FUNC1(cos, cos,
+FUNC2(copysign, copysign,
+      "copysign(x,y)\n\nReturn x with the sign of y.")
+FUNC1(cos, cos, 0,
       "cos(x)\n\nReturn the cosine of x (measured in radians).")
-FUNC1(cosh, cosh,
+FUNC1(cosh, cosh, 1,
       "cosh(x)\n\nReturn the hyperbolic cosine of x.")
-
-#ifdef MS_WINDOWS
-#  define copysign _copysign
-#  define HAVE_COPYSIGN 1
-#endif
-#ifdef HAVE_COPYSIGN
-FUNC2(copysign, copysign,
-      "copysign(x,y)\n\nReturn x with the sign of y.");
-#endif
-
-FUNC1(exp, exp,
+FUNC1(exp, exp, 1,
       "exp(x)\n\nReturn e raised to the power of x.")
-FUNC1(fabs, fabs,
+FUNC1(fabs, fabs, 0,
       "fabs(x)\n\nReturn the absolute value of the float x.")
 
 static PyObject * math_floor(PyObject *self, PyObject *number) {
@@ -178,7 +300,7 @@ static PyObject * math_floor(PyObject *self, PyObject *number) {
 
 	method = _PyType_Lookup(Py_TYPE(number), floor_str);
 	if (method == NULL)
-        	return math_1_to_int(number, floor);
+        	return math_1_to_int(number, floor, 0);
 	else
 		return PyObject_CallFunction(method, "O", number);
 }
@@ -187,22 +309,18 @@ PyDoc_STRVAR(math_floor_doc,
 	     "floor(x)\n\nReturn the floor of x as an int.\n"
 	     "This is the largest integral value <= x.");
 
-FUNC2(fmod, fmod,
-      "fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
-      "  x % y may differ.")
-FUNC2(hypot, hypot,
-      "hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).")
-FUNC2(pow, pow,
-      "pow(x,y)\n\nReturn x**y (x to the power of y).")
-FUNC1(sin, sin,
+FUNC1(log1p, log1p, 1,
+      "log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n\
+      The result is computed in a way which is accurate for x near zero.")
+FUNC1(sin, sin, 0,
       "sin(x)\n\nReturn the sine of x (measured in radians).")
-FUNC1(sinh, sinh,
+FUNC1(sinh, sinh, 1,
       "sinh(x)\n\nReturn the hyperbolic sine of x.")
-FUNC1(sqrt, sqrt,
+FUNC1(sqrt, sqrt, 0,
       "sqrt(x)\n\nReturn the square root of x.")
-FUNC1(tan, tan,
+FUNC1(tan, tan, 0,
       "tan(x)\n\nReturn the tangent of x (measured in radians).")
-FUNC1(tanh, tanh,
+FUNC1(tanh, tanh, 0,
       "tanh(x)\n\nReturn the hyperbolic tangent of x.")
 
 static PyObject *
@@ -244,13 +362,17 @@ math_frexp(PyObject *self, PyObject *arg)
 	double x = PyFloat_AsDouble(arg);
 	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
-	errno = 0;
-	x = frexp(x, &i);
-	Py_SET_ERRNO_ON_MATH_ERROR(x);
-	if (errno && is_error(x))
-		return NULL;
-	else
-		return Py_BuildValue("(di)", x, i);
+	/* deal with special cases directly, to sidestep platform
+	   differences */
+	if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
+		i = 0;
+	}
+	else {
+		PyFPE_START_PROTECT("in math_frexp", return 0);
+		x = frexp(x, &i);
+		PyFPE_END_PROTECT(x);
+	}
+	return Py_BuildValue("(di)", x, i);
 }
 
 PyDoc_STRVAR(math_frexp_doc,
@@ -263,19 +385,24 @@ PyDoc_STRVAR(math_frexp_doc,
 static PyObject *
 math_ldexp(PyObject *self, PyObject *args)
 {
-	double x;
+	double x, r;
 	int exp;
 	if (! PyArg_ParseTuple(args, "di:ldexp", &x, &exp))
 		return NULL;
 	errno = 0;
-	PyFPE_START_PROTECT("ldexp", return 0)
-	x = ldexp(x, exp);
-	PyFPE_END_PROTECT(x)
-	Py_SET_ERRNO_ON_MATH_ERROR(x);
-	if (errno && is_error(x))
+	PyFPE_START_PROTECT("in math_ldexp", return 0)
+	r = ldexp(x, exp);
+	PyFPE_END_PROTECT(r)
+	if (Py_IS_FINITE(x) && Py_IS_INFINITY(r))
+		errno = ERANGE;
+	/* Windows MSVC8 sets errno = EDOM on ldexp(NaN, i);
+	   we unset it to avoid raising a ValueError here. */
+	if (errno == EDOM)
+		errno = 0;
+	if (errno && is_error(r))
 		return NULL;
 	else
-		return PyFloat_FromDouble(x);
+		return PyFloat_FromDouble(r);
 }
 
 PyDoc_STRVAR(math_ldexp_doc,
@@ -288,12 +415,10 @@ math_modf(PyObject *self, PyObject *arg)
 	if (x == -1.0 && PyErr_Occurred())
 		return NULL;
 	errno = 0;
+	PyFPE_START_PROTECT("in math_modf", return 0);
 	x = modf(x, &y);
-	Py_SET_ERRNO_ON_MATH_ERROR(x);
-	if (errno && is_error(x))
-		return NULL;
-	else
-		return Py_BuildValue("(dd)", x, y);
+	PyFPE_END_PROTECT(x);
+	return Py_BuildValue("(dd)", x, y);
 }
 
 PyDoc_STRVAR(math_modf_doc,
@@ -332,7 +457,7 @@ loghelper(PyObject* arg, double (*func)(double), char *funcname)
 	}
 
 	/* Else let libm handle it by itself. */
-	return math_1(arg, func);
+	return math_1(arg, func, 0);
 }
 
 static PyObject *
@@ -375,6 +500,141 @@ math_log10(PyObject *self, PyObject *arg)
 PyDoc_STRVAR(math_log10_doc,
 "log10(x) -> the base 10 logarithm of x.");
 
+static PyObject *
+math_fmod(PyObject *self, PyObject *args)
+{
+	PyObject *ox, *oy;
+	double r, x, y;
+	if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
+		return NULL;
+	x = PyFloat_AsDouble(ox);
+	y = PyFloat_AsDouble(oy);
+	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+		return NULL;
+	/* fmod(x, +/-Inf) returns x for finite x. */
+	if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
+		return PyFloat_FromDouble(x);
+	errno = 0;
+	PyFPE_START_PROTECT("in math_fmod", return 0);
+	r = fmod(x, y);
+	PyFPE_END_PROTECT(r);
+	if (Py_IS_NAN(r)) {
+		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+			errno = EDOM;
+		else
+			errno = 0;
+	}
+	if (errno && is_error(r))
+		return NULL;
+	else
+		return PyFloat_FromDouble(r);
+}
+
+PyDoc_STRVAR(math_fmod_doc,
+"fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
+"  x % y may differ.");
+
+static PyObject *
+math_hypot(PyObject *self, PyObject *args)
+{
+	PyObject *ox, *oy;
+	double r, x, y;
+	if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
+		return NULL;
+	x = PyFloat_AsDouble(ox);
+	y = PyFloat_AsDouble(oy);
+	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+		return NULL;
+	/* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
+	if (Py_IS_INFINITY(x))
+		return PyFloat_FromDouble(fabs(x));
+	if (Py_IS_INFINITY(y))
+		return PyFloat_FromDouble(fabs(y));
+	errno = 0;
+	PyFPE_START_PROTECT("in math_hypot", return 0);
+	r = hypot(x, y);
+	PyFPE_END_PROTECT(r);
+	if (Py_IS_NAN(r)) {
+		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+			errno = EDOM;
+		else
+			errno = 0;
+	}
+	else if (Py_IS_INFINITY(r)) {
+		if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
+			errno = ERANGE;
+		else
+			errno = 0;
+	}
+	if (errno && is_error(r))
+		return NULL;
+	else
+		return PyFloat_FromDouble(r);
+}
+
+PyDoc_STRVAR(math_hypot_doc,
+"hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
+
+/* pow can't use math_2, but needs its own wrapper: the problem is
+   that an infinite result can arise either as a result of overflow
+   (in which case OverflowError should be raised) or as a result of
+   e.g. 0.**-5. (for which ValueError needs to be raised.)
+*/
+
+static PyObject *
+math_pow(PyObject *self, PyObject *args)
+{
+	PyObject *ox, *oy;
+	double r, x, y;
+
+	if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
+		return NULL;
+	x = PyFloat_AsDouble(ox);
+	y = PyFloat_AsDouble(oy);
+	if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
+		return NULL;
+	/* 1**x and x**0 return 1., even if x is a NaN or infinity. */
+	if (x == 1.0 || y == 0.0)
+	        return PyFloat_FromDouble(1.);
+	errno = 0;
+	PyFPE_START_PROTECT("in math_pow", return 0);
+	r = pow(x, y);
+	PyFPE_END_PROTECT(r);
+	if (Py_IS_NAN(r)) {
+		if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
+			errno = EDOM;
+		else
+			errno = 0;
+	}
+	/* an infinite result arises either from:
+
+	   (A) (+/-0.)**negative,
+	   (B) overflow of x**y with both x and y finite (and x nonzero)
+	   (C) (+/-inf)**positive, or
+	   (D) x**inf with |x| > 1, or x**-inf with |x| < 1.
+
+	   In case (A) we want ValueError to be raised.  In case (B)
+	   OverflowError should be raised.  In cases (C) and (D) the infinite
+	   result should be returned.
+	*/
+	else if (Py_IS_INFINITY(r)) {
+		if (x == 0.)
+			errno = EDOM;
+		else if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
+			errno = ERANGE;
+		else
+			errno = 0;
+	}
+
+	if (errno && is_error(r))
+		return NULL;
+	else
+		return PyFloat_FromDouble(r);
+}
+
+PyDoc_STRVAR(math_pow_doc,
+"pow(x,y)\n\nReturn x**y (x to the power of y).");
+
 static const double degToRad = Py_MATH_PI / 180.0;
 static const double radToDeg = 180.0 / Py_MATH_PI;
 
@@ -428,16 +688,16 @@ PyDoc_STRVAR(math_isinf_doc,
 "isinf(x) -> bool\n\
 Checks if float x is infinite (positive or negative)");
 
-
 static PyMethodDef math_methods[] = {
 	{"acos",	math_acos,	METH_O,		math_acos_doc},
+	{"acosh",	math_acosh,	METH_O,		math_acosh_doc},
 	{"asin",	math_asin,	METH_O,		math_asin_doc},
+	{"asinh",	math_asinh,	METH_O,		math_asinh_doc},
 	{"atan",	math_atan,	METH_O,		math_atan_doc},
 	{"atan2",	math_atan2,	METH_VARARGS,	math_atan2_doc},
+	{"atanh",	math_atanh,	METH_O,		math_atanh_doc},
 	{"ceil",	math_ceil,	METH_O,		math_ceil_doc},
-#ifdef HAVE_COPYSIGN
 	{"copysign",	math_copysign,	METH_VARARGS,	math_copysign_doc},
-#endif
 	{"cos",		math_cos,	METH_O,		math_cos_doc},
 	{"cosh",	math_cosh,	METH_O,		math_cosh_doc},
 	{"degrees",	math_degrees,	METH_O,		math_degrees_doc},
@@ -451,6 +711,7 @@ static PyMethodDef math_methods[] = {
 	{"isnan",	math_isnan,	METH_O,		math_isnan_doc},
 	{"ldexp",	math_ldexp,	METH_VARARGS,	math_ldexp_doc},
 	{"log",		math_log,	METH_VARARGS,	math_log_doc},
+	{"log1p",	math_log1p,	METH_O,		math_log1p_doc},
 	{"log10",	math_log10,	METH_O,		math_log10_doc},
 	{"modf",	math_modf,	METH_O,		math_modf_doc},
 	{"pow",		math_pow,	METH_VARARGS,	math_pow_doc},
@@ -472,27 +733,15 @@ PyDoc_STRVAR(module_doc,
 PyMODINIT_FUNC
 initmath(void)
 {
-	PyObject *m, *d, *v;
+	PyObject *m;
 
 	m = Py_InitModule3("math", math_methods, module_doc);
 	if (m == NULL)
 		goto finally;
-	d = PyModule_GetDict(m);
-	if (d == NULL)
-		goto finally;
-
-        if (!(v = PyFloat_FromDouble(Py_MATH_PI)))
-                goto finally;
-	if (PyDict_SetItemString(d, "pi", v) < 0)
-                goto finally;
-	Py_DECREF(v);
 
-        if (!(v = PyFloat_FromDouble(Py_MATH_E)))
-                goto finally;
-	if (PyDict_SetItemString(d, "e", v) < 0)
-                goto finally;
-	Py_DECREF(v);
+	PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
+	PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
 
-  finally:
+    finally:
 	return;
 }