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 ...
........

27 files changed, 5096 insertions, 1162 deletions

diff --git a/Doc/library/cmath.rst b/Doc/library/cmath.rst
index 5a9ae05707..f78f69c5bd 100644
--- a/Doc/library/cmath.rst
+++ b/Doc/library/cmath.rst
@@ -14,8 +14,81 @@ 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:
+.. note::
 
+   On platforms with hardware and system-level support for signed
+   zeros, functions involving branch cuts are continuous on *both*
+   sides of the branch cut: the sign of the zero distinguishes one
+   side of the branch cut from the other.  On platforms that do not
+   support signed zeros the continuity is as specified below.
+
+
+Complex coordinates
+-------------------
+
+Complex numbers can be expressed by two important coordinate systems.
+Python's :class:`complex` type uses rectangular coordinates where a number
+on the complex plain is defined by two floats, the real part and the imaginary
+part.
+
+Definition::
+
+   z = x + 1j * y
+
+   x := real(z)
+   y := imag(z)
+
+In engineering the polar coordinate system is popular for complex numbers. In
+polar coordinates a complex number is defined by the radius *r* and the phase
+angle *φ*. The radius *r* is the absolute value of the complex, which can be
+viewed as distance from (0, 0). The radius *r* is always 0 or a positive float.
+The phase angle *φ* is the counter clockwise angle from the positive x axis,
+e.g. *1* has the angle *0*, *1j* has the angle *π/2* and *-1* the angle *-π*.
+
+.. note::
+   While :func:`phase` and func:`polar` return *+π* for a negative real they
+   may return *-π* for a complex with a very small negative imaginary
+   part, e.g. *-1-1E-300j*.
+
+
+Definition::
+
+   z = r * exp(1j * φ)
+   z = r * cis(φ)
+
+   r := abs(z) := sqrt(real(z)**2 + imag(z)**2)
+   phi := phase(z) := atan2(imag(z), real(z))
+   cis(φ) := cos(φ) + 1j * sin(φ)
+
+
+.. function:: phase(x)
+
+   Return phase, also known as the argument, of a complex.
+
+   .. versionadded:: 2.6
+
+
+.. function:: polar(x)
+
+   Convert a :class:`complex` from rectangular coordinates to polar 
+   coordinates. The function returns a tuple with the two elements
+   *r* and *phi*. *r* is the distance from 0 and *phi* the phase 
+   angle.
+
+   .. versionadded:: 2.6
+
+
+.. function:: rect(r, phi)
+
+   Convert from polar coordinates to rectangular coordinates and return
+   a :class:`complex`.
+
+   .. versionadded:: 2.6
+
+
+
+cmath functions
+---------------
 
 .. function:: acos(x)
 
@@ -37,30 +110,35 @@ The functions are:
 
 .. function:: asinh(x)
 
-   Return the hyperbolic arc sine of *x*. There are two branch cuts, extending
-   left from ``±1j`` to ``±∞j``, both continuous from above. These branch cuts
-   should be considered a bug to be corrected in a future release. The correct
-   branch cuts should extend along the imaginary axis, one from ``1j`` up to
-   ``∞j`` and continuous from the right, and one from ``-1j`` down to ``-∞j``
-   and continuous from the left.
+   Return the hyperbolic arc sine of *x*. There are two branch cuts:
+   One extends from ``1j`` along the imaginary axis to ``∞j``,
+   continuous from the right.  The other extends from ``-1j`` along
+   the imaginary axis to ``-∞j``, continuous from the left.
+
+   .. versionchanged:: 2.6
+      branch cuts moved to match those recommended by the C99 standard
 
 
 .. function:: atan(x)
 
    Return the arc tangent of *x*. There are two branch cuts: One extends from
-   ``1j`` along the imaginary axis to ``∞j``, continuous from the left. The
+   ``1j`` along the imaginary axis to ``∞j``, continuous from the right. The
    other extends from ``-1j`` along the imaginary axis to ``-∞j``, continuous
-   from the left. (This should probably be changed so the upper cut becomes
-   continuous from the other side.)
+   from the left.
+
+   .. versionchanged:: 2.6
+      direction of continuity of upper cut reversed
 
 
 .. function:: atanh(x)
 
    Return the hyperbolic arc tangent of *x*. There are two branch cuts: One
-   extends from ``1`` along the real axis to ``∞``, continuous from above. The
+   extends from ``1`` along the real axis to ``∞``, continuous from below. The
    other extends from ``-1`` along the real axis to ``-∞``, continuous from
-   above. (This should probably be changed so the right cut becomes continuous
-   from the other side.)
+   above.
+
+   .. versionchanged:: 2.6
+      direction of continuity of right cut reversed
 
 
 .. function:: cos(x)
@@ -78,6 +156,21 @@ The functions are:
    Return the exponential value ``e**x``.
 
 
+.. function:: isinf(x)
+
+   Return *True* if the real or the imaginary part of x is positive
+   or negative infinity.
+
+   .. versionadded:: 2.6
+
+
+.. function:: isnan(x)
+
+   Return *True* if the real or imaginary part of x is not a number (NaN).
+
+   .. versionadded:: 2.6
+
+
 .. function:: log(x[, base])
 
    Returns the logarithm of *x* to the given *base*. If the *base* is not
@@ -151,3 +244,4 @@ cuts for numerical purposes, a good reference should be the following:
    nothing's sign bit.  In Iserles, A., and Powell, M. (eds.), The state of the art
    in numerical analysis. Clarendon Press (1987) pp165-211.
 
+
diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index f69c0a0198..024897f1be 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -128,6 +128,14 @@ Power and logarithmic functions:
    return the natural logarithm of *x* (that is, the logarithm to base *e*).
 
 
+.. function:: log1p(x)
+
+   Return the natural logarithm of *1+x* (base *e*). The
+   result is calculated in a way which is accurate for *x* near zero.
+
+   .. versionadded:: 2.6
+
+
 .. function:: log10(x)
 
    Return the base-10 logarithm of *x*.
@@ -135,7 +143,11 @@ Power and logarithmic functions:
 
 .. function:: pow(x, y)
 
-   Return ``x**y``.
+   Return ``x**y``. ``1.0**y`` returns *1.0*, even for ``1.0**nan``. ``0**y``
+   returns *0.* for all positive *y*, *0* and *NAN*.
+
+   .. versionchanged:: 2.6
+      The outcome of ``1**nan`` and ``0**nan`` was undefined.
 
 
 .. function:: sqrt(x)
@@ -186,6 +198,13 @@ Trigonometric functions:
    Return the sine of *x* radians.
 
 
+.. function:: asinh(x)
+
+   Return the inverse hyperbolic sine of *x*, in radians.
+
+   .. versionadded:: 2.6
+
+
 .. function:: tan(x)
 
    Return the tangent of *x* radians.
@@ -210,6 +229,13 @@ Hyperbolic functions:
    Return the hyperbolic cosine of *x*.
 
 
+.. function:: acosh(x)
+
+   Return the inverse hyperbolic cosine of *x*, in radians.
+
+   .. versionadded:: 2.6
+
+
 .. function:: sinh(x)
 
    Return the hyperbolic sine of *x*.
@@ -219,6 +245,14 @@ Hyperbolic functions:
 
    Return the hyperbolic tangent of *x*.
 
+
+.. function:: atanh(x)
+
+   Return the inverse hyperbolic tangent of *x*, in radians.
+
+   .. versionadded:: 2.6
+
+
 The module also defines two mathematical constants:
 
 
@@ -231,6 +265,7 @@ The module also defines two mathematical constants:
 
    The mathematical constant *e*.
 
+
 .. note::
 
    The :mod:`math` module consists mostly of thin wrappers around the platform C
@@ -244,9 +279,17 @@ The module also defines two mathematical constants:
    :exc:`OverflowError` isn't defined, and in cases where ``math.log(0)`` raises
    :exc:`OverflowError`, ``math.log(0L)`` may raise :exc:`ValueError` instead.
 
+   All functions return a quite *NaN* if at least one of the args is *NaN*.
+   Signaling *NaN*s raise an exception. The exception type still depends on the
+   platform and libm implementation. It's usually :exc:`ValueError` for *EDOM*
+   and :exc:`OverflowError` for errno *ERANGE*.
+
+   ..versionchanged:: 2.6
+      In earlier versions of Python the outcome of an operation with NaN as
+      input depended on platform and libm implementation.
+
 
 .. seealso::
 
    Module :mod:`cmath`
       Complex number versions of many of these functions.
-
diff --git a/Include/Python.h b/Include/Python.h
index b241c869a4..53f7f594f0 100644
--- a/Include/Python.h
+++ b/Include/Python.h
@@ -57,6 +57,7 @@
 #if defined(PYMALLOC_DEBUG) && !defined(WITH_PYMALLOC)
 #error "PYMALLOC_DEBUG requires WITH_PYMALLOC"
 #endif
+#include "pymath.h"
 #include "pymem.h"
 
 #include "object.h"
diff --git a/Include/complexobject.h b/Include/complexobject.h
index b0364440d1..84b6d8b7e1 100644
--- a/Include/complexobject.h
+++ b/Include/complexobject.h
@@ -19,6 +19,7 @@ typedef struct {
 #define c_prod _Py_c_prod
 #define c_quot _Py_c_quot
 #define c_pow _Py_c_pow
+#define c_abs _Py_c_abs
 
 PyAPI_FUNC(Py_complex) c_sum(Py_complex, Py_complex);
 PyAPI_FUNC(Py_complex) c_diff(Py_complex, Py_complex);
@@ -26,6 +27,7 @@ PyAPI_FUNC(Py_complex) c_neg(Py_complex);
 PyAPI_FUNC(Py_complex) c_prod(Py_complex, Py_complex);
 PyAPI_FUNC(Py_complex) c_quot(Py_complex, Py_complex);
 PyAPI_FUNC(Py_complex) c_pow(Py_complex, Py_complex);
+PyAPI_FUNC(double) c_abs(Py_complex);
 
 
 /* Complex object interface */
diff --git a/Include/floatobject.h b/Include/floatobject.h
index 459b029a3a..2021313c42 100644
--- a/Include/floatobject.h
+++ b/Include/floatobject.h
@@ -21,6 +21,17 @@ PyAPI_DATA(PyTypeObject) PyFloat_Type;
 #define PyFloat_Check(op) PyObject_TypeCheck(op, &PyFloat_Type)
 #define PyFloat_CheckExact(op) (Py_TYPE(op) == &PyFloat_Type)
 
+#ifdef Py_NAN
+#define Py_RETURN_NAN return PyFloat_FromDouble(Py_NAN)
+#endif
+
+#define Py_RETURN_INF(sign) do					\
+	if (copysign(1., sign) == 1.) {				\
+		return PyFloat_FromDouble(Py_HUGE_VAL);	\
+	} else {						\
+		return PyFloat_FromDouble(-Py_HUGE_VAL);	\
+	} while(0)
+
 PyAPI_FUNC(double) PyFloat_GetMax(void);
 PyAPI_FUNC(double) PyFloat_GetMin(void);
 PyAPI_FUNC(PyObject *) PyFloat_GetInfo(void);
diff --git a/Include/pymath.h b/Include/pymath.h
new file mode 100644
index 0000000000..a3735c2286
--- /dev/null
+++ b/Include/pymath.h
@@ -0,0 +1,182 @@
+#ifndef Py_PYMATH_H
+#define Py_PYMATH_H
+
+#include "pyconfig.h" /* include for defines */
+
+#ifdef HAVE_STDINT_H
+#include <stdint.h>
+#endif
+
+/**************************************************************************
+Symbols and macros to supply platform-independent interfaces to mathematical
+functions and constants
+**************************************************************************/
+
+/* Python provides implementations for copysign, acosh, asinh, atanh, 
+ * log1p and hypot in Python/pymath.c just in case your math library doesn't
+ * provide the functions.
+ *
+ *Note: PC/pyconfig.h defines copysign as _copysign
+ */
+#ifndef HAVE_COPYSIGN
+extern double copysign(doube, double);
+#endif
+
+#ifndef HAVE_ACOSH
+extern double acosh(double);
+#endif
+
+#ifndef HAVE_ASINH
+extern double asinh(double);
+#endif
+
+#ifndef HAVE_ATANH
+extern double atanh(double);
+#endif
+
+#ifndef HAVE_LOG1P
+extern double log1p(double);
+#endif
+
+#ifndef HAVE_HYPOT
+extern double hypot(double, double);
+#endif
+
+/* extra declarations */
+#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 *);
+extern double pow(double, double);
+#endif /* __STDC__ */
+#endif /* _MSC_VER */
+
+#ifdef _OSF_SOURCE
+/* OSF1 5.1 doesn't make these available with XOPEN_SOURCE_EXTENDED defined */
+extern int finite(double);
+extern double copysign(double, double);
+#endif
+
+/* High precision defintion of pi and e (Euler)
+ * The values are taken from libc6's math.h.
+ */
+#ifndef Py_MATH_PIl
+#define Py_MATH_PIl 3.1415926535897932384626433832795029L
+#endif
+#ifndef Py_MATH_PI
+#define Py_MATH_PI 3.14159265358979323846
+#endif
+
+#ifndef Py_MATH_El
+#define Py_MATH_El 2.7182818284590452353602874713526625L
+#endif
+
+#ifndef Py_MATH_E
+#define Py_MATH_E 2.7182818284590452354
+#endif
+
+/* Py_IS_NAN(X)
+ * Return 1 if float or double arg is a NaN, else 0.
+ * Caution:
+ *     X is evaluated more than once.
+ *     This may not work on all platforms.  Each platform has *some*
+ *     way to spell this, though -- override in pyconfig.h if you have
+ *     a platform where it doesn't work.
+ * Note: PC/pyconfig.h defines Py_IS_NAN as _isnan
+ */
+#ifndef Py_IS_NAN
+#ifdef HAVE_ISNAN
+#define Py_IS_NAN(X) isnan(X)
+#else
+#define Py_IS_NAN(X) ((X) != (X))
+#endif
+#endif
+
+/* Py_IS_INFINITY(X)
+ * Return 1 if float or double arg is an infinity, else 0.
+ * Caution:
+ *    X is evaluated more than once.
+ *    This implementation may set the underflow flag if |X| is very small;
+ *    it really can't be implemented correctly (& easily) before C99.
+ *    Override in pyconfig.h if you have a better spelling on your platform.
+ * Note: PC/pyconfig.h defines Py_IS_INFINITY as _isinf
+ */
+#ifndef Py_IS_INFINITY
+#ifdef HAVE_ISINF
+#define Py_IS_INFINITY(X) isinf(X)
+#else
+#define Py_IS_INFINITY(X) ((X) && (X)*0.5 == (X))
+#endif
+#endif
+
+/* Py_IS_FINITE(X)
+ * Return 1 if float or double arg is neither infinite nor NAN, else 0.
+ * Some compilers (e.g. VisualStudio) have intrisics for this, so a special
+ * macro for this particular test is useful
+ * Note: PC/pyconfig.h defines Py_IS_FINITE as _finite
+ */
+#ifndef Py_IS_FINITE
+#ifdef HAVE_FINITE
+#define Py_IS_FINITE(X) finite(X)
+#else
+#define Py_IS_FINITE(X) (!Py_IS_INFINITY(X) && !Py_IS_NAN(X))
+#endif
+#endif
+
+/* HUGE_VAL is supposed to expand to a positive double infinity.  Python
+ * uses Py_HUGE_VAL instead because some platforms are broken in this
+ * respect.  We used to embed code in pyport.h to try to worm around that,
+ * but different platforms are broken in conflicting ways.  If you're on
+ * a platform where HUGE_VAL is defined incorrectly, fiddle your Python
+ * config to #define Py_HUGE_VAL to something that works on your platform.
+ */
+#ifndef Py_HUGE_VAL
+#define Py_HUGE_VAL HUGE_VAL
+#endif
+
+/* Py_NAN
+ * A value that evaluates to a NaN. On IEEE 754 platforms INF*0 or
+ * INF/INF works. Define Py_NO_NAN in pyconfig.h if your platform
+ * doesn't support NaNs.
+ */
+#if !defined(Py_NAN) && !defined(Py_NO_NAN)
+#define Py_NAN (Py_HUGE_VAL * 0.)
+#endif
+
+/* Py_OVERFLOWED(X)
+ * Return 1 iff a libm function overflowed.  Set errno to 0 before calling
+ * a libm function, and invoke this macro after, passing the function
+ * result.
+ * Caution:
+ *    This isn't reliable.  C99 no longer requires libm to set errno under
+ *	  any exceptional condition, but does require +- HUGE_VAL return
+ *	  values on overflow.  A 754 box *probably* maps HUGE_VAL to a
+ *	  double infinity, and we're cool if that's so, unless the input
+ *	  was an infinity and an infinity is the expected result.  A C89
+ *	  system sets errno to ERANGE, so we check for that too.  We're
+ *	  out of luck if a C99 754 box doesn't map HUGE_VAL to +Inf, or
+ *	  if the returned result is a NaN, or if a C89 box returns HUGE_VAL
+ *	  in non-overflow cases.
+ *    X is evaluated more than once.
+ * Some platforms have better way to spell this, so expect some #ifdef'ery.
+ *
+ * OpenBSD uses 'isinf()' because a compiler bug on that platform causes
+ * the longer macro version to be mis-compiled. This isn't optimal, and
+ * should be removed once a newer compiler is available on that platform.
+ * The system that had the failure was running OpenBSD 3.2 on Intel, with
+ * gcc 2.95.3.
+ *
+ * According to Tim's checkin, the FreeBSD systems use isinf() to work
+ * around a FPE bug on that platform.
+ */
+#if defined(__FreeBSD__) || defined(__OpenBSD__)
+#define Py_OVERFLOWED(X) isinf(X)
+#else
+#define Py_OVERFLOWED(X) ((X) != 0.0 && (errno == ERANGE ||    \
+					 (X) == Py_HUGE_VAL || \
+					 (X) == -Py_HUGE_VAL))
+#endif
+
+#endif /* Py_PYMATH_H */
diff --git a/Include/pyport.h b/Include/pyport.h
index 3755e38a34..18bdb0cb02 100644
--- a/Include/pyport.h
+++ b/Include/pyport.h
@@ -336,123 +336,6 @@ extern "C" {
 #define Py_SAFE_DOWNCAST(VALUE, WIDE, NARROW) (NARROW)(VALUE)
 #endif
 
-/* High precision defintion of pi and e (Euler)
- * The values are taken from libc6's math.h.
- */
-#ifndef Py_MATH_PIl
-#define Py_MATH_PIl 3.1415926535897932384626433832795029L
-#endif
-#ifndef Py_MATH_PI
-#define Py_MATH_PI 3.14159265358979323846
-#endif
-
-#ifndef Py_MATH_El
-#define Py_MATH_El 2.7182818284590452353602874713526625L
-#endif
-
-#ifndef Py_MATH_E
-#define Py_MATH_E 2.7182818284590452354
-#endif
-
-/* Py_IS_NAN(X)
- * Return 1 if float or double arg is a NaN, else 0.
- * Caution:
- *     X is evaluated more than once.
- *     This may not work on all platforms.  Each platform has *some*
- *     way to spell this, though -- override in pyconfig.h if you have
- *     a platform where it doesn't work.
- */
-#ifndef Py_IS_NAN
-#ifdef HAVE_ISNAN
-#define Py_IS_NAN(X) isnan(X)
-#else
-#define Py_IS_NAN(X) ((X) != (X))
-#endif
-#endif
-
-/* Py_IS_INFINITY(X)
- * Return 1 if float or double arg is an infinity, else 0.
- * Caution:
- *    X is evaluated more than once.
- *    This implementation may set the underflow flag if |X| is very small;
- *    it really can't be implemented correctly (& easily) before C99.
- *    Override in pyconfig.h if you have a better spelling on your platform.
- */
-#ifndef Py_IS_INFINITY
-#ifdef HAVE_ISINF
-#define Py_IS_INFINITY(X) isinf(X)
-#else
-#define Py_IS_INFINITY(X) ((X) && (X)*0.5 == (X))
-#endif
-#endif
-
-/* Py_IS_FINITE(X)
- * Return 1 if float or double arg is neither infinite nor NAN, else 0.
- * Some compilers (e.g. VisualStudio) have intrisics for this, so a special
- * macro for this particular test is useful
- */
-#ifndef Py_IS_FINITE
-#ifdef HAVE_FINITE
-#define Py_IS_FINITE(X) finite(X)
-#else
-#define Py_IS_FINITE(X) (!Py_IS_INFINITY(X) && !Py_IS_NAN(X))
-#endif
-#endif
-
-/* HUGE_VAL is supposed to expand to a positive double infinity.  Python
- * uses Py_HUGE_VAL instead because some platforms are broken in this
- * respect.  We used to embed code in pyport.h to try to worm around that,
- * but different platforms are broken in conflicting ways.  If you're on
- * a platform where HUGE_VAL is defined incorrectly, fiddle your Python
- * config to #define Py_HUGE_VAL to something that works on your platform.
- */
-#ifndef Py_HUGE_VAL
-#define Py_HUGE_VAL HUGE_VAL
-#endif
-
-/* Py_NAN
- * A value that evaluates to a NaN. On IEEE 754 platforms INF*0 or
- * INF/INF works. Define Py_NO_NAN in pyconfig.h if your platform
- * doesn't support NaNs.
- */
-#if !defined(Py_NAN) && !defined(Py_NO_NAN)
-#define Py_NAN (Py_HUGE_VAL * 0.)
-#endif
-
-/* Py_OVERFLOWED(X)
- * Return 1 iff a libm function overflowed.  Set errno to 0 before calling
- * a libm function, and invoke this macro after, passing the function
- * result.
- * Caution:
- *    This isn't reliable.  C99 no longer requires libm to set errno under
- *	  any exceptional condition, but does require +- HUGE_VAL return
- *	  values on overflow.  A 754 box *probably* maps HUGE_VAL to a
- *	  double infinity, and we're cool if that's so, unless the input
- *	  was an infinity and an infinity is the expected result.  A C89
- *	  system sets errno to ERANGE, so we check for that too.  We're
- *	  out of luck if a C99 754 box doesn't map HUGE_VAL to +Inf, or
- *	  if the returned result is a NaN, or if a C89 box returns HUGE_VAL
- *	  in non-overflow cases.
- *    X is evaluated more than once.
- * Some platforms have better way to spell this, so expect some #ifdef'ery.
- *
- * OpenBSD uses 'isinf()' because a compiler bug on that platform causes
- * the longer macro version to be mis-compiled. This isn't optimal, and
- * should be removed once a newer compiler is available on that platform.
- * The system that had the failure was running OpenBSD 3.2 on Intel, with
- * gcc 2.95.3.
- *
- * According to Tim's checkin, the FreeBSD systems use isinf() to work
- * around a FPE bug on that platform.
- */
-#if defined(__FreeBSD__) || defined(__OpenBSD__)
-#define Py_OVERFLOWED(X) isinf(X)
-#else
-#define Py_OVERFLOWED(X) ((X) != 0.0 && (errno == ERANGE ||    \
-					 (X) == Py_HUGE_VAL || \
-					 (X) == -Py_HUGE_VAL))
-#endif
-
 /* Py_SET_ERRNO_ON_MATH_ERROR(x)
  * If a libm function did not set errno, but it looks like the result
  * overflowed or not-a-number, set errno to ERANGE or EDOM.  Set errno
@@ -559,15 +442,6 @@ extern pid_t forkpty(int *, char *, struct termios *, struct winsize *);
 #endif /* defined(HAVE_OPENPTY) || defined(HAVE_FORKPTY) */
 
 
-/************************
- * WRAPPER FOR <math.h> *
- ************************/
-
-#ifndef HAVE_HYPOT
-extern double hypot(double, double);
-#endif
-
-
 /* On 4.4BSD-descendants, ctype functions serves the whole range of
  * wchar_t character set rather than single byte code points only.
  * This characteristic can break some operations of string object
diff --git a/Lib/test/cmath_testcases.txt b/Lib/test/cmath_testcases.txt
new file mode 100644
index 0000000000..2fabebfc8c
--- /dev/null
+++ b/Lib/test/cmath_testcases.txt
@@ -0,0 +1,2355 @@
+-- Testcases for functions in cmath.
+--
+-- Each line takes the form:
+--
+-- <testid> <function> <input_value> -> <output_value> <flags>
+--
+-- where:
+--
+--   <testid> is a short name identifying the test,
+--
+--   <function> is the function to be tested (exp, cos, asinh, ...),
+--
+--   <input_value> is a pair of floats separated by whitespace
+--     representing real and imaginary parts of a complex number, and
+--
+--   <output_value> is the expected (ideal) output value, again
+--     represented as a pair of floats.
+--
+--   <flags> is a list of the floating-point flags required by C99
+--
+-- The possible flags are:
+--
+--   divide-by-zero : raised when a finite input gives a
+--     mathematically infinite result.
+--
+--   overflow : raised when a finite input gives a finite result whose
+--     real or imaginary part is too large to fit in the usual range
+--     of an IEEE 754 double.
+--
+--   invalid : raised for invalid inputs.
+--
+--   ignore-real-sign : indicates that the sign of the real part of
+--     the result is unspecified; if the real part of the result is
+--     given as inf, then both -inf and inf should be accepted as
+--     correct.
+--
+--   ignore-imag-sign : indicates that the sign of the imaginary part
+--     of the result is unspecified.
+--
+-- Flags may appear in any order.
+--
+-- Lines beginning with '--' (like this one) start a comment, and are
+-- ignored.  Blank lines, or lines containing only whitespace, are also
+-- ignored.
+
+
+--------------------------
+-- acos: Inverse cosine --
+--------------------------
+
+-- zeros
+acos0000 acos 0.0 0.0 -> 1.5707963267948966 -0.0
+acos0001 acos 0.0 -0.0 -> 1.5707963267948966 0.0
+acos0002 acos -0.0 0.0 -> 1.5707963267948966 -0.0
+acos0003 acos -0.0 -0.0 -> 1.5707963267948966 0.0
+
+-- branch points: +/-1
+acos0010 acos 1.0 0.0 -> 0.0 -0.0
+acos0011 acos 1.0 -0.0 -> 0.0 0.0
+acos0012 acos -1.0 0.0 -> 3.1415926535897931 -0.0
+acos0013 acos -1.0 -0.0 -> 3.1415926535897931 0.0
+
+-- values along both sides of real axis
+acos0020 acos -9.8813129168249309e-324 0.0 -> 1.5707963267948966 -0.0
+acos0021 acos -9.8813129168249309e-324 -0.0 -> 1.5707963267948966 0.0
+acos0022 acos -1e-305 0.0 -> 1.5707963267948966 -0.0
+acos0023 acos -1e-305 -0.0 -> 1.5707963267948966 0.0
+acos0024 acos -1e-150 0.0 -> 1.5707963267948966 -0.0
+acos0025 acos -1e-150 -0.0 -> 1.5707963267948966 0.0
+acos0026 acos -9.9999999999999998e-17 0.0 -> 1.5707963267948968 -0.0
+acos0027 acos -9.9999999999999998e-17 -0.0 -> 1.5707963267948968 0.0
+acos0028 acos -0.001 0.0 -> 1.5717963269615634 -0.0
+acos0029 acos -0.001 -0.0 -> 1.5717963269615634 0.0
+acos0030 acos -0.57899999999999996 0.0 -> 2.1882979816120667 -0.0
+acos0031 acos -0.57899999999999996 -0.0 -> 2.1882979816120667 0.0
+acos0032 acos -0.99999999999999989 0.0 -> 3.1415926386886319 -0.0
+acos0033 acos -0.99999999999999989 -0.0 -> 3.1415926386886319 0.0
+acos0034 acos -1.0000000000000002 0.0 -> 3.1415926535897931 -2.1073424255447014e-08
+acos0035 acos -1.0000000000000002 -0.0 -> 3.1415926535897931 2.1073424255447014e-08
+acos0036 acos -1.0009999999999999 0.0 -> 3.1415926535897931 -0.044717633608306849
+acos0037 acos -1.0009999999999999 -0.0 -> 3.1415926535897931 0.044717633608306849
+acos0038 acos -2.0 0.0 -> 3.1415926535897931 -1.3169578969248168
+acos0039 acos -2.0 -0.0 -> 3.1415926535897931 1.3169578969248168
+acos0040 acos -23.0 0.0 -> 3.1415926535897931 -3.8281684713331012
+acos0041 acos -23.0 -0.0 -> 3.1415926535897931 3.8281684713331012
+acos0042 acos -10000000000000000.0 0.0 -> 3.1415926535897931 -37.534508668464674
+acos0043 acos -10000000000000000.0 -0.0 -> 3.1415926535897931 37.534508668464674
+acos0044 acos -9.9999999999999998e+149 0.0 -> 3.1415926535897931 -346.08091112966679
+acos0045 acos -9.9999999999999998e+149 -0.0 -> 3.1415926535897931 346.08091112966679
+acos0046 acos -1.0000000000000001e+299 0.0 -> 3.1415926535897931 -689.16608998577965
+acos0047 acos -1.0000000000000001e+299 -0.0 -> 3.1415926535897931 689.16608998577965
+acos0048 acos 9.8813129168249309e-324 0.0 -> 1.5707963267948966 -0.0
+acos0049 acos 9.8813129168249309e-324 -0.0 -> 1.5707963267948966 0.0
+acos0050 acos 1e-305 0.0 -> 1.5707963267948966 -0.0
+acos0051 acos 1e-305 -0.0 -> 1.5707963267948966 0.0
+acos0052 acos 1e-150 0.0 -> 1.5707963267948966 -0.0
+acos0053 acos 1e-150 -0.0 -> 1.5707963267948966 0.0
+acos0054 acos 9.9999999999999998e-17 0.0 -> 1.5707963267948966 -0.0
+acos0055 acos 9.9999999999999998e-17 -0.0 -> 1.5707963267948966 0.0
+acos0056 acos 0.001 0.0 -> 1.56979632662823 -0.0
+acos0057 acos 0.001 -0.0 -> 1.56979632662823 0.0
+acos0058 acos 0.57899999999999996 0.0 -> 0.95329467197772655 -0.0
+acos0059 acos 0.57899999999999996 -0.0 -> 0.95329467197772655 0.0
+acos0060 acos 0.99999999999999989 0.0 -> 1.4901161193847656e-08 -0.0
+acos0061 acos 0.99999999999999989 -0.0 -> 1.4901161193847656e-08 0.0
+acos0062 acos 1.0000000000000002 0.0 -> 0.0 -2.1073424255447014e-08
+acos0063 acos 1.0000000000000002 -0.0 -> 0.0 2.1073424255447014e-08
+acos0064 acos 1.0009999999999999 0.0 -> 0.0 -0.044717633608306849
+acos0065 acos 1.0009999999999999 -0.0 -> 0.0 0.044717633608306849
+acos0066 acos 2.0 0.0 -> 0.0 -1.3169578969248168
+acos0067 acos 2.0 -0.0 -> 0.0 1.3169578969248168
+acos0068 acos 23.0 0.0 -> 0.0 -3.8281684713331012
+acos0069 acos 23.0 -0.0 -> 0.0 3.8281684713331012
+acos0070 acos 10000000000000000.0 0.0 -> 0.0 -37.534508668464674
+acos0071 acos 10000000000000000.0 -0.0 -> 0.0 37.534508668464674
+acos0072 acos 9.9999999999999998e+149 0.0 -> 0.0 -346.08091112966679
+acos0073 acos 9.9999999999999998e+149 -0.0 -> 0.0 346.08091112966679
+acos0074 acos 1.0000000000000001e+299 0.0 -> 0.0 -689.16608998577965
+acos0075 acos 1.0000000000000001e+299 -0.0 -> 0.0 689.16608998577965
+
+-- random inputs
+acos0100 acos -3.3307113324596682 -10.732007530863266 -> 1.8706085694482339 3.113986806554613
+acos0101 acos -2863.952991743291 -2681013315.2571239 -> 1.5707973950301699 22.402607843274758
+acos0102 acos -0.33072639793220088 -0.85055464658253055 -> 1.8219426895922601 0.79250166729311966
+acos0103 acos -2.5722325842097802 -12.703940809821574 -> 1.7699942413107408 3.2565170156527325
+acos0104 acos -42.495233785459583 -0.54039320751337161 -> 3.1288732573153304 4.4424815519735601
+acos0105 acos -1.1363818625856401 9641.1325498630376 -> 1.5709141948820049 -9.8669410553254284
+acos0106 acos -2.4398426824157866e-11 0.33002051890266165 -> 1.570796326818066 -0.32430578041578667
+acos0107 acos -1.3521340428186552 2.9369737912076772 -> 1.9849059192339338 -1.8822893674117942
+acos0108 acos -1.827364706477915 1.0355459232147557 -> 2.5732246307960032 -1.4090688267854969
+acos0109 acos -0.25978373706403546 10.09712669185833 -> 1.5963940386378306 -3.0081673050196063
+acos0110 acos 0.33561778471072551 -4587350.6823999118 -> 1.5707962536333251 16.031960402579539
+acos0111 acos 0.49133444610998445 -0.8071422362990015 -> 1.1908761712801788 0.78573345813187867
+acos0112 acos 0.42196734507823974 -2.4812965431745115 -> 1.414091186100692 1.651707260988172
+acos0113 acos 2.961426210100655 -219.03295695248664 -> 1.5572768319822778 6.0824659885827304
+acos0114 acos 2.886209063652641 -20.38011207220606 -> 1.4302765252297889 3.718201853147642
+acos0115 acos 0.4180568075276509 1.4833433990823484 -> 1.3393834558303042 -1.2079847758301576
+acos0116 acos 52.376111405924718 0.013930429001941001 -> 0.00026601761804024188 -4.6515066691204714
+acos0117 acos 41637948387.625969 1.563418292894041 -> 3.7547918507883548e-11 -25.145424989809381
+acos0118 acos 0.061226659122249526 0.8447234394615154 -> 1.5240280306367315 -0.76791798971140812
+acos0119 acos 2.4480466420442959e+26 0.18002339201384662 -> 7.353756620564798e-28 -61.455650015996376
+
+-- values near infinity
+acos0200 acos 1.6206860518683021e+308 1.0308426226285283e+308 -> 0.56650826093826223 -710.54206874241561
+acos0201 acos 1.2067735875070062e+308 -1.3429173724390276e+308 -> 0.83874369390864889 710.48017794027498
+acos0202 acos -7.4130145132549047e+307 1.1759130543927645e+308 -> 2.1332729346478536 -710.21871115698752
+acos0203 acos -8.6329426442257249e+307 -1.2316282952184133e+308 -> 2.1821511032444838 710.29752145697148
+acos0204 acos 0.0 1.4289713855849746e+308 -> 1.5707963267948966 -710.24631069738996
+acos0205 acos -0.0 1.3153524545987432e+308 -> 1.5707963267948966 -710.1634604787539
+acos0206 acos 0.0 -9.6229037669269321e+307 -> 1.5707963267948966 709.85091679573691
+acos0207 acos -0.0 -4.9783616421107088e+307 -> 1.5707963267948966 709.19187157911233
+acos0208 acos 1.3937541925739389e+308 0.0 -> 0.0 -710.22135678707264
+acos0209 acos 9.1362388967371536e+307 -0.0 -> 0.0 709.79901953124613
+acos0210 acos -1.3457361220697436e+308 0.0 -> 3.1415926535897931 -710.18629698871848
+acos0211 acos -5.4699090056144284e+307 -0.0 -> 3.1415926535897931 709.28603271085649
+acos0212 acos 1.5880716932358901e+308 5.5638401252339929 -> 3.503519487773873e-308 -710.35187633140583
+acos0213 acos 1.2497211663463164e+308 -3.0456477717911024 -> 2.4370618453197486e-308 710.11227628223412
+acos0214 acos -9.9016224006029528e+307 4.9570427340789056 -> 3.1415926535897931 -709.87946935229468
+acos0215 acos -1.5854071066874139e+308 -4.4233577741497783 -> 3.1415926535897931 710.35019704672004
+acos0216 acos 9.3674623083647628 1.5209559051877979e+308 -> 1.5707963267948966 -710.30869484491086
+acos0217 acos 8.1773832021784383 -6.6093445795000056e+307 -> 1.5707963267948966 709.4752552227792
+acos0218 acos -3.1845935000665104 1.5768856396650893e+308 -> 1.5707963267948966 -710.34480761042687
+acos0219 acos -1.0577303880953903 -6.4574626815735613e+307 -> 1.5707963267948966 709.45200719662046
+
+-- values near 0
+acos0220 acos 1.8566986970714045e-320 3.1867234156760402e-321 -> 1.5707963267948966 -3.1867234156760402e-321
+acos0221 acos 7.9050503334599447e-323 -8.8931816251424378e-323 -> 1.5707963267948966 8.8931816251424378e-323
+acos0222 acos -4.4465908125712189e-323 2.4654065097222727e-311 -> 1.5707963267948966 -2.4654065097222727e-311
+acos0223 acos -6.1016916408192619e-311 -2.4703282292062327e-323 -> 1.5707963267948966 2.4703282292062327e-323
+acos0224 acos 0.0 3.4305783621842729e-311 -> 1.5707963267948966 -3.4305783621842729e-311
+acos0225 acos -0.0 1.6117409498633145e-319 -> 1.5707963267948966 -1.6117409498633145e-319
+acos0226 acos 0.0 -4.9900630229965901e-322 -> 1.5707963267948966 4.9900630229965901e-322
+acos0227 acos -0.0 -4.4889279210592818e-311 -> 1.5707963267948966 4.4889279210592818e-311
+acos0228 acos 5.3297678681477214e-312 0.0 -> 1.5707963267948966 -0.0
+acos0229 acos 6.2073425897211614e-313 -0.0 -> 1.5707963267948966 0.0
+acos0230 acos -4.9406564584124654e-324 0.0 -> 1.5707963267948966 -0.0
+acos0231 acos -1.7107517052899003e-318 -0.0 -> 1.5707963267948966 0.0
+
+-- special values
+acos1000 acos 0.0 0.0 -> 1.5707963267948966 -0.0
+acos1001 acos 0.0 -0.0 -> 1.5707963267948966 0.0
+acos1002 acos -0.0 0.0 -> 1.5707963267948966 -0.0
+acos1003 acos -0.0 -0.0 -> 1.5707963267948966 0.0
+acos1004 acos 0.0 nan -> 1.5707963267948966 nan
+acos1005 acos -0.0 nan -> 1.5707963267948966 nan
+acos1006 acos -2.3 inf -> 1.5707963267948966 -inf
+acos1007 acos -0.0 inf -> 1.5707963267948966 -inf
+acos1008 acos 0.0 inf -> 1.5707963267948966 -inf
+acos1009 acos 2.3 inf -> 1.5707963267948966 -inf
+acos1010 acos -2.3 nan -> nan nan
+acos1011 acos 2.3 nan -> nan nan
+acos1012 acos -inf 2.3 -> 3.1415926535897931 -inf
+acos1013 acos -inf 0.0 -> 3.1415926535897931 -inf
+acos1014 acos inf 2.3 -> 0.0 -inf
+acos1015 acos inf 0.0 -> 0.0 -inf
+acos1016 acos -inf inf -> 2.3561944901923448 -inf
+acos1017 acos inf inf -> 0.78539816339744828 -inf
+acos1018 acos inf nan -> nan inf                        ignore-imag-sign
+acos1019 acos -inf nan -> nan inf                       ignore-imag-sign
+acos1020 acos nan 0.0 -> nan nan
+acos1021 acos nan 2.3 -> nan nan
+acos1022 acos nan inf -> nan -inf
+acos1023 acos nan nan -> nan nan
+acos1024 acos -2.3 -inf -> 1.5707963267948966 inf
+acos1025 acos -0.0 -inf -> 1.5707963267948966 inf
+acos1026 acos 0.0 -inf -> 1.5707963267948966 inf
+acos1027 acos 2.3 -inf -> 1.5707963267948966 inf
+acos1028 acos -inf -2.3 -> 3.1415926535897931 inf
+acos1029 acos -inf -0.0 -> 3.1415926535897931 inf
+acos1030 acos inf -2.3 -> 0.0 inf
+acos1031 acos inf -0.0 -> 0.0 inf
+acos1032 acos -inf -inf -> 2.3561944901923448 inf
+acos1033 acos inf -inf -> 0.78539816339744828 inf
+acos1034 acos nan -0.0 -> nan nan
+acos1035 acos nan -2.3 -> nan nan
+acos1036 acos nan -inf -> nan inf
+
+
+--------------------------------------
+-- acosh: Inverse hyperbolic cosine --
+--------------------------------------
+
+-- zeros
+acosh0000 acosh 0.0 0.0 -> 0.0 1.5707963267948966
+acosh0001 acosh 0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh0002 acosh -0.0 0.0 -> 0.0 1.5707963267948966
+acosh0003 acosh -0.0 -0.0 -> 0.0 -1.5707963267948966
+
+-- branch points: +/-1
+acosh0010 acosh 1.0 0.0 -> 0.0 0.0
+acosh0011 acosh 1.0 -0.0 -> 0.0 -0.0
+acosh0012 acosh -1.0 0.0 -> 0.0 3.1415926535897931
+acosh0013 acosh -1.0 -0.0 -> 0.0 -3.1415926535897931
+
+-- values along both sides of real axis
+acosh0020 acosh -9.8813129168249309e-324 0.0 -> 0.0 1.5707963267948966
+acosh0021 acosh -9.8813129168249309e-324 -0.0 -> 0.0 -1.5707963267948966
+acosh0022 acosh -1e-305 0.0 -> 0.0 1.5707963267948966
+acosh0023 acosh -1e-305 -0.0 -> 0.0 -1.5707963267948966
+acosh0024 acosh -1e-150 0.0 -> 0.0 1.5707963267948966
+acosh0025 acosh -1e-150 -0.0 -> 0.0 -1.5707963267948966
+acosh0026 acosh -9.9999999999999998e-17 0.0 -> 0.0 1.5707963267948968
+acosh0027 acosh -9.9999999999999998e-17 -0.0 -> 0.0 -1.5707963267948968
+acosh0028 acosh -0.001 0.0 -> 0.0 1.5717963269615634
+acosh0029 acosh -0.001 -0.0 -> 0.0 -1.5717963269615634
+acosh0030 acosh -0.57899999999999996 0.0 -> 0.0 2.1882979816120667
+acosh0031 acosh -0.57899999999999996 -0.0 -> 0.0 -2.1882979816120667
+acosh0032 acosh -0.99999999999999989 0.0 -> 0.0 3.1415926386886319
+acosh0033 acosh -0.99999999999999989 -0.0 -> 0.0 -3.1415926386886319
+acosh0034 acosh -1.0000000000000002 0.0 -> 2.1073424255447014e-08 3.1415926535897931
+acosh0035 acosh -1.0000000000000002 -0.0 -> 2.1073424255447014e-08 -3.1415926535897931
+acosh0036 acosh -1.0009999999999999 0.0 -> 0.044717633608306849 3.1415926535897931
+acosh0037 acosh -1.0009999999999999 -0.0 -> 0.044717633608306849 -3.1415926535897931
+acosh0038 acosh -2.0 0.0 -> 1.3169578969248168 3.1415926535897931
+acosh0039 acosh -2.0 -0.0 -> 1.3169578969248168 -3.1415926535897931
+acosh0040 acosh -23.0 0.0 -> 3.8281684713331012 3.1415926535897931
+acosh0041 acosh -23.0 -0.0 -> 3.8281684713331012 -3.1415926535897931
+acosh0042 acosh -10000000000000000.0 0.0 -> 37.534508668464674 3.1415926535897931
+acosh0043 acosh -10000000000000000.0 -0.0 -> 37.534508668464674 -3.1415926535897931
+acosh0044 acosh -9.9999999999999998e+149 0.0 -> 346.08091112966679 3.1415926535897931
+acosh0045 acosh -9.9999999999999998e+149 -0.0 -> 346.08091112966679 -3.1415926535897931
+acosh0046 acosh -1.0000000000000001e+299 0.0 -> 689.16608998577965 3.1415926535897931
+acosh0047 acosh -1.0000000000000001e+299 -0.0 -> 689.16608998577965 -3.1415926535897931
+acosh0048 acosh 9.8813129168249309e-324 0.0 -> 0.0 1.5707963267948966
+acosh0049 acosh 9.8813129168249309e-324 -0.0 -> 0.0 -1.5707963267948966
+acosh0050 acosh 1e-305 0.0 -> 0.0 1.5707963267948966
+acosh0051 acosh 1e-305 -0.0 -> 0.0 -1.5707963267948966
+acosh0052 acosh 1e-150 0.0 -> 0.0 1.5707963267948966
+acosh0053 acosh 1e-150 -0.0 -> 0.0 -1.5707963267948966
+acosh0054 acosh 9.9999999999999998e-17 0.0 -> 0.0 1.5707963267948966
+acosh0055 acosh 9.9999999999999998e-17 -0.0 -> 0.0 -1.5707963267948966
+acosh0056 acosh 0.001 0.0 -> 0.0 1.56979632662823
+acosh0057 acosh 0.001 -0.0 -> 0.0 -1.56979632662823
+acosh0058 acosh 0.57899999999999996 0.0 -> 0.0 0.95329467197772655
+acosh0059 acosh 0.57899999999999996 -0.0 -> 0.0 -0.95329467197772655
+acosh0060 acosh 0.99999999999999989 0.0 -> 0.0 1.4901161193847656e-08
+acosh0061 acosh 0.99999999999999989 -0.0 -> 0.0 -1.4901161193847656e-08
+acosh0062 acosh 1.0000000000000002 0.0 -> 2.1073424255447014e-08 0.0
+acosh0063 acosh 1.0000000000000002 -0.0 -> 2.1073424255447014e-08 -0.0
+acosh0064 acosh 1.0009999999999999 0.0 -> 0.044717633608306849 0.0
+acosh0065 acosh 1.0009999999999999 -0.0 -> 0.044717633608306849 -0.0
+acosh0066 acosh 2.0 0.0 -> 1.3169578969248168 0.0
+acosh0067 acosh 2.0 -0.0 -> 1.3169578969248168 -0.0
+acosh0068 acosh 23.0 0.0 -> 3.8281684713331012 0.0
+acosh0069 acosh 23.0 -0.0 -> 3.8281684713331012 -0.0
+acosh0070 acosh 10000000000000000.0 0.0 -> 37.534508668464674 0.0
+acosh0071 acosh 10000000000000000.0 -0.0 -> 37.534508668464674 -0.0
+acosh0072 acosh 9.9999999999999998e+149 0.0 -> 346.08091112966679 0.0
+acosh0073 acosh 9.9999999999999998e+149 -0.0 -> 346.08091112966679 -0.0
+acosh0074 acosh 1.0000000000000001e+299 0.0 -> 689.16608998577965 0.0
+acosh0075 acosh 1.0000000000000001e+299 -0.0 -> 689.16608998577965 -0.0
+
+-- random inputs
+acosh0100 acosh -1.4328589581250843 -1.8370347775558309 -> 1.5526962646549587 -2.190250168435786
+acosh0101 acosh -0.31075819156220957 -1.0772555786839297 -> 0.95139168286193709 -1.7812228089636479
+acosh0102 acosh -1.9044776578070453 -20.485370158932124 -> 3.7177411088932359 -1.6633888745861227
+acosh0103 acosh -0.075642506000858742 -21965976320.873051 -> 24.505907742881991 -1.5707963267983402
+acosh0104 acosh -1.6162271181056307 -3.0369343458696099 -> 1.9407057262861227 -2.0429549461750209
+acosh0105 acosh -0.3103780280298063 0.00018054880018078987 -> 0.00018992877058761416 1.886386995096728
+acosh0106 acosh -9159468751.5897655 5.8014747664273649 -> 23.631201197959193 3.1415926529564078
+acosh0107 acosh -0.037739157550933884 0.21841357493510705 -> 0.21685844960602488 1.6076735133449402
+acosh0108 acosh -8225991.0508394297 0.28318543008913644 -> 16.615956520420287 3.1415926191641019
+acosh0109 acosh -35.620070502302639 0.31303237005015 -> 4.2658980006943965 3.1328013255541873
+acosh0110 acosh 96.729939906820917 -0.029345228372365334 -> 5.2650434775863548 -0.00030338895866972843
+acosh0111 acosh 0.59656024007966491 -2.0412294654163978 -> 1.4923002024287835 -1.312568421900338
+acosh0112 acosh 109.29384112677828 -0.00015454863061533812 -> 5.3871662961545477 -1.4141245154061214e-06
+acosh0113 acosh 8.6705651969361597 -3.6723631649787465 -> 2.9336180958363545 -0.40267362031872861
+acosh0114 acosh 1.8101646445052686 -0.012345132721855478 -> 1.1997148566285769 -0.0081813912760150265
+acosh0115 acosh 52.56897195025288 0.001113916065985443 -> 4.6551827622264135 2.1193445872040307e-05
+acosh0116 acosh 0.28336786164214739 355643992457.40485 -> 27.290343226816528 1.5707963267940999
+acosh0117 acosh 0.73876621291911437 2.8828594541104322e-20 -> 4.2774820978159067e-20 0.73955845836827927
+acosh0118 acosh 0.025865471781718878 37125746064318.492 -> 31.938478989418012 1.5707963267948959
+acosh0119 acosh 2.2047353511780132 0.074712248143489271 -> 1.4286403248698021 0.037997904971626598
+
+-- values near infinity
+acosh0200 acosh 8.1548592876467785e+307 9.0943779335951128e+307 -> 710.08944620800605 0.83981165425478954
+acosh0201 acosh 1.4237229680972531e+308 -1.0336966617874858e+308 -> 710.4543331094759 -0.6279972876348755
+acosh0202 acosh -1.5014526899738939e+308 1.5670700378448792e+308 -> 710.66420706795464 2.3348137299106697
+acosh0203 acosh -1.0939040375213928e+308 -1.0416960351127978e+308 -> 710.30182863115886 -2.380636147787027
+acosh0204 acosh 0.0 1.476062433559588e+308 -> 710.27873384716929 1.5707963267948966
+acosh0205 acosh -0.0 6.2077210326221094e+307 -> 709.41256457484769 1.5707963267948966
+acosh0206 acosh 0.0 -1.5621899909968308e+308 -> 710.33544449990734 -1.5707963267948966
+acosh0207 acosh -0.0 -8.3556624833839122e+307 -> 709.70971018048317 -1.5707963267948966
+acosh0208 acosh 1.3067079752499342e+308 0.0 -> 710.15686680107228 0.0
+acosh0209 acosh 1.5653640340214026e+308 -0.0 -> 710.33747422926706 -0.0
+acosh0210 acosh -6.9011375992290636e+307 0.0 -> 709.51845699719922 3.1415926535897931
+acosh0211 acosh -9.9539576809926973e+307 -0.0 -> 709.88474095870185 -3.1415926535897931
+acosh0212 acosh 7.6449598518914925e+307 9.5706540768268358 -> 709.62081731754802 1.2518906916769345e-307
+acosh0213 acosh 5.4325410972602197e+307 -7.8064807816522706 -> 709.279177727925 -1.4369851312471974e-307
+acosh0214 acosh -1.1523626112360465e+308 7.0617510038869336 -> 710.03117010216909 3.1415926535897931
+acosh0215 acosh -1.1685027786862599e+308 -5.1568558357925625 -> 710.04507907571417 -3.1415926535897931
+acosh0216 acosh 3.0236370339788721 1.7503248720096417e+308 -> 710.44915723458064 1.5707963267948966
+acosh0217 acosh 6.6108007926031149 -9.1469968225806149e+307 -> 709.80019633903328 -1.5707963267948966
+acosh0218 acosh -5.1096262905623959 6.4484926785412395e+307 -> 709.45061713997973 1.5707963267948966
+acosh0219 acosh -2.8080920608735846 -1.7716118836519368e+308 -> 710.46124562363445 -1.5707963267948966
+
+-- values near 0
+acosh0220 acosh 4.5560530326699304e-317 7.3048989121436657e-318 -> 7.3048989121436657e-318 1.5707963267948966
+acosh0221 acosh 4.8754274133585331e-314 -9.8469794897684199e-315 -> 9.8469794897684199e-315 -1.5707963267948966
+acosh0222 acosh -4.6748876009960097e-312 9.7900342887557606e-318 -> 9.7900342887557606e-318 1.5707963267948966
+acosh0223 acosh -4.3136871538399236e-320 -4.9406564584124654e-323 -> 4.9406564584124654e-323 -1.5707963267948966
+acosh0224 acosh 0.0 4.3431013866496774e-314 -> 4.3431013866496774e-314 1.5707963267948966
+acosh0225 acosh -0.0 6.0147334335829184e-317 -> 6.0147334335829184e-317 1.5707963267948966
+acosh0226 acosh 0.0 -1.2880291387081297e-320 -> 1.2880291387081297e-320 -1.5707963267948966
+acosh0227 acosh -0.0 -1.4401563976534621e-317 -> 1.4401563976534621e-317 -1.5707963267948966
+acosh0228 acosh 1.3689680570863091e-313 0.0 -> 0.0 1.5707963267948966
+acosh0229 acosh 1.5304346893494371e-312 -0.0 -> 0.0 -1.5707963267948966
+acosh0230 acosh -3.7450175954766488e-320 0.0 -> 0.0 1.5707963267948966
+acosh0231 acosh -8.4250563080885801e-311 -0.0 -> 0.0 -1.5707963267948966
+
+-- special values
+acosh1000 acosh 0.0 0.0 -> 0.0 1.5707963267948966
+acosh1001 acosh -0.0 0.0 -> 0.0 1.5707963267948966
+acosh1002 acosh 0.0 inf -> inf 1.5707963267948966
+acosh1003 acosh 2.3 inf -> inf 1.5707963267948966
+acosh1004 acosh -0.0 inf -> inf 1.5707963267948966
+acosh1005 acosh -2.3 inf -> inf 1.5707963267948966
+acosh1006 acosh 0.0 nan -> nan nan
+acosh1007 acosh 2.3 nan -> nan nan
+acosh1008 acosh -0.0 nan -> nan nan
+acosh1009 acosh -2.3 nan -> nan nan
+acosh1010 acosh -inf 0.0 -> inf 3.1415926535897931
+acosh1011 acosh -inf 2.3 -> inf 3.1415926535897931
+acosh1012 acosh inf 0.0 -> inf 0.0
+acosh1013 acosh inf 2.3 -> inf 0.0
+acosh1014 acosh -inf inf -> inf 2.3561944901923448
+acosh1015 acosh inf inf -> inf 0.78539816339744828
+acosh1016 acosh inf nan -> inf nan
+acosh1017 acosh -inf nan -> inf nan
+acosh1018 acosh nan 0.0 -> nan nan
+acosh1019 acosh nan 2.3 -> nan nan
+acosh1020 acosh nan inf -> inf nan
+acosh1021 acosh nan nan -> nan nan
+acosh1022 acosh 0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh1023 acosh -0.0 -0.0 -> 0.0 -1.5707963267948966
+acosh1024 acosh 0.0 -inf -> inf -1.5707963267948966
+acosh1025 acosh 2.3 -inf -> inf -1.5707963267948966
+acosh1026 acosh -0.0 -inf -> inf -1.5707963267948966
+acosh1027 acosh -2.3 -inf -> inf -1.5707963267948966
+acosh1028 acosh -inf -0.0 -> inf -3.1415926535897931
+acosh1029 acosh -inf -2.3 -> inf -3.1415926535897931
+acosh1030 acosh inf -0.0 -> inf -0.0
+acosh1031 acosh inf -2.3 -> inf -0.0
+acosh1032 acosh -inf -inf -> inf -2.3561944901923448
+acosh1033 acosh inf -inf -> inf -0.78539816339744828
+acosh1034 acosh nan -0.0 -> nan nan
+acosh1035 acosh nan -2.3 -> nan nan
+acosh1036 acosh nan -inf -> inf nan
+
+
+------------------------
+-- asin: Inverse sine --
+------------------------
+
+-- zeros
+asin0000 asin 0.0 0.0 -> 0.0 0.0
+asin0001 asin 0.0 -0.0 -> 0.0 -0.0
+asin0002 asin -0.0 0.0 -> -0.0 0.0
+asin0003 asin -0.0 -0.0 -> -0.0 -0.0
+
+-- branch points: +/-1
+asin0010 asin 1.0 0.0 -> 1.5707963267948966 0.0
+asin0011 asin 1.0 -0.0 -> 1.5707963267948966 -0.0
+asin0012 asin -1.0 0.0 -> -1.5707963267948966 0.0
+asin0013 asin -1.0 -0.0 -> -1.5707963267948966 -0.0
+
+-- values along both sides of real axis
+asin0020 asin -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0
+asin0021 asin -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0
+asin0022 asin -1e-305 0.0 -> -1e-305 0.0
+asin0023 asin -1e-305 -0.0 -> -1e-305 -0.0
+asin0024 asin -1e-150 0.0 -> -1e-150 0.0
+asin0025 asin -1e-150 -0.0 -> -1e-150 -0.0
+asin0026 asin -9.9999999999999998e-17 0.0 -> -9.9999999999999998e-17 0.0
+asin0027 asin -9.9999999999999998e-17 -0.0 -> -9.9999999999999998e-17 -0.0
+asin0028 asin -0.001 0.0 -> -0.0010000001666667416 0.0
+asin0029 asin -0.001 -0.0 -> -0.0010000001666667416 -0.0
+asin0030 asin -0.57899999999999996 0.0 -> -0.61750165481717001 0.0
+asin0031 asin -0.57899999999999996 -0.0 -> -0.61750165481717001 -0.0
+asin0032 asin -0.99999999999999989 0.0 -> -1.5707963118937354 0.0
+asin0033 asin -0.99999999999999989 -0.0 -> -1.5707963118937354 -0.0
+asin0034 asin -1.0000000000000002 0.0 -> -1.5707963267948966 2.1073424255447014e-08
+asin0035 asin -1.0000000000000002 -0.0 -> -1.5707963267948966 -2.1073424255447014e-08
+asin0036 asin -1.0009999999999999 0.0 -> -1.5707963267948966 0.044717633608306849
+asin0037 asin -1.0009999999999999 -0.0 -> -1.5707963267948966 -0.044717633608306849
+asin0038 asin -2.0 0.0 -> -1.5707963267948966 1.3169578969248168
+asin0039 asin -2.0 -0.0 -> -1.5707963267948966 -1.3169578969248168
+asin0040 asin -23.0 0.0 -> -1.5707963267948966 3.8281684713331012
+asin0041 asin -23.0 -0.0 -> -1.5707963267948966 -3.8281684713331012
+asin0042 asin -10000000000000000.0 0.0 -> -1.5707963267948966 37.534508668464674
+asin0043 asin -10000000000000000.0 -0.0 -> -1.5707963267948966 -37.534508668464674
+asin0044 asin -9.9999999999999998e+149 0.0 -> -1.5707963267948966 346.08091112966679
+asin0045 asin -9.9999999999999998e+149 -0.0 -> -1.5707963267948966 -346.08091112966679
+asin0046 asin -1.0000000000000001e+299 0.0 -> -1.5707963267948966 689.16608998577965
+asin0047 asin -1.0000000000000001e+299 -0.0 -> -1.5707963267948966 -689.16608998577965
+asin0048 asin 9.8813129168249309e-324 0.0 -> 9.8813129168249309e-324 0.0
+asin0049 asin 9.8813129168249309e-324 -0.0 -> 9.8813129168249309e-324 -0.0
+asin0050 asin 1e-305 0.0 -> 1e-305 0.0
+asin0051 asin 1e-305 -0.0 -> 1e-305 -0.0
+asin0052 asin 1e-150 0.0 -> 1e-150 0.0
+asin0053 asin 1e-150 -0.0 -> 1e-150 -0.0
+asin0054 asin 9.9999999999999998e-17 0.0 -> 9.9999999999999998e-17 0.0
+asin0055 asin 9.9999999999999998e-17 -0.0 -> 9.9999999999999998e-17 -0.0
+asin0056 asin 0.001 0.0 -> 0.0010000001666667416 0.0
+asin0057 asin 0.001 -0.0 -> 0.0010000001666667416 -0.0
+asin0058 asin 0.57899999999999996 0.0 -> 0.61750165481717001 0.0
+asin0059 asin 0.57899999999999996 -0.0 -> 0.61750165481717001 -0.0
+asin0060 asin 0.99999999999999989 0.0 -> 1.5707963118937354 0.0
+asin0061 asin 0.99999999999999989 -0.0 -> 1.5707963118937354 -0.0
+asin0062 asin 1.0000000000000002 0.0 -> 1.5707963267948966 2.1073424255447014e-08
+asin0063 asin 1.0000000000000002 -0.0 -> 1.5707963267948966 -2.1073424255447014e-08
+asin0064 asin 1.0009999999999999 0.0 -> 1.5707963267948966 0.044717633608306849
+asin0065 asin 1.0009999999999999 -0.0 -> 1.5707963267948966 -0.044717633608306849
+asin0066 asin 2.0 0.0 -> 1.5707963267948966 1.3169578969248168
+asin0067 asin 2.0 -0.0 -> 1.5707963267948966 -1.3169578969248168
+asin0068 asin 23.0 0.0 -> 1.5707963267948966 3.8281684713331012
+asin0069 asin 23.0 -0.0 -> 1.5707963267948966 -3.8281684713331012
+asin0070 asin 10000000000000000.0 0.0 -> 1.5707963267948966 37.534508668464674
+asin0071 asin 10000000000000000.0 -0.0 -> 1.5707963267948966 -37.534508668464674
+asin0072 asin 9.9999999999999998e+149 0.0 -> 1.5707963267948966 346.08091112966679
+asin0073 asin 9.9999999999999998e+149 -0.0 -> 1.5707963267948966 -346.08091112966679
+asin0074 asin 1.0000000000000001e+299 0.0 -> 1.5707963267948966 689.16608998577965
+asin0075 asin 1.0000000000000001e+299 -0.0 -> 1.5707963267948966 -689.16608998577965
+
+-- random inputs
+asin0100 asin -1.5979555835086083 -0.15003009814595247 -> -1.4515369557405788 -1.0544476399790823
+asin0101 asin -0.57488225895317679 -9.6080397838952743e-13 -> -0.61246024460412851 -1.174238005400403e-12
+asin0102 asin -3.6508087930516249 -0.36027527093220152 -> -1.4685890605305874 -1.9742273007152038
+asin0103 asin -1.5238659792326819 -1.1360813516996364 -> -0.86080051691147275 -1.3223742205689195
+asin0104 asin -1592.0639045555306 -0.72362427935018236 -> -1.5703418071175179 -8.0659336918729228
+asin0105 asin -0.19835471371312019 4.2131508416697709 -> -0.045777831019935149 2.1461732751933171
+asin0106 asin -1.918471054430213 0.40603305079779234 -> -1.3301396585791556 1.30263642314981
+asin0107 asin -254495.01623373642 0.71084414434470822 -> -1.5707935336394359 13.140183712762321
+asin0108 asin -0.31315882715691157 3.9647994288429866 -> -0.076450403840916004 2.0889762138713457
+asin0109 asin -0.90017064284720816 1.2530659485907105 -> -0.53466509741943447 1.1702811557577
+asin0110 asin 2.1615181696571075 -0.14058647488229523 -> 1.4976166323896871 -1.4085811039334604
+asin0111 asin 1.2104749210707795 -0.85732484485298999 -> 0.83913071588343924 -1.0681719250525901
+asin0112 asin 1.7059733185128891 -0.84032966373156581 -> 1.0510900815816229 -1.2967979791361652
+asin0113 asin 9.9137085017290687 -1.4608383970250893 -> 1.4237704820128891 -2.995414677560686
+asin0114 asin 117.12344751041495 -5453908091.5334015 -> 2.1475141411392012e-08 -23.112745450217066
+asin0115 asin 0.081041187798029227 0.067054349860173196 -> 0.080946786856771813 0.067223991060639698
+asin0116 asin 46.635472322049949 2.3835190718056678 -> 1.5197194940010779 4.5366989600972083
+asin0117 asin 3907.0687961127105 19.144021886390181 -> 1.5658965233083235 8.9637018715924217
+asin0118 asin 1.0889312322308273 509.01577883554768 -> 0.0021392803817829316 6.9256294494524706
+asin0119 asin 0.10851518277509224 1.5612510908217476 -> 0.058491014243902621 1.2297075725621327
+
+-- values near infinity
+asin0200 asin 1.5230241998821499e+308 5.5707228994084525e+307 -> 1.2201446370892068 710.37283486535966
+asin0201 asin 8.1334317698672204e+307 -9.2249425197872451e+307 -> 0.72259991284020042 -710.0962453049026
+asin0202 asin -9.9138506659241768e+307 6.701544526434995e+307 -> -0.97637511742194594 710.06887486671371
+asin0203 asin -1.4141298868173842e+308 -5.401505134514191e+307 -> -1.2059319055160587 -710.30396478954628
+asin0204 asin 0.0 9.1618092977897431e+307 -> 0.0 709.80181441050593
+asin0205 asin -0.0 6.8064342551939755e+307 -> -0.0 709.50463910853489
+asin0206 asin 0.0 -6.4997516454798215e+307 -> 0.0 -709.45853469751592
+asin0207 asin -0.0 -1.6767449053345242e+308 -> -0.0 -710.4062101803022
+asin0208 asin 5.4242749957378916e+307 0.0 -> 1.5707963267948966 709.27765497888902
+asin0209 asin 9.5342145121164749e+307 -0.0 -> 1.5707963267948966 -709.84165758595907
+asin0210 asin -7.0445698006201847e+307 0.0 -> -1.5707963267948966 709.53902780872136
+asin0211 asin -1.0016025569769706e+308 -0.0 -> -1.5707963267948966 -709.89095709697881
+asin0212 asin 1.6552203778877204e+308 0.48761543336249491 -> 1.5707963267948966 710.39328998153474
+asin0213 asin 1.2485712830384869e+308 -4.3489311161278899 -> 1.5707963267948966 -710.1113557467786
+asin0214 asin -1.5117842813353125e+308 5.123452666102434 -> -1.5707963267948966 710.30264641923031
+asin0215 asin -1.3167634313008016e+308 -0.52939679793528982 -> -1.5707963267948966 -710.16453260239768
+asin0216 asin 0.80843929176985907 1.0150851827767876e+308 -> 7.9642507396113875e-309 709.90432835561637
+asin0217 asin 8.2544809829680901 -1.7423548140539474e+308 -> 4.7375430746865733e-308 -710.44459336242164
+asin0218 asin -5.2499000118824295 4.6655578977512214e+307 -> -1.1252459249113292e-307 709.1269781491103
+asin0219 asin -5.9904782760833433 -4.7315689314781163e+307 -> -1.2660659419394637e-307 -709.14102757522312
+
+-- special values
+asin1000 asin -0.0 0.0 -> -0.0 0.0
+asin1001 asin 0.0 0.0 -> 0.0 0.0
+asin1002 asin -0.0 -0.0 -> -0.0 -0.0
+asin1003 asin 0.0 -0.0 -> 0.0 -0.0
+asin1004 asin -inf 0.0 -> -1.5707963267948966 inf
+asin1005 asin -inf 2.2999999999999998 -> -1.5707963267948966 inf
+asin1006 asin nan 0.0 -> nan nan
+asin1007 asin nan 2.2999999999999998 -> nan nan
+asin1008 asin -0.0 inf -> -0.0 inf
+asin1009 asin -2.2999999999999998 inf -> -0.0 inf
+asin1010 asin -inf inf -> -0.78539816339744828 inf
+asin1011 asin nan inf -> nan inf
+asin1012 asin -0.0 nan -> -0.0 nan
+asin1013 asin -2.2999999999999998 nan -> nan nan
+asin1014 asin -inf nan -> nan inf ignore-imag-sign
+asin1015 asin nan nan -> nan nan
+asin1016 asin inf 0.0 -> 1.5707963267948966 inf
+asin1017 asin inf 2.2999999999999998 -> 1.5707963267948966 inf
+asin1018 asin 0.0 inf -> 0.0 inf
+asin1019 asin 2.2999999999999998 inf -> 0.0 inf
+asin1020 asin inf inf -> 0.78539816339744828 inf
+asin1021 asin 0.0 nan -> 0.0 nan
+asin1022 asin 2.2999999999999998 nan -> nan nan
+asin1023 asin inf nan -> nan inf ignore-imag-sign
+asin1024 asin inf -0.0 -> 1.5707963267948966 -inf
+asin1025 asin inf -2.2999999999999998 -> 1.5707963267948966 -inf
+asin1026 asin nan -0.0 -> nan nan
+asin1027 asin nan -2.2999999999999998 -> nan nan
+asin1028 asin 0.0 -inf -> 0.0 -inf
+asin1029 asin 2.2999999999999998 -inf -> 0.0 -inf
+asin1030 asin inf -inf -> 0.78539816339744828 -inf
+asin1031 asin nan -inf -> nan -inf
+asin1032 asin -inf -0.0 -> -1.5707963267948966 -inf
+asin1033 asin -inf -2.2999999999999998 -> -1.5707963267948966 -inf
+asin1034 asin -0.0 -inf -> -0.0 -inf
+asin1035 asin -2.2999999999999998 -inf -> -0.0 -inf
+asin1036 asin -inf -inf -> -0.78539816339744828 -inf
+
+
+------------------------------------
+-- asinh: Inverse hyperbolic sine --
+------------------------------------
+
+-- zeros
+asinh0000 asinh 0.0 0.0 -> 0.0 0.0
+asinh0001 asinh 0.0 -0.0 -> 0.0 -0.0
+asinh0002 asinh -0.0 0.0 -> -0.0 0.0
+asinh0003 asinh -0.0 -0.0 -> -0.0 -0.0
+
+-- branch points: +/-i
+asinh0010 asinh 0.0 1.0 -> 0.0 1.5707963267948966
+asinh0011 asinh 0.0 -1.0 -> 0.0 -1.5707963267948966
+asinh0012 asinh -0.0 1.0 -> -0.0 1.5707963267948966
+asinh0013 asinh -0.0 -1.0 -> -0.0 -1.5707963267948966
+
+-- values along both sides of imaginary axis
+asinh0020 asinh 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324
+asinh0021 asinh -0.0 -9.8813129168249309e-324 -> -0.0 -9.8813129168249309e-324
+asinh0022 asinh 0.0 -1e-305 -> 0.0 -1e-305
+asinh0023 asinh -0.0 -1e-305 -> -0.0 -1e-305
+asinh0024 asinh 0.0 -1e-150 -> 0.0 -1e-150
+asinh0025 asinh -0.0 -1e-150 -> -0.0 -1e-150
+asinh0026 asinh 0.0 -9.9999999999999998e-17 -> 0.0 -9.9999999999999998e-17
+asinh0027 asinh -0.0 -9.9999999999999998e-17 -> -0.0 -9.9999999999999998e-17
+asinh0028 asinh 0.0 -0.001 -> 0.0 -0.0010000001666667416
+asinh0029 asinh -0.0 -0.001 -> -0.0 -0.0010000001666667416
+asinh0030 asinh 0.0 -0.57899999999999996 -> 0.0 -0.61750165481717001
+asinh0031 asinh -0.0 -0.57899999999999996 -> -0.0 -0.61750165481717001
+asinh0032 asinh 0.0 -0.99999999999999989 -> 0.0 -1.5707963118937354
+asinh0033 asinh -0.0 -0.99999999999999989 -> -0.0 -1.5707963118937354
+asinh0034 asinh 0.0 -1.0000000000000002 -> 2.1073424255447014e-08 -1.5707963267948966
+asinh0035 asinh -0.0 -1.0000000000000002 -> -2.1073424255447014e-08 -1.5707963267948966
+asinh0036 asinh 0.0 -1.0009999999999999 -> 0.044717633608306849 -1.5707963267948966
+asinh0037 asinh -0.0 -1.0009999999999999 -> -0.044717633608306849 -1.5707963267948966
+asinh0038 asinh 0.0 -2.0 -> 1.3169578969248168 -1.5707963267948966
+asinh0039 asinh -0.0 -2.0 -> -1.3169578969248168 -1.5707963267948966
+asinh0040 asinh 0.0 -20.0 -> 3.6882538673612966 -1.5707963267948966
+asinh0041 asinh -0.0 -20.0 -> -3.6882538673612966 -1.5707963267948966
+asinh0042 asinh 0.0 -10000000000000000.0 -> 37.534508668464674 -1.5707963267948966
+asinh0043 asinh -0.0 -10000000000000000.0 -> -37.534508668464674 -1.5707963267948966
+asinh0044 asinh 0.0 -9.9999999999999998e+149 -> 346.08091112966679 -1.5707963267948966
+asinh0045 asinh -0.0 -9.9999999999999998e+149 -> -346.08091112966679 -1.5707963267948966
+asinh0046 asinh 0.0 -1.0000000000000001e+299 -> 689.16608998577965 -1.5707963267948966
+asinh0047 asinh -0.0 -1.0000000000000001e+299 -> -689.16608998577965 -1.5707963267948966
+asinh0048 asinh 0.0 9.8813129168249309e-324 -> 0.0 9.8813129168249309e-324
+asinh0049 asinh -0.0 9.8813129168249309e-324 -> -0.0 9.8813129168249309e-324
+asinh0050 asinh 0.0 1e-305 -> 0.0 1e-305
+asinh0051 asinh -0.0 1e-305 -> -0.0 1e-305
+asinh0052 asinh 0.0 1e-150 -> 0.0 1e-150
+asinh0053 asinh -0.0 1e-150 -> -0.0 1e-150
+asinh0054 asinh 0.0 9.9999999999999998e-17 -> 0.0 9.9999999999999998e-17
+asinh0055 asinh -0.0 9.9999999999999998e-17 -> -0.0 9.9999999999999998e-17
+asinh0056 asinh 0.0 0.001 -> 0.0 0.0010000001666667416
+asinh0057 asinh -0.0 0.001 -> -0.0 0.0010000001666667416
+asinh0058 asinh 0.0 0.57899999999999996 -> 0.0 0.61750165481717001
+asinh0059 asinh -0.0 0.57899999999999996 -> -0.0 0.61750165481717001
+asinh0060 asinh 0.0 0.99999999999999989 -> 0.0 1.5707963118937354
+asinh0061 asinh -0.0 0.99999999999999989 -> -0.0 1.5707963118937354
+asinh0062 asinh 0.0 1.0000000000000002 -> 2.1073424255447014e-08 1.5707963267948966
+asinh0063 asinh -0.0 1.0000000000000002 -> -2.1073424255447014e-08 1.5707963267948966
+asinh0064 asinh 0.0 1.0009999999999999 -> 0.044717633608306849 1.5707963267948966
+asinh0065 asinh -0.0 1.0009999999999999 -> -0.044717633608306849 1.5707963267948966
+asinh0066 asinh 0.0 2.0 -> 1.3169578969248168 1.5707963267948966
+asinh0067 asinh -0.0 2.0 -> -1.3169578969248168 1.5707963267948966
+asinh0068 asinh 0.0 20.0 -> 3.6882538673612966 1.5707963267948966
+asinh0069 asinh -0.0 20.0 -> -3.6882538673612966 1.5707963267948966
+asinh0070 asinh 0.0 10000000000000000.0 -> 37.534508668464674 1.5707963267948966
+asinh0071 asinh -0.0 10000000000000000.0 -> -37.534508668464674 1.5707963267948966
+asinh0072 asinh 0.0 9.9999999999999998e+149 -> 346.08091112966679 1.5707963267948966
+asinh0073 asinh -0.0 9.9999999999999998e+149 -> -346.08091112966679 1.5707963267948966
+asinh0074 asinh 0.0 1.0000000000000001e+299 -> 689.16608998577965 1.5707963267948966
+asinh0075 asinh -0.0 1.0000000000000001e+299 -> -689.16608998577965 1.5707963267948966
+
+-- random inputs
+asinh0100 asinh -0.5946402853710423 -0.044506548910000145 -> -0.56459775392653022 -0.038256221441536356
+asinh0101 asinh -0.19353958046180916 -0.017489624793193454 -> -0.19237926804196651 -0.017171741895336792
+asinh0102 asinh -0.033117585138955893 -8.5256414015933757 -> -2.8327758348650969 -1.5668848791092411
+asinh0103 asinh -1.5184043184035716 -0.73491245339073275 -> -1.2715891419764005 -0.39204624408542355
+asinh0104 asinh -0.60716120271208818 -0.28900743958436542 -> -0.59119299421187232 -0.24745931678118135
+asinh0105 asinh -0.0237177865112429 2.8832601052166313 -> -1.7205820772413236 1.5620261702963094
+asinh0106 asinh -2.3906812342743979 2.6349216848574013 -> -1.9609636249445124 0.8142142660574706
+asinh0107 asinh -0.0027605019787620517 183.85588476550555 -> -5.9072920005445066 1.5707813120847871
+asinh0108 asinh -0.99083661164404713 0.028006797051617648 -> -0.8750185251283995 0.019894099615994653
+asinh0109 asinh -3.0362951937986393 0.86377266758504867 -> -1.8636030714685221 0.26475058859950168
+asinh0110 asinh 0.34438464536152769 -0.71603790174885029 -> 0.43985415690734164 -0.71015037409294324
+asinh0111 asinh 4.4925124413876256 -60604595352.871613 -> 25.520783738612078 -1.5707963267207683
+asinh0112 asinh 2.3213991428170337 -7.5459667007307258 -> 2.7560464993451643 -1.270073210856117
+asinh0113 asinh 0.21291939741682028 -1.2720428814784408 -> 0.77275088137338266 -1.3182099250896895
+asinh0114 asinh 6.6447359379455957 -0.97196191666946996 -> 2.602830695139672 -0.14368247412319965
+asinh0115 asinh 7.1326256655083746 2.1516360452706857 -> 2.7051146374367212 0.29051701669727581
+asinh0116 asinh 0.18846550905063442 3.4705348585339832 -> 1.917697875799296 1.514155593347924
+asinh0117 asinh 0.19065075303281598 0.26216814548222012 -> 0.19603050785932474 0.26013422809614117
+asinh0118 asinh 2.0242004665739719 0.70510281647495787 -> 1.4970366212896002 0.30526007200481453
+asinh0119 asinh 37.336596461576057 717.29157391678234 -> 7.269981997945294 1.5187910219576033
+
+-- values near infinity
+asinh0200 asinh 1.0760517500874541e+308 1.1497786241240167e+308 -> 710.34346055651815 0.81850936961793475
+asinh0201 asinh 1.1784839328845529e+308 -1.6478429586716638e+308 -> 710.59536255783678 -0.94996311735607697
+asinh0202 asinh -4.8777682248909193e+307 1.4103736217538474e+308 -> -710.28970147376992 1.2378239519096443
+asinh0203 asinh -1.2832478903233108e+308 -1.5732392613155698e+308 -> -710.59750164290745 -0.88657181439322452
+asinh0204 asinh 0.0 6.8431383856345372e+307 -> 709.51001718444604 1.5707963267948966
+asinh0205 asinh -0.0 8.601822432238051e+307 -> -709.73874482126689 1.5707963267948966
+asinh0206 asinh 0.0 -5.5698396067303782e+307 -> 709.30413698733742 -1.5707963267948966
+asinh0207 asinh -0.0 -7.1507777734621804e+307 -> -709.55399186002705 -1.5707963267948966
+asinh0208 asinh 1.6025136110019349e+308 0.0 -> 710.3609292261076 0.0
+asinh0209 asinh 1.3927819858239114e+308 -0.0 -> 710.22065899832899 -0.0
+asinh0210 asinh -6.0442994056210995e+307 0.0 -> -709.38588631057621 0.0
+asinh0211 asinh -1.2775271979042634e+308 -0.0 -> -710.13428215553972 -0.0
+asinh0212 asinh 1.0687496260268489e+308 1.0255615699476961 -> 709.95584521407841 9.5959010882679093e-309
+asinh0213 asinh 1.0050967333370962e+308 -0.87668970117333433 -> 709.89443961168183 -8.7224410556242882e-309
+asinh0214 asinh -5.7161452814862392e+307 8.2377808413450122 -> -709.33006540611166 1.4411426644501116e-307
+asinh0215 asinh -8.2009040727653315e+307 -6.407409526654976 -> -709.69101513070109 -7.8130526461510088e-308
+asinh0216 asinh 6.4239368496483982 1.6365990821551427e+308 -> 710.38197618101287 1.5707963267948966
+asinh0217 asinh 5.4729111423315882 -1.1227237438144211e+308 -> 710.00511346983546 -1.5707963267948966
+asinh0218 asinh -8.3455818297412723 1.443172020182019e+308 -> -710.25619930551818 1.5707963267948966
+asinh0219 asinh -2.6049726230372441 -1.7952291144022702e+308 -> -710.47448847685644 -1.5707963267948966
+
+-- values near 0
+asinh0220 asinh 1.2940113339664088e-314 6.9169190417774516e-323 -> 1.2940113339664088e-314 6.9169190417774516e-323
+asinh0221 asinh 2.3848478863874649e-315 -3.1907655025717717e-310 -> 2.3848478863874649e-315 -3.1907655025717717e-310
+asinh0222 asinh -3.0097643679641622e-316 4.6936236354918422e-322 -> -3.0097643679641622e-316 4.6936236354918422e-322
+asinh0223 asinh -1.787997087755751e-308 -8.5619622834902341e-310 -> -1.787997087755751e-308 -8.5619622834902341e-310
+asinh0224 asinh 0.0 1.2491433448427325e-314 -> 0.0 1.2491433448427325e-314
+asinh0225 asinh -0.0 2.5024072154538062e-308 -> -0.0 2.5024072154538062e-308
+asinh0226 asinh 0.0 -2.9643938750474793e-323 -> 0.0 -2.9643938750474793e-323
+asinh0227 asinh -0.0 -2.9396905927554169e-320 -> -0.0 -2.9396905927554169e-320
+asinh0228 asinh 5.64042930029359e-317 0.0 -> 5.64042930029359e-317 0.0
+asinh0229 asinh 3.3833911866596068e-318 -0.0 -> 3.3833911866596068e-318 -0.0
+asinh0230 asinh -4.9406564584124654e-324 0.0 -> -4.9406564584124654e-324 0.0
+asinh0231 asinh -2.2211379227994845e-308 -0.0 -> -2.2211379227994845e-308 -0.0
+
+-- special values
+asinh1000 asinh 0.0 0.0 -> 0.0 0.0
+asinh1001 asinh 0.0 -0.0 -> 0.0 -0.0
+asinh1002 asinh -0.0 0.0 -> -0.0 0.0
+asinh1003 asinh -0.0 -0.0 -> -0.0 -0.0
+asinh1004 asinh 0.0 inf -> inf 1.5707963267948966
+asinh1005 asinh 2.3 inf -> inf 1.5707963267948966
+asinh1006 asinh 0.0 nan -> nan nan
+asinh1007 asinh 2.3 nan -> nan nan
+asinh1008 asinh inf 0.0 -> inf 0.0
+asinh1009 asinh inf 2.3 -> inf 0.0
+asinh1010 asinh inf inf -> inf 0.78539816339744828
+asinh1011 asinh inf nan -> inf nan
+asinh1012 asinh nan 0.0 -> nan 0.0
+asinh1013 asinh nan 2.3 -> nan nan
+asinh1014 asinh nan inf -> inf nan                      ignore-real-sign
+asinh1015 asinh nan nan -> nan nan
+asinh1016 asinh 0.0 -inf -> inf -1.5707963267948966
+asinh1017 asinh 2.3 -inf -> inf -1.5707963267948966
+asinh1018 asinh inf -0.0 -> inf -0.0
+asinh1019 asinh inf -2.3 -> inf -0.0
+asinh1020 asinh inf -inf -> inf -0.78539816339744828
+asinh1021 asinh nan -0.0 -> nan -0.0
+asinh1022 asinh nan -2.3 -> nan nan
+asinh1023 asinh nan -inf -> inf nan                     ignore-real-sign
+asinh1024 asinh -0.0 -inf -> -inf -1.5707963267948966
+asinh1025 asinh -2.3 -inf -> -inf -1.5707963267948966
+asinh1026 asinh -0.0 nan -> nan nan
+asinh1027 asinh -2.3 nan -> nan nan
+asinh1028 asinh -inf -0.0 -> -inf -0.0
+asinh1029 asinh -inf -2.3 -> -inf -0.0
+asinh1030 asinh -inf -inf -> -inf -0.78539816339744828
+asinh1031 asinh -inf nan -> -inf nan
+asinh1032 asinh -0.0 inf -> -inf 1.5707963267948966
+asinh1033 asinh -2.3 inf -> -inf 1.5707963267948966
+asinh1034 asinh -inf 0.0 -> -inf 0.0
+asinh1035 asinh -inf 2.3 -> -inf 0.0
+asinh1036 asinh -inf inf -> -inf 0.78539816339744828
+
+
+---------------------------
+-- atan: Inverse tangent --
+---------------------------
+
+-- zeros
+atan0000 atan 0.0 0.0 -> 0.0 0.0
+atan0001 atan 0.0 -0.0 -> 0.0 -0.0
+atan0002 atan -0.0 0.0 -> -0.0 0.0
+atan0003 atan -0.0 -0.0 -> -0.0 -0.0
+
+-- values along both sides of imaginary axis
+atan0010 atan 0.0 -9.8813129168249309e-324 -> 0.0 -9.8813129168249309e-324
+atan0011 atan -0.0 -9.8813129168249309e-324 -> -0.0 -9.8813129168249309e-324
+atan0012 atan 0.0 -1e-305 -> 0.0 -1e-305
+atan0013 atan -0.0 -1e-305 -> -0.0 -1e-305
+atan0014 atan 0.0 -1e-150 -> 0.0 -1e-150
+atan0015 atan -0.0 -1e-150 -> -0.0 -1e-150
+atan0016 atan 0.0 -9.9999999999999998e-17 -> 0.0 -9.9999999999999998e-17
+atan0017 atan -0.0 -9.9999999999999998e-17 -> -0.0 -9.9999999999999998e-17
+atan0018 atan 0.0 -0.001 -> 0.0 -0.0010000003333335333
+atan0019 atan -0.0 -0.001 -> -0.0 -0.0010000003333335333
+atan0020 atan 0.0 -0.57899999999999996 -> 0.0 -0.6609570902866303
+atan0021 atan -0.0 -0.57899999999999996 -> -0.0 -0.6609570902866303
+atan0022 atan 0.0 -0.99999999999999989 -> 0.0 -18.714973875118524
+atan0023 atan -0.0 -0.99999999999999989 -> -0.0 -18.714973875118524
+atan0024 atan 0.0 -1.0000000000000002 -> 1.5707963267948966 -18.36840028483855
+atan0025 atan -0.0 -1.0000000000000002 -> -1.5707963267948966 -18.36840028483855
+atan0026 atan 0.0 -1.0009999999999999 -> 1.5707963267948966 -3.8007011672919218
+atan0027 atan -0.0 -1.0009999999999999 -> -1.5707963267948966 -3.8007011672919218
+atan0028 atan 0.0 -2.0 -> 1.5707963267948966 -0.54930614433405489
+atan0029 atan -0.0 -2.0 -> -1.5707963267948966 -0.54930614433405489
+atan0030 atan 0.0 -20.0 -> 1.5707963267948966 -0.050041729278491265
+atan0031 atan -0.0 -20.0 -> -1.5707963267948966 -0.050041729278491265
+atan0032 atan 0.0 -10000000000000000.0 -> 1.5707963267948966 -9.9999999999999998e-17
+atan0033 atan -0.0 -10000000000000000.0 -> -1.5707963267948966 -9.9999999999999998e-17
+atan0034 atan 0.0 -9.9999999999999998e+149 -> 1.5707963267948966 -1e-150
+atan0035 atan -0.0 -9.9999999999999998e+149 -> -1.5707963267948966 -1e-150
+atan0036 atan 0.0 -1.0000000000000001e+299 -> 1.5707963267948966 -9.9999999999999999e-300
+atan0037 atan -0.0 -1.0000000000000001e+299 -> -1.5707963267948966 -9.9999999999999999e-300
+atan0038 atan 0.0 9.8813129168249309e-324 -> 0.0 9.8813129168249309e-324
+atan0039 atan -0.0 9.8813129168249309e-324 -> -0.0 9.8813129168249309e-324
+atan0040 atan 0.0 1e-305 -> 0.0 1e-305
+atan0041 atan -0.0 1e-305 -> -0.0 1e-305
+atan0042 atan 0.0 1e-150 -> 0.0 1e-150
+atan0043 atan -0.0 1e-150 -> -0.0 1e-150
+atan0044 atan 0.0 9.9999999999999998e-17 -> 0.0 9.9999999999999998e-17
+atan0045 atan -0.0 9.9999999999999998e-17 -> -0.0 9.9999999999999998e-17
+atan0046 atan 0.0 0.001 -> 0.0 0.0010000003333335333
+atan0047 atan -0.0 0.001 -> -0.0 0.0010000003333335333
+atan0048 atan 0.0 0.57899999999999996 -> 0.0 0.6609570902866303
+atan0049 atan -0.0 0.57899999999999996 -> -0.0 0.6609570902866303
+atan0050 atan 0.0 0.99999999999999989 -> 0.0 18.714973875118524
+atan0051 atan -0.0 0.99999999999999989 -> -0.0 18.714973875118524
+atan0052 atan 0.0 1.0000000000000002 -> 1.5707963267948966 18.36840028483855
+atan0053 atan -0.0 1.0000000000000002 -> -1.5707963267948966 18.36840028483855
+atan0054 atan 0.0 1.0009999999999999 -> 1.5707963267948966 3.8007011672919218
+atan0055 atan -0.0 1.0009999999999999 -> -1.5707963267948966 3.8007011672919218
+atan0056 atan 0.0 2.0 -> 1.5707963267948966 0.54930614433405489
+atan0057 atan -0.0 2.0 -> -1.5707963267948966 0.54930614433405489
+atan0058 atan 0.0 20.0 -> 1.5707963267948966 0.050041729278491265
+atan0059 atan -0.0 20.0 -> -1.5707963267948966 0.050041729278491265
+atan0060 atan 0.0 10000000000000000.0 -> 1.5707963267948966 9.9999999999999998e-17
+atan0061 atan -0.0 10000000000000000.0 -> -1.5707963267948966 9.9999999999999998e-17
+atan0062 atan 0.0 9.9999999999999998e+149 -> 1.5707963267948966 1e-150
+atan0063 atan -0.0 9.9999999999999998e+149 -> -1.5707963267948966 1e-150
+atan0064 atan 0.0 1.0000000000000001e+299 -> 1.5707963267948966 9.9999999999999999e-300
+atan0065 atan -0.0 1.0000000000000001e+299 -> -1.5707963267948966 9.9999999999999999e-300
+
+-- random inputs
+atan0100 atan -0.32538873661060214 -1.5530461550412578 -> -1.3682728427554227 -0.69451401598762041
+atan0101 atan -0.45863393495197929 -4799.1747094903594 -> -1.5707963068820623 -0.00020836916050636145
+atan0102 atan -8.3006999685976162 -2.6788890251790938 -> -1.4619862771810199 -0.034811669653327826
+atan0103 atan -1.8836307682985314 -1.1441976638861771 -> -1.1839984370871612 -0.20630956157312796
+atan0104 atan -0.00063230482407491669 -4.9312520961829485 -> -1.5707692093223147 -0.20563867743008304
+atan0105 atan -0.84278137150065946 179012.37493146997 -> -1.5707963267685969 5.5862059836425272e-06
+atan0106 atan -0.95487853984049287 14.311334539886177 -> -1.5661322859434561 0.069676024526232005
+atan0107 atan -1.3513252539663239 6.0500727021632198e-08 -> -0.93371676315220975 2.140800269742656e-08
+atan0108 atan -0.20566254458595795 0.11933771944159823 -> -0.20556463711174916 0.11493405387141732
+atan0109 atan -0.58563718795408559 0.64438965423212868 -> -0.68361089300233124 0.46759762751800249
+atan0110 atan 48.479267751948292 -78.386382460112543 -> 1.5650888770910523 -0.0092276811373297584
+atan0111 atan 1.0575373914056061 -0.75988012377296987 -> 0.94430886722043594 -0.31915698126703118
+atan0112 atan 4444810.4314677203 -0.56553404593942558 -> 1.5707961018134231 -2.8625446437701909e-14
+atan0113 atan 0.010101405082520009 -0.032932668550282478 -> 0.01011202676646334 -0.032941214776834996
+atan0114 atan 1.5353585300154911 -2.1947099346796519 -> 1.3400310739206394 -0.29996003607449045
+atan0115 atan 0.21869457055670882 9.9915684254007093 -> 1.5685846078876444 0.1003716881759439
+atan0116 atan 0.17783290150246836 0.064334689863650957 -> 0.17668728064286277 0.062435808728873846
+atan0117 atan 15.757474087615918 383.57262142534 -> 1.5706894060369621 0.0026026817278826603
+atan0118 atan 10.587017408533317 0.21720238081843438 -> 1.4766594681336236 0.0019199097383010061
+atan0119 atan 0.86026078678781204 0.1230148609359502 -> 0.7147259322534929 0.070551221954286605
+
+-- values near infinity
+atan0200 atan 7.8764397011195798e+307 8.1647921137746308e+307 -> 1.5707963267948966 6.3439446939604493e-309
+atan0201 atan 1.5873698696131487e+308 -1.0780367422960641e+308 -> 1.5707963267948966 -2.9279309368530781e-309
+atan0202 atan -1.5844551864825834e+308 1.0290657809098675e+308 -> -1.5707963267948966 2.8829614736961417e-309
+atan0203 atan -1.3168792562524032e+308 -9.088432341614825e+307 -> -1.5707963267948966 -3.5499373057390056e-309
+atan0204 atan 0.0 1.0360465742258337e+308 -> 1.5707963267948966 9.6520757355646018e-309
+atan0205 atan -0.0 1.0045063210373196e+308 -> -1.5707963267948966 9.955138947929503e-309
+atan0206 atan 0.0 -9.5155296715763696e+307 -> 1.5707963267948966 -1.050913648020118e-308
+atan0207 atan -0.0 -1.5565700490496501e+308 -> -1.5707963267948966 -6.4243816114189071e-309
+atan0208 atan 1.2956339389525244e+308 0.0 -> 1.5707963267948966 0.0
+atan0209 atan 1.4408126243772151e+308 -0.0 -> 1.5707963267948966 -0.0
+atan0210 atan -1.0631786461936417e+308 0.0 -> -1.5707963267948966 0.0
+atan0211 atan -1.0516056964171069e+308 -0.0 -> -1.5707963267948966 -0.0
+atan0212 atan 1.236162319603838e+308 4.6827953496242936 -> 1.5707963267948966 0.0
+atan0213 atan 7.000516472897218e+307 -5.8631608017844163 -> 1.5707963267948966 -0.0
+atan0214 atan -1.5053444003338508e+308 5.1199197268420313 -> -1.5707963267948966 0.0
+atan0215 atan -1.399172518147259e+308 -3.5687766472913673 -> -1.5707963267948966 -0.0
+atan0216 atan 8.1252833070803021 6.2782953917343822e+307 -> 1.5707963267948966 1.5927890256908564e-308
+atan0217 atan 2.8034285947515167 -1.3378049775753878e+308 -> 1.5707963267948966 -7.4749310756219562e-309
+atan0218 atan -1.4073509988974953 1.6776381785968355e+308 -> -1.5707963267948966 5.9607608646364569e-309
+atan0219 atan -2.7135551527592119 -1.281567445525738e+308 -> -1.5707963267948966 -7.8029447727565326e-309
+
+-- imaginary part = +/-1, real part tiny
+atan0300 atan -1e-150 -1.0 -> -0.78539816339744828 -173.04045556483339
+atan0301 atan 1e-155 1.0 -> 0.78539816339744828 178.79691829731851
+atan0302 atan 9.9999999999999999e-161 -1.0 -> 0.78539816339744828 -184.55338102980363
+atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875
+atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692
+
+-- special values
+atan1000 atan -0.0 0.0 -> -0.0 0.0
+atan1001 atan nan 0.0 -> nan 0.0
+atan1002 atan -0.0 1.0 -> -0.0 inf divide-by-zero
+atan1003 atan -inf 0.0 -> -1.5707963267948966 0.0
+atan1004 atan -inf 2.2999999999999998 -> -1.5707963267948966 0.0
+atan1005 atan nan 2.2999999999999998 -> nan nan
+atan1006 atan -0.0 inf -> -1.5707963267948966 0.0
+atan1007 atan -2.2999999999999998 inf -> -1.5707963267948966 0.0
+atan1008 atan -inf inf -> -1.5707963267948966 0.0
+atan1009 atan nan inf -> nan 0.0
+atan1010 atan -0.0 nan -> nan nan
+atan1011 atan -2.2999999999999998 nan -> nan nan
+atan1012 atan -inf nan -> -1.5707963267948966 0.0 ignore-imag-sign
+atan1013 atan nan nan -> nan nan
+atan1014 atan 0.0 0.0 -> 0.0 0.0
+atan1015 atan 0.0 1.0 -> 0.0 inf divide-by-zero
+atan1016 atan inf 0.0 -> 1.5707963267948966 0.0
+atan1017 atan inf 2.2999999999999998 -> 1.5707963267948966 0.0
+atan1018 atan 0.0 inf -> 1.5707963267948966 0.0
+atan1019 atan 2.2999999999999998 inf -> 1.5707963267948966 0.0
+atan1020 atan inf inf -> 1.5707963267948966 0.0
+atan1021 atan 0.0 nan -> nan nan
+atan1022 atan 2.2999999999999998 nan -> nan nan
+atan1023 atan inf nan -> 1.5707963267948966 0.0 ignore-imag-sign
+atan1024 atan 0.0 -0.0 -> 0.0 -0.0
+atan1025 atan nan -0.0 -> nan -0.0
+atan1026 atan 0.0 -1.0 -> 0.0 -inf divide-by-zero
+atan1027 atan inf -0.0 -> 1.5707963267948966 -0.0
+atan1028 atan inf -2.2999999999999998 -> 1.5707963267948966 -0.0
+atan1029 atan nan -2.2999999999999998 -> nan nan
+atan1030 atan 0.0 -inf -> 1.5707963267948966 -0.0
+atan1031 atan 2.2999999999999998 -inf -> 1.5707963267948966 -0.0
+atan1032 atan inf -inf -> 1.5707963267948966 -0.0
+atan1033 atan nan -inf -> nan -0.0
+atan1034 atan -0.0 -0.0 -> -0.0 -0.0
+atan1035 atan -0.0 -1.0 -> -0.0 -inf divide-by-zero
+atan1036 atan -inf -0.0 -> -1.5707963267948966 -0.0
+atan1037 atan -inf -2.2999999999999998 -> -1.5707963267948966 -0.0
+atan1038 atan -0.0 -inf -> -1.5707963267948966 -0.0
+atan1039 atan -2.2999999999999998 -inf -> -1.5707963267948966 -0.0
+atan1040 atan -inf -inf -> -1.5707963267948966 -0.0
+
+
+---------------------------------------
+-- atanh: Inverse hyperbolic tangent --
+---------------------------------------
+
+-- zeros
+atanh0000 atanh 0.0 0.0 -> 0.0 0.0
+atanh0001 atanh 0.0 -0.0 -> 0.0 -0.0
+atanh0002 atanh -0.0 0.0 -> -0.0 0.0
+atanh0003 atanh -0.0 -0.0 -> -0.0 -0.0
+
+-- values along both sides of real axis
+atanh0010 atanh -9.8813129168249309e-324 0.0 -> -9.8813129168249309e-324 0.0
+atanh0011 atanh -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0
+atanh0012 atanh -1e-305 0.0 -> -1e-305 0.0
+atanh0013 atanh -1e-305 -0.0 -> -1e-305 -0.0
+atanh0014 atanh -1e-150 0.0 -> -1e-150 0.0
+atanh0015 atanh -1e-150 -0.0 -> -1e-150 -0.0
+atanh0016 atanh -9.9999999999999998e-17 0.0 -> -9.9999999999999998e-17 0.0
+atanh0017 atanh -9.9999999999999998e-17 -0.0 -> -9.9999999999999998e-17 -0.0
+atanh0018 atanh -0.001 0.0 -> -0.0010000003333335333 0.0
+atanh0019 atanh -0.001 -0.0 -> -0.0010000003333335333 -0.0
+atanh0020 atanh -0.57899999999999996 0.0 -> -0.6609570902866303 0.0
+atanh0021 atanh -0.57899999999999996 -0.0 -> -0.6609570902866303 -0.0
+atanh0022 atanh -0.99999999999999989 0.0 -> -18.714973875118524 0.0
+atanh0023 atanh -0.99999999999999989 -0.0 -> -18.714973875118524 -0.0
+atanh0024 atanh -1.0000000000000002 0.0 -> -18.36840028483855 1.5707963267948966
+atanh0025 atanh -1.0000000000000002 -0.0 -> -18.36840028483855 -1.5707963267948966
+atanh0026 atanh -1.0009999999999999 0.0 -> -3.8007011672919218 1.5707963267948966
+atanh0027 atanh -1.0009999999999999 -0.0 -> -3.8007011672919218 -1.5707963267948966
+atanh0028 atanh -2.0 0.0 -> -0.54930614433405489 1.5707963267948966
+atanh0029 atanh -2.0 -0.0 -> -0.54930614433405489 -1.5707963267948966
+atanh0030 atanh -23.0 0.0 -> -0.043505688494814884 1.5707963267948966
+atanh0031 atanh -23.0 -0.0 -> -0.043505688494814884 -1.5707963267948966
+atanh0032 atanh -10000000000000000.0 0.0 -> -9.9999999999999998e-17 1.5707963267948966
+atanh0033 atanh -10000000000000000.0 -0.0 -> -9.9999999999999998e-17 -1.5707963267948966
+atanh0034 atanh -9.9999999999999998e+149 0.0 -> -1e-150 1.5707963267948966
+atanh0035 atanh -9.9999999999999998e+149 -0.0 -> -1e-150 -1.5707963267948966
+atanh0036 atanh -1.0000000000000001e+299 0.0 -> -9.9999999999999999e-300 1.5707963267948966
+atanh0037 atanh -1.0000000000000001e+299 -0.0 -> -9.9999999999999999e-300 -1.5707963267948966
+atanh0038 atanh 9.8813129168249309e-324 0.0 -> 9.8813129168249309e-324 0.0
+atanh0039 atanh 9.8813129168249309e-324 -0.0 -> 9.8813129168249309e-324 -0.0
+atanh0040 atanh 1e-305 0.0 -> 1e-305 0.0
+atanh0041 atanh 1e-305 -0.0 -> 1e-305 -0.0
+atanh0042 atanh 1e-150 0.0 -> 1e-150 0.0
+atanh0043 atanh 1e-150 -0.0 -> 1e-150 -0.0
+atanh0044 atanh 9.9999999999999998e-17 0.0 -> 9.9999999999999998e-17 0.0
+atanh0045 atanh 9.9999999999999998e-17 -0.0 -> 9.9999999999999998e-17 -0.0
+atanh0046 atanh 0.001 0.0 -> 0.0010000003333335333 0.0
+atanh0047 atanh 0.001 -0.0 -> 0.0010000003333335333 -0.0
+atanh0048 atanh 0.57899999999999996 0.0 -> 0.6609570902866303 0.0
+atanh0049 atanh 0.57899999999999996 -0.0 -> 0.6609570902866303 -0.0
+atanh0050 atanh 0.99999999999999989 0.0 -> 18.714973875118524 0.0
+atanh0051 atanh 0.99999999999999989 -0.0 -> 18.714973875118524 -0.0
+atanh0052 atanh 1.0000000000000002 0.0 -> 18.36840028483855 1.5707963267948966
+atanh0053 atanh 1.0000000000000002 -0.0 -> 18.36840028483855 -1.5707963267948966
+atanh0054 atanh 1.0009999999999999 0.0 -> 3.8007011672919218 1.5707963267948966
+atanh0055 atanh 1.0009999999999999 -0.0 -> 3.8007011672919218 -1.5707963267948966
+atanh0056 atanh 2.0 0.0 -> 0.54930614433405489 1.5707963267948966
+atanh0057 atanh 2.0 -0.0 -> 0.54930614433405489 -1.5707963267948966
+atanh0058 atanh 23.0 0.0 -> 0.043505688494814884 1.5707963267948966
+atanh0059 atanh 23.0 -0.0 -> 0.043505688494814884 -1.5707963267948966
+atanh0060 atanh 10000000000000000.0 0.0 -> 9.9999999999999998e-17 1.5707963267948966
+atanh0061 atanh 10000000000000000.0 -0.0 -> 9.9999999999999998e-17 -1.5707963267948966
+atanh0062 atanh 9.9999999999999998e+149 0.0 -> 1e-150 1.5707963267948966
+atanh0063 atanh 9.9999999999999998e+149 -0.0 -> 1e-150 -1.5707963267948966
+atanh0064 atanh 1.0000000000000001e+299 0.0 -> 9.9999999999999999e-300 1.5707963267948966
+atanh0065 atanh 1.0000000000000001e+299 -0.0 -> 9.9999999999999999e-300 -1.5707963267948966
+
+-- random inputs
+atanh0100 atanh -0.54460925980633501 -0.54038050126721027 -> -0.41984265808446974 -0.60354153938352828
+atanh0101 atanh -1.6934614269829051 -0.48807386108113621 -> -0.58592769102243281 -1.3537837470975898
+atanh0102 atanh -1.3467293985501207 -0.47868354895395876 -> -0.69961624370709985 -1.1994450156570076
+atanh0103 atanh -5.6142232418984888 -544551613.39307702 -> -1.8932657550925744e-17 -1.5707963249585235
+atanh0104 atanh -0.011841460381263651 -3.259978899823385 -> -0.0010183936547405188 -1.2731614020743838
+atanh0105 atanh -0.0073345736950029532 0.35821949670922248 -> -0.0065004869024682466 0.34399359971920895
+atanh0106 atanh -13.866782244320014 0.9541129545860273 -> -0.071896852055058899 1.5658322704631409
+atanh0107 atanh -708.59964982780775 21.984802159266675 -> -0.0014098779074189741 1.5707525842838959
+atanh0108 atanh -30.916832076030602 1.3691897138829843 -> -0.032292682045743676 1.5693652094847115
+atanh0109 atanh -0.57461806339861754 0.29534797443913063 -> -0.56467464472482765 0.39615612824172625
+atanh0110 atanh 0.40089246737415685 -1.632285984300659 -> 0.1063832707890608 -1.0402821335326482
+atanh0111 atanh 2119.6167688262176 -1.5383653437377242e+17 -> 8.9565008518382049e-32 -1.5707963267948966
+atanh0112 atanh 756.86017850941641 -6.6064087133223817 -> 0.0013211481136820046 -1.5707847948702234
+atanh0113 atanh 4.0490617718041602 -2.5784456791040652e-12 -> 0.25218425538553618 -1.5707963267947291
+atanh0114 atanh 10.589254957173523 -0.13956391149624509 -> 0.094700890282197664 -1.5695407140217623
+atanh0115 atanh 1.0171187553160499 0.70766113465354019 -> 0.55260251975367791 0.96619711116641682
+atanh0116 atanh 0.031645502527750849 0.067319983726544394 -> 0.031513018344086742 0.067285437670549036
+atanh0117 atanh 0.13670177624994517 0.43240089361857947 -> 0.11538933151017253 0.41392008145336212
+atanh0118 atanh 0.64173899243596688 2.9008577686695256 -> 0.065680142424134405 1.2518535724053921
+atanh0119 atanh 0.19313813528025942 38.799619150741869 -> 0.00012820765917366644 1.5450292202823612
+
+-- values near infinity
+atanh0200 atanh 5.3242646831347954e+307 1.3740396080084153e+308 -> 2.4519253616695576e-309 1.5707963267948966
+atanh0201 atanh 1.158701641241358e+308 -6.5579268873375853e+307 -> 6.5365375267795098e-309 -1.5707963267948966
+atanh0202 atanh -1.3435325735762247e+308 9.8947369259601547e+307 -> -4.8256680906589956e-309 1.5707963267948966
+atanh0203 atanh -1.4359857522598942e+308 -9.4701204702391004e+307 -> -4.8531282262872645e-309 -1.5707963267948966
+atanh0204 atanh 0.0 5.6614181068098497e+307 -> 0.0 1.5707963267948966
+atanh0205 atanh -0.0 6.9813212721450139e+307 -> -0.0 1.5707963267948966
+atanh0206 atanh 0.0 -7.4970613060311453e+307 -> 0.0 -1.5707963267948966
+atanh0207 atanh -0.0 -1.5280601880314068e+308 -> -0.0 -1.5707963267948966
+atanh0208 atanh 8.2219472336000745e+307 0.0 -> 1.2162568933954813e-308 1.5707963267948966
+atanh0209 atanh 1.4811519617280899e+308 -0.0 -> 6.7515017083951325e-309 -1.5707963267948966
+atanh0210 atanh -1.2282016263598785e+308 0.0 -> -8.1419856360537615e-309 1.5707963267948966
+atanh0211 atanh -1.0616427760154426e+308 -0.0 -> -9.4193642399489563e-309 -1.5707963267948966
+atanh0212 atanh 1.2971536510180682e+308 5.2847948452333293 -> 7.7091869510998328e-309 1.5707963267948966
+atanh0213 atanh 1.1849860977411851e+308 -7.9781906447459949 -> 8.4389175696339014e-309 -1.5707963267948966
+atanh0214 atanh -1.4029969422586635e+308 0.93891986543663375 -> -7.127599283218073e-309 1.5707963267948966
+atanh0215 atanh -4.7508098912248211e+307 -8.2702421247039908 -> -2.1049042645278043e-308 -1.5707963267948966
+atanh0216 atanh 8.2680742115769998 8.1153898410918065e+307 -> 0.0 1.5707963267948966
+atanh0217 atanh 1.2575325146218885 -1.4746679147661649e+308 -> 0.0 -1.5707963267948966
+atanh0218 atanh -2.4618803682310899 1.3781522717005568e+308 -> -0.0 1.5707963267948966
+atanh0219 atanh -4.0952386694788112 -1.231083376353703e+308 -> -0.0 -1.5707963267948966
+
+-- values near 0
+atanh0220 atanh 3.8017563659811628e-314 2.6635484239074319e-312 -> 3.8017563659811628e-314 2.6635484239074319e-312
+atanh0221 atanh 1.7391110733611878e-321 -4.3547800672541419e-313 -> 1.7391110733611878e-321 -4.3547800672541419e-313
+atanh0222 atanh -5.9656816081325078e-317 9.9692253555416263e-313 -> -5.9656816081325078e-317 9.9692253555416263e-313
+atanh0223 atanh -6.5606671178400239e-313 -2.1680936406357335e-309 -> -6.5606671178400239e-313 -2.1680936406357335e-309
+atanh0224 atanh 0.0 2.5230944401820779e-319 -> 0.0 2.5230944401820779e-319
+atanh0225 atanh -0.0 5.6066569490064658e-320 -> -0.0 5.6066569490064658e-320
+atanh0226 atanh 0.0 -2.4222487249468377e-317 -> 0.0 -2.4222487249468377e-317
+atanh0227 atanh -0.0 -3.0861101089206037e-316 -> -0.0 -3.0861101089206037e-316
+atanh0228 atanh 3.1219222884393986e-310 0.0 -> 3.1219222884393986e-310 0.0
+atanh0229 atanh 9.8926337564976196e-309 -0.0 -> 9.8926337564976196e-309 -0.0
+atanh0230 atanh -1.5462535092918154e-312 0.0 -> -1.5462535092918154e-312 0.0
+atanh0231 atanh -9.8813129168249309e-324 -0.0 -> -9.8813129168249309e-324 -0.0
+
+-- real part = +/-1, imaginary part tiny
+atanh0300 atanh 1.0 1e-153 -> 176.49433320432448 0.78539816339744828
+atanh0301 atanh 1.0 9.9999999999999997e-155 -> 177.64562575082149 0.78539816339744828
+atanh0302 atanh -1.0 1e-161 -> -185.70467357630065 0.78539816339744828
+atanh0303 atanh 1.0 -1e-165 -> 190.30984376228875 -0.78539816339744828
+atanh0304 atanh -1.0 -9.8813129168249309e-324 -> -372.22003596069061 -0.78539816339744828
+
+-- special values
+atanh1000 atanh 0.0 0.0 -> 0.0 0.0
+atanh1001 atanh 0.0 nan -> 0.0 nan
+atanh1002 atanh 1.0 0.0 -> inf 0.0                      divide-by-zero
+atanh1003 atanh 0.0 inf -> 0.0 1.5707963267948966
+atanh1004 atanh 2.3 inf -> 0.0 1.5707963267948966
+atanh1005 atanh 2.3 nan -> nan nan
+atanh1006 atanh inf 0.0 -> 0.0 1.5707963267948966
+atanh1007 atanh inf 2.3 -> 0.0 1.5707963267948966
+atanh1008 atanh inf inf -> 0.0 1.5707963267948966
+atanh1009 atanh inf nan -> 0.0 nan
+atanh1010 atanh nan 0.0 -> nan nan
+atanh1011 atanh nan 2.3 -> nan nan
+atanh1012 atanh nan inf -> 0.0 1.5707963267948966       ignore-real-sign
+atanh1013 atanh nan nan -> nan nan
+atanh1014 atanh 0.0 -0.0 -> 0.0 -0.0
+atanh1015 atanh 1.0 -0.0 -> inf -0.0                    divide-by-zero
+atanh1016 atanh 0.0 -inf -> 0.0 -1.5707963267948966
+atanh1017 atanh 2.3 -inf -> 0.0 -1.5707963267948966
+atanh1018 atanh inf -0.0 -> 0.0 -1.5707963267948966
+atanh1019 atanh inf -2.3 -> 0.0 -1.5707963267948966
+atanh1020 atanh inf -inf -> 0.0 -1.5707963267948966
+atanh1021 atanh nan -0.0 -> nan nan
+atanh1022 atanh nan -2.3 -> nan nan
+atanh1023 atanh nan -inf -> 0.0 -1.5707963267948966     ignore-real-sign
+atanh1024 atanh -0.0 -0.0 -> -0.0 -0.0
+atanh1025 atanh -0.0 nan -> -0.0 nan
+atanh1026 atanh -1.0 -0.0 -> -inf -0.0                  divide-by-zero
+atanh1027 atanh -0.0 -inf -> -0.0 -1.5707963267948966
+atanh1028 atanh -2.3 -inf -> -0.0 -1.5707963267948966
+atanh1029 atanh -2.3 nan -> nan nan
+atanh1030 atanh -inf -0.0 -> -0.0 -1.5707963267948966
+atanh1031 atanh -inf -2.3 -> -0.0 -1.5707963267948966
+atanh1032 atanh -inf -inf -> -0.0 -1.5707963267948966
+atanh1033 atanh -inf nan -> -0.0 nan
+atanh1034 atanh -0.0 0.0 -> -0.0 0.0
+atanh1035 atanh -1.0 0.0 -> -inf 0.0                    divide-by-zero
+atanh1036 atanh -0.0 inf -> -0.0 1.5707963267948966
+atanh1037 atanh -2.3 inf -> -0.0 1.5707963267948966
+atanh1038 atanh -inf 0.0 -> -0.0 1.5707963267948966
+atanh1039 atanh -inf 2.3 -> -0.0 1.5707963267948966
+atanh1040 atanh -inf inf -> -0.0 1.5707963267948966
+
+
+----------------------------
+-- log: Natural logarithm --
+----------------------------
+
+log0000 log 1.0 0.0 -> 0.0 0.0
+log0001 log 1.0 -0.0 -> 0.0 -0.0
+log0002 log -1.0 0.0 -> 0.0 3.1415926535897931
+log0003 log -1.0 -0.0 -> 0.0 -3.1415926535897931
+-- values along both sides of real axis
+log0010 log -9.8813129168249309e-324 0.0 -> -743.74692474082133 3.1415926535897931
+log0011 log -9.8813129168249309e-324 -0.0 -> -743.74692474082133 -3.1415926535897931
+log0012 log -1e-305 0.0 -> -702.28845336318398 3.1415926535897931
+log0013 log -1e-305 -0.0 -> -702.28845336318398 -3.1415926535897931
+log0014 log -1e-150 0.0 -> -345.38776394910684 3.1415926535897931
+log0015 log -1e-150 -0.0 -> -345.38776394910684 -3.1415926535897931
+log0016 log -9.9999999999999998e-17 0.0 -> -36.841361487904734 3.1415926535897931
+log0017 log -9.9999999999999998e-17 -0.0 -> -36.841361487904734 -3.1415926535897931
+log0018 log -0.001 0.0 -> -6.9077552789821368 3.1415926535897931
+log0019 log -0.001 -0.0 -> -6.9077552789821368 -3.1415926535897931
+log0020 log -0.57899999999999996 0.0 -> -0.54645280140914188 3.1415926535897931
+log0021 log -0.57899999999999996 -0.0 -> -0.54645280140914188 -3.1415926535897931
+log0022 log -0.99999999999999989 0.0 -> -1.1102230246251565e-16 3.1415926535897931
+log0023 log -0.99999999999999989 -0.0 -> -1.1102230246251565e-16 -3.1415926535897931
+log0024 log -1.0000000000000002 0.0 -> 2.2204460492503128e-16 3.1415926535897931
+log0025 log -1.0000000000000002 -0.0 -> 2.2204460492503128e-16 -3.1415926535897931
+log0026 log -1.0009999999999999 0.0 -> 0.00099950033308342321 3.1415926535897931
+log0027 log -1.0009999999999999 -0.0 -> 0.00099950033308342321 -3.1415926535897931
+log0028 log -2.0 0.0 -> 0.69314718055994529 3.1415926535897931
+log0029 log -2.0 -0.0 -> 0.69314718055994529 -3.1415926535897931
+log0030 log -23.0 0.0 -> 3.1354942159291497 3.1415926535897931
+log0031 log -23.0 -0.0 -> 3.1354942159291497 -3.1415926535897931
+log0032 log -10000000000000000.0 0.0 -> 36.841361487904734 3.1415926535897931
+log0033 log -10000000000000000.0 -0.0 -> 36.841361487904734 -3.1415926535897931
+log0034 log -9.9999999999999998e+149 0.0 -> 345.38776394910684 3.1415926535897931
+log0035 log -9.9999999999999998e+149 -0.0 -> 345.38776394910684 -3.1415926535897931
+log0036 log -1.0000000000000001e+299 0.0 -> 688.47294280521965 3.1415926535897931
+log0037 log -1.0000000000000001e+299 -0.0 -> 688.47294280521965 -3.1415926535897931
+log0038 log 9.8813129168249309e-324 0.0 -> -743.74692474082133 0.0
+log0039 log 9.8813129168249309e-324 -0.0 -> -743.74692474082133 -0.0
+log0040 log 1e-305 0.0 -> -702.28845336318398 0.0
+log0041 log 1e-305 -0.0 -> -702.28845336318398 -0.0
+log0042 log 1e-150 0.0 -> -345.38776394910684 0.0
+log0043 log 1e-150 -0.0 -> -345.38776394910684 -0.0
+log0044 log 9.9999999999999998e-17 0.0 -> -36.841361487904734 0.0
+log0045 log 9.9999999999999998e-17 -0.0 -> -36.841361487904734 -0.0
+log0046 log 0.001 0.0 -> -6.9077552789821368 0.0
+log0047 log 0.001 -0.0 -> -6.9077552789821368 -0.0
+log0048 log 0.57899999999999996 0.0 -> -0.54645280140914188 0.0
+log0049 log 0.57899999999999996 -0.0 -> -0.54645280140914188 -0.0
+log0050 log 0.99999999999999989 0.0 -> -1.1102230246251565e-16 0.0
+log0051 log 0.99999999999999989 -0.0 -> -1.1102230246251565e-16 -0.0
+log0052 log 1.0000000000000002 0.0 -> 2.2204460492503128e-16 0.0
+log0053 log 1.0000000000000002 -0.0 -> 2.2204460492503128e-16 -0.0
+log0054 log 1.0009999999999999 0.0 -> 0.00099950033308342321 0.0
+log0055 log 1.0009999999999999 -0.0 -> 0.00099950033308342321 -0.0
+log0056 log 2.0 0.0 -> 0.69314718055994529 0.0
+log0057 log 2.0 -0.0 -> 0.69314718055994529 -0.0
+log0058 log 23.0 0.0 -> 3.1354942159291497 0.0
+log0059 log 23.0 -0.0 -> 3.1354942159291497 -0.0
+log0060 log 10000000000000000.0 0.0 -> 36.841361487904734 0.0
+log0061 log 10000000000000000.0 -0.0 -> 36.841361487904734 -0.0
+log0062 log 9.9999999999999998e+149 0.0 -> 345.38776394910684 0.0
+log0063 log 9.9999999999999998e+149 -0.0 -> 345.38776394910684 -0.0
+log0064 log 1.0000000000000001e+299 0.0 -> 688.47294280521965 0.0
+log0065 log 1.0000000000000001e+299 -0.0 -> 688.47294280521965 -0.0
+
+-- random inputs
+log0066 log -1.9830454945186191e-16 -2.0334448025673346 -> 0.70973130194329803 -1.5707963267948968
+log0067 log -0.96745853024741857 -0.84995816228299692 -> 0.25292811398722387 -2.4207570438536905
+log0068 log -0.1603644313948418 -0.2929942111041835 -> -1.0965857872427374 -2.0715870859971419
+log0069 log -0.15917913168438699 -0.25238799251132177 -> -1.2093477313249901 -2.1334784232033863
+log0070 log -0.68907818535078802 -3.0693105853476346 -> 1.1460398629184565 -1.7916403813913211
+log0071 log -17.268133447565589 6.8165120014604756 -> 2.9212694465974836 2.7656245081603164
+log0072 log -1.7153894479690328 26.434055372802636 -> 3.2767542953718003 1.6355986276341734
+log0073 log -8.0456794648936578e-06 0.19722758057570208 -> -1.6233969848296075 1.5708371206810101
+log0074 log -2.4306442691323173 0.6846919750700996 -> 0.92633592001969589 2.8670160576718331
+log0075 log -3.5488049250888194 0.45324040643185254 -> 1.2747008374256426 3.0145640007885111
+log0076 log 0.18418516851510189 -0.26062518836212617 -> -1.1421287121940344 -0.95558440841183434
+log0077 log 2.7124837795638399 -13.148769067133387 -> 2.5971659975706802 -1.3673583045209439
+log0078 log 3.6521275476169149e-13 -3.7820543023170673e-05 -> -10.182658136741569 -1.5707963171384316
+log0079 log 5.0877545813862239 -1.2834978326786852 -> 1.6576856213076328 -0.24711583497738485
+log0080 log 0.26477986808461512 -0.67659001194187429 -> -0.31944085207999973 -1.197773671987121
+log0081 log 0.0014754261398071962 5.3514691608205442 -> 1.6773711707153829 1.5705206219261802
+log0082 log 0.29667334462157885 0.00020056045042584795 -> -1.2151233667079588 0.00067603114168689204
+log0083 log 0.82104233671099425 3.9005387130133102 -> 1.3827918965299593 1.3633304701848363
+log0084 log 0.27268135358180667 124.42088110945804 -> 4.8236724223559229 1.5686047258789015
+log0085 log 0.0026286959168267485 0.47795808180573013 -> -0.73821712137809126 1.5652965360960087
+
+-- values near infinity
+log0100 log 1.0512025744003172e+308 7.2621669750664611e+307 -> 709.44123967814494 0.60455434048332968
+log0101 log 5.5344249034372126e+307 -1.2155859158431275e+308 -> 709.48562300345679 -1.143553056717973
+log0102 log -1.3155575403469408e+308 1.1610793541663864e+308 -> 709.75847809546428 2.41848796504974
+log0103 log -1.632366720973235e+308 -1.54299446211448e+308 -> 710.00545236515586 -2.3843326028455087
+log0104 log 0.0 5.9449276692327712e+307 -> 708.67616191258526 1.5707963267948966
+log0105 log -0.0 1.1201850459025692e+308 -> 709.30970253338171 1.5707963267948966
+log0106 log 0.0 -1.6214225933466528e+308 -> 709.6795125501086 -1.5707963267948966
+log0107 log -0.0 -1.7453269791591058e+308 -> 709.75315056087379 -1.5707963267948966
+log0108 log 1.440860577601428e+308 0.0 -> 709.56144920058262 0.0
+log0109 log 1.391515176148282e+308 -0.0 -> 709.52660185041327 -0.0
+log0110 log -1.201354401295296e+308 0.0 -> 709.37965823023956 3.1415926535897931
+log0111 log -1.6704337825976804e+308 -0.0 -> 709.70929198492399 -3.1415926535897931
+log0112 log 7.2276974655190223e+307 7.94879711369164 -> 708.87154406512104 1.0997689307850458e-307
+log0113 log 1.1207859593716076e+308 -6.1956200868221147 -> 709.31023883080104 -5.5279244310803286e-308
+log0114 log -4.6678933874471045e+307 9.947107893220382 -> 708.43433142431388 3.1415926535897931
+log0115 log -1.5108012453950142e+308 -5.3117197179375619 -> 709.60884877835008 -3.1415926535897931
+log0116 log 7.4903750871504435 1.5320703776626352e+308 -> 709.62282865085137 1.5707963267948966
+log0117 log 5.9760325525654778 -8.0149473997349123e+307 -> 708.97493177248396 -1.5707963267948966
+log0118 log -7.880194206386629 1.7861845814767441e+308 -> 709.77629046837137 1.5707963267948966
+log0119 log -9.886438993852865 -6.19235781080747e+307 -> 708.71693946977302 -1.5707963267948966
+
+-- values near 0
+log0120 log 2.2996867579227779e-308 6.7861840770939125e-312 -> -708.36343567717392 0.00029509166223339815
+log0121 log 6.9169190417774516e-323 -9.0414013188948118e-322 -> -739.22766796468386 -1.4944423210001669
+log0122 log -1.5378064962914011e-316 1.8243628389354635e-310 -> -713.20014803142965 1.5707971697228842
+log0123 log -2.3319898483706837e-321 -2.2358763941866371e-313 -> -719.9045008332522 -1.570796337224766
+log0124 log 0.0 3.872770101081121e-315 -> -723.96033425374401 1.5707963267948966
+log0125 log -0.0 9.6342800939043076e-322 -> -739.16707236281752 1.5707963267948966
+log0126 log 0.0 -2.266099393427834e-308 -> -708.37814861757965 -1.5707963267948966
+log0127 log -0.0 -2.1184695673766626e-315 -> -724.56361036731812 -1.5707963267948966
+log0128 log 1.1363509854348671e-322 0.0 -> -741.30457770545206 0.0
+log0129 log 3.5572726500569751e-322 -0.0 -> -740.16340580236522 -0.0
+log0130 log -2.3696071074040593e-310 0.0 -> -712.93865466421641 3.1415926535897931
+log0131 log -2.813283897266934e-317 -0.0 -> -728.88512203138862 -3.1415926535897931
+
+-- values near the unit circle
+log0200 log -0.59999999999999998 0.80000000000000004 -> 2.2204460492503132e-17 2.2142974355881808
+log0201 log 0.79999999999999993 0.60000000000000009 -> 6.1629758220391547e-33 0.64350110879328448
+
+-- special values
+log1000 log -0.0 0.0 -> -inf 3.1415926535897931         divide-by-zero
+log1001 log 0.0 0.0 -> -inf 0.0                         divide-by-zero
+log1002 log 0.0 inf -> inf 1.5707963267948966
+log1003 log 2.3 inf -> inf 1.5707963267948966
+log1004 log -0.0 inf -> inf 1.5707963267948966
+log1005 log -2.3 inf -> inf 1.5707963267948966
+log1006 log 0.0 nan -> nan nan
+log1007 log 2.3 nan -> nan nan
+log1008 log -0.0 nan -> nan nan
+log1009 log -2.3 nan -> nan nan
+log1010 log -inf 0.0 -> inf 3.1415926535897931
+log1011 log -inf 2.3 -> inf 3.1415926535897931
+log1012 log inf 0.0 -> inf 0.0
+log1013 log inf 2.3 -> inf 0.0
+log1014 log -inf inf -> inf 2.3561944901923448
+log1015 log inf inf -> inf 0.78539816339744828
+log1016 log inf nan -> inf nan
+log1017 log -inf nan -> inf nan
+log1018 log nan 0.0 -> nan nan
+log1019 log nan 2.3 -> nan nan
+log1020 log nan inf -> inf nan
+log1021 log nan nan -> nan nan
+log1022 log -0.0 -0.0 -> -inf -3.1415926535897931       divide-by-zero
+log1023 log 0.0 -0.0 -> -inf -0.0                       divide-by-zero
+log1024 log 0.0 -inf -> inf -1.5707963267948966
+log1025 log 2.3 -inf -> inf -1.5707963267948966
+log1026 log -0.0 -inf -> inf -1.5707963267948966
+log1027 log -2.3 -inf -> inf -1.5707963267948966
+log1028 log -inf -0.0 -> inf -3.1415926535897931
+log1029 log -inf -2.3 -> inf -3.1415926535897931
+log1030 log inf -0.0 -> inf -0.0
+log1031 log inf -2.3 -> inf -0.0
+log1032 log -inf -inf -> inf -2.3561944901923448
+log1033 log inf -inf -> inf -0.78539816339744828
+log1034 log nan -0.0 -> nan nan
+log1035 log nan -2.3 -> nan nan
+log1036 log nan -inf -> inf nan
+
+
+------------------------------
+-- log10: Logarithm base 10 --
+------------------------------
+
+logt0000 log10 1.0 0.0 -> 0.0 0.0
+logt0001 log10 1.0 -0.0 -> 0.0 -0.0
+logt0002 log10 -1.0 0.0 -> 0.0 1.3643763538418414
+logt0003 log10 -1.0 -0.0 -> 0.0 -1.3643763538418414
+-- values along both sides of real axis
+logt0010 log10 -9.8813129168249309e-324 0.0 -> -323.0051853474518 1.3643763538418414
+logt0011 log10 -9.8813129168249309e-324 -0.0 -> -323.0051853474518 -1.3643763538418414
+logt0012 log10 -1e-305 0.0 -> -305.0 1.3643763538418414
+logt0013 log10 -1e-305 -0.0 -> -305.0 -1.3643763538418414
+logt0014 log10 -1e-150 0.0 -> -150.0 1.3643763538418414
+logt0015 log10 -1e-150 -0.0 -> -150.0 -1.3643763538418414
+logt0016 log10 -9.9999999999999998e-17 0.0 -> -16.0 1.3643763538418414
+logt0017 log10 -9.9999999999999998e-17 -0.0 -> -16.0 -1.3643763538418414
+logt0018 log10 -0.001 0.0 -> -3.0 1.3643763538418414
+logt0019 log10 -0.001 -0.0 -> -3.0 -1.3643763538418414
+logt0020 log10 -0.57899999999999996 0.0 -> -0.23732143627256383 1.3643763538418414
+logt0021 log10 -0.57899999999999996 -0.0 -> -0.23732143627256383 -1.3643763538418414
+logt0022 log10 -0.99999999999999989 0.0 -> -4.821637332766436e-17 1.3643763538418414
+logt0023 log10 -0.99999999999999989 -0.0 -> -4.821637332766436e-17 -1.3643763538418414
+logt0024 log10 -1.0000000000000002 0.0 -> 9.6432746655328696e-17 1.3643763538418414
+logt0025 log10 -1.0000000000000002 -0.0 -> 9.6432746655328696e-17 -1.3643763538418414
+logt0026 log10 -1.0009999999999999 0.0 -> 0.0004340774793185929 1.3643763538418414
+logt0027 log10 -1.0009999999999999 -0.0 -> 0.0004340774793185929 -1.3643763538418414
+logt0028 log10 -2.0 0.0 -> 0.3010299956639812 1.3643763538418414
+logt0029 log10 -2.0 -0.0 -> 0.3010299956639812 -1.3643763538418414
+logt0030 log10 -23.0 0.0 -> 1.3617278360175928 1.3643763538418414
+logt0031 log10 -23.0 -0.0 -> 1.3617278360175928 -1.3643763538418414
+logt0032 log10 -10000000000000000.0 0.0 -> 16.0 1.3643763538418414
+logt0033 log10 -10000000000000000.0 -0.0 -> 16.0 -1.3643763538418414
+logt0034 log10 -9.9999999999999998e+149 0.0 -> 150.0 1.3643763538418414
+logt0035 log10 -9.9999999999999998e+149 -0.0 -> 150.0 -1.3643763538418414
+logt0036 log10 -1.0000000000000001e+299 0.0 -> 299.0 1.3643763538418414
+logt0037 log10 -1.0000000000000001e+299 -0.0 -> 299.0 -1.3643763538418414
+logt0038 log10 9.8813129168249309e-324 0.0 -> -323.0051853474518 0.0
+logt0039 log10 9.8813129168249309e-324 -0.0 -> -323.0051853474518 -0.0
+logt0040 log10 1e-305 0.0 -> -305.0 0.0
+logt0041 log10 1e-305 -0.0 -> -305.0 -0.0
+logt0042 log10 1e-150 0.0 -> -150.0 0.0
+logt0043 log10 1e-150 -0.0 -> -150.0 -0.0
+logt0044 log10 9.9999999999999998e-17 0.0 -> -16.0 0.0
+logt0045 log10 9.9999999999999998e-17 -0.0 -> -16.0 -0.0
+logt0046 log10 0.001 0.0 -> -3.0 0.0
+logt0047 log10 0.001 -0.0 -> -3.0 -0.0
+logt0048 log10 0.57899999999999996 0.0 -> -0.23732143627256383 0.0
+logt0049 log10 0.57899999999999996 -0.0 -> -0.23732143627256383 -0.0
+logt0050 log10 0.99999999999999989 0.0 -> -4.821637332766436e-17 0.0
+logt0051 log10 0.99999999999999989 -0.0 -> -4.821637332766436e-17 -0.0
+logt0052 log10 1.0000000000000002 0.0 -> 9.6432746655328696e-17 0.0
+logt0053 log10 1.0000000000000002 -0.0 -> 9.6432746655328696e-17 -0.0
+logt0054 log10 1.0009999999999999 0.0 -> 0.0004340774793185929 0.0
+logt0055 log10 1.0009999999999999 -0.0 -> 0.0004340774793185929 -0.0
+logt0056 log10 2.0 0.0 -> 0.3010299956639812 0.0
+logt0057 log10 2.0 -0.0 -> 0.3010299956639812 -0.0
+logt0058 log10 23.0 0.0 -> 1.3617278360175928 0.0
+logt0059 log10 23.0 -0.0 -> 1.3617278360175928 -0.0
+logt0060 log10 10000000000000000.0 0.0 -> 16.0 0.0
+logt0061 log10 10000000000000000.0 -0.0 -> 16.0 -0.0
+logt0062 log10 9.9999999999999998e+149 0.0 -> 150.0 0.0
+logt0063 log10 9.9999999999999998e+149 -0.0 -> 150.0 -0.0
+logt0064 log10 1.0000000000000001e+299 0.0 -> 299.0 0.0
+logt0065 log10 1.0000000000000001e+299 -0.0 -> 299.0 -0.0
+
+-- random inputs
+logt0066 log10 -1.9830454945186191e-16 -2.0334448025673346 -> 0.30823238806798503 -0.68218817692092071
+logt0067 log10 -0.96745853024741857 -0.84995816228299692 -> 0.10984528422284802 -1.051321426174086
+logt0068 log10 -0.1603644313948418 -0.2929942111041835 -> -0.47624115633305419 -0.89967884023059597
+logt0069 log10 -0.15917913168438699 -0.25238799251132177 -> -0.52521304641665956 -0.92655790645688119
+logt0070 log10 -0.68907818535078802 -3.0693105853476346 -> 0.4977187885066448 -0.77809953119328823
+logt0071 log10 -17.268133447565589 6.8165120014604756 -> 1.2686912008098534 1.2010954629104202
+logt0072 log10 -1.7153894479690328 26.434055372802636 -> 1.423076309032751 0.71033145859005309
+logt0073 log10 -8.0456794648936578e-06 0.19722758057570208 -> -0.70503235244987561 0.68220589348055516
+logt0074 log10 -2.4306442691323173 0.6846919750700996 -> 0.40230257845332595 1.2451292533748923
+logt0075 log10 -3.5488049250888194 0.45324040643185254 -> 0.55359553977141063 1.3092085108866405
+logt0076 log10 0.18418516851510189 -0.26062518836212617 -> -0.49602019732913638 -0.41500503556604301
+logt0077 log10 2.7124837795638399 -13.148769067133387 -> 1.1279348613317008 -0.59383616643803216
+logt0078 log10 3.6521275476169149e-13 -3.7820543023170673e-05 -> -4.4222722398941112 -0.68218817272717114
+logt0079 log10 5.0877545813862239 -1.2834978326786852 -> 0.71992371806426847 -0.10732104352159283
+logt0080 log10 0.26477986808461512 -0.67659001194187429 -> -0.13873139935281681 -0.52018649631300229
+logt0081 log10 0.0014754261398071962 5.3514691608205442 -> 0.72847304354528819 0.6820684398178033
+logt0082 log10 0.29667334462157885 0.00020056045042584795 -> -0.52772137299296806 0.00029359659442937261
+logt0083 log10 0.82104233671099425 3.9005387130133102 -> 0.60053889028349361 0.59208690021184018
+logt0084 log10 0.27268135358180667 124.42088110945804 -> 2.094894315538069 0.68123637673656989
+logt0085 log10 0.0026286959168267485 0.47795808180573013 -> -0.32060362226100814 0.67979964816877081
+
+-- values near infinity
+logt0100 log10 1.0512025744003172e+308 7.2621669750664611e+307 -> 308.10641562682065 0.26255461408256975
+logt0101 log10 5.5344249034372126e+307 -1.2155859158431275e+308 -> 308.12569106009209 -0.496638782296212
+logt0102 log10 -1.3155575403469408e+308 1.1610793541663864e+308 -> 308.24419052091019 1.0503359777705266
+logt0103 log10 -1.632366720973235e+308 -1.54299446211448e+308 -> 308.3514500834093 -1.0355024924378222
+logt0104 log10 0.0 5.9449276692327712e+307 -> 307.77414657501117 0.68218817692092071
+logt0105 log10 -0.0 1.1201850459025692e+308 -> 308.04928977068465 0.68218817692092071
+logt0106 log10 0.0 -1.6214225933466528e+308 -> 308.20989622030174 -0.68218817692092071
+logt0107 log10 -0.0 -1.7453269791591058e+308 -> 308.24187680203539 -0.68218817692092071
+logt0108 log10 1.440860577601428e+308 0.0 -> 308.15862195908755 0.0
+logt0109 log10 1.391515176148282e+308 -0.0 -> 308.14348794720007 -0.0
+logt0110 log10 -1.201354401295296e+308 0.0 -> 308.07967114380773 1.3643763538418414
+logt0111 log10 -1.6704337825976804e+308 -0.0 -> 308.22282926451624 -1.3643763538418414
+logt0112 log10 7.2276974655190223e+307 7.94879711369164 -> 307.85899996571993 4.7762357800858463e-308
+logt0113 log10 1.1207859593716076e+308 -6.1956200868221147 -> 308.04952268169455 -2.4007470767963597e-308
+logt0114 log10 -4.6678933874471045e+307 9.947107893220382 -> 307.66912092839902 1.3643763538418414
+logt0115 log10 -1.5108012453950142e+308 -5.3117197179375619 -> 308.1792073341565 -1.3643763538418414
+logt0116 log10 7.4903750871504435 1.5320703776626352e+308 -> 308.18527871564157 0.68218817692092071
+logt0117 log10 5.9760325525654778 -8.0149473997349123e+307 -> 307.90390067652424 -0.68218817692092071
+logt0118 log10 -7.880194206386629 1.7861845814767441e+308 -> 308.25192633617331 0.68218817692092071
+logt0119 log10 -9.886438993852865 -6.19235781080747e+307 -> 307.79185604308338 -0.68218817692092071
+
+-- values near 0
+logt0120 log10 2.2996867579227779e-308 6.7861840770939125e-312 -> -307.63833129662572 0.00012815668056362305
+logt0121 log10 6.9169190417774516e-323 -9.0414013188948118e-322 -> -321.04249706727148 -0.64902805353306059
+logt0122 log10 -1.5378064962914011e-316 1.8243628389354635e-310 -> -309.73888878263222 0.68218854299989429
+logt0123 log10 -2.3319898483706837e-321 -2.2358763941866371e-313 -> -312.65055220919641 -0.68218818145055538
+logt0124 log10 0.0 3.872770101081121e-315 -> -314.41197828323476 0.68218817692092071
+logt0125 log10 -0.0 9.6342800939043076e-322 -> -321.01618073175331 0.68218817692092071
+logt0126 log10 0.0 -2.266099393427834e-308 -> -307.64472104545649 -0.68218817692092071
+logt0127 log10 -0.0 -2.1184695673766626e-315 -> -314.67397777042407 -0.68218817692092071
+logt0128 log10 1.1363509854348671e-322 0.0 -> -321.94448750709819 0.0
+logt0129 log10 3.5572726500569751e-322 -0.0 -> -321.44888284668451 -0.0
+logt0130 log10 -2.3696071074040593e-310 0.0 -> -309.62532365619722 1.3643763538418414
+logt0131 log10 -2.813283897266934e-317 -0.0 -> -316.55078643961042 -1.3643763538418414
+
+-- values near the unit circle
+logt0200 log10 -0.59999999999999998 0.80000000000000004 -> 9.6432746655328709e-18 0.96165715756846815
+logt0201 log10 0.79999999999999993 0.60000000000000009 -> 2.6765463916147622e-33 0.2794689806475476
+
+-- special values
+logt1000 log10 -0.0 0.0 -> -inf 1.3643763538418414         divide-by-zero
+logt1001 log10 0.0 0.0 -> -inf 0.0                         divide-by-zero
+logt1002 log10 0.0 inf -> inf 0.68218817692092071
+logt1003 log10 2.3 inf -> inf 0.68218817692092071
+logt1004 log10 -0.0 inf -> inf 0.68218817692092071
+logt1005 log10 -2.3 inf -> inf 0.68218817692092071
+logt1006 log10 0.0 nan -> nan nan
+logt1007 log10 2.3 nan -> nan nan
+logt1008 log10 -0.0 nan -> nan nan
+logt1009 log10 -2.3 nan -> nan nan
+logt1010 log10 -inf 0.0 -> inf 1.3643763538418414
+logt1011 log10 -inf 2.3 -> inf 1.3643763538418414
+logt1012 log10 inf 0.0 -> inf 0.0
+logt1013 log10 inf 2.3 -> inf 0.0
+logt1014 log10 -inf inf -> inf 1.0232822653813811
+logt1015 log10 inf inf -> inf 0.34109408846046035
+logt1016 log10 inf nan -> inf nan
+logt1017 log10 -inf nan -> inf nan
+logt1018 log10 nan 0.0 -> nan nan
+logt1019 log10 nan 2.3 -> nan nan
+logt1020 log10 nan inf -> inf nan
+logt1021 log10 nan nan -> nan nan
+logt1022 log10 -0.0 -0.0 -> -inf -1.3643763538418414       divide-by-zero
+logt1023 log10 0.0 -0.0 -> -inf -0.0                       divide-by-zero
+logt1024 log10 0.0 -inf -> inf -0.68218817692092071
+logt1025 log10 2.3 -inf -> inf -0.68218817692092071
+logt1026 log10 -0.0 -inf -> inf -0.68218817692092071
+logt1027 log10 -2.3 -inf -> inf -0.68218817692092071
+logt1028 log10 -inf -0.0 -> inf -1.3643763538418414
+logt1029 log10 -inf -2.3 -> inf -1.3643763538418414
+logt1030 log10 inf -0.0 -> inf -0.0
+logt1031 log10 inf -2.3 -> inf -0.0
+logt1032 log10 -inf -inf -> inf -1.0232822653813811
+logt1033 log10 inf -inf -> inf -0.34109408846046035
+logt1034 log10 nan -0.0 -> nan nan
+logt1035 log10 nan -2.3 -> nan nan
+logt1036 log10 nan -inf -> inf nan
+
+
+-----------------------
+-- sqrt: Square root --
+-----------------------
+
+-- zeros
+sqrt0000 sqrt 0.0 0.0 -> 0.0 0.0
+sqrt0001 sqrt 0.0 -0.0 -> 0.0 -0.0
+sqrt0002 sqrt -0.0 0.0 -> 0.0 0.0
+sqrt0003 sqrt -0.0 -0.0 -> 0.0 -0.0
+
+-- values along both sides of real axis
+sqrt0010 sqrt -9.8813129168249309e-324 0.0 -> 0.0 3.1434555694052576e-162
+sqrt0011 sqrt -9.8813129168249309e-324 -0.0 -> 0.0 -3.1434555694052576e-162
+sqrt0012 sqrt -1e-305 0.0 -> 0.0 3.1622776601683791e-153
+sqrt0013 sqrt -1e-305 -0.0 -> 0.0 -3.1622776601683791e-153
+sqrt0014 sqrt -1e-150 0.0 -> 0.0 9.9999999999999996e-76
+sqrt0015 sqrt -1e-150 -0.0 -> 0.0 -9.9999999999999996e-76
+sqrt0016 sqrt -9.9999999999999998e-17 0.0 -> 0.0 1e-08
+sqrt0017 sqrt -9.9999999999999998e-17 -0.0 -> 0.0 -1e-08
+sqrt0018 sqrt -0.001 0.0 -> 0.0 0.031622776601683791
+sqrt0019 sqrt -0.001 -0.0 -> 0.0 -0.031622776601683791
+sqrt0020 sqrt -0.57899999999999996 0.0 -> 0.0 0.76092049518987193
+sqrt0021 sqrt -0.57899999999999996 -0.0 -> 0.0 -0.76092049518987193
+sqrt0022 sqrt -0.99999999999999989 0.0 -> 0.0 0.99999999999999989
+sqrt0023 sqrt -0.99999999999999989 -0.0 -> 0.0 -0.99999999999999989
+sqrt0024 sqrt -1.0000000000000002 0.0 -> 0.0 1.0
+sqrt0025 sqrt -1.0000000000000002 -0.0 -> 0.0 -1.0
+sqrt0026 sqrt -1.0009999999999999 0.0 -> 0.0 1.000499875062461
+sqrt0027 sqrt -1.0009999999999999 -0.0 -> 0.0 -1.000499875062461
+sqrt0028 sqrt -2.0 0.0 -> 0.0 1.4142135623730951
+sqrt0029 sqrt -2.0 -0.0 -> 0.0 -1.4142135623730951
+sqrt0030 sqrt -23.0 0.0 -> 0.0 4.7958315233127191
+sqrt0031 sqrt -23.0 -0.0 -> 0.0 -4.7958315233127191
+sqrt0032 sqrt -10000000000000000.0 0.0 -> 0.0 100000000.0
+sqrt0033 sqrt -10000000000000000.0 -0.0 -> 0.0 -100000000.0
+sqrt0034 sqrt -9.9999999999999998e+149 0.0 -> 0.0 9.9999999999999993e+74
+sqrt0035 sqrt -9.9999999999999998e+149 -0.0 -> 0.0 -9.9999999999999993e+74
+sqrt0036 sqrt -1.0000000000000001e+299 0.0 -> 0.0 3.1622776601683796e+149
+sqrt0037 sqrt -1.0000000000000001e+299 -0.0 -> 0.0 -3.1622776601683796e+149
+sqrt0038 sqrt 9.8813129168249309e-324 0.0 -> 3.1434555694052576e-162 0.0
+sqrt0039 sqrt 9.8813129168249309e-324 -0.0 -> 3.1434555694052576e-162 -0.0
+sqrt0040 sqrt 1e-305 0.0 -> 3.1622776601683791e-153 0.0
+sqrt0041 sqrt 1e-305 -0.0 -> 3.1622776601683791e-153 -0.0
+sqrt0042 sqrt 1e-150 0.0 -> 9.9999999999999996e-76 0.0
+sqrt0043 sqrt 1e-150 -0.0 -> 9.9999999999999996e-76 -0.0
+sqrt0044 sqrt 9.9999999999999998e-17 0.0 -> 1e-08 0.0
+sqrt0045 sqrt 9.9999999999999998e-17 -0.0 -> 1e-08 -0.0
+sqrt0046 sqrt 0.001 0.0 -> 0.031622776601683791 0.0
+sqrt0047 sqrt 0.001 -0.0 -> 0.031622776601683791 -0.0
+sqrt0048 sqrt 0.57899999999999996 0.0 -> 0.76092049518987193 0.0
+sqrt0049 sqrt 0.57899999999999996 -0.0 -> 0.76092049518987193 -0.0
+sqrt0050 sqrt 0.99999999999999989 0.0 -> 0.99999999999999989 0.0
+sqrt0051 sqrt 0.99999999999999989 -0.0 -> 0.99999999999999989 -0.0
+sqrt0052 sqrt 1.0000000000000002 0.0 -> 1.0 0.0
+sqrt0053 sqrt 1.0000000000000002 -0.0 -> 1.0 -0.0
+sqrt0054 sqrt 1.0009999999999999 0.0 -> 1.000499875062461 0.0
+sqrt0055 sqrt 1.0009999999999999 -0.0 -> 1.000499875062461 -0.0
+sqrt0056 sqrt 2.0 0.0 -> 1.4142135623730951 0.0
+sqrt0057 sqrt 2.0 -0.0 -> 1.4142135623730951 -0.0
+sqrt0058 sqrt 23.0 0.0 -> 4.7958315233127191 0.0
+sqrt0059 sqrt 23.0 -0.0 -> 4.7958315233127191 -0.0
+sqrt0060 sqrt 10000000000000000.0 0.0 -> 100000000.0 0.0
+sqrt0061 sqrt 10000000000000000.0 -0.0 -> 100000000.0 -0.0
+sqrt0062 sqrt 9.9999999999999998e+149 0.0 -> 9.9999999999999993e+74 0.0
+sqrt0063 sqrt 9.9999999999999998e+149 -0.0 -> 9.9999999999999993e+74 -0.0
+sqrt0064 sqrt 1.0000000000000001e+299 0.0 -> 3.1622776601683796e+149 0.0
+sqrt0065 sqrt 1.0000000000000001e+299 -0.0 -> 3.1622776601683796e+149 -0.0
+
+-- random inputs
+sqrt0100 sqrt -0.34252542541549913 -223039880.15076211 -> 10560.300180587592 -10560.300196805192
+sqrt0101 sqrt -0.88790791393018909 -5.3307751730827402 -> 1.5027154613689004 -1.7737140896343291
+sqrt0102 sqrt -113916.89291310767 -0.018143374626153858 -> 2.6877817875351178e-05 -337.51576691038952
+sqrt0103 sqrt -0.63187172386197121 -0.26293913366617694 -> 0.16205707495266153 -0.81125471918761971
+sqrt0104 sqrt -0.058185169308906215 -2.3548312990430991 -> 1.0717660342420072 -1.0985752598086966
+sqrt0105 sqrt -1.0580584765935896 0.14400319259151736 -> 0.069837489270111242 1.030987755262468
+sqrt0106 sqrt -1.1667595947504932 0.11159711473953678 -> 0.051598531319315251 1.0813981705111229
+sqrt0107 sqrt -0.5123728411449906 0.026175433648339085 -> 0.018278026262418718 0.71603556293597614
+sqrt0108 sqrt -3.7453400060067228 1.0946500314809635 -> 0.27990088541692498 1.9554243814742367
+sqrt0109 sqrt -0.0027736121575097673 1.0367943000839817 -> 0.71903560338719175 0.72096172651250545
+sqrt0110 sqrt 1501.2559699453188 -1.1997325207283589 -> 38.746047664730959 -0.015481998720355024
+sqrt0111 sqrt 1.4830075326850578 -0.64100878436755349 -> 1.244712815741096 -0.25749264258434584
+sqrt0112 sqrt 0.095395618499734602 -0.48226565701639595 -> 0.54175904053472879 -0.44509239434231551
+sqrt0113 sqrt 0.50109185681863277 -0.54054037379892561 -> 0.7868179858332387 -0.34349772344520979
+sqrt0114 sqrt 0.98779807595367897 -0.00019848758437225191 -> 0.99388031770665153 -9.9854872279921968e-05
+sqrt0115 sqrt 11.845472380792259 0.0010051104581506761 -> 3.4417252072345397 0.00014601840612346451
+sqrt0116 sqrt 2.3558249686735975 0.25605157371744403 -> 1.5371278477386647 0.083288964575761404
+sqrt0117 sqrt 0.77584894123159098 1.0496420627016076 -> 1.0200744386390885 0.51449287568756552
+sqrt0118 sqrt 1.8961715669604893 0.34940793467158854 -> 1.3827991781411615 0.12634080935066902
+sqrt0119 sqrt 0.96025378316565801 0.69573224860140515 -> 1.0358710342209998 0.33581991658093457
+
+-- values near 0
+sqrt0120 sqrt 7.3577938365086866e-313 8.1181408465112743e-319 -> 8.5777583531543516e-157 4.732087634251168e-163
+sqrt0121 sqrt 1.2406883874892108e-310 -5.1210133324269776e-312 -> 1.1140990057468052e-155 -2.2982756945349973e-157
+sqrt0122 sqrt -7.1145453001139502e-322 2.9561379244703735e-314 -> 1.2157585807480286e-157 1.2157586100077242e-157
+sqrt0123 sqrt -4.9963244206801218e-314 -8.4718424423690227e-319 -> 1.8950582312540437e-162 -2.2352459419578971e-157
+sqrt0124 sqrt 0.0 7.699553609385195e-318 -> 1.9620848107797476e-159 1.9620848107797476e-159
+sqrt0125 sqrt -0.0 3.3900826606499415e-309 -> 4.1170879639922327e-155 4.1170879639922327e-155
+sqrt0126 sqrt 0.0 -9.8907989772250828e-319 -> 7.032353438652342e-160 -7.032353438652342e-160
+sqrt0127 sqrt -0.0 -1.3722939367590908e-315 -> 2.6194407196566702e-158 -2.6194407196566702e-158
+sqrt0128 sqrt 7.9050503334599447e-323 0.0 -> 8.8910349979403099e-162 0.0
+sqrt0129 sqrt 1.8623241768349486e-309 -0.0 -> 4.3154654173506579e-155 -0.0
+sqrt0130 sqrt -2.665971134499887e-308 0.0 -> 0.0 1.6327801856036491e-154
+sqrt0131 sqrt -1.5477066694467245e-310 -0.0 -> 0.0 -1.2440685951533077e-155
+
+-- inputs whose absolute value overflows
+sqrt0140 sqrt 1.6999999999999999e+308 -1.6999999999999999e+308 -> 1.4325088230154573e+154 -5.9336458271212207e+153
+sqrt0141 sqrt -1.797e+308 -9.9999999999999999e+306 -> 3.7284476432057307e+152 -1.3410406899802901e+154
+
+-- special values
+sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0
+sqrt1001 sqrt -0.0 0.0 -> 0.0 0.0
+sqrt1002 sqrt 0.0 inf -> inf inf
+sqrt1003 sqrt 2.3 inf -> inf inf
+sqrt1004 sqrt inf inf -> inf inf
+sqrt1005 sqrt -0.0 inf -> inf inf
+sqrt1006 sqrt -2.3 inf -> inf inf
+sqrt1007 sqrt -inf inf -> inf inf
+sqrt1008 sqrt nan inf -> inf inf
+sqrt1009 sqrt 0.0 nan -> nan nan
+sqrt1010 sqrt 2.3 nan -> nan nan
+sqrt1011 sqrt -0.0 nan -> nan nan
+sqrt1012 sqrt -2.3 nan -> nan nan
+sqrt1013 sqrt -inf 0.0 -> 0.0 inf
+sqrt1014 sqrt -inf 2.3 -> 0.0 inf
+sqrt1015 sqrt inf 0.0 -> inf 0.0
+sqrt1016 sqrt inf 2.3 -> inf 0.0
+sqrt1017 sqrt -inf nan -> nan inf       ignore-imag-sign
+sqrt1018 sqrt inf nan -> inf nan
+sqrt1019 sqrt nan 0.0 -> nan nan
+sqrt1020 sqrt nan 2.3 -> nan nan
+sqrt1021 sqrt nan nan -> nan nan
+sqrt1022 sqrt 0.0 -0.0 -> 0.0 -0.0
+sqrt1023 sqrt -0.0 -0.0 -> 0.0 -0.0
+sqrt1024 sqrt 0.0 -inf -> inf -inf
+sqrt1025 sqrt 2.3 -inf -> inf -inf
+sqrt1026 sqrt inf -inf -> inf -inf
+sqrt1027 sqrt -0.0 -inf -> inf -inf
+sqrt1028 sqrt -2.3 -inf -> inf -inf
+sqrt1029 sqrt -inf -inf -> inf -inf
+sqrt1030 sqrt nan -inf -> inf -inf
+sqrt1031 sqrt -inf -0.0 -> 0.0 -inf
+sqrt1032 sqrt -inf -2.3 -> 0.0 -inf
+sqrt1033 sqrt inf -0.0 -> inf -0.0
+sqrt1034 sqrt inf -2.3 -> inf -0.0
+sqrt1035 sqrt nan -0.0 -> nan nan
+sqrt1036 sqrt nan -2.3 -> nan nan
+
+
+-- For exp, cosh, sinh, tanh we limit tests to arguments whose
+-- imaginary part is less than 10 in absolute value:  most math
+-- libraries have poor accuracy for (real) sine and cosine for
+-- large arguments, and the accuracy of these complex functions
+-- suffer correspondingly.
+--
+-- Similarly, for cos, sin and tan we limit tests to arguments
+-- with relatively small real part.
+
+
+-------------------------------
+-- exp: Exponential function --
+-------------------------------
+
+-- zeros
+exp0000 exp 0.0 0.0 -> 1.0 0.0
+exp0001 exp 0.0 -0.0 -> 1.0 -0.0
+exp0002 exp -0.0 0.0 -> 1.0 0.0
+exp0003 exp -0.0 -0.0 -> 1.0 -0.0
+
+-- random inputs
+exp0004 exp -17.957359009564684 -1.108613895795274 -> 7.0869292576226611e-09 -1.4225929202377833e-08
+exp0005 exp -1.4456149663368642e-15 -0.75359817331772239 -> 0.72923148323917997 -0.68426708517419033
+exp0006 exp -0.76008654883512661 -0.46657235480105019 -> 0.41764393109928666 -0.21035108396792854
+exp0007 exp -5.7071614697735731 -2.3744161818115816e-11 -> 0.0033220890242068356 -7.8880219364953578e-14
+exp0008 exp -0.4653981327927097 -5.2236706667445587e-21 -> 0.62788507378216663 -3.2798648420026468e-21
+exp0009 exp -3.2444565242295518 1.1535625304243959 -> 0.015799936931457641 0.035644950380024749
+exp0010 exp -3.0651456337977727 0.87765086532391878 -> 0.029805595629855953 0.035882775180855669
+exp0011 exp -0.11080823753233926 0.96486386300873106 -> 0.50979112534376314 0.73575512419561562
+exp0012 exp -2.5629722598928648 0.019636235754708079 -> 0.077060452853917397 0.0015133717341137684
+exp0013 exp -3.3201709957983357e-10 1.2684017344487268 -> 0.29780699855434889 0.95462610007689186
+exp0014 exp 0.88767276057993272 -0.18953422986895557 -> 2.3859624049858095 -0.45771559132044426
+exp0015 exp 1.5738333486794742 -2.2576803075544328e-11 -> 4.8251091132458654 -1.0893553826776623e-10
+exp0016 exp 1.6408702341813795 -1.438879484380837 -> 0.6786733590689048 -5.1148284173168825
+exp0017 exp 1.820279424202033 -0.020812040370785722 -> 6.1722462896420902 -0.1284755888435051
+exp0018 exp 1.7273965735945873 -0.61140621328954947 -> 4.6067931898799976 -3.2294267694441308
+exp0019 exp 2.5606034306862995 0.098153136008435504 -> 12.881325889966629 1.2684184812864494
+exp0020 exp 10.280368619483029 3.4564622559748535 -> -27721.283321551502 -9028.9663215568835
+exp0021 exp 1.104007405129741e-155 0.21258803067317278 -> 0.97748813933531764 0.21099037290544478
+exp0022 exp 0.027364777809295172 0.00059226603500623363 -> 1.0277424518451876 0.0006086970181346579
+exp0023 exp 0.94356313429255245 3.418530463518592 -> -2.4712285695346194 -0.70242654900218349
+
+-- cases where exp(z) representable, exp(z.real) not
+exp0030 exp 710.0 0.78500000000000003 -> 1.5803016909637158e+308 1.5790437551806911e+308
+exp0031 exp 710.0 -0.78500000000000003 -> 1.5803016909637158e+308 -1.5790437551806911e+308
+
+-- values for which exp(x) is subnormal, or underflows to 0
+exp0040 exp -735.0 0.78500000000000003 -> 4.3976783136329355e-320 4.3942198541120468e-320
+exp0041 exp -735.0 -2.3559999999999999 -> -4.3952079854037293e-320 -4.396690182341253e-320
+exp0042 exp -745.0 0.0 -> 4.9406564584124654e-324 0.0
+exp0043 exp -745.0 0.7 -> 0.0 0.0
+exp0044 exp -745.0 2.1 -> -0.0 0.0
+exp0045 exp -745.0 3.7 -> -0.0 -0.0
+exp0046 exp -745.0 5.3 -> 0.0 -0.0
+
+-- values for which exp(z) overflows
+exp0050 exp 710.0 0.0 -> inf 0.0                        overflow
+exp0051 exp 711.0 0.7 -> inf inf                        overflow
+exp0052 exp 710.0 1.5 -> 1.5802653829857376e+307 inf    overflow
+exp0053 exp 710.0 1.6 -> -6.5231579995501372e+306 inf   overflow
+exp0054 exp 710.0 2.8 -> -inf 7.4836177417448528e+307   overflow
+
+-- special values
+exp1000 exp 0.0 0.0 -> 1.0 0.0
+exp1001 exp -0.0 0.0 -> 1.0 0.0
+exp1002 exp 0.0 inf -> nan nan          invalid
+exp1003 exp 2.3 inf -> nan nan          invalid
+exp1004 exp -0.0 inf -> nan nan         invalid
+exp1005 exp -2.3 inf -> nan nan         invalid
+exp1006 exp 0.0 nan -> nan nan
+exp1007 exp 2.3 nan -> nan nan
+exp1008 exp -0.0 nan -> nan nan
+exp1009 exp -2.3 nan -> nan nan
+exp1010 exp -inf 0.0 -> 0.0 0.0
+exp1011 exp -inf 1.4 -> 0.0 0.0
+exp1012 exp -inf 2.8 -> -0.0 0.0
+exp1013 exp -inf 4.2 -> -0.0 -0.0
+exp1014 exp -inf 5.6 -> 0.0 -0.0
+exp1015 exp -inf 7.0 -> 0.0 0.0
+exp1016 exp inf 0.0 -> inf 0.0
+exp1017 exp inf 1.4 -> inf inf
+exp1018 exp inf 2.8 -> -inf inf
+exp1019 exp inf 4.2 -> -inf -inf
+exp1020 exp inf 5.6 -> inf -inf
+exp1021 exp inf 7.0 -> inf inf
+exp1022 exp -inf inf -> 0.0 0.0         ignore-real-sign ignore-imag-sign
+exp1023 exp inf inf -> inf nan          invalid ignore-real-sign
+exp1024 exp -inf nan -> 0.0 0.0         ignore-real-sign ignore-imag-sign
+exp1025 exp inf nan -> inf nan          ignore-real-sign
+exp1026 exp nan 0.0 -> nan 0.0
+exp1027 exp nan 2.3 -> nan nan
+exp1028 exp nan inf -> nan nan
+exp1029 exp nan nan -> nan nan
+exp1030 exp 0.0 -0.0 -> 1.0 -0.0
+exp1031 exp -0.0 -0.0 -> 1.0 -0.0
+exp1032 exp 0.0 -inf -> nan nan         invalid
+exp1033 exp 2.3 -inf -> nan nan         invalid
+exp1034 exp -0.0 -inf -> nan nan        invalid
+exp1035 exp -2.3 -inf -> nan nan        invalid
+exp1036 exp -inf -0.0 -> 0.0 -0.0
+exp1037 exp -inf -1.4 -> 0.0 -0.0
+exp1038 exp -inf -2.8 -> -0.0 -0.0
+exp1039 exp -inf -4.2 -> -0.0 0.0
+exp1040 exp -inf -5.6 -> 0.0 0.0
+exp1041 exp -inf -7.0 -> 0.0 -0.0
+exp1042 exp inf -0.0 -> inf -0.0
+exp1043 exp inf -1.4 -> inf -inf
+exp1044 exp inf -2.8 -> -inf -inf
+exp1045 exp inf -4.2 -> -inf inf
+exp1046 exp inf -5.6 -> inf inf
+exp1047 exp inf -7.0 -> inf -inf
+exp1048 exp -inf -inf -> 0.0 0.0        ignore-real-sign ignore-imag-sign
+exp1049 exp inf -inf -> inf nan         invalid ignore-real-sign
+exp1050 exp nan -0.0 -> nan -0.0
+exp1051 exp nan -2.3 -> nan nan
+exp1052 exp nan -inf -> nan nan
+
+
+-----------------------------
+-- cosh: Hyperbolic Cosine --
+-----------------------------
+
+-- zeros
+cosh0000 cosh 0.0 0.0 -> 1.0 0.0
+cosh0001 cosh 0.0 -0.0 -> 1.0 -0.0
+cosh0002 cosh -0.0 0.0 -> 1.0 -0.0
+cosh0003 cosh -0.0 -0.0 -> 1.0 0.0
+
+-- random inputs
+cosh0004 cosh -0.85395264297414253 -8.8553756148671958 -> -1.1684340348021185 0.51842195359787435
+cosh0005 cosh -19.584904237211223 -0.066582627994906177 -> 159816812.23336992 10656776.050406246
+cosh0006 cosh -0.11072618401130772 -1.484820215073247 -> 0.086397164744949503 0.11054275637717284
+cosh0007 cosh -3.4764840250681752 -0.48440348288275276 -> 14.325931955190844 7.5242053548737955
+cosh0008 cosh -0.52047063604524602 -0.3603805382775585 -> 1.0653940354683802 0.19193293606252473
+cosh0009 cosh -1.39518962975995 0.0074738604700702906 -> 2.1417031027235969 -0.01415518712296308
+cosh0010 cosh -0.37107064757653541 0.14728085307856609 -> 1.0580601496776991 -0.055712531964568587
+cosh0011 cosh -5.8470200958739653 4.0021722388336292 -> -112.86220667618285 131.24734033545013
+cosh0012 cosh -0.1700261444851883 0.97167540135354513 -> 0.57208748253577946 -0.1410904820240203
+cosh0013 cosh -0.44042397902648783 1.0904791964139742 -> 0.50760322393058133 -0.40333966652010816
+cosh0014 cosh 0.052267552491867299 -3.8889011430644174 -> -0.73452303414639297 0.035540704833537134
+cosh0015 cosh 0.98000764177127453 -1.2548829247784097 -> 0.47220747341416142 -1.0879421432180316
+cosh0016 cosh 0.083594701222644008 -0.88847899930181284 -> 0.63279782419312613 -0.064954566816002285
+cosh0017 cosh 1.38173531783776 -0.43185040816732229 -> 1.9221663374671647 -0.78073830858849347
+cosh0018 cosh 0.57315681120148465 -0.22255760951027942 -> 1.1399733125173004 -0.1335512343605956
+cosh0019 cosh 1.8882512333062347 4.5024932182383797 -> -0.7041602065362691 -3.1573822131964615
+cosh0020 cosh 0.5618219206858317 0.92620452129575348 -> 0.69822380405378381 0.47309067471054522
+cosh0021 cosh 0.54361442847062591 0.64176483583018462 -> 0.92234462074193491 0.34167906495845501
+cosh0022 cosh 0.0014777403107920331 1.3682028122677661 -> 0.2012106963899549 0.001447518137863219
+cosh0023 cosh 2.218885944363501 2.0015727395883687 -> -1.94294321081968 4.1290269176083196
+
+-- 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
+
+-- special values
+cosh1000 cosh 0.0 0.0 -> 1.0 0.0
+cosh1001 cosh 0.0 inf -> nan 0.0        invalid ignore-imag-sign
+cosh1002 cosh 0.0 nan -> nan 0.0        ignore-imag-sign
+cosh1003 cosh 2.3 inf -> nan nan        invalid
+cosh1004 cosh 2.3 nan -> nan nan
+cosh1005 cosh inf 0.0 -> inf 0.0
+cosh1006 cosh inf 1.4 -> inf inf
+cosh1007 cosh inf 2.8 -> -inf inf
+cosh1008 cosh inf 4.2 -> -inf -inf
+cosh1009 cosh inf 5.6 -> inf -inf
+cosh1010 cosh inf 7.0 -> inf inf
+cosh1011 cosh inf inf -> inf nan        invalid ignore-real-sign
+cosh1012 cosh inf nan -> inf nan
+cosh1013 cosh nan 0.0 -> nan 0.0        ignore-imag-sign
+cosh1014 cosh nan 2.3 -> nan nan
+cosh1015 cosh nan inf -> nan nan
+cosh1016 cosh nan nan -> nan nan
+cosh1017 cosh 0.0 -0.0 -> 1.0 -0.0
+cosh1018 cosh 0.0 -inf -> nan 0.0       invalid ignore-imag-sign
+cosh1019 cosh 2.3 -inf -> nan nan       invalid
+cosh1020 cosh inf -0.0 -> inf -0.0
+cosh1021 cosh inf -1.4 -> inf -inf
+cosh1022 cosh inf -2.8 -> -inf -inf
+cosh1023 cosh inf -4.2 -> -inf inf
+cosh1024 cosh inf -5.6 -> inf inf
+cosh1025 cosh inf -7.0 -> inf -inf
+cosh1026 cosh inf -inf -> inf nan       invalid ignore-real-sign
+cosh1027 cosh nan -0.0 -> nan 0.0       ignore-imag-sign
+cosh1028 cosh nan -2.3 -> nan nan
+cosh1029 cosh nan -inf -> nan nan
+cosh1030 cosh -0.0 -0.0 -> 1.0 0.0
+cosh1031 cosh -0.0 -inf -> nan 0.0      invalid ignore-imag-sign
+cosh1032 cosh -0.0 nan -> nan 0.0       ignore-imag-sign
+cosh1033 cosh -2.3 -inf -> nan nan      invalid
+cosh1034 cosh -2.3 nan -> nan nan
+cosh1035 cosh -inf -0.0 -> inf 0.0
+cosh1036 cosh -inf -1.4 -> inf inf
+cosh1037 cosh -inf -2.8 -> -inf inf
+cosh1038 cosh -inf -4.2 -> -inf -inf
+cosh1039 cosh -inf -5.6 -> inf -inf
+cosh1040 cosh -inf -7.0 -> inf inf
+cosh1041 cosh -inf -inf -> inf nan      invalid ignore-real-sign
+cosh1042 cosh -inf nan -> inf nan
+cosh1043 cosh -0.0 0.0 -> 1.0 -0.0
+cosh1044 cosh -0.0 inf -> nan 0.0       invalid ignore-imag-sign
+cosh1045 cosh -2.3 inf -> nan nan       invalid
+cosh1046 cosh -inf 0.0 -> inf -0.0
+cosh1047 cosh -inf 1.4 -> inf -inf
+cosh1048 cosh -inf 2.8 -> -inf -inf
+cosh1049 cosh -inf 4.2 -> -inf inf
+cosh1050 cosh -inf 5.6 -> inf inf
+cosh1051 cosh -inf 7.0 -> inf -inf
+cosh1052 cosh -inf inf -> inf nan       invalid ignore-real-sign
+
+
+---------------------------
+-- sinh: Hyperbolic Sine --
+---------------------------
+
+-- zeros
+sinh0000 sinh 0.0 0.0 -> 0.0 0.0
+sinh0001 sinh 0.0 -0.0 -> 0.0 -0.0
+sinh0002 sinh -0.0 0.0 -> -0.0 0.0
+sinh0003 sinh -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+sinh0004 sinh -17.282588091462742 -0.38187948694103546 -> -14867386.857248396 -5970648.6553516639
+sinh0005 sinh -343.91971203143208 -5.0172868877771525e-22 -> -1.1518691776521735e+149 -5.7792581214689021e+127
+sinh0006 sinh -14.178122253300922 -1.9387157579351293 -> 258440.37909034826 -670452.58500946441
+sinh0007 sinh -1.0343810581686239 -1.0970235266369905 -> -0.56070858278092739 -1.4098883258046697
+sinh0008 sinh -0.066126561416368204 -0.070461584169961872 -> -0.066010558700938124 -0.070557276738637542
+sinh0009 sinh -0.37630149150308484 3.3621734692162173 -> 0.37591118119332617 -0.23447115926369383
+sinh0010 sinh -0.049941960978670055 0.40323767020414625 -> -0.045955482136329009 0.3928878494430646
+sinh0011 sinh -16.647852603903715 0.0026852219129082098 -> -8492566.5739382561 22804.480671133562
+sinh0012 sinh -1.476625314303694 0.89473773116683386 -> -1.2982943334382224 1.7966593367791204
+sinh0013 sinh -422.36429577556913 0.10366634502307912 -> -1.3400321008920044e+183 1.3941600948045599e+182
+sinh0014 sinh 0.09108340745641981 -0.40408227416070353 -> 0.083863724802237902 -0.39480716553935602
+sinh0015 sinh 2.036064132067386 -2.6831729961386239 -> -3.37621124363175 -1.723868330002817
+sinh0016 sinh 2.5616717223063317 -0.0078978498622717767 -> 6.4399415853815869 -0.051472264400722133
+sinh0017 sinh 0.336804011985188 -6.5654622971649337 -> 0.32962499307574578 -0.29449170159995197
+sinh0018 sinh 0.23774603755649693 -0.92467195799232049 -> 0.14449839490603389 -0.82109449053556793
+sinh0019 sinh 0.0011388273541465494 1.9676196882949855 -> -0.00044014605389634999 0.92229398407098806
+sinh0020 sinh 3.2443870105663759 0.8054287559616895 -> 8.8702890778527426 9.2610748597042196
+sinh0021 sinh 0.040628908857054738 0.098206391190944958 -> 0.04044426841671233 0.098129544739707392
+sinh0022 sinh 4.7252283918217696e-30 9.1198155642656697 -> -4.5071980561644404e-30 0.30025730701661713
+sinh0023 sinh 0.043713693678420068 0.22512549887532657 -> 0.042624198673416713 0.22344201231217961
+
+-- 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
+
+-- special values
+sinh1000 sinh 0.0 0.0 -> 0.0 0.0
+sinh1001 sinh 0.0 inf -> 0.0 nan        invalid ignore-real-sign
+sinh1002 sinh 0.0 nan -> 0.0 nan        ignore-real-sign
+sinh1003 sinh 2.3 inf -> nan nan        invalid
+sinh1004 sinh 2.3 nan -> nan nan
+sinh1005 sinh inf 0.0 -> inf 0.0
+sinh1006 sinh inf 1.4 -> inf inf
+sinh1007 sinh inf 2.8 -> -inf inf
+sinh1008 sinh inf 4.2 -> -inf -inf
+sinh1009 sinh inf 5.6 -> inf -inf
+sinh1010 sinh inf 7.0 -> inf inf
+sinh1011 sinh inf inf -> inf nan        invalid ignore-real-sign
+sinh1012 sinh inf nan -> inf nan        ignore-real-sign
+sinh1013 sinh nan 0.0 -> nan 0.0
+sinh1014 sinh nan 2.3 -> nan nan
+sinh1015 sinh nan inf -> nan nan
+sinh1016 sinh nan nan -> nan nan
+sinh1017 sinh 0.0 -0.0 -> 0.0 -0.0
+sinh1018 sinh 0.0 -inf -> 0.0 nan       invalid ignore-real-sign
+sinh1019 sinh 2.3 -inf -> nan nan       invalid
+sinh1020 sinh inf -0.0 -> inf -0.0
+sinh1021 sinh inf -1.4 -> inf -inf
+sinh1022 sinh inf -2.8 -> -inf -inf
+sinh1023 sinh inf -4.2 -> -inf inf
+sinh1024 sinh inf -5.6 -> inf inf
+sinh1025 sinh inf -7.0 -> inf -inf
+sinh1026 sinh inf -inf -> inf nan       invalid ignore-real-sign
+sinh1027 sinh nan -0.0 -> nan -0.0
+sinh1028 sinh nan -2.3 -> nan nan
+sinh1029 sinh nan -inf -> nan nan
+sinh1030 sinh -0.0 -0.0 -> -0.0 -0.0
+sinh1031 sinh -0.0 -inf -> 0.0 nan      invalid ignore-real-sign
+sinh1032 sinh -0.0 nan -> 0.0 nan       ignore-real-sign
+sinh1033 sinh -2.3 -inf -> nan nan      invalid
+sinh1034 sinh -2.3 nan -> nan nan
+sinh1035 sinh -inf -0.0 -> -inf -0.0
+sinh1036 sinh -inf -1.4 -> -inf -inf
+sinh1037 sinh -inf -2.8 -> inf -inf
+sinh1038 sinh -inf -4.2 -> inf inf
+sinh1039 sinh -inf -5.6 -> -inf inf
+sinh1040 sinh -inf -7.0 -> -inf -inf
+sinh1041 sinh -inf -inf -> inf nan      invalid ignore-real-sign
+sinh1042 sinh -inf nan -> inf nan       ignore-real-sign
+sinh1043 sinh -0.0 0.0 -> -0.0 0.0
+sinh1044 sinh -0.0 inf -> 0.0 nan       invalid ignore-real-sign
+sinh1045 sinh -2.3 inf -> nan nan       invalid
+sinh1046 sinh -inf 0.0 -> -inf 0.0
+sinh1047 sinh -inf 1.4 -> -inf inf
+sinh1048 sinh -inf 2.8 -> inf inf
+sinh1049 sinh -inf 4.2 -> inf -inf
+sinh1050 sinh -inf 5.6 -> -inf -inf
+sinh1051 sinh -inf 7.0 -> -inf inf
+sinh1052 sinh -inf inf -> inf nan       invalid ignore-real-sign
+
+
+------------------------------
+-- tanh: Hyperbolic Tangent --
+------------------------------
+
+-- zeros
+tanh0000 tanh 0.0 0.0 -> 0.0 0.0
+tanh0001 tanh 0.0 -0.0 -> 0.0 -0.0
+tanh0002 tanh -0.0 0.0 -> -0.0 0.0
+tanh0003 tanh -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+tanh0004 tanh -21.200500450664993 -1.6970729480342996 -> -1.0 1.9241352344849399e-19
+tanh0005 tanh -0.34158771504251928 -8.0848504951747131 -> -2.123711225855613 1.2827526782026006
+tanh0006 tanh -15.454144725193689 -0.23619582288265617 -> -0.99999999999993283 -3.4336684248260036e-14
+tanh0007 tanh -7.6103163119661952 -0.7802748320307008 -> -0.99999999497219438 -4.9064845343755437e-07
+tanh0008 tanh -0.15374717235792129 -0.6351086327306138 -> -0.23246081703561869 -0.71083467433910219
+tanh0009 tanh -0.49101115474392465 0.09723001264886301 -> -0.45844445715492133 0.077191158541805888
+tanh0010 tanh -0.10690612157664491 2.861612800856395 -> -0.11519761626257358 -0.28400488355647507
+tanh0011 tanh -0.91505774192066702 1.5431174597727007 -> -1.381109893068114 0.025160819663709356
+tanh0012 tanh -0.057433367093792223 0.35491159541246459 -> -0.065220499046696953 0.36921788332369498
+tanh0013 tanh -1.3540418621233514 0.18969415642242535 -> -0.88235642861151387 0.043764069984411721
+tanh0014 tanh 0.94864783961003529 -0.11333689578867717 -> 0.74348401861861368 -0.051271042543855221
+tanh0015 tanh 1.9591698133845488 -0.0029654444904578339 -> 0.9610270776968135 -0.00022664240049212933
+tanh0016 tanh 1.0949715796669197 -0.24706642853984456 -> 0.81636574501369386 -0.087767436914149954
+tanh0017 tanh 5770428.2113731047 -3.7160580339833165 -> 1.0 -0.0
+tanh0018 tanh 1.5576782321399629 -1.0357943787966468 -> 1.0403002384895388 -0.081126347894671463
+tanh0019 tanh 0.62378536230552961 2.3471393579560216 -> 0.85582499238960363 -0.53569473646842869
+tanh0020 tanh 17.400628602508025 9.3987059533841979 -> 0.99999999999999845 -8.0175867720530832e-17
+tanh0021 tanh 0.15026177509871896 0.50630349159505472 -> 0.19367536571827768 0.53849847858853661
+tanh0022 tanh 0.57433977530711167 1.0071604546265627 -> 1.0857848159262844 0.69139213955872214
+tanh0023 tanh 0.16291181500449456 0.006972810241567544 -> 0.16149335907551157 0.0067910772903467817
+
+-- large real part
+tanh0030 tanh 710 0.13 -> 1.0 0.0
+tanh0031 tanh -711 7.4000000000000004 -> -1.0 0.0
+tanh0032 tanh 1000 -2.3199999999999998 -> 1.0 0.0
+tanh0033 tanh -1.0000000000000001e+300 -9.6699999999999999 -> -1.0 -0.0
+
+--special values
+tanh1000 tanh 0.0 0.0 -> 0.0 0.0
+tanh1001 tanh 0.0 inf -> nan nan        invalid
+tanh1002 tanh 2.3 inf -> nan nan        invalid
+tanh1003 tanh 0.0 nan -> nan nan
+tanh1004 tanh 2.3 nan -> nan nan
+tanh1005 tanh inf 0.0 -> 1.0 0.0
+tanh1006 tanh inf 0.7 -> 1.0 0.0
+tanh1007 tanh inf 1.4 -> 1.0 0.0
+tanh1008 tanh inf 2.1 -> 1.0 -0.0
+tanh1009 tanh inf 2.8 -> 1.0 -0.0
+tanh1010 tanh inf 3.5 -> 1.0 0.0
+tanh1011 tanh inf inf -> 1.0 0.0        ignore-imag-sign
+tanh1012 tanh inf nan -> 1.0 0.0        ignore-imag-sign
+tanh1013 tanh nan 0.0 -> nan 0.0
+tanh1014 tanh nan 2.3 -> nan nan
+tanh1015 tanh nan inf -> nan nan
+tanh1016 tanh nan nan -> nan nan
+tanh1017 tanh 0.0 -0.0 -> 0.0 -0.0
+tanh1018 tanh 0.0 -inf -> nan nan       invalid
+tanh1019 tanh 2.3 -inf -> nan nan       invalid
+tanh1020 tanh inf -0.0 -> 1.0 -0.0
+tanh1021 tanh inf -0.7 -> 1.0 -0.0
+tanh1022 tanh inf -1.4 -> 1.0 -0.0
+tanh1023 tanh inf -2.1 -> 1.0 0.0
+tanh1024 tanh inf -2.8 -> 1.0 0.0
+tanh1025 tanh inf -3.5 -> 1.0 -0.0
+tanh1026 tanh inf -inf -> 1.0 0.0       ignore-imag-sign
+tanh1027 tanh nan -0.0 -> nan -0.0
+tanh1028 tanh nan -2.3 -> nan nan
+tanh1029 tanh nan -inf -> nan nan
+tanh1030 tanh -0.0 -0.0 -> -0.0 -0.0
+tanh1031 tanh -0.0 -inf -> nan nan      invalid
+tanh1032 tanh -2.3 -inf -> nan nan      invalid
+tanh1033 tanh -0.0 nan -> nan nan
+tanh1034 tanh -2.3 nan -> nan nan
+tanh1035 tanh -inf -0.0 -> -1.0 -0.0
+tanh1036 tanh -inf -0.7 -> -1.0 -0.0
+tanh1037 tanh -inf -1.4 -> -1.0 -0.0
+tanh1038 tanh -inf -2.1 -> -1.0 0.0
+tanh1039 tanh -inf -2.8 -> -1.0 0.0
+tanh1040 tanh -inf -3.5 -> -1.0 -0.0
+tanh1041 tanh -inf -inf -> -1.0 0.0     ignore-imag-sign
+tanh1042 tanh -inf nan -> -1.0 0.0      ignore-imag-sign
+tanh1043 tanh -0.0 0.0 -> -0.0 0.0
+tanh1044 tanh -0.0 inf -> nan nan       invalid
+tanh1045 tanh -2.3 inf -> nan nan       invalid
+tanh1046 tanh -inf 0.0 -> -1.0 0.0
+tanh1047 tanh -inf 0.7 -> -1.0 0.0
+tanh1048 tanh -inf 1.4 -> -1.0 0.0
+tanh1049 tanh -inf 2.1 -> -1.0 -0.0
+tanh1050 tanh -inf 2.8 -> -1.0 -0.0
+tanh1051 tanh -inf 3.5 -> -1.0 0.0
+tanh1052 tanh -inf inf -> -1.0 0.0      ignore-imag-sign
+
+
+-----------------
+-- cos: Cosine --
+-----------------
+
+-- zeros
+cos0000 cos 0.0 0.0 -> 1.0 -0.0
+cos0001 cos 0.0 -0.0 -> 1.0 0.0
+cos0002 cos -0.0 0.0 -> 1.0 0.0
+cos0003 cos -0.0 -0.0 -> 1.0 -0.0
+
+-- random inputs
+cos0004 cos -2.0689194692073034 -0.0016802181751734313 -> -0.47777827208561469 -0.0014760401501695971
+cos0005 cos -0.4209627318177977 -1.8238516774258027 -> 2.9010402201444108 -1.2329207042329617
+cos0006 cos -1.9402181630694557 -2.9751857392891217 -> -3.5465459297970985 -9.1119163586282248
+cos0007 cos -3.3118320290191616 -0.87871302909286142 -> -1.3911528636565498 0.16878141517391701
+cos0008 cos -4.9540404623376872 -0.57949232239026827 -> 0.28062445586552065 0.59467861308508008
+cos0009 cos -0.45374584316245026 1.3950283448373935 -> 1.9247665574290578 0.83004572204761107
+cos0010 cos -0.42578172040176843 1.2715881615413049 -> 1.7517161459489148 0.67863902697363332
+cos0011 cos -0.13862985354300136 0.43587635877670328 -> 1.0859880290361912 0.062157548146672272
+cos0012 cos -0.11073221308966584 9.9384082307326475e-15 -> 0.99387545040722947 1.0982543264065479e-15
+cos0013 cos -1.5027633662054623e-07 0.0069668060249955498 -> 1.0000242682912412 1.0469545565660995e-09
+cos0014 cos 4.9728645490503052 -0.00027479808860952822 -> 0.25754011731975501 -0.00026552849549083186
+cos0015 cos 7.81969303486719 -0.79621523445878783 -> 0.045734882501585063 0.88253139933082991
+cos0016 cos 0.13272421880766716 -0.74668445308718201 -> 1.2806012244432847 0.10825373267437005
+cos0017 cos 4.2396521985973274 -2.2178848380884881 -> -2.1165117057056855 -4.0416492444641401
+cos0018 cos 1.1622206624927296 -0.50400115461197081 -> 0.44884072613370379 0.4823469915034318
+cos0019 cos 1.628772864620884e-08 0.58205705428979282 -> 1.1742319995791435 -1.0024839481956604e-08
+cos0020 cos 2.6385212606111241 2.9886107100937296 -> -8.7209475927161417 -4.7748352107199796
+cos0021 cos 4.8048375263775256 0.0062248852898515658 -> 0.092318702015846243 0.0061983430422306142
+cos0022 cos 7.9914515433858515 0.71659966615501436 -> -0.17375439906936566 -0.77217043527294582
+cos0023 cos 0.45124351152540226 1.6992693993812158 -> 2.543477948972237 -1.1528193694875477
+
+-- special values
+cos1000 cos -0.0 0.0 -> 1.0 0.0
+cos1001 cos -inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1002 cos nan 0.0 -> nan 0.0 ignore-imag-sign
+cos1003 cos -inf 2.2999999999999998 -> nan nan invalid
+cos1004 cos nan 2.2999999999999998 -> nan nan
+cos1005 cos -0.0 inf -> inf 0.0
+cos1006 cos -1.3999999999999999 inf -> inf inf
+cos1007 cos -2.7999999999999998 inf -> -inf inf
+cos1008 cos -4.2000000000000002 inf -> -inf -inf
+cos1009 cos -5.5999999999999996 inf -> inf -inf
+cos1010 cos -7.0 inf -> inf inf
+cos1011 cos -inf inf -> inf nan invalid ignore-real-sign
+cos1012 cos nan inf -> inf nan
+cos1013 cos -0.0 nan -> nan 0.0 ignore-imag-sign
+cos1014 cos -2.2999999999999998 nan -> nan nan
+cos1015 cos -inf nan -> nan nan
+cos1016 cos nan nan -> nan nan
+cos1017 cos 0.0 0.0 -> 1.0 -0.0
+cos1018 cos inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1019 cos inf 2.2999999999999998 -> nan nan invalid
+cos1020 cos 0.0 inf -> inf -0.0
+cos1021 cos 1.3999999999999999 inf -> inf -inf
+cos1022 cos 2.7999999999999998 inf -> -inf -inf
+cos1023 cos 4.2000000000000002 inf -> -inf inf
+cos1024 cos 5.5999999999999996 inf -> inf inf
+cos1025 cos 7.0 inf -> inf -inf
+cos1026 cos inf inf -> inf nan invalid ignore-real-sign
+cos1027 cos 0.0 nan -> nan 0.0 ignore-imag-sign
+cos1028 cos 2.2999999999999998 nan -> nan nan
+cos1029 cos inf nan -> nan nan
+cos1030 cos 0.0 -0.0 -> 1.0 0.0
+cos1031 cos inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1032 cos nan -0.0 -> nan 0.0 ignore-imag-sign
+cos1033 cos inf -2.2999999999999998 -> nan nan invalid
+cos1034 cos nan -2.2999999999999998 -> nan nan
+cos1035 cos 0.0 -inf -> inf 0.0
+cos1036 cos 1.3999999999999999 -inf -> inf inf
+cos1037 cos 2.7999999999999998 -inf -> -inf inf
+cos1038 cos 4.2000000000000002 -inf -> -inf -inf
+cos1039 cos 5.5999999999999996 -inf -> inf -inf
+cos1040 cos 7.0 -inf -> inf inf
+cos1041 cos inf -inf -> inf nan invalid ignore-real-sign
+cos1042 cos nan -inf -> inf nan
+cos1043 cos -0.0 -0.0 -> 1.0 -0.0
+cos1044 cos -inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+cos1045 cos -inf -2.2999999999999998 -> nan nan invalid
+cos1046 cos -0.0 -inf -> inf -0.0
+cos1047 cos -1.3999999999999999 -inf -> inf -inf
+cos1048 cos -2.7999999999999998 -inf -> -inf -inf
+cos1049 cos -4.2000000000000002 -inf -> -inf inf
+cos1050 cos -5.5999999999999996 -inf -> inf inf
+cos1051 cos -7.0 -inf -> inf -inf
+cos1052 cos -inf -inf -> inf nan invalid ignore-real-sign
+
+
+---------------
+-- sin: Sine --
+---------------
+
+-- zeros
+sin0000 sin 0.0 0.0 -> 0.0 0.0
+sin0001 sin 0.0 -0.0 -> 0.0 -0.0
+sin0002 sin -0.0 0.0 -> -0.0 0.0
+sin0003 sin -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+sin0004 sin -0.18691829163163759 -0.74388741985507034 -> -0.2396636733773444 -0.80023231101856751
+sin0005 sin -0.45127453702459158 -461.81339920716164 -> -7.9722299331077877e+199 -1.6450205811004628e+200
+sin0006 sin -0.47669228345768921 -2.7369936564987514 -> -3.557238022267124 -6.8308030771226615
+sin0007 sin -0.31024285525950857 -1.4869219939188296 -> -0.70972676047175209 -1.9985029635426839
+sin0008 sin -4.4194573407025608 -1.405999210989288 -> 2.0702480800802685 0.55362250792180601
+sin0009 sin -1.7810832046434898e-05 0.0016439555384379083 -> -1.7810856113185261e-05 0.0016439562786668375
+sin0010 sin -0.8200017874897666 0.61724876887771929 -> -0.8749078195948865 0.44835295550987758
+sin0011 sin -1.4536502806107114 0.63998575534150415 -> -1.2035709929437679 0.080012187489163708
+sin0012 sin -2.2653412155506079 0.13172760685583729 -> -0.77502093809190431 -0.084554426868229532
+sin0013 sin -0.02613983069491858 0.18404766597776073 -> -0.026580778863127943 0.18502525396735642
+sin0014 sin 1.5743065001054617 -0.53125574272642029 -> 1.1444596332092725 0.0019537598099352077
+sin0015 sin 7.3833101791283289e-20 -0.16453221324236217 -> 7.4834720674379429e-20 -0.16527555646466915
+sin0016 sin 0.34763834641254038 -2.8377416421089565 -> 2.918883541504663 -8.0002718053250224
+sin0017 sin 0.077105785180421563 -0.090056027316200674 -> 0.077341973814471304 -0.089909869380524587
+sin0018 sin 3.9063227798142329e-17 -0.05954098654295524 -> 3.9132490348956512e-17 -0.059576172859837351
+sin0019 sin 0.57333917932544598 8.7785221430594696e-06 -> 0.54244029338302935 7.3747869125301368e-06
+sin0020 sin 0.024861722816513169 0.33044620756118515 -> 0.026228801369651 0.3363889671570689
+sin0021 sin 1.4342727387492671 0.81361889790284347 -> 1.3370960060947923 0.12336137961387163
+sin0022 sin 1.1518087354403725 4.8597235966150558 -> 58.919141989603041 26.237003403758852
+sin0023 sin 0.00087773078406649192 34.792379211312095 -> 565548145569.38245 644329685822700.62
+
+-- special values
+sin1000 sin -0.0 0.0 -> -0.0 0.0
+sin1001 sin -inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1002 sin nan 0.0 -> nan 0.0 ignore-imag-sign
+sin1003 sin -inf 2.2999999999999998 -> nan nan invalid
+sin1004 sin nan 2.2999999999999998 -> nan nan
+sin1005 sin -0.0 inf -> -0.0 inf
+sin1006 sin -1.3999999999999999 inf -> -inf inf
+sin1007 sin -2.7999999999999998 inf -> -inf -inf
+sin1008 sin -4.2000000000000002 inf -> inf -inf
+sin1009 sin -5.5999999999999996 inf -> inf inf
+sin1010 sin -7.0 inf -> -inf inf
+sin1011 sin -inf inf -> nan inf invalid ignore-imag-sign
+sin1012 sin nan inf -> nan inf ignore-imag-sign
+sin1013 sin -0.0 nan -> -0.0 nan
+sin1014 sin -2.2999999999999998 nan -> nan nan
+sin1015 sin -inf nan -> nan nan
+sin1016 sin nan nan -> nan nan
+sin1017 sin 0.0 0.0 -> 0.0 0.0
+sin1018 sin inf 0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1019 sin inf 2.2999999999999998 -> nan nan invalid
+sin1020 sin 0.0 inf -> 0.0 inf
+sin1021 sin 1.3999999999999999 inf -> inf inf
+sin1022 sin 2.7999999999999998 inf -> inf -inf
+sin1023 sin 4.2000000000000002 inf -> -inf -inf
+sin1024 sin 5.5999999999999996 inf -> -inf inf
+sin1025 sin 7.0 inf -> inf inf
+sin1026 sin inf inf -> nan inf invalid ignore-imag-sign
+sin1027 sin 0.0 nan -> 0.0 nan
+sin1028 sin 2.2999999999999998 nan -> nan nan
+sin1029 sin inf nan -> nan nan
+sin1030 sin 0.0 -0.0 -> 0.0 -0.0
+sin1031 sin inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1032 sin nan -0.0 -> nan 0.0 ignore-imag-sign
+sin1033 sin inf -2.2999999999999998 -> nan nan invalid
+sin1034 sin nan -2.2999999999999998 -> nan nan
+sin1035 sin 0.0 -inf -> 0.0 -inf
+sin1036 sin 1.3999999999999999 -inf -> inf -inf
+sin1037 sin 2.7999999999999998 -inf -> inf inf
+sin1038 sin 4.2000000000000002 -inf -> -inf inf
+sin1039 sin 5.5999999999999996 -inf -> -inf -inf
+sin1040 sin 7.0 -inf -> inf -inf
+sin1041 sin inf -inf -> nan inf invalid ignore-imag-sign
+sin1042 sin nan -inf -> nan inf ignore-imag-sign
+sin1043 sin -0.0 -0.0 -> -0.0 -0.0
+sin1044 sin -inf -0.0 -> nan 0.0 invalid ignore-imag-sign
+sin1045 sin -inf -2.2999999999999998 -> nan nan invalid
+sin1046 sin -0.0 -inf -> -0.0 -inf
+sin1047 sin -1.3999999999999999 -inf -> -inf -inf
+sin1048 sin -2.7999999999999998 -inf -> -inf inf
+sin1049 sin -4.2000000000000002 -inf -> inf inf
+sin1050 sin -5.5999999999999996 -inf -> inf -inf
+sin1051 sin -7.0 -inf -> -inf -inf
+sin1052 sin -inf -inf -> nan inf invalid ignore-imag-sign
+
+
+------------------
+-- tan: Tangent --
+------------------
+
+-- zeros
+tan0000 tan 0.0 0.0 -> 0.0 0.0
+tan0001 tan 0.0 -0.0 -> 0.0 -0.0
+tan0002 tan -0.0 0.0 -> -0.0 0.0
+tan0003 tan -0.0 -0.0 -> -0.0 -0.0
+
+-- random inputs
+tan0004 tan -0.56378561833861074 -1.7110276237187664e+73 -> -0.0 -1.0
+tan0005 tan -3.5451633993471915e-12 -2.855471863564059 -> -4.6622441304889575e-14 -0.99340273843093951
+tan0006 tan -2.502442719638696 -0.26742234390504221 -> 0.66735215252994995 -0.39078997935420956
+tan0007 tan -0.87639597720371365 -55.586225523280206 -> -1.0285264565948176e-48 -1.0
+tan0008 tan -0.015783869596427243 -520.05944436039272 -> -0.0 -1.0
+tan0009 tan -0.84643549990725164 2.0749097935396343 -> -0.031412661676959573 1.0033548479526764
+tan0010 tan -0.43613792248559646 8.1082741629458059 -> -1.3879848444644593e-07 0.99999988344224011
+tan0011 tan -1.0820906367833114 0.28571868992480248 -> -1.3622485737936536 0.99089269377971245
+tan0012 tan -1.1477859580220084 1.9021637002708041 -> -0.034348450042071196 1.0293954097901687
+tan0013 tan -0.12465543176953409 3.0606851016344815e-05 -> -0.12530514290387343 3.1087420769945479e-05
+tan0014 tan 3.7582848717525343 -692787020.44038939 -> 0.0 -1.0
+tan0015 tan 2.2321967655142176e-06 -10.090069423008169 -> 1.5369846120622643e-14 -0.99999999655723759
+tan0016 tan 0.88371172390245012 -1.1635053630132823 -> 0.19705017118625889 -1.0196452280843129
+tan0017 tan 2.1347414231849267 -1.9311339960416831 -> -0.038663576915982524 -1.0174399993980778
+tan0018 tan 5.9027945255899974 -2.1574195684607135e-183 -> -0.39986591539281496 -2.5023753167976915e-183
+tan0019 tan 0.44811489490805362 683216075670.07556 -> 0.0 1.0
+tan0020 tan 4.1459766396068325 12.523017205605756 -> 2.4022514758988068e-11 1.0000000000112499
+tan0021 tan 1.7809617968443272 1.5052381702853379 -> -0.044066222118946903 1.0932684517702778
+tan0022 tan 1.1615313900880577 1.7956298728647107 -> 0.041793186826390362 1.0375339546034792
+tan0023 tan 0.067014779477908945 5.8517361577457097 -> 2.2088639754800034e-06 0.9999836182420061
+
+-- special values
+tan1000 tan -0.0 0.0 -> -0.0 0.0
+tan1001 tan -inf 0.0 -> nan nan invalid
+tan1002 tan -inf 2.2999999999999998 -> nan nan invalid
+tan1003 tan nan 0.0 -> nan nan
+tan1004 tan nan 2.2999999999999998 -> nan nan
+tan1005 tan -0.0 inf -> -0.0 1.0
+tan1006 tan -0.69999999999999996 inf -> -0.0 1.0
+tan1007 tan -1.3999999999999999 inf -> -0.0 1.0
+tan1008 tan -2.1000000000000001 inf -> 0.0 1.0
+tan1009 tan -2.7999999999999998 inf -> 0.0 1.0
+tan1010 tan -3.5 inf -> -0.0 1.0
+tan1011 tan -inf inf -> -0.0 1.0 ignore-real-sign
+tan1012 tan nan inf -> -0.0 1.0 ignore-real-sign
+tan1013 tan -0.0 nan -> -0.0 nan
+tan1014 tan -2.2999999999999998 nan -> nan nan
+tan1015 tan -inf nan -> nan nan
+tan1016 tan nan nan -> nan nan
+tan1017 tan 0.0 0.0 -> 0.0 0.0
+tan1018 tan inf 0.0 -> nan nan invalid
+tan1019 tan inf 2.2999999999999998 -> nan nan invalid
+tan1020 tan 0.0 inf -> 0.0 1.0
+tan1021 tan 0.69999999999999996 inf -> 0.0 1.0
+tan1022 tan 1.3999999999999999 inf -> 0.0 1.0
+tan1023 tan 2.1000000000000001 inf -> -0.0 1.0
+tan1024 tan 2.7999999999999998 inf -> -0.0 1.0
+tan1025 tan 3.5 inf -> 0.0 1.0
+tan1026 tan inf inf -> -0.0 1.0 ignore-real-sign
+tan1027 tan 0.0 nan -> 0.0 nan
+tan1028 tan 2.2999999999999998 nan -> nan nan
+tan1029 tan inf nan -> nan nan
+tan1030 tan 0.0 -0.0 -> 0.0 -0.0
+tan1031 tan inf -0.0 -> nan nan invalid
+tan1032 tan inf -2.2999999999999998 -> nan nan invalid
+tan1033 tan nan -0.0 -> nan nan
+tan1034 tan nan -2.2999999999999998 -> nan nan
+tan1035 tan 0.0 -inf -> 0.0 -1.0
+tan1036 tan 0.69999999999999996 -inf -> 0.0 -1.0
+tan1037 tan 1.3999999999999999 -inf -> 0.0 -1.0
+tan1038 tan 2.1000000000000001 -inf -> -0.0 -1.0
+tan1039 tan 2.7999999999999998 -inf -> -0.0 -1.0
+tan1040 tan 3.5 -inf -> 0.0 -1.0
+tan1041 tan inf -inf -> -0.0 -1.0 ignore-real-sign
+tan1042 tan nan -inf -> -0.0 -1.0 ignore-real-sign
+tan1043 tan -0.0 -0.0 -> -0.0 -0.0
+tan1044 tan -inf -0.0 -> nan nan invalid
+tan1045 tan -inf -2.2999999999999998 -> nan nan invalid
+tan1046 tan -0.0 -inf -> -0.0 -1.0
+tan1047 tan -0.69999999999999996 -inf -> -0.0 -1.0
+tan1048 tan -1.3999999999999999 -inf -> -0.0 -1.0
+tan1049 tan -2.1000000000000001 -inf -> 0.0 -1.0
+tan1050 tan -2.7999999999999998 -inf -> 0.0 -1.0
+tan1051 tan -3.5 -inf -> -0.0 -1.0
+tan1052 tan -inf -inf -> -0.0 -1.0 ignore-real-sign
+
+
+------------------------------------------------------------------------
+-- rect: Conversion from polar coordinates to rectangular coordinates --
+------------------------------------------------------------------------
+--
+-- For cmath.rect, we can use the same testcase syntax as for the
+-- complex -> complex functions above, but here the input arguments
+-- should be interpreted as a pair of floating-point numbers rather
+-- than the real and imaginary parts of a complex number.
+--
+-- Here are the 'spirit of C99' rules for rect.  First, the short
+-- version:
+--
+--    rect(x, t) = exp(log(x)+it) for positive-signed x
+--    rect(x, t) = -exp(log(-x)+it) for negative-signed x
+--    rect(nan, t) = exp(nan + it), except that in rect(nan, +-0) the
+--      sign of the imaginary part is unspecified.
+--
+-- and now the long version:
+--
+--   rect(x, -t) = conj(rect(x, t)) for all x and t
+--   rect(-x, t) = -rect(x, t) for all x and t
+--   rect(+0, +0) returns +0 + i0
+--   rect(+0, inf) returns +- 0 +- i0, where the signs of the real and
+--     imaginary parts are unspecified.
+--   rect(x, inf) returns NaN + i NaN and raises the "invalid"
+--     floating-point exception, for finite nonzero x.
+--   rect(inf, inf) returns +-inf + i NaN and raises the "invalid"
+--     floating-point exception (where the sign of the real part of the
+--     result is unspecified).
+--   rect(inf, +0) returns inf+i0
+--   rect(inf, x) returns inf*cis(x), for finite nonzero x
+--   rect(inf, NaN) returns +-inf+i NaN, where the sign of the real part
+--     of the result is unspecified.
+--   rect(NaN, x) returns NaN + i NaN for all nonzero numbers (including
+--     infinities) x
+--   rect(NaN, 0) returns NaN +- i0, where the sign of the imaginary
+--     part is unspecified
+--   rect(NaN, NaN) returns NaN + i NaN
+--   rect(x, NaN) returns NaN + i NaN for finite nonzero x
+--   rect(+0, NaN) return +-0 +- i0, where the signs of the real and
+--     imaginary parts are unspecified.
+
+-- special values
+rect1000 rect 0.0 0.0 -> 0.0 0.0
+rect1001 rect 0.0 inf -> 0.0 0.0        ignore-real-sign ignore-imag-sign
+rect1002 rect 2.3 inf -> nan nan        invalid
+rect1003 rect inf inf -> inf nan        invalid ignore-real-sign
+rect1004 rect inf 0.0 -> inf 0.0
+rect1005 rect inf 1.4 -> inf inf
+rect1006 rect inf 2.8 -> -inf inf
+rect1007 rect inf 4.2 -> -inf -inf
+rect1008 rect inf 5.6 -> inf -inf
+rect1009 rect inf 7.0 -> inf inf
+rect1010 rect nan 0.0 -> nan 0.0        ignore-imag-sign
+rect1011 rect nan 2.3 -> nan nan
+rect1012 rect nan inf -> nan nan
+rect1013 rect nan nan -> nan nan
+rect1014 rect inf nan -> inf nan        ignore-real-sign
+rect1015 rect 2.3 nan -> nan nan
+rect1016 rect 0.0 nan -> 0.0 0.0        ignore-real-sign ignore-imag-sign
+rect1017 rect 0.0 -0.0 -> 0.0 -0.0
+rect1018 rect 0.0 -inf -> 0.0 0.0       ignore-real-sign ignore-imag-sign
+rect1019 rect 2.3 -inf -> nan nan       invalid
+rect1020 rect inf -inf -> inf nan       invalid ignore-real-sign
+rect1021 rect inf -0.0 -> inf -0.0
+rect1022 rect inf -1.4 -> inf -inf
+rect1023 rect inf -2.8 -> -inf -inf
+rect1024 rect inf -4.2 -> -inf inf
+rect1025 rect inf -5.6 -> inf inf
+rect1026 rect inf -7.0 -> inf -inf
+rect1027 rect nan -0.0 -> nan 0.0       ignore-imag-sign
+rect1028 rect nan -2.3 -> nan nan
+rect1029 rect nan -inf -> nan nan
+rect1030 rect -0.0 0.0 -> -0.0 -0.0
+rect1031 rect -0.0 inf -> 0.0 0.0       ignore-real-sign ignore-imag-sign
+rect1032 rect -2.3 inf -> nan nan       invalid
+rect1033 rect -inf inf -> -inf nan      invalid ignore-real-sign
+rect1034 rect -inf 0.0 -> -inf -0.0
+rect1035 rect -inf 1.4 -> -inf -inf
+rect1036 rect -inf 2.8 -> inf -inf
+rect1037 rect -inf 4.2 -> inf inf
+rect1038 rect -inf 5.6 -> -inf inf
+rect1039 rect -inf 7.0 -> -inf -inf
+rect1040 rect -inf nan -> inf nan       ignore-real-sign
+rect1041 rect -2.3 nan -> nan nan
+rect1042 rect -0.0 nan -> 0.0 0.0       ignore-real-sign ignore-imag-sign
+rect1043 rect -0.0 -0.0 -> -0.0 0.0
+rect1044 rect -0.0 -inf -> 0.0 0.0      ignore-real-sign ignore-imag-sign
+rect1045 rect -2.3 -inf -> nan nan      invalid
+rect1046 rect -inf -inf -> -inf nan     invalid ignore-real-sign
+rect1047 rect -inf -0.0 -> -inf 0.0
+rect1048 rect -inf -1.4 -> -inf inf
+rect1049 rect -inf -2.8 -> inf inf
+rect1050 rect -inf -4.2 -> inf -inf
+rect1051 rect -inf -5.6 -> -inf -inf
+rect1052 rect -inf -7.0 -> -inf inf
+
+-------------------------------------------------------------------------
+-- polar: Conversion from rectangular coordinates to polar coordinates --
+-------------------------------------------------------------------------
+--
+-- For cmath.polar, we can use the same testcase syntax as for the
+-- complex -> complex functions above, but here the output arguments
+-- should be interpreted as a pair of floating-point numbers rather
+-- than the real and imaginary parts of a complex number.
+--
+-- Annex G of the C99 standard describes fully both the real and
+-- imaginary parts of polar (as cabs and carg, respectively, which in turn
+-- are defined in terms of the functions hypot and atan2).
+
+-- overflow
+polar0100 polar 1.4e308 1.4e308 -> inf 0.78539816339744828      overflow
+
+-- special values
+polar1000 polar 0.0 0.0 -> 0.0 0.0
+polar1001 polar 0.0 -0.0 -> 0.0 -0.0
+polar1002 polar -0.0 0.0 -> 0.0 3.1415926535897931
+polar1003 polar -0.0 -0.0 -> 0.0 -3.1415926535897931
+polar1004 polar inf 0.0 -> inf 0.0
+polar1005 polar inf 2.3 -> inf 0.0
+polar1006 polar inf inf -> inf 0.78539816339744828
+polar1007 polar 2.3 inf -> inf 1.5707963267948966
+polar1008 polar 0.0 inf -> inf 1.5707963267948966
+polar1009 polar -0.0 inf -> inf 1.5707963267948966
+polar1010 polar -2.3 inf -> inf 1.5707963267948966
+polar1011 polar -inf inf -> inf 2.3561944901923448
+polar1012 polar -inf 2.3 -> inf 3.1415926535897931
+polar1013 polar -inf 0.0 -> inf 3.1415926535897931
+polar1014 polar -inf -0.0 -> inf -3.1415926535897931
+polar1015 polar -inf -2.3 -> inf -3.1415926535897931
+polar1016 polar -inf -inf -> inf -2.3561944901923448
+polar1017 polar -2.3 -inf -> inf -1.5707963267948966
+polar1018 polar -0.0 -inf -> inf -1.5707963267948966
+polar1019 polar 0.0 -inf -> inf -1.5707963267948966
+polar1020 polar 2.3 -inf -> inf -1.5707963267948966
+polar1021 polar inf -inf -> inf -0.78539816339744828
+polar1022 polar inf -2.3 -> inf -0.0
+polar1023 polar inf -0.0 -> inf -0.0
+polar1024 polar nan -inf -> inf nan
+polar1025 polar nan -2.3 -> nan nan
+polar1026 polar nan -0.0 -> nan nan
+polar1027 polar nan 0.0 -> nan nan
+polar1028 polar nan 2.3 -> nan nan
+polar1029 polar nan inf -> inf nan
+polar1030 polar nan nan -> nan nan
+polar1031 polar inf nan -> inf nan
+polar1032 polar 2.3 nan -> nan nan
+polar1033 polar 0.0 nan -> nan nan
+polar1034 polar -0.0 nan -> nan nan
+polar1035 polar -2.3 nan -> nan nan
+polar1036 polar -inf nan -> inf nan
diff --git a/Lib/test/ieee754.txt b/Lib/test/ieee754.txt
new file mode 100644
index 0000000000..5a41c8fe50
--- /dev/null
+++ b/Lib/test/ieee754.txt
@@ -0,0 +1,183 @@
+======================================
+Python IEEE 754 floating point support
+======================================
+
+>>> from sys import float_info as FI
+>>> from math import *
+>>> PI = pi
+>>> E = e
+
+You must never compare two floats with == because you are not going to get
+what you expect. We treat two floats as equal if the difference between them
+is small than epsilon.
+>>> EPS = 1E-15
+>>> def equal(x, y):
+...     """Almost equal helper for floats"""
+...     return abs(x - y) < EPS
+
+
+NaNs and INFs
+=============
+
+In Python 2.6 and newer NaNs (not a number) and infinity can be constructed
+from the strings 'inf' and 'nan'.
+
+>>> INF = float('inf')
+>>> NINF = float('-inf')
+>>> NAN = float('nan')
+
+>>> INF
+inf
+>>> NINF
+-inf
+>>> NAN
+nan
+
+The math module's ``isnan`` and ``isinf`` functions can be used to detect INF
+and NAN:
+>>> isinf(INF), isinf(NINF), isnan(NAN)
+(True, True, True)
+>>> INF == -NINF
+True
+
+Infinity
+--------
+
+Ambiguous operations like ``0 * inf`` or ``inf - inf`` result in NaN.
+>>> INF * 0
+nan
+>>> INF - INF
+nan
+>>> INF / INF
+nan
+
+However unambigous operations with inf return inf:
+>>> INF * INF
+inf
+>>> 1.5 * INF
+inf
+>>> 0.5 * INF
+inf
+>>> INF / 1000
+inf
+
+Not a Number
+------------
+
+NaNs are never equal to another number, even itself
+>>> NAN == NAN
+False
+>>> NAN < 0
+False
+>>> NAN >= 0
+False
+
+All operations involving a NaN return a NaN except for the power of *0* and *1*.
+>>> 1 + NAN
+nan
+>>> 1 * NAN
+nan
+>>> 0 * NAN
+nan
+>>> 1 ** NAN
+1.0
+>>> 0 ** NAN
+0.0
+>>> (1.0 + FI.epsilon) * NAN
+nan
+
+Misc Functions
+==============
+
+The power of 1 raised to x is always 1.0, even for special values like 0,
+infinity and NaN.
+
+>>> pow(1, 0)
+1.0
+>>> pow(1, INF)
+1.0
+>>> pow(1, -INF)
+1.0
+>>> pow(1, NAN)
+1.0
+
+The power of 0 raised to x is defined as 0, if x is positive. Negative
+values are a domain error or zero division error and NaN result in a
+silent NaN.
+
+>>> pow(0, 0)
+1.0
+>>> pow(0, INF)
+0.0
+>>> pow(0, -INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> 0 ** -1
+Traceback (most recent call last):
+...
+ZeroDivisionError: 0.0 cannot be raised to a negative power
+>>> pow(0, NAN)
+nan
+
+
+Trigonometric Functions
+=======================
+
+>>> sin(INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> sin(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> sin(NAN)
+nan
+>>> cos(INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> cos(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> cos(NAN)
+nan
+>>> tan(INF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> tan(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> tan(NAN)
+nan
+
+Neither pi nor tan are exact, but you can assume that tan(pi/2) is a large value
+and tan(pi) is a very small value:
+>>> tan(PI/2) > 1E10
+True
+>>> -tan(-PI/2) > 1E10
+True
+>>> tan(PI) < 1E-15
+True
+
+>>> asin(NAN), acos(NAN), atan(NAN)
+(nan, nan, nan)
+>>> asin(INF), asin(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> acos(INF), acos(NINF)
+Traceback (most recent call last):
+...
+ValueError: math domain error
+>>> equal(atan(INF), PI/2), equal(atan(NINF), -PI/2)
+(True, True)
+
+
+Hyberbolic Functions
+====================
+
diff --git a/Lib/test/test_cmath.py b/Lib/test/test_cmath.py
index 7c5f4a555a..ca4945d18c 100755
--- a/Lib/test/test_cmath.py
+++ b/Lib/test/test_cmath.py
@@ -1,6 +1,81 @@
 from test.test_support import run_unittest
+from test.test_math import parse_testfile, test_file
 import unittest
+import os, sys
 import cmath, math
+from cmath import phase, polar, rect, pi
+
+INF = float('inf')
+NAN = float('nan')
+
+complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
+complex_infinities = [complex(x, y) for x, y in [
+        (INF, 0.0),  # 1st quadrant
+        (INF, 2.3),
+        (INF, INF),
+        (2.3, INF),
+        (0.0, INF),
+        (-0.0, INF), # 2nd quadrant
+        (-2.3, INF),
+        (-INF, INF),
+        (-INF, 2.3),
+        (-INF, 0.0),
+        (-INF, -0.0), # 3rd quadrant
+        (-INF, -2.3),
+        (-INF, -INF),
+        (-2.3, -INF),
+        (-0.0, -INF),
+        (0.0, -INF), # 4th quadrant
+        (2.3, -INF),
+        (INF, -INF),
+        (INF, -2.3),
+        (INF, -0.0)
+        ]]
+complex_nans = [complex(x, y) for x, y in [
+        (NAN, -INF),
+        (NAN, -2.3),
+        (NAN, -0.0),
+        (NAN, 0.0),
+        (NAN, 2.3),
+        (NAN, INF),
+        (-INF, NAN),
+        (-2.3, NAN),
+        (-0.0, NAN),
+        (0.0, NAN),
+        (2.3, NAN),
+        (INF, NAN)
+        ]]
+
+def almostEqualF(a, b, rel_err=2e-15, abs_err = 5e-323):
+    """Determine whether floating-point values a and b are equal to within
+    a (small) rounding error.  The default values for rel_err and
+    abs_err are chosen to be suitable for platforms where a float is
+    represented by an IEEE 754 double.  They allow an error of between
+    9 and 19 ulps."""
+
+    # special values testing
+    if math.isnan(a):
+        return math.isnan(b)
+    if math.isinf(a):
+        return a == b
+
+    # if both a and b are zero, check whether they have the same sign
+    # (in theory there are examples where it would be legitimate for a
+    # and b to have opposite signs; in practice these hardly ever
+    # occur).
+    if not a and not b:
+        return math.copysign(1., a) == math.copysign(1., b)
+
+    # if a-b overflows, or b is infinite, return False.  Again, in
+    # theory there are examples where a is within a few ulps of the
+    # max representable float, and then b could legitimately be
+    # infinite.  In practice these examples are rare.
+    try:
+        absolute_error = abs(b-a)
+    except OverflowError:
+        return False
+    else:
+        return absolute_error <= max(abs_err, rel_err * abs(a))
 
 class CMathTests(unittest.TestCase):
     # list of all functions in cmath
@@ -12,25 +87,51 @@ class CMathTests(unittest.TestCase):
     test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
     test_functions.append(lambda x : cmath.log(14.-27j, x))
 
-    def cAssertAlmostEqual(self, a, b, rel_eps = 1e-10, abs_eps = 1e-100):
-        """Check that two complex numbers are almost equal."""
-        # the two complex numbers are considered almost equal if
-        # either the relative error is <= rel_eps or the absolute error
-        # is tiny, <= abs_eps.
-        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 setUp(self):
+        self.test_values = open(test_file)
+
+    def tearDown(self):
+        self.test_values.close()
+
+    def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323):
+        """Check that two floating-point numbers are almost equal."""
+
+        # special values testing
+        if math.isnan(a):
+            if math.isnan(b):
+                return
+            self.fail("%s should be nan" % repr(b))
+
+        if math.isinf(a):
+            if a == b:
+                return
+            self.fail("finite result where infinity excpected: "
+                      "expected %s, got %s" % (repr(a), repr(b)))
+
+        if not a and not b:
+            if math.atan2(a, -1.) != math.atan2(b, -1.):
+                self.fail("zero has wrong sign: expected %s, got %s" %
+                          (repr(a), repr(b)))
+
+        # test passes if either the absolute error or the relative
+        # error is sufficiently small.  The defaults amount to an
+        # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
+        # machine.
+
+        try:
+            absolute_error = abs(b-a)
+        except OverflowError:
+            pass
+        else:
+            if absolute_error <= max(abs_err, rel_err * abs(a)):
+                return
+        self.fail("%s and %s are not sufficiently close" % (repr(a), repr(b)))
 
     def test_constants(self):
         e_expected = 2.71828182845904523536
         pi_expected = 3.14159265358979323846
-        self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
-            msg="cmath.pi is %s; should be %s" % (cmath.pi, pi_expected))
-        self.assertAlmostEqual(cmath.e,  e_expected, places=9,
-            msg="cmath.e is %s; should be %s" % (cmath.e, e_expected))
+        self.assertAlmostEqual(cmath.pi, pi_expected)
+        self.assertAlmostEqual(cmath.e,  e_expected)
 
     def test_user_object(self):
         # Test automatic calling of __complex__ and __float__ by cmath
@@ -109,13 +210,13 @@ class CMathTests(unittest.TestCase):
 
         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))
+            self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
+            self.assertEqual(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))
+            self.assertEqual(f(FloatAndComplex()), f(cx_arg))
+            self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
+            self.assertEqual(f(JustFloat()), f(flt_arg))
+            self.assertEqual(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
@@ -138,7 +239,7 @@ class CMathTests(unittest.TestCase):
         # functions, by virtue of providing a __float__ method
         for f in self.test_functions:
             for arg in [2, 2.]:
-                self.cAssertAlmostEqual(f(arg), f(arg.__float__()))
+                self.assertEqual(f(arg), f(arg.__float__()))
 
         # but strings should give a TypeError
         for f in self.test_functions:
@@ -182,12 +283,201 @@ class CMathTests(unittest.TestCase):
             float_fn = getattr(math, fn)
             complex_fn = getattr(cmath, fn)
             for v in values:
-                self.cAssertAlmostEqual(float_fn(v), complex_fn(v))
+                z = complex_fn(v)
+                self.rAssertAlmostEqual(float_fn(v), z.real)
+                self.assertEqual(0., z.imag)
 
         # 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))
+                z = cmath.log(v, base)
+                self.rAssertAlmostEqual(math.log(v, base), z.real)
+                self.assertEqual(0., z.imag)
+
+    def test_specific_values(self):
+        if not float.__getformat__("double").startswith("IEEE"):
+            return
+
+        def rect_complex(z):
+            """Wrapped version of rect that accepts a complex number instead of
+            two float arguments."""
+            return cmath.rect(z.real, z.imag)
+
+        def polar_complex(z):
+            """Wrapped version of polar that returns a complex number instead of
+            two floats."""
+            return complex(*polar(z))
+
+        for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
+            arg = complex(ar, ai)
+            expected = complex(er, ei)
+            if fn == 'rect':
+                function = rect_complex
+            elif fn == 'polar':
+                function = polar_complex
+            else:
+                function = getattr(cmath, fn)
+            if 'divide-by-zero' in flags or 'invalid' in flags:
+                try:
+                    actual = function(arg)
+                except ValueError:
+                    continue
+                else:
+                    test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai)
+                    self.fail('ValueError not raised in test %s' % test_str)
+
+            if 'overflow' in flags:
+                try:
+                    actual = function(arg)
+                except OverflowError:
+                    continue
+                else:
+                    test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai)
+                    self.fail('OverflowError not raised in test %s' % test_str)
+
+            actual = function(arg)
+
+            if 'ignore-real-sign' in flags:
+                actual = complex(abs(actual.real), actual.imag)
+                expected = complex(abs(expected.real), expected.imag)
+            if 'ignore-imag-sign' in flags:
+                actual = complex(actual.real, abs(actual.imag))
+                expected = complex(expected.real, abs(expected.imag))
+
+            # for the real part of the log function, we allow an
+            # absolute error of up to 2e-15.
+            if fn in ('log', 'log10'):
+                real_abs_err = 2e-15
+            else:
+                real_abs_err = 5e-323
+
+            if not (almostEqualF(expected.real, actual.real,
+                                 abs_err = real_abs_err) and
+                    almostEqualF(expected.imag, actual.imag)):
+                error_message = (
+                    "%s: %s(complex(%r, %r))\n" % (id, fn, ar, ai) +
+                    "Expected: complex(%r, %r)\n" %
+                                    (expected.real, expected.imag) +
+                    "Received: complex(%r, %r)\n" %
+                                    (actual.real, actual.imag) +
+                    "Received value insufficiently close to expected value.")
+                self.fail(error_message)
+
+    def assertCISEqual(self, a, b):
+        eps = 1E-7
+        if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:
+            self.fail((a ,b))
+
+    def test_polar(self):
+        self.assertCISEqual(polar(0), (0., 0.))
+        self.assertCISEqual(polar(1.), (1., 0.))
+        self.assertCISEqual(polar(-1.), (1., pi))
+        self.assertCISEqual(polar(1j), (1., pi/2))
+        self.assertCISEqual(polar(-1j), (1., -pi/2))
+
+    def test_phase(self):
+        self.assertAlmostEqual(phase(0), 0.)
+        self.assertAlmostEqual(phase(1.), 0.)
+        self.assertAlmostEqual(phase(-1.), pi)
+        self.assertAlmostEqual(phase(-1.+1E-300j), pi)
+        self.assertAlmostEqual(phase(-1.-1E-300j), -pi)
+        self.assertAlmostEqual(phase(1j), pi/2)
+        self.assertAlmostEqual(phase(-1j), -pi/2)
+
+        # zeros
+        self.assertEqual(phase(complex(0.0, 0.0)), 0.0)
+        self.assertEqual(phase(complex(0.0, -0.0)), -0.0)
+        self.assertEqual(phase(complex(-0.0, 0.0)), pi)
+        self.assertEqual(phase(complex(-0.0, -0.0)), -pi)
+
+        # infinities
+        self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)
+        self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)
+        self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)
+        self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)
+        self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)
+        self.assertEqual(phase(complex(INF, -2.3)), -0.0)
+        self.assertEqual(phase(complex(INF, -0.0)), -0.0)
+        self.assertEqual(phase(complex(INF, 0.0)), 0.0)
+        self.assertEqual(phase(complex(INF, 2.3)), 0.0)
+        self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)
+        self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)
+        self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)
+        self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)
+        self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)
+
+        # real or imaginary part NaN
+        for z in complex_nans:
+            self.assert_(math.isnan(phase(z)))
+
+    def test_abs(self):
+        # zeros
+        for z in complex_zeros:
+            self.assertEqual(abs(z), 0.0)
+
+        # infinities
+        for z in complex_infinities:
+            self.assertEqual(abs(z), INF)
+
+        # real or imaginary part NaN
+        self.assertEqual(abs(complex(NAN, -INF)), INF)
+        self.assert_(math.isnan(abs(complex(NAN, -2.3))))
+        self.assert_(math.isnan(abs(complex(NAN, -0.0))))
+        self.assert_(math.isnan(abs(complex(NAN, 0.0))))
+        self.assert_(math.isnan(abs(complex(NAN, 2.3))))
+        self.assertEqual(abs(complex(NAN, INF)), INF)
+        self.assertEqual(abs(complex(-INF, NAN)), INF)
+        self.assert_(math.isnan(abs(complex(-2.3, NAN))))
+        self.assert_(math.isnan(abs(complex(-0.0, NAN))))
+        self.assert_(math.isnan(abs(complex(0.0, NAN))))
+        self.assert_(math.isnan(abs(complex(2.3, NAN))))
+        self.assertEqual(abs(complex(INF, NAN)), INF)
+        self.assert_(math.isnan(abs(complex(NAN, NAN))))
+
+        # result overflows
+        if float.__getformat__("double").startswith("IEEE"):
+            self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))
+
+    def assertCEqual(self, a, b):
+        eps = 1E-7
+        if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:
+            self.fail((a ,b))
+
+    def test_rect(self):
+        self.assertCEqual(rect(0, 0), (0, 0))
+        self.assertCEqual(rect(1, 0), (1., 0))
+        self.assertCEqual(rect(1, -pi), (-1., 0))
+        self.assertCEqual(rect(1, pi/2), (0, 1.))
+        self.assertCEqual(rect(1, -pi/2), (0, -1.))
+
+    def test_isnan(self):
+        self.failIf(cmath.isnan(1))
+        self.failIf(cmath.isnan(1j))
+        self.failIf(cmath.isnan(INF))
+        self.assert_(cmath.isnan(NAN))
+        self.assert_(cmath.isnan(complex(NAN, 0)))
+        self.assert_(cmath.isnan(complex(0, NAN)))
+        self.assert_(cmath.isnan(complex(NAN, NAN)))
+        self.assert_(cmath.isnan(complex(NAN, INF)))
+        self.assert_(cmath.isnan(complex(INF, NAN)))
+
+    def test_isinf(self):
+        self.failIf(cmath.isinf(1))
+        self.failIf(cmath.isinf(1j))
+        self.failIf(cmath.isinf(NAN))
+        self.assert_(cmath.isinf(INF))
+        self.assert_(cmath.isinf(complex(INF, 0)))
+        self.assert_(cmath.isinf(complex(0, INF)))
+        self.assert_(cmath.isinf(complex(INF, INF)))
+        self.assert_(cmath.isinf(complex(NAN, INF)))
+        self.assert_(cmath.isinf(complex(INF, NAN)))
+
 
 def test_main():
     run_unittest(CMathTests)
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index b9ad8c5ce7..e89d723fb5 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -2,12 +2,12 @@
 import unittest, struct
 import os
 from test import test_support
+import math
+from math import isinf, isnan
+import operator
 
-def isinf(x):
-    return x * 0.5 == x
-
-def isnan(x):
-    return x != x
+INF = float("inf")
+NAN = float("nan")
 
 class FormatFunctionsTestCase(unittest.TestCase):
 
@@ -239,6 +239,17 @@ class InfNanTest(unittest.TestCase):
         self.assertEqual(str(1e300 * 1e300 * 0), "nan")
         self.assertEqual(str(-1e300 * 1e300 * 0), "nan")
 
+    def notest_float_nan(self):
+        self.assert_(NAN.is_nan())
+        self.failIf(INF.is_nan())
+        self.failIf((0.).is_nan())
+
+    def notest_float_inf(self):
+        self.assert_(INF.is_inf())
+        self.failIf(NAN.is_inf())
+        self.failIf((0.).is_inf())
+
+
 def test_main():
     test_support.run_unittest(
         FormatFunctionsTestCase,
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index aa44253d2b..b8c23db638 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -4,9 +4,45 @@
 from test.test_support import run_unittest, verbose
 import unittest
 import math
+import os
+import sys
 
-seps='1e-05'
-eps = eval(seps)
+eps = 1E-05
+NAN = float('nan')
+INF = float('inf')
+NINF = float('-inf')
+
+# locate file with test values
+if __name__ == '__main__':
+    file = sys.argv[0]
+else:
+    file = __file__
+test_dir = os.path.dirname(file) or os.curdir
+test_file = os.path.join(test_dir, 'cmath_testcases.txt')
+
+def parse_testfile(fname):
+    """Parse a file with test values
+
+    Empty lines or lines starting with -- are ignored
+    yields id, fn, arg_real, arg_imag, exp_real, exp_imag
+    """
+    with open(fname) as fp:
+        for line in fp:
+            # skip comment lines and blank lines
+            if line.startswith('--') or not line.strip():
+                continue
+
+            lhs, rhs = line.split('->')
+            id, fn, arg_real, arg_imag = lhs.split()
+            rhs_pieces = rhs.split()
+            exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
+            flags = rhs_pieces[2:]
+
+            yield (id, fn,
+                   float(arg_real), float(arg_imag),
+                   float(exp_real), float(exp_imag),
+                   flags
+                  )
 
 class MathTests(unittest.TestCase):
 
@@ -28,18 +64,57 @@ class MathTests(unittest.TestCase):
         self.ftest('acos(-1)', math.acos(-1), math.pi)
         self.ftest('acos(0)', math.acos(0), math.pi/2)
         self.ftest('acos(1)', math.acos(1), 0)
+        self.assertRaises(ValueError, math.acos, INF)
+        self.assertRaises(ValueError, math.acos, NINF)
+        self.assert_(math.isnan(math.acos(NAN)))
+
+    def testAcosh(self):
+        self.assertRaises(TypeError, math.acosh)
+        self.ftest('acosh(1)', math.acosh(1), 0)
+        self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
+        self.assertRaises(ValueError, math.acosh, 0)
+        self.assertRaises(ValueError, math.acosh, -1)
+        self.assertEquals(math.acosh(INF), INF)
+        self.assertRaises(ValueError, math.acosh, NINF)
+        self.assert_(math.isnan(math.acosh(NAN)))
 
     def testAsin(self):
         self.assertRaises(TypeError, math.asin)
         self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
         self.ftest('asin(0)', math.asin(0), 0)
         self.ftest('asin(1)', math.asin(1), math.pi/2)
+        self.assertRaises(ValueError, math.asin, INF)
+        self.assertRaises(ValueError, math.asin, NINF)
+        self.assert_(math.isnan(math.asin(NAN)))
+
+    def testAsinh(self):
+        self.assertRaises(TypeError, math.asinh)
+        self.ftest('asinh(0)', math.asinh(0), 0)
+        self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
+        self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
+        self.assertEquals(math.asinh(INF), INF)
+        self.assertEquals(math.asinh(NINF), NINF)
+        self.assert_(math.isnan(math.asinh(NAN)))
 
     def testAtan(self):
         self.assertRaises(TypeError, math.atan)
         self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
         self.ftest('atan(0)', math.atan(0), 0)
         self.ftest('atan(1)', math.atan(1), math.pi/4)
+        self.ftest('atan(inf)', math.atan(INF), math.pi/2)
+        self.ftest('atan(-inf)', math.atan(-INF), -math.pi/2)
+        self.assert_(math.isnan(math.atan(NAN)))
+
+    def testAtanh(self):
+        self.assertRaises(TypeError, math.atan)
+        self.ftest('atanh(0)', math.atanh(0), 0)
+        self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
+        self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
+        self.assertRaises(ValueError, math.atanh, 1)
+        self.assertRaises(ValueError, math.atanh, -1)
+        self.assertRaises(ValueError, math.atanh, INF)
+        self.assertRaises(ValueError, math.atanh, NINF)
+        self.assert_(math.isnan(math.atanh(NAN)))
 
     def testAtan2(self):
         self.assertRaises(TypeError, math.atan2)
@@ -58,6 +133,9 @@ class MathTests(unittest.TestCase):
         self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
         self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
         self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
+        #self.assertEquals(math.ceil(INF), INF)
+        #self.assertEquals(math.ceil(NINF), NINF)
+        #self.assert_(math.isnan(math.ceil(NAN)))
 
         class TestCeil:
             def __ceil__(self):
@@ -72,17 +150,55 @@ class MathTests(unittest.TestCase):
         self.assertRaises(TypeError, math.ceil, t)
         self.assertRaises(TypeError, math.ceil, t, 0)
 
+    if float.__getformat__("double").startswith("IEEE"):
+        def testCopysign(self):
+            self.assertRaises(TypeError, math.copysign)
+            # copysign should let us distinguish signs of zeros
+            self.assertEquals(copysign(1., 0.), 1.)
+            self.assertEquals(copysign(1., -0.), -1.)
+            self.assertEquals(copysign(INF, 0.), INF)
+            self.assertEquals(copysign(INF, -0.), NINF)
+            self.assertEquals(copysign(NINF, 0.), INF)
+            self.assertEquals(copysign(NINF, -0.), NINF)
+            # and of infinities
+            self.assertEquals(copysign(1., INF), 1.)
+            self.assertEquals(copysign(1., NINF), -1.)
+            self.assertEquals(copysign(INF, INF), INF)
+            self.assertEquals(copysign(INF, NINF), NINF)
+            self.assertEquals(copysign(NINF, INF), INF)
+            self.assertEquals(copysign(NINF, NINF), NINF)
+            self.assert_(math.isnan(copysign(NAN, 1.)))
+            self.assert_(math.isnan(copysign(NAN, INF)))
+            self.assert_(math.isnan(copysign(NAN, NINF)))
+            self.assert_(math.isnan(copysign(NAN, NAN)))
+            # copysign(INF, NAN) may be INF or it may be NINF, since
+            # we don't know whether the sign bit of NAN is set on any
+            # given platform.
+            self.assert_(math.isinf(copysign(INF, NAN)))
+            # similarly, copysign(2., NAN) could be 2. or -2.
+            self.assertEquals(abs(copysign(2., NAN)), 2.)
+
     def testCos(self):
         self.assertRaises(TypeError, math.cos)
         self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
         self.ftest('cos(0)', math.cos(0), 1)
         self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
         self.ftest('cos(pi)', math.cos(math.pi), -1)
+        try:
+            self.assert_(math.isnan(math.cos(INF)))
+            self.assert_(math.isnan(math.cos(NINF)))
+        except ValueError:
+            self.assertRaises(ValueError, math.cos, INF)
+            self.assertRaises(ValueError, math.cos, NINF)
+        self.assert_(math.isnan(math.cos(NAN)))
 
     def testCosh(self):
         self.assertRaises(TypeError, math.cosh)
         self.ftest('cosh(0)', math.cosh(0), 1)
         self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
+        self.assertEquals(math.cosh(INF), INF)
+        self.assertEquals(math.cosh(NINF), INF)
+        self.assert_(math.isnan(math.cosh(NAN)))
 
     def testDegrees(self):
         self.assertRaises(TypeError, math.degrees)
@@ -95,6 +211,9 @@ class MathTests(unittest.TestCase):
         self.ftest('exp(-1)', math.exp(-1), 1/math.e)
         self.ftest('exp(0)', math.exp(0), 1)
         self.ftest('exp(1)', math.exp(1), math.e)
+        self.assertEquals(math.exp(INF), INF)
+        self.assertEquals(math.exp(NINF), 0.)
+        self.assert_(math.isnan(math.exp(NAN)))
 
     def testFabs(self):
         self.assertRaises(TypeError, math.fabs)
@@ -115,6 +234,9 @@ class MathTests(unittest.TestCase):
         # This fails on some platforms - so check it here
         self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
         self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
+        #self.assertEquals(math.ceil(INF), INF)
+        #self.assertEquals(math.ceil(NINF), NINF)
+        #self.assert_(math.isnan(math.floor(NAN)))
 
         class TestFloor:
             def __floor__(self):
@@ -137,6 +259,19 @@ class MathTests(unittest.TestCase):
         self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
         self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
         self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)
+        self.assert_(math.isnan(math.fmod(NAN, 1.)))
+        self.assert_(math.isnan(math.fmod(1., NAN)))
+        self.assert_(math.isnan(math.fmod(NAN, NAN)))
+        self.assertRaises(ValueError, math.fmod, 1., 0.)
+        self.assertRaises(ValueError, math.fmod, INF, 1.)
+        self.assertRaises(ValueError, math.fmod, NINF, 1.)
+        self.assertRaises(ValueError, math.fmod, INF, 0.)
+        self.assertEquals(math.fmod(3.0, INF), 3.0)
+        self.assertEquals(math.fmod(-3.0, INF), -3.0)
+        self.assertEquals(math.fmod(3.0, NINF), 3.0)
+        self.assertEquals(math.fmod(-3.0, NINF), -3.0)
+        self.assertEquals(math.fmod(0.0, 3.0), 0.0)
+        self.assertEquals(math.fmod(0.0, NINF), 0.0)
 
     def testFrexp(self):
         self.assertRaises(TypeError, math.frexp)
@@ -152,10 +287,20 @@ class MathTests(unittest.TestCase):
         testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
         testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
 
+        self.assertEquals(math.frexp(INF)[0], INF)
+        self.assertEquals(math.frexp(NINF)[0], NINF)
+        self.assert_(math.isnan(math.frexp(NAN)[0]))
+
     def testHypot(self):
         self.assertRaises(TypeError, math.hypot)
         self.ftest('hypot(0,0)', math.hypot(0,0), 0)
         self.ftest('hypot(3,4)', math.hypot(3,4), 5)
+        self.assertEqual(math.hypot(NAN, INF), INF)
+        self.assertEqual(math.hypot(INF, NAN), INF)
+        self.assertEqual(math.hypot(NAN, NINF), INF)
+        self.assertEqual(math.hypot(NINF, NAN), INF)
+        self.assert_(math.isnan(math.hypot(1.0, NAN)))
+        self.assert_(math.isnan(math.hypot(NAN, -2.0)))
 
     def testLdexp(self):
         self.assertRaises(TypeError, math.ldexp)
@@ -163,6 +308,13 @@ class MathTests(unittest.TestCase):
         self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
         self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
         self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
+        self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
+        self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
+        self.assertEquals(math.ldexp(1., -1000000), 0.)
+        self.assertEquals(math.ldexp(-1., -1000000), -0.)
+        self.assertEquals(math.ldexp(INF, 30), INF)
+        self.assertEquals(math.ldexp(NINF, -213), NINF)
+        self.assert_(math.isnan(math.ldexp(NAN, 0)))
 
     def testLog(self):
         self.assertRaises(TypeError, math.log)
@@ -172,12 +324,31 @@ class MathTests(unittest.TestCase):
         self.ftest('log(32,2)', math.log(32,2), 5)
         self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
         self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
+        self.assertEquals(math.log(INF), INF)
+        self.assertRaises(ValueError, math.log, NINF)
+        self.assert_(math.isnan(math.log(NAN)))
+
+    def testLog1p(self):
+        self.assertRaises(TypeError, math.log1p)
+        self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)
+        self.ftest('log1p(0)', math.log1p(0), 0)
+        self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)
+        self.ftest('log1p(1)', math.log1p(1), math.log(2))
+        self.assertEquals(math.log1p(INF), INF)
+        self.assertRaises(ValueError, math.log1p, NINF)
+        self.assert_(math.isnan(math.log1p(NAN)))
+        n= 2**90
+        self.assertAlmostEquals(math.log1p(n), 62.383246250395075)
+        self.assertAlmostEquals(math.log1p(n), math.log1p(float(n)))
 
     def testLog10(self):
         self.assertRaises(TypeError, math.log10)
         self.ftest('log10(0.1)', math.log10(0.1), -1)
         self.ftest('log10(1)', math.log10(1), 0)
         self.ftest('log10(10)', math.log10(10), 1)
+        self.assertEquals(math.log(INF), INF)
+        self.assertRaises(ValueError, math.log10, NINF)
+        self.assert_(math.isnan(math.log10(NAN)))
 
     def testModf(self):
         self.assertRaises(TypeError, math.modf)
@@ -191,12 +362,35 @@ class MathTests(unittest.TestCase):
         testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
         testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
 
+        self.assertEquals(math.modf(INF), (0.0, INF))
+        self.assertEquals(math.modf(NINF), (-0.0, NINF))
+
+        modf_nan = math.modf(NAN)
+        self.assert_(math.isnan(modf_nan[0]))
+        self.assert_(math.isnan(modf_nan[1]))
+
     def testPow(self):
         self.assertRaises(TypeError, math.pow)
         self.ftest('pow(0,1)', math.pow(0,1), 0)
         self.ftest('pow(1,0)', math.pow(1,0), 1)
         self.ftest('pow(2,1)', math.pow(2,1), 2)
         self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
+        self.assertEqual(math.pow(INF, 1), INF)
+        self.assertEqual(math.pow(NINF, 1), NINF)
+        self.assertEqual((math.pow(1, INF)), 1.)
+        self.assertEqual((math.pow(1, NINF)), 1.)
+        self.assert_(math.isnan(math.pow(NAN, 1)))
+        self.assert_(math.isnan(math.pow(2, NAN)))
+        self.assert_(math.isnan(math.pow(0, NAN)))
+        self.assertEqual(math.pow(1, NAN), 1)
+        self.assertEqual(1**NAN, 1)
+        self.assertEqual(1**INF, 1)
+        self.assertEqual(1**NINF, 1)
+        self.assertEqual(1**0, 1)
+        self.assertEqual(1.**NAN, 1)
+        self.assertEqual(1.**INF, 1)
+        self.assertEqual(1.**NINF, 1)
+        self.assertEqual(1.**0, 1)
 
     def testRadians(self):
         self.assertRaises(TypeError, math.radians)
@@ -209,29 +403,52 @@ class MathTests(unittest.TestCase):
         self.ftest('sin(0)', math.sin(0), 0)
         self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
         self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
+        try:
+            self.assert_(math.isnan(math.sin(INF)))
+            self.assert_(math.isnan(math.sin(NINF)))
+        except ValueError:
+            self.assertRaises(ValueError, math.sin, INF)
+            self.assertRaises(ValueError, math.sin, NINF)
+        self.assert_(math.isnan(math.sin(NAN)))
 
     def testSinh(self):
         self.assertRaises(TypeError, math.sinh)
         self.ftest('sinh(0)', math.sinh(0), 0)
         self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
         self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
+        self.assertEquals(math.sinh(INF), INF)
+        self.assertEquals(math.sinh(-INF), -INF)
+        self.assert_(math.isnan(math.sinh(NAN)))
 
     def testSqrt(self):
         self.assertRaises(TypeError, math.sqrt)
         self.ftest('sqrt(0)', math.sqrt(0), 0)
         self.ftest('sqrt(1)', math.sqrt(1), 1)
         self.ftest('sqrt(4)', math.sqrt(4), 2)
+        self.assertEquals(math.sqrt(INF), INF)
+        self.assertRaises(ValueError, math.sqrt, NINF)
+        self.assert_(math.isnan(math.sqrt(NAN)))
 
     def testTan(self):
         self.assertRaises(TypeError, math.tan)
         self.ftest('tan(0)', math.tan(0), 0)
         self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
         self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
+        try:
+            self.assert_(math.isnan(math.tan(INF)))
+            self.assert_(math.isnan(math.tan(NINF)))
+        except:
+            self.assertRaises(ValueError, math.tan, INF)
+            self.assertRaises(ValueError, math.tan, NINF)
+        self.assert_(math.isnan(math.tan(NAN)))
 
     def testTanh(self):
         self.assertRaises(TypeError, math.tanh)
         self.ftest('tanh(0)', math.tanh(0), 0)
         self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
+        self.ftest('tanh(inf)', math.tanh(INF), 1)
+        self.ftest('tanh(-inf)', math.tanh(NINF), -1)
+        self.assert_(math.isnan(math.tanh(NAN)))
 
     def test_trunc(self):
         self.assertEqual(math.trunc(1), 1)
@@ -326,9 +543,27 @@ class MathTests(unittest.TestCase):
             else:
                 self.fail("sqrt(-1) didn't raise ValueError")
 
+    def test_testfile(self):
+        if not float.__getformat__("double").startswith("IEEE"):
+            return
+        for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
+            # Skip if either the input or result is complex, or if
+            # flags is nonempty
+            if ai != 0. or ei != 0. or flags:
+                continue
+            if fn in ['rect', 'polar']:
+                # no real versions of rect, polar
+                continue
+            func = getattr(math, fn)
+            result = func(ar)
+            self.ftest("%s:%s(%r)" % (id, fn, ar), result, er)
 
 def test_main():
-    run_unittest(MathTests)
+    from doctest import DocFileSuite
+    suite = unittest.TestSuite()
+    suite.addTest(unittest.makeSuite(MathTests))
+    suite.addTest(DocFileSuite("ieee754.txt"))
+    run_unittest(suite)
 
 if __name__ == '__main__':
     test_main()
diff --git a/Makefile.pre.in b/Makefile.pre.in
index 2a773548b1..d9627e01aa 100644
--- a/Makefile.pre.in
+++ b/Makefile.pre.in
@@ -276,6 +276,7 @@ PYTHON_OBJS=	\
 		Python/peephole.o \
 		Python/pyarena.o \
 		Python/pyfpe.o \
+		Python/pymath.o \
 		Python/pystate.o \
 		Python/pythonrun.o \
 		Python/structmember.o \
@@ -622,6 +623,7 @@ PYTHON_HEADERS= \
 		Include/pydebug.h \
 		Include/pyerrors.h \
 		Include/pyfpe.h \
+		Include/pymath.h \
 		Include/pygetopt.h \
 		Include/pymem.h \
 		Include/pyport.h \
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
index ec48ce8d72..8e3c31eabb 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 cf2bf6463a..8c48316099 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;
 }
diff --git a/Objects/complexobject.c b/Objects/complexobject.c
index 90b970eea9..acd5a4a1a2 100644
--- a/Objects/complexobject.c
+++ b/Objects/complexobject.c
@@ -187,6 +187,38 @@ c_powi(Py_complex x, long n)
 
 }
 
+double
+c_abs(Py_complex z)
+{
+	/* sets errno = ERANGE on overflow;  otherwise errno = 0 */
+	double result;
+
+	if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
+		/* C99 rules: if either the real or the imaginary part is an
+		   infinity, return infinity, even if the other part is a
+		   NaN. */
+		if (Py_IS_INFINITY(z.real)) {
+			result = fabs(z.real);
+			errno = 0;
+			return result;
+		}
+		if (Py_IS_INFINITY(z.imag)) {
+			result = fabs(z.imag);
+			errno = 0;
+			return result;
+		}
+		/* either the real or imaginary part is a NaN,
+		   and neither is infinite. Result should be NaN. */
+		return Py_NAN;
+	}
+	result = hypot(z.real, z.imag);
+	if (!Py_IS_FINITE(result))
+		errno = ERANGE;
+	else
+		errno = 0;
+	return result;
+}
+
 static PyObject *
 complex_subtype_from_c_complex(PyTypeObject *type, Py_complex cval)
 {
@@ -321,8 +353,7 @@ complex_to_buf(char *buf, int bufsz, PyComplexObject *v, int precision)
 		if (!Py_IS_FINITE(v->cval.imag)) {
 			if (Py_IS_NAN(v->cval.imag))
 				strncpy(buf, "nan*j", 6);
-			/* else if (copysign(1, v->cval.imag) == 1) */
-			else if (v->cval.imag > 0)
+			else if (copysign(1, v->cval.imag) == 1)
 				strncpy(buf, "inf*j", 6);
 			else
 				strncpy(buf, "-inf*j", 7);
@@ -578,9 +609,16 @@ static PyObject *
 complex_abs(PyComplexObject *v)
 {
 	double result;
+
 	PyFPE_START_PROTECT("complex_abs", return 0)
-	result = hypot(v->cval.real,v->cval.imag);
+	result = c_abs(v->cval);
 	PyFPE_END_PROTECT(result)
+
+	if (errno == ERANGE) {
+		PyErr_SetString(PyExc_OverflowError,
+				"absolute value too large");
+		return NULL;
+	}
 	return PyFloat_FromDouble(result);
 }
 
@@ -658,9 +696,29 @@ complex_getnewargs(PyComplexObject *v)
 	return Py_BuildValue("(D)", &v->cval);
 }
 
+#if 0
+static PyObject *
+complex_is_finite(PyObject *self)
+{
+	Py_complex c;
+	c = ((PyComplexObject *)self)->cval;
+	return PyBool_FromLong((long)(Py_IS_FINITE(c.real) &&
+				      Py_IS_FINITE(c.imag)));
+}
+
+PyDoc_STRVAR(complex_is_finite_doc,
+"complex.is_finite() -> bool\n"
+"\n"
+"Returns True if the real and the imaginary part is finite.");
+#endif
+
 static PyMethodDef complex_methods[] = {
 	{"conjugate",	(PyCFunction)complex_conjugate,	METH_NOARGS,
 	 complex_conjugate_doc},
+#if 0
+	{"is_finite",	(PyCFunction)complex_is_finite,	METH_NOARGS,
+	 complex_is_finite_doc},
+#endif
 	{"__getnewargs__",	(PyCFunction)complex_getnewargs,	METH_NOARGS},
 	{NULL,		NULL}		/* sentinel */
 };
diff --git a/Objects/doubledigits.c b/Objects/doubledigits.c
deleted file mode 100644
index 1f1c91cce7..0000000000
--- a/Objects/doubledigits.c
+++ /dev/null
@@ -1,601 +0,0 @@
-/* Free-format floating point printer
- * 
- * Based on "Floating-Point Printer Sample Code", by Robert G. Burger,
- * http://www.cs.indiana.edu/~burger/fp/index.html
- */
-
-#include "Python.h"
-
-#if defined(__alpha) || defined(__i386) || defined(_M_IX86) || defined(_M_X64) || defined(_M_IA64)
-#define LITTLE_ENDIAN_IEEE_DOUBLE
-#elif !(defined(__ppc__) || defined(sparc) || defined(__sgi) || defined(_IBMR2) || defined(hpux))
-#error unknown machine type
-#endif
-
-#if defined(_M_IX86)
-#define UNSIGNED64 unsigned __int64
-#elif defined(__alpha)
-#define UNSIGNED64 unsigned long
-#else
-#define UNSIGNED64 unsigned long long
-#endif
-
-#ifndef U32
-#define U32 unsigned int
-#endif
-
-/* exponent stored + 1024, hidden bit to left of decimal point */
-#define bias 1023
-#define bitstoright 52
-#define m1mask 0xf
-#define hidden_bit 0x100000
-#ifdef LITTLE_ENDIAN_IEEE_DOUBLE
-struct dblflt {
-    unsigned int m4: 16;
-    unsigned int m3: 16;
-    unsigned int m2: 16;
-    unsigned int m1: 4;
-    unsigned int e: 11;
-    unsigned int s: 1;
-};
-#else
-/* Big Endian IEEE Double Floats */
-struct dblflt {
-    unsigned int s: 1;
-    unsigned int e: 11;
-    unsigned int m1: 4;
-    unsigned int m2: 16;
-    unsigned int m3: 16;
-    unsigned int m4: 16;
-};
-#endif
-#define float_radix 2.147483648e9
-
-
-typedef UNSIGNED64 Bigit;
-#define BIGSIZE 24
-#define MIN_E -1074
-#define MAX_FIVE 325
-#define B_P1 ((Bigit)1 << 52)
-
-typedef struct {
-   int l;
-   Bigit d[BIGSIZE];
-} Bignum;
-
-static Bignum R, S, MP, MM, five[MAX_FIVE];
-static Bignum S2, S3, S4, S5, S6, S7, S8, S9;
-static int ruf, k, s_n, use_mp, qr_shift, sl, slr;
-
-static void mul10(Bignum *x);
-static void big_short_mul(Bignum *x, Bigit y, Bignum *z);
-/*
-static void print_big(Bignum *x);
-*/
-static int estimate(int n);
-static void one_shift_left(int y, Bignum *z);
-static void short_shift_left(Bigit x, int y, Bignum *z);
-static void big_shift_left(Bignum *x, int y, Bignum *z);
-static int big_comp(Bignum *x, Bignum *y);
-static int sub_big(Bignum *x, Bignum *y, Bignum *z);
-static void add_big(Bignum *x, Bignum *y, Bignum *z);
-static int add_cmp(void);
-static int qr(void);
-
-/*static int _PyFloat_Digits(char *buf, double v, int *signum);*/
-/*static void _PyFloat_DigitsInit(void);*/
-
-#define ADD(x, y, z, k) {\
-   Bigit x_add, z_add;\
-   x_add = (x);\
-   if ((k))\
-     z_add = x_add + (y) + 1, (k) = (z_add <= x_add);\
-   else\
-     z_add = x_add + (y), (k) = (z_add < x_add);\
-   (z) = z_add;\
-}
-
-#define SUB(x, y, z, b) {\
-   Bigit x_sub, y_sub;\
-   x_sub = (x); y_sub = (y);\
-   if ((b))\
-     (z) = x_sub - y_sub - 1, b = (y_sub >= x_sub);\
-   else\
-     (z) = x_sub - y_sub, b = (y_sub > x_sub);\
-}
-
-#define MUL(x, y, z, k) {\
-   Bigit x_mul, low, high;\
-   x_mul = (x);\
-   low = (x_mul & 0xffffffff) * (y) + (k);\
-   high = (x_mul >> 32) * (y) + (low >> 32);\
-   (k) = high >> 32;\
-   (z) = (low & 0xffffffff) | (high << 32);\
-}
-
-#define SLL(x, y, z, k) {\
-   Bigit x_sll = (x);\
-   (z) = (x_sll << (y)) | (k);\
-   (k) = x_sll >> (64 - (y));\
-}
-
-static void
-mul10(Bignum *x)
-{
-   int i, l;
-   Bigit *p, k;
-
-   l = x->l;
-   for (i = l, p = &x->d[0], k = 0; i >= 0; i--)
-      MUL(*p, 10, *p++, k);
-   if (k != 0)
-      *p = k, x->l = l+1;
-}
-
-static void
-big_short_mul(Bignum *x, Bigit y, Bignum *z)
-{
-   int i, xl, zl;
-   Bigit *xp, *zp, k;
-   U32 high, low;
-
-   xl = x->l;
-   xp = &x->d[0];
-   zl = xl;
-   zp = &z->d[0];
-   high = y >> 32;
-   low = y & 0xffffffff;
-   for (i = xl, k = 0; i >= 0; i--, xp++, zp++) {
-      Bigit xlow, xhigh, z0, t, c, z1;
-      xlow = *xp & 0xffffffff;
-      xhigh = *xp >> 32;
-      z0 = (xlow * low) + k; /* Cout is (z0 < k) */
-      t = xhigh * low;
-      z1 = (xlow * high) + t;
-      c = (z1 < t);
-      t = z0 >> 32;
-      z1 += t;
-      c += (z1 < t);
-      *zp = (z1 << 32) | (z0 & 0xffffffff);
-      k = (xhigh * high) + (c << 32) + (z1 >> 32) + (z0 < k);
-   }
-   if (k != 0)
-      *zp = k, zl++;
-   z->l = zl;
-}
-
-/*
-static void
-print_big(Bignum *x)
-{
-   int i;
-   Bigit *p;
-
-   printf("#x");
-   i = x->l;
-   p = &x->d[i];
-   for (p = &x->d[i]; i >= 0; i--) {
-      Bigit b = *p--;
-      printf("%08x%08x", (int)(b >> 32), (int)(b & 0xffffffff));
-   }
-}
-*/
-
-static int
-estimate(int n)
-{
-   if (n < 0)
-      return (int)(n*0.3010299956639812);
-   else
-      return 1+(int)(n*0.3010299956639811);
-}
-
-static void
-one_shift_left(int y, Bignum *z)
-{
-   int n, m, i;
-   Bigit *zp;
-
-   n = y / 64;
-   m = y % 64;
-   zp = &z->d[0];
-   for (i = n; i > 0; i--) *zp++ = 0;
-   *zp = (Bigit)1 << m;
-   z->l = n;
-}
-
-static void
-short_shift_left(Bigit x, int y, Bignum *z)
-{
-   int n, m, i, zl;
-   Bigit *zp;
-   
-   n = y / 64;
-   m = y % 64;
-   zl = n;
-   zp = &(z->d[0]);
-   for (i = n; i > 0; i--) *zp++ = 0;
-   if (m == 0)
-      *zp = x;
-   else {
-      Bigit high = x >> (64 - m);
-      *zp = x << m;
-      if (high != 0)
-         *++zp = high, zl++;
-   }
-   z->l = zl;
-}
-
-static void
-big_shift_left(Bignum *x, int y, Bignum *z)
-{
-   int n, m, i, xl, zl;
-   Bigit *xp, *zp, k;
-   
-   n = y / 64;
-   m = y % 64;
-   xl = x->l;
-   xp = &(x->d[0]);
-   zl = xl + n;
-   zp = &(z->d[0]);
-   for (i = n; i > 0; i--) *zp++ = 0;
-   if (m == 0)
-      for (i = xl; i >= 0; i--) *zp++ = *xp++;
-   else {
-      for (i = xl, k = 0; i >= 0; i--)
-         SLL(*xp++, m, *zp++, k);
-      if (k != 0)
-         *zp = k, zl++;
-   }
-   z->l = zl;
-}
-
-
-static int
-big_comp(Bignum *x, Bignum *y)
-{
-   int i, xl, yl;
-   Bigit *xp, *yp;
-
-   xl = x->l;
-   yl = y->l;
-   if (xl > yl) return 1;
-   if (xl < yl) return -1;
-   xp = &x->d[xl];
-   yp = &y->d[xl];
-   for (i = xl; i >= 0; i--, xp--, yp--) {
-      Bigit a = *xp;
-      Bigit b = *yp;
-
-      if (a > b) return 1;
-      else if (a < b) return -1;
-   }
-   return 0;
-}
-
-static int
-sub_big(Bignum *x, Bignum *y, Bignum *z)
-{
-  int xl, yl, zl, b, i;
-  Bigit *xp, *yp, *zp;
-
-  xl = x->l;
-  yl = y->l;
-  if (yl > xl) return 1;
-  xp = &x->d[0];
-  yp = &y->d[0];
-  zp = &z->d[0];
-  
-  for (i = yl, b = 0; i >= 0; i--)
-    SUB(*xp++, *yp++, *zp++, b);
-  for (i = xl-yl; b && i > 0; i--) {
-    Bigit x_sub;
-    x_sub = *xp++;
-    *zp++ = x_sub - 1;
-    b = (x_sub == 0);
-  }
-  for (; i > 0; i--) *zp++ = *xp++;
-  if (b) return 1;
-  zl = xl;
-  while (*--zp == 0) zl--;
-  z->l = zl;
-  return 0;
-}
-
-static void
-add_big(Bignum *x, Bignum *y, Bignum *z)
-{
-  int xl, yl, k, i;
-  Bigit *xp, *yp, *zp;
-
-  xl = x->l;
-  yl = y->l;
-  if (yl > xl) {
-    int tl;
-    Bignum *tn;
-    tl = xl; xl = yl; yl = tl;
-    tn = x; x = y; y = tn;
-  }
-
-  xp = &x->d[0];
-  yp = &y->d[0];
-  zp = &z->d[0];
-  
-  for (i = yl, k = 0; i >= 0; i--)
-    ADD(*xp++, *yp++, *zp++, k);
-  for (i = xl-yl; k && i > 0; i--) {
-    Bigit z_add;
-    z_add = *xp++ + 1;
-    k = (z_add == 0);
-    *zp++ = z_add;
-  }
-  for (; i > 0; i--) *zp++ = *xp++;
-  if (k)
-    *zp = 1, z->l = xl+1;
-  else
-    z->l = xl;
-}
-
-static int
-add_cmp()
-{
-   int rl, ml, sl, suml;
-   static Bignum sum;
-
-   rl = R.l;
-   ml = (use_mp ? MP.l : MM.l);
-   sl = S.l;
-   
-   suml = rl >= ml ? rl : ml;
-   if ((sl > suml+1) || ((sl == suml+1) && (S.d[sl] > 1))) return -1;
-   if (sl < suml) return 1;
-
-   add_big(&R, (use_mp ? &MP : &MM), &sum);
-   return big_comp(&sum, &S);
-}
-
-static int
-qr()
-{
-  if (big_comp(&R, &S5) < 0)
-    if (big_comp(&R, &S2) < 0)
-      if (big_comp(&R, &S) < 0)
-        return 0;
-      else {
-        sub_big(&R, &S, &R);
-        return 1;
-      }
-    else if (big_comp(&R, &S3) < 0) {
-      sub_big(&R, &S2, &R);
-      return 2;
-    }
-    else if (big_comp(&R, &S4) < 0) {
-      sub_big(&R, &S3, &R);
-      return 3;
-    }
-    else {
-      sub_big(&R, &S4, &R);
-      return 4;
-    }
-  else if (big_comp(&R, &S7) < 0)
-    if (big_comp(&R, &S6) < 0) {
-      sub_big(&R, &S5, &R);
-      return 5;
-    }
-    else {
-      sub_big(&R, &S6, &R);
-      return 6;
-    }
-  else if (big_comp(&R, &S9) < 0)
-    if (big_comp(&R, &S8) < 0) {
-      sub_big(&R, &S7, &R);
-      return 7;
-    }
-    else {
-      sub_big(&R, &S8, &R);
-      return 8;
-    }
-  else {
-    sub_big(&R, &S9, &R);
-    return 9;
-  }
-}
-
-#define OUTDIG(d) { *buf++ = (d) + '0'; *buf = 0; return k; }
-
-int
-_PyFloat_Digits(char *buf, double v, int *signum)
-{
-   struct dblflt *x;
-   int sign, e, f_n, m_n, i, d, tc1, tc2;
-   Bigit f;
-
-   /* decompose float into sign, mantissa & exponent */
-   x = (struct dblflt *)&v;
-   sign = x->s;
-   e = x->e; 
-   f = (Bigit)(x->m1 << 16 | x->m2) << 32 | (U32)(x->m3 << 16 | x->m4);
-   if (e != 0) {
-      e = e - bias - bitstoright;
-      f |= (Bigit)hidden_bit << 32;
-   }
-   else if (f != 0)
-      /* denormalized */
-      e = 1 - bias - bitstoright;
-
-   *signum = sign;
-   if (f == 0) {
-     *buf++ = '0';
-     *buf = 0;
-     return 0;
-   }
-   
-   ruf = !(f & 1); /* ruf = (even? f) */
-
-   /* Compute the scaling factor estimate, k */
-   if (e > MIN_E)
-      k = estimate(e+52);
-   else {
-      int n;
-      Bigit y;
-      
-      for (n = e+52, y = (Bigit)1 << 52; f < y; n--) y >>= 1;
-      k = estimate(n);
-   }
-
-   if (e >= 0)
-      if (f != B_P1)
-         use_mp = 0, f_n = e+1, s_n = 1, m_n = e;
-      else
-         use_mp = 1, f_n = e+2, s_n = 2, m_n = e;
-   else
-      if ((e == MIN_E) || (f != B_P1))
-         use_mp = 0, f_n = 1, s_n = 1-e, m_n = 0;
-      else
-         use_mp = 1, f_n = 2, s_n = 2-e, m_n = 0;
-   
-   /* Scale it! */
-   if (k == 0) {
-      short_shift_left(f, f_n, &R);
-      one_shift_left(s_n, &S);
-      one_shift_left(m_n, &MM);
-      if (use_mp) one_shift_left(m_n+1, &MP);
-      qr_shift = 1;
-   }
-   else if (k > 0) {
-      s_n += k;
-      if (m_n >= s_n)
-         f_n -= s_n, m_n -= s_n, s_n = 0;
-      else 
-         f_n -= m_n, s_n -= m_n, m_n = 0;
-      short_shift_left(f, f_n, &R);
-      big_shift_left(&five[k-1], s_n, &S);
-      one_shift_left(m_n, &MM);
-      if (use_mp) one_shift_left(m_n+1, &MP);
-      qr_shift = 0;
-   }
-   else {
-      Bignum *power = &five[-k-1];
-
-      s_n += k;
-      big_short_mul(power, f, &S);
-      big_shift_left(&S, f_n, &R);
-      one_shift_left(s_n, &S);
-      big_shift_left(power, m_n, &MM);
-      if (use_mp) big_shift_left(power, m_n+1, &MP);
-      qr_shift = 1;
-   }
-
-   /* fixup */
-   if (add_cmp() <= -ruf) {
-     k--;
-     mul10(&R);
-     mul10(&MM);
-     if (use_mp) mul10(&MP);
-   }
-
-   /*
-   printf("\nk = %d\n", k);
-   printf("R = "); print_big(&R);
-   printf("\nS = "); print_big(&S);
-   printf("\nM- = "); print_big(&MM);
-   if (use_mp) printf("\nM+ = "), print_big(&MP);
-   putchar('\n');
-   fflush(0);
-   */
-   
-   if (qr_shift) {
-     sl = s_n / 64;
-     slr = s_n % 64;
-   }
-   else {
-     big_shift_left(&S, 1, &S2);
-     add_big(&S2, &S, &S3);
-     big_shift_left(&S2, 1, &S4);
-     add_big(&S4, &S, &S5);
-     add_big(&S4, &S2, &S6);
-     add_big(&S4, &S3, &S7);
-     big_shift_left(&S4, 1, &S8);
-     add_big(&S8, &S, &S9);
-   }
-
-again:
-   if (qr_shift) { /* Take advantage of the fact that S = (ash 1 s_n) */
-      if (R.l < sl)
-         d = 0;
-      else if (R.l == sl) {
-            Bigit *p;
-
-            p = &R.d[sl];
-            d = *p >> slr;
-            *p &= ((Bigit)1 << slr) - 1;
-            for (i = sl; (i > 0) && (*p == 0); i--) p--;
-            R.l = i;
-         }
-      else {
-         Bigit *p;
-         
-         p = &R.d[sl+1];
-         d = *p << (64 - slr) | *(p-1) >> slr;
-         p--;
-         *p &= ((Bigit)1 << slr) - 1;
-         for (i = sl; (i > 0) && (*p == 0); i--) p--;
-         R.l = i;
-      }
-   }
-   else /* We need to do quotient-remainder */
-     d = qr();
-
-   tc1 = big_comp(&R, &MM) < ruf;
-   tc2 = add_cmp() > -ruf;
-   if (!tc1)
-      if (!tc2) {
-         mul10(&R);
-         mul10(&MM);
-         if (use_mp) mul10(&MP);
-         *buf++ = d + '0';
-         goto again;
-      }
-      else
-        OUTDIG(d+1)
-   else
-      if (!tc2)
-         OUTDIG(d)
-      else {
-         big_shift_left(&R, 1, &MM);
-         if (big_comp(&MM, &S) == -1)
-            OUTDIG(d)
-         else
-            OUTDIG(d+1)
-      }
-}
-
-void
-_PyFloat_DigitsInit()
-{
-   int n, i, l;
-   Bignum *b;
-   Bigit *xp, *zp, k;
-
-   five[0].l = l = 0;
-   five[0].d[0] = 5;
-   for (n = MAX_FIVE-1, b = &five[0]; n > 0; n--) {
-      xp = &b->d[0];
-      b++;
-      zp = &b->d[0];
-      for (i = l, k = 0; i >= 0; i--)
-         MUL(*xp++, 5, *zp++, k);
-      if (k != 0)
-         *zp = k, l++;
-      b->l = l;
-   }
-
-   /*
-   for (n = 1, b = &five[0]; n <= MAX_FIVE; n++) {
-      big_shift_left(b++, n, &R);
-      print_big(&R);
-      putchar('\n');
-   }
-   fflush(0);
-   */
-}
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 745dfc3938..a748abbdad 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -16,10 +16,6 @@
 #include <ieeefp.h>
 #endif
 
-#if !defined(__STDC__)
-extern double fmod(double, double);
-extern double pow(double, double);
-#endif
 
 #ifdef _OSF_SOURCE
 /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
@@ -224,11 +220,11 @@ PyFloat_FromString(PyObject *v)
 			p++;
 		}
 		if (PyOS_strnicmp(p, "inf", 4) == 0) {
-			return PyFloat_FromDouble(sign * Py_HUGE_VAL);
+			Py_RETURN_INF(sign);
 		}
 #ifdef Py_NAN
 		if(PyOS_strnicmp(p, "nan", 4) == 0) {
-			return PyFloat_FromDouble(Py_NAN);
+			Py_RETURN_NAN;
 		}
 #endif
 		PyOS_snprintf(buffer, sizeof(buffer),
@@ -378,110 +374,6 @@ format_float(char *buf, size_t buflen, PyFloatObject *v, int precision)
 	format_double(buf, buflen, PyFloat_AS_DOUBLE(v), precision);
 }
 
-#ifdef Py_BROKEN_REPR
-/* The following function is based on Tcl_PrintDouble,
- * from tclUtil.c.
- */
-
-#define is_infinite(d)	( (d) > DBL_MAX || (d) < -DBL_MAX )
-#define is_nan(d)		((d) != (d))
-
-static void
-format_double_repr(char *dst, double value)
-{
-    char *p, c;
-    int exp;
-    int signum;
-    char buffer[30];
-
-	/*
-	 * Handle NaN.
-	 */
-
-	if (is_nan(value)) {
-	    strcpy(dst, "nan");
-	    return;
-	}
-
-	/*
-	 * Handle infinities.
-	 */
-
-	if (is_infinite(value)) {
-	    if (value < 0) {
-		strcpy(dst, "-inf");
-	    } else {
-		strcpy(dst, "inf");
-	    }
-	    return;
-	}
-
-	/*
-	 * Ordinary (normal and denormal) values.
-	 */
-
-	exp = _PyFloat_Digits(buffer, value, &signum)+1;
-	if (signum) {
-	    *dst++ = '-';
-	}
-	p = buffer;
-	if (exp < -3 || exp > 17) {
-	    /*
-	     * E format for numbers < 1e-3 or >= 1e17.
-	     */
-
-	    *dst++ = *p++;
-	    c = *p;
-	    if (c != '\0') {
-		*dst++ = '.';
-		while (c != '\0') {
-		    *dst++ = c;
-		    c = *++p;
-		}
-	    }
-	    sprintf(dst, "e%+d", exp-1);
-	} else {
-	    /*
-	     * F format for others.
-	     */
-
-	    if (exp <= 0) {
-		*dst++ = '0';
-	    }
-	    c = *p;
-	    while (exp-- > 0) {
-		if (c != '\0') {
-		    *dst++ = c;
-		    c = *++p;
-		} else {
-		    *dst++ = '0';
-		}
-	    }
-	    *dst++ = '.';
-	    if (c == '\0') {
-		*dst++ = '0';
-	    } else {
-		while (++exp < 0) {
-		    *dst++ = '0';
-		}
-		while (c != '\0') {
-		    *dst++ = c;
-		    c = *++p;
-		}
-	    }
-	    *dst++ = '\0';
-	}
-}
-
-static void
-format_float_repr(char *buf, PyFloatObject *v)
-{
-	assert(PyFloat_Check(v));
-	format_double_repr(buf, PyFloat_AS_DOUBLE(v));
-}
-
-#endif /* Py_BROKEN_REPR */
-
 /* Macro and helper that convert PyObject obj to a C double and store
    the value in dbl.  If conversion to double raises an exception, obj is
    set to NULL, and the function invoking this macro returns NULL.  If
@@ -534,13 +426,8 @@ convert_to_double(PyObject **v, double *dbl)
 static PyObject *
 float_repr(PyFloatObject *v)
 {
-#ifdef Py_BROKEN_REPR
-	char buf[30];
-	format_float_repr(buf, v);
-#else
 	char buf[100];
 	format_float(buf, sizeof(buf), v, PREC_REPR);
-#endif
 
 	return PyUnicode_FromString(buf);
 }
@@ -804,10 +691,13 @@ float_div(PyObject *v, PyObject *w)
 	double a,b;
 	CONVERT_TO_DOUBLE(v, a);
 	CONVERT_TO_DOUBLE(w, b);
+#ifdef Py_NAN
 	if (b == 0.0) {
-		PyErr_SetString(PyExc_ZeroDivisionError, "float division");
+		PyErr_SetString(PyExc_ZeroDivisionError,
+				"float division");
 		return NULL;
 	}
+#endif
 	PyFPE_START_PROTECT("divide", return 0)
 	a = a / b;
 	PyFPE_END_PROTECT(a)
@@ -819,12 +709,15 @@ float_rem(PyObject *v, PyObject *w)
 {
 	double vx, wx;
 	double mod;
- 	CONVERT_TO_DOUBLE(v, vx);
- 	CONVERT_TO_DOUBLE(w, wx);
+	CONVERT_TO_DOUBLE(v, vx);
+	CONVERT_TO_DOUBLE(w, wx);
+#ifdef Py_NAN
 	if (wx == 0.0) {
-		PyErr_SetString(PyExc_ZeroDivisionError, "float modulo");
+		PyErr_SetString(PyExc_ZeroDivisionError,
+				"float modulo");
 		return NULL;
 	}
+#endif
 	PyFPE_START_PROTECT("modulo", return 0)
 	mod = fmod(vx, wx);
 	/* note: checking mod*wx < 0 is incorrect -- underflows to
@@ -928,6 +821,9 @@ float_pow(PyObject *v, PyObject *w, PyObject *z)
 		}
 		return PyFloat_FromDouble(0.0);
 	}
+	if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
+		return PyFloat_FromDouble(1.0);
+	}
 	if (iv < 0.0) {
 		/* Whether this is an error is a mess, and bumps into libm
 		 * bugs so we have to figure it out ourselves.
@@ -995,6 +891,57 @@ float_bool(PyFloatObject *v)
 }
 
 static PyObject *
+float_is_integer(PyObject *v)
+{
+	double x = PyFloat_AsDouble(v);
+	PyObject *o;
+	
+	if (x == -1.0 && PyErr_Occurred())
+		return NULL;
+	if (!Py_IS_FINITE(x))
+		Py_RETURN_FALSE;
+	PyFPE_START_PROTECT("is_integer", return NULL)
+	o = (floor(x) == x) ? Py_True : Py_False;
+	PyFPE_END_PROTECT(x)
+	if (errno != 0) {
+		PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
+						     PyExc_ValueError);
+		return NULL;
+	}
+	Py_INCREF(o);
+	return o;
+}
+
+#if 0
+static PyObject *
+float_is_inf(PyObject *v)
+{
+	double x = PyFloat_AsDouble(v);
+	if (x == -1.0 && PyErr_Occurred())
+		return NULL;
+	return PyBool_FromLong((long)Py_IS_INFINITY(x));
+}
+
+static PyObject *
+float_is_nan(PyObject *v)
+{
+	double x = PyFloat_AsDouble(v);
+	if (x == -1.0 && PyErr_Occurred())
+		return NULL;
+	return PyBool_FromLong((long)Py_IS_NAN(x));
+}
+
+static PyObject *
+float_is_finite(PyObject *v)
+{
+	double x = PyFloat_AsDouble(v);
+	if (x == -1.0 && PyErr_Occurred())
+		return NULL;
+	return PyBool_FromLong((long)Py_IS_FINITE(x));
+}
+#endif
+
+static PyObject *
 float_trunc(PyObject *v)
 {
 	double x = PyFloat_AsDouble(v);
@@ -1368,7 +1315,7 @@ PyDoc_STRVAR(float__format__doc,
 
 
 static PyMethodDef float_methods[] = {
-  	{"conjugate",	(PyCFunction)float_float,	METH_NOARGS,
+	{"conjugate",	(PyCFunction)float_float,	METH_NOARGS,
 	 "Returns self, the complex conjugate of any float."},
 	{"__trunc__",	(PyCFunction)float_trunc, METH_NOARGS,
          "Returns the Integral closest to x between 0 and x."},
@@ -1377,6 +1324,16 @@ static PyMethodDef float_methods[] = {
          "When an argument is passed, works like built-in round(x, ndigits)."},
 	{"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS,
 	 float_as_integer_ratio_doc},
+	{"is_integer",	(PyCFunction)float_is_integer,	METH_NOARGS,
+	 "Returns True if the float is an integer."},
+#if 0
+	{"is_inf",	(PyCFunction)float_is_inf,	METH_NOARGS,
+	 "Returns True if the float is positive or negative infinite."},
+	{"is_finite",	(PyCFunction)float_is_finite,	METH_NOARGS,
+	 "Returns True if the float is finite, neither infinite nor NaN."},
+	{"is_nan",	(PyCFunction)float_is_nan,	METH_NOARGS,
+	 "Returns True if the float is not a number (NaN)."},
+#endif
 	{"__getnewargs__",	(PyCFunction)float_getnewargs,	METH_NOARGS},
 	{"__getformat__",	(PyCFunction)float_getformat,	
 	 METH_O|METH_CLASS,		float_getformat_doc},
@@ -1534,10 +1491,6 @@ _PyFloat_Init(void)
 	double_format = detected_double_format;
 	float_format = detected_float_format;
 
-#ifdef Py_BROKEN_REPR	
-	/* Initialize floating point repr */
-	_PyFloat_DigitsInit();
-#endif
 	/* Init float info */
 	if (FloatInfoType.tp_name == 0)
 		PyStructSequence_InitType(&FloatInfoType, &floatinfo_desc);
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 44b040cf9e..d88a13e390 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -3611,9 +3611,21 @@ long_round(PyObject *self, PyObject *args)
 #undef UNDEF_NDIGITS
 }
 
+#if 0
+static PyObject *
+long_is_finite(PyObject *v)
+{
+	Py_RETURN_TRUE;
+}
+#endif
+
 static PyMethodDef long_methods[] = {
 	{"conjugate",	(PyCFunction)long_long,	METH_NOARGS,
 	 "Returns self, the complex conjugate of any int."},
+#if 0
+	{"is_finite",	(PyCFunction)long_is_finite,	METH_NOARGS,
+	 "Returns always True."},
+#endif
 	{"__trunc__",	(PyCFunction)long_long,	METH_NOARGS,
          "Truncating an Integral returns itself."},
 	{"__floor__",	(PyCFunction)long_long,	METH_NOARGS,
diff --git a/PC/VC6/pythoncore.dsp b/PC/VC6/pythoncore.dsp
index de8860f982..969e9df012 100644
--- a/PC/VC6/pythoncore.dsp
+++ b/PC/VC6/pythoncore.dsp
@@ -587,6 +587,10 @@ SOURCE=..\..\Python\pyfpe.c
 # End Source File

 # Begin Source File

 

+SOURCE=..\..\Python\pymath.c

+# End Source File

+# Begin Source File

+

 SOURCE=..\..\Python\pystate.c

 # End Source File

 # Begin Source File

diff --git a/PC/VS7.1/pythoncore.vcproj b/PC/VS7.1/pythoncore.vcproj
index 304b11999f..cc46faf0d7 100644
--- a/PC/VS7.1/pythoncore.vcproj
+++ b/PC/VS7.1/pythoncore.vcproj
@@ -698,6 +698,9 @@
 			RelativePath="..\..\Python\pyfpe.c">
 		</File>
 		<File
+			RelativePath="..\..\Python\pymath.c">
+		</File>
+		<File
 			RelativePath="..\..\Python\pystate.c">
 		</File>
 		<File
diff --git a/PC/VS8.0/pythoncore.vcproj b/PC/VS8.0/pythoncore.vcproj
index b63ed88501..6bc471557c 100644
--- a/PC/VS8.0/pythoncore.vcproj
+++ b/PC/VS8.0/pythoncore.vcproj
@@ -1707,6 +1707,10 @@
 				>

 			</File>

 			<File

+				RelativePath="..\..\Python\pymath.c"

+				>

+			</File>

+			<File

 				RelativePath="..\..\Python\pystate.c"

 				>

 			</File>

diff --git a/PC/pyconfig.h b/PC/pyconfig.h
index 4291192d70..e38e823530 100644
--- a/PC/pyconfig.h
+++ b/PC/pyconfig.h
@@ -207,12 +207,13 @@ typedef _W64 int ssize_t;
 #endif /* MS_WIN32 && !MS_WIN64 */
 
 typedef int pid_t;
-#define hypot _hypot
 
 #include <float.h>
 #define Py_IS_NAN _isnan
 #define Py_IS_INFINITY(X) (!_finite(X) && !_isnan(X))
 #define Py_IS_FINITE(X) _finite(X)
+#define copysign _copysign
+#define hypot _hypot
 
 #endif /* _MSC_VER */
 
@@ -392,7 +393,7 @@ Py_NO_ENABLE_SHARED to find out.  Also support MS_NO_COREDLL for b/w compat */
 /* Fairly standard from here! */
 
 /* Define to 1 if you have the `copysign' function. */
-/* #define HAVE_COPYSIGN 1*/
+#define HAVE_COPYSIGN 1
 
 /* Define to 1 if you have the `isinf' function. */
 #define HAVE_ISINF 1
diff --git a/PCbuild/pythoncore.vcproj b/PCbuild/pythoncore.vcproj
index 1f69bcad4f..c93bc71dac 100644
--- a/PCbuild/pythoncore.vcproj
+++ b/PCbuild/pythoncore.vcproj
@@ -871,6 +871,10 @@
 				>
 			</File>
 			<File
+				RelativePath="..\Include\pymath.h"
+				>
+			</File>
+			<File
 				RelativePath="..\Include\pymem.h"
 				>
 			</File>
@@ -1707,6 +1711,10 @@
 				>
 			</File>
 			<File
+				RelativePath="..\Python\pymath.c"
+				>
+			</File>
+			<File
 				RelativePath="..\Python\pystate.c"
 				>
 			</File>
diff --git a/Python/hypot.c b/Python/hypot.c
deleted file mode 100644
index a18ce166d0..0000000000
--- a/Python/hypot.c
+++ /dev/null
@@ -1,25 +0,0 @@
-/* hypot() replacement */
-
-#include "Python.h"
-
-#ifndef HAVE_HYPOT
-double hypot(double x, double y)
-{
-	double yx;
-
-	x = fabs(x);
-	y = fabs(y);
-	if (x < y) {
-		double temp = x;
-		x = y;
-		y = temp;
-	}
-	if (x == 0.)
-		return 0.;
-	else {
-		yx = y/x;
-		return x*sqrt(1.+yx*yx);
-	}
-}
-#endif /* HAVE_HYPOT */
-
diff --git a/Python/pymath.c b/Python/pymath.c
new file mode 100644
index 0000000000..7c0010675a
--- /dev/null
+++ b/Python/pymath.c
@@ -0,0 +1,232 @@
+#include "Python.h"
+
+#ifndef HAVE_HYPOT
+double hypot(double x, double y)
+{
+	double yx;
+
+	x = fabs(x);
+	y = fabs(y);
+	if (x < y) {
+		double temp = x;
+		x = y;
+		y = temp;
+	}
+	if (x == 0.)
+		return 0.;
+	else {
+		yx = y/x;
+		return x*sqrt(1.+yx*yx);
+	}
+}
+#endif /* HAVE_HYPOT */
+
+#ifndef HAVE_COPYSIGN
+static double
+copysign(double x, double y)
+{
+	/* use atan2 to distinguish -0. from 0. */
+	if (y > 0. || (y == 0. && atan2(y, -1.) > 0.)) {
+		return fabs(x);
+	} else {
+		return -fabs(x);
+	}
+}
+#endif /* HAVE_COPYSIGN */
+
+#ifndef HAVE_LOG1P
+double
+log1p(double x)
+{
+	/* For x small, we use the following approach.  Let y be the nearest
+	   float to 1+x, then
+
+	     1+x = y * (1 - (y-1-x)/y)
+
+	   so log(1+x) = log(y) + log(1-(y-1-x)/y).  Since (y-1-x)/y is tiny,
+	   the second term is well approximated by (y-1-x)/y.  If abs(x) >=
+	   DBL_EPSILON/2 or the rounding-mode is some form of round-to-nearest
+	   then y-1-x will be exactly representable, and is computed exactly
+	   by (y-1)-x.
+
+	   If abs(x) < DBL_EPSILON/2 and the rounding mode is not known to be
+	   round-to-nearest then this method is slightly dangerous: 1+x could
+	   be rounded up to 1+DBL_EPSILON instead of down to 1, and in that
+	   case y-1-x will not be exactly representable any more and the
+	   result can be off by many ulps.  But this is easily fixed: for a
+	   floating-point number |x| < DBL_EPSILON/2., the closest
+	   floating-point number to log(1+x) is exactly x.
+	*/
+
+	double y;
+	if (fabs(x) < DBL_EPSILON/2.) {
+		return x;
+	} else if (-0.5 <= x && x <= 1.) {
+		/* WARNING: it's possible than an overeager compiler
+		   will incorrectly optimize the following two lines
+		   to the equivalent of "return log(1.+x)". If this
+		   happens, then results from log1p will be inaccurate
+		   for small x. */
+		y = 1.+x;
+		return log(y)-((y-1.)-x)/y;
+	} else {
+		/* NaNs and infinities should end up here */
+		return log(1.+x);
+	}
+}
+#endif /* HAVE_LOG1P */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+static const double ln2 = 6.93147180559945286227E-01;
+static const double two_pow_m28 = 3.7252902984619141E-09; /* 2**-28 */
+static const double two_pow_p28 = 268435456.0; /* 2**28 */
+static const double zero = 0.0;
+
+/* asinh(x)
+ * Method :
+ *	Based on 
+ *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
+ *	we have
+ *	asinh(x) := x  if  1+x*x=1,
+ *		 := sign(x)*(log(x)+ln2)) for large |x|, else
+ *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
+ *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))  
+ */
+
+#ifndef HAVE_ASINH
+double
+asinh(double x)
+{	
+	double w;
+	double absx = fabs(x);
+
+	if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
+		return x+x;
+	}
+	if (absx < two_pow_m28) {	/* |x| < 2**-28 */
+		return x;	/* return x inexact except 0 */
+	} 
+	if (absx > two_pow_p28) {	/* |x| > 2**28 */
+		w = log(absx)+ln2;
+	}
+	else if (absx > 2.0) {		/* 2 < |x| < 2**28 */
+		w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
+	}
+	else {				/* 2**-28 <= |x| < 2= */
+		double t = x*x;
+		w = log1p(absx + t / (1.0 + sqrt(1.0 + t)));
+	}
+	return copysign(w, x);
+	
+}
+#endif /* HAVE_ASINH */
+
+/* acosh(x)
+ * Method :
+ *      Based on
+ *	      acosh(x) = log [ x + sqrt(x*x-1) ]
+ *      we have
+ *	      acosh(x) := log(x)+ln2, if x is large; else
+ *	      acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+ *	      acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+ *
+ * Special cases:
+ *      acosh(x) is NaN with signal if x<1.
+ *      acosh(NaN) is NaN without signal.
+ */
+
+#ifndef HAVE_ACOSH
+double
+acosh(double x)
+{
+	if (Py_IS_NAN(x)) {
+		return x+x;
+	}
+	if (x < 1.) {			/* x < 1;  return a signaling NaN */
+		errno = EDOM;
+#ifdef Py_NAN
+		return Py_NAN;
+#else
+		return (x-x)/(x-x);
+#endif
+	}
+	else if (x >= two_pow_p28) {	/* x > 2**28 */
+		if (Py_IS_INFINITY(x)) {
+			return x+x;
+		} else {
+			return log(x)+ln2;	/* acosh(huge)=log(2x) */
+		}
+	}
+	else if (x == 1.) {
+		return 0.0;			/* acosh(1) = 0 */
+	}
+	else if (x > 2.) {			/* 2 < x < 2**28 */
+		double t = x*x;
+		return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
+	}
+	else {				/* 1 < x <= 2 */
+		double t = x - 1.0;
+		return log1p(t + sqrt(2.0*t + t*t));
+	}
+}
+#endif /* HAVE_ACOSH */
+
+/* atanh(x)
+ * Method :
+ *    1.Reduced x to positive by atanh(-x) = -atanh(x)
+ *    2.For x>=0.5
+ *		  1	      2x			  x
+ *      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
+ *		  2	     1 - x		      1 - x
+ *
+ *      For x<0.5
+ *      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
+ *
+ * Special cases:
+ *      atanh(x) is NaN if |x| >= 1 with signal;
+ *      atanh(NaN) is that NaN with no signal;
+ *
+ */
+
+#ifndef HAVE_ATANH
+double
+atanh(double x)
+{
+	double absx;
+	double t;
+
+	if (Py_IS_NAN(x)) {
+		return x+x;
+	}
+	absx = fabs(x);
+	if (absx >= 1.) {		/* |x| >= 1 */
+		errno = EDOM;
+#ifdef Py_NAN
+		return Py_NAN;
+#else
+		return x/zero;
+#endif
+	}
+	if (absx < two_pow_m28) {	/* |x| < 2**-28 */
+		return x;
+	}
+	if (absx < 0.5) {		/* |x| < 0.5 */
+		t = absx+absx;
+		t = 0.5 * log1p(t + t*absx / (1.0 - absx));
+	} 
+	else {				/* 0.5 <= |x| <= 1.0 */
+		t = 0.5 * log1p((absx + absx) / (1.0 - absx));
+	}
+	return copysign(t, x);
+}
+#endif /* HAVE_ATANH */
diff --git a/configure b/configure
index 0e9e7bbabd..86d4c46c28 100755
--- a/configure
+++ b/configure
@@ -1,5 +1,5 @@
 #! /bin/sh
-# From configure.in Revision: 62003 .
+# From configure.in Revision: 62146 .
 # Guess values for system-dependent variables and create Makefiles.
 # Generated by GNU Autoconf 2.61 for python 3.0.
 #