Merged revisions 62380,62382-62383 via svnmerge from

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

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  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 :)
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  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
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  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 ...
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1 files changed, 183 insertions, 0 deletions

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
+====================
+