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Diffstat (limited to 'lib/python2.7/test/ieee754.txt')
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diff --git a/lib/python2.7/test/ieee754.txt b/lib/python2.7/test/ieee754.txt new file mode 100644 index 0000000..89bb0c5 --- /dev/null +++ b/lib/python2.7/test/ieee754.txt @@ -0,0 +1,185 @@ +====================================== +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 nan**0 and 1**nan. +>>> 1 + NAN +nan +>>> 1 * NAN +nan +>>> 0 * NAN +nan +>>> 1 ** NAN +1.0 +>>> NAN ** 0 +1.0 +>>> 0 ** NAN +nan +>>> (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 +==================== + |