/usr/lib/python2.7/test/ieee754.txt is in libpython2.7-testsuite 2.7.6-8.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 | ======================================
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
====================
|