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Revision dae5d728bc3f1d4039b64e4ec3a9036fd5d19587 authored by Miss Islington (bot) on 10 November 2020, 19:58:27 UTC, committed by GitHub on 10 November 2020, 19:58:27 UTC
Fix an assertion error in format() in debug build for floating point formatting with "n" format, zero padding and small width. Release build is not impacted. Patch by Karthikeyan Singaravelan. (cherry picked from commit 3f7983a25a3d19779283c707fbdd5bc91b1587ef) Co-authored-by: Xtreak <tir.karthi@gmail.com>
1 parent a63234c
Tip revision: dae5d728bc3f1d4039b64e4ec3a9036fd5d19587 authored by Miss Islington (bot) on 10 November 2020, 19:58:27 UTC
bpo-35560: Remove assertion from format(float, "n") (GH-11288) (GH-23231)
bpo-35560: Remove assertion from format(float, "n") (GH-11288) (GH-23231)
Tip revision: dae5d72
ieee754.txt
======================================
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
====================
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