decimal — 十进制定点和浮点算术
decimal
fractions
源代码： Lib/fractions.py
The fractions 模块提供有理数算术支持。
Fraction 实例可以构造自一对整数、另一有理数或字符串。
第 1 个版本要求 numerator and denominator 是实例化的 numbers.Rational 并返回新的 Fraction 实例采用值 numerator/denominator 。若 denominator is 0 ，引发 ZeroDivisionError 。第 2 个版本要求 other_fraction 是实例化的 numbers.Rational 并返回 Fraction instance with the same value. The next two versions accept either a float 或 decimal.Decimal instance, and return a Fraction instance with exactly the same value. Note that due to the usual issues with binary floating-point (see 浮点算术：问题和局限性 ), the argument to Fraction(1.1) is not exactly equal to 11/10, and so Fraction(1.1) does not return Fraction(11, 10) as one might expect. (But see the documentation for the limit_denominator() method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is:
numbers.Rational
Fraction
numerator/denominator
0
ZeroDivisionError
float
decimal.Decimal
Fraction(1.1)
Fraction(11, 10)
limit_denominator()
[sign] numerator ['/' denominator]
其中可选 sign may be either ‘+’ or ‘-’ and numerator and denominator (if present) are strings of decimal digits (underscores may be used to delimit digits as with integral literals in code). In addition, any string that represents a finite value and is accepted by the float constructor is also accepted by the Fraction constructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples:
sign
numerator
denominator
>>> from fractions import Fraction >>> Fraction(16, -10) Fraction(-8, 5) >>> Fraction(123) Fraction(123, 1) >>> Fraction() Fraction(0, 1) >>> Fraction('3/7') Fraction(3, 7) >>> Fraction(' -3/7 ') Fraction(-3, 7) >>> Fraction('1.414213 \t\n') Fraction(1414213, 1000000) >>> Fraction('-.125') Fraction(-1, 8) >>> Fraction('7e-6') Fraction(7, 1000000) >>> Fraction(2.25) Fraction(9, 4) >>> Fraction(1.1) Fraction(2476979795053773, 2251799813685248) >>> from decimal import Decimal >>> Fraction(Decimal('1.1')) Fraction(11, 10)
The Fraction class inherits from the abstract base class numbers.Rational , and implements all of the methods and operations from that class. Fraction instances are hashable , and should be treated as immutable. In addition, Fraction has the following properties and methods:
3.2 版改变： The Fraction 构造函数现在接受 float and decimal.Decimal 实例。
3.9 版改变： The math.gcd() function is now used to normalize the numerator and denominator . math.gcd() always return a int type. Previously, the GCD type depended on numerator and denominator .
math.gcd()
int
3.11 版改变： Underscores are now permitted when creating a Fraction instance from a string, following PEP 515 规则。
3.11 版改变： Fraction 实现 __int__ now to satisfy typing.SupportsInt instance checks.
__int__
typing.SupportsInt
Changed in version 3.12: Space is allowed around the slash for string inputs: Fraction('2 / 3') .
Fraction('2 / 3')
Changed in version 3.12: Fraction instances now support float-style formatting, with presentation types "e" , "E" , "f" , "F" , "g" , "G" and "%"" .
"e"
"E"
"f"
"F"
"g"
"G"
"%""
Numerator of the Fraction in lowest term.
Denominator of the Fraction in lowest term.
Return a tuple of two integers, whose ratio is equal to the original Fraction. The ratio is in lowest terms and has a positive denominator.
Added in version 3.8.
返回 True if the Fraction is an integer.
True
3.12 版添加。
Alternative constructor which only accepts instances of float or numbers.Integral . Beware that Fraction.from_float(0.3) is not the same value as Fraction(3, 10) .
numbers.Integral
Fraction.from_float(0.3)
Fraction(3, 10)
注意
From Python 3.2 onwards, you can also construct a Fraction instance directly from a float .
Alternative constructor which only accepts instances of decimal.Decimal or numbers.Integral .
From Python 3.2 onwards, you can also construct a Fraction instance directly from a decimal.Decimal 实例。
Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number:
self
>>> from fractions import Fraction >>> Fraction('3.1415926535897932').limit_denominator(1000) Fraction(355, 113)
or for recovering a rational number that’s represented as a float:
>>> from math import pi, cos >>> Fraction(cos(pi/3)) Fraction(4503599627370497, 9007199254740992) >>> Fraction(cos(pi/3)).limit_denominator() Fraction(1, 2) >>> Fraction(1.1).limit_denominator() Fraction(11, 10)
Returns the greatest int <= self . This method can also be accessed through the math.floor() 函数：
<= self
math.floor()
>>> from math import floor >>> floor(Fraction(355, 113)) 3
Returns the least int >= self . This method can also be accessed through the math.ceil() 函数。
>= self
math.ceil()
The first version returns the nearest int to self , rounding half to even. The second version rounds self to the nearest multiple of Fraction(1, 10**ndigits) (logically, if ndigits is negative), again rounding half toward even. This method can also be accessed through the round() 函数。
Fraction(1, 10**ndigits)
ndigits
round()
Provides support for float-style formatting of Fraction instances via the str.format() method, the format() built-in function, or 格式化字符串文字 . The presentation types "e" , "E" , "f" , "F" , "g" , "G" and "%" are supported. For these presentation types, formatting for a Fraction 对象 x follows the rules outlined for the float 类型在 格式规范迷你语言 章节。
str.format()
format()
"%"
x
这里是一些范例：
>>> from fractions import Fraction >>> format(Fraction(1, 7), '.40g') '0.1428571428571428571428571428571428571429' >>> format(Fraction('1234567.855'), '_.2f') '1_234_567.86' >>> f"{Fraction(355, 113):*>20.6e}" '********3.141593e+00' >>> old_price, new_price = 499, 672 >>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1) '34.67% price increase'
另请参阅
numbers
组成数值塔的抽象基类。
random — 生成伪随机数
random
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