3
\W\ � @ s� d dl mZ d dlZd dlZd dlZd dlZd dlZddgZdd� Zdd� Z ej
j Z ej
j
ZejdejejB �ZG d d� dej�ZdS )
� )�DecimalN�Fraction�gcdc C sf dd l }|jdtd� t| �t ko0t|�kn r\|p<| dk rPtj| |� S tj| |�S t| |�S )Nr z6fractions.gcd() is deprecated. Use math.gcd() instead.� )�warnings�warn�DeprecationWarning�type�int�mathr �_gcd)�a�br � r �!/usr/lib64/python3.6/fractions.pyr s c C s x|r|| | } }qW | S )Nr )r
r r r r r s r aC
\A\s* # optional whitespace at the start, then
(?P<sign>[-+]?) # an optional sign, then
(?=\d|\.\d) # lookahead for digit or .digit
(?P<num>\d*) # numerator (possibly empty)
(?: # followed by
(?:/(?P<denom>\d+))? # an optional denominator
| # or
(?:\.(?P<decimal>\d*))? # an optional fractional part
(?:E(?P<exp>[-+]?\d+))? # and optional exponent
)
\s*\Z # and optional whitespace to finish
c s� e Zd ZdRZdSdd�� fdd� Zed d
� �Zed d � �ZdTdd�Ze dd� �Z
e dd� �Z dd� Z dd� Z
dd� Zdd� Zeeej�\ZZd d � Zeeej�\ZZd d � Zeeej�\ZZd d!� Z ee ej �\Z Z d"d#� Z d$d%� Z!d&d'� Z"d(d)� Z#d*d+� Z$d,d-� Z%d.d/� Z&d0d1� Z'd2d3� Z(d4d5� Z)d6d7� Z*d8d9� Z+dUd:d;�Z,d<d=� Z-d>d?� Z.d@dA� Z/dBdC� Z0dDdE� Z1dFdG� Z2dHdI� Z3dJdK� Z4dLdM� Z5dNdO� Z6dPdQ� Z7� Z8S )Vr �
_numerator� _denominatorr NT)�
_normalizec sR t t| �j| �}|d k�rdt|�tkr6||_d|_|S t|tj �rV|j
|_|j |_|S t|t t
f�rx|j� \|_|_|S t|t��rZtj|�}|d kr�td| ��t|jd�p�d�}|jd�}|r�t|�}nvd}|jd�}|�rdt|� }|| t|� }||9 }|jd�} | �rBt| �} | d k�r4|d| 9 }n|d| 9 }|jd
�d k�rb| }ntd ��nft|�t k�o�t|�kn �r�n@t|tj ��r�t|tj ��r�|j
|j |j
|j }}ntd
��|d k�r�td| ��|�rBt|�t k�ot|�kn �r(tj||�}
|d k �r2|
}
n
t||�}
||
}||
}||_||_|S )N� z Invalid literal for Fraction: %rZnum�0�denom�decimal�
�expr Zsign�-z2argument should be a string or a Rational instancez+both arguments should be Rational instanceszFraction(%s, 0))�superr �__new__r r
r r �
isinstance�numbers�Rational� numerator� denominator�floatr �as_integer_ratio�str�_RATIONAL_FORMAT�match�
ValueError�group�len� TypeError�ZeroDivisionErrorr r r ) �clsr r! r �self�mr r Zscaler �g)� __class__r r r T sr
$
$
zFraction.__new__c C sD t |tj�r| |�S t |t�s8td| j|t|�jf ��| |j� � S )Nz.%s.from_float() only takes floats, not %r (%s))r r �Integralr" r* �__name__r r# )r, �fr r r �
from_float� s
zFraction.from_floatc C sV ddl m} t|tj�r&|t|��}n$t||�sJtd| j|t|�jf ��| |j � � S )Nr )r z2%s.from_decimal() only takes Decimals, not %r (%s))
r r r r r1 r
r* r2 r r# )r, Zdecr r r r � from_decimal� s
zFraction.from_decimal�@B c
C s� |dk rt d��| j|kr"t| �S d\}}}}| j| j }}xP|| }||| } | |kr\P ||||| | f\}}}}|||| }}q>W || | }
t||
| ||
| �} t||�} t| | �t| | �kr�| S | S d S )Nr z$max_denominator should be at least 1r )r r r r )r' r r r �abs)
r- Zmax_denominatorZp0Zq0Zp1Zq1�n�dr
Zq2�kZbound1Zbound2r r r �limit_denominator� s&
zFraction.limit_denominatorc C s | j S )N)r )r
r r r r s zFraction.numeratorc C s | j S )N)r )r
r r r r! s zFraction.denominatorc C s d| j j| j| jf S )Nz
%s(%s, %s))r0 r2 r r )r- r r r �__repr__ s zFraction.__repr__c C s( | j dkrt| j�S d| j| j f S d S )Nr z%s/%s)r r$ r )r- r r r �__str__ s
zFraction.__str__c sT � �fdd�}d� j d |_ �j|_� �fdd�}d� j d |_ �j|_||fS )Nc sP t |ttf�r�| |�S t |t�r0� t| �|�S t |t�rH� t| �|�S tS d S )N)r r
r r" �complex�NotImplemented)r
r )�fallback_operator�monomorphic_operatorr r �forwardv s
z-Fraction._operator_fallbacks.<locals>.forward�__c sZ t |tj�r�|| �S t |tj�r4� t|�t| ��S t |tj�rR� t|�t| ��S tS d S )N)r r r ZRealr" �Complexr> r? )r r
)r@ rA r r �reverse� s
z-Fraction._operator_fallbacks.<locals>.reverseZ__r)r2 �__doc__)rA r@ rB rE r )r@ rA r �_operator_fallbacks& s P
z Fraction._operator_fallbacksc C s, | j |j }}t| j| |j| || �S )N)r! r r )r
r �da�dbr r r �_add� s z
Fraction._addc C s, | j |j }}t| j| |j| || �S )N)r! r r )r
r rH rI r r r �_sub� s z
Fraction._subc C s t | j|j | j|j �S )N)r r r! )r
r r r r �_mul� s z
Fraction._mulc C s t | j|j | j|j �S )N)r r r! )r
r r r r �_div� s z
Fraction._divc C s t j| | �S )N)r �floor)r
r r r r � __floordiv__� s zFraction.__floordiv__c C s t j|| �S )N)r rN )r r
r r r �
__rfloordiv__� s zFraction.__rfloordiv__c C s | | }| || S )Nr )r
r �divr r r �__mod__� s zFraction.__mod__c C s || }|| | S )Nr )r r
rQ r r r �__rmod__� s zFraction.__rmod__c C s� t |tj�r�|jdkr�|j}|dkr>t| j| | j| dd�S | jdkrft| j| | j| dd�S t| j | | j | dd�S q�t| �t|� S n t| �| S d S )Nr r F)r ) r r r r! r r r r r" )r
r Zpowerr r r �__pow__� s
zFraction.__pow__c C s\ | j dkr | jdkr || j S t|tj�r<t|j|j�| S | j dkrP|| j S |t| � S )Nr r ) r r r r r r r r! r" )r r
r r r �__rpow__� s
zFraction.__rpow__c C s t | j| jdd�S )NF)r )r r r )r
r r r �__pos__� s zFraction.__pos__c C s t | j | jdd�S )NF)r )r r r )r
r r r �__neg__� s zFraction.__neg__c C s t t| j�| jdd�S )NF)r )r r7 r r )r
r r r �__abs__� s zFraction.__abs__c C s* | j dk r| j | j S | j | j S d S )Nr )r r )r
r r r � __trunc__� s
zFraction.__trunc__c C s | j | j S )N)r r! )r
r r r � __floor__� s zFraction.__floor__c C s | j | j S )N)r r! )r
r r r �__ceil__ s zFraction.__ceil__c C s� |d krZt | j| j�\}}|d | jk r,|S |d | jkrB|d S |d dkrR|S |d S dt|� }|dkr�tt| | �|�S tt| | �| �S d S )Nr r r r )�divmodr r! r7 r �round)r- ZndigitsrN Z remainderZshiftr r r � __round__ s zFraction.__round__c C sP t | jtd t�}|s t}nt| j�| t }| dkr:|n| }|dkrLdS |S )Nr r r ������)�powr �_PyHASH_MODULUS� _PyHASH_INFr7 r )r- ZdinvZhash_�resultr r r �__hash__! s zFraction.__hash__c C s� t |�tkr | j|ko | jdkS t|tj�rD| j|jkoB| j|jkS t|tj �r`|j
dkr`|j }t|t �r�t
j|�s~t
j|�r�d|kS | | j|�kS ntS d S )Nr r g )r r
r r r r r r r! rD �imag�realr" r �isnan�isinfr4 r? )r
r r r r �__eq__7 s
zFraction.__eq__c C sh t |tj�r&|| j|j | j|j �S t |t�r`tj |�sDtj
|�rN|d|�S || | j |��S nt S d S )Ng )
r r r r r! r r r" r rh ri r4 r? )r- �other�opr r r �_richcmpL s
zFraction._richcmpc C s | j |tj�S )N)rm �operator�lt)r
r r r r �__lt__b s zFraction.__lt__c C s | j |tj�S )N)rm rn �gt)r
r r r r �__gt__f s zFraction.__gt__c C s | j |tj�S )N)rm rn �le)r
r r r r �__le__j s zFraction.__le__c C s | j |tj�S )N)rm rn �ge)r
r r r r �__ge__n s zFraction.__ge__c C s
| j dkS )Nr )r )r
r r r �__bool__r s zFraction.__bool__c C s | j t| �ffS )N)r0 r$ )r- r r r �
__reduce__x s zFraction.__reduce__c C s t | �tkr| S | j| j| j�S )N)r r r0 r r )r- r r r �__copy__{ s zFraction.__copy__c C s t | �tkr| S | j| j| j�S )N)r r r0 r r )r- �memor r r � __deepcopy__� s zFraction.__deepcopy__)r r )r N)r6 )N)9r2 �
__module__� __qualname__� __slots__r � classmethodr4 r5 r; �propertyr r! r< r= rG rJ rn �add�__add__�__radd__rK �sub�__sub__�__rsub__rL �mul�__mul__�__rmul__rM �truediv� __truediv__� __rtruediv__rO rP rR rS rT rU rV rW rX rY rZ r[ r^ re rj rm rp rr rt rv rw rx ry r{ �
__classcell__r r )r0 r r < sT m
7 k
)r r r r rn �re�sys�__all__r r � hash_info�modulusrb �infrc �compile�VERBOSE�
IGNORECASEr% r r r r r r �<module> s