U
e5d _ � @ s� d dl mZ d dlZd dlZd dlZd dlZd dlZddgZdd� Zdd� Z ej
j Z ej
j
Ze�dejejB �ZG d d� dej�ZdS )
� ��DecimalN�Fraction�gcdc C sf dd l }|�dtd� t| �t kr2t|�kr\n n&|p<| dk rPt�| |� S t�| |�S t| |�S )Nr z6fractions.gcd() is deprecated. Use math.gcd() instead.� )�warnings�warn�DeprecationWarning�type�int�mathr �_gcd)�a�br � r �!/usr/lib64/python3.8/fractions.pyr s � c C s |r|| | } }q | S �Nr �r r r r r r
s r
aC
\A\s* # optional whitespace at the start, then
(?P[-+]?) # an optional sign, then
(?=\d|\.\d) # lookahead for digit or .digit
(?P\d*) # numerator (possibly empty)
(?: # followed by
(?:/(?P\d+))? # an optional denominator
| # or
(?:\.(?P\d*))? # an optional fractional part
(?:E(?P[-+]?\d+))? # and optional exponent
)
\s*\Z # and optional whitespace to finish
c s� e Zd ZdZdQdd�� fdd� Zedd � �Zed
d � �Zd d
� ZdRdd�Z e
dd� �Z e
dd� �Z dd� Z
dd� Zdd� Zdd � Zeeej�\ZZd d � Zeeej�\ZZd d � Zeeej�\ZZ d!d"� Z ee ej �\Z Z d#d$� Z!ee!ej"�\Z#Z$d%d&� Z%ee%e&�\Z'Z(d'd(� Z)ee)ej*�\Z+Z,d)d*� Z-d+d,� Z.d-d.� Z/d/d0� Z0d1d2� Z1d3d4� Z2d5d6� Z3d7d8� Z4dSd9d:�Z5d;d<� Z6d=d>� Z7d?d@� Z8dAdB� Z9dCdD� Z:dEdF� Z;dGdH� ZdMdN� Z?dOdP� Z@� ZAS )Tr ��
_numerator� _denominatorr NT��
_normalizec sR t t| ��| �}|d k�rdt|�tkr6||_d|_|S t|tj �rV|j
|_|j |_|S t|t t
f�rx|�� \|_|_|S t|t��rZt�|�}|d kr�td| ��t|�d�p�d�}|�d�}|r�t|�}nvd}|�d�}|�rdt|� }|| t|� }||9 }|�d�} | �rBt| �} | d k�r4|d| 9 }n|d| 9 }|�d
�d k�rb| }ntd ��nft|�t k�r�t|�k�r�n nn@t|tj ��r�t|tj ��r�|j
|j |j
|j }}ntd
��|d k�r�td| ��|�rBt|�t k�rt|�k�r(n n t�||�}
|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 sx
�
$
�
�
$
zFraction.__new__c C sD t |tj�r| |�S t |t�s8td| j|t|�jf ��| |�� � S )Nz.%s.from_float() only takes floats, not %r (%s))r" r# �Integralr' r/ �__name__r
r( )r1 �fr r r �
from_float� s
�zFraction.from_floatc C sV ddl m} t|tj�r&|t|��}n$t||�sJtd| j|t|�jf ��| |� � � S )Nr r z2%s.from_decimal() only takes Decimals, not %r (%s))
r r r" r# r7 r r/ r8 r
r( )r1 Zdecr r r r � from_decimal� s
��zFraction.from_decimalc C s | j | jfS r r �r2 r r r r( � s zFraction.as_integer_ratio�@B c
C s� |dk rt d��| j|kr"t| �S d\}}}}| j| j }}|| }||| } | |krZq�||||| | f\}}}}|||| }}q<|| | }
t||
| ||
| �} t||�} t| | �t| | �kr�| S | S d S )Nr z$max_denominator should be at least 1)r r r r )r, r r r �abs)
r2 Zmax_denominatorZp0Zq0Zp1Zq1�n�dr Zq2�kZbound1Zbound2r r r �limit_denominator� s$
zFraction.limit_denominatorc C s | j S r )r �r r r r r% s zFraction.numeratorc C s | j S r )r rC r r r r& s zFraction.denominatorc C s d| j j| j| jf S )Nz
%s(%s, %s))r6 r8 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 r )r" r r r' �complex�NotImplementedr ��fallback_operator�monomorphic_operatorr r �forward~ s
z-Fraction._operator_fallbacks..forward�__c sZ t |tj�r�|| �S t |tj�r4� t|�t| ��S t |tj�rR� t|�t| ��S tS d S r )r" r# r$ ZRealr' �ComplexrF rG �r r rH r r �reverse� s
z-Fraction._operator_fallbacks..reverseZ__r)r8 �__doc__)rJ rI rK rO r rH r �_operator_fallbacks. s P
z Fraction._operator_fallbacksc C s, | j |j }}t| j| |j| || �S r �r& r r% �r r �da�dbr r r �_add� s �z
Fraction._addc C s, | j |j }}t| j| |j| || �S r rR rS r r r �_sub� s �z
Fraction._subc C s t | j|j | j|j �S r �r r% r& r r r r �_mul� s z
Fraction._mulc C s t | j|j | j|j �S r rX r r r r �_div� s
�z
Fraction._divc C s | j |j | j|j S r �r% r& r r r r � _floordiv� s zFraction._floordivc C s: | j |j }}t| j| ||j �\}}|t||| �fS r )r& �divmodr% r )r r rT rU ZdivZn_modr r r �_divmod� s zFraction._divmodc C s, | j |j }}t| j| |j| || �S r rR rS r r r �_mod� s z
Fraction._modc 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 Fr ) 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 r r rC r r r �__abs__� s zFraction.__abs__c C s* | j dk r| j | j S | j | j S d S )Nr r rC r r r � __trunc__ s
zFraction.__trunc__c C s | j | j S r r[ rC r r r � __floor__
s zFraction.__floor__c C s | j | j S r r[ rC 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 )r] r% r& r> r �round)r2 ZndigitsZfloorZ remainder�shiftr r r � __round__ s zFraction.__round__c C sP t | jtd t�}|s t}nt| j�| t }| dkr:|n| }|dkrLdS |S )Nr r ����������)�powr �_PyHASH_MODULUS� _PyHASH_INFr> r )r2 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
�|�s~t
�|�r�d|kS | | �|�kS ntS d S )Nr r � )r
r r r r" r# r$ r% r& rM �imag�realr' r �isnan�isinfr: rG r r r r �__eq__B s
�
zFraction.__eq__c C sh t |tj�r&|| j|j | j|j �S t |t�r`t� |�sDt�
|�rN|d|�S || | � |��S nt S d S )Nrt )
r" r# r$ r r& r r% r' r rw rx r: rG )r2 �other�opr r r �_richcmpW s
�
zFraction._richcmpc C s | � |tj�S r )r| �operator�ltr r r r �__lt__m s zFraction.__lt__c C s | � |tj�S r )r| r} �gtr r r r �__gt__q s zFraction.__gt__c C s | � |tj�S r )r| r} �ler r r r �__le__u s zFraction.__le__c C s | � |tj�S r )r| r} �ger r r r �__ge__y s zFraction.__ge__c C s
t | j�S r )�boolr rC r r r �__bool__} s zFraction.__bool__c C s | j t| �ffS r )r6 r) r< r r r �
__reduce__� s zFraction.__reduce__c C s t | �tkr| S | �| j| j�S r �r
r r6 r r r< r r r �__copy__� s zFraction.__copy__c C s t | �tkr| S | �| j| j�S r r� )r2 Zmemor r r � __deepcopy__� s zFraction.__deepcopy__)r N)r= )N)Br8 �
__module__� __qualname__� __slots__r! � classmethodr: r; r( rB �propertyr% r& rD rE rQ rV r} �add�__add__�__radd__rW �sub�__sub__�__rsub__rY �mul�__mul__�__rmul__rZ �truediv� __truediv__� __rtruediv__r\ �floordiv� __floordiv__�
__rfloordiv__r^ r] �
__divmod__� __rdivmod__r_ �mod�__mod__�__rmod__r` ra rd re rf rg rh ri rl rs ry r| r r� r� r� r� r� r� r� �
__classcell__r r r5 r r < sb m
7
k
)r r r r# r} �re�sys�__all__r r
� hash_info�modulusrp �infrq �compile�VERBOSE�
IGNORECASEr* r$ r r r r r � s
�