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�W S ty> | jdkr4Y dS Y dS Y n0 d S �Nr ���)r1 r r � OverflowError�r �posr r r � __rshift__� s zIntegerNative.__rshift__c C sD z| j t|�L _ W n( ty> | j dkr4Y dS Y dS Y n0 | S rP )r r rR rS r r r � __irshift__� s zIntegerNative.__irshift__c C s6 z| � | jt|�> �W S ty0 td��Y n0 d S �NzIncorrect shift count)r1 r r rR r rS r r r � __lshift__� s zIntegerNative.__lshift__c C s6 z| j t|�K _ W n ty0 td��Y n0 | S rW )r r rR r rS r r r � __ilshift__� s zIntegerNative.__ilshift__c C s� | j dk rtd��z\z&| j |j ? d@ }|j dk r8td��W n0 tyj | j |? d@ }|dk rftd��Y n0 W n ty� d}Y n0 |S )Nr z)no bit representation for negative valuesr znegative bit count)r r r rR )r �nr r r r �get_bit� s zIntegerNative.get_bitc C s | j d@ dkS )Nr r r r r r �is_odd� s zIntegerNative.is_oddc C s | j d@ dkS )Nr r r r r r r �is_even s zIntegerNative.is_evenc C sD | j dk rtd��| j dkr dS d}| j }|r@|dL }|d7 }q*|S )Nr r r )r r )r Zbit_size�tmpr r r � size_in_bits s zIntegerNative.size_in_bitsc C s | � � d d d S )Nr � )r_ r r r r � size_in_bytes s zIntegerNative.size_in_bytesc C sb | j dk rdS | j dv r dS | j d }|d }|| j krT|| j d| }|d }q.| j |d kS )Nr F)r r TrF r )r rG Zsquare_xr r r �is_perfect_square s z IntegerNative.is_perfect_squarec C s | j t|� dkrtd��d S )Nr zValue is composite)r r r )r Z small_primer r r �fail_if_divisible_by& s z"IntegerNative.fail_if_divisible_byc C s | j t|�t|� 7 _ | S r r$ )r �a�br r r �multiply_accumulate* s z!IntegerNative.multiply_accumulatec C s t |�| _d S r r )r �sourcer r r �set. s zIntegerNative.setc C s� t |�}|dkrtd��|dk r(td��| j| }}d\}}|dkrr|| }|||| }}|||| }}q<|dkr�tdt|� ��|dk r�||7 }q�|| _| S )Nr r= zModulus cannot be negative)r r r z No inverse value can be computed)r r> r r r )r rA �r_p�r_nZs_pZs_n�qr r r �inplace_inverse1 s" z IntegerNative.inplace_inversec C s | � | �}|�|� |S r )r1 rl )r rA r r r r �inverseD s zIntegerNative.inversec C sF t | j�t t|�� }}|dkr<|| }|||| }}q| �|�S r- )rD r r r1 )r r& ri rj rk r r r �gcdI s zIntegerNative.gcdc C sD t |�}| jdks|dkr$| �d�S | �t| j| | �|�j ��S r- )r r r1 rD rn r% r r r �lcmP s zIntegerNative.lcmc C s� t | �} t |�}|dkr td��|d@ dkr4td��| | } | dksL|dkrPdS | dkr\dS d}| }|d@ dkr�|dL }|d7 }qd|d@ dkr�d}n|d dv r�d}nd}|d d kr�|d d kr�| }|| }|t�||� S ) Nr z n must be a positive integerr z$n must be even for the Jacobi symbolr` )r � rQ � � )r r r � jacobi_symbol)rd rZ �eZa1�sZn1r r r rs V s2 zIntegerNative.jacobi_symbol)r )N)N)N)8�__name__� __module__� __qualname__�__doc__r r r r r r r! � classmethodr# r' r( r) r* r+ r, r. �__bool__r/ r4 r5 r7 r: r< rB rC rE rI rJ rK rL rM rN rO rU rV rX rY r[ r\ r] r_ ra rb rc rf rh rl rm rn ro � staticmethodrs r r r r r $ sj r N)Z _IntegerBaser ZCrypto.Util.numberr r r r r r r �<module> s
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