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r( )� _ignore_flagsr< r� r) r) r+ r� � s zContext._ignore_all_flagsc G s | j t|� | _ t|�S r( )r� ro )r0 r> r) r) r+ r� � s zContext._ignore_flagsc G s8 |r t |d ttf�r |d }|D ]}| j�|� q"d S r� )rd rp ro r� �remove)r0 r> r� r) r) r+ � _regard_flags� s zContext._regard_flagsc C s t | j| j d �S ri )rV rH rE r� r) r) r+ r� � s z Context.Etinyc C s t | j| j d �S ri )rV rF rE r� r) r) r+ r � s z Context.Etopc C s | j }|| _ |S r( )rD )r0 r� rD r) r) r+ rP � s zContext._set_roundingrR c C sj t |t�r*||�� ks d|v r*| �td�S t|| d�}|�� r`t|j�| j | j kr`| �td�S |� | �S )NrS zAtrailing or leading whitespace and underscores are not permitted.rK z diagnostic info too long in NaN) rd re rg ri r r r� rk r; rE r� r� )r0 rp r� r) r) r+ �create_decimal� s � �zContext.create_decimalc C s t �|�}|�| �S r( )r rv r� )r0 r� r� r) r) r+ �create_decimal_from_float s z!Context.create_decimal_from_floatc C s t |dd�}|j| d�S r[ )r� r� �r0 r7 r) r) r+ rm ! s z Context.absc C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S �NTr� rK � Unable to convert %s to Decimal)r� r� r� rw �r0 r7 r� r� r) r) r+ �add6 s z Context.addc C s t |�| ��S r( )re r� r� r) r) r+ �_applyK s zContext._applyc C s t |t�std��|�� S )Nz,canonical requires a Decimal as an argument.)rd r rw rZ r� r) r) r+ rZ N s zContext.canonicalc C s t |dd�}|j|| d�S r[ )r� r� �r0 r7 r� r) r) r+ r� [ s ! zContext.comparec C s t |dd�}|j|| d�S r[ )r� r\ r� r) r) r+ r\ s zContext.compare_signalc C s t |dd�}|�|�S r� )r� rW r� r) r) r+ rW � s zContext.compare_totalc C s t |dd�}|�|�S r� )r� r` r� r) r) r+ r` � s zContext.compare_total_magc C s t |dd�}|�� S r� )r� r� r� r) r) r+ r� � s zContext.copy_absc C s t |dd�}t|�S r� )r� r r� r) r) r+ � copy_decimal� s zContext.copy_decimalc C s t |dd�}|�� S r� )r� r� r� r) r) r+ r� � s zContext.copy_negatec C s t |dd�}|�|�S r� )r� ra r� r) r) r+ ra � s zContext.copy_signc C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S r� )r� r� r� rw r� r) r) r+ �divide s zContext.dividec C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S r� )r� r� r� rw r� r) r) r+ � divide_int+ s zContext.divide_intc C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S r� )r� r� r� rw r� r) r) r+ r� B s zContext.divmodc C s t |dd�}|j| d�S r[ )r� rW r� r) r) r+ rW W s z Context.expc C s t |dd�}|j||| d�S r[ )r� r )r0 r7 r� rR r) r) r+ r o s z Context.fmac C s t |t�std��|�� S )Nz/is_canonical requires a Decimal as an argument.)rd r rw rd r� r) r) r+ rd � s zContext.is_canonicalc C s t |dd�}|�� S r� )r� re r� r) r) r+ re � s zContext.is_finitec C s t |dd�}|�� S r� )r� rI r� r) r) r+ rI � s zContext.is_infinitec C s t |dd�}|�� S r� )r� r� r� r) r) r+ r� � s zContext.is_nanc C s t |dd�}|j| d�S r[ )r� rh r� r) r) r+ rh � s zContext.is_normalc C s t |dd�}|�� S r� )r� r� r� r) r) r+ r� � s zContext.is_qnanc C s t |dd�}|�� S r� )r� rj r� r) r) r+ rj � s zContext.is_signedc C s t |dd�}|�� S r� )r� r� r� r) r) r+ r� � s zContext.is_snanc C s t |dd�}|j| d�S r[ )r� rk r� r) r) r+ rk s zContext.is_subnormalc C s t |dd�}|�� S r� )r� rl r� r) r) r+ rl % s zContext.is_zeroc C s t |dd�}|j| d�S r[ )r� rv r� r) r) r+ rv 6 s z Context.lnc C s t |dd�}|j| d�S r[ )r� ry r� r) r) r+ ry L s z Context.log10c C s t |dd�}|j| d�S r[ )r� rz r� r) r) r+ rz h s z Context.logbc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s zContext.logical_andc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ r� � s zContext.logical_invertc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s zContext.logical_orc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s zContext.logical_xorc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s z Context.maxc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� s zContext.max_magc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� s z Context.minc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� - s zContext.min_magc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ �minus> s z Context.minusc C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S r� )r� r� r� rw r� r) r) r+ �multiplyO s zContext.multiplyc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ r� o s zContext.next_minusc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ r� � s zContext.next_plusc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s zContext.next_towardc C s t |dd�}|j| d�S r[ )r� rG r� r) r) r+ rG � s zContext.normalizec C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ r� � s / zContext.number_classc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ �plus s z Context.plusc C s: t |dd�}|j||| d�}|tu r2td| ��n|S d S r� )r� rC r� rw )r0 r7 r� r r� r) r) r+ �power s I z Context.powerc C s t |dd�}|j|| d�S r[ )r� r r� r) r) r+ r e s 7 zContext.quantizec C s t d�S r� r� r� r) r) r+ r� � s z Context.radixc C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S r� )r� r� r� rw r� r) r) r+ r� � s zContext.remainderc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s zContext.remainder_nearc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� � s zContext.rotatec C s t |dd�}|�|�S r� )r� rJ r� r) r) r+ rJ s zContext.same_quantumc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� $ s zContext.scalebc C s t |dd�}|j|| d�S r[ )r� r� r� r) r) r+ r� 7 s z Context.shiftc C s t |dd�}|j| d�S r[ )r� rT r� r) r) r+ rT U s z Context.sqrtc C s8 t |dd�}|j|| d�}|tu r0td| ��n|S d S r� )r� r� r� rw r� r) r) r+ �subtractu s zContext.subtractc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ r� � s zContext.to_eng_stringc C s t |dd�}|j| d�S r[ )r� r� r� r) r) r+ � to_sci_string� s zContext.to_sci_stringc C s t |dd�}|j| d�S r[ )r� rN r� r) r) r+ rN � s zContext.to_integral_exactc C s t |dd�}|j| d�S r[ )r� r r� r) r) r+ r � s zContext.to_integral_value) NNNNNNNNN)N)rR )N)Wr4 r5 r6 r� r� r� r� r� r� r� rM r� rO rL r� ri r� r� r� r� r� r rP r� r� rm r� r� rZ r� r\ rW r` r� r� r� ra r� r� r� rW r rd re rI r� rh r� rj r� rk rl rv ry rz r� r� r� r� r� r� r� r� r� r� r� r� r� rG r� r� r� r r� r� r� r� rJ r� r� rT r� r� r� rN r r� r) r) r) r+ r s� � $ $# % #2 P:&" r c @ s" e Zd ZdZddd�Zdd� ZdS )rn �rB rV rW Nc C sf |d u r d | _ d| _d | _nFt|t�rD|j| _ t|j�| _|j| _n |d | _ |d | _|d | _d S )Nr& r. r^ )rB rV rW rd r r: r; rP )r0 ry r) r) r+ r� � s z_WorkRep.__init__c C s d| j | j| jf S )Nz (%r, %r, %r)r� r� r) r) r+ r� s z_WorkRep.__repr__)N)r4 r5 r6 r� r� r� r) r) r) r+ rn � s rn c C s� | j |j k r|}| }n| }|}tt|j��}tt|j��}|j td|| d � }||j d |k rpd|_||_ | jd|j |j 9 _|j |_ | |fS )Nr� r^ r. r� )rW rk re rV r� )r� r� rE �tmpr� Ztmp_lenZ other_lenrW r) r) r+ r� s r� c C sb | dkr dS |dkr | d| S t t| ��}t|�t|�d�� }|| k rPd S | d| S d S )Nr& r� rR )re rm rk �rstrip)r8 r� Zstr_nZval_nr) r) r+ r- ( s r- c C sB | dks|dkrt d��d}||kr>||| | d? }}q |S )Nr& z3Both arguments to _sqrt_nearest should be positive.r. )rq )r8 r7 r� r) r) r+ � _sqrt_nearest= s r� c C s2 d|> | |? }}|d| |d @ |d@ |k S )Nr. r^ r) )r0 r� r� r� r) r) r+ �_rshift_nearestL s r� c C s& t | |�\}}|d| |d@ |k S )Nr^ r. )r� )r7 r� r� r� r) r) r+ � _div_nearestT s r� r' c C s� | | }d}||kr(t |�|| > |ksD||krxt |�|| ? |krxt|| d> |t||t||� |� �}|d7 }q tdtt|�� d| � }t||�}t||�}t|d dd�D ] }t||�t|| |� }q�t|| |�S )Nr& r. ���r\ r� )rm r� r� r� rV rk re r ) r0 �M�Lr3 �R�TZyshift�wr� r) r) r+ �_ilog\ s" �� � r c C s� |d7 }t t| ��}|| || dk }|dkr�d| }|| | }|dkrZ| d| 9 } nt| d| �} t| |�}t|�}t|| |�}|| } nd}t|d| �} t| | d�S �Nr^ r. r& r� r+ )rk re r� r � _log10_digits) rR r� r/ rS r� r� r� �log_dZlog_10Z log_tenpowerr) r) r+ rx � s rx c C s� |d7 }t t| ��}|| || dk }|dkrr|| | }|dkrR| d| 9 } nt| d| �} t| d| �}nd}|r�t tt|���d }|| dkr�t|t|| � d| �}q�d}nd}t|| d�S r )rk re r� r rm r ) rR r� r/ rS r� r� r rA Z f_log_tenr) r) r+ rt � s" rt c @ s e Zd Zdd� Zdd� ZdS )� _Log10Memoizec C s d| _ d S )NZ/23025850929940456840179914546843642076011014886)r} r� r) r) r+ r� � s z_Log10Memoize.__init__c C s� |dk rt d��|t| j�kr�d}d|| d }tttd| |�d��}|| d � d| krbql|d7 }q"|�d�d d� | _t| jd |d � �S ) Nr& zp should be nonnegativer\ r� r^ r+ rR r� r. )rq rk r} re r� r r� rV )r0 r/ rA r� r} r) r) r+ � getdigits� s z_Log10Memoize.getdigitsN)r4 r5 r6 r� r r) r) r) r+ r � s r c C s� t | |> | �}tdtt|�� d| � }t| |�}||> }t|d dd�D ]}t| || || �}qPt|d dd�D ]"}||d > }t||| |�}q||| S )Nr� r\ r. r& r� r^ )r, rV rk re r� r ) r0 r� r r r r3 ZMshiftr# r� r) r) r+ �_iexp� s r c C s� |d7 }t d|tt| �� d �}|| }|| }|dkrH| d| }n| d| }t|t|��\}}t|d| �}tt|d| �d�|| d fS )Nr^ r& r. r� i� r\ )r� rk re r� r r� r ) rR r� r/ rA r� r� ZcshiftZquotr6 r) r) r+ rb $ s rb c C s� t tt|���| }t| ||| d �}|| }|dkrJ|| d| }nt|| d| �}|dkr�t t| ��| dk|dkkr�d|d d d| } } q�d| d | } } n,t||d |d �\} } t| d�} | d7 } | | fS )Nr. r& r� )rk re rm rt r� rb ) r1 r2 r4 r5 r/ r� Zlxcr� Zpcr� rW r) r) r+ r; H s r; r+ �F �5 �( � rm � r� r~ ) r� �2�3�4�5�6�7�8rC c C s0 | dkrt d��t| �}dt|� ||d S )Nr& z0The argument to _log10_lb should be nonnegative.r+ )rq re rk )rR Z correctionZstr_cr) r) r+ r. r s r. c C sL t | t�r| S t | t�r t| �S |r8t | t�r8t�| �S |rHtd| ��tS )Nr� )rd r rV ru rv rw r� )r� r� Z allow_floatr) r) r+ r� } s r� c C s� t |t�r| |fS t |tj�rR| jsDt| jtt| j �|j �| j �} | t|j �fS |rrt |tj �rr|jdkrr|j}t |t�r�t� }|r�d|jt< n |�td� | t�|�fS ttfS )Nr& r. ra )rd r �_numbersZRationalrQ r9 r: re rV r; � denominatorrP � numeratorZComplexr� r� ru r r> r ri rv r� )r0 r� r� r1 r) r) r+ r� � s( � �r� r* i?B i���)rE rD r= r> rF rH r� r� r_ )rE rD r= r> a� # A numeric string consists of: # \s* (?P<sign>[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P<int>\d*) # having a (possibly empty) integer part (\.(?P<frac>\d*))? # followed by an optional fractional part (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?P<signal>s)? # ...an (optionally signaling) NaN # NaN (?P<diag>\d*) # with (possibly empty) diagnostic info. ) # \s* \Z z0*$z50*$z�\A (?: (?P<fill>.)? (?P<align>[<>=^]) )? (?P<sign>[-+ ])? (?P<alt>\#)? (?P<zeropad>0)? (?P<minimumwidth>(?!0)\d+)? (?P<thousands_sep>,)? (?:\.(?P<precision>0|(?!0)\d+))? (?P<type>[eEfFgGn%])? \Z c C s� t �| �}|d u r td| ��|�� }|d }|d }|d d u|d< |d rv|d urbtd| ��|d urvtd| ��|p|d|d< |p�d|d< |d d u r�d |d < t|d p�d �|d < |d d ur�t|d �|d < |d dkr�|d d u s�|d dv r�d|d < |d dk�rfd|d< |d u �r&t�� }|d d u�r@td| ��|d |d< |d |d< |d |d< n*|d d u �r|d|d< ddg|d< d|d< |S )NzInvalid format specifier: �fill�align�zeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: � �>rB rU � minimumwidthrR r� r& r� ZgGnr. r8 r� � thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: �grouping� decimal_pointrT r\ r� )� _parse_format_specifier_regex�matchrq � groupdictrV �_locale� localeconv)� format_specr� rz Z format_dictr r r) r) r+ r� sT �� � r� c C s� |d }|d }||t | � t |� }|d }|dkrF| | | }nj|dkr\|| | }nT|dkrr| | | }n>|dkr�t |�d }|d |� | | ||d � }ntd ��|S ) Nr r r �<r �=�^r^ z Unrecognised alignment field)rk rq ) rB r� r� r r Zpaddingr r� Zhalfr) r) r+ r� m s "r� c C sp ddl m}m} | sg S | d dkrJt| �dkrJ|| d d� || d ��S | d tjkrd| d d� S td��d S )Nr& )�chain�repeatr� r^ r� z unrecognised format for grouping)� itertoolsr, r- rk r& �CHAR_MAXrq )r! r, r- r) r) r+ �_group_lengths� s r0 c C s� |d }|d }g }t |�D ]�}|dkr0td��ttt| �|d�|�}|�d|t| � | | d � � | d | � } ||8 }| s�|dkr� q�|t|�8 }q tt| �|d�}|�d|t| � | | d � � |�t|��S )Nr r! r& z group length should be positiver. rR )r0 rq r� r� rk rr rs �reversed)r} r� � min_width�sepr! �groupsrS r) r) r+ �_insert_thousands_sep� s $ $r5 c C s$ | rdS |d dv r |d S dS d S )NrU rB z +rT r) )� is_negativer� r) r) r+ r� � s r� c C s� t | |�}|s|d r"|d | }|dks6|d dv r\ddddd�|d }|d �||�7 }|d d krp|d 7 }|d r�|d t|� t|� }nd}t|||�}t||| |�S ) NZaltr" r& r� r� r� r� )r� r� r� r� z{0}{1:+}r� r r )r� �formatrk r5 r� )r6 r{ r| rW r� rB Zecharr2 r) r) r+ r� � s r� ZInfz-Infr� r� r^ )N)F)r& )r' )r' )FF)F)N)r. )y�__all__r4 Z __xname__� __version__Z__libmpdec_version__�mathr Znumbersr �sys� collectionsr' Z _namedtupler � ImportErrorr r r r r r r r r$ r% �maxsizer r! r" r# �ArithmeticErrorr r r r �ZeroDivisionErrorr r r r r r r r r rw r r< r� r� Z contextvarsZ ContextVarrG r r r rb r r9 �Number�registerrN r rn r� rV r� r, r- r� r� r� r rx rt r r r r rb r; r. r� r� r r r �re�compile�VERBOSE� IGNORECASEr$ rf r r �DOTALLr# �localer& r� r� r0 r5 r� r� rs rr r= r^ r9 r] r@ � hash_info�modulusr� r� r� r� r� r� r� r) r) r) r+ �<module>s s` # & ��� . ^ 0",# %$+ � *� �� � � P % )
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