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� l ��N�Zoi@�Tc @ s e Z d Z d d � Z d S)r c G s d S)Nr' )�self�contextr( r' r' r) �handle� s zDecimalException.handleN)�__name__� __module__� __qualname__r0 r' r' r' r) r � s c @ s e Z d Z d S)r N)r1 r2 r3 r' r' r' r) r � s c @ s e Z d Z d d � Z d S)r c G s: | r6 t | d j | d j d d � } | j | � St S)Nr% �nT)�_dec_from_triple�_sign�_int�_fix_nan�_NaN)r. r/ r( �ansr' r' r) r0 � s # zInvalidOperation.handleN)r1 r2 r3 r0 r' r' r' r) r � s c @ s e Z d Z d d � Z d S)r c G s t S)N)r9 )r. r/ r( r' r' r) r0 s zConversionSyntax.handleN)r1 r2 r3 r0 r' r' r' r) r � s c @ s e Z d Z d d � Z d S)r c G s t | S)N)�_SignedInfinity)r. r/ �signr( r' r' r) r0 s zDivisionByZero.handleN)r1 r2 r3 r0 r' r' r' r) r s c @ s e Z d Z d d � Z d S)r c G s t S)N)r9 )r. r/ r( r' r' r) r0 s zDivisionImpossible.handleN)r1 r2 r3 r0 r' r' r' r) r s c @ s e Z d Z d d � Z d S)r c G s t S)N)r9 )r. r/ r( r' r' r) r0 ) s zDivisionUndefined.handleN)r1 r2 r3 r0 r' r' r' r) r ! s c @ s e Z d Z d S)r N)r1 r2 r3 r' r' r' r) r , s c @ s e Z d Z d d � Z d S)r c G s t S)N)r9 )r. r/ r( r' r' r) r0 C s zInvalidContext.handleN)r1 r2 r3 r0 r' r' r' r) r 8 s c @ s e Z d Z d S)r N)r1 r2 r3 r' r' r' r) r F s c @ s e Z d Z d S)r N)r1 r2 r3 r' r' r' r) r R s c @ s e Z d Z d d � Z d S)r c G s� | j t t t t f k r# t | S| d k rk | j t k rF t | St | d | j | j | j d � S| d k r� | j t k r� t | St | d | j | j | j d � Sd S)Nr% �9r- ) �roundingr r r r r; r r5 �prec�Emaxr )r. r/ r< r( r' r' r) r0 s s zOverflow.handleN)r1 r2 r3 r0 r' r' r' r) r ] s c @ s e Z d Z d S)r N)r1 r2 r3 r' r' r' r) r � s c @ s e Z d Z d S)r N)r1 r2 r3 r' r' r' r) r � s c @ s e Z d Z e d d � Z d S)� MockThreadingc C s | j t S)N)�modules� __xname__)r. �sysr' r' r) �local� s zMockThreading.localN)r1 r2 r3 rD rE r' r' r' r) rA � s rA �__decimal_context__c C s> | t t t f k r+ | j � } | j � | t j � _ d S)N)r r r �copy� clear_flags� threading�current_threadrF )r/ r' r' r) r � s c C sF y t j � j SWn. t k rA t � } | t j � _ | SYn Xd S)N)rI rJ rF �AttributeErrorr )r/ r' r' r) r � s c C s: y | j SWn( t k r5 t � } | | _ | SYn Xd S)N)rF rK r )�_localr/ r' r' r) r � s c C s8 | t t t f k r+ | j � } | j � | | _ d S)N)r r r rG rH rF )r/ rL r' r' r) r � s c C s | d k r t � } t | � S)N)r �_ContextManager)�ctxr' r' r) r � s $ c @ s� e Z d Z d� Z d d d d � Z e d d � � Z d d � Z d d � Z d d d d � Z d d � Z d d � Z d d � Z d d d � Z d d d � Z d d d � Z d d d � Z d d d � Z d d! d" � Z d# d$ � Z d% d& � Z d' d( � Z d) d d* d+ � Z d d, d- � Z d d. d/ � Z d d0 d1 � Z d2 d d3 d4 � Z d d5 d6 � Z e Z d d7 d8 � Z d d9 d: � Z d d; d< � Z e Z d d= d> � Z! d? d@ � Z" d dA dB � Z# d dC dD � Z$ d dE dF � Z% d dG dH � Z& d dI dJ � Z' d dK dL � Z( d dM dN � Z) d dO dP � Z* dQ dR � Z+ dS dT � Z, e, Z- dU dV � Z. e/ e. � Z. dW dX � Z0 e/ e0 � Z0 dY dZ � Z1 d[ d\ � Z2 d] d^ � Z3 d_ d` � Z4 da db � Z5 dc dd � Z6 de df � Z7 dg dh � Z8 di dj � Z9 dk dl � Z: dm dn � Z; do dp � Z< e= dq e5 dr e6 ds e7 dt e8 du e9 dv e: dw e; dx e< � Z> d dy dz � Z? d{ d| � Z@ d} d~ � ZA d d d� � ZB d d� d� � ZC d� d� � ZD d d d� d� � ZE d d� d� � ZF d d� d� � ZG d d d� d� � ZH d d� d� � ZI d� d� � ZJ d� d� � ZK d d d� d� � ZL d d d� d� � ZM eM ZN d d� d� � ZO d d� d� � ZP d d� d� � ZQ d� d� � ZR d� d� � ZS d� d� � ZT d� d� � ZU d d� d� � ZV d d� d� � ZW d d� d� � ZX d� d� � ZY d� d� � ZZ d d� d� � Z[ d d� d� � Z\ d� d� � Z] d� d� � Z^ d� d� � Z_ d� d� � Z` d d� d� � Za d� d� � Zb d� d� � Zc d� d� � Zd d d� d� � Ze d� d� � Zf d� d� � Zg d d� d� � Zh d� d� � Zi d d� d� � Zj d d� d� � Zk d� d� � Zl d� d� � Zm d d� d� � Zn d d� d� � Zo d d� d� � Zp d d� d� � Zq d d� d� � Zr d d� d� � Zs d d� d� � Zt d d� d� � Zu d d� d� � Zv d d� d� � Zw d� d� � Zx d d� d� � Zy d d� d� � Zz d d� d� � Z{ d� d� � Z| d� d� � Z} d� d� � Z~ d d d� d� � Z d S)�r �_expr7 r6 � _is_special�0Nc C s� t j | � } t | t � r�t | j � � } | d k re | d k rQ t � } | j t d | � S| j d � d k r� d | _ n d | _ | j d � } | d k r| j d � p� d } t | j d � p� d � } t t | | � � | _ | t | � | _ d | _ n� | j d � } | d k rxt t | p<d � � j d � | _ | j d � rld | _ q�d | _ n d | _ d | _ d | _ | St | t � r�| d k r�d | _ n d | _ d | _ t t | � � | _ d | _ | St | t � r5| j | _ | j | _ | j | _ | j | _ | St | t � r�| j | _ t | j � | _ t | j � | _ d | _ | St | t t f � r:t | � d k r�t d � � t | d t � o�| d d k s�t d � � | d | _ | d d k r"d | _ | d | _ d | _ ng } xk | d D]_ } t | t � r�d | k o_d k n r�| sv| d k r�| j | � q3t d � � q3W| d d k r�d j t t | � � | _ | d | _ d | _ n\ t | d t � r*d j t t | pd g � � | _ | d | _ d | _ n t d � � | St | t � r�| d k r^t � } | j t d � t j | � } | j | _ | j | _ | j | _ | j | _ | St d | � � d S) Nz Invalid literal for Decimal: %rr< �-r- r% �intZfrac� �exprQ F�diag�signal�Nr4 �FT� ztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.z|Invalid sign. The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number.r+ � zTThe second value in the tuple must be composed of integers in the range 0 through 9.zUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.z;strict semantics for mixing floats and Decimals are enabledz Cannot convert %r to Decimal)r% r- )r4 rX ) �object�__new__� isinstance�str�_parser�stripr � _raise_errorr �groupr6 rS r7 �lenrO rP �lstrip�absr �_WorkRepr< rU �list�tuple� ValueError�append�join�map�floatr � from_float� TypeError) �cls�valuer/ r. �m�intpart�fracpartrU rV �digitsZdigitr' r' r) r] 4 s� $ # + $ zDecimal.__new__c C s� t | t � r | | � St | t � s4 t d � � t j | � sR t j | � rb | t | � � St j d | � d k r� d } n d } t | � j � \ } } | j � d } t | t | d | � | � } | t k r� | S| | � Sd S)Nz argument must be int or float.g �?r% r- � )r^ rS rn rp �_math�isinf�isnan�repr�copysignrf �as_integer_ratio� bit_lengthr5 r_ r )rq �fr< r4 �d�k�resultr' r' r) ro � s ! zDecimal.from_floatc C s6 | j r2 | j } | d k r" d S| d k r2 d Sd S)Nr4 r- rX r+ r% )rP rO )r. rU r' r' r) �_isnan� s zDecimal._isnanc C s$ | j d k r | j r d Sd Sd S)NrY r- r% ���)rO r6 )r. r' r' r) � _isinfinity s zDecimal._isinfinityc C s� | j � } | d k r! d } n | j � } | s9 | r� | d k rN t � } | d k rm | j t d | � S| d k r� | j t d | � S| r� | j | � S| j | � Sd S)NFr+ �sNaNr% )r� r rb r r8 )r. �otherr/ � self_is_nan� other_is_nanr' r' r) � _check_nans s" zDecimal._check_nansc C s� | d k r t � } | j s' | j r� | j � rF | j t d | � S| j � re | j t d | � S| j � r� | j t d | � S| j � r� | j t d | � Sd S)Nzcomparison involving sNaNzcomparison involving NaNr% )r rP �is_snanrb r �is_qnan)r. r� r/ r' r' r) �_compare_check_nans. s( zDecimal._compare_check_nansc C s | j p | j d k S)NrQ )rP r7 )r. r' r' r) �__bool__O s zDecimal.__bool__c C s^ | j s | j rN | j � } | j � } | | k r: d S| | k rJ d Sd S| sj | s^ d Sd | j S| s{ d | j S| j | j k r� d S| j | j k r� d S| j � } | j � } | | k r7| j d | j | j } | j d | j | j } | | k rd S| | k r)d | j Sd | j Sn# | | k rNd | j Sd | j Sd S) Nr% r- rQ r� r� r� r� r� r� r� r� )rP r� r6 �adjustedr7 rO )r. r� Zself_infZ other_inf� self_adjustedZother_adjusted� self_paddedZ other_paddedr' r' r) �_cmpV s> z Decimal._cmpc C sT t | | d d �\ } } | t k r+ | S| j | | � rA d S| j | � d k S)N� equality_opTFr% )�_convert_for_comparison�NotImplementedr� r� )r. r� r/ r' r' r) �__eq__� s zDecimal.__eq__c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S)NFr% )r� r� r� r� )r. r� r/ r: r' r' r) �__lt__� s zDecimal.__lt__c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S)NFr% )r� r� r� r� )r. r� r/ r: r' r' r) �__le__� s zDecimal.__le__c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S)NFr% )r� r� r� r� )r. r� r/ r: r' r' r) �__gt__� s zDecimal.__gt__c C sT t | | � \ } } | t k r% | S| j | | � } | rA d S| j | � d k S)NFr% )r� r� r� r� )r. r� r/ r: r' r' r) �__ge__� s zDecimal.__ge__c C sY t | d d �} | j s* | rF | j rF | j | | � } | rF | St | j | � � S)N�raiseitT)�_convert_otherrP r� r r� )r. r� r/ r: r' r' r) �compare� s zDecimal.comparec C s� | j rF | j � r$ t d � � n" | j � r4 t S| j rB t St S| j d k rm t d | j t � } n t t | j t � } t | j � | t } | d k r� | n | } | d k r� d S| S)Nz"Cannot hash a signaling NaN value.r% � r- r+ r� ���) rP r� rp �is_nan� _PyHASH_NANr6 � _PyHASH_INFrO �pow�_PyHASH_MODULUS� _PyHASH_10INVrS r7 )r. Zexp_hashZhash_r: r' r' r) �__hash__� s zDecimal.__hash__c C s( t | j t t t | j � � | j � S)N)r r6 ri rm rS r7 rO )r. r' r' r) �as_tuple� s zDecimal.as_tuplec C s d t | � S)Nz Decimal('%s'))r_ )r. r' r' r) �__repr__� s zDecimal.__repr__Fc C s� d d g | j } | j r` | j d k r3 | d S| j d k rQ | d | j S| d | j S| j t | j � } | j d k r� | d k r� | } nE | s� d } n6 | j d k r� | d d d } n | d d d } | d k r d } d d | | j } nf | t | j � k rF| j d | t | j � } d } n* | j d | � } d | j | d � } | | k r�d } n4 | d k r�t � } d d g | j d | | } | | | | S)NrT rR rY ZInfinityr4 �NaNr� r% � r- rQ rZ �.�e�Ez%+di����)r6 rP rO r7 rd r �capitals) r. �engr/ r< � leftdigits�dotplacert ru rU r' r' r) �__str__� s: zDecimal.__str__c C s | j d d d | � S)Nr� Tr/ )r� )r. r/ r' r' r) � to_eng_string. s zDecimal.to_eng_stringc C sx | j r% | j d | � } | r% | S| d k r: t � } | r_ | j t k r_ | j � } n | j � } | j | � S)Nr/ )rP r� r r> r �copy_abs� copy_negate�_fix)r. r/ r: r' r' r) �__neg__7 s zDecimal.__neg__c C sx | j r% | j d | � } | r% | S| d k r: t � } | r_ | j t k r_ | j � } n t | � } | j | � S)Nr/ )rP r� r r> r r� r r� )r. r/ r: r' r' r) �__pos__M s zDecimal.__pos__Tc C si | s | j � S| j r5 | j d | � } | r5 | S| j rS | j d | � } n | j d | � } | S)Nr/ )r� rP r� r6 r� r� )r. �roundr/ r: r' r' r) �__abs__b s zDecimal.__abs__c C sb t | � } | t k r | S| d k r1 t � } | j sC | j r� | j | | � } | r_ | S| j � r� | j | j k r� | j � r� | j t d � St | � S| j � r� t | � St | j | j � } d } | j t k r� | j | j k r� d } | rO| rOt | j | j � } | r*d } t | d | � } | j | � } | S| s�t | | j | j d � } | j | | j � } | j | � } | S| s�t | | j | j d � } | j | | j � } | j | � } | St | � } t | � } t | | | j � \ } } t � } | j | j k r�| j | j k rjt | d | � } | j | � } | S| j | j k r�| | } } | j d k r�d | _ | j | j | _ | _ q�d | _ n6 | j d k r�d | _ d \ | _ | _ n d | _ | j d k r$| j | j | _ n | j | j | _ | j | _ t | � } | j | � } | S)Nz -INF + INFr% r- rQ )r% r% )r� r� r rP r� r� r6 rb r r �minrO r> r r5 r� �maxr? �_rescalerg � _normalizer< rS rU ) r. r� r/ r: rU Z negativezeror< �op1�op2r� r' r' r) �__add__x s| ! zDecimal.__add__c C sf t | � } | t k r | S| j s. | j rM | j | d | �} | rM | S| j | j � d | �S)Nr/ )r� r� rP r� r� r� )r. r� r/ r: r' r' r) �__sub__� s zDecimal.__sub__c C s/ t | � } | t k r | S| j | d | �S)Nr/ )r� r� r� )r. r� r/ r' r' r) �__rsub__� s zDecimal.__rsub__c C s� t | � } | t k r | S| d k r1 t � } | j | j A} | j sS | j r� | j | | � } | ro | S| j � r� | s� | j t d � St | S| j � r� | s� | j t d � St | S| j | j } | s� | rt | d | � } | j | � } | S| j d k r=t | | j | � } | j | � } | S| j d k rtt | | j | � } | j | � } | St | � } t | � } t | t | j | j � | � } | j | � } | S)Nz (+-)INF * 0z 0 * (+-)INFrQ �1)r� r� r r6 rP r� r� rb r r; rO r5 r� r7 rg r_ rS )r. r� r/ Z resultsignr: Z resultexpr� r� r' r' r) �__mul__� sH "zDecimal.__mul__c C sc t | � } | t k r t S| d k r1 t � } | j | j A} | j sS | j r� | j | | � } | ro | S| j � r� | j � r� | j t d � S| j � r� t | S| j � r� | j t d � t | d | j � � S| s | s� | j t d � S| j t d | � S| s+| j | j } d } nt | j � t | j � | j d } | j | j | } t | � } t | � } | d k r�t | j d | | j � \ } } n$ t | j | j d | � \ } } | r�| d d k r>| d 7} nG | j | j } x4 | | k r=| d d k r=| d } | d 7} q Wt | t | � | � } | j | � S) Nz(+-)INF/(+-)INFzDivision by infinityrQ z0 / 0zx / 0r% r- r� rw )r� r� r r6 rP r� r� rb r r; r r5 �Etinyr r rO rd r7 r? rg �divmodrS r_ r� ) r. r� r/ r< r: rU �coeff�shiftr� r� � remainder� ideal_expr' r' r) � __truediv__ sP ' &$ zDecimal.__truediv__c C s� | j | j A} | j � r( | j } n t | j | j � } | j � | j � } | sr | j � sr | d k r� t | d d � | j | | j � f S| | j k rlt | � } t | � } | j | j k r� | j d | j | j 9_ n | j d | j | j 9_ t | j | j � \ } } | d | j k rlt | t | � d � t | j t | � | � f S| j t d � } | | f S)Nr+ rQ r% r� z%quotient too large in //, % or divmodr� )r6 r� rO r� r� r5 r� r> r? rg rU rS r� r_ rb r ) r. r� r/ r< r� �expdiffr� r� �q�rr: r' r' r) �_divideZ s* zDecimal._dividec C s/ t | � } | t k r | S| j | d | �S)Nr/ )r� r� r� )r. r� r/ r' r' r) � __rtruediv__{ s zDecimal.__rtruediv__c C s/ t | � } | t k r | S| d k r1 t � } | j | | � } | rS | | f S| j | j A} | j � r� | j � r� | j t d � } | | f St | | j t d � f S| s� | s� | j t d � } | | f S| j t d | � | j t d � f S| j | | � \ } } | j | � } | | f S)Nzdivmod(INF, INF)zINF % xz divmod(0, 0)zx // 0zx % 0) r� r� r r� r6 r� rb r r; r r r� r� )r. r� r/ r: r< Zquotientr� r' r' r) � __divmod__� s0 zDecimal.__divmod__c C s/ t | � } | t k r | S| j | d | �S)Nr/ )r� r� r� )r. r� r/ r' r' r) � __rdivmod__� s zDecimal.__rdivmod__c C s� t | � } | t k r | S| d k r1 t � } | j | | � } | rM | S| j � ri | j t d � S| s� | r� | j t d � S| j t d � S| j | | � d } | j | � } | S)NzINF % xzx % 0z0 % 0r- ) r� r� r r� r� rb r r r� r� )r. r� r/ r: r� r' r' r) �__mod__� s" zDecimal.__mod__c C s/ t | � } | t k r | S| j | d | �S)Nr/ )r� r� r� )r. r� r/ r' r' r) �__rmod__� s zDecimal.__rmod__c C sp | d k r t � } t | d d �} | j | | � } | rC | S| j � r_ | j t d � S| s� | r{ | j t d � S| j t d � S| j � r� t | � } | j | � St | j | j � } | s� t | j d | � } | j | � S| j � | j � } | | j d k r#| j t � S| d k rQ| j | | j � } | j | � St | � } t | � } | j | j k r�| j d | j | j 9_ n | j d | j | j 9_ t | j | j � \ } } d | | d @| j k r| | j 8} | d 7} | d | j k r%| j t � S| j } | d k rKd | } | } t | t | � | � } | j | � S) Nr� Tzremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)rQ r- r+ r� r% r� )r r� r� r� rb r r r r� r� rO r5 r6 r� r? r r� r> rg rU rS r� r_ ) r. r� r/ r: �ideal_exponentr� r� r� r� r� r< r' r' r) �remainder_near� sZ zDecimal.remainder_nearc C s� t | � } | t k r | S| d k r1 t � } | j | | � } | rM | S| j � r� | j � ru | j t d � St | j | j AS| s� | r� | j t d | j | j A� S| j t d � S| j | | � d S)Nz INF // INFzx // 0z0 // 0r% ) r� r� r r� r� rb r r; r6 r r r� )r. r� r/ r: r' r' r) � __floordiv__ s$ zDecimal.__floordiv__c C s/ t | � } | t k r | S| j | d | �S)Nr/ )r� r� r� )r. r� r/ r' r' r) � __rfloordiv__6 s zDecimal.__rfloordiv__c C sR | j � r< | j � r$ t d � � | j r3 d n d } n t | � } t | � S)Nz%Cannot convert signaling NaN to floatz-nan�nan)r� r� rj r6 r_ rn )r. �sr' r' r) � __float__= s zDecimal.__float__c C s� | j r< | j � r$ t d � � n | j � r< t d � � d | j } | j d k rt | t | j � d | j S| t | j d | j � p� d � Sd S)Nz Cannot convert NaN to integerz"Cannot convert infinity to integerr- r% r� rQ r� ) rP r� rj r� � OverflowErrorr6 rO rS r7 )r. r� r' r' r) �__int__G s zDecimal.__int__c C s | S)Nr' )r. r' r' r) �realV s z Decimal.realc C s t d � S)Nr% )r )r. r' r' r) �imagZ s z Decimal.imagc C s | S)Nr' )r. r' r' r) � conjugate^ s zDecimal.conjugatec C s t t | � � S)N)�complexrn )r. r' r' r) � __complex__a s zDecimal.__complex__c C sq | j } | j | j } t | � | k rg | t | � | d � j d � } t | j | | j d � St | � S)NrQ T) r7 r? �clamprd re r5 r6 rO r )r. r/ ZpayloadZmax_payload_lenr' r' r) r8 d s #zDecimal._fix_nanc C s | j r, | j � r" | j | � St | � S| j � } | j � } | s� | j | g | j } t t | j | � | � } | | j k r� | j t � t | j d | � St | � St | j � | j | j } | | k r| j t d | j � } | j t � | j t � | S| | k } | r+| } | j | k r�t | j � | j | } | d k rt | j d | d � } d } | j | j } | | | � } | j d | � p�d } | d k rt t | � d � } t | � | j k r| d d � } | d 7} | | k r/| j t d | j � } n t | j | | � } | r]| r]| j t � | rp| j t � | r�| j t � | j t � | s�| j t � | S| r�| j t � | j d k r| j | k r| j t � | j d | j | } t | j | | � St | � S)NrQ z above Emaxr% r� r- r� )rP r� r8 r r� �Etopr@ r� r� r� rO rb r r5 r6 rd r7 r? r r r �_pick_rounding_functionr> r_ rS r r )r. r/ r� r� �exp_maxZnew_expZexp_minr: Zself_is_subnormalrv Zrounding_method�changedr� r� r' r' r) r� p sn z Decimal._fixc C s t | j | � r d Sd Sd S)Nr% r- r� )� _all_zerosr7 )r. r? r' r' r) � _round_down� s zDecimal._round_downc C s | j | � S)N)r� )r. r? r' r' r) � _round_up� s zDecimal._round_upc C s5 | j | d k r d St | j | � r- d Sd Sd S)NZ56789r- r% r� )r7 r� )r. r? r' r' r) �_round_half_up� s zDecimal._round_half_upc C s' t | j | � r d S| j | � Sd S)Nr- r� )� _exact_halfr7 r� )r. r? r' r' r) �_round_half_down� s zDecimal._round_half_downc C sJ t | j | � r9 | d k s5 | j | d d k r9 d S| j | � Sd S)Nr% r- �02468r� )r� r7 r� )r. r? r' r' r) �_round_half_even� s #zDecimal._round_half_evenc C s( | j r | j | � S| j | � Sd S)N)r6 r� )r. r? r' r' r) �_round_ceiling� s zDecimal._round_ceilingc C s( | j s | j | � S| j | � Sd S)N)r6 r� )r. r? r' r' r) � _round_floor s zDecimal._round_floorc C s< | r* | j | d d k r* | j | � S| j | � Sd S)Nr- Z05)r7 r� )r. r? r' r' r) � _round_05up s zDecimal._round_05upr r r r r r r r c C s� | d k rG t | t � s' t d � � t d d | � } | j | � S| j rw | j � rk t d � � n t d � � t | j d t � � S)Nz+Second argument to round should be integralr% r� zcannot round a NaNzcannot round an infinity) r^ rS rp r5 �quantizerP r� rj r� r� r )r. r4 rU r' r' r) � __round__ s / zDecimal.__round__c C sF | j r0 | j � r$ t d � � n t d � � t | j d t � � S)Nzcannot round a NaNzcannot round an infinityr% )rP r� rj r� rS r� r )r. r' r' r) � __floor__W s zDecimal.__floor__c C sF | j r0 | j � r$ t d � � n t d � � t | j d t � � S)Nzcannot round a NaNzcannot round an infinityr% )rP r� rj r� rS r� r )r. r' r' r) �__ceil__f s zDecimal.__ceil__c C s� t | d d �} t | d d �} | j s6 | j r7| d k rK t � } | j d k rm | j t d | � S| j d k r� | j t d | � S| j d k r� | } qy| j d k r� | } qy| j d k r� | s� | j t d � St | j | j A} qy| j d k ry| s | j t d � St | j | j A} nB t | j | j At t | j � t | j � � | j | j � } | j | | � S) Nr� TrX r� r4 rY zINF * 0 in fmaz0 * INF in fma) r� rP r rO rb r r; r6 r5 r_ rS r7 r� )r. r� Zthirdr/ �productr' r' r) �fmau s6 z Decimal.fmac C s� t | � } | t k r | St | � } | t k r8 | S| d k rM t � } | j � } | j � } | j � } | s� | s� | r| d k r� | j t d | � S| d k r� | j t d | � S| d k r� | j t d | � S| r� | j | � S| r| j | � S| j | � S| j � o4| j � o4| j � sG| j t d � S| d k rc| j t d � S| sy| j t d � S| j � | j k r�| j t d � S| r�| r�| j t d � S| j � r�d } n | j } t t | � � } t | j � � } t | j � � } | j | t d | j | � | } x) t | j � D] } t | d | � } qDWt | | j | � } t | t | � d � S) Nr+ r� z@pow() 3rd argument not allowed unless all arguments are integersr% zApow() 2nd argument cannot be negative when 3rd argument specifiedz pow() 3rd argument cannot be 0zSinsufficient precision: pow() 3rd argument must not have more than precision digitszXat least one of pow() 1st argument and 2nd argument must be nonzero ;0**0 is not definedr� )r� r� r r� rb r r8 � _isintegerr� r? �_isevenr6 rf rS rg �to_integral_valuer� rU �ranger5 r_ ) r. r� �modulor/ r� r� Z modulo_is_nanr< �base�exponent�ir' r' r) � _power_modulo� sl $zDecimal._power_moduloc C s9 t | � } | j | j } } x( | d d k rI | d } | d 7} q" Wt | � } | j | j } } x( | d d k r� | d } | d 7} ql W| d k rs| | 9} x( | d d k r� | d } | d 7} q� W| d k r� d S| d | } | j d k r | } | j � rQ| j d k rQ| j t | � } t | | | d � } n d } t d d d | | | � S| j d k rv| d } | d k rF| | @| k r�d St | � d } | d d } | t t | � � k r�d St | | | � } t | | | � } | d k s%| d k r)d S| | k r9d Sd | } n� | d k r=t | � d d } t d | | � \ } } | r�d Sx( | d d k r�| d } | d 8} q�W| d d } | t t | � � k r�d St | | | � } t | | | � } | d k s | d k r d S| | k r0d Sd | } n d S| d | k rUd S| | } t d t | � | � S| d k r�| d | d } } n| d k r�t t t | | � � � | k r�d St | � } | d k r t t t | � | � � | k r d S| d | } } x< | d | d k o@d k n r\| d } | d } q!Wx< | d | d k od k n r�| d } | d } q`W| d k rk| d k r�| | k r�d St | | � \ } } | d k r�d Sd t | � | >} xG t | | | d � \ } } | | k r/Pq| | d | | } qW| | k o^| d k sed S| } | d k r�| | d t | � k r�d S| | } | | 9} | d | k r�d St | � } | j � r| j d k r| j t | � } t | | | t | � � } n d } t d | d | | | � S)Nr� r% r- r� rQ r+ � r� � �] �A rw � rZ �d )r+ r r� r )rg rS rU r< r� r6 rO r� r5 �_nbitsrd r_ �_decimal_lshift_exactr� rf � _log10_lb)r. r� �p�x�xc�xe�y�yc�yer r� ZzerosZ last_digitr� Zemaxr� rs r4 Zxc_bits�rem�ar� r� Zstr_xcr' r' r) � _power_exact� s� : / /' ' & zDecimal._power_exactc C s� | d k r | j | | | � St | � } | t k r; | S| d k rP t � } | j | | � } | rl | S| s� | s� | j t d � St Sd } | j d k r� | j � r� | j � s� d } n | r� | j t d � S| j � } | s| j d k r t | d d � St | S| j � rD| j d k r4t | St | d d � S| t k r| j � r�| j d k rtd } n' | | j k r�| j } n t | � } | j | } | d | j k r�d | j } | j t � n' | j t � | j t � d | j } t | d d | | � S| j � } | j � rc| j d k | d k k r[t | d d � St | Sd } d } | j � | j � } | d k | j d k k r�| t t | j � � k rt | d | j d � } n; | j � } | t t | � � k rt | d | d � } | d k rm| j | | j d � } | d k rm| d k rgt d | j | j � } d } | d k rN| j } t | � } | j | j } } t | � } | j | j } } | j d k r�| } d } xW t | | | | | | � \ } } | d d t t | � � | d r(P| d 7} q�Wt | t | � | � } | r�| j � r�t | j � | j k r�| j d t | j � } t | j | j d | | j | � } | j � } | j! � x t" D] } d | j# | <q�W| j$ | � } | j t � | j% t& r$| j t' � | j% t( rG| j t( d | j � xI t' t& t t t) f D] } | j% | r]| j | � q]Wn | j$ | � } | S) Nz0 ** 0r% r- z+x ** y with x negative and y not an integerrQ r� FTrZ rw r� z above Emax)*r r� r� r r� rb r �_Oner6 r� r� r� r5 r; r� r? rS rO r r r� �_log10_exp_boundrd r_ r@ r� r r7 rg rU r< �_dpowerrG rH �_signals�trapsr� �flagsr r r r )r. r� r� r/ r: Z result_signZ multiplierrU Zself_adj�exactZboundr� r r r r r r r �extrar� r� Z newcontext� exceptionr' r' r) �__pow__� s� "& zDecimal.__pow__c C s/ t | � } | t k r | S| j | d | �S)Nr/ )r� r� r )r. r� r/ r' r' r) �__rpow__� s zDecimal.__rpow__c C s | d k r t � } | j r: | j d | � } | r: | S| j | � } | j � rY | S| sr t | j d d � S| j | j � g | j } t | j � } | j } x; | j | d d k r� | | k r� | d 7} | d 8} q� Wt | j | j d | � | � S)Nr/ rQ r% r- ) r rP r� r� r� r5 r6 r@ r� r� rd r7 rO )r. r/ r: �dupr� �endrU r' r' r) � normalize� s$ & zDecimal.normalizec C sA t | d d �} | d k r' t � } | d k r< | j } | j sN | j r� | j | | � } | rj | S| j � s� | j � r� | j � r� | j � r� t | � S| j t d � S| j � | j k o� | j k n s� | j t d � S| st | j d | j � } | j | � S| j � } | | j k rB| j t d � S| | j d | j k rl| j t d � S| j | j | � } | j � | j k r�| j t d � St | j � | j k r�| j t d � S| r�| j � | j k r�| j t � | j | j k r.| | k r!| j t � | j t � | j | � } | S) Nr� Tzquantize with one INFz)target exponent out of bounds in quantizerQ z9exponent of quantize result too large for current contextr- z7quantize result has too many digits for current context)r� r r> rP r� r� r rb r r� rO r@ r5 r6 r� r� r? r� rd r7 �Eminr r r )r. rU r> r/ r: r� r' r' r) r� � sT ( zDecimal.quantizec C sb t | d d �} | j s$ | j rR | j � r< | j � pQ | j � oQ | j � S| j | j k S)Nr� T)r� rP r� � is_infiniterO )r. r� r/ r' r' r) � same_quantum s zDecimal.same_quantumc C s | j r t | � S| s, t | j d | � S| j | k r` t | j | j d | j | | � St | j � | j | } | d k r� t | j d | d � } d } | j | } | | | � } | j d | � p� d } | d k r� t t | � d � } t | j | | � S)NrQ r% r� r- ) rP r r5 r6 rO r7 rd r� r_ rS )r. rU r> rv Z this_functionr� r� r' r' r) r� ' s" zDecimal._rescalec C s� | d k r t d � � | j s( | r2 t | � S| j | j � d | | � } | j � | j � k r� | j | j � d | | � } | S)Nr% z'argument should be at least 1 in _roundr- )rj rP r r� r� )r. �placesr> r: r' r' r) �_roundI s zDecimal._roundc C s� | j r/ | j d | � } | r% | St | � S| j d k rH t | � S| sa t | j d d � S| d k rv t � } | d k r� | j } | j d | � } | | k r� | j t � | j t � | S)Nr/ r% rQ ) rP r� r rO r5 r6 r r> r� rb r r )r. r> r/ r: r' r' r) �to_integral_exact` s$ zDecimal.to_integral_exactc C s� | d k r t � } | d k r* | j } | j rY | j d | � } | rO | St | � S| j d k rr t | � S| j d | � Sd S)Nr/ r% )r r> rP r� r rO r� )r. r> r/ r: r' r' r) r� } s zDecimal.to_integral_valuec C sv | d k r t � } | j r_ | j d | � } | r: | S| j � r_ | j d k r_ t | � S| s� t | j d | j d � } | j | � S| j d k r� | j t d � S| j d } t | � } | j d ?} | j d @r| j d } t | j � d ?d } n | j } t | j � d d ?} | | } | d k rT| d | 9} d } n! t | d | � \ } } | } | | 8} d | } x, | | } | | k r�Pq�| | d ?} q�W| o�| | | k } | r | d k r�| d | } n | d | 9} | | 7} n | d d k r'| d 7} t d t | � | � } | j � } | j t � } | j | � } | | _ | S) Nr/ r% rQ r+ r- zsqrt(-x), x > 0r� r Trw )r rP r� r� r6 r r5 rO r� rb r r? rg rU rS rd r7 r� r_ � _shallow_copy� _set_roundingr r> )r. r/ r: r? �opr� �c�lr� r r� r4 r� r> r' r' r) �sqrt� s` z Decimal.sqrtc C s t | d d �} | d k r' t � } | j s9 | j r� | j � } | j � } | s] | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � S| j | � } | d k r� | j | � } | d k r� | } n | } | j | � S)Nr� Tr- r% r� )r� r rP r� r� r� r� � compare_total)r. r� r/ �sn�onr- r: r' r' r) r� � s& z Decimal.maxc C s t | d d �} | d k r' t � } | j s9 | j r� | j � } | j � } | s] | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � S| j | � } | d k r� | j | � } | d k r� | } n | } | j | � S)Nr� Tr- r% r� )r� r rP r� r� r� r� r0 )r. r� r/ r1 r2 r- r: r' r' r) r� s& z Decimal.minc C sJ | j r d S| j d k r d S| j | j d � } | d t | � k S)NFr% TrQ )rP rO r7 rd )r. �restr' r' r) r� ? s zDecimal._isintegerc C s2 | s | j d k r d S| j d | j d k S)Nr% Tr- r� r� )rO r7 )r. r' r' r) r� H s zDecimal._isevenc C s9 y | j t | j � d SWn t k r4 d SYn Xd S)Nr- r% )rO rd r7 rp )r. r' r' r) r� N s zDecimal.adjustedc C s | S)Nr' )r. r' r' r) � canonicalV s zDecimal.canonicalc C sA t | d d �} | j | | � } | r. | S| j | d | �S)Nr� Tr/ )r� r� r� )r. r� r/ r: r' r' r) �compare_signal^ s zDecimal.compare_signalc C s� t | d d �} | j r) | j r) t S| j r@ | j r@ t S| j } | j � } | j � } | sm | rj| | k r� t | j � | j f } t | j � | j f } | | k r� | r� t St S| | k r� | r� t St St S| r*| d k r� t S| d k rt S| d k rt S| d k rjt Sn@ | d k r:t S| d k rJt S| d k rZt S| d k rjt S| | k rzt S| | k r�t S| j | j k r�| r�t St S| j | j k r�| r�t St St S)Nr� Tr- r+ ) r� r6 � _NegativeOner r� rd r7 �_ZerorO )r. r� r/ r< Zself_nanZ other_nanZself_keyZ other_keyr' r' r) r0 j sf zDecimal.compare_totalc C s7 t | d d �} | j � } | j � } | j | � S)Nr� T)r� r� r0 )r. r� r/ r� �or' r' r) �compare_total_mag� s zDecimal.compare_total_magc C s t d | j | j | j � S)Nr% )r5 r7 rO rP )r. r' r' r) r� � s zDecimal.copy_absc C sE | j r% t d | j | j | j � St d | j | j | j � Sd S)Nr% r- )r6 r5 r7 rO rP )r. r' r' r) r� � s zDecimal.copy_negatec C s1 t | d d �} t | j | j | j | j � S)Nr� T)r� r5 r6 r7 rO rP )r. r� r/ r' r' r) � copy_sign� s zDecimal.copy_signc C s� | d k r t � } | j d | � } | r1 | S| j � d k rG t S| sQ t S| j � d k rm t | � S| j } | j � } | j d k r� | t t | j d d � � k r� t d d | j d � } n�| j d k r%| t t | j � d d � � k r%t d d | j � d � } n+| j d k rg| | k rgt d d d | d d | � } n� | j d k r�| | d k r�t d d | d | d � } n� t | � } | j | j } } | j d k r�| } d } xQ t | | | | � \ } } | d d t t | � � | d r*P| d 7} q�Wt d t | � | � } | j � } | j t � } | j | � } | | _ | S) Nr/ r- r% rZ r� rQ r= rw r� r� )r r� r� r7 r r r? r� r6 rd r_ r@ r5 r� rg rS rU r< �_dexpr* r+ r r� r> ) r. r/ r: r �adjr, r- r� r r� rU r> r' r' r) rU � sJ 2 6 & " & z Decimal.expc C s d S)NTr' )r. r' r' r) � is_canonical s zDecimal.is_canonicalc C s | j S)N)rP )r. r' r' r) � is_finite" s zDecimal.is_finitec C s | j d k S)NrY )rO )r. r' r' r) r% * s zDecimal.is_infinitec C s | j d k S)Nr4 rX )r4 rX )rO )r. r' r' r) r� . s zDecimal.is_nanc C s< | j s | r d S| d k r) t � } | j | j � k S)NF)rP r r$ r� )r. r/ r' r' r) � is_normal2 s zDecimal.is_normalc C s | j d k S)Nr4 )rO )r. r' r' r) r� : s zDecimal.is_qnanc C s | j d k S)Nr- )r6 )r. r' r' r) � is_signed> s zDecimal.is_signedc C s | j d k S)NrX )rO )r. r' r' r) r� B s zDecimal.is_snanc C s< | j s | r d S| d k r) t � } | j � | j k S)NF)rP r r� r$ )r. r/ r' r' r) � is_subnormalF s zDecimal.is_subnormalc C s | j o | j d k S)NrQ )rP r7 )r. r' r' r) �is_zeroN s zDecimal.is_zeroc C s� | j t | j � d } | d k rB t t | d d � � d S| d k rn t t d | d d � � d St | � } | j | j } } | d k r� t | d | � } t | � } t | � t | � | | k S| t t d | | � � d S)Nr- � r� r+ r% r� r� )rO rd r7 r_ rg rS rU )r. r< r, r- r� �num�denr' r' r) � _ln_exp_boundR s zDecimal._ln_exp_boundc C sn | d k r t � } | j d | � } | r1 | S| s; t S| j � d k rQ t S| t k ra t S| j d k r� | j t d � St | � } | j | j } } | j } | | j � d } xM t | | | � } | d d t t t | � � � | d r� P| d 7} q� Wt t | d k � t t | � � | � } | j � } | j t � } | j | � } | | _ | S) Nr/ r- zln of a negative valuer+ rw r� rZ r% )r r� �_NegativeInfinityr� � _Infinityr r7 r6 rb r rg rS rU r? rF �_dlogrd r_ rf r5 r* r+ r r� r> ) r. r/ r: r, r- r� r r' r� r> r' r' r) �lnk s: ,+ z Decimal.lnc C s | j t | j � d } | d k r: t t | � � d S| d k r^ t t d | � � d St | � } | j | j } } | d k r� t | d | � } t d | � } t | � t | � | | k d St d | | � } t | � | | d k d S) Nr- r+ r% r� �� Z231r� r� )rO rd r7 r_ rg rS rU )r. r< r, r- r� rD rE r' r' r) r � s "zDecimal._log10_exp_boundc C s� | d k r t � } | j d | � } | r1 | S| s; t S| j � d k rQ t S| j d k rp | j t d � S| j d d k r� | j d d � d t | j � d k r� t | j t | j � d � } n� t | � } | j | j } } | j } | | j � d } xM t | | | � } | d d t t t | � � � | d rNP| d 7} qWt t | d k � t t | � � | � } | j � } | j t � } | j | � } | | _ | S) Nr/ r- zlog10 of a negative valuer% r� rQ r+ rw r� rZ )r r� rG r� rH r6 rb r r7 rd r rO rg rS rU r? r �_dlog10r_ rf r5 r* r+ r r� r> ) r. r/ r: r, r- r� r r' r� r> r' r' r) �log10� s: =# ,+ z Decimal.log10c C sy | j d | � } | r | S| d k r1 t � } | j � rA t S| sZ | j t d d � St | j � � } | j | � S)Nr/ zlogb(0)r- ) r� r r� rH rb r r r� r� )r. r/ r: r' r' r) �logb� s z Decimal.logbc C sJ | j d k s | j d k r" d Sx! | j D] } | d k r, d Sq, Wd S)Nr% FZ01T)r6 rO r7 )r. �digr' r' r) � _islogical s zDecimal._islogicalc C s� | j t | � } | d k r0 d | | } n | d k rP | | j d � } | j t | � } | d k r� d | | } n | d k r� | | j d � } | | f S)Nr% rQ )r? rd )r. r/ �opa�opbZdifr' r' r) � _fill_logical s zDecimal._fill_logicalc C s� | d k r t � } t | d d �} | j � sA | j � rN | j t � S| j | | j | j � \ } } d j d d � t | | � D� � } t d | j d � p� d d � S)Nr� TrT c S s2 g | ]( \ } } t t | � t | � @� � q Sr' )r_ rS )�.0r �br' r' r) � <listcomp>5 s z'Decimal.logical_and.<locals>.<listcomp>r% rQ ) r r� rP rb r rS r7 rl �zipr5 re )r. r� r/ rQ rR r� r' r' r) � logical_and' s !%zDecimal.logical_andc C s8 | d k r t � } | j t d d | j d � | � S)Nr% r� )r � logical_xorr5 r? )r. r/ r' r' r) �logical_invert8 s zDecimal.logical_invertc C s� | d k r t � } t | d d �} | j � sA | j � rN | j t � S| j | | j | j � \ } } d j d d � t | | � D� � } t d | j d � p� d d � S)Nr� TrT c S s2 g | ]( \ } } t t | � t | � B� � q Sr' )r_ rS )rT r rU r' r' r) rV M s z&Decimal.logical_or.<locals>.<listcomp>r% rQ ) r r� rP rb r rS r7 rl rW r5 re )r. r� r/ rQ rR r� r' r' r) � logical_or? s !%zDecimal.logical_orc C s� | d k r t � } t | d d �} | j � sA | j � rN | j t � S| j | | j | j � \ } } d j d d � t | | � D� � } t d | j d � p� d d � S)Nr� TrT c S s2 g | ]( \ } } t t | � t | � A� � q Sr' )r_ rS )rT r rU r' r' r) rV ^ s z'Decimal.logical_xor.<locals>.<listcomp>r% rQ ) r r� rP rb r rS r7 rl rW r5 re )r. r� r/ rQ rR r� r' r' r) rY P s !%zDecimal.logical_xorc C s t | d d �} | d k r' t � } | j s9 | j r� | j � } | j � } | s] | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � S| j � j | j � � } | d k r� | j | � } | d k r| } n | } | j | � S)Nr� Tr- r% r� ) r� r rP r� r� r� r� r� r0 )r. r� r/ r1 r2 r- r: r' r' r) �max_maga s& zDecimal.max_magc C s t | d d �} | d k r' t � } | j s9 | j r� | j � } | j � } | s] | r� | d k r� | d k r� | j | � S| d k r� | d k r� | j | � S| j | | � S| j � j | j � � } | d k r� | j | � } | d k r| } n | } | j | � S)Nr� Tr- r% r� ) r� r rP r� r� r� r� r� r0 )r. r� r/ r1 r2 r- r: r' r' r) �min_mag s& zDecimal.min_magc C s� | d k r t � } | j d | � } | r1 | S| j � d k rG t S| j � d k rv t d d | j | j � � S| j � } | j t � | j � | j | � } | | k r� | S| j t d d | j � d � | � S)Nr/ r- r% r= r� r� )r r� r� rG r5 r? r� rG r+ r �_ignore_all_flagsr� r� r� )r. r/ r: �new_selfr' r' r) � next_minus� s" zDecimal.next_minusc C s� | d k r t � } | j d | � } | r1 | S| j � d k rG t S| j � d k rv t d d | j | j � � S| j � } | j t � | j � | j | � } | | k r� | S| j t d d | j � d � | � S)Nr/ r- r= r% r� r� )r r� r� rH r5 r? r� rG r+ r r^ r� r� r� )r. r/ r: r_ r' r' r) � next_plus� s" zDecimal.next_plusc C s7 t | d d �} | d k r' t � } | j | | � } | rC | S| j | � } | d k rk | j | � S| d k r� | j | � } n | j | � } | j � r� | j t d | j � | j t � | j t � n\ | j � | j k r3| j t � | j t � | j t � | j t � | s3| j t � | S)Nr� Tr% r- z Infinite result from next_towardr� )r� r r� r� r: ra r` r� rb r r6 r r r� r$ r r r )r. r� r/ r: Z comparisonr' r' r) � next_toward� s4 zDecimal.next_towardc C s� | j � r d S| j � r d S| j � } | d k r< d S| d k rL d S| j � ri | j re d Sd S| d k r~ t � } | j d | � r� | j r� d Sd S| j r� d Sd Sd S)Nr� r� r- z +Infinityz -Infinityz-Zeroz+Zeror/ z -Subnormalz +Subnormalz-Normalz+Normalr� )r� r� r� rB r6 r rA )r. r/ �infr' r' r) � number_class� s, zDecimal.number_classc C s t d � S)Nr� )r )r. r' r' r) �radix# s z Decimal.radixc C sP | d k r t � } t | d d �} | j | | � } | rC | S| j d k r_ | j t � S| j t | � k o� | j k n s� | j t � S| j � r� t | � St | � } | j } | j t | � } | d k r� d | | } n | d k r | | d � } | | d � | d | � } t | j | j d � pFd | j � S)Nr� Tr% rQ )r r� r� rO rb r r? rS r� r r7 rd r5 r6 re )r. r� r/ r: �torot�rotdig�topadZrotatedr' r' r) �rotate' s, ) zDecimal.rotatec C s | d k r t � } t | d d �} | j | | � } | rC | S| j d k r_ | j t � Sd | j | j } d | j | j } | t | � k o� | k n s� | j t � S| j � r� t | � St | j | j | j t | � � } | j | � } | S)Nr� Tr% r+ r� )r r� r� rO rb r r@ r? rS r� r r5 r6 r7 r� )r. r� r/ r: ZliminfZlimsupr� r' r' r) �scalebH s" " %zDecimal.scalebc C ss | d k r t � } t | d d �} | j | | � } | rC | S| j d k r_ | j t � S| j t | � k o� | j k n s� | j t � S| j � r� t | � St | � } | j } | j t | � } | d k r� d | | } n | d k r | | d � } | d k r,| d | � } n" | d | } | | j d � } t | j | j d � pid | j � S)Nr� Tr% rQ )r r� r� rO rb r r? rS r� r r7 rd r5 r6 re )r. r� r/ r: rf rg rh Zshiftedr' r' r) r� a s2 ) z Decimal.shiftc C s | j t | � f f S)N)� __class__r_ )r. r' r' r) � __reduce__� s zDecimal.__reduce__c C s) t | � t k r | S| j t | � � S)N)�typer rk r_ )r. r' r' r) �__copy__� s zDecimal.__copy__c C s) t | � t k r | S| j t | � � S)N)rm r rk r_ )r. �memor' r' r) � __deepcopy__� s zDecimal.__deepcopy__c C s | d k r t � } t | d | �} | j r~ t | j | � } t | j � � } | d d k rn | d 7} t | | | � S| d d k r� d d g | j | d <| d d k r� t | j | j | j d � } | j } | d } | d k ry| d d k r | j | d | � } n] | d d k rB| j | | � } n7 | d d k ryt | j � | k ry| j | | � } | r�| j d k r�| d d k r�| j d | � } | j t | j � } | d d k r | r�| d k r�d | } qSd } nS | d d k r| } n: | d d k rS| j d k rM| d k rM| } n d } | d k rzd } d | | j } nh | t | j � k r�| j d | t | j � } d } n, | j d | � p�d } | j | d � } | | } t | j | | | | � S)N� _localeconvrm �%�g�Gr+ � precision�eEr- zfF%ZgGr% r� rQ rT i����)r �_parse_format_specifierrP � _format_signr6 r_ r� � _format_alignr� r5 r7 rO r> r( r� rd �_format_number)r. Z specifierr/ rq �specr< �bodyr> ru r� r� rt ru rU r' r' r) � __format__� sZ %& zDecimal.__format__)rO r7 r6 rP )�r1 r2 r3 � __slots__r] � classmethodro r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� r� �__radd__r� r� r� �__rmul__r� r� r� r� r� r� r� r� r� r� r� r� � __trunc__r� �propertyr� r� r� r8 r� r� r� r� r� r� r� r� r� �dictr� r� r� r� r� r r r r r# r� r& r� r( r) r� � to_integralr/ r� r� r� r� r� r4 r5 r0 r9 r� r� r: rU r= r> r% r� r? r� r@ r� rA rB rF rJ r rM rN rP rS rX rZ r[ rY r\ r] r` ra rb rd re ri rj r� rl rn rp r} r' r' r' r) r + s �( ! @ 4 V7; !$K f > ,U ��= " c*" I K 2 3 .* !' Fc C s7 t j t � } | | _ | | _ | | _ | | _ | S)N)r\ r] r r6 r7 rO rP )r< Z coefficientr Zspecialr. r' r' r) r5 � s r5 c @ s4 e Z d Z d d � Z d d � Z d d � Z d S)rM c C s | j � | _ d S)N)rG � new_context)r. r� r' r' r) �__init__ s z_ContextManager.__init__c C s t � | _ t | j � | j S)N)r � saved_contextr r� )r. r' r' r) � __enter__ s z_ContextManager.__enter__c C s t | j � d S)N)r r� )r. �t�v�tbr' r' r) �__exit__ s z_ContextManager.__exit__N)r1 r2 r3 r� r� r� r' r' r' r) rM s rM c @ s e Z d Z d d d d d d d d d d d � Z d d � Z d d � Z d d � Z d d � Z d d � Z d d � Z d d � Z d d � Z d d � Z d d � Z e Z d d d � Z d d � Z d d � Z d d � Z d Z d d! � Z d" d# � Z d$ d% � Z d& d' d( � Z d) d* � Z d+ d, � Z d- d. � Z d/ d0 � Z d1 d2 � Z d3 d4 � Z d5 d6 � Z d7 d8 � Z d9 d: � Z d; d< � Z! d= d> � Z" d? d@ � Z# dA dB � Z$ dC dD � Z% dE dF � Z& dG dH � Z' dI dJ � Z( dK dL � Z) dM dN � Z* dO dP � Z+ dQ dR � Z, dS dT � Z- dU dV � Z. dW dX � Z/ dY dZ � Z0 d[ d\ � Z1 d] d^ � Z2 d_ d` � Z3 da db � Z4 dc dd � Z5 de df � Z6 dg dh � Z7 di dj � Z8 dk dl � Z9 dm dn � Z: do dp � Z; dq dr � Z< ds dt � Z= du dv � Z> dw dx � Z? dy dz � Z@ d{ d| � ZA d} d~ � ZB d d� � ZC d� d� � ZD d� d� � ZE d� d� � ZF d d� d� � ZG d� d� � ZH d� d� � ZI d� d� � ZJ d� d� � ZK d� d� � ZL d� d� � ZM d� d� � ZN d� d� � ZO d� d� � ZP d� d� � ZQ d� d� � ZR d� d� � ZS d� d� � ZT d� d� � ZU eU ZV d S)�r Nc s� y t } Wn t k r Yn X| d k r1 | n | j | _ | d k rO | n | j | _ | d k rm | n | j | _ | d k r� | n | j | _ | d k r� | n | j | _ | d k r� | n | j | _ | d k r� g | _ n | | _ � d k r| j j � | _ nA t � t � sMt � f d d � t � D� � | _ n � | _ � d k rzt j t d � | _ nA t � t � s�t � f d d � t � D� � | _ n � | _ d S)Nc 3 s' | ] } | t | � k � f Vq d S)N)rS )rT r� )r r' r) � <genexpr>< s z#Context.__init__.<locals>.<genexpr>r% c 3 s' | ] } | t | � k � f Vq d S)N)rS )rT r� )r r' r) r� C s )r � NameErrorr? r> r$ r@ r� r� �_ignored_flagsr rG r^ r� r �fromkeysr ) r. r? r> r$ r@ r� r� r r r� Zdcr' )r r r) r� # s. ) )zContext.__init__c C s� t | t � s t d | � � | d k rV | | k r� t d | | | | f � � nk | d k r� | | k r� t d | | | | f � � n4 | | k s� | | k r� t d | | | | f � � t j | | | � S)Nz%s must be an integerz-infz %s must be in [%s, %d]. got: %src z %s must be in [%d, %s]. got: %sz %s must be in [%d, %d]. got %s)r^ rS rp rj r\ � __setattr__)r. �namerr ZvminZvmaxr' r' r) �_set_integer_checkG s zContext._set_integer_checkc C s� t | t � s t d | � � x* | D]" } | t k r& t d | � � q& Wx* t D]" } | | k rS t d | � � qS Wt j | | | � S)Nz%s must be a signal dictz %s is not a valid signal dict)r^ r� rp r �KeyErrorr\ r� )r. r� r� �keyr' r' r) �_set_signal_dictU s zContext._set_signal_dictc C s@ | d k r" | j | | d d � S| d k rD | j | | d d � S| d k rf | j | | d d � S| d k r� | j | | d d � S| d k r� | j | | d d � S| d k r� | t k r� t d | � � t j | | | � S| d k s� | d k r | j | | � S| d k r,t j | | | � St d | � � d S)Nr? r- rc r$ z-infr% r@ r� r� r> z%s: invalid rounding moder r r� z.'decimal.Context' object has no attribute '%s')r� �_rounding_modesrp r\ r� r� rK )r. r� rr r' r' r) r� ` s( zContext.__setattr__c C s t d | � � d S)Nz%s cannot be deleted)rK )r. r� r' r' r) � __delattr__y s zContext.__delattr__c C so d d � | j j � D� } d d � | j j � D� } | j | j | j | j | j | j | j | | f f S)Nc S s" g | ] \ } } | r | � q Sr' r' )rT �sigr� r' r' r) rV ~ s z&Context.__reduce__.<locals>.<listcomp>c S s" g | ] \ } } | r | � q Sr' r' )rT r� r� r' r' r) rV s ) r �itemsr rk r? r> r$ r@ r� r� )r. r r r' r' r) rl } s zContext.__reduce__c C s� g } | j d t | � � d d � | j j � D� } | j d d j | � d � d d � | j j � D� } | j d d j | � d � d j | � d S) NzrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dc S s% g | ] \ } } | r | j � q Sr' )r1 )rT r r� r' r' r) rV � s z$Context.__repr__.<locals>.<listcomp>zflags=[z, �]c S s% g | ] \ } } | r | j � q Sr' )r1 )rT r� r� r' r' r) rV � s ztraps=[�))rk �varsr r� rl r )r. r� �namesr' r' r) r� � s zContext.__repr__c C s% x | j D] } d | j | <q Wd S)Nr% )r )r. �flagr' r' r) rH � s zContext.clear_flagsc C s% x | j D] } d | j | <q Wd S)Nr% )r )r. r� r' r' r) � clear_traps� s zContext.clear_trapsc C sC t | j | j | j | j | j | j | j | j | j � } | S)N) r r? r> r$ r@ r� r� r r r� )r. �ncr' r' r) r* � s zContext._shallow_copyc C sO t | j | j | j | j | j | j | j j � | j j � | j � } | S)N) r r? r> r$ r@ r� r� r rG r r� )r. r� r' r' r) rG � s z Context.copyc G sq t j | | � } | | j k r4 | � j | | � Sd | j | <| j | sa | � j | | � S| | � � d S)Nr- )�_condition_map�getr� r0 r r )r. Z conditionZ explanationr( �errorr' r' r) rb � s zContext._raise_errorc C s | j t � S)N)� _ignore_flagsr )r. r' r' r) r^ � s zContext._ignore_all_flagsc G s | j t | � | _ t | � S)N)r� rh )r. r r' r' r) r� � s zContext._ignore_flagsc G sN | r) t | d t t f � r) | d } x | D] } | j j | � q0 Wd S)Nr% )r^ ri rh r� �remove)r. r r� r' r' r) � _regard_flags� s zContext._regard_flagsc C s t | j | j d � S)Nr- )rS r$ r? )r. r' r' r) r� � s z Context.Etinyc C s t | j | j d � S)Nr- )rS r@ r? )r. r' r' r) r� � s z Context.Etopc C s | j } | | _ | S)N)r> )r. rm r> r' r' r) r+ � s zContext._set_roundingrQ c C s� t | t � r1 | | j � k r1 | j t d � St | d | �} | j � r~ t | j � | j | j k r~ | j t d � S| j | � S)Nz/no trailing or leading whitespace is permitted.r/ z diagnostic info too long in NaN) r^ r_ ra rb r r r� rd r7 r? r� r� )r. rD r� r' r' r) �create_decimal� s ! + zContext.create_decimalc C s t j | � } | j | � S)N)r ro r� )r. r r� r' r' r) �create_decimal_from_float s z!Context.create_decimal_from_floatc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r� )r. r r' r' r) rf s z Context.absc C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) �add) s z Context.addc C s t | j | � � S)N)r_ r� )r. r r' r' r) �_apply> s zContext._applyc C s% t | t � s t d � � | j � S)Nz,canonical requires a Decimal as an argument.)r^ r rp r4 )r. r r' r' r) r4 A s zContext.canonicalc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r� )r. r rU r' r' r) r� N s !zContext.comparec C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r5 )r. r rU r' r' r) r5 r s zContext.compare_signalc C s t | d d �} | j | � S)Nr� T)r� r0 )r. r rU r' r' r) r0 � s zContext.compare_totalc C s t | d d �} | j | � S)Nr� T)r� r9 )r. r rU r' r' r) r9 � s zContext.compare_total_magc C s t | d d �} | j � S)Nr� T)r� r� )r. r r' r' r) r� � s zContext.copy_absc C s t | d d �} t | � S)Nr� T)r� r )r. r r' r' r) � copy_decimal� s zContext.copy_decimalc C s t | d d �} | j � S)Nr� T)r� r� )r. r r' r' r) r� � s zContext.copy_negatec C s t | d d �} | j | � S)Nr� T)r� r: )r. r rU r' r' r) r: � s zContext.copy_signc C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) �divide� s zContext.dividec C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) � divide_int s zContext.divide_intc C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) r� 5 s zContext.divmodc C s" t | d d �} | j d | � S)Nr� Tr/ )r� rU )r. r r' r' r) rU J s z Context.expc C s( t | d d �} | j | | d | �S)Nr� Tr/ )r� r� )r. r rU r- r' r' r) r� b s z Context.fmac C s% t | t � s t d � � | j � S)Nz/is_canonical requires a Decimal as an argument.)r^ r rp r= )r. r r' r' r) r= y s zContext.is_canonicalc C s t | d d �} | j � S)Nr� T)r� r> )r. r r' r' r) r> � s zContext.is_finitec C s t | d d �} | j � S)Nr� T)r� r% )r. r r' r' r) r% � s zContext.is_infinitec C s t | d d �} | j � S)Nr� T)r� r� )r. r r' r' r) r� � s zContext.is_nanc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r? )r. r r' r' r) r? � s zContext.is_normalc C s t | d d �} | j � S)Nr� T)r� r� )r. r r' r' r) r� � s zContext.is_qnanc C s t | d d �} | j � S)Nr� T)r� r@ )r. r r' r' r) r@ � s zContext.is_signedc C s t | d d �} | j � S)Nr� T)r� r� )r. r r' r' r) r� � s zContext.is_snanc C s" t | d d �} | j d | � S)Nr� Tr/ )r� rA )r. r r' r' r) rA s zContext.is_subnormalc C s t | d d �} | j � S)Nr� T)r� rB )r. r r' r' r) rB s zContext.is_zeroc C s" t | d d �} | j d | � S)Nr� Tr/ )r� rJ )r. r r' r' r) rJ ) s z Context.lnc C s" t | d d �} | j d | � S)Nr� Tr/ )r� rM )r. r r' r' r) rM ? s z Context.log10c C s" t | d d �} | j d | � S)Nr� Tr/ )r� rN )r. r r' r' r) rN [ s z Context.logbc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� rX )r. r rU r' r' r) rX u s zContext.logical_andc C s" t | d d �} | j d | � S)Nr� Tr/ )r� rZ )r. r r' r' r) rZ � s zContext.logical_invertc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r[ )r. r rU r' r' r) r[ � s zContext.logical_orc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� rY )r. r rU r' r' r) rY � s zContext.logical_xorc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r� )r. r rU r' r' r) r� � s z Context.maxc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r\ )r. r rU r' r' r) r\ � s zContext.max_magc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r� )r. r rU r' r' r) r� s z Context.minc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r] )r. r rU r' r' r) r] s zContext.min_magc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r� )r. r r' r' r) �minus1 s z Context.minusc C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) �multiplyB s zContext.multiplyc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r` )r. r r' r' r) r` b s zContext.next_minusc C s" t | d d �} | j d | � S)Nr� Tr/ )r� ra )r. r r' r' r) ra v s zContext.next_plusc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� rb )r. r rU r' r' r) rb � s zContext.next_towardc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r# )r. r r' r' r) r# � s zContext.normalizec C s" t | d d �} | j d | � S)Nr� Tr/ )r� rd )r. r r' r' r) rd � s /zContext.number_classc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r� )r. r r' r' r) �plus� s z Context.plusc C sQ t | d d �} | j | | d | �} | t k rI t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r r� rp )r. r rU r� r� r' r' r) �power s I z Context.powerc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r� )r. r rU r' r' r) r� X s 7zContext.quantizec C s t d � S)Nr� )r )r. r' r' r) re � s z Context.radixc C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) r� � s zContext.remainderc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r� )r. r rU r' r' r) r� � s zContext.remainder_nearc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� ri )r. r rU r' r' r) ri � s zContext.rotatec C s t | d d �} | j | � S)Nr� T)r� r& )r. r rU r' r' r) r& � s zContext.same_quantumc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� rj )r. r rU r' r' r) rj s zContext.scalebc C s% t | d d �} | j | d | �S)Nr� Tr/ )r� r� )r. r rU r' r' r) r� * s z Context.shiftc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r/ )r. r r' r' r) r/ H s z Context.sqrtc C sN t | d d �} | j | d | �} | t k rF t d | � � n | Sd S)Nr� Tr/ z Unable to convert %s to Decimal)r� r� r� rp )r. r rU r� r' r' r) �subtracth s zContext.subtractc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r� )r. r r' r' r) r� s zContext.to_eng_stringc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r� )r. r r' r' r) � to_sci_string� s zContext.to_sci_stringc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r) )r. r r' r' r) r) � s zContext.to_integral_exactc C s" t | d d �} | j d | � S)Nr� Tr/ )r� r� )r. r r' r' r) r� � s zContext.to_integral_value)Wr1 r2 r3 r� r� r� r� r� rl r� rH r� r* rG rn rb r^ r� r� r� r� r� r+ r� r� rf r� r� r4 r� r5 r0 r9 r� r� r� r: r� r� r� rU r� r= r> r% r� r? r� r@ r� rA rB rJ rM rN rX rZ r[ rY r� r\ r� r] r� r� r` ra rb r# rd r� r� r� re r� r� ri r& rj r� r/ r� r� r� r) r� r� r' r' r' r) r s� " $ # % # 2 P : & " c @ s7 e Z d Z d Z d d d � Z d d � Z e Z d S) rg r< rS rU Nc C s� | d k r* d | _ d | _ d | _ nc t | t � rf | j | _ t | j � | _ | j | _ n' | d | _ | d | _ | d | _ d S)Nr% r- r+ )r< rS rU r^ r r6 r7 rO )r. rr r' r' r) r� � s z_WorkRep.__init__c C s d | j | j | j f S)Nz (%r, %r, %r))r< rS rU )r. r' r' r) r� � s z_WorkRep.__repr__)r< rS rU )r1 r2 r3 r~ r� r� r� r' r' r' r) rg � s rg c C s� | j | j k r! | } | } n | } | } t t | j � � } t t | j � � } | j t d | | d � } | | j d | k r� d | _ | | _ | j d | j | j 9_ | j | _ | | f S)Nr- r+ r� r� )rU rd r_ rS r� )r� r� r? �tmpr� Ztmp_lenZ other_lenrU r' r' r) r� � s r� c C s{ | d k r d S| d k r( | d | St t | � � } t | � t | j d � � } | | k rj d S| d | Sd S)Nr% r� rQ )r_ rf rd �rstrip)r4 r� Zstr_nZval_nr' r' r) r s r c C s[ | d k s | d k r$ t d � � d } x* | | k rV | | | | d ?} } q- W| S)Nr% z3Both arguments to _sqrt_nearest should be positive.r- )rj )r4 r rU r' r' r) � _sqrt_nearest2 s r� c C s7 d | >| | ?} } | d | | d @| d @| k S)Nr- r+ r' )r r� rU r� r' r' r) �_rshift_nearestA s r� c C s/ t | | � \ } } | d | | d @| k S)Nr+ r- )r� )r rU r� r� r' r' r) � _div_nearestI s r� r c C s7 | | } d } x� | | k r9 t | � | | >| k s_ | | k r� t | � | | ?| k r� t | | d >| t | | t | | � | � � } | d 7} q Wt d t t | � � d | � } t | | � } t | | � } x> t | d d d � D]& } t | | � t | | | � } q� Wt | | | � S)Nr% r- r� rZ i����r� )rf r� r� r� rS rd r_ r� ) r �M�Lr �R�TZyshift�wr� r' r' r) �_ilogQ s )&'% $r� c C s� | d 7} t t | � � } | | | | d k } | d k r� d | } | | | } | d k ru | d | 9} n t | d | � } t | | � } t | � } t | | | � } | | } n d } t | d | � } t | | d � S)Nr+ r- r% r� r )rd r_ r� r� � _log10_digits) r- r� r r. r r� r� �log_dZlog_10Z log_tenpowerr' r' r) rL � s rL c C s | d 7} t t | � � } | | | | d k } | d k r� | | | } | d k rk | d | 9} n t | d | � } t | d | � } n d } | r� t t t | � � � d } | | d k r� t | t | | � d | � } q d } n d } t | | d � S)Nr+ r- r% r� r )rd r_ r� r� rf r� ) r- r� r r. r r� r� r Z f_log_tenr' r' r) rI � s" $ rI c @ s( e Z d Z d d � Z d d � Z d S)� _Log10Memoizec C s d | _ d S)NZ/23025850929940456840179914546843642076011014886)rv )r. r' r' r) r� � s z_Log10Memoize.__init__c C s� | d k r t d � � | t | j � k r� d } x^ d | | d } t t t d | | � d � � } | | d � d | k r� P| d 7} q6 W| j d � d d � | _ t | j d | d � � S) Nr% zp should be nonnegativerZ r� r+ r rQ r- r� )rj rd rv r_ r� r� r� rS )r. r r r� rv r' r' r) � getdigits� s " z_Log10Memoize.getdigitsN)r1 r2 r3 r� r� r' r' r' r) r� � s r� c C s� t | | >| � } t d t t | � � d | � } t | | � } | | >} x9 t | d d d � D]! } t | | | | | � } qi WxC t | d d d � D]+ } | | d >} t | | | | � } q� W| | S) Nr� rZ r- r% r+ i����r� r� r� )r rS rd r_ r� r� ) r r� r� r� r� r ZMshiftr r� r' r' r) �_iexp� s % r� c C s� | d 7} t d | t t | � � d � } | | } | | } | d k r^ | d | } n | d | } t | t | � � \ } } t | d | � } t t | d | � d � | | d f S)Nr+ r% r- r� i� rZ )r� rd r_ r� r� r� r� ) r- r� r r r� r� ZcshiftZquotr r' r' r) r; s # r; c C s* t t t | � � � | } t | | | | d � } | | } | d k ra | | d | } n t | | d | � } | d k r� t t | � � | d k | d k k r� d | d d d | } } q d | d | } } n: t | | d | d � \ } } t | d � } | d 7} | | f S)Nr- r% r� )rd r_ rf rI r� r; ) r r r r r rU Zlxcr� Zpcr� rU r' r' r) r = s ( ! r r� r �2�F �3�5 �4�( �5� �6rC �7� �8r� r= rw c C s> | d k r t d � � t | � } d t | � | | d S)Nr% z0The argument to _log10_lb should be nonnegative.r )rj r_ rd )r- Z correctionZstr_cr' r' r) r g s r c C sh t | t � r | St | t � r, t | � S| rN t | t � rN t j | � S| rd t d | � � t S)Nz Unable to convert %s to Decimal)r^ r rS rn ro rp r� )r� r� Z allow_floatr' r' r) r� r s r� c C s t | t � r | | f St | t j � ru | j sb t | j t t | j � | j � | j � } | t | j � f S| r� t | t j � r� | j d k r� | j } t | t � r� t � } | r� d | j t <n | j t d � | t j | � f St t f S)Nr% r- z;strict semantics for mixing floats and Decimals are enabled)r^ r �_numbersZRationalrP r5 r6 r_ rS r7 � denominatorrO � numeratorZComplexr� r� rn r r r rb ro r� )r. r� r� r/ r' r' r) r� � s$ ' r� r? r r> r r r@ i?B r$ r� 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 j | � } | d k r+ t d | � � | j � } | d } | d } | d d k | d <| d r� | d k r� t d | � � | d k r� t d | � � | p� d | d <| p� d | d <| d d k r� d | d <t | d p� d � | d <| d d k rt | d � | d <| d d k rS| d d k sI| d d k rSd | d <| d d k r�d | d <| d k r�t j � } | d d k r�t d | � � | d | d <| d | d <| d | d <n4 | d d k r�d | d <d d g | d <d | d <| S)NzInvalid format specifier: �fill�align�zeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: � �>r< rR � minimumwidthrQ ru r% rm ZgGnr- r4 rs � thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: �grouping� decimal_pointrT rZ r� )� _parse_format_specifier_regex�matchrj � groupdictrS �_locale� localeconv)� format_specrq rs Z format_dictr� r� r' r' r) rw sN rw c C s� | d } | d } | | t | � t | � } | d } | d k rY | | | } n� | d k rv | | | } nn | d k r� | | | } nQ | d k r� t | � d } | d | � | | | | d � } n t d � � | S) Nr� r� r� �<r� �=�^r+ z Unrecognised alignment field)rd rj ) r< r| r{ r� r� Zpaddingr� r� Zhalfr' r' r) ry b s ) ry c C s� d d l m } m } | s g S| d d k rc t | � d k rc | | d d � | | d � � S| d t j k r� | d d � St d � � d S) Nr% )�chain�repeatr- r+ z unrecognised format for groupingr� r� r� r� r� )� itertoolsr� r� rd r� �CHAR_MAXrj )r� r� r� r' r' r) �_group_lengths} s "!r� c C s( | d } | d } g } x� t | � D]� } | d k rE t d � � t t t | � | d � | � } | j d | t | � | | d � � | d | � } | | 8} | r� | d k r� P| t | � 8} q' Wt t | � | d � } | j d | t | � | | d � � | j t | � � S)Nr� r� r% z group length should be positiver- rQ )r� rj r� r� rd rk rl �reversed)rv r{ � min_width�sepr� �groupsr. r' r' r) �_insert_thousands_sep� s !* *r� c C s* | r d S| d d k r" | d Sd Sd S)NrR r< z +rT r' )� is_negativer{ r' r' r) rx � s rx c C s� t | | � } | s | d r- | d | } | d k sI | d d k r� d d d d d d d d i | d } | d j | | � 7} | d d k r� | d 7} | d r� | d t | � t | � } n d } t | | | � } t | | | | � S)NZaltr� r% rm rv r� r� rt rs z{0}{1:+}rr r� r� )rx �formatrd r� ry )r� rt ru rU r{ r< Zecharr� r' r' r) rz � s & !rz ZInfz-Infr� )|�__all__r1 rC � __version__Z__libmpdec_version__�mathrx Znumbersr� rD � collectionsr& Z _namedtupler � ImportErrorr 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 rp r r r� r� rI r\ rA rE rK �hasattrrJ rF r r r r r5 �Number�registerrM r rg r� rS r~ r r r� r� r� r� rL rI r� r� r� r� r; r r r� r� r r r �re�compile�VERBOSE� IGNORECASEr� r` r� r� �DOTALLr� �localer� rw ry r� r� rx rz rH rG r9 r7 r r6 r; � hash_info�modulusr� rc r� r� r� r� r� r' r' r' r) �<module>u sT & .� � � � � � � � � � � � �� � � � � � � 0 " ,# % $ + ' * P % )
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