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_pydecimal.cpython-39.opt-2.pyc
a DOg:} @ sl g d Z eZdZdZdZddlZddlZddl Z zddl m Z e ddZ W n eyd d d Z Y n0 d Zd Zd ZdZdZdZdZdZdZdZe jdkrdZdZdZ n dZdZdZ e ed Z G dd de Z G d d d e Z G d d d e Z!G d d! d!e!Z"G d"d# d#e e#Z$G d$d% d%e!Z%G d&d' d'e!e#Z&G d(d) d)e Z'G d*d+ d+e!Z(G d,d- d-e Z)G d.d/ d/e Z*G d0d1 d1e'e)Z+G d2d3 d3e'e)e*Z,G d4d5 d5e e-Z.e e$e'e+e)e,e!e*e.g Z/e"e!e%e!e&e!e(e!iZ0eeeeeeeefZ1ddl2Z2e23d6Z4d7d8 Z5d9d: Z6[2dd;d<Z7G d=d> d>e8Z9dd@dAZ:ej;<e9 G dBdC dCe8Z=G dDdE dEe8Z>G dFdG dGe8Z?ddHdIZ@eAjBZCdJdK ZDdLdM ZEdNdO ZFdPdQ ZGddSdTZHdUdV ZIdWdX ZJG dYdZ dZe8ZKeK jLZMdd[d\ZNd]d^ ZOd_d` ZPdadbdcdddedfdgdhdidj fdkdlZQddmdnZRddodpZSe>dqee$e+e!gg drdsdddtZTe>duee$e+e!e e,gg dvZUe>dueg g dvZVddlWZWeWXdweWjYeWjZB j[Z\eWXdxj[Z]eWXdyj[Z^eWXdzeWjYeWj_B Z`[Wz ddlaZbW n ey Y n0 dd{d|Zcd}d~ Zddd ZedddZfdd Zgdd Zhe9dZie9dZje9dZke9dZle9dZme9dZneiejfZoe jpjqZre jpjsZte jpjuZvewdherd erZx[ dS ))%DecimalContext DecimalTupleDefaultContext BasicContextExtendedContextDecimalExceptionClampedInvalidOperationDivisionByZeroInexactRounded SubnormalOverflow UnderflowFloatOperationDivisionImpossibleInvalidContextConversionSyntaxDivisionUndefined ROUND_DOWN ROUND_HALF_UPROUND_HALF_EVEN ROUND_CEILING ROUND_FLOORROUND_UPROUND_HALF_DOWN ROUND_05UP setcontext getcontext localcontextMAX_PRECMAX_EMAXMIN_EMIN MIN_ETINY HAVE_THREADSHAVE_CONTEXTVARZdecimalz1.70z2.4.2 N) namedtupler zsign digits exponentc G s | S N )argsr) r) "/usr/lib64/python3.9/_pydecimal.py<lambda> r, r r r r r r r r Tl l NZolNZoi@Ti c @ s e Zd Zdd ZdS )r c G s d S r( r) selfcontextr* r) r) r+ handle s zDecimalException.handleN__name__ __module__ __qualname__r2 r) r) r) r+ r s r c @ s e Zd ZdS )r Nr4 r5 r6 r) r) r) r+ r s r c @ s e Zd Zdd ZdS )r c G s, |r(t |d j|d jdd}||S tS )Nr& nT)_dec_from_triple_sign_int_fix_nan_NaN)r0 r1 r* ansr) r) r+ r2 s zInvalidOperation.handleNr3 r) r) r) r+ r s r c @ s e Zd Zdd ZdS )r c G s t S r( r= r/ r) r) r+ r2 s zConversionSyntax.handleNr3 r) r) r) r+ r s r c @ s e Zd Zdd ZdS )r c G s t | S r( )_SignedInfinityr0 r1 signr* r) r) r+ r2 s zDivisionByZero.handleNr3 r) r) r) r+ r s r c @ s e Zd Zdd ZdS )r c G s t S r( r? r/ r) r) r+ r2 " s zDivisionImpossible.handleNr3 r) r) r) r+ r s r c @ s e Zd Zdd ZdS )r c G s t S r( r? r/ r) r) r+ r2 - s zDivisionUndefined.handleNr3 r) r) r) r+ r % s r c @ s e Zd ZdS )r Nr7 r) r) r) r+ r 0 s r c @ s e Zd Zdd ZdS )r c G s t S r( r? r/ r) r) r+ r2 G s zInvalidContext.handleNr3 r) r) r) r+ r < s r c @ s e Zd ZdS )r Nr7 r) r) r) r+ r J s r c @ s e Zd ZdS )r Nr7 r) r) r) r+ r V s r c @ s e Zd Zdd ZdS )r c G s |j ttttfv rt| S |dkrR|j tkr4t| S t|d|j |j |j d S |dkr|j t krlt| S t|d|j |j |j d S d S )Nr& 9r. ) roundingr r r r r@ r r9 precEmaxr rA r) r) r+ r2 w s zOverflow.handleNr3 r) r) r) r+ r a s r c @ s e Zd ZdS )r Nr7 r) r) r) r+ r s r c @ s e Zd ZdS )r Nr7 r) r) r) r+ r s r Zdecimal_contextc C s6 z t W S ty0 t } t | | Y S 0 d S r( )_current_context_varget LookupErrorr setr1 r) r) r+ r s r c C s, | t ttfv r | } | t| d S r( )r r r copy clear_flagsrG rJ rK r) r) r+ r s r c C s | d u rt } t| S r( )r _ContextManager)ctxr) r) r+ r s $r c @ s e Zd ZdZdddZedd Zdd Zd d Zdd d Z dd Z dd Z dd Z dddZ dddZdddZdddZdd d Zdd d Zd d! Zd"d# Zd$d% Zd&d' Zdd)d*Zdd+d,Zdd-d.Zdd/d0Zdd2d3Zdd4d5Z e Z dd6d7Z d d8d9Z dd:d;Z e Z!dd<d=Z"d>d? Z#dd@dAZ$ddBdCZ%ddDdEZ&ddFdGZ'ddHdIZ(ddJdKZ)d dLdMZ*d dNdOZ+dPdQ Z,dRdS Z-e-Z.e/dTdU Z0e/dVdW Z1dXdY Z2dZd[ Z3d\d] Z4d^d_ Z5d`da Z6dbdc Z7ddde Z8dfdg Z9dhdi Z:djdk Z;dldm Z<dndo Z=e>e6e7e8e9e:e;e<e=dpZ?d dqdrZ@dsdt ZAdudv ZBd dwdxZCd dydzZDd{d| ZEdd}d~ZFdddZGdddZHdddZIdddZJdd ZKdd ZLdddZMdddZNeNZOdddZPdddZQdddZRdd ZSdd ZTdd ZUdd ZVdddZWdddZXdddZYdd ZZdd Z[dddZ\d ddZ]dd Z^dd Z_dd Z`dd Zad ddZbdd Zcdd Zddd Zed ddZfdd Zgdd Zhd ddZiddĄ Zjd ddƄZkd!ddȄZlddʄ Zmdd̄ Znd"dd΄Zod#ddЄZpd$dd҄Zqd%ddԄZrd&ddքZsd'ddZtd(ddڄZud)dd܄Zvd*ddބZwd+ddZxdd Zyd,ddZzd-ddZ{d.ddZ|dd Z}dd Z~dd Zd/ddZdS (0 r )_expr; r: _is_special0Nc C s t | }t|tr$t| dd}|d u rP|d u r@t }|t d| S | ddkrfd|_ nd|_ | d}|d ur| d pd}t | d pd }tt || |_ |t| |_d |_nZ| d }|d urtt |pd d |_ | drd|_nd|_n d |_ d|_d|_|S t|t rf|dkrBd|_ nd|_ d|_tt||_ d |_|S t|tr|j|_|j |_ |j |_ |j|_|S t|tr|j|_ t|j |_ t |j|_d |_|S t|ttfr"t|dkrtdt|d t r|d dv std|d |_ |d dkrHd |_ |d |_d|_ng } |d D ]R} t| t rd| kr|dkrn n | s| dkr| | ntdqT|d dv rdt t| |_ |d |_d|_nDt|d t rdt t| pdg|_ |d |_d |_ntd|S t|t rx|d u r>t }|t d t |}|j|_|j |_ |j |_ |j|_|S t d | d S ) N_ z Invalid literal for Decimal: %rrB -r. r& intZfracexprR FdiagsignalNr8 FT ztInvalid tuple size in creation of Decimal from list or tuple. The list or tuple should have exactly three elements.r& r. z|Invalid sign. The first value in the tuple should be an integer; either 0 for a positive number or 1 for a negative number. zTThe second value in the tuple must be composed of integers in the range 0 through 9.r8 rZ zUThe third value in the tuple must be an integer, or one of the strings 'F', 'n', 'N'.;strict semantics for mixing floats and Decimals are enabledz Cannot convert %r to Decimal)!object__new__ isinstancestr_parserstripreplacer _raise_errorr groupr: rV r; lenrP rQ lstripabsr _WorkReprB rW listtuple ValueErrorappendjoinmapfloatr from_float TypeError) clsvaluer1 r0 mintpartfracpartrW rX digitsZdigitr) r) r+ rc s ( zDecimal.__new__c C s t |tr,|dkrdnd}d}tt|}nzt |trt|sJt|rV| t|S t d|dkrld}nd}t| \}}| d }t|d| }nt dt ||| }| tu r|S | |S d S )Nr& r. g ? z argument must be int or float.)rd rV re rm ru _mathisinfisnanreprcopysignas_integer_ratio bit_lengthrw r9 r )rx frB kcoeffr8 dresultr) r) r+ rv s$ zDecimal.from_floatc C s( | j r$| j}|dkrdS |dkr$dS dS )Nr8 r. rZ r^ r& )rQ rP )r0 rW r) r) r+ _isnan s zDecimal._isnanc C s | j dkr| jrdS dS dS )Nr[ r. r& )rP r: r0 r) r) r+ _isinfinity s zDecimal._isinfinityc C s| | }|d u rd}n| }|s&|rx|d u r4t }|dkrJ|td| S |dkr`|td|S |rn| |S ||S dS )NFr^ sNaNr& )r r ri r r< )r0 otherr1 self_is_nan other_is_nanr) r) r+ _check_nans s& zDecimal._check_nansc C sv |d u rt }| js|jrr| r0|td| S | rF|td|S | r\|td| S | rr|td|S dS )Nzcomparison involving sNaNzcomparison involving NaNr& )r rQ is_snanri r is_qnanr0 r r1 r) r) r+ _compare_check_nans s0 zDecimal._compare_check_nansc C s | j p| jdkS NrR rQ r; r r) r) r+ __bool__* s zDecimal.__bool__c C s | j s |j r8| }| }||kr(dS ||k r4dS dS | sP|sDdS d|j S |s^d| j S |j| jk rndS | j|jk r~dS | }| }||kr| jd| j|j }|jd|j| j }||krdS ||k rd| j S d| j S n ||krd| j S d| j S d S )Nr& r r. rR )rQ r r: adjustedr; rP )r0 r Zself_infZ other_inf self_adjustedZother_adjusted self_paddedZ other_paddedr) r) r+ _cmp1 s> z Decimal._cmpc C s< t | |dd\} }|tu r |S | ||r.dS | |dkS )NT) equality_opFr& )_convert_for_comparisonNotImplementedr r r r) r) r+ __eq__q s zDecimal.__eq__c C s< t | |\} }|tu r|S | ||}|r.dS | |dk S NFr& r r r r r0 r r1 r> r) r) r+ __lt__y s zDecimal.__lt__c C s< t | |\} }|tu r|S | ||}|r.dS | |dkS r r r r) r) r+ __le__ s zDecimal.__le__c C s< t | |\} }|tu r|S | ||}|r.dS | |dkS r r r r) r) r+ __gt__ s zDecimal.__gt__c C s< t | |\} }|tu r|S | ||}|r.dS | |dkS r r r r) r) r+ __ge__ s zDecimal.__ge__c C s> t |dd}| js |r0|jr0| ||}|r0|S t| |S NTraiseit)_convert_otherrQ r r r r r) r) r+ compare s zDecimal.comparec C s | j r4| rtdn | r$tS | jr0t S tS | jdkrNtd| jt }ntt | j t }t | j | t }| dkr||n| }|dkrdS |S )Nz"Cannot hash a signaling NaN value.r& r ) rQ r rw is_nan _PyHASH_NANr: _PyHASH_INFrP pow_PyHASH_MODULUS _PyHASH_10INVrV r; )r0 Zexp_hashZhash_r> r) r) r+ __hash__ s zDecimal.__hash__c C s t | jttt| j| jS r( )r r: rp rt rV r; rP r r) r) r+ as_tuple s zDecimal.as_tuplec C s | j r | rtdntd| s(dS t| j}| jdkrR|d| j d }}nn| j }|dkr|d dkr|d }|d8 }qZ| j }t|| @ d |}|r||L }||8 }d| |> }| j r| }||fS )Nz#cannot convert NaN to integer ratioz(cannot convert Infinity to integer ratior] r& r r. r~ ) rQ r rq OverflowErrorrV r; rP minr r: )r0 r8 r Zd5Zd2Zshift2r) r) r+ r s, zDecimal.as_integer_ratioc C s dt | S )Nz Decimal('%s'))re r r) r) r+ __repr__ s zDecimal.__repr__Fc C sb ddg| j }| jrL| jdkr&|d S | jdkr>|d | j S |d | j S | jt| j }| jdkrt|d krt|}n6|s~d }n,| jd kr|d d d }n|d d d }|dkrd }d d | | j }nL|t| jkr| jd |t| j }d}n | jd | }d | j|d }||kr(d}n*|d u r8t }ddg|j d|| }|| | | S )NrT rU r[ ZInfinityr8 NaNr r& r. rR r\ .eEz%+d)r: rQ rP r; rk r capitals) r0 engr1 rB leftdigitsdotplacer{ r| rW r) r) r+ __str__ s: zDecimal.__str__c C s | j d|dS )NT)r r1 )r r0 r1 r) r) r+ to_eng_string; s zDecimal.to_eng_stringc C sR | j r| j|d}|r|S |d u r(t }| s@|jtkr@| }n| }||S NrK )rQ r r rD r copy_abs copy_negate_fixr0 r1 r> r) r) r+ __neg__D s zDecimal.__neg__c C sR | j r| j|d}|r|S |d u r(t }| s@|jtkr@| }nt| }||S r )rQ r r rD r r r r r r) r) r+ __pos__Z s zDecimal.__pos__Tc C sJ |s | S | jr&| j|d}|r&|S | jr:| j|d}n | j|d}|S r )r rQ r r: r r )r0 roundr1 r> r) r) r+ __abs__o s zDecimal.__abs__c C sh t |}|tu r|S |d u r"t }| js.|jr| ||}|rB|S | rr| j|jkrj| rj|tdS t | S | rt |S t | j |j }d}|j t kr| j|jkrd}| s|st | j|j}|rd}t|d|}||}|S | s t||j |j d }|||j }||}|S |sVt|| j |j d }| ||j }||}|S t| }t|}t|||j\}}t } |j|jkr|j|jkrt|d|}||}|S |j|jk r|| }}|jdkrd| _|j|j |_|_nd| _n&|jdkrd| _d\|_|_nd| _|jdkr<|j|j | _n|j|j | _|j| _t | }||}|S )Nz -INF + INFr& r. rR )r& r& )r r r rQ r r r: ri r r r rP rD r r9 r maxrE _rescalern _normalizerB rV rW ) r0 r r1 r> rW Z negativezerorB op1op2r r) r) r+ __add__ s| zDecimal.__add__c C sH t |}|tu r|S | js |jr6| j||d}|r6|S | j| |dS r )r r rQ r r r r r) r) r+ __sub__ s zDecimal.__sub__c C s" t |}|tu r|S |j| |dS r )r r r r r) r) r+ __rsub__ s zDecimal.__rsub__c C s@ t |}|tu r|S |d u r"t }| j|jA }| js:|jr| ||}|rN|S | rn|sf|tdS t | S | r| s|tdS t | S | j |j }| r|st |d|}| |}|S | j dkrt ||j |}| |}|S |j dkr t || j |}| |}|S t| }t|}t |t|j|j |}| |}|S )Nz (+-)INF * 0z 0 * (+-)INFrR 1)r r r r: rQ r r ri r r@ rP r9 r r; rn re rV )r0 r r1 Z resultsignr> Z resultexpr r r) r) r+ __mul__ sH zDecimal.__mul__c C s t |}|tu rtS |d u r"t }| j|jA }| js:|jr| ||}|rN|S | rj| rj|tdS | rzt | S | r|t d t |d| S |s| s|t dS |td|S | s| j|j }d}nt|jt| j |j d }| j|j | }t| }t|} |dkr:t|jd| | j\}} n t|j| jd| \}} | rt|d dkr|d7 }n8| j|j } || k r|d dkr|d }|d7 }qt |t||}||S ) Nz(+-)INF/(+-)INFzDivision by infinityrR z0 / 0zx / 0r& r. r r~ )r r r r: rQ r r ri r r@ r r9 Etinyr r rP rk r; rE rn divmodrV re r ) r0 r r1 rB r> rW r shiftr r remainder ideal_expr) r) r+ __truediv__, sP zDecimal.__truediv__c C s | j |j A }| r | j}nt| j|j}| | }| rN| sN|dkrht|dd| ||jfS ||jkr t | }t |}|j |j kr| j d|j |j 9 _ n| j d|j |j 9 _ t |j |j \}} |d|j k r t|t |dt| j t | |fS |td} | | fS )Nr rR r& r z%quotient too large in //, % or divmod)r: r rP r r r9 r rD rE rn rW rV r re ri r ) r0 r r1 rB r expdiffr r qrr> r) r) r+ _divideg s0 zDecimal._dividec C s" t |}|tu r|S |j| |dS r )r r r r r) r) r+ __rtruediv__ s zDecimal.__rtruediv__c C s t |}|tu r|S |d u r"t }| ||}|r:||fS | j|jA }| r~| rj|td}||fS t| |tdfS |s| s|t d}||fS |t d||tdfS | ||\}}| |}||fS )Nzdivmod(INF, INF)INF % xz divmod(0, 0)x // 0x % 0) r r r r r: r ri r r@ r r r r )r0 r r1 r> rB Zquotientr r) r) r+ __divmod__ s4 zDecimal.__divmod__c C s" t |}|tu r|S |j| |dS r )r r r r r) r) r+ __rdivmod__ s zDecimal.__rdivmod__c C s t |}|tu r|S |d u r"t }| ||}|r6|S | rJ|tdS |sj| r^|tdS |tdS | ||d }| |}|S )Nr r z0 % 0r. ) r r r r r ri r r r r )r0 r r1 r> r r) r) r+ __mod__ s" zDecimal.__mod__c C s" t |}|tu r|S |j| |dS r )r r r r r) r) r+ __rmod__ s zDecimal.__rmod__c C s |d u rt }t|dd}| ||}|r.|S | rB|tdS |sb| rV|tdS |tdS | r|t| }||S t | j |j }| st | j d|}||S | | }||jd kr|tS |dkr| ||j}||S t| }t|}|j|jkr(| jd |j|j 9 _n| jd |j|j 9 _t|j|j\}} d | |d@ |jkr~| |j8 } |d7 }|d |j kr|tS | j } | d k rd| } | } t | t| |}||S ) NTr zremainder_near(infinity, x)zremainder_near(x, 0)zremainder_near(0, 0)rR r. r r r^ r& )r r r r ri r r r r r rP r9 r: r rE r r rD rn rW rV r re ) r0 r r1 r> ideal_exponentr r r r r rB r) r) r+ remainder_near s` zDecimal.remainder_nearc C s t |}|tu r|S |d u r"t }| ||}|r6|S | rb| rR|tdS t| j|jA S |s| r|t d| j|jA S |t dS | ||d S )Nz INF // INFr z0 // 0r& ) r r r r r ri r r@ r: r r r r r) r) r+ __floordiv__' s& zDecimal.__floordiv__c C s" t |}|tu r|S |j| |dS r )r r r r r) r) r+ __rfloordiv__C s zDecimal.__rfloordiv__c C s8 | r(| rtd| jr"dnd}nt| }t|S )Nz%Cannot convert signaling NaN to floatz-nannan)r r rq r: re ru r0 sr) r) r+ __float__J s zDecimal.__float__c C st | j r(| rtdn| r(tdd| j }| jdkrT|t| j d| j S |t| jd | j pjd S d S )Nz Cannot convert NaN to integerz"Cannot convert infinity to integerr r& r rR ) rQ r rq r r r: rP rV r; r r) r) r+ __int__T s zDecimal.__int__c C s | S r( r) r r) r) r+ realc s z Decimal.realc C s t dS Nr& r r r) r) r+ imagg s z Decimal.imagc C s | S r( r) r r) r) r+ conjugatek s zDecimal.conjugatec C s t t| S r( )complexru r r) r) r+ __complex__n s zDecimal.__complex__c C sR | j }|j|j }t||krJ|t|| d d}t| j|| jdS t| S )NrR T) r; rE clamprk rl r9 r: rP r )r0 r1 payloadZmax_payload_lenr) r) r+ r< q s zDecimal._fix_nanc C sX | j r | r| |S t| S | }| }| s|j|g|j }tt | j ||}|| j krx| t t | jd|S t| S t| j| j |j }||kr| td| j}| t | t |S ||k }|r|}| j |k rt| j| j | } | dk rt | jd|d } d} | j|j } | | | } | jd | p>d} | dkr~tt| d } t| |jkr~| d d } |d7 }||kr| td| j}nt | j| |}| r|r| t |r| t | r| t | t |s| t |S |r | t |jdkrP| j |krP| t | jd| j | } t | j| |S t| S )NrR above Emaxr& r r. r )rQ r r< r r EtoprF r r r rP ri r r9 r: rk r; rE r r r _pick_rounding_functionrD re rV r r )r0 r1 r r exp_maxZnew_expZexp_minr> Zself_is_subnormalr} Zrounding_methodchangedr r r) r) r+ r } sn z Decimal._fixc C s t | j|rdS dS d S )Nr& r ) _all_zerosr; r0 rE r) r) r+ _round_down s zDecimal._round_downc C s | | S r( )r r r) r) r+ _round_up s zDecimal._round_upc C s* | j | dv rdS t| j |r"dS dS d S )NZ56789r. r& r )r; r r r) r) r+ _round_half_up s zDecimal._round_half_upc C s t | j|rdS | |S d S )Nr _exact_halfr; r r r) r) r+ _round_half_down s zDecimal._round_half_downc C s8 t | j|r*|dks&| j|d dv r*dS | |S d S )Nr& r. 02468r r r r) r) r+ _round_half_even s zDecimal._round_half_evenc C s | j r| |S | | S d S r( r: r r r) r) r+ _round_ceiling s zDecimal._round_ceilingc C s | j s| |S | | S d S r( r r r) r) r+ _round_floor s zDecimal._round_floorc C s0 |r | j |d dvr | |S | | S d S )Nr. Z05)r; r r r) r) r+ _round_05up s zDecimal._round_05up)r r r r r r r r c C sb |d ur2t |tstdtdd| }| |S | jrR| rJtdntdt| dt S )Nz+Second argument to round should be integralr& r cannot round a NaNcannot round an infinity) rd rV rw r9 quantizerQ r rq r r r )r0 r8 rW r) r) r+ __round__& s / zDecimal.__round__c C s0 | j r | rtdntdt| dtS Nr r r& )rQ r rq r rV r r r r) r) r+ __floor__d s zDecimal.__floor__c C s0 | j r | rtdntdt| dtS r )rQ r rq r rV r r r r) r) r+ __ceil__s s zDecimal.__ceil__c C s t |dd}t |dd}| js$|jr|d u r2t }| jdkrJ|td| S |jdkrb|td|S | jdkrr| }nf|jdkr|}nV| jdkr|s|tdS t| j|jA }n*|jdkr| s|tdS t| j|jA }n0t| j|jA t t | j t |j | j|j }| ||S ) NTr rZ r r8 r[ zINF * 0 in fmaz0 * INF in fma) r rQ r rP ri r r@ r: r9 re rV r; r )r0 r thirdr1 productr) r) r+ fma s< z Decimal.fmac C s t |}|tu r|S t |}|tu r(|S |d u r6t }| }| }| }|sZ|sZ|r|dkrp|td| S |dkr|td|S |dkr|td|S |r| |S |r||S ||S | r| r| s|tdS |dk r|tdS |s |tdS | |j kr(|tdS |s@| s@|tdS | rPd}n| j }t t |}t| }t| } |j | td |j| | }t| jD ]} t|d |}qt|| j |}t|t|dS ) 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; 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rn rW rB _dpowerrL rM _signalstrapsr flagsr r r r )r0 r r r1 r> Z result_signZ multiplierrW Zself_adjexactboundr r/ r0 r1 r2 r3 r4 r5 extrar r Z newcontext exceptionr) r) r+ __pow__ s " zDecimal.__pow__c C s" t |}|tu r|S |j| |dS r )r r rC r r) r) r+ __rpow__ s zDecimal.__rpow__c C s |d u rt }| jr(| j|d}|r(|S | |}| r>|S |sPt|jddS |j| g|j }t |j }|j }|j |d dkr||k r|d7 }|d8 }qtt|j|j d | |S )NrK rR r& r. ) r rQ r r r r9 r: rF r r rk r; rP )r0 r1 r> dupr endrW r) r) r+ normalize s$ zDecimal.normalizec C s t |dd}|d u rt }|d u r(|j}| js4|jr|| ||}|rH|S | sX| r|| rp| rpt| S |tdS | |j kr|j ksn |tdS | st | j d|j }||S | }||j kr|tdS ||j d |jkr|tdS | |j |}| |j kr.|tdS t|j|jkrL|tdS |rl| |jk rl|t |j | j kr|| kr|t |t ||}|S ) NTr zquantize with one INFz)target exponent out of bounds in quantizerR z9exponent of quantize result too large for current contextr. z7quantize result has too many digits for current context)r r rD rQ r r r ri r r rP rF r9 r: r r rE r rk r; Eminr r r )r0 rW rD r1 r> r r) r) r+ r s` zDecimal.quantizec C sD t |dd}| js|jr8| r(| p6| o6| S | j|jkS r )r rQ r is_infiniterP r r) r) r+ same_quantum% s zDecimal.same_quantumc C s | j rt| S | s t| jd|S | j|krHt| j| jd| j| |S t| j| j | }|dk rzt| jd|d } d}| j| }|| |}| jd | pd}|dkrtt |d }t| j||S )NrR r& r r. ) rQ r r9 r: rP r; rk r re rV )r0 rW rD r} Z this_functionr r r) r) r+ r 4 s$ zDecimal._rescalec C sf |dkrt d| js| s"t| S | | d | |}| | krb|| d | |}|S )Nr& z'argument should be at least 1 in _roundr. )rq rQ r r r )r0 placesrD r> r) r) r+ _roundV s zDecimal._roundc C s | j r"| j|d}|r|S t| S | jdkr4t| S | sFt| jddS |d u rTt }|d u rb|j}| d|}|| kr| t | t |S )NrK r& rR ) rQ r r rP r9 r: r rD r ri r r r0 rD r1 r> r) r) r+ to_integral_exactm s$ zDecimal.to_integral_exactc C s` |d u rt }|d u r |j}| jr>| j|d}|r6|S t| S | jdkrPt| S | d|S d S )NrK r& )r rD rQ r r rP r rM r) r) r+ r s zDecimal.to_integral_valuec C s |d u rt }| jrB| j|d}|r(|S | rB| jdkrBt| S | sdt| jd| jd }||S | jdkrz| t dS |j d }t | }|j d? }|j d@ r|jd }t| jd? d }n|j}t| jd d? }|| }|dkr|d| 9 }d } nt|d| \}} | } ||8 }d| } || } | | kr:qJn | | d? } q"| oZ| | |k} | r|dkrz| d| } n| d| 9 } ||7 }n| d dkr| d7 } tdt| |}| }|t} ||}| |_|S ) NrK r& rR r^ r. zsqrt(-x), x > 0r r+ Tr~ )r rQ r r r: r r9 rP r ri r rE rn rW rV rk r; r re _shallow_copy _set_roundingr rD )r0 r1 r> rE opr clr r? r r8 r rD r) r) r+ sqrt s^ z Decimal.sqrtc C s t |dd}|d u rt }| js&|jr~| }| }|s>|r~|dkrX|dkrX| |S |dkrr|dkrr||S | ||S | |}|dkr| |}|dkr|}n| }||S NTr r. r& r r r rQ r r r r compare_totalr0 r r1 ZsnZonrR r> r) r) r+ r s& z Decimal.maxc C s t |dd}|d u rt }| js&|jr~| }| }|s>|r~|dkrX|dkrX| |S |dkrr|dkrr||S | ||S | |}|dkr| |}|dkr| }n|}||S rU rV rX r) r) r+ r * s& z Decimal.minc C s8 | j r dS | jdkrdS | j| jd }|dt| kS )NFr& TrR )rQ rP r; rk )r0 restr) r) r+ r L s zDecimal._isintegerc C s& | r| j dkrdS | jd| j dv S )Nr& Tr r )rP r; r r) r) r+ r U s zDecimal._isevenc C s0 z| j t| j d W S ty* Y dS 0 d S )Nr. r& )rP rk r; rw r r) r) r+ r [ s zDecimal.adjustedc C s | S r( r) r r) r) r+ canonicalc s zDecimal.canonicalc C s. t |dd}| ||}|r |S | j||dS NTr rK )r r r r r) r) r+ compare_signalk s zDecimal.compare_signalc C s` t |dd}| jr |js tS | js,|jr,tS | j}| }| }|sL|r||krt| j| jf}t|j|jf}||k r|rtS tS ||kr|rtS tS tS |r|dkrtS |dkrtS |dkrtS |dkrtS n2|dkrtS |dkrtS |dkrtS |dkrtS | |k rtS | |kr$tS | j|jk r@|r<tS tS | j|jkr\|rXtS tS tS )NTr r. r^ ) r r: _NegativeOner9 r rk r; _ZerorP )r0 r r1 rB Zself_nanZ other_nanZself_keyZ other_keyr) r) r+ rW w sf zDecimal.compare_totalc C s& t |dd}| }| }||S r )r r rW )r0 r r1 r or) r) r+ compare_total_mag s zDecimal.compare_total_magc C s t d| j| j| jS r )r9 r; rP rQ r r) r) r+ r s zDecimal.copy_absc C s2 | j rtd| j| j| jS td| j| j| jS d S )Nr& r. )r: r9 r; rP rQ r r) r) r+ r s zDecimal.copy_negatec C s" t |dd}t|j| j| j| jS r )r r9 r: r; rP rQ r r) r) r+ copy_sign s zDecimal.copy_signc C s |d u rt }| j|d}|r"|S | dkr2tS | s:tS | dkrNt| S |j}| }| jdkr|t t |j d d krt dd|j d }n0| jdkr|t t | d d krt dd| d }n| jdkr || k r t ddd|d d | }n| jdkrD|| d k rDt dd|d | d }nt| }|j|j }}|jdkrl| }d}t|||| \} } | d d t t | | d rq|d7 }qpt dt | | }| }|t} ||}| |_|S ) NrK r r. r& r\ r rR rC r~ r )r r r r^ r9 r rE r r: rk re rF r9 r rn rV rW rB _dexprO rP r r rD ) r0 r1 r> r/ adjrQ rR r rA r rW rD r) r) r+ rW sH $( " z Decimal.expc C s dS )NTr) r r) r) r+ is_canonical' s zDecimal.is_canonicalc C s | j S r( )rQ r r) r) r+ is_finite/ s zDecimal.is_finitec C s | j dkS )Nr[ rP r r) r) r+ rI 7 s zDecimal.is_infinitec C s | j dv S )Nr` rf r r) r) r+ r ; s zDecimal.is_nanc C s* | j s | sdS |d u r t }|j| kS NF)rQ r rH r r r) r) r+ is_normal? s zDecimal.is_normalc C s | j dkS )Nr8 rf r r) r) r+ r G s zDecimal.is_qnanc C s | j dkS Nr. )r: r r) r) r+ is_signedK s zDecimal.is_signedc C s | j dkS )NrZ rf r r) r) r+ r O s zDecimal.is_snanc C s* | j s | sdS |d u r t }| |jk S rg )rQ r r rH r r) r) r+ is_subnormalS s zDecimal.is_subnormalc C s | j o| jdkS r r r r) r) r+ is_zero[ s zDecimal.is_zeroc C s | j t| j d }|dkr4tt|d d d S |dkrXttd| d d d S t| }|j|j }}|dkrt|d| }t|}t|t| ||k S |ttd| | d S )Nr. r r r r& rP rk r; re rn rV rW r0 rc rQ rR r numZdenr) r) r+ _ln_exp_bound_ s zDecimal._ln_exp_boundc C s |d u rt }| j|d}|r"|S | s*tS | dkr:tS | tkrFtS | jdkr\|t dS t | }|j |j }}|j }|| d }t|||}|ddttt|| d rq|d7 }qtt |dk tt|| }| }|t} ||}| |_|S ) NrK r. zln of a negative valuer^ r~ r r\ r& )r r _NegativeInfinityr _Infinityr9 r^ r: ri r rn rV rW rE rq _dlogrk re rm r9 rO rP r r rD r0 r1 r> rQ rR r r/ rK r rD r) r) r+ lnx s: $ z Decimal.lnc C s | j t| j d }|dkr,tt|d S |dkrHttd| d S t| }|j|j }}|dkrt|d| }td| }t|t| ||k d S td| | }t|| |dk d S ) Nr. r r r& r r^ Z231rn ro r) r) r+ r: s zDecimal._log10_exp_boundc C sF |d u rt }| j|d}|r"|S | s*tS | dkr:tS | jdkrP|tdS | jd dkr| jdd dt | jd krt | j t | j d }nt | }|j |j }}|j}|| d }t|||}|dd t tt|| d rq|d 7 }qtt |dk tt|| }| }|t} ||}| |_|S ) NrK r. zlog10 of a negative valuer& r rR r^ r~ r r\ )r r rr r rs r: ri r r; rk r rP rn rV rW rE r: _dlog10re rm r9 rO rP r r rD ru r) r) r+ log10 s: . $ z Decimal.log10c C sV | j |d}|r|S |d u r"t }| r.tS | s@|tddS t| }||S )NrK zlogb(0)r. ) r r r rs ri r r r r r r) r) r+ logb s z Decimal.logbc C s6 | j dks| jdkrdS | jD ]}|dvr dS q dS )Nr& FZ01T)r: rP r; )r0 digr) r) r+ _islogical s zDecimal._islogicalc C s |j t| }|dkr$d| | }n|dk r<||j d }|j t| }|dkr`d| | }n|dk rx||j d }||fS )Nr& rR )rE rk )r0 r1 opaopbZdifr) r) r+ _fill_logical' s zDecimal._fill_logicalc C sz |d u rt }t|dd}| r*| s4|tS | || j|j\}}ddd t||D }t d| dptddS )NTr rT c S s$ g | ] \}}t t|t|@ qS r) re rV .0r7 br) r) r+ <listcomp>B r- z'Decimal.logical_and.<locals>.<listcomp>r& rR r r r| ri r r r; rs zipr9 rl r0 r r1 r} r~ r r) r) r+ logical_and4 s zDecimal.logical_andc C s( |d u rt }| tdd|j d|S )Nr& r )r logical_xorr9 rE r r) r) r+ logical_invertE s zDecimal.logical_invertc C sz |d u rt }t|dd}| r*| s4|tS | || j|j\}}ddd t||D }t d| dptddS )NTr rT c S s$ g | ] \}}t t|t|B qS r) r r r) r) r+ r Z r- z&Decimal.logical_or.<locals>.<listcomp>r& rR r r r) r) r+ logical_orL s zDecimal.logical_orc C sz |d u rt }t|dd}| r*| s4|tS | || j|j\}}ddd t||D }t d| dptddS )NTr rT c S s$ g | ] \}}t t|t|A qS r) r r r) r) r+ r k r- z'Decimal.logical_xor.<locals>.<listcomp>r& rR r r r) r) r+ r ] s zDecimal.logical_xorc C s t |dd}|d u rt }| js&|jr~| }| }|s>|r~|dkrX|dkrX| |S |dkrr|dkrr||S | ||S | | }|dkr| |}|dkr|}n| }||S rU r r rQ r r r r r rW rX r) r) r+ max_magn s& zDecimal.max_magc C s t |dd}|d u rt }| js&|jr~| }| }|s>|r~|dkrX|dkrX| |S |dkrr|dkrr||S | ||S | | }|dkr| |}|dkr| }n|}||S rU r rX r) r) r+ min_mag s& zDecimal.min_magc C s |d u rt }| j|d}|r"|S | dkr2tS | dkrTtdd|j | S | }|t | | |}|| kr|S | tdd| d |S )NrK r r. r& rC r )r r r rr r9 rE r rL rP r _ignore_all_flagsr r r r0 r1 r> Znew_selfr) r) r+ next_minus s$ zDecimal.next_minusc C s |d u rt }| j|d}|r"|S | dkr2tS | dkrTtdd|j | S | }|t | | |}|| kr|S | tdd| d |S )NrK r. r rC r& r )r r r rs r9 rE r rL rP r r r r r r r) r) r+ next_plus s$ zDecimal.next_plusc C s t |dd}|d u rt }| ||}|r.|S | |}|dkrJ| |S |dkr^| |}n | |}| r|t d|j |t |t nD| |jk r|t |t |t |t |s|t |S )NTr r& r z Infinite result from next_toward)r r r r ra r r r ri r r: r r r rH r r r )r0 r r1 r> Z comparisonr) r) r+ next_toward s6 zDecimal.next_towardc C s | r dS | rdS | }|dkr,dS |dkr8dS | rN| jrJdS dS |d u r\t }| j|d rv| jrrd S d S | jrd S d S d S )Nr r r. z +Infinityr z -Infinityz-Zeroz+ZerorK z -Subnormalz +Subnormalz-Normalz+Normal)r r r rl r: r rk )r0 r1 infr) r) r+ number_class s, zDecimal.number_classc C s t dS Nr r r r) r) r+ radix0 s z Decimal.radixc C s |d u rt }t|dd}| ||}|r.|S |jdkrB|tS |j t| kr`|jksln |tS | r|t | S t|}| j }|jt | }|dkrd| | }n|dk r|| d }||d |d | }t | j |dpd| jS NTr r& rR r r r rP ri r rE rV r r r; rk r9 r: rl )r0 r r1 r> torotrotdigtopadZrotatedr) r) r+ rotate4 s. zDecimal.rotatec C s |d u rt }t|dd}| ||}|r.|S |jdkrB|tS d|j|j }d|j|j }|t| krz|ksn |tS | rt | S t | j | j | jt| }||}|S )NTr r& r r^ )r r r rP ri r rF rE rV r r r9 r: r; r )r0 r r1 r> ZliminfZlimsupr r) r) r+ scalebU s" zDecimal.scalebc C s |d u rt }t|dd}| ||}|r.|S |jdkrB|tS |j t| kr`|jksln |tS | r|t | S t|}| j }|jt | }|dkrd| | }n|dk r|| d }|dk r|d | }n |d| }||j d }t | j |dp d| jS r r )r0 r r1 r> r r r Zshiftedr) r) r+ r n s4 z Decimal.shiftc C s | j t| ffS r( ) __class__re r r) r) r+ __reduce__ s zDecimal.__reduce__c C s t | tu r| S | t| S r( typer r re r r) r) r+ __copy__ s zDecimal.__copy__c C s t | tu r| S | t| S r( r )r0 memor) r) r+ __deepcopy__ s zDecimal.__deepcopy__c C sJ |d u rt }t||d}| jrXt| j|}t| }|d dkrL|d7 }t|||S |d d u rvddg|j |d< |d dkrt | j| j | j d } |j }|d }|d ur|d dv r| |d |} nF|d d v r| | |} n*|d d v rt| j |kr| ||} | s@| j d kr@|d d v r@| d |} | j t| j } |d dv r~| sx|d urxd | } nd } nB|d d v r| } n.|d d v r| j d kr| d kr| } nd } | d k rd} d| | j } nP| t| j kr| j d| t| j } d} n"| j d | p d} | j | d } | | } t| j| | | |S )N) _localeconvr %gGr^ precisioneEr. zfF%ZgGr& r rR rT )r _parse_format_specifierrQ _format_signr: re r _format_alignr r9 r; rP rD rL r rk _format_number)r0 Z specifierr1 r specrB bodyrD r r r r{ r| rW r) r) r+ __format__ sZ zDecimal.__format__)rR N)NN)N)N)N)N)N)N)FN)N)N)N)TN)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)NN)N)N)NN)N)NN)NN)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)NN)r4 r5 r6 __slots__rc classmethodrv r 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__propertyr r r r r< r r r r r r r r r dictr r r r r r$ r8 rC rD rG r rJ r rL rN r to_integralrT r r r r r rZ r\ rW r` r r ra rW rd re rI r rh r rj r rk rl rq rv r: ry rz r| r r r r r r r r r r r r r r r r r r r r) r) r) r+ r s , !@ 2 4 V 7 ;! $ K f > , U n Y = " c * " I K 2 3 . * ! 'r Fc C s& t t}| |_||_||_||_|S r( )rb rc r r: r; rP rQ )rB Z coefficientr" Zspecialr0 r) r) r+ r9 s r9 c @ s$ e Zd Zdd Zdd Zdd ZdS )rN c C s | | _d S r( )rL new_context)r0 r r) r) r+ __init__ s z_ContextManager.__init__c C s t | _t| j | jS r( )r saved_contextr r r r) r) r+ __enter__ s z_ContextManager.__enter__c C s t | j d S r( )r r )r0 tvtbr) r) r+ __exit__ s z_ContextManager.__exit__N)r4 r5 r6 r r r r) r) r) r+ rN s rN c @ s e Zd ZdddZdd Zdd Zdd Zd d Zd d Zdd Z dd Z dd Z dd Z dd Z e ZdddZdd Zd d Zd d ZdZd d! Zd"d# Zd$d% Zdd'd(Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Z d3d4 Z d5d6 Z d7d8 Z d9d: Z d;d< Z!d=d> Z"d?d@ Z#dAdB Z$dCdD Z%dEdF Z&dGdH Z'dIdJ Z(dKdL Z)dMdN Z*dOdP Z+dQdR Z,dSdT Z-dUdV Z.dWdX Z/dYdZ Z0d[d\ Z1d]d^ Z2d_d` Z3dadb Z4dcdd Z5dedf Z6dgdh Z7didj Z8dkdl Z9dmdn Z:dodp Z;dqdr Z<dsdt Z=dudv Z>dwdx Z?dydz Z@d{d| ZAd}d~ ZBdd ZCdd ZDdd ZEdd ZFdddZGdd ZHdd ZIdd ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUeUZVdS )r Nc s< zt } W n ty Y n0 |d ur(|n| j| _|d ur<|n| j| _|d urP|n| j| _|d urd|n| j| _|d urx|n| j| _|d ur|n| j| _| d u rg | _n| | _d u r| j | _ n.t t st fddt D | _ n| _ d u rt t d| _n0t t s2t fddt D | _n | _d S )Nc 3 s | ]}|t | v fV qd S r( rV r r r= r) r+ <genexpr>I r- z#Context.__init__.<locals>.<genexpr>r& c 3 s | ]}|t | v fV qd S r( r r r> r) r+ r P r- )r NameErrorrE rD rH rF r r _ignored_flagsr= rL rd r r< fromkeysr> ) r0 rE rD rH rF r r r> r= r Zdcr) )r> r= r+ r 0 s. zContext.__init__c C s t |tstd| |dkr<||krtd||||f nJ|dkrb||k rtd||||f n$||k sr||krtd||||f t| ||S )Nz%s must be an integer-infz %s must be in [%s, %d]. got: %sr z %s must be in [%d, %s]. got: %sz %s must be in [%d, %d]. got %s)rd rV rw rq rb __setattr__)r0 namery ZvminZvmaxr) r) r+ _set_integer_checkT s zContext._set_integer_checkc C s` t |tstd| |D ]}|tvrtd| qtD ]}||vr8td| q8t| ||S )Nz%s must be a signal dictz %s is not a valid signal dict)rd r rw r< KeyErrorrb r )r0 r r keyr) r) r+ _set_signal_dictb s zContext._set_signal_dictc C s |dkr| ||ddS |dkr0| ||ddS |dkrH| ||ddS |dkr`| ||ddS |d krx| ||ddS |d kr|tvrtd | t| ||S |d ks|d kr| ||S |dkrt| ||S td| d S )NrE r. r rH r r& rF r r rD z%s: invalid rounding moder> r= r z.'decimal.Context' object has no attribute '%s')r _rounding_modesrw rb r r AttributeError)r0 r ry r) r) r+ r m s* zContext.__setattr__c C s t d| d S )Nz%s cannot be deleted)r )r0 r r) r) r+ __delattr__ s zContext.__delattr__c C sN dd | j D }dd | j D }| j| j| j| j| j| j| j ||ffS )Nc S s g | ]\}}|r|qS r) r) r sigr r) r) r+ r r- z&Context.__reduce__.<locals>.<listcomp>c S s g | ]\}}|r|qS r) r) r r) r) r+ r r- ) r> itemsr= r rE rD rH rF r r )r0 r> r= r) r) r+ r s zContext.__reduce__c C s| g }| dt| dd | j D }| dd| d dd | j D }| dd| d d|d S ) NzrContext(prec=%(prec)d, rounding=%(rounding)s, Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, clamp=%(clamp)dc S s g | ]\}}|r|j qS r) r4 )r r r r) r) r+ r r- z$Context.__repr__.<locals>.<listcomp>zflags=[z, ]c S s g | ]\}}|r|j qS r) r )r r r r) r) r+ r r- ztraps=[))rr varsr> r rs r= )r0 r namesr) r) r+ r s zContext.__repr__c C s | j D ]}d| j |< qd S r r r0 flagr) r) r+ rM s zContext.clear_flagsc C s | j D ]}d| j |< qd S r r r r) r) r+ clear_traps s zContext.clear_trapsc C s. t | j| j| j| j| j| j| j| j| j }|S r( ) r rE rD rH rF r r r> r= r r0 Zncr) r) r+ rO s zContext._shallow_copyc C s6 t | j| j| j| j| j| j| j | j | j }|S r( ) r rE rD rH rF r r r> rL r= r r r) r) r+ rL s z Context.copyc G s^ t ||}|| jv r*| j| g|R S d| j|< | j| sR| j| g|R S ||d S ri )_condition_maprH r r2 r> r= )r0 Z conditionZ explanationr* errorr) r) r+ ri s zContext._raise_errorc C s | j t S 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 ttfr |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 |tr*|| ks d|v r*| tdS t|| d}| r`t|j| j | j kr`| tdS | | 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| dS 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 |tstd| 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|| dS r[ )r r r0 r7 r r) r) r+ r [ s ! zContext.comparec C s t |dd}|j|| dS 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| dS r[ )r rW r r) r) r+ rW W s z Context.expc C s t |dd}|j||| dS r[ )r r )r0 r7 r rR r) r) r+ r o s z Context.fmac C s t |tstd| 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| dS 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| dS 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| dS r[ )r rv r r) r) r+ rv 6 s z Context.lnc C s t |dd}|j| dS r[ )r ry r r) r) r+ ry L s z Context.log10c C s t |dd}|j| dS r[ )r rz r r) r) r+ rz h s z Context.logbc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s zContext.logical_andc C s t |dd}|j| dS r[ )r r r r) r) r+ r s zContext.logical_invertc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s zContext.logical_orc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s zContext.logical_xorc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s z Context.maxc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s zContext.max_magc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s z Context.minc C s t |dd}|j|| dS r[ )r r r r) r) r+ r - s zContext.min_magc C s t |dd}|j| dS 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| dS r[ )r r r r) r) r+ r o s zContext.next_minusc C s t |dd}|j| dS r[ )r r r r) r) r+ r s zContext.next_plusc C s t |dd}|j|| dS r[ )r r r r) r) r+ r s zContext.next_towardc C s t |dd}|j| dS r[ )r rG r r) r) r+ rG s zContext.normalizec C s t |dd}|j| dS r[ )r r r r) r) r+ r s / zContext.number_classc C s t |dd}|j| dS 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|| dS r[ )r r r r) r) r+ r e s 7 zContext.quantizec C s t dS 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|| dS r[ )r r r r) r) r+ r s zContext.remainder_nearc C s t |dd}|j|| dS 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|| dS r[ )r r r r) r) r+ r $ s zContext.scalebc C s t |dd}|j|| dS r[ )r r r r) r) r+ r 7 s z Context.shiftc C s t |dd}|j| dS 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| dS r[ )r r r r) r) r+ r s zContext.to_eng_stringc C s t |dd}|j| dS r[ )r r r r) r) r+ to_sci_string s zContext.to_sci_stringc C s t |dd}|j| dS r[ )r rN r r) r) r+ rN s zContext.to_integral_exactc C s t |dd}|j| dS 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 ZdZdddZdd ZdS )rn rB rV rW Nc C sf |d u r d | _ d| _d | _nFt|trD|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 dd}||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 ddD ] }t||t|| | }qt|| |S )Nr& r. r\ r )rm r r r rV rk re r ) r0 MLr3 RTZyshiftwr r) r) r+ _ilog\ s" r c C s |d7 }t t| }|| || dk }|dkrd| }|| | }|dkrZ| d| 9 } nt| d| } t| |}t|}t|| |}|| } nd}t|d| } t| | dS 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}|rt tt|d }|| dkrt|t|| d| }qd}nd}t|| dS 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| jkrd}d|| d }tttd| |d}|| d d| krbql|d7 }q"|dd 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 ddD ]}t| || || }qPt|d ddD ]"}||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| }|dkrt t| | dk|dkkrd|d d d| } } qd| 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 2345678rC c C s0 | dkrt dt| }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 | tr| S t | tr t| S |r8t | tr8t| 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 |tr| |fS t |tjrR| jsDt| jtt| j |j | j } | t|j fS |rrt |tj rr|jdkrr|j}t |trt }|rd|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< |pd|d< |d d u rd |d < t|d pd |d < |d d urt|d |d < |d dkr|d d u s|d dv rd|d < |d dkrfd|d< |d u r&t }|d d ur@td| |d |d< |d |d< |d |d< n*|d d u r|d|d< ddg|d< d|d< |S )NzInvalid format specifier: fillalignzeropadz7Fill 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_regexmatchrq 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>|dkrt |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 tdd S )Nr& )chainrepeatr 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 ]}|dkr0tdttt| |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_widthsepr! 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 NumberregisterrN 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 recompileVERBOSE IGNORECASEr$ rf r r DOTALLr# localer& r r r0 r5 r r rs rr r= r^ r9 r] r@ hash_infomodulusr r r r r r r r) r) r) r+ <module>s s` # & . ^ 0",# %$+ * P % )