/opt/alt/python35/lib64/python3.5/__pycache__/_pydecimal.cpython-35.pyc (172101B)
0r r Trw )r rP r r r7 r r6 rO r rb r r@ rg rU rS rd r8 r r_ _shallow_copy _set_roundingr r? )r. r/ r; r@ opr clr r r r5 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)zReturns the larger value. Like max(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. r TNr- r% r )r r rP r r r r compare_total)r. r r/ snonr) 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)zReturns the smaller value. Like min(self, other) except if one is not a number, returns NaN (and signals if one is sNaN). Also rounds. r TNr- r% r )r r rP r r r r r, )r. r r/ r- r. 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)z"Returns whether self is an integerFr% TNrQ )rP rO r8 rd )r. restr' r' r) r ? s zDecimal._isintegerc C s2 | s | j d k r d S| j d | j d k S)z:Returns True if self is even. Assumes self is an integer.r% Tr- r r )rO r8 )r. r' r' r) r H s zDecimal._isevenc C s9 y | j t | j d SWn t k r4 d SYn Xd S)z$Return the adjusted exponent of selfr- r% N)rO rd r8 rp )r. r' r' r) r N s zDecimal.adjustedc C s | S)zReturns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. r' )r. r' r' r) canonicalV s zDecimal.canonicalc C sA t | d d } | j | | } | r. | S| j | d | S)zCompares self to the other operand numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. r Tr/ )r r r )r. r r/ r; r' r' r) compare_signal^ s zDecimal.compare_signalc C s t | d d } | j r) | j r) t S| j r@ | j r@ t S| j } | j } | j } | sm | rj| | k r t | j | j f } t | j | j f } | | k r | r t St S| | k r | r t St St S| r*| d k r t S| d k rt S| d k rt S| d k rjt Sn@ | d k r:t S| d k rJt S| d k rZt S| d k rjt S| | k rzt S| | k rt S| j | j k r| rt St S| j | j k r| rt St St S)zCompares self to other using the abstract representations. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. r Tr- r+ ) r r7 _NegativeOner r rd r8 _ZerorO )r. r r/ r= Zself_nanZ other_nanZself_keyZ other_keyr' r' r) r, j sf zDecimal.compare_totalc C s7 t | d d } | j } | j } | j | S)zCompares self to other using abstract repr., ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. r T)r r r, )r. r r/ r or' r' r) compare_total_mag s zDecimal.compare_total_magc C s t d | j | j | j S)z'Returns a copy with the sign set to 0. r% )r6 r8 rO rP )r. r' r' r) r s zDecimal.copy_absc C sE | j r% t d | j | j | j St d | j | j | j Sd S)z&Returns a copy with the sign inverted.r% r- N)r7 r6 r8 rO rP )r. r' r' r) r s zDecimal.copy_negatec C s1 t | d d } t | j | j | j | j S)z$Returns self with the sign of other.r T)r r6 r7 r8 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 rt d d | d | d } n t | } | j | j } } | j d k r| } d } xQ t | | | | \ } } | d d t t | | d r*P| d 7} qWt d t | | } | j } | j t } | j | } | | _ | S) zReturns e ** self.Nr/ r- r% rZ r rQ r> rw r r )r r r r3 r r r@ r r7 rd r_ rA r6 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)zReturn True if self is canonical; otherwise return False. Currently, the encoding of a Decimal instance is always canonical, so this method returns True for any Decimal. Tr' )r. r' r' r) is_canonical s zDecimal.is_canonicalc C s | j S)zReturn True if self is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. )rP )r. r' r' r) is_finite" s zDecimal.is_finitec C s | j d k S)z8Return True if self is infinite; otherwise return False.rY )rO )r. r' r' r) r! * s zDecimal.is_infinitec C s | j d k S)z>Return True if self is a qNaN or sNaN; otherwise return False.r5 rX )r5 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)z?Return True if self is a normal number; otherwise return False.FN)rP r r r )r. r/ r' r' r) is_normal2 s zDecimal.is_normalc C s | j d k S)z;Return True if self is a quiet NaN; otherwise return False.r5 )rO )r. r' r' r) r : s zDecimal.is_qnanc C s | j d k S)z8Return True if self is negative; otherwise return False.r- )r7 )r. r' r' r) is_signed> s zDecimal.is_signedc C s | j d k S)z?Return True if self is a signaling NaN; otherwise return False.rX )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)z9Return True if self is subnormal; otherwise return False.FN)rP r r r )r. r/ r' r' r) is_subnormalF s zDecimal.is_subnormalc C s | j o | j d k S)z6Return True if self is a zero; otherwise return False.rQ )rP r8 )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)zCompute a lower bound for the adjusted exponent of self.ln(). In other words, compute r such that self.ln() >= 10**r. Assumes that self is finite and positive and that self != 1. r- r r+ r% r r )rO rd r8 r_ rg rS rU )r. r8 r( r) r numdenr' 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) z/Returns the natural (base e) logarithm of self.Nr/ r- zln of a negative valuer+ rw r rZ r% )r r _NegativeInfinityr _Infinityr r3 r7 rb r rg rS rU r@ rB _dlogrd r_ rf r6 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) zCompute a lower bound for the adjusted exponent of self.log10(). In other words, find r such that self.log10() >= 10**r. Assumes that self is finite and positive and that self != 1. r- r+ r% r Z231r r )rO rd r8 r_ rg rS rU )r. r8 r( r) r r@ rA 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) z&Returns the base 10 logarithm of self.Nr/ r- zlog10 of a negative valuer% r rQ r+ rw r rZ )r r rC r rD r7 rb r r8 rd r rO rg rS rU r@ r _dlog10r_ rf r6 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)aM Returns the exponent of the magnitude of self's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of self (as though it were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). r/ Nzlogb(0)r- ) r r r rD 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)zReturn True if self is a logical operand. For being logical, it must be a finite number with a sign of 0, an exponent of 0, and a coefficient whose digits must all be either 0 or 1. r% FZ01T)r7 rO r8 )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/ opaopbZdifr' 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) z;Applies an 'and' operation between self and other's digits.Nr TrT c S s2 g | ]( \ } } t t | t | @ q Sr' )r_ rS ).0r br' r' r)5 s z'Decimal.logical_and. . r% rQ ) r r rL rb r rO r8 rl zipr6 re )r. r r/ rM rN r r' r' r) logical_and' s !%zDecimal.logical_andc C s8 | d k r t } | j t d d | j d | S)zInvert all its digits.Nr% r )r logical_xorr6 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) z:Applies an 'or' operation between self and other's digits.Nr TrT c S s2 g | ]( \ } } t t | t | B q Sr' )r_ rS )rP r rQ r' r' r) rR M s z&Decimal.logical_or. . r% rQ ) r r rL rb r rO r8 rl rS r6 re )r. r r/ rM rN 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) z;Applies an 'xor' operation between self and other's digits.Nr TrT c S s2 g | ]( \ } } t t | t | A q Sr' )r_ rS )rP r rQ r' r' r) rR ^ s z'Decimal.logical_xor. . r% rQ ) r r rL rb r rO r8 rl rS r6 re )r. r r/ rM rN r r' r' r) rU 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)z8Compares the values numerically with their sign ignored.r TNr- r% r ) r r rP r r r r r r, )r. r r/ r- r. 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)z8Compares the values numerically with their sign ignored.r TNr- r% r ) r r rP r r r r r r, )r. r r/ r- r. 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)z=Returns the largest representable number smaller than itself.Nr/ r- r% r> r r )r r r rC r6 r@ r rH 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)z=Returns the smallest representable number larger than itself.Nr/ r- r> r% r r )r r r rD r6 r@ r rH r' r rZ 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)a Returns the number closest to self, in the direction towards other. The result is the closest representable number to self (excluding self) that is in the direction towards other, unless both have the same value. If the two operands are numerically equal, then the result is a copy of self with the sign set to be the same as the sign of other. r TNr% r- z Infinite result from next_towardr )r r r r r6 r] r\ r rb r r7 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)a Returns an indication of the class of self. The class is one of the following strings: sNaN NaN -Infinity -Normal -Subnormal -Zero +Zero +Subnormal +Normal +Infinity r r r- z +Infinityz -Infinityz-Zeroz+ZeroNr/ z -Subnormalz +Subnormalz-Normalz+Normalr )r r r r> r7 r r= )r. r/ infr' r' r) number_class s, zDecimal.number_classc C s t d S)z'Just returns 10, as this is Decimal, :)r )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)z5Returns a rotated copy of self, value-of-other times.Nr Tr% rQ )r r r rO rb r r@ rS r r r8 rd r6 r7 re )r. r r/ r; torotrotdigtopadZrotatedr' 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)z>Returns self operand after adding the second value to its exp.Nr Tr% r+ r )r r r rO rb r rA r@ rS r r r6 r7 r8 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)z5Returns a shifted copy of self, value-of-other times.Nr Tr% rQ )r r r rO rb r r@ rS r r r8 rd r6 r7 re )r. r r/ r; rb rc rd 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 rg r_ )r. r' r' r) __copy__ s zDecimal.__copy__c C s) t | t k r | S| j t | S)N)ri r rg 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 rd | } 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 | pd } | j | d } | | } t | j | | | | S)a| Format a Decimal instance according to the given specifier. The specifier should be a standard format specifier, with the form described in PEP 3101. Formatting types 'e', 'E', 'f', 'F', 'g', 'G', 'n' and '%' are supported. If the formatting type is omitted it defaults to 'g' or 'G', depending on the value of context.capitals. N _localeconvri %gGr+ precisioneEr- zfF%ZgGr% r rQ rT i)r _parse_format_specifierrP _format_signr7 r_ r _format_alignr r6 r8 rO r? r$ r rd _format_number)r. Z specifierr/ rm specr= bodyr? rq r r rt ru rU r' r' r) __format__ sZ %& zDecimal.__format__)rO r8 r7 rP )r1 r2 r3 r4 __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 r9 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 r0 r1 r, r5 r r r6 rU r9 r: r! r r; r r< r r= r> rB rF r rI rJ rL rO rT rV rW rU rX rY r\ r] r^ r` ra re rf r rh rj rl ry r' r' r' r) r + s ( ! @ 4 V7; !$K f > ,U = " c*" I K 2 3 .* !' Fc C s7 t j t } | | _ | | _ | | _ | | _ | S)zCreate a decimal instance directly, without any validation, normalization (e.g. removal of leading zeros) or argument conversion. This function is for *internal use only*. )r\ r] r r7 r8 rO rP )r= Z coefficientr Zspecialr. r' r' r) r6 s r6 c @ s: e Z d Z d Z d d Z d d Z d d Z d S) rN zContext manager class to support localcontext(). Sets a copy of the supplied context in __enter__() and restores the previous decimal context in __exit__() c C s | j | _ d S)N)rH new_context)r. r r' r' r) __init__ s z_ContextManager.__init__c C s t | _ t | j | j S)N)r saved_contextr r )r. r' r' r) __enter__ s z_ContextManager.__enter__c C s t | j d S)N)r r )r. tvtbr' r' r) __exit__ s z_ContextManager.__exit__N)r1 r2 r3 r4 r r r r' r' r' r) rN s rN c @ s e Z d Z d Z d d d d d d d d d d d Z d d Z d d Z d d Z d d Z d d Z d d Z d d Z d d Z d d Z d d Z e Z d d d Z d d Z d d Z d d Z d Z d! d" Z d# d$ Z d% d& Z d' d( d) Z d* d+ Z d, d- Z d. d/ Z d0 d1 Z d2 d3 Z d4 d5 Z d6 d7 Z d8 d9 Z d: d; Z! d< d= Z" d> d? Z# d@ dA Z$ dB dC Z% dD dE Z& dF dG Z' dH dI Z( dJ dK Z) dL dM Z* dN dO Z+ dP dQ Z, dR dS Z- dT dU Z. dV dW Z/ dX dY Z0 dZ d[ Z1 d\ d] Z2 d^ d_ Z3 d` da Z4 db dc Z5 dd de Z6 df dg Z7 dh di Z8 dj dk Z9 dl dm Z: dn do Z; dp dq Z< dr ds Z= dt du Z> dv dw Z? dx dy Z@ dz d{ ZA d| d} ZB d~ d ZC d d ZD d d ZE d d ZF d d ZG d 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 d d ZV eV ZW d S)r a Contains the context for a Decimal instance. Contains: prec - precision (for use in rounding, division, square roots..) rounding - rounding type (how you round) traps - If traps[exception] = 1, then the exception is raised when it is caused. Otherwise, a value is substituted in. flags - When an exception is caused, flags[exception] is set. (Whether or not the trap_enabler is set) Should be reset by user of Decimal instance. Emin - Minimum exponent Emax - Maximum exponent capitals - If 1, 1*10^1 is printed as 1E+1. If 0, printed as 1e1 clamp - If 1, change exponents if too high (Default 0) 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 st f d d t D | _ n | _ d S)Nc 3 s' | ] } | t | k f Vq d S)N)rS )rP r )r r' r) < s z#Context.__init__. . r% c 3 s' | ] } | t | k f Vq d S)N)rS )rP r )r r' r) r C s )r NameErrorr@ r? r rA r r _ignored_flagsr rH r^ r r fromkeysr ) r. r@ r? r rA 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: %sr_ 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- r_ r z-infr% rA r r r? z%s: invalid rounding moder r r z.'decimal.Context' object has no attribute '%s')r _rounding_modesrp r\ r r rL )r. r rr r' r' r) r ` s( zContext.__setattr__c C s t d | d S)Nz%s cannot be deleted)rL )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' )rP sigr r' r' r) rR ~ s z&Context.__reduce__. . c S s" g | ] \ } } | r | q Sr' r' )rP r r r' r' r) rR s ) r itemsr rg r@ r? r rA r r )r. r r r' r' r) rh } 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) zShow the current context.zrContext(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 )rP r| r r' r' r) rR s z$Context.__repr__. . zflags=[z, ]c S s% g | ] \ } } | r | j q Sr' )r1 )rP r r r' r' r) rR s ztraps=[))rk varsr r rl r )r. r namesr' r' r) r s zContext.__repr__c C s% x | j D] } d | j | >> context = Context(prec=5, rounding=ROUND_DOWN) >>> context.create_decimal_from_float(3.1415926535897932) Decimal('3.1415') >>> context = Context(prec=5, traps=[Inexact]) >>> context.create_decimal_from_float(3.1415926535897932) Traceback (most recent call last): ... decimal.Inexact: None )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)a[ Returns the absolute value of the operand. If the operand is negative, the result is the same as using the minus operation on the operand. Otherwise, the result is the same as using the plus operation on the operand. >>> ExtendedContext.abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.abs(Decimal('101.5')) Decimal('101.5') >>> ExtendedContext.abs(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.abs(-1) Decimal('1') r 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)a Return the sum of the two operands. >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) Decimal('19.00') >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) Decimal('1.02E+4') >>> ExtendedContext.add(1, Decimal(2)) Decimal('3') >>> ExtendedContext.add(Decimal(8), 5) Decimal('13') >>> ExtendedContext.add(5, 5) Decimal('10') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ 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)zReturns the same Decimal object. As we do not have different encodings for the same number, the received object already is in its canonical form. >>> ExtendedContext.canonical(Decimal('2.50')) Decimal('2.50') z,canonical requires a Decimal as an argument.)r^ r rp r0 )r. r r' r' r) r0 A s zContext.canonicalc C s% t | d d } | j | d | S)a Compares values numerically. If the signs of the operands differ, a value representing each operand ('-1' if the operand is less than zero, '0' if the operand is zero or negative zero, or '1' if the operand is greater than zero) is used in place of that operand for the comparison instead of the actual operand. The comparison is then effected by subtracting the second operand from the first and then returning a value according to the result of the subtraction: '-1' if the result is less than zero, '0' if the result is zero or negative zero, or '1' if the result is greater than zero. >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) Decimal('-1') >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) Decimal('0') >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) Decimal('0') >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) Decimal('1') >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) Decimal('1') >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) Decimal('-1') >>> ExtendedContext.compare(1, 2) Decimal('-1') >>> ExtendedContext.compare(Decimal(1), 2) Decimal('-1') >>> ExtendedContext.compare(1, Decimal(2)) Decimal('-1') r Tr/ )r r )r. r rQ r' r' r) r N s !zContext.comparec C s% t | d d } | j | d | S)a Compares the values of the two operands numerically. It's pretty much like compare(), but all NaNs signal, with signaling NaNs taking precedence over quiet NaNs. >>> c = ExtendedContext >>> c.compare_signal(Decimal('2.1'), Decimal('3')) Decimal('-1') >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) Decimal('0') >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) Decimal('NaN') >>> print(c.flags[InvalidOperation]) 1 >>> c.flags[InvalidOperation] = 0 >>> print(c.flags[InvalidOperation]) 0 >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) Decimal('NaN') >>> print(c.flags[InvalidOperation]) 1 >>> c.compare_signal(-1, 2) Decimal('-1') >>> c.compare_signal(Decimal(-1), 2) Decimal('-1') >>> c.compare_signal(-1, Decimal(2)) Decimal('-1') r Tr/ )r r1 )r. r rQ r' r' r) r1 r s zContext.compare_signalc C s t | d d } | j | S)a+ Compares two operands using their abstract representation. This is not like the standard compare, which use their numerical value. Note that a total ordering is defined for all possible abstract representations. >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) Decimal('-1') >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) Decimal('0') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) Decimal('1') >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) Decimal('-1') >>> ExtendedContext.compare_total(1, 2) Decimal('-1') >>> ExtendedContext.compare_total(Decimal(1), 2) Decimal('-1') >>> ExtendedContext.compare_total(1, Decimal(2)) Decimal('-1') r T)r r, )r. r rQ r' r' r) r, s zContext.compare_totalc C s t | d d } | j | S)zCompares two operands using their abstract representation ignoring sign. Like compare_total, but with operand's sign ignored and assumed to be 0. r T)r r5 )r. r rQ r' r' r) r5 s zContext.compare_total_magc C s t | d d } | j S)a Returns a copy of the operand with the sign set to 0. >>> ExtendedContext.copy_abs(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_abs(Decimal('-100')) Decimal('100') >>> ExtendedContext.copy_abs(-1) Decimal('1') r T)r r )r. r r' r' r) r s zContext.copy_absc C s t | d d } t | S)a Returns a copy of the decimal object. >>> ExtendedContext.copy_decimal(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.copy_decimal(Decimal('-1.00')) Decimal('-1.00') >>> ExtendedContext.copy_decimal(1) Decimal('1') r T)r r )r. r r' r' r) copy_decimal s zContext.copy_decimalc C s t | d d } | j S)a( Returns a copy of the operand with the sign inverted. >>> ExtendedContext.copy_negate(Decimal('101.5')) Decimal('-101.5') >>> ExtendedContext.copy_negate(Decimal('-101.5')) Decimal('101.5') >>> ExtendedContext.copy_negate(1) Decimal('-1') r T)r r )r. r r' r' r) r s zContext.copy_negatec C s t | d d } | j | S)a Copies the second operand's sign to the first one. In detail, it returns a copy of the first operand with the sign equal to the sign of the second operand. >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) Decimal('1.50') >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) Decimal('-1.50') >>> ExtendedContext.copy_sign(1, -2) Decimal('-1') >>> ExtendedContext.copy_sign(Decimal(1), -2) Decimal('-1') >>> ExtendedContext.copy_sign(1, Decimal(-2)) Decimal('-1') r T)r r6 )r. r rQ r' r' r) r6 s zContext.copy_signc C sN t | d d } | j | d | } | t k rF t d | n | Sd S)a Decimal division in a specified context. >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) Decimal('0.333333333') >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) Decimal('0.666666667') >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) Decimal('2.5') >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) Decimal('0.1') >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) Decimal('1') >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) Decimal('4.00') >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) Decimal('1.20') >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) Decimal('10') >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) Decimal('1000') >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) Decimal('1.20E+6') >>> ExtendedContext.divide(5, 5) Decimal('1') >>> ExtendedContext.divide(Decimal(5), 5) Decimal('1') >>> ExtendedContext.divide(5, Decimal(5)) Decimal('1') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ r r' r' r) divide s zContext.dividec C sN t | d d } | j | d | } | t k rF t d | n | Sd S)a/ Divides two numbers and returns the integer part of the result. >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) Decimal('0') >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) Decimal('3') >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) Decimal('3') >>> ExtendedContext.divide_int(10, 3) Decimal('3') >>> ExtendedContext.divide_int(Decimal(10), 3) Decimal('3') >>> ExtendedContext.divide_int(10, Decimal(3)) Decimal('3') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ 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)a Return (a // b, a % b). >>> ExtendedContext.divmod(Decimal(8), Decimal(3)) (Decimal('2'), Decimal('2')) >>> ExtendedContext.divmod(Decimal(8), Decimal(4)) (Decimal('2'), Decimal('0')) >>> ExtendedContext.divmod(8, 4) (Decimal('2'), Decimal('0')) >>> ExtendedContext.divmod(Decimal(8), 4) (Decimal('2'), Decimal('0')) >>> ExtendedContext.divmod(8, Decimal(4)) (Decimal('2'), Decimal('0')) r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ r r' r' r) r 5 s zContext.divmodc C s" t | d d } | j d | S)a# Returns e ** a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.exp(Decimal('-Infinity')) Decimal('0') >>> c.exp(Decimal('-1')) Decimal('0.367879441') >>> c.exp(Decimal('0')) Decimal('1') >>> c.exp(Decimal('1')) Decimal('2.71828183') >>> c.exp(Decimal('0.693147181')) Decimal('2.00000000') >>> c.exp(Decimal('+Infinity')) Decimal('Infinity') >>> c.exp(10) Decimal('22026.4658') r Tr/ )r rU )r. r r' r' r) rU J s z Context.expc C s( t | d d } | j | | d | S)a Returns a multiplied by b, plus c. The first two operands are multiplied together, using multiply, the third operand is then added to the result of that multiplication, using add, all with only one final rounding. >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) Decimal('22') >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) Decimal('-8') >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) Decimal('1.38435736E+12') >>> ExtendedContext.fma(1, 3, 4) Decimal('7') >>> ExtendedContext.fma(1, Decimal(3), 4) Decimal('7') >>> ExtendedContext.fma(1, 3, Decimal(4)) Decimal('7') r Tr/ )r r )r. r rQ r) r' r' r) r b s z Context.fmac C s% t | t s t d | j S)a Return True if the operand is canonical; otherwise return False. Currently, the encoding of a Decimal instance is always canonical, so this method returns True for any Decimal. >>> ExtendedContext.is_canonical(Decimal('2.50')) True z/is_canonical requires a Decimal as an argument.)r^ r rp r9 )r. r r' r' r) r9 y s zContext.is_canonicalc C s t | d d } | j S)a, Return True if the operand is finite; otherwise return False. A Decimal instance is considered finite if it is neither infinite nor a NaN. >>> ExtendedContext.is_finite(Decimal('2.50')) True >>> ExtendedContext.is_finite(Decimal('-0.3')) True >>> ExtendedContext.is_finite(Decimal('0')) True >>> ExtendedContext.is_finite(Decimal('Inf')) False >>> ExtendedContext.is_finite(Decimal('NaN')) False >>> ExtendedContext.is_finite(1) True r T)r r: )r. r r' r' r) r: s zContext.is_finitec C s t | d d } | j S)aU Return True if the operand is infinite; otherwise return False. >>> ExtendedContext.is_infinite(Decimal('2.50')) False >>> ExtendedContext.is_infinite(Decimal('-Inf')) True >>> ExtendedContext.is_infinite(Decimal('NaN')) False >>> ExtendedContext.is_infinite(1) False r T)r r! )r. r r' r' r) r! s zContext.is_infinitec C s t | d d } | j S)aO Return True if the operand is a qNaN or sNaN; otherwise return False. >>> ExtendedContext.is_nan(Decimal('2.50')) False >>> ExtendedContext.is_nan(Decimal('NaN')) True >>> ExtendedContext.is_nan(Decimal('-sNaN')) True >>> ExtendedContext.is_nan(1) False r T)r r )r. r r' r' r) r s zContext.is_nanc C s" t | d d } | j d | S)a Return True if the operand is a normal number; otherwise return False. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.is_normal(Decimal('2.50')) True >>> c.is_normal(Decimal('0.1E-999')) False >>> c.is_normal(Decimal('0.00')) False >>> c.is_normal(Decimal('-Inf')) False >>> c.is_normal(Decimal('NaN')) False >>> c.is_normal(1) True r Tr/ )r r; )r. r r' r' r) r; s zContext.is_normalc C s t | d d } | j S)aH Return True if the operand is a quiet NaN; otherwise return False. >>> ExtendedContext.is_qnan(Decimal('2.50')) False >>> ExtendedContext.is_qnan(Decimal('NaN')) True >>> ExtendedContext.is_qnan(Decimal('sNaN')) False >>> ExtendedContext.is_qnan(1) False r T)r r )r. r r' r' r) r s zContext.is_qnanc C s t | d d } | j S)a Return True if the operand is negative; otherwise return False. >>> ExtendedContext.is_signed(Decimal('2.50')) False >>> ExtendedContext.is_signed(Decimal('-12')) True >>> ExtendedContext.is_signed(Decimal('-0')) True >>> ExtendedContext.is_signed(8) False >>> ExtendedContext.is_signed(-8) True r T)r r< )r. r r' r' r) r< s zContext.is_signedc C s t | d d } | j S)aT Return True if the operand is a signaling NaN; otherwise return False. >>> ExtendedContext.is_snan(Decimal('2.50')) False >>> ExtendedContext.is_snan(Decimal('NaN')) False >>> ExtendedContext.is_snan(Decimal('sNaN')) True >>> ExtendedContext.is_snan(1) False r T)r r )r. r r' r' r) r s zContext.is_snanc C s" t | d d } | j d | S)a Return True if the operand is subnormal; otherwise return False. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.is_subnormal(Decimal('2.50')) False >>> c.is_subnormal(Decimal('0.1E-999')) True >>> c.is_subnormal(Decimal('0.00')) False >>> c.is_subnormal(Decimal('-Inf')) False >>> c.is_subnormal(Decimal('NaN')) False >>> c.is_subnormal(1) False r Tr/ )r r= )r. r r' r' r) r= s zContext.is_subnormalc C s t | d d } | j S)au Return True if the operand is a zero; otherwise return False. >>> ExtendedContext.is_zero(Decimal('0')) True >>> ExtendedContext.is_zero(Decimal('2.50')) False >>> ExtendedContext.is_zero(Decimal('-0E+2')) True >>> ExtendedContext.is_zero(1) False >>> ExtendedContext.is_zero(0) True r T)r r> )r. r r' r' r) r> s zContext.is_zeroc C s" t | d d } | j d | S)a Returns the natural (base e) logarithm of the operand. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.ln(Decimal('0')) Decimal('-Infinity') >>> c.ln(Decimal('1.000')) Decimal('0') >>> c.ln(Decimal('2.71828183')) Decimal('1.00000000') >>> c.ln(Decimal('10')) Decimal('2.30258509') >>> c.ln(Decimal('+Infinity')) Decimal('Infinity') >>> c.ln(1) Decimal('0') r Tr/ )r rF )r. r r' r' r) rF ) s z Context.lnc C s" t | d d } | j d | S)a Returns the base 10 logarithm of the operand. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.log10(Decimal('0')) Decimal('-Infinity') >>> c.log10(Decimal('0.001')) Decimal('-3') >>> c.log10(Decimal('1.000')) Decimal('0') >>> c.log10(Decimal('2')) Decimal('0.301029996') >>> c.log10(Decimal('10')) Decimal('1') >>> c.log10(Decimal('70')) Decimal('1.84509804') >>> c.log10(Decimal('+Infinity')) Decimal('Infinity') >>> c.log10(0) Decimal('-Infinity') >>> c.log10(1) Decimal('0') r Tr/ )r rI )r. r r' r' r) rI ? s z Context.log10c C s" t | d d } | j d | S)a4 Returns the exponent of the magnitude of the operand's MSD. The result is the integer which is the exponent of the magnitude of the most significant digit of the operand (as though the operand were truncated to a single digit while maintaining the value of that digit and without limiting the resulting exponent). >>> ExtendedContext.logb(Decimal('250')) Decimal('2') >>> ExtendedContext.logb(Decimal('2.50')) Decimal('0') >>> ExtendedContext.logb(Decimal('0.03')) Decimal('-2') >>> ExtendedContext.logb(Decimal('0')) Decimal('-Infinity') >>> ExtendedContext.logb(1) Decimal('0') >>> ExtendedContext.logb(10) Decimal('1') >>> ExtendedContext.logb(100) Decimal('2') r Tr/ )r rJ )r. r r' r' r) rJ [ s z Context.logbc C s% t | d d } | j | d | S)a Applies the logical operation 'and' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) Decimal('0') >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) Decimal('1000') >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) Decimal('10') >>> ExtendedContext.logical_and(110, 1101) Decimal('100') >>> ExtendedContext.logical_and(Decimal(110), 1101) Decimal('100') >>> ExtendedContext.logical_and(110, Decimal(1101)) Decimal('100') r Tr/ )r rT )r. r rQ r' r' r) rT u s zContext.logical_andc C s" t | d d } | j d | S)a Invert all the digits in the operand. The operand must be a logical number. >>> ExtendedContext.logical_invert(Decimal('0')) Decimal('111111111') >>> ExtendedContext.logical_invert(Decimal('1')) Decimal('111111110') >>> ExtendedContext.logical_invert(Decimal('111111111')) Decimal('0') >>> ExtendedContext.logical_invert(Decimal('101010101')) Decimal('10101010') >>> ExtendedContext.logical_invert(1101) Decimal('111110010') r Tr/ )r rV )r. r r' r' r) rV s zContext.logical_invertc C s% t | d d } | j | d | S)a Applies the logical operation 'or' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) Decimal('1110') >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) Decimal('1110') >>> ExtendedContext.logical_or(110, 1101) Decimal('1111') >>> ExtendedContext.logical_or(Decimal(110), 1101) Decimal('1111') >>> ExtendedContext.logical_or(110, Decimal(1101)) Decimal('1111') r Tr/ )r rW )r. r rQ r' r' r) rW s zContext.logical_orc C s% t | d d } | j | d | S)a Applies the logical operation 'xor' between each operand's digits. The operands must be both logical numbers. >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) Decimal('0') >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) Decimal('1') >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) Decimal('1') >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) Decimal('0') >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) Decimal('110') >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) Decimal('1101') >>> ExtendedContext.logical_xor(110, 1101) Decimal('1011') >>> ExtendedContext.logical_xor(Decimal(110), 1101) Decimal('1011') >>> ExtendedContext.logical_xor(110, Decimal(1101)) Decimal('1011') r Tr/ )r rU )r. r rQ r' r' r) rU s zContext.logical_xorc C s% t | d d } | j | d | S)a max compares two values numerically and returns the maximum. If either operand is a NaN then the general rules apply. Otherwise, the operands are compared as though by the compare operation. If they are numerically equal then the left-hand operand is chosen as the result. Otherwise the maximum (closer to positive infinity) of the two operands is chosen as the result. >>> ExtendedContext.max(Decimal('3'), Decimal('2')) Decimal('3') >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) Decimal('3') >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) Decimal('1') >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) Decimal('7') >>> ExtendedContext.max(1, 2) Decimal('2') >>> ExtendedContext.max(Decimal(1), 2) Decimal('2') >>> ExtendedContext.max(1, Decimal(2)) Decimal('2') r Tr/ )r r )r. r rQ r' r' r) r s z Context.maxc C s% t | d d } | j | d | S)a Compares the values numerically with their sign ignored. >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN')) Decimal('7') >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10')) Decimal('-10') >>> ExtendedContext.max_mag(1, -2) Decimal('-2') >>> ExtendedContext.max_mag(Decimal(1), -2) Decimal('-2') >>> ExtendedContext.max_mag(1, Decimal(-2)) Decimal('-2') r Tr/ )r rX )r. r rQ r' r' r) rX s zContext.max_magc C s% t | d d } | j | d | S)a min compares two values numerically and returns the minimum. If either operand is a NaN then the general rules apply. Otherwise, the operands are compared as though by the compare operation. If they are numerically equal then the left-hand operand is chosen as the result. Otherwise the minimum (closer to negative infinity) of the two operands is chosen as the result. >>> ExtendedContext.min(Decimal('3'), Decimal('2')) Decimal('2') >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) Decimal('-10') >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) Decimal('1.0') >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) Decimal('7') >>> ExtendedContext.min(1, 2) Decimal('1') >>> ExtendedContext.min(Decimal(1), 2) Decimal('1') >>> ExtendedContext.min(1, Decimal(29)) Decimal('1') r Tr/ )r r )r. r rQ r' r' r) r s z Context.minc C s% t | d d } | j | d | S)a Compares the values numerically with their sign ignored. >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2')) Decimal('-2') >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN')) Decimal('-3') >>> ExtendedContext.min_mag(1, -2) Decimal('1') >>> ExtendedContext.min_mag(Decimal(1), -2) Decimal('1') >>> ExtendedContext.min_mag(1, Decimal(-2)) Decimal('1') r Tr/ )r rY )r. r rQ r' r' r) rY s zContext.min_magc C s" t | d d } | j d | S)a Minus corresponds to unary prefix minus in Python. The operation is evaluated using the same rules as subtract; the operation minus(a) is calculated as subtract('0', a) where the '0' has the same exponent as the operand. >>> ExtendedContext.minus(Decimal('1.3')) Decimal('-1.3') >>> ExtendedContext.minus(Decimal('-1.3')) Decimal('1.3') >>> ExtendedContext.minus(1) Decimal('-1') r 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)a multiply multiplies two operands. If either operand is a special value then the general rules apply. Otherwise, the operands are multiplied together ('long multiplication'), resulting in a number which may be as long as the sum of the lengths of the two operands. >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) Decimal('3.60') >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) Decimal('21') >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) Decimal('0.72') >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) Decimal('-0.0') >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) Decimal('4.28135971E+11') >>> ExtendedContext.multiply(7, 7) Decimal('49') >>> ExtendedContext.multiply(Decimal(7), 7) Decimal('49') >>> ExtendedContext.multiply(7, Decimal(7)) Decimal('49') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ r r' r' r) multiplyB s zContext.multiplyc C s" t | d d } | j d | S)a" Returns the largest representable number smaller than a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> ExtendedContext.next_minus(Decimal('1')) Decimal('0.999999999') >>> c.next_minus(Decimal('1E-1007')) Decimal('0E-1007') >>> ExtendedContext.next_minus(Decimal('-1.00000003')) Decimal('-1.00000004') >>> c.next_minus(Decimal('Infinity')) Decimal('9.99999999E+999') >>> c.next_minus(1) Decimal('0.999999999') r Tr/ )r r\ )r. r r' r' r) r\ b s zContext.next_minusc C s" t | d d } | j d | S)a Returns the smallest representable number larger than a. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> ExtendedContext.next_plus(Decimal('1')) Decimal('1.00000001') >>> c.next_plus(Decimal('-1E-1007')) Decimal('-0E-1007') >>> ExtendedContext.next_plus(Decimal('-1.00000003')) Decimal('-1.00000002') >>> c.next_plus(Decimal('-Infinity')) Decimal('-9.99999999E+999') >>> c.next_plus(1) Decimal('1.00000001') r Tr/ )r r] )r. r r' r' r) r] v s zContext.next_plusc C s% t | d d } | j | d | S)a Returns the number closest to a, in direction towards b. The result is the closest representable number from the first operand (but not the first operand) that is in the direction towards the second operand, unless the operands have the same value. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.next_toward(Decimal('1'), Decimal('2')) Decimal('1.00000001') >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) Decimal('-0E-1007') >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) Decimal('-1.00000002') >>> c.next_toward(Decimal('1'), Decimal('0')) Decimal('0.999999999') >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) Decimal('0E-1007') >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) Decimal('-1.00000004') >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) Decimal('-0.00') >>> c.next_toward(0, 1) Decimal('1E-1007') >>> c.next_toward(Decimal(0), 1) Decimal('1E-1007') >>> c.next_toward(0, Decimal(1)) Decimal('1E-1007') r Tr/ )r r^ )r. r rQ r' r' r) r^ s zContext.next_towardc C s" t | d d } | j d | S)a normalize reduces an operand to its simplest form. Essentially a plus operation with all trailing zeros removed from the result. >>> ExtendedContext.normalize(Decimal('2.1')) Decimal('2.1') >>> ExtendedContext.normalize(Decimal('-2.0')) Decimal('-2') >>> ExtendedContext.normalize(Decimal('1.200')) Decimal('1.2') >>> ExtendedContext.normalize(Decimal('-120')) Decimal('-1.2E+2') >>> ExtendedContext.normalize(Decimal('120.00')) Decimal('1.2E+2') >>> ExtendedContext.normalize(Decimal('0.00')) Decimal('0') >>> ExtendedContext.normalize(6) Decimal('6') r Tr/ )r r )r. r r' r' r) r s zContext.normalizec C s" t | d d } | j d | S)a Returns an indication of the class of the operand. The class is one of the following strings: -sNaN -NaN -Infinity -Normal -Subnormal -Zero +Zero +Subnormal +Normal +Infinity >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.number_class(Decimal('Infinity')) '+Infinity' >>> c.number_class(Decimal('1E-10')) '+Normal' >>> c.number_class(Decimal('2.50')) '+Normal' >>> c.number_class(Decimal('0.1E-999')) '+Subnormal' >>> c.number_class(Decimal('0')) '+Zero' >>> c.number_class(Decimal('-0')) '-Zero' >>> c.number_class(Decimal('-0.1E-999')) '-Subnormal' >>> c.number_class(Decimal('-1E-10')) '-Normal' >>> c.number_class(Decimal('-2.50')) '-Normal' >>> c.number_class(Decimal('-Infinity')) '-Infinity' >>> c.number_class(Decimal('NaN')) 'NaN' >>> c.number_class(Decimal('-NaN')) 'NaN' >>> c.number_class(Decimal('sNaN')) 'sNaN' >>> c.number_class(123) '+Normal' r Tr/ )r r` )r. r r' r' r) r` s /zContext.number_classc C s" t | d d } | j d | S)a Plus corresponds to unary prefix plus in Python. The operation is evaluated using the same rules as add; the operation plus(a) is calculated as add('0', a) where the '0' has the same exponent as the operand. >>> ExtendedContext.plus(Decimal('1.3')) Decimal('1.3') >>> ExtendedContext.plus(Decimal('-1.3')) Decimal('-1.3') >>> ExtendedContext.plus(-1) Decimal('-1') r 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)a Raises a to the power of b, to modulo if given. With two arguments, compute a**b. If a is negative then b must be integral. The result will be inexact unless b is integral and the result is finite and can be expressed exactly in 'precision' digits. With three arguments, compute (a**b) % modulo. For the three argument form, the following restrictions on the arguments hold: - all three arguments must be integral - b must be nonnegative - at least one of a or b must be nonzero - modulo must be nonzero and have at most 'precision' digits The result of pow(a, b, modulo) is identical to the result that would be obtained by computing (a**b) % modulo with unbounded precision, but is computed more efficiently. It is always exact. >>> c = ExtendedContext.copy() >>> c.Emin = -999 >>> c.Emax = 999 >>> c.power(Decimal('2'), Decimal('3')) Decimal('8') >>> c.power(Decimal('-2'), Decimal('3')) Decimal('-8') >>> c.power(Decimal('2'), Decimal('-3')) Decimal('0.125') >>> c.power(Decimal('1.7'), Decimal('8')) Decimal('69.7575744') >>> c.power(Decimal('10'), Decimal('0.301029996')) Decimal('2.00000000') >>> c.power(Decimal('Infinity'), Decimal('-1')) Decimal('0') >>> c.power(Decimal('Infinity'), Decimal('0')) Decimal('1') >>> c.power(Decimal('Infinity'), Decimal('1')) Decimal('Infinity') >>> c.power(Decimal('-Infinity'), Decimal('-1')) Decimal('-0') >>> c.power(Decimal('-Infinity'), Decimal('0')) Decimal('1') >>> c.power(Decimal('-Infinity'), Decimal('1')) Decimal('-Infinity') >>> c.power(Decimal('-Infinity'), Decimal('2')) Decimal('Infinity') >>> c.power(Decimal('0'), Decimal('0')) Decimal('NaN') >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) Decimal('11') >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) Decimal('-11') >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) Decimal('1') >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) Decimal('11') >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) Decimal('11729830') >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) Decimal('-0') >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) Decimal('1') >>> ExtendedContext.power(7, 7) Decimal('823543') >>> ExtendedContext.power(Decimal(7), 7) Decimal('823543') >>> ExtendedContext.power(7, Decimal(7), 2) Decimal('1') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ r r r' r' r) power s I z Context.powerc C s% t | d d } | j | d | S)a Returns a value equal to 'a' (rounded), having the exponent of 'b'. The coefficient of the result is derived from that of the left-hand operand. It may be rounded using the current rounding setting (if the exponent is being increased), multiplied by a positive power of ten (if the exponent is being decreased), or is unchanged (if the exponent is already equal to that of the right-hand operand). Unlike other operations, if the length of the coefficient after the quantize operation would be greater than precision then an Invalid operation condition is raised. This guarantees that, unless there is an error condition, the exponent of the result of a quantize is always equal to that of the right-hand operand. Also unlike other operations, quantize will never raise Underflow, even if the result is subnormal and inexact. >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) Decimal('2.170') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) Decimal('2.17') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) Decimal('2.2') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) Decimal('2') >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) Decimal('0E+1') >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) Decimal('-Infinity') >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) Decimal('-0') >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) Decimal('-0E+5') >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) Decimal('NaN') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) Decimal('217.0') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) Decimal('217') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) Decimal('2.2E+2') >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) Decimal('2E+2') >>> ExtendedContext.quantize(1, 2) Decimal('1') >>> ExtendedContext.quantize(Decimal(1), 2) Decimal('1') >>> ExtendedContext.quantize(1, Decimal(2)) Decimal('1') r Tr/ )r r )r. r rQ r' r' r) r X s 7zContext.quantizec C s t d S)zkJust returns 10, as this is Decimal, :) >>> ExtendedContext.radix() Decimal('10') r )r )r. r' r' r) ra s z Context.radixc C sN t | d d } | j | d | } | t k rF t d | n | Sd S)a Returns the remainder from integer division. The result is the residue of the dividend after the operation of calculating integer division as described for divide-integer, rounded to precision digits if necessary. The sign of the result, if non-zero, is the same as that of the original dividend. This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated). >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) Decimal('2.1') >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) Decimal('1') >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) Decimal('-1') >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) Decimal('0.2') >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) Decimal('0.1') >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) Decimal('1.0') >>> ExtendedContext.remainder(22, 6) Decimal('4') >>> ExtendedContext.remainder(Decimal(22), 6) Decimal('4') >>> ExtendedContext.remainder(22, Decimal(6)) Decimal('4') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ r r' r' r) r s zContext.remainderc C s% t | d d } | j | d | S)aG Returns to be "a - b * n", where n is the integer nearest the exact value of "x / b" (if two integers are equally near then the even one is chosen). If the result is equal to 0 then its sign will be the sign of a. This operation will fail under the same conditions as integer division (that is, if integer division on the same two operands would fail, the remainder cannot be calculated). >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) Decimal('-0.9') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) Decimal('-2') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) Decimal('1') >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) Decimal('-1') >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) Decimal('0.2') >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) Decimal('0.1') >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) Decimal('-0.3') >>> ExtendedContext.remainder_near(3, 11) Decimal('3') >>> ExtendedContext.remainder_near(Decimal(3), 11) Decimal('3') >>> ExtendedContext.remainder_near(3, Decimal(11)) Decimal('3') r Tr/ )r r )r. r rQ r' r' r) r s zContext.remainder_nearc C s% t | d d } | j | d | S)aN Returns a rotated copy of a, b times. The coefficient of the result is a rotated copy of the digits in the coefficient of the first operand. The number of places of rotation is taken from the absolute value of the second operand, with the rotation being to the left if the second operand is positive or to the right otherwise. >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) Decimal('400000003') >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) Decimal('12') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) Decimal('891234567') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) Decimal('123456789') >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) Decimal('345678912') >>> ExtendedContext.rotate(1333333, 1) Decimal('13333330') >>> ExtendedContext.rotate(Decimal(1333333), 1) Decimal('13333330') >>> ExtendedContext.rotate(1333333, Decimal(1)) Decimal('13333330') r Tr/ )r re )r. r rQ r' r' r) re s zContext.rotatec C s t | d d } | j | S)a Returns True if the two operands have the same exponent. The result is never affected by either the sign or the coefficient of either operand. >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) False >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) True >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) False >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) True >>> ExtendedContext.same_quantum(10000, -1) True >>> ExtendedContext.same_quantum(Decimal(10000), -1) True >>> ExtendedContext.same_quantum(10000, Decimal(-1)) True r T)r r" )r. r rQ r' r' r) r" s zContext.same_quantumc C s% t | d d } | j | d | S)a3 Returns the first operand after adding the second value its exp. >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) Decimal('0.0750') >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) Decimal('7.50') >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) Decimal('7.50E+3') >>> ExtendedContext.scaleb(1, 4) Decimal('1E+4') >>> ExtendedContext.scaleb(Decimal(1), 4) Decimal('1E+4') >>> ExtendedContext.scaleb(1, Decimal(4)) Decimal('1E+4') r Tr/ )r rf )r. r rQ r' r' r) rf s zContext.scalebc C s% t | d d } | j | d | S)a{ Returns a shifted copy of a, b times. The coefficient of the result is a shifted copy of the digits in the coefficient of the first operand. The number of places to shift is taken from the absolute value of the second operand, with the shift being to the left if the second operand is positive or to the right otherwise. Digits shifted into the coefficient are zeros. >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) Decimal('400000000') >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) Decimal('0') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) Decimal('1234567') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) Decimal('123456789') >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) Decimal('345678900') >>> ExtendedContext.shift(88888888, 2) Decimal('888888800') >>> ExtendedContext.shift(Decimal(88888888), 2) Decimal('888888800') >>> ExtendedContext.shift(88888888, Decimal(2)) Decimal('888888800') r Tr/ )r r )r. r rQ r' r' r) r * s z Context.shiftc C s" t | d d } | j d | S)a Square root of a non-negative number to context precision. If the result must be inexact, it is rounded using the round-half-even algorithm. >>> ExtendedContext.sqrt(Decimal('0')) Decimal('0') >>> ExtendedContext.sqrt(Decimal('-0')) Decimal('-0') >>> ExtendedContext.sqrt(Decimal('0.39')) Decimal('0.624499800') >>> ExtendedContext.sqrt(Decimal('100')) Decimal('10') >>> ExtendedContext.sqrt(Decimal('1')) Decimal('1') >>> ExtendedContext.sqrt(Decimal('1.0')) Decimal('1.0') >>> ExtendedContext.sqrt(Decimal('1.00')) Decimal('1.0') >>> ExtendedContext.sqrt(Decimal('7')) Decimal('2.64575131') >>> ExtendedContext.sqrt(Decimal('10')) Decimal('3.16227766') >>> ExtendedContext.sqrt(2) Decimal('1.41421356') >>> ExtendedContext.prec 9 r 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)a& Return the difference between the two operands. >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) Decimal('0.23') >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) Decimal('0.00') >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) Decimal('-0.77') >>> ExtendedContext.subtract(8, 5) Decimal('3') >>> ExtendedContext.subtract(Decimal(8), 5) Decimal('3') >>> ExtendedContext.subtract(8, Decimal(5)) Decimal('3') r Tr/ z Unable to convert %s to DecimalN)r r r rp )r. r rQ r r' r' r) subtracth s zContext.subtractc C s" t | d d } | j d | S)a Convert to a string, using engineering notation if an exponent is needed. Engineering notation has an exponent which is a multiple of 3. This can leave up to 3 digits to the left of the decimal place and may require the addition of either one or two trailing zeros. The operation is not affected by the context. >>> ExtendedContext.to_eng_string(Decimal('123E+1')) '1.23E+3' >>> ExtendedContext.to_eng_string(Decimal('123E+3')) '123E+3' >>> ExtendedContext.to_eng_string(Decimal('123E-10')) '12.3E-9' >>> ExtendedContext.to_eng_string(Decimal('-123E-12')) '-123E-12' >>> ExtendedContext.to_eng_string(Decimal('7E-7')) '700E-9' >>> ExtendedContext.to_eng_string(Decimal('7E+1')) '70' >>> ExtendedContext.to_eng_string(Decimal('0E+1')) '0.00E+3' r Tr/ )r r )r. r r' r' r) r s zContext.to_eng_stringc C s" t | d d } | j d | S)zyConverts a number to a string, using scientific notation. The operation is not affected by the context. r Tr/ )r r )r. r r' r' r) to_sci_string s zContext.to_sci_stringc C s" t | d d } | j d | S)ak Rounds to an integer. When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting; Inexact and Rounded flags are allowed in this operation. The rounding mode is taken from the context. >>> ExtendedContext.to_integral_exact(Decimal('2.1')) Decimal('2') >>> ExtendedContext.to_integral_exact(Decimal('100')) Decimal('100') >>> ExtendedContext.to_integral_exact(Decimal('100.0')) Decimal('100') >>> ExtendedContext.to_integral_exact(Decimal('101.5')) Decimal('102') >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) Decimal('-102') >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) Decimal('1.0E+6') >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) Decimal('7.89E+77') >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) Decimal('-Infinity') r Tr/ )r r% )r. r r' r' r) r% s zContext.to_integral_exactc C s" t | d d } | j d | S)aL Rounds to an integer. When the operand has a negative exponent, the result is the same as using the quantize() operation using the given operand as the left-hand-operand, 1E+0 as the right-hand-operand, and the precision of the operand as the precision setting, except that no flags will be set. The rounding mode is taken from the context. >>> ExtendedContext.to_integral_value(Decimal('2.1')) Decimal('2') >>> ExtendedContext.to_integral_value(Decimal('100')) Decimal('100') >>> ExtendedContext.to_integral_value(Decimal('100.0')) Decimal('100') >>> ExtendedContext.to_integral_value(Decimal('101.5')) Decimal('102') >>> ExtendedContext.to_integral_value(Decimal('-101.5')) Decimal('-102') >>> ExtendedContext.to_integral_value(Decimal('10E+5')) Decimal('1.0E+6') >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) Decimal('7.89E+77') >>> ExtendedContext.to_integral_value(Decimal('-Inf')) Decimal('-Infinity') r Tr/ )r r )r. r r' r' r) r s zContext.to_integral_value)Xr1 r2 r3 r4 r r r r r rh r rI r r& rH rj rb rZ r r r r r r' r r rf r r r0 r r1 r, r5 r r r r6 r r r rU r r9 r: r! r r; r r< r r= r> rF rI rJ rT rV rW rU r rX r rY r r r\ r] r^ r r` r r r ra r r re r" rf 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 r7 r8 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 rz 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)zcNormalizes op1, op2 to have the same exp and length of coefficient. Done during addition. r- r+ r r )rU rd r_ rS r )r r r@ Ztmpr 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)a Given integers n and e, return n * 10**e if it's an integer, else None. The computation is designed to avoid computing large powers of 10 unnecessarily. >>> _decimal_lshift_exact(3, 4) 30000 >>> _decimal_lshift_exact(300, -999999999) # returns None r% r rQ N)r_ rf rd rstrip)r5 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)zClosest integer to the square root of the positive integer n. a is an initial approximation to the square root. Any positive integer will do for a, but the closer a is to the square root of n the faster convergence will be. r% z3Both arguments to _sqrt_nearest should be positive.r- )rj )r5 r rQ r' r' r) _sqrt_nearest2 s r c C s7 d | >| | ?} } | d | | d @| d @| k S)zGiven an integer x and a nonnegative integer shift, return closest integer to x / 2**shift; use round-to-even in case of a tie. r- r+ r' )r r rQ r r' r' r) _rshift_nearestA s r c C s/ t | | \ } } | d | | d @| k S)zaClosest integer to a/b, a and b positive integers; rounds to even in the case of a tie. r+ r- )r )r rQ 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)a Integer approximation to M*log(x/M), with absolute error boundable in terms only of x/M. Given positive integers x and M, return an integer approximation to M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference between the approximation and the exact result is at most 22. For L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In both cases these are upper bounds on the error; it will usually be much smaller.r% r- r rZ ir )rf r r r rS rd r_ r ) r MLr RTZyshiftwr~ 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)zGiven integers c, e and p with c > 0, p >= 0, compute an integer approximation to 10**p * log10(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.r+ r- r% r r )rd r_ r r _log10_digits) r) r r r* r| r r~ log_dZlog_10Z log_tenpowerr' r' r) rH s rH 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)zGiven integers c, e and p with c > 0, compute an integer approximation to 10**p * log(c*10**e), with an absolute error of at most 1. Assumes that c*10**e is not exactly 1.r+ r- r% r r )rd r_ r r rf r ) r) r r r* r| r~ r r Z f_log_tenr' r' r) rE s" $ rE c @ s. e Z d Z d Z d d Z d d Z d S) _Log10MemoizezClass to compute, store, and allow retrieval of, digits of the constant log(10) = 2.302585.... This constant is needed by Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.c 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) ztGiven an integer p >= 0, return floor(10**p)*log(10). For example, self.getdigits(3) returns 2302. r% zp should be nonnegativerZ r r+ r NrQ 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 r4 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) zGiven integers x and M, M > 0, such that x/M is small in absolute value, compute an integer approximation to M*exp(x/M). For 0 <= x/M <= 2.4, the absolute error in the result is bounded by 60 (and is usually much smaller).r rZ r- r% r+ ir 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)a Compute an approximation to exp(c*10**e), with p decimal places of precision. Returns integers d, f such that: 10**(p-1) <= d <= 10**p, and (d-1)*10**f < exp(c*10**e) < (d+1)*10**f In other words, d*10**f is an approximation to exp(c*10**e) with p digits of precision, and with an error in d of at most 1. This is almost, but not quite, the same as the error being < 1ulp: when d = 10**(p-1) the error could be up to 10 ulp.r+ r% r- r i rZ )r rd r_ r r r r ) r) r r r r r ZcshiftZquotr r' r' r) r7 s # r7 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)a5 Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 10**(p-1) <= c <= 10**p, and (c-1)*10**e < x**y < (c+1)*10**e in other words, c*10**e is an approximation to x**y with p digits of precision, and with an error in c of at most 1. (This is almost, but not quite, the same as the error being < 1ulp: when c == 10**(p-1) we can only guarantee error < 10ulp.) We assume that: x is positive and not equal to 1, and y is nonzero. r- r% r )rd r_ rf rE r r7 ) r r r r r rQ Zlxcr Zpcr rU r' r' r) r = s ( ! r r r 2F 35 4( 5 6r? 7 8r r> rw c C s> | d k r t d t | } d t | | | d S)z@Compute a lower bound for 100*log10(c) for a positive integer c.r% 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)zConvert other to Decimal. Verifies that it's ok to use in an implicit construction. If allow_float is true, allow conversion from float; this is used in the comparison methods (__eq__ and friends). z 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[-+])? # an optional sign, followed by either... ( (?=\d|\.\d) # ...a number (with at least one digit) (?P \d*) # having a (possibly empty) integer part (\.(?P \d*))? # followed by an optional fractional part (E(?P [-+]?\d+))? # followed by an optional exponent, or... | Inf(inity)? # ...an infinity, or... | (?P s)? # ...an (optionally signaling) NaN # NaN (?P \d*) # with (possibly empty) diagnostic info. ) # \s* \Z z0*$z50*$z\A (?: (?P .)? (?P [<>=^]) )? (?P [-+ ])? (?P \#)? (?P 0)? (?P (?!0)\d+)? (?P ,)? (?:\.(?P 0|(?!0)\d+))? (?P [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 ', '=' or '^' sign: either '+', '-' or ' ' minimumwidth: nonnegative integer giving minimum width zeropad: boolean, indicating whether to pad with zeros thousands_sep: string to use as thousands separator, or '' grouping: grouping for thousands separators, in format used by localeconv decimal_point: string to use for decimal point precision: nonnegative integer giving precision, or None type: one of the characters 'eEfFgG%', or None NzInvalid format specifier: fillalignzeropadz7Fill character conflicts with '0' in format specifier: z2Alignment conflicts with '0' in format specifier: >r= rR minimumwidthrQ rq r% ri ZgGnr- r5 ro thousands_sepzJExplicit thousands separator conflicts with 'n' type in format specifier: grouping decimal_pointrT rZ r ) _parse_format_specifier_regexmatchrj groupdictrS _locale localeconv)Z format_specrm rs Z format_dictr r r' r' r) rs sN rs 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) zGiven an unpadded, non-aligned numeric string 'body' and sign string 'sign', add padding and alignment conforming to the given format specifier dictionary 'spec' (as produced by parse_format_specifier). r r r q sV & . 0 " ,# % $ + ' * P % )