n5[c@sdZdZddlZddlmZddlZdaddlmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZddlmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"edkrd Z#n d Z#d Z$d e%fd YZ&ye'Wne(k rNdZ'nXe'dZ)e'dZ*e'dZ+e'dZ,e'dZ-e-Z.dZ/dZ0dZ1de ddfZ2de ddfZ3de ddfZ4de ddfZ5de ddfZ6de ddfZ7de ddfZ8de ddfZ9de ddfZ:de ddfZ;dgZ<dZ=d dhd!YZ>dgge?dd"D]Z@e e@d>d^qZAe>eAgZBidie*6dje+6dke-6dle,6ZCd#ZDd$ZEyeFeGfZHWne(k r&eFfZHnXd%ZId&ZJed'krld(eKekrlejLZDejLZEnedkrejMZDZEnereIZMeJZNn eDZMeEZNde.d)ZOePd*e?d+d,DZQed'krd-eKekrejRZOnedkrejOZOnde.d.ZSd/ZTdd0ZUd1ZVde.d2ZWde.d3ZXde.d4ZYde.d5ZZd6e.d7Z[d8e.d9Z\de.d:Z]e^e.d;Z_e.d<Z`d=Zad>Zbd?Zcd@ZddAZedBZfdCZgdDZhdEZidFZjdGZkde.dHZlde.dIZmde.dJZndKZode.ddLZpde.dMZqde.e^dNZrde.dOZse.dPZtde.dQZue.dRZved'kresZwetZxn euZwevZxdSZydTZze.dUZ{e.dVZ|e.dWZ}ie,e-6e-e,6e+e*6e*e+6e)e)6Z~ie-e-6e,e,6e+e*6e*e+6e)e)6Ze.dXZdYZdZZedde^d[Zd\d]Zie:d^6e:d_6e;d`6e9da6Ze.dbZdcZddZe.deZe.dfZedkr{yFddljjjZejpZpejqZqejwZwej{Z{ejZWq{ek rwq{XndS(msH Low-level functions for arbitrary-precision floating-point arithmetic. t plaintextiN(tbisecti( tMPZtMPZ_TYPEtMPZ_ZEROtMPZ_ONEtMPZ_TWOtMPZ_FIVEtBACKENDtSTRICTt HASH_MODULUSt HASH_BITStgmpytsaget sage_utils( t giant_stepst trailtabletbctabletlshifttrshifttbitcountttrailingt sqrt_fixedtnumeraltisqrtt isqrt_fasttsqrtremt bin_to_radixR cCs(|\}}}}|t|||fS(N(thex(txtsigntmantexptbc((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt to_pickablescCs,|\}}}}|t|d||fS(Ni(R(RRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyR"#scCs+|\}}}}|t|d||fS(Ni(R(RRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_pickable'st ComplexResultcBseZRS((t__name__t __module__(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyR$+scCs|S(N((R((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt1stntftctutdcCs'tdttt|ddS(sZReturn number of accurate decimals that can be represented with a precision of n bits.igry O @(tmaxtinttround(R(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt prec_to_dps;scCs'tdttt|ddS(sJReturn the number of bits required to represent n decimals accurately.igry O @(R-R.R/(R(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt dps_to_prec@scCs$t|}|dkrdS|dS(sReturn the number of decimal digits required to represent a number with n-bit precision so that it can be uniquely reconstructed from the representation.iii(R0(R(tdps((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytrepr_dpsEs  iiii8iiigu<7~cCs|tkr~|dkri||d?}|d@r^|d@sR|t|dk|@r^|d?dS|d?Sq~t| || Sn|tkr||?S|tkr| |? S|tkr|dkr||?S| |? S|tkr|dkr| |? S||?SdS(Niiii,(t round_nearestth_maskt round_intt round_floort round_ceilingt round_downtround_up(RR(trndtt((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyR6ks&  ,           t h_mask_bigcBseZdZRS(cCst|d>dS(Ni(R(tselfR(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt __getitem__s(R%R&R?(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyR=si,cCsn|s tS||}|dkr|tkr||d?}|d@rw|d@sf|t|dk|@rw|d?d}q|d?}n't||r||L}n | |? }||7}|}n|d@sItt|d@}|s(x,|d@s|dL}|d7}|d8}qWtt|d@}n||L}||7}||8}n|dkr^d}n||||fS(s Create a raw mpf tuple with value (-1)**sign * man * 2**exp and normalized mantissa. The mantissa is rounded in the specified direction if its size exceeds the precision. Trailing zero bits are also stripped from the mantissa to ensure that the representation is canonical. Conditions on the input: * The input must represent a regular (finite) number * The sign bit must be 0 or 1 * The mantissa must be positive * The exponent must be an integer * The bitcount must be exact If these conditions are not met, use from_man_exp, mpf_pos, or any of the conversion functions to create normalized raw mpf tuples. iiii,ii(tfzeroR4R5t shifts_downRR.(RRR R!tprecR;R(R<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt _normalizes8   ,              cCs{|s tS||kr&||||fS||}|tkr||d?}|d@r|d@sv|t|dk|@r|d?d}q|d?}n't||r||L}n | |? }||7}|}|d@sVtt|d@}|s5x,|d@s|dL}|d7}|d8}qWtt|d@}n||L}||7}||8}n|dkrkd}n||||fS(sSsame as normalize, but with the added condition that man is odd or zero iii,ii(R@R4R5RARR.(RRR R!RBR;R(R<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt _normalize1s:   ,             cCsyt|tkstt|tks0tt|tksHt|t|ks`tt||||||S(szAdditional checks on the components of an mpf. Enable tests by setting the environment variable MPMATH_STRICT to Y.(ttypeRtAssertionErrort _exp_typesRRC(RRR R!RBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytstrict_normalizes cCst|tkstt|tks0tt|tksHt|t|ks`t| sw|d@swtt||||||S(szAdditional checks on the components of an mpf. Enable tests by setting the environment variable MPMATH_STRICT to Y.i(RERRFRGRRD(RRR R!RBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytstrict_normalize1s R t_mpmath_normalizecCsCt|}d}|dkr.d}| }n|dkrMtt|}n t|}|s*|sitS|d@s|d@r||d?|d|dfStt|d@}|sx,|d@s|dL}|d7}|d8}qWtt|d@}n||L}||7}||8}n||||fSt||||||S(sCreate raw mpf from (man, exp) pair. The mantissa may be signed. If no precision is specified, the mantissa is stored exactly.iiiiii(RRR.RR@Rt normalize(RR RBR;RR!R<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_man_exp#s4             ccs$|]}|t|dfVqdS(iN(RL(t.0R(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pys Bsiit_mpmath_createcCs0|s|tkrt|Snt|d||S(scCreate a raw mpf from an integer. If no precision is specified, the mantissa is stored exactly.i(t int_cacheRL(R(RBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytfrom_intJs  cCs<|\}}}}| r2|r2td|n||fS(s:Return (man, exp) of a raw mpf. Raise an error if inf/nan.s*mantissa and exponent are undefined for %s(t ValueError(tsRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt to_man_expRs cCs|\}}}}| r.|r.tdn|dkrQ|rI| |>S||>S|ss|rg|| ? S|| ?Sn|rt| | |St|| |SdS(sConvert a raw mpf to the nearest int. Rounding is done down by default (same as int(float) in Python), but can be changed. If the input is inf/nan, an exception is raised.s cannot convert inf or nan to intiN(RQR6(RRR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytto_intYs     cCs|\}}}}| r#|r#|S|dkr3|S||}|dkr|tkrf|r_tStSq|tkr|r|tStSq|tkr|dks|tkrtS|rtStSqtnt|t |||S(Nii( R8R@tfoneR7tfnoneR4RtNotImplementedErrortmpf_postmin(RRR;RRR R!tmag((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_round_intos.        cCs.t|t}|r*t|||}n|S(N(R[R7RX(RRRBR;tv((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_floorscCs.t|t}|r*t|||}n|S(N(R[R8RX(RRRBR;R\((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_ceilscCs.t|t}|r*t|||}n|S(N(R[R4RX(RRRBR;R\((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_nintscCst|t|||S(N(tmpf_subR](RRRBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_fracsi5cCs||krtSytj|\}}Wn)|tkr?tS|t krPtStSX|tkretS|t krvtStt|d|d||S(sCreate a raw mpf from a Python float, rounding if necessary. If prec >= 53, the result is guaranteed to represent exactly the same number as the input. If prec is not specified, use prec=53.ii5I (tfnantmathtfrexptmath_float_inftfinftfninfRLR.(RRBR;tmte((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_floats     iqcCst|}||kr(t|||Sddl}|j|r|j|\}}tt|j|dt|d||S|j|rt S|j |rt St S(sCreate a raw mpf from a numpy float, rounding if necessary. If prec >= 113, the result is guaranteed to represent exactly the same number as the input. If prec is not specified, use prec=113.iNiq( tfloatRjtnumpytisfiniteRdRLR.tldexptisposinfRftisneginfRgRb(RRBR;tytnpRhRi((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_npfloats   /cCsu|jrtS|jr0|jr,tStS|dkr_tt|j dd}nt t |||S(sCreate a raw mpf from a Decimal, rounding if necessary. If prec is not specified, use the equivalent bit precision of the number of significant digits in x.igry O @N( tis_nanRbt is_infinitet is_signedRgRftNoneR.tlentas_tupletfrom_strtstr(RRBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_Decimals   #cCs|\}}}}|sQ|tkr(dS|tkr8tS|tkrIt SttS|dkrt||||d|\}}}}n|r| }nytj||SWn@tk r|rn||dkr|rt StSndSXdS(s  Convert a raw mpf to a Python float. The result is exact if the bitcount of s is <= 53 and no underflow/overflow occurs. If the number is too large or too small to represent as a regular float, it will be converted to inf or 0.0. Setting strict=True forces an OverflowError to be raised instead. Warning: with a directed rounding mode, the correct nearest representable floating-point number in the specified direction might not be computed in case of overflow or (gradual) underflow. gi5iN(R@RfReRgt normalize1RcRnt OverflowError(RRtstrictR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytto_floats.     *  cCstt|t|||S(sDCreate a raw mpf from a rational number p/q, round if necessary.(tmpf_divRP(tptqRBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_rationalscCsr|\}}}}|r"| }n|dkrAtd|n|dkr_|d|>dfS|d| >fSdS(s]Convert a raw mpf to a rational number. Return integers (p, q) such that s = p/q exactly.is&cannot convert %s to a rational numberiiN(RQ(RRRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt to_rationals   cCse|\}}}}||}|rD|dkr7| |>S| | ?Sn|dkrX||>S|| ?SdS(s.Convert a raw mpf to a fixed-point big integeriN((RRRBRRR R!toffset((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytto_fixeds    cCs8tsddl}|jantt|| |tS(sQReturn a raw mpf chosen randomly from [0, 1), with prec bits in the mantissa.iN(t getrandbitstrandomRLR7(RBR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_rands  cCs?|d s|d r5|tks.|tkr5tSn||kS(sTest equality of two raw mpfs. This is simply tuple comparison unless either number is nan, in which case the result is False.i(RbtFalse(RRR<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_eqscCs tjdkr|\}}}}|sm|tkr=tjjS|tkrStjjS|tkrmtjj Sn|t}|dkr|t }nt dd|t }||>t}|r| }n|dkr|dknt |Syt t |ddSWnt k rt |SXdS(Ns3.2iiiiR(tsystversionRbt hash_infotnanRftinfRgR R R.thashRR~(RRtssigntsmantsexptsbcth((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_hash!s.          c Cs|\}}}}|\}}}} | s2| r|tkrIt| S|tkr_t|S||krodS|tkrdS|tkrdS|tkrdSdS||kr|sdSdS||kr||krdS||kr|rdSdSq|rdSdSn||} | |} |rD| | kr1dS| | krddSn | | krTdS| | krddSt||dt} | drdSdS(sCompare the raw mpfs s and t. Return -1 if s < t, 0 if s == t, and 1 if s > t. (Same convention as Python's cmp() function.)iiii(R@tmpf_signRbRfRgR`R7( RRR<RRRRttsignttmanttexpttbctatbtdelta((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_cmp>sZ                 cCs/|tks|tkrtSt||dkS(Ni(RbRR(RRR<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_ltrscCs/|tks|tkrtSt||dkS(Ni(RbRR(RRR<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_lewscCs/|tks|tkrtSt||dkS(Ni(RbRR(RRR<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_gt|scCs/|tks|tkrtSt||dkS(Ni(RbRR(RRR<((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_gescCs]|d}}xB|dD]6}t||r7|}nt||r|}qqW||fS(Nii(RR(tseqRYR-R((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_min_maxs  cCsF|rB|\}}}}| r)|r)|St||||||S|S(sPCalculate 0+s for a raw mpf (i.e., just round s to the specified precision).(R}(RRRBR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyRXs  cCs||\}}}}|sE|rA|tkr.tS|tkrAtSn|S|s_d||||fStd||||||S(sNegate a raw mpf (return -s), rounding the result to the specified precision. The prec argument can be omitted to do the operation exactly.i(RfRgR}(RRRBR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_negs  cCsl|\}}}}| r3|r3|tkr/tS|S|sS|rOd|||fS|Std|||||S(sReturn abs(s) of the raw mpf s, rounded to the specified precision. The prec argument can be omitted to generate an exact result.i(RgRfR}(RRRBR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_abss  cCsD|\}}}}|s<|tkr(dS|tkr8dSdSd|S(sReturn -1, 0, or 1 (as a Python int, not a raw mpf) depending on whether s is negative, zero, or positive. (Nan is taken to give 0.)iii(RfRg(RRRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyRs  cCs|\}}}}|\} } } } | |N} |r+| r+|| } | r| dkrv| dkr|r||| | }||dkr|d} || K}| |kr|d7}n |d8}t|||| t|||Sn|| kr| || >}nG|r| || >}n|| >| }|dkr>d}n | }d}t|}t||| ||po||S| dkr| dkr|r| | ||}||dkr|d} | | K} || kr| d7} n | d8} t| | | | t| ||Sn|| kr1|| | >}nI| rI|| | >}n| | >|}|dkrmd}n | }d}t|}t|||||p||Sn|| kr| |}n?|r| |}n || }|dkrd}n | }d}t|}t||| ||p$||S|r@t|}n|s|rm||kse| se| ri|StS| rt| | | | |p| |S|S| r|S|rt|||||p||S|S(s Add the two raw mpf values s and t. With prec=0, no rounding is performed. Note that this can produce a very large mantissa (potentially too large to fit in memory) if exponents are far apart. iidiii(R}RRKRRb(RRR<RBR;t_subRRRRRRRRRRRR!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_adds                     "       cCst||||dS(sxReturn the difference of two raw mpfs, s-t. This function is simply a wrapper of mpf_add that changes the sign of t.i(R(RRR<RBR;((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyR`scCsad}d}|dpd}d}x|D]}|\} } } } | r | r^| r^| } n| |} | |kr| |kr| s| tt||kr| }| }q|| | >7}q@| } | | |kr|s| | }}qq@|| >| }| }q)| r)|r%t|}nt|p1t|d}q)q)W|rN|St||||S(s> Sum a list of mpf values efficiently and accurately (typically no temporary roundoff occurs). If prec=0, the final result will not be rounded either. There may be roundoff error or cancellation if extremely large exponent differences occur. With absolute=True, sums the absolute values. iii@BiN(RwRtabsRRR@RL(txsRBR;tabsoluteRR tmax_extra_prectspecialRtxsigntxmantxexptxbcR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_sum"s:       #  cCs|\}}}}|\}} } } ||A} || } | rt| }|rmt| | || |||S| | || |fSn| o|}| o| }| r| rtSt||fkrtS| r| r||}}n|tkrtSitd6td6t|t|S(sMultiply two raw mpfsii(RR}R@RbRfRgR(RRR<RBR;RRRRRRRRRRR!t s_specialt t_special((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt gmpy_mpf_mulRs(       cCs|\}}}}|s1t|t|||S|s;tS|dkr[|dN}| }n||9}t|||t|||S(sMultiply by a Python integer.ii(tmpf_mulRPR@RKR(RRR(RBR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytgmpy_mpf_mul_intgs    cCs/|\}}}}|\}} } } ||A} || } | r|| d}|t| |?7}|rt| | || |||S| | || |fSn| o|}| o| }| r| rtSt||fkrtS| r| r||}}n|tkr tSitd6td6t|t|S(sMultiply two raw mpfsii(R.R}R@RbRfRgR(RRR<RBR;RRRRRRRRRRR!RR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytpython_mpf_mults*      cCs|\}}}}|s1t|t|||S|s;tS|dkr[|dN}| }n||9}|dkr|tt|d7}n|t|d7}|t||?7}t||||||S(sMultiply by a Python integer.iii(RRPR@RR.RRK(RRR(RBR;RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytpython_mpf_mul_ints     cCs0|\}}}}|s|S|||||fS(s8Quickly multiply the raw mpf s by 2**n without rounding.((RRR(RRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_shiftscCsS|\}}}}|s7|tkr.tdfStnt|| |||fS(s?Convert x = y*2**n to (y, n) with abs(y) in [0.5, 1) if nonzeroi(R@RQR(RRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_frexps    cCs|\}}}}|\}} } } | s2| r|tkrg|tkrStn|tkrctStS|tkr|tn| o|} | o| } | r| rtS|tks|tkrtS| s|tkrtSitd6td6t|t|StS||A}| dkr5t|||| |||S||| d}|dkr\d}nt||>| \}}|r|d>d}|d7}t|||| |t|||St |||| |t|||S(sFloating-point divisioniii( R@tZeroDivisionErrorRbRfRgRR}tdivmodRRK(RRR<RBR;RRRRRRRRRRRtextratquottrem((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyRsD         &     'c Cs|\}}}}| s | r9tt||||S|dkrY|dN}| }n||d}t||>|\} } | r| d>d} |d7}t|| | |t| ||St|| | |t| ||S(s>Floating-point division n/t with a Python integer as numeratoriii(RRPRR}RRK( R(R<RBR;RRR R!RRR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_rdiv_ints    $cCs|\}}}}|\}} } } | r1|s>| rB| rBtS||krb| ||krb|S| dkr|| | krtSt|| } d||}d|| } ||| >| | | >} | dkrd}n | } d}t|| | t| ||S(Niii(RbR@RYRKR(RRR<RBR;RRRRRRRRtbaseRR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_mods"  cCs|\}}}}| r|r|tkrO|dkr;|S|dkrKtStS|tkr|dkryttg|d@S|dkrtStStSt|}|dkrtS|dkrt|||S|dkr^|\}}}}|stS||}|dkrdt||dfS||d}|tt||?7}t d||||||S|dkr}t t|||S|dkrt || |dt |} t t| ||S||@} |dkr| t||dfS||dkr!||C}t | |||t |||S|tkp8t|| } |dt |d} t\}} }}x7|d@r | |} ||}||d7}|tt| |?}|| kr| r| || ?} n| || ? } ||| 7}| }n|d8}|s Pq n||}||}||d}|tt||?}|| kr| rj||| ?}n| || ? }||| 7}| }n|d}qhWt| | ||||S(s=Compute s**n, where s is a raw mpf and n is a Python integer.iiiiiii(RfRbR@RgR.RURXRRR}Rt mpf_pow_inttreciprocal_rndRR4RARK(RRR(RBR;RRR R!t_tinverset result_signt rounds_downtworkprectpmtpetpbc((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyRs                  #           c Cs|tkrt|||S|\}}}}|t|||ddf}|rk|ttfk|A} n|ttfk|A} | rt||||St|||SdS(s For nonzero x, calculate x + eps with directed rounding, where eps < prec relatively and eps has the given sign (0 for positive, 1 for negative). With rounding to nearest, this is taken to simply normalize x to the given precision. iN(R4RXRR9R8R:R( Rteps_signRBR;RRR R!tepstaway((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_perturbfs cCs|drd}t|}nd}|\}}}}|sAdSt|tjddd}||}t|dkr'dd lm} m} tt|d } t |} t | | | } t | | | | } t | } t |t t| ||}|\}}}}| }nd}t|||d}t|tjddd }t||}t||d|}t|d dd |}|t||d7}|||fS(s0Helper function for representing the floating-point number s as a decimal with dps digits. Returns (sign, string, exponent) where sign is '' or '-', string is the digit string, and exponent is the decimal exponent as an int. If inexact, the decimal representation is rounded toward zero.it-tt0i ii i(tmpf_ln2tmpf_ln10ig?Rtsize(RRi(RR.RctlogRt libelefunRRRRPRRRTRtftenR-RRRRx(RRR2Rt_signRR R!tbitprect exp_from_1RRtexpprecttmpRtexponenttfixprectfixdpstsftsdtdigits((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt to_digits_exps6       c Cs|ds{|tkrB|r%d}nd}|r>|d7}n|S|tkrRdS|tkrbdS|tkrrdStn|dkrt|d d }n|dkr|}nt||d\}}} |s|d d kr| d7} nd}nt||kr||d kr|| }|d} x*| d kr]|| d kr]| d8} q4W| d kr|| t t || dd || d}qdd |d}| d7} n || }|| ko|knrB| d krd t | |}d} n+| d} | |kr9|d | |7}nd } nd} || d|| }|r|j d }|ddkr|d 7}qn| d kr|r| r||S| d kr||dt | S| d kr||dt | SdS(s{ Convert a raw mpf to a decimal floating-point literal with at most `dps` decimal digits in the mantissa (not counting extra zeros that may be inserted for visual purposes). The number will be printed in fixed-point format if the position of the leading digit is strictly between min_fixed (default = min(-dps/3,-5)) and max_fixed (default = dps). To force fixed-point format always, set min_fixed = -inf, max_fixed = +inf. To force floating-point format, set min_fixed >= max_fixed. The literal is formatted so that it can be parsed back to a number by to_str, float() or Decimal(). is0.0s.0se+0s+infs-infRiiit56789t9Rt1t.ise+RiN( R@RfRgRbRQRwRYRRxR{R.trstrip( RRR2t strip_zerost min_fixedt max_fixedtshow_zero_exponentR<RRRtitsplit((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytto_strsl            "   5         i cCs|jjd}t||jd}t|dkrId}n|d}t|d}|jd}t|dkr|d|djd}}|t|8}||}ntt||}||fS(sHelper function for from_str.tlRiiiRiR(tlowerRRkRRxR.R(RRtpartsR RR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytstr_to_man_exp s    Rs+infs-infRcCs1|jj}|tkr&t|Sd|kr|jd\}}|jd|jd}}tt|t|||St|dd\}}t|dkrt ||d}t |t t ||d||}nC|dkrt |d|||}nt|d| ||}|S(sVCreate a raw mpf from a decimal literal, rounding in the specified direction if the input number cannot be represented exactly as a binary floating-point number with the given number of bits. The literal syntax accepted is the same as for Python floats. TODO: the rounding does not work properly for large exponents. t/RRi ii( Rtstript special_strRRRR.RRRPRRR(RRBR;RRRR RR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyRz!s   ( cCskt|dd\}}t|}d}|dkrF| }d}nt|}t|||||tS(NRiii(RRRRKR7(RRR RR!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt from_bstrDs    cCsD|\}}}}ddg|t|dt|ddd|S(NRRRRise%i(RR(RRRR R!((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytto_bstrNsc Cs|\}}}}|r'tdn|s1|S|d@r\|d8}|dK}|d7}n)|dkrt|||d|||Stdd||d}||d@7}|dkrt||>}n7t||>\}}|r|d>d}|d7}nt|||d||S(sb Compute the square root of a nonnegative mpf value. The result is correctly rounded. s square root of a negative numberiiitfd(R$R}R-RRRL( RRRBR;RRR R!tshiftR((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pytmpf_sqrtXs(       cCsp|tkrt|||S|tkr8t|||Stt||t|||d}t|||S(sICompute the Euclidean norm sqrt(x**2 + y**2) of two raw mpfs x and y.i(R@RRRR(RRqRBR;thypot2((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyt mpf_hypotts   (g((ii(ii(ii(ii(t__doc__t __docformat__RcRRRwRtbackendRRRRRRRR R R R R Rt libintmathRRRRRRRRRRRRRR"R#RQR$tinternt NameErrorR4R7R8R:R9t round_fastR0R1R3R@tfnzeroRURVtftwoRtfhalfRbRfRgReR6R=trangeRt h_mask_smallR5RARCRDR.tlongRGRHRItdirRJRKR}RLtdictRORNRPRSRTR[R]R^R_RaRjRsR|RRRRRRRRRRRRRRRXRRRRR`RRRRRRt mpf_mul_intRRRRRRt negative_rndRRRtTrueRRRRzRRRRtsage.libs.mpmath.ext_libmptlibstmpmatht ext_libmptext_libt ImportError(((s2lib/python2.7/site-packages/mpmath/libmp/libmpf.pyts"  XX               5 7 )              %     4       _0      %     T  4  T " #