+ jݯ LRtRt^RIt^RIHt^RItRs^RIHtHtH t H t H t H t H t HtHtHtHtHtHt^RIHtHtHtHtHtHtHtHtHtHtHtH t H!t!] R8XdRt"MRt"R t#!R R ]$4t%]&]&!R 4t(]&!R4t)]&!R4t*]&!R4t+]&!R4t,],t-Rt.Rt/Rt0^] ^^3t1^] ^^3t2^] ^^3t3^] ^^3t4^] ^^3t5^] ^^3t6^] RZ^3t7^] R[RZ3t8^] R\R]3t9^] R^R_3t:R`t;Rt<!RR4t=^.]>!^R4Uu.uFp] V^, ,^, NK up,t?]=!4]?.t@])Ra]*Rb],Rc]+Rd/tARtBRtC]D]E3tFRtGRtH] R8Xd&R]I!]49d]PtB]PtC] R8Xd]P;tBtC]'d]GtK]HtLM]BtK]CtLR]-3RltM]N!R ]>!ReR!444tO] R8XdR"]I!]49d ]PtM] R8Xd ]PtM^]-3R#ltQR$tRRfR%ltSR&tT^]-3R'ltU^]-3R(ltV^]-3R)ltW^]-3R*ltX^5]-3R+ltY^q]-3R,ltZR]-3R-lt[R.]-3R/lt\]-3R0lt]R1t^R2t_R3t`R4taR5tbR6tcR7tdR8teR9tfR:tgR;th^]-3R<ltiR]-3R=ltjR]-3R>ltkR?tl^]-^3R@ltm^]-3RAltn^]-R.3RBlto^]-3RCltp]-3RDltq^]-3REltr]-3RFlts] R8Xd]ptt]qtuM]rtt]stuRGtvRHtw]-3RIltx]-3RJlty]-3RKltz],]+]+],])]*]*])](](/t{],],]+]+])]*]*])](](/t|]-3RLlt}RMt~RNtRgROltRhRPltRQ]9RR]9RS]:RT]8/t]-3RUltRVtRWt]-3RXlt]-3RYlt] R8XdM^RIHuHuHt]Ptm]Ptn]Ptt]Ptx]EP tR#R# ]'dR t&ELi;iuupi ]'d]D3tFELRi;i ]dR#i;i)izH Low-level functions for arbitrary-precision floating-point arithmetic. plaintextN)bisect) MPZMPZ_TYPEMPZ_ZEROMPZ_ONEMPZ_TWOMPZ_FIVEBACKENDSTRICT HASH_MODULUS HASH_BITSgmpysage sage_utils) giant_steps trailtablebctablelshiftrshiftbitcounttrailing sqrt_fixednumeralisqrt isqrt_fastsqrtrem bin_to_radixrc(Vwrr4V\V4W43#Nhexxsignmanexpbcs& T/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/libmp/libmpf.py to_pickabler)s3SXs&&c6Vwrr4V\V4R,W43#):NNr r"s& r(r)r)#s!3SXb\3**r*c*Vwrr4V\V^4W43#))rr"s& r( from_pickabler/'sDs #c2, ((r*c]tRt^+tRtR#) ComplexResultN)__name__ __module__ __qualname____firstlineno____static_attributes__r2r*r(r1r1+sr*r1cV#rr2)r#s&r(r91sqr*nfcudc l\^\\\V4R, 4^, 44#)zVReturn number of accurate decimals that can be represented with a precision of n bits.ry O @maxintroundr:s&r( prec_to_dpsrF;s* q#eCF#556q89 ::r*c l\^\\\V4^,R,444#)zFReturn the number of bits required to represent n decimals accurately.r@rArEs&r( dps_to_precrH@s) q#eSVAX'99:; <*A     ax  c r*cV'g\#W48:dWW#3#W4, pV\8XdmW^, , pV^,'dEV^,'g%V\VR8,V,,'dV^, ^,pM8V^, pM.\V,V,'d W,pM V)V, )pW&, pTpV^,'g\\ V^,4,pV'gJV^,'gV^,pV^, pV^,pK,\\ V^,4,pW,pW', pW7,pV^8Xd^pWW#3#)zHsame as normalize, but with the added condition that man is odd or zero rNrbres&&&&&& r( _normalize1ris&   z#!! A m aCL q55q1uu#qu a(8"8"8a4(CQ$C S $    lHC B 77 s39~ &Cii qa3sSy>*A     ax  c r*c\V4\8XgQh\V4\9gQh\V4\9gQhV\V48XgQh\ WW#WE4#zsAdditional checks on the components of an mpf. Enable tests by setting the environment variable MPMATH_STRICT to Y.)typer _exp_typesrrgr$r%r&r'rfrVs&&&&&&r(strict_normalizeros[ 9  8z !! ! 9 "" " #   d$ 44r*c\V4\8XgQh\V4\9gQh\V4\9gQhV\V48XgQhV'dV^,'gQh\ WW#WE4#rk)rlrrmrrirns&&&&&&r(strict_normalize1rqsl 9  8z !! ! 9 "" " #  q! ! t#4 55r*r_mpmath_normalizecP\V4p^pV^8d^pV)pVR8d\\V4,pM \V4pV'gV'g\#V^,'gV^,'dW@^, V^,V^, 3#\ \V^,4,pV'gJV^,'gV^,pV^, pV^,pK,\ \V^,4,pW,pW, pWV,pW@W3#\ W@WW#4#)z~Create raw mpf from (man, exp) pair. The mantissa may be signed. If no precision is specified, the mantissa is stored exactly.)rrrCrrcr normalize)r%r&rfrVr$r'rWs&&&& r( from_man_exprv#s c(C D Qwd Tz SX  c] LQwwQwwQhaa883sSy>*A))AIC1HC!GBs39~. IC HC GB3## T 33r*c#<"TFq\V^43xK R#5i)rMN)rv).0r:s& r( ryBsB/Q\!Q'(/si_mpmath_createc\V'gV\9d\V,#\V^W4#)z_Create a raw mpf from an integer. If no precision is specified, the mantissa is stored exactly.) int_cacherv)r:rfrVs&&&r(from_intr}Js'  >Q<  1d ((r*cVVwrr4V'gV'd\RV,4hW#3#)z:Return (man, exp) of a raw mpf. Raise an error if inf/nan.z*mantissa and exponent are undefined for %s ValueErrorsr$r%r&r's& r( to_man_exprRs)Ds SEKLL 8Or*cVwr#rEV'gV'd \R4hV^8dV'd V)V,#W4,#V'gV'd W4), )#W4), #V'd\V)V)V4#\W4)V4#)zConvert 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.z cannot convert inf or nan to int)rrQ)rrVr$r%r&r's&& r(to_intrYsDs S;<< ax DS= z  T]# #4=  #tS))dC((r*cVwr#rEV'g V'dV#V^8dV#WE,pV^8d|V\8XdV'd\#\#V\8XdV'd\#\#V\ 8Xd-V^8g V\ 8Xd\#V'd\#\#\h\V\WV4V4#)rM) rSrcfonerRfnonerOrNotImplementedErrormpf_posmin)rrVr$r%r&r'mags&& r( mpf_round_introsDs S ax &C Qw - E\ [ K E\!\ M !Qw#.,e|"{% % 1c"lC ((r*cN\V\4pV'd \W1V4pV#r)rrRrrrfrVvs&&& r( mpf_floorrs"a%A AS ! Hr*cN\V\4pV'd \W1V4pV#r)rrSrrs&&& r(mpf_ceilr"a'A AS ! Hr*cN\V\4pV'd \W1V4pV#r)rrOrrs&&& r(mpf_nintrrr*c.\V\V4W4#r)mpf_subr)rrfrVs&&&r(mpf_fracrs 1ilD ..r*cBW8wd\#\P!V4wr4T\8Xd\#T\)8Xd\ #\ \TR,4T^5, Y4# T\8Xd \u#T\)8Xd \ u#\u#;i)zCreate 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.l)fnanmathfrexpmath_float_inffinffninfrvrC)r#rfrVmes&&& r( from_floatrs  v zz!}  N4K^OE\ AuI"d 88   t   sA--BBBc\V4pW8Xd \W1V4#^RIpVPV4'dJVP V4wrV\ \ VPV^q44\ V^q, 4W4#VPV4'd\#VPV4'd\#\#)zCreate 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.N) floatrnumpyisfiniterrvrCldexpisposinfrisneginfrr)r#rfrVynprrs&&& r( from_npfloatrs aAv!3'' {{1~~xx{CC 013qu:tII {{1~~d{ {{1~~e| Kr*c<VP4'd\#VP4'd#VP4'd\#\ #Vf1\ \VP4^,4R,4p\\V4W4#)zCreate 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.r@) is_nanr is_infinite is_signedrrrClenas_tuplefrom_strstr)r#rfrVs&&&r( from_Decimalrsg xxzz$;}} u?4? |3qzz|A'(::; CFD &&r*FcVwr4rVV'gBV\8XdR#V\8Xd\#V\8Xd\)#\\, #V^58d\ W4WV^5V4wr4rVV'dV)p\ P !WE4# \d4T'dhYV,^8dT'd \)u#\u#R#i;i)a 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. g)rcrrr normalize1rr OverflowError)rstrictrVr$r%r&r's&&& r(to_floatrsDs  :c 9^+ :~o-n,, Bw'3BD3 d zz###     8a<&&%% s$3B CC2C;CCc@\\V4\V4W#4#)z@Create a raw mpf from a rational number p/q, round if necessary.)mpf_divr})pqrfrVs&&&&r( from_rationalrs 8A; T 77r*cVwrr4V'dV)pVR8Xd\RV,4hV^8dV^V,,^3#V^V),3#)zYConvert a raw mpf to a rational number. Return integers (p, q) such that s = p/q exactly.z&cannot convert %s to a rational numberrrs& r( to_rationalrsZDs d RxACGHH axaf~q  AI~r*cVwr#rEWA,pV'dV^8d V)V,#V)V), #V^8d W6,#W6), #)z.Convert a raw mpf to a fixed-point big integerr2)rrfr$r%r&r'offsets&& r(to_fixedrsQDs ZF Q;//!$6'22 Q;s},"w//r*cr\'g^RIpVPs\\V4V)V\4#)zMReturn a raw mpf chosen randomly from [0, 1), with prec bits in the mantissa.N) getrandbitsrandomrvrR)rfrs& r(mpf_randrs/ ;((  D)D5$ DDr*cvV^,'dV^,'gV\8Xg V\8XdR#W8H#)z~Test equality of two raw mpfs. This is simply tuple comparison unless either number is nan, in which case the result is False.F)rrrWs&&r(mpf_eqrs, Q44qtt 9T  6Mr*c\PR8dVwrr4V'gqV\8Xd\PP#V\ 8Xd\PP #V\8Xd\PP )#V\,pV^8dV\,pM&\^, RV, \,, pWS,\,pV'dV)pVR8XdRp\V4#\\V^R74# \d\T4u#i;i))r)rr,r)sys version_infor hash_infonanrinfrr r rChashrr)rssignsmansexpsbchs& r(mpf_hashr!s 6!!"TDy!2!22Dy!2!22Ez3==#4#4"44 <  19)#Dq=R$Y)$; t. (Same convention as Python's cmp() function.)r)rcmpf_signrrrrrR) rrWrrrrtsigntmantexptbcabdeltas && r(mpf_cmpr>sEE t :x{l* :hqk) 6! 9Q 9Q :a  ~Q  | < ;RiQi A A 5 5)5 5) 5 A![ )E Qxx r*cNV\8Xg V\8XdR#\W4^8#Frrrs&&r(mpf_ltrr!DyAI 1=1 r*cNV\8Xg V\8XdR#\W4^8*#rrrs&&r(mpf_lerw!DyAI 1=A r*cNV\8Xg V\8XdR#\W4^8#rrrs&&r(mpf_gtr|rr*cNV\8Xg V\8XdR#\W4^8#rrrs&&r(mpf_gerrr*cV^,;rVR,F+p\W14'dTp\W24'gK)TpK- W3#)rM:r[NN)rr)seqrrBr#s& r( mpf_min_maxrsAAC WW !>>3 !>>3 8Or*c^V'd%Vwr4rVV'g V'dV#\W4WVW4#V#)zLCalculate 0+s for a raw mpf (i.e., just round s to the specified precision).)rrrfrVr$r%r&r's&&& r(rrs/ 3H$Sd88 Hr*cVwr4rVV'g-V'd#V\8Xd\#V\8Xd\#V#V'g ^V, WEV3#\^V, WEWaV4#)zNegate a raw mpf (return -s), rounding the result to the specified precision. The prec argument can be omitted to do the operation exactly.)rrrrs&&& r(mpf_negrsXDs  Dy,Ez$; $"%% afc# 66r*cVwr4rVV'gV'dV\8Xd\#V#V'gV'd^WEV3#V#\^WEWaV4#)zReturn abs(s) of the raw mpf s, rounded to the specified precision. The prec argument can be omitted to generate an exact result.)rrrrs&&& r(mpf_absrsMDs S :K  s$ $ a2S 11r*cfVwrr4V'gV\8Xd^#V\8XdR#^#RV,#)zReturn -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.)r)rrrs& r(rrs2Ds  9Q :by 4<r*cVwrVrxVwrrW,p V'EdYV 'EdPW{, p V 'EdV ^8dV ^d8dsV'dkW,V , V , pW^,8dHV^,p Wm,pW8Xd V^, pM V^,p\WVW}, \V4W#4#WY8XdWV ,,pM6V'dWV ,, pMWm,V , pV^8d^pMV)p^p\V4p\Y_T TT;'gTV4#V ^8dV R8dsV'dkW,V, V, pW^,8dHV^,p W,p WY8Xd V ^, p M V ^,p \WW, \V 4W#4#WY8XdWjV ),,pM8V 'dWjV ),, pMW),V, pV^8d^pMV)p^p\V4p\Y_TTT;'gTV4#WY8Xd W,pM(V'd W, pMWj, pV^8d^pMV)p^p\V4p\Y_T TT;'gTV4#V'd \V4pV'gIV'dW8XgV 'g V 'gV#\#V 'd\YYT;'gT V4#V#V 'dV#V'd\YVYxT;'gTV4#V#)z 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. i)rrrurr)rrWrfrV_subrrrrrrrrrrr%r's&&&&& r(mpf_addrsEE ME t 6zC4194+/194)%t{$TND 77>&.1CDFN$;c%)^t$;cax !"d !c]!%dB CHH!D=TJ,t3Eax'!% >4194+/194)%t{$TND 77>6'/2CDVGO$+CDKc Kcaxd c]T2tzzr3?? AJ  vTK e4dkkc3G G  %t$++#sCC Hr*c\WW#^4#)ztReturn the difference of two raw mpfs, s-t. This function is simply a wrapper of mpf_add that changes the sign of t.)r)rrWrfrVs&&&&r(rrs 1A &&r*c*^p^pV^,;'gRpRpVFpVwrrV 'dV 'd V'gV )p W, p W8dFW8d/V'd!V \\V44, V8dT pT pKeWJV ,, pKvV )p W, V8dV'gYrTKKWM,V ,pT pKV 'gKV'd \V4p\T;'g\V^4pK V'dV#\ WEW4#)a" 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. i@BN)rabsrrrcrv)xsrfrVabsoluter%r&max_extra_precspecialr#xsignxmanxexpxbcrs&&&& r(mpf_sumr "s C C!V&&wNG !"T XuJE{*%S(:":^"KCCEM*C9~-#'S<4/CC TAJg..15G7: $ ,,r*cVwrErgVwrrWH, p WY,p V 'd3\V 4pV'd\WWj,WV4#WWj,V3#V'*;'dTpV '*;'dT pV'gV'g\#\W39d\#V 'g V 'dYrV\8Xd\#^\R\ /\ V4\ V4,,#zMultiply two raw mpfsr)rrrcrrrrrrWrfrVrrrrrrrrr$r%r' s_special t_specials&&&& r( gmpy_mpf_mulrRsEE =D )C c] dBcB Bty"- -##tI##tI Y  v~d{ d1qEz$; dBu hqkHQK7 88r*cVwrErgV'g\V\V4W#4#V'g\#V^8d V^,pV)pWQ,p\WEV\ V4W#4#)Multiply by a Python integer.)mpf_mulr}rcrurrr:rfrVr$r%r&r's&&&& r(gmpy_mpf_mul_intrgs]Ds q(1+t11  1u   BHC TXc]D >>r*cVwrErgVwrrWH, p WY,p V 'dOW{,^, pV\W, 4, pV'd\WWj,WV4#WWj,V3#V'*;'dTpV '*;'dT pV'gV'g\#\W39d\#V 'g V 'dYrV\8Xd\#^\R\ /\ V4\ V4,,#r )rCrrcrrrrrs&&&& r(python_mpf_mulrtsEE =D )C Y] c#'l dBcB Bty"- -##tI##tI Y  v~d{ d1qEz$; dBu hqkHQK7 88r*cnVwrErgV'g\V\V4W#4#V'g\#V^8d V^,pV)pWQ,pVR8d&V\\ V4,^, , pMV\ V4^, , pV\ WW, 4, p\ WEWgW#4#)rrt)rr}rcrrCrrurs&&&& r(python_mpf_mul_intrsDs q(1+t11  1u   BHC4x gc!fo!! hqkAo#cg,B T 33r*c6Vwr#rEV'gV#W#WA,V3#)z8Quickly multiply the raw mpf s by 2**n without rounding.r2)rr:r$r%r&r's&& r( mpf_shiftrs#Ds  ceR r*cVwrr4V'gV\8Xd \^3#\h\W)V, 4WC,3#)z?Convert x = y*2**n to (y, n) with abs(y) in [0.5, 1) if nonzero)rcrrr"s& r( mpf_frexprs>Ds  :1:   QC "& ((r*cVwrErgVwrrV'd V 'gV\8Xd)V\8Xd\hV\8Xd\#\#V\8Xd\hV'*;'dTp V '*;'dT p V 'dV 'd\#V\8Xg V\8Xd\#V 'g@V\8Xd\#^\R\/\ V4\ V4,,#\#WH, pV ^8Xd\ WWj, WrV4#W', V ,^,pV^8d^p\W_,V 4wppV'd?V^,^,pV^, p\ VVWj, V, \V4W#4#\VVWj, V, \V4W#4#)zFloating-point divisionr) rcZeroDivisionErrorrrrrrdivmodrru)rrWrfrVrrrrrrrrrrr$extraquotrems&&&& r(rrs`EE t :Ez!22Dy+L :# #X''4 X''4 K 9T KEz dBu%hqkHQK&?@ @ =D qy$diC@@ J q E qyt{D)ID# a1}  $diox~tQQ T45(4.$ LLr*cVwrErgV'd V'g\\V4WV4#V^8d V^,pV)pW',^,p\W,V4wrV 'd9V ^,^,p V^, p\WIV)V, \ V 4W#4#\ WIV)V, \ V 4W#4#)z>Floating-point division n/t with a Python integer as numerator)rr}r!rrru) r:rWrfrVr$r%r&r'r"r#r$s &&&& r( mpf_rdiv_intr&sDs Cx{AS111u   B IMEqx%ID a1}  $sd5j(4.$LL T#eXd^T GGr*cVwrErgVwrrV'g V'gV 'gV 'd\#WH8XdWV,8dV#V ^8XdWjV ,8d\#\Wj4p RV,V,pRV,V ,p WVV , ,WV , ,,p V ^8d^pMV )p ^p\WV \ V 4W#4#)r[r)rrcrrur)rrWrfrVrrrrrrrrbaser%r$s&&&& r(mpf_modr)sEE td  ~$c/ qyTH_ t?D ; D ; D I 4I#6 7C axd ThsmT ??r*cVwrErgV'guV'dmV\8XdV^8dV#V^8Xd\#\#V\8Xd5V^8d\\.V^,,#V^8Xd\#\#\#\ V4pV^8Xd\ #V^8Xd \ WV4#V^8XdzVwrrgV'g\#WU,pV^8Xd^\Wf,^3#Ww,^, pV\\ WW, 4,, p\^WVV,WrV4#VR8Xd\\ WV4#V^8d2\W)V^,\V,4p \\ WV4#WA,p V^8XdV \Wa,^3#Wq,R8d&WQ,p\WWa,\V4W#4#V\8H;'g\V,V ,p V^\V4,,^,p \ wrrV^,'dW,p W,pW^, , pV\\ W, 4,,pW8d;V 'dWV , , p MV )W, , )p WV , , pT pV^,pV'gMWU,pWf,pWw,^, pV\\ WW, 4,,pW|8d;V 'dWWV , , pMV)W|, , )pWgV , , pT pV^,pEK2\!WWW#4#)z=Compute s**n, where s is a raw mpf and n is a Python integer.ir)rrrcrrCrrrrrr mpf_pow_intreciprocal_rndrrOrdru)rr:rfrVr$r%r&r'_inverse result_sign rounds_downworkprecpmpepbcs&&&& r(r+r+sDs S 91uQhAvd{L :1udE]1q511Avd{L  AAAvd{Avgas++AvLg !8w+ + Wq[ gc#'l##!Sc'2S99BwwtQc221uaT!V^C-@AtWC00(K axWceQ// td{ +CE8C=$LL-'&&C% a m#a'HNA2 q55BB 6MCBI//C~H -BCS\23BHn$ FAgg Wq[ '#ci.) ) =k*2;/0 = CB F [bt 99r*c V\8Xd \WV4#VwrErgV\Wg,V, ^, ^3pV'dV\\39V, p MV\ \39V, p V 'd \ WW#4#\WV4#)z 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. )rOrrrTrSrUr) r#eps_signrfrVr$r%r&r'epsaways &&&& r( mpf_perturbr9fs mq$$Ds WcfTk!mQ /C  M22h>-00H< qt))q$$r*cV^,'dRp\V4pMRpVwr4rVV'gR#\V\P!^ ^4,4^ ,pWV,p\ V4R8d^RIHp Hp \\ V44^,p \V4p \W!V 44p \W!V 4V 4p \V 4p \V\\W4V4pVwr4rVT pM^p\Wu, V, ^4p\V\P!^ ^4, R,4p\!W4p\#VV^ V4p\%V^ VR7pV\'V4V, ^, , pVVV3#)a Helper 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.-i )mpf_ln2mpf_ln10g?)r(size)r<0rM)rrCrlogr libelefunr=r>rr}rrrr+ftenrBrrrr)rrJr$_signr%r&r'bitprec exp_from_1r=r>expprectmprexponentfixprecfixdpssfsddigitss&& r( to_digits_exprOs] tt AJE #A&'",GJ :03s8$q(smc77+,c8G,g6 3K A{44g >C '-"$a(G 488Bq>)C/ 0F ! B b'2v .B Rbs +F F f$q((H  !!r*cV^,'gYV\8Xd!V'dRpMRpV'd VR, pV#V\8XdR#V\8XdR#V\8XdR#\hVf\ V^,)R4pVfTp\ W^,4wrxp V'gV^,R9d V ^, p RpEMb\V4V8dW,R9dVRVpV^, p V ^8dW,R 8Xd V ^,p KV ^8dHVRV \\W,4^,4,R W, ^, ,,pM&R R V^, ,,pV ^, p MVRVpY9u;8dV8dPMMLV ^8dR \V )4,V,p^p M%V ^,p W8dVR W, ,, p^p M^p VRV R ,WR,pV'd)VPR 4pVR,R 8Xd VR , pV ^8XdV'dV'g Wx,#V ^8d Wx,R ,\V 4,#V ^8d Wx,R,\V 4,#R#)aK 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(). z0.0z.0ze+0+inf-infrN567899r@1.ze+rr) rcrrrrrrOrrrCrstrip) rrJ strip_zeros min_fixed max_fixedshow_zero_exponentrWr$rNrIisplits &&&&&& r(to_strr_s+( Q44 :AA!U H 9V :f 9UcCF)R&8)c)+1!e4D(  !9  MH v; !7DS\FaAq&VY#-QAvc#fi.1*<&==swQR{@SSscAg.A DS\F  +) +!|c8)n,6 1 ;c59o-FHE%.3&7 ]]3'FbzS # 1}%7 9M1}T]T1CMAA!|DMC/#h-??|r*cVP4PR4p\V4VPR4p\ V4^8Xd^pMV^,p\ V^,4pVPR4p\ V4^8Xd;V^,V^,PR4rTV\ V4,pWE,p\ \ W44pW3#)zHelper function for from_str.lrrVr@)lowerrXrr^rrCr)r#r(partsr&rrs&& r(str_to_man_exprd s  A !H GGCLE 5zQ !H%(m GGCLE 5zQQxq-1 s1v  E CLA 6Mr*rrQrRrc @VP4P4pV\9d\V,#RV9dTVPR4wr4VP R4VP R4rC\ \ V4\ V4W4#\V^ R7wrV\V4R8d7\WQ^ ,4p\V\\Wa^ ,4W4pV#V^8d\V^ V,,W4pV#\ V^ V),W4pV#)a>Create a raw mpf from a decimal literal, rounding in the specified direction if the input number cannot be represented exactly as a binary floating-point number with the given number of bits. The literal syntax accepted is the same as for Python floats. TODO: the rounding does not work properly for large exponents. /rar(i) rbstrip special_strr^rXrrCrdrr}rr+rC)r#rfrVrrr%r&rs&&& r(rr!s  AK1~ axwws|xx}ahhsm1SVSVT77ab)HC 3x#~ Sr' " A{42g6 B H !8r3w2A Hc2t8T7A Hr*c\V^R7wr\V4p^pV^8dV)p^p\V4p\W1W$V\4#)r,rg)rdrrrurR)r#r%r&r$r's& r( from_bstrrkDsKaa(HC c(C D Qwd #B T[ 99r*cvVwrr4RR.V,\V\V4^R7,RV,,#)r<r;)r?r(ze%i)rrr"s& r(to_bstrrmNs6Ds s8D>GChsm!D DPS TTr*cVwr4rVV'd \R4hV'gV#V^,'dV^,pV^,pV^, pMV^8Xd\W4V^,WaV4#\^^V,V, ^,4pWw^,, pVR9d\WG,4pM4\ WG,4wrHV'dV^,^,pV^, p\ WEV, ^,W4#)zV Compute the square root of a nonnegative mpf value. The result is correctly rounded. z square root of a negative numberfd)r1rrBrrrv) rrfrVr$r%r&r'shiftr$s &&& r(mpf_sqrtrqXs Ds >??  Qww q   a $S!VRs;; 1T6"9Q; E QYE d{CJ3:& 61*C QJE %i!^T 77r*cV\8Xd \WV4#V\8Xd \WV4#\\W4\W4V^,4p\ WBV4#)zECompute the Euclidean norm sqrt(x**2 + y**2) of two raw mpfs x and y.)rcrrrrq)r#rrfrVhypot2s&&&& r( mpf_hypotrttsQ Ez'!3//Ez'!3// WQ\71<a 8F F# &&r*rii8rig)r[rM)rMr[)r[r[)rMrMir)TNNF) )__doc__ __docformat__rrrrbackendrrrrrr r r r r rrr libintmathrrrrrrrrrrrrrr)r/rr1intern NameErrorrOrRrSrUrT round_fastrFrHrKrcfnzerorrftworCfhalfrrrrrQrYrange h_mask_smallrPrdrgrirClongrmrorqdirrrrurrvdictr|rzr}rrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrrrr mpf_mul_intrrrr&r)r, negative_rndr+r9rOr_rdrirrkrmrqrtsage.libs.mpmath.ext_libmplibsmpmath ext_libmpext_lib ImportError)r-s0r(rsT   FFFF f'+) J  s Sk s #; C[  ; =  Ha Xq!  7Aq GQ 7Aq 8Q GR 8T2 8T2 HdB2""s%3-@-Qg!na''-@@ , % 5-uhu& 5n'RtJ56 f,D 9''J((K f)333J  I"JIJ !%*4> B%S/B B  f)SY6&&L f**LJ)),),Z J J J/z9&* :'*#J#-8  0&E:2 h    : j 7j 2jq] ~j' J.-`:9*&0 ? Z9,(24( fG"KG$K )'#MJ",H '@0 x Z +-  z X +-  !+Q:h%62"hS@j*T6$ueDA $ F:U%88)' f 44////////##[* FpAfJT$    s=.M1; N>N$A N1 M?>M? NNN#"N#