U Zʹjk@sTdZddlmZddlmZmZmZmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.ddl/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7ddl8m9Z9m:Z:m;Z;meefZ?dd Z@d d ZAd d ZBddZCddZDddZEdddZFdddZGddZHddZIddZJddd ZKdd!d"ZLd#d$ZMd%d&ZNdd'd(ZOdd)d*ZPd+d,ZQd-d.ZRd/d0ZSd1d2ZTd3d4ZUd5d6ZVd7d8ZWd9d:ZXd;d<ZYd=d>ZZd?d@Z[dAdBZ\dCdDZ]dEdFZ^dGdHZ_dIdJZ`dKdLZadMdNZbddSdTZcdUdVZddWdXZeddYdZZfd[d\Zgd]d^Zhd_d`ZidadbZjdcddZkdedfZldgdhZmdidjZndkdlZodmdnZpdodpZqdqdrZrdsdtZsdudvZtdwdxZuedyZvedzZwevewfZxed{Zyed|Zzd}d~Z{dddZ|dddZ}ddZ~ddZddZddZddZddZdS)z3 Computational functions for interval arithmetic. )xrange)+ ComplexResult round_downround_up round_floor round_ceiling round_nearest prec_to_dpsrepr_dps dps_to_precbitcount from_floatfnanfinffninffzerofhalffonefnonempf_signmpf_ltmpf_lempf_gtmpf_gempf_eqmpf_cmp mpf_min_max mpf_floorfrom_intto_intto_strfrom_strmpf_absmpf_negmpf_posmpf_addmpf_submpf_mul mpf_mul_intmpf_div mpf_shift mpf_pow_int from_man_expMPZ_ONE)mpf_logmpf_expmpf_sqrtmpf_atan mpf_atan2mpf_pimod_pi2 mpf_cos_sin) mpf_gamma mpf_rgamma mpf_loggamma mpc_loggammacCs,|\}}t|d}dt||t||fS)Nz[%s, %s])r r )sprecsasbdpsr@R/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mpmath/libmp/libmpi.pympi_strs rBcCs||kSNr@r;tr@r@rAmpi_eq)srFcCs||kSrCr@rDr@r@rAmpi_ne,srGcCs0|\}}|\}}t||rdSt||r,dSdSNTF)rrr;rEr=r>tatbr@r@rAmpi_lt/s  rLcCs0|\}}|\}}t||rdSt||r,dSdSrH)rrrIr@r@rAmpi_le6s  rMcCs t||SrC)rLrDr@r@rAmpi_gt=rNcCs t||SrC)rMrDr@r@rAmpi_ge>rOrPc CsL|\}}|\}}t|||t}t|||t}|tkr8t}|tkrDt}||fSrC)r%rrrrr r;rEr<r=r>rJrKabr@r@rAmpi_add@srUc CsL|\}}|\}}t|||t}t|||t}|tkr8t}|tkrDt}||fSrC)r&rrrrrrRr@r@rAmpi_subIsrVcCs|\}}t|||tSrC)r&rr;r<r=r>r@r@rA mpi_deltaRsrXcCs|\}}tt|||tdS)N)r*r%rrWr@r@rAmpi_midVsrZcCs(|\}}t||t}t||t}||fSrC)r$rrr;r<r=r>rSrTr@r@rAmpi_posZs  r\cCs(|\}}t||t}t||t}||fSrC)r#rrr[r@r@rAmpi_neg`s  r]c Cs|\}}t|}t|}|dkr:t||t}t||t}nR|dkrtt}t|}t||rft||t}qt||t}nt||t}t||t}||fSNrQ)rr$rrrr#r) r;r<r=r>sassbsrSrTZnegsar@r@rAmpi_absfs    racCst|||f|SrC)mpi_mulr;rEr<r@r@rA mpi_mul_mpf}srdcCst|||f|SrC)mpi_divrcr@r@rA mpi_div_mpfsrfcCs|\}}|\}}t|}t|}t|} t|} ||krDdkrhnn |tksX|tkr`ttfSttfS| | kr|dkrnn |tks|tkrttfSttfS|dkrh| dkrt|||t} t|||t} | tkrt} | tkrt} n|| dkr,t|||t} t|||t} | tkrt} | tkrdt} n8t|||t} t|||t} | tkrVt} | tkrt} n*|dkr4| dkrt|||t} t|||t} | tkrt} | tkr2t} n|| dkrt|||t} t|||t} | tkrt} | tkr2t} n8t|||t} t|||t} | tkr$t} | tkrt} n^t||t||t||t||g} t| krntt} } n$t| \} } t | |t} t | |t} | | fSr^) rrrrr'rrrrr$)r;rEr<r=r>rJrKr_r`tastbsrSrTZcasesr@r@rArbs~               $     rbcCs|\}}t|tr0t|||t}t|||t}nRt|trXt|||t}t|||t}n*t|}t||g\}}t}t|||t}||fSrC)rrr'rrrr#rr[r@r@rA mpi_squares  ric Cs|\}}|\}}t|}t|}t|} t|} ||krDdkrxnn0| dkrX| dksh| dksh| dkrpttfSttfS| dkr| dkrttfS| dkrtt|t||S| dkr|dkr|dkrttfS| | krttfS|dkrt|||t} t} |dkrt} t|||t} n|dkrZt|||t} t|||t} | t krJt} | t krt} n||dkrt|||t} t|||t} | t krt} | t krt} n8t|||t} t|||t} | t krt} | t krt} | | fSr^) rrrrrer]r)rrr) r;rEr<r=r>rJrKr_r`rgrhrSrTr@r@rAres\           recCst|t}t|t}||fSrC)r3rr)r<rSrTr@r@rAmpi_pis  rjcCs(|\}}t||t}t||t}||fSrC)r/rrr[r@r@rAmpi_exps  rkcCs(|\}}t||t}t||t}||fSrC)r.rrr[r@r@rAmpi_logs  rlcCs(|\}}t||t}t||t}||fSrC)r0rrr[r@r@rAmpi_sqrt$s  rmcCs(|\}}t||t}t||t}||fSrC)r1rrr[r@r@rAmpi_atan+s  rnc Cs|\}}|dkr.tttft|| |d|S|dkr>ttfS|dkrJ|S|dkr\t||S|d@rt|||t}t|||t}nt|}t|}|dkrt|||t}t|||t}n\|dkrt|||t}t|||t}n6t}t |}t ||rt|||t}nt|||t}||fSNrQr) rer mpi_pow_intrir+rrrrr#r) r;nr<r=r>rSrTr_r`r@r@rArr1s4  rrcCsv|\}}||krN|ttfkrN|tt|krtd>| tt|>td>| fdd} | |t }| |t }| |t }| | t } ||f|| ffS) Nrprqr csTt|d|tkkr}n}t|||}|\}}}}||dkrP|rLtStS|S)NrQr)boolrr'rr)rvroundingprrrrlessmorer<r@rAfinalizes  zmpi_cos_sin..finalize) rrrrrrrr,r-rr) ryr<rSrTr~car=nacbr>nbrr@rrA mpi_cos_sinvs<     rcCst||dSr^rryr<r@r@rAmpi_cossrcCst||dSNrrrr@r@rAmpi_sinsrcCst||d\}}t|||Srtrreryr<cossinr@r@rAmpi_tansrcCst||d\}}t|||Srtrrr@r@rAmpi_cotsrc Cs|d}t||t}t||t}t||t}t|ts:t|rlttt|t|||t}t |t d|t}t |||t}t |||t}||fS)Nrpd) r!rrrrAssertionErrorr'r|r"r)rr&r%) ryrzpercentr<r~xaxbrSrTr@r@rAmpi_from_str_a_bs   rc Cstd|}|dd}|d}d|krD|d\}}t||d|Sd|kr|ddks`d |krd||d d}d}d |kr|d d kr|d }|d d}|d\}}t||||Sd |krd|ksd|kr||ddkr*|dd}|dd}|d \}}t||t}t||t}||fS|d\}}|d \}} d|kr`| d\} }n| dd} }t||||t}t|| ||t}||fSn t||t}t||t}||fSdS)a Parse an interval number given as a string. Allowed forms are "-1.23e-27" Any single decimal floating-point literal. "a +- b" or "a (b)" a is the midpoint of the interval and b is the half-width "a +- b%" or "a (b%)" a is the midpoint of the interval and the half-width is b percent of a (`a imes b / 100`). "[a, b]" The interval indicated directly. "x[y,z]e" x are shared digits, y and z are unequal digits, e is the exponent. z&Improperly formed interval number '%s' rp+-F(rQ)%rYT,[]eN) ValueErrorreplacesplitrr!rrrstrip) r;r<rr~ryrzrrSrTzr@r@rA mpi_from_strsN              rT[]bracketsrcKst|}|d}|\} } t||} t||} t| |f|} t| |f|}t| |f|}d}|rbd}|\}}|dkrtt| d|f|}||d||}n|dkr| tkrt}n$t| td}t|t| td |}||d t||d }n|d kr|| d |||}n|dkr| |krTt| |df|} t| |df|}| d} t | dkrv| d| d} t | dkr| d| d| dkr| d| dkrXt t | ddD]&}| d|| d|krqq| dd||| d|dd || d|d|dt t | dd| d}n.| d||dt t | dd| d}n$|d| d |d| |}n td||S)a Convert a mpi interval to a string. **Arguments** *dps* decimal places to use for printing *use_spaces* use spaces for more readable output, defaults to true *brackets* pair of strings (or two-character string) giving left and right brackets *mode* mode of display: 'plusminus', 'percent', 'brackets' (default) or 'diff' *error_dps* limit the error to *error_dps* digits (mode 'plusminus and 'percent') Additional keyword arguments are forwarded to the mpf-to-string conversion for the components of the output. **Examples** >>> from mpmath import mpi, mp >>> mp.dps = 30 >>> x = mpi(1, 2)._mpi_ >>> mpi_to_str(x, 2, mode='plusminus') '1.5 +- 0.5' >>> mpi_to_str(x, 2, mode='percent') '1.5 (33.33%)' >>> mpi_to_str(x, 2, mode='brackets') '[1.0, 2.0]' >>> mpi_to_str(x, 2, mode='brackets' , brackets=('<', '>')) '<1.0, 2.0>' >>> x = mpi('5.2582327113062393041', '5.2582327113062749951')._mpi_ >>> mpi_to_str(x, 15, mode='diff') '5.2582327113062[4, 7]' >>> mpi_to_str(mpi(0)._mpi_, 2, mode='percent') '0.0 (0.0%)' rprrZ plusminusrYrrrrqrz%)rrdiffrrrrQNz%'%s' is unknown mode for printing mpi)r rZrXr r*rr'rr)rlenappendrminjoinr)ryr?Z use_spacesrmodeZ error_dpskwargsr<r~rSrTmiddeltaZa_strZb_strZmid_strspZbr1Zbr2Z delta_strr;rir@r@rA mpi_to_strs^(          >0& rcCs(|\}}|\}}t|||t|||fSrC)rUryrzr<rSrTrdr@r@rAmpci_adddsrcCs(|\}}|\}}t|||t|||fSrC)rVrr@r@rAmpci_subisrcCs|\}}t||t||fSrC)r]ryr<rSrTr@r@rAmpci_negnsrcCs|\}}t||t||fSrC)r\rr@r@rAmpci_posrsrc CsX|\}}|\}}t||}t||}t|||} t||} t||} t| | |} | | fSrC)rbrVrU) ryrzr<rSrTrrr1r2rei1i2imr@r@rAmpci_mulvs      rc Cs|\}}|\}}|d}t|}t|} t|| |} tt||t|||} tt||t|||} t| | |} t| | |} | | fSrt)rirUrbrVre) ryrzr<rSrTrrr~m1m2mrrr@r@rAmpci_divs   rcCsH|\}}|d}t||}t||\}}t|||}t|||}||fSrt)rkrrb)ryr<rSrTr~rrr;r@r@rAmpci_exps   rcCs|\}}t||t||fSrC)r*)ryrsrSrTr@r@rA mpi_shiftsrcCsR|d}t||}tt||}t|||}t|||}t|d}t|d}||fS)NrprY)rkrempi_onerUrVr)ryr<r~e1e2rr;r@r@rA mpi_cosh_sinhs      rc CsP|\}}|d}t||\}}t||\}}t|||} t|||} | t| fSNr)rrrbr] ryr<rSrTr~rr;chshrrr@r@rAmpci_coss  rc CsL|\}}|d}t||\}}t||\}}t|||} t|||} | | fSr)rrrbrr@r@rAmpci_sins  rcCsR|\}}|tkrt|S|tkr(t|St|}t|}t|||d}t||Srt)mpi_zerorarirUrm)ryr<rSrTrEr@r@rAmpci_abssrc Cs<|\}}|\}}||kr$tkr>nnt|tr6tSt|St|trt|trbt|||t}nt|||t}t|trt|||t}nt|||t}nt|trt|||t}t|trt|||t}nt|||t}nXt|tr"t|||t}t|trt|||t}nt|||t}nt|t}t |}||fSrC) rrrrjr2rrrr3r#) rzryr<yaybrrrSrTr@r@rA mpi_atan2s4         rcCs|\}}t|||SrC)r)rr<ryrzr@r@rAmpci_argsrcCs.|\}}tt||d|}t||}||fSrt)rlrr)rr<ryrzrrr@r@rAmpci_logs rc Cs|\}}|tkrh|\}}||krh|\}}} } |rT| dkrTt|d|t|| >|S|tkrht|d|S|d} tt|t|| | |S)NrQrYrp)r mpci_pow_intintrrrr) ryrzr<ZyreZyimrrrrrrr~r@r@rAmpci_pows   rcCs:|\}}tt|t||}t|||}t|d}||fSr)rVrirbr)ryr<rSrTrrr@r@rA mpci_squares   rcCs|dkr&tttft|| |d|S|dkr6ttfS|dkrHt||S|dkrZt||S|d}ttf}|r|d@rt|||}|d8}t||}|dL}qjt||Sro)rrrrrrr)ryrsr<r~resultr@r@rAr s"     rg#+Vcb?gVcb?gg?cCs0|\}}|\}}t||rdSt||r,dSdS)NFT)rr)ryrzrSrTrrr@r@rA mpi_overlap&s  rc Cs|\}}|d}|dkr,tt|t||dSt|tr|dkrXt||t}t||t}nB|dkrzt||t}t||t}n |dkrt ||t}t ||t}nt|t rt |t r|dkrt||t}t||t}nD|dkrt||t}t||t}n"|dkrt ||t}t ||t}n|t|t|}|dkrJt t||dd||S|dkrltt||dd||S|dkrtt||ddt||d|S||fS)NrprrQrqr) mpi_gammarUrr gamma_min_br6rrr7r8rr gamma_min_arerbrVrl) rr<typerSrTr~rrznewr@r@rAr2s@            "rcCs|\\}}\}}||kr$tkrJnn"|dks:t|trJt|||tfS|d}|dkr|d|d}|d|d} |tkrt|| } n| } tt|} tt|} t| | } td| | }|t|7}|dkrt||ft |\}}||f||ff}d}t |t rt ||ft tfrt||ft |||ff}|dkrXtt||dd||S|dkrztt||dd||S|dkrtt||ddt||d|St|trt||f|t}t||f|t}t||f|t}t||f|t}nt|trBt||f|t}t||f|t}t||f|t}t||f|t}nbt|tf|t}tt||rtt||f|t}nt||f|t}t||f|t}t||f|t}|d|df|d|dff}|dkrt|d|t|d|fS|dkrt|}t||S)NrrprqrQr)rrrrmaxabsrr rUrrrrgamma_mono_imag_agamma_mono_imag_br mpci_gammarrrrr9rrrr#r\rr)rr<rZa1Za2b1b2r~ZamagZbmagmagZanZbnZabsnZ gamma_sizerZminreZmaxreZminimZmaximwr@r@rArWsd*         "     rcCst||ddSNrrrrr<r@r@rA mpi_loggammarOrcCst||ddSrrrr@r@rA mpci_loggammarOrcCst||ddSNrqrrrr@r@rA mpi_rgammarOrcCst||ddSrrrr@r@rA mpci_rgammarOrcCst||ddSNrrrrr@r@rA mpi_factorialrOrcCst||ddSrrrr@r@rAmpci_factorialrOr N)rQ)rQ)rQ)rQ)rQ)rQ)Trrr)rQ)rQ)rQ)__doc__backendrZlibmpfrrrrrrr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r-Z libelefunr.r/r0r1r2r3r4r5Z gammazetar6r7r8r9rBrrrFrGrLrMrNrPrUrVrXrZr\r]rardrfrbrirerjrkrlrmrnrrrwr{r|rrrrrrrrrrrrrrrrrrrrrrrrrrrrrZ gamma_minrrrrrrrrrrr r@r@r@rAs (     D ;%  4B \       & % I