o l hk@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$ZMd%d&ZNdd'd(ZOdd)d*ZPd+d,ZQd-d.ZRd/d0ZSd1d2ZTd3d4ZUd5d6ZVd7d8ZWd9d:ZXd;d<ZYd=d>ZZd?d@Z[dAdBZ\dCdDZ]dEdFZ^dGdHZ_dIdJZ`dKdLZadMdNZbddSdTZcdUdVZddWdXZeddYdZZfd[d\Zgd]d^Zhd_d`ZidadbZjdcddZkdedfZldgdhZmdidjZndkdlZodmdnZpdodpZqdqdrZrdsdtZsdudvZtdwdxZuedyZvedzZwevewfZxed{Zyed|Zzd}d~Z{dddZ|dddZ}ddZ~ddZddZddZddZddZdS)z3 Computational functions for interval arithmetic. )xrange)+ ComplexResult round_downround_up round_floor round_ceiling round_nearest prec_to_dpsrepr_dps dps_to_precbitcount from_floatfnanfinffninffzerofhalffonefnonempf_signmpf_ltmpf_lempf_gtmpf_gempf_eqmpf_cmp mpf_min_max mpf_floorfrom_intto_intto_strfrom_strmpf_absmpf_negmpf_posmpf_addmpf_submpf_mul mpf_mul_intmpf_div mpf_shift mpf_pow_int from_man_expMPZ_ONE)mpf_logmpf_expmpf_sqrtmpf_atan mpf_atan2mpf_pimod_pi2 mpf_cos_sin) mpf_gamma mpf_rgamma mpf_loggamma mpc_loggammacCs,|\}}t|d}dt||t||fS)Nz[%s, %s])r r )sprecsasbdpsr@g/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/mpmath/libmp/libmpi.pympi_strs rBcCs||kSNr@r;tr@r@rAmpi_eq)rFcCs||kSrCr@rDr@r@rAmpi_ne,rGrHcC0|\}}|\}}t||rdSt||rdSdSNTF)rrr;rEr=r>tatbr@r@rAmpi_lt/ rNcCrIrJ)rrrKr@r@rAmpi_le6rOrPcC t||SrC)rNrDr@r@rAmpi_gt= rRcCrQrC)rPrDr@r@rAmpi_ge>rSrTc CsL|\}}|\}}t|||t}t|||t}|tkrt}|tkr"t}||fSrC)r%rrrrr r;rEr<r=r>rLrMabr@r@rAmpi_add@  rYc CsL|\}}|\}}t|||t}t|||t}|tkrt}|tkr"t}||fSrC)r&rrrrrrVr@r@rAmpi_subIrZr[cCs|\}}t|||tSrC)r&rr;r<r=r>r@r@rA mpi_deltaRsr]cCs|\}}tt|||tdS)N)r*r%rr\r@r@rAmpi_midVr_cC(|\}}t||t}t||t}||fSrC)r$rrr;r<r=r>rWrXr@r@rAmpi_posZ  rccCs(|\}}t||t}t||t}||fSrC)r#rrrbr@r@rAmpi_neg`rdrec Cs|\}}t|}t|}|dkr t||t}t||t}||fS|dkrCt}t|}t||r9t||t}||fSt||t}||fSt||t}t||t}||fSNrU)rr$rrrr#r) r;r<r=r>sassbsrWrXnegsar@r@rAmpi_absfs$       rjcCt|||f|SrC)mpi_mulr;rEr<r@r@rA mpi_mul_mpf}rncCrkrC)mpi_divrmr@r@rA mpi_div_mpfrorqcCs|\}}|\}}t|}t|}t|} t|} ||kr"dkr4nn|tks,|tkr0ttfSttfS| | kr>dkrPnn|tksH|tkrLttfSttfS|dkr| dkrvt|||t} t|||t} | tkrlt} | tkrrt} | | fS| dkrt|||t} t|||t} | tkrt} | tkrt} | | fSt|||t} t|||t} | tkrt} | tkrt} | | fS|dkr| dkrt|||t} t|||t} | tkrt} | tkrt} | | fS| dkrt|||t} t|||t} | tkrt} | tkrt} | | fSt|||t} t|||t} | tkrt} | tkrt} | | fSt||t||t||t||g} t| vr?tt} } | | fSt| \} } t | |t} t | |t} | | fSrf) rrrrr'rrrrr$)r;rEr<r=r>rLrMrgrhtastbsrWrXcasesr@r@rArlst  +  %        $    rlcCs|\}}t|trt|||t}t|||t}||fSt|tr2t|||t}t|||t}||fSt|}t||g\}}t}t|||t}||fSrC)rrr'rrrr#rrbr@r@rA mpi_squares  ruc Cs|\}}|\}}t|}t|}t|} t|} ||kr"dkrrLrMrgrhrrrsrWrXr@r@rArpsV        rpcCst|t}t|t}||fSrC)r3rr)r<rWrXr@r@rAmpi_pis  rvcCrarC)r/rrrbr@r@rAmpi_exp  rwcCrarC)r.rrrbr@r@rAmpi_logrxrycCrarC)r0rrrbr@r@rAmpi_sqrt$rxrzcCrarC)r1rrrbr@r@rAmpi_atan+rdr{c Cs2|\}}|dkrtttft|| |d|S|dkrttfS|dkr%|S|dkr.t||S|d@rDt|||t}t|||t}||fSt|}t|}|dkrbt|||t}t|||t}||fS|dkrxt|||t}t|||t}||fSt}t |}t ||rt|||t}||fSt|||t}||fSNrUr) rpr mpi_pow_intrur+rrrrr#r) r;nr<r=r>rWrXrgrhr@r@rAr1s<   rcCsv|\}}||kr'|ttfvr'|tt|krt|t||S|tkr't||St||d}t|||d}t ||SNr}) rrrrrrrzryrlrw)r;rEr<rLrMuvr@r@rAmpi_powVs  rcCt||r|S|SrC)rxyr@r@rAMINa rcCrrC)rrr@r@rAMAXfrrc CsZ|\}}}}|tkrttdfSt||\}}t||||d\}} } |r(d| } ||| fS)NrUr^)rrr5r4) rwpsignmanexpbccr;rErwp_r@r@rAcos_sin_quadrantks   rc s|\}}||krtkrnnttfttffSt|vs t|vr(ttfttffSd}t||\}}}t||\}} } t||g\}}t|| g\}} || krQnB| |dkr_ttfttffS|d| dkrit}|dd| ddkrwt}|dd| ddkrt} |dd| ddkrt}tt|>td>| tt|>td>| fdd} | |t }| |t }| |t }| | t } ||f|| ffS) Nr}r~r csTt|d|tkkr }n}t|||}|\}}}}||dkr(|r&tStS|S)NrUr)boolrr'rr)rroundingprrrrlessmorer<r@rAfinalizes  zmpi_cos_sin..finalize) rrrrrrrr,r-rr) rr<rWrXrcar=nacbr>nbrr@rrA mpi_cos_sinvs<    rcCt||dSrfrrr<r@r@rAmpi_cosrcCrNrrrr@r@rAmpi_sinrrcCst||d\}}t|||Srrrprr<cossinr@r@rAmpi_tan rcCst||d\}}t|||Srrrr@r@rAmpi_cotrrc Cs|d}t||t}t||t}t||t}t|tsJ|r6ttt|t|||t}t|t d|t}t |||t}t |||t}||fS)Nr}d) r!rrrrr'rr"r)rr&r%) rrpercentr<rxaxbrWrXr@r@rAmpi_from_str_a_bs   rc Cstd|}|dd}|d}d|vr"|d\}}t||d|Sd|vr\|ddks0d |vr2||d d}d}d |vrN|d d krF|d }|d d}|d\}}t||||Sd |vrd|vshd|vrj||ddkr|dd}|dd}|d \}}t||t}t||t}||fS|d\}}|d \}} d|vr| d\} }n| dd} }t||||t}t|| ||t}||fSt||t}t||t}||fS)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' r}+-F(rU)%r^T,[]e) ValueErrorreplacesplitrr!rrrstrip) r;r<rrrrrrWrXzr@r@rA mpi_from_strsN            rT[]bracketsrcKst|}|d}|\} } t||} t||} t| |fi|} t| |fi|}t| |fi|}d}|r7d}|\}}|dkrWtt| d|fi|}||d||}|S|dkr| tkrbt}nt| td}t|t| td |}||d t||d }|S|d kr|| d |||}|S|dkr`| |krt| |dfi|} t| |dfi|}| d} t | dkr| d| d} t | dkr| d| d| dkrL| d| dkr3t t | ddD]}| d|| d|krnq| dd||| d|dd || d|d|dt t | dd| d}|S| d||dt t | dd| d}|S|d| d |d| |}|Std|)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%)' r}rr plusminusr^rrrr~rz%)rrdiffrrrrUNz%'%s' is unknown mode for printing mpi)r r_r]r r*rr'rr)rlenappendrminjoinr)rr? use_spacesrmode error_dpskwargsr<rrWrXmiddeltaa_strb_strmid_strspbr1br2 delta_strr;rir@r@rA mpi_to_strsj(  $       >.$ rcC(|\}}|\}}t|||t|||fSrC)rYrrr<rWrXrdr@r@rAmpci_adddrcCrrC)r[rr@r@rAmpci_subirrcC|\}}t||t||fSrC)rerr<rWrXr@r@rAmpci_negnr`rcCrrC)rcrr@r@rAmpci_posrr`rc CsX|\}}|\}}t||}t||}t|||} t||} t||} t| | |} | | fSrC)rlr[rY) rrr<rWrXrrr1r2rei1i2imr@r@rAmpci_mulvs      rc Cs|\}}|\}}|d}t|}t|} t|| |} tt||t|||} tt||t|||} t| | |} t| | |} | | fSr)rurYrlr[rp) rrr<rWrXrrrm1m2mrrr@r@rAmpci_divs   rcCsH|\}}|d}t||}t||\}}t|||}t|||}||fSr)rwrrl)rr<rWrXrrrr;r@r@rAmpci_exps   rcCrrC)r*)rrrWrXr@r@rA mpi_shiftr`rcCsR|d}t||}tt||}t|||}t|||}t|d}t|d}||fS)Nr}r^)rwrpmpi_onerYr[r)rr<re1e2rr;r@r@rA mpi_cosh_sinhs      rc CsP|\}}|d}t||\}}t||\}}t|||} t|||} | t| fSNr)rrrlre rr<rWrXrrr;chshrrr@r@rAmpci_coss   rc CsL|\}}|d}t||\}}t||\}}t|||} t|||} | | fSr)rrrlrr@r@rAmpci_sinrZrcCsR|\}}|tkr t|S|tkrt|St|}t|}t|||d}t||Sr)mpi_zerorjrurYrz)rr<rWrXrEr@r@rAmpci_abss rc Cs\|\}}|\}}||krtkrnn t|trtSt|St|trSt|tr1t|||t}nt|||t}t|trHt|||t}||fSt|||t}||fSt|trzt|||t}t|trot|||t}||fSt|||t}||fSt|trt|||t}t|trt|||t}||fSt|||t}||fSt|t}t |}||fSrC) rrrrvr2rrrr3r#) rrr<yaybrrrWrXr@r@rA mpi_atan2s@         rcCs|\}}t|||SrC)r)rr<rrr@r@rAmpci_args rcCs.|\}}tt||d|}t||}||fSr)ryrr)rr<rrrrr@r@rAmpci_logs rc Cs|\}}|tkr4|\}}||kr4|\}}} } |r*| dkr*t|d|t|| >|S|tkr4t|d|S|d} tt|t|| | |S)NrUr^r})r mpci_pow_intintrrrr) rrr<yreyimrrrrrrrr@r@rAmpci_pows   r cCs:|\}}tt|t||}t|||}t|d}||fSr)r[rurlr)rr<rWrXrrr@r@rA mpci_squares   r cCs|dkrtttft|| |d|S|dkrttfS|dkr$t||S|dkr-t||S|d}ttf}|rP|d@rEt|||}|d8}t||}|dL}|s7t||Sr|)rrrrrr r)rrr<rresultr@r@rAr s$     rg#+Vcb?gVcb?gg?cCs0|\}}|\}}t||rdSt||rdSdS)NFT)rr)rrrWrXrrr@r@rA mpi_overlap&rOrc Cs|\}}|d}|dkrtt|t||dSt|trW|dkr/t||t}t||t}||fS|dkrCt||t}t||t}||fS|dkrSt ||t}t ||t}||fSt|t rt |t r|dkrut||t}t||t}||fS|dkrt||t}t||t}||fS|dkrt ||t}t ||t}||fSt|t|}|dkrt t||dd||S|dkrtt||dd||S|dkrtt||ddt||d|S||fS)Nr}rrUr~r) mpi_gammarYrr gamma_min_br6rrr7r8rr gamma_min_arprlr[ry) rr<typerWrXrrrznewr@r@rAr2sF                 *rcCs|\\}}\}}||krtkr%nn|dkst|tr%t|||tfS|d}|dkrg|d|d}|d|d} |tkrGt|| } n| } tt|} tt|} t| | } td| | }|t|7}|dkrt||ft |\}}||f||ff}d}t |t rt ||ft tfrt||ft |||ff}|dkrtt||dd||S|dkrtt||dd||S|dkrtt||ddt||d|St|trt||f|t}t||f|t}t||f|t}t||f|t}nXt|trt||f|t}t||f|t}t||f|t}t||f|t}n1t|tf|t}tt||r4t||f|t}nt||f|t}t||f|t}t||f|t}|d|df|d|dff}|dkrot|d|t|d|fS|dkrxt|}t||S)Nrr}r~rUr)rrrrmaxabsrr rYrrrrgamma_mono_imag_agamma_mono_imag_br mpci_gammarrrrr9rrrr#rcrr)rr<ra1a2b1b2ramagbmagmaganbnabsn gamma_sizerminremaxreminimmaximwr@r@rArWs\*     $   *      rcCt||ddSNrrrrr<r@r@rA mpi_loggammar.cCr)r*rr-r@r@rA mpci_loggammar/r1cCr)Nr~r+r,r-r@r@rA mpi_rgammar/r3cCr)r2r0r-r@r@rA mpci_rgammar/r4cCr)Nrr+r,r-r@r@rA mpi_factorialr/r6cCr)r5r0r-r@r@rAmpci_factorialr/r7N)rU)Trrr)__doc__backendrlibmpfrrrrrrr r r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'r(r)r*r+r,r- libelefunr.r/r0r1r2r3r4r5 gammazetar6r7r8r9rBrrrFrHrNrPrRrTrYr[r]r_rcrerjrnrqrlrurprvrwryrzr{rrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrr gamma_minrrrrrr.r1r3r4r6r7r@r@r@rAs (        D;%  4 B\       & %I