+
    i;C                        ^ RI t ^RIHt ^RIHt ^RIHtHtHtHtH	t	H
t
HtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t"H#t#H$t$H%t%H&t&H't'H(t(H)t)H*t*H)t)H+t+H,t,H-t-H.t.H/t/ ^RI0H1t1 ]]3t2^RI3H4t4 ]5Pl                  t7R t8 ! R R	]54      t9 ! R
 R]54      t:R t;];! ]]%4      w  ]9n<        ]9n=        ]:n<        ]:n=        ];! ]]&4      w  ]9n>        ]9n?        ]:n>        ]:n?        ];! ]]'4      w  ]9n@        ]9nA        ]:n@        ]:nA        ];! ]](4      w  ]9nB        ]9nC        ]:nB        ]:nC        ];! ]!])4      w  ]9nD        ]9nE        ]:nD        ]:nE        ]9P                  ]9nF        ]9P                  ]9nG        ]:P                  ]:nF        ]:P                  ]:nG         ! R R]94      tH ! R R]44      tI ^ RIJtJ]JP                  P                  ]:4       ]JP                  P                  ]94       R#   ]N d     R# i ; i)    N)libmp)
basestring),	int_typesMPZ_ONEprec_to_dpsdps_to_precrepr_dpsround_floorround_ceilingfzerofinffninffnanmpf_lempf_negfrom_int
from_floatfrom_strfrom_rationalmpi_mid	mpi_deltampi_strmpi_absmpi_posmpi_negmpi_addmpi_submpi_mulmpi_divmpi_pow_intmpi_powmpi_from_strmpci_posmpci_negmpci_addmpci_submpci_mulmpci_divmpci_powmpci_absr)   mpci_expmpci_logComplexResultmpf_hashmpc_hash)_matrix)StandardBaseContextc                    \        V R 4      '       d   V P                  # \        V \        4      '       d   \	        WV4      # \        V \
        4      '       d   \        WV4      # \        V \        4      '       d   \        WV4      # \        h)_mpf_)
hasattrr3   
isinstancer   r   floatr   r   r   NotImplementedError)xprecroundings   &&&m/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/mpmath/ctx_iv.pyconvert_mpf_r<      sh    q'177N!Y((C!C!UJq$AA!Z  !8)D"D
    c                   0  a  ] tR t^&t o RtR!R ltR tR tR tR t	R t
]R 4       t]R	 4       tR
 t]R 4       t]R 4       t]R 4       t]R 4       t]R 4       tR t]t]t]t]tR tR tR tR tR tR tR tR tR tR tR tR tR t R"R lt!R t"V t#R# )#ivmpfz@
Interval arithmetic class. Precision is controlled by iv.prec.
c                8    V P                   P                  V4      # N)ctxconvert)clsr8   s   &&r;   __new__ivmpf.__new__+   s    wwq!!r=   c                R    V P                   w  r4W48X  d   V! V! V4      4      # \        hrA   )_mpi_
ValueError)selfrD   	f_convertabs   &&&  r;   cast
ivmpf.cast.   s'    zz6y|$$r=   c                J    V P                  \        \        P                  4      # rA   )rN   intr   to_intrJ   s   &r;   __int__ivmpf.__int__4   s    yyell++r=   c                J    V P                  \        \        P                  4      # rA   )rN   r6   r   to_floatrS   s   &r;   	__float__ivmpf.__float__7   s    yy//r=   c                J    V P                  \        \        P                  4      # rA   )rN   complexr   rW   rS   s   &r;   __complex__ivmpf.__complex__:   s    yy%..11r=   c                j    V P                   w  rW8X  d   \        V4      # \        V P                   4      # rA   )rH   r.   hashrJ   rL   rM   s   &  r;   __hash__ivmpf.__hash__=   s+    zz6A;

##r=   c                    V # rA    rS   s   &r;   real
ivmpf.realD   s    Kr=   c                .    V P                   P                  # rA   )rB   zerorS   s   &r;   imag
ivmpf.imagG   s    88==(r=   c                    V # rA   rd   rS   s   &r;   	conjugateivmpf.conjugateJ   s    r=   c                V    V P                   w  rV P                  P                  W34      # rA   rH   rB   make_mpfr`   s   &  r;   rL   ivmpf.aL   $    zzxx  !((r=   c                V    V P                   w  rV P                  P                  W"34      # rA   ro   r`   s   &  r;   rM   ivmpf.bQ   rr   r=   c                ~    V P                   p\        V P                  VP                  4      pVP	                  W"34      # rA   )rB   r   rH   r9   rp   rJ   rB   vs   &  r;   mid	ivmpf.midV   s0    hhDJJ)||QF##r=   c                ~    V P                   p\        V P                  VP                  4      pVP	                  W"34      # rA   )rB   r   rH   r9   rp   rv   s   &  r;   deltaivmpf.delta\   s0    hhdjj#((+||QE""r=   c                &    V P                   \        3# rA   )rH   mpi_zerorS   s   &r;   _mpci_ivmpf._mpci_b   s    zz8##r=   c                     \        R 4      h)z-no ordering relation is defined for intervals	TypeError)argss   *r;   _compareivmpf._comparef   s    GHHr=   c                    V P                   P                  V4      pV P                  VP                  8*  ;'       d    VP                  V P                  8*  # rA   )rB   mpfrL   rM   )rJ   ts   &&r;   __contains__ivmpf.__contains__n   s9    HHLLO!##22ACC466M2r=   c                V    \        V P                  V P                  P                  4      # rA   )r   rH   rB   r9   rS   s   &r;   __str__ivmpf.__str__r   s    tzz488==11r=   c                   V P                   P                  '       d   \        V 4      # V P                  w  r\	        V P                   P
                  4      p\        P                  ! W4      p\        P                  ! W#4      pR V: RV: R2# )zmpi(, ))rB   prettystrrH   r	   r9   r   to_str)rJ   rL   rM   ns   &   r;   __repr__ivmpf.__repr__u   s]    88???t9zzTXX]]#LLLL !1%%r=   c                    \        VR 4      '       g    V P                  P                  V4      pV! V P                  VP                  4      #    \        u # ; i)rH   )r4   rB   rC   NotImplementedrH   )sr   cmpfuns   &&&r;   r   r   ~   sJ    q'""&EEMM!$ aggqww''&%%s   A Ac                B    V P                  V\        P                  4      # rA   )r   r   mpi_eqr   r   s   &&r;   __eq__ivmpf.__eq__       QZZ5<<88r=   c                B    V P                  V\        P                  4      # rA   )r   r   mpi_ner   s   &&r;   __ne__ivmpf.__ne__   r   r=   c                B    V P                  V\        P                  4      # rA   )r   r   mpi_ltr   s   &&r;   __lt__ivmpf.__lt__   r   r=   c                B    V P                  V\        P                  4      # rA   )r   r   mpi_ler   s   &&r;   __le__ivmpf.__le__   r   r=   c                B    V P                  V\        P                  4      # rA   )r   r   mpi_gtr   s   &&r;   __gt__ivmpf.__gt__   r   r=   c                B    V P                  V\        P                  4      # rA   )r   r   mpi_ger   s   &&r;   __ge__ivmpf.__ge__   r   r=   c                    V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r   rH   r9   rS   s   &r;   __abs__ivmpf.__abs__   *    xx  TXX]]!CDDr=   c                    V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r   rH   r9   rS   s   &r;   __pos__ivmpf.__pos__   r   r=   c                    V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r   rH   r9   rS   s   &r;   __neg__ivmpf.__neg__   r   r=   Nc                :    V P                   P                  WW#4      # rA   rB   almosteqr   r   rel_epsabs_epss   &&&&r;   aeivmpf.ae       uu~~aG55r=   rd   r   NN)$__name__
__module____qualname____firstlineno____doc__rE   rN   rT   rX   r\   ra   propertyre   ri   rl   rL   rM   rx   r{   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   __static_attributes____classdictcell____classdict__s   @r;   r?   r?   &   s    ",02$  ( ($) ) ) ) $ $
 # #
 $ $I FFFF32&( 988888EEE6 6r=   r?   c                      a  ] tR t^t o RR ltR tR tR t]R 4       t	]R 4       t
]R 4       t]R 4       t]R	 4       t]R
 4       tR tR tR tRR ltR tR tR t];t;ttR tR tR tRR ltRtV tR# )ivmpcc                    V P                   P                  V4      pV P                   P                  V4      p\        V 4      pVP                  VP                  3Vn        V# rA   )rB   rC   newrH   r   )rD   reimys   &&& r;   rE   ivmpc.__new__   sH    WW__R WW__R H88RXX%r=   c                    V P                   w  w  rw  r4W8X  d   W48X  d   \        W34      # \        V P                   4      # rA   )r   r/   r_   rJ   rL   rM   cds   &    r;   ra   ivmpc.__hash__   s8    6afQF##$$r=   c                    V P                   P                  '       d   \        V 4      # R \        V P                  4      : R\        V P
                  4      : R2# )ziv.mpc(r   r   )rB   r   r   reprre   ri   r   s   &r;   r   ivmpc.__repr__   s8    55<<<q6M #'<aff>>r=   c                d    R \        V P                  4      : R\        V P                  4      : R2# )( + *j))r   re   ri   r   s   &r;   r   ivmpc.__str__   s     #AFFS[99r=   c                `    V P                   w  w  rw  r4V P                  P                  W34      # rA   r   rB   rp   r   s   &    r;   rL   ivmpc.a   *    xx  !((r=   c                `    V P                   w  w  rw  r4V P                  P                  W"34      # rA   r   r   s   &    r;   rM   ivmpc.b   r   r=   c                `    V P                   w  w  rw  r4V P                  P                  W334      # rA   r   r   s   &    r;   r   ivmpc.c   r   r=   c                `    V P                   w  w  rw  r4V P                  P                  WD34      # rA   r   r   s   &    r;   r   ivmpc.d   r   r=   c                Z    V P                   P                  V P                  ^ ,          4      # r   rB   rp   r   r   s   &r;   re   
ivmpc.real       uu~~ahhqk**r=   c                Z    V P                   P                  V P                  ^,          4      #    r   r   s   &r;   ri   
ivmpc.imag   r   r=   c                j    V P                   w  rV P                  P                  V\        V4      34      # rA   )r   rB   make_mpcr   )r   rL   rM   s   &  r;   rl   ivmpc.conjugate   s(    xxuu~~q'!*o..r=   c                   V P                   P                  V4      pV P                  VP                  u;8*  ;'       d    V P                  8*  Mu ;'       g    V P                  VP                  u;8*  ;'       d    V P                  8*  Mu ;'       gq    VP                  V P                  u;8*  ;'       d    VP                  8*  Mu ;'       g5    VP                  V P                  u;8*  ;'       d    VP                  8*  Mu pV P                  VP                  u;8*  ;'       d    V P
                  8*  Mu ;'       g    V P                  VP
                  u;8*  ;'       d    V P
                  8*  Mu ;'       gq    VP                  V P                  u;8*  ;'       d    VP
                  8*  Mu ;'       g5    VP                  V P
                  u;8*  ;'       d    VP
                  8*  Mu pT;'       d    T# rA   )rB   rC   rL   rM   r   r   )r   r   real_overlapimag_overlaps   &&  r;   overlapivmpc.overlap   s<   EEMM!qss))acc)ooqssacc/@/@QSS/@ooaccQSSFWFWTUTWTWFWoo]^]`]`dedgdg]n]nklknkn]nqss))acc)ooqssacc/@/@QSS/@ooaccQSSFWFWTUTWTWFWoo]^]`]`dedgdg]n]nklknkn]n,,,r=   c                    V P                   P                  V4      pVP                  V P                  9   ;'       d    VP                  V P                  9   # rA   )rB   rC   re   ri   r   s   &&r;   r   ivmpc.__contains__   s<    EEMM!vv44AFFaff$44r=   c                p   \        WP                  P                  4      '       g    V P                  P                  V4      p\        VR 4      '       d   VP                  \        3pM\        VR4      '       d   VP                  pV'       d   V P                  X8g  # V P                  X8H  #    \        u # ; irH   r   )	r5   rB   _typesrC   r   r4   rH   r~   r   )r   r   netvals   &&& r;   r   ivmpc._compare   s    !UU\\**&EEMM!$ 1g77H$DQ!!88D88t##xx4&%%s   B+ +B5c                $    V P                  V4      # rA   r   r   s   &&r;   r   ivmpc.__eq__   s    QZZ]*r=   c                &    V P                  VR 4      # )Tr  r   s   &&r;   r   ivmpc.__ne__   s    QZZ400r=   c                    \        R 4      h)z#complex intervals cannot be orderedr   r   s   &&r;   r   ivmpc.__lt__   s    I&KLLr=   c                    V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   r   r$   r   r9   r   s   &r;   r   ivmpc.__neg__   '    155>>(188QUUZZ*HIIr=   c                    V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   r   r#   r   r9   r   s   &r;   r   ivmpc.__pos__   r  r=   c                    V P                   P                  \        V P                  V P                   P                  4      4      # rA   )rB   rp   r*   r   r9   r   s   &r;   r   ivmpc.__abs__   r  r=   Nc                :    V P                   P                  WW#4      # rA   r   r   s   &&&&r;   r   ivmpc.ae   r   r=   rd   )r   r   Fr   )r   r   r   r   rE   ra   r   r   r   rL   rM   r   r   re   ri   rl   r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   s   @r;   r   r      s     %?
: ) ) ) ) ) ) ) ) + + + +/-5  +0L%%F%VfIII6 6r=   r   c                 `   a aaa V3R  loV V3R loVV3R lpVV3R lpV3R lpV3R lpW#WE3# )c                 H   < V P                  S! WV P                  4      4      # rA   )r   r9   )rB   svalr  	f_complexs   &&&r;   	g_complex_binary_op.<locals>.g_complex   s    ||Id#((;<<r=   c                    <  V P                  S! WV P                  4      4      #   \         d    T\        3pT\        3pS! YT4      u # i ; irA   )rp   r9   r-   r~   )rB   r   r  f_realr"  s   &&&r;   g_real_binary_op.<locals>.g_real   sR    	.<<t388 <== 	.(#D(#DS--	.s   !% $AAc                   < \        V\        4      '       d   \        # V P                  p\        WP                  4      '       g   VP                  V4      p\        VR 4      '       d   S! W P                  VP                  4      # \        VR4      '       d$   S! W P                  \        3VP                  4      # \        # r  )
r5   r0   r   rB   r	  rC   r4   rH   r~   r   r   r   rB   r"  r&  s   && r;   lop_real_binary_op.<locals>.lop_real   s    a!!.#8ee!ZZ((ckk!n!1gvc77AGG'D D1h	#7JAHH(U!Ur=   c                 H  < V P                   p\        WP                  4      '       g   VP                  V4      p\	        VR 4      '       d   S! W!P
                  V P
                  4      # \	        VR4      '       d$   S! W!P                  V P
                  \        34      # \        # r  )	rB   r5   r	  rC   r4   rH   r   r~   r   r)  s   && r;   rop_real_binary_op.<locals>.rop_real  st    ee!ZZ((ckk!n!1gvc77AGG'D D1h	#xx!''8AT(U!Ur=   c                 J  < \        V\        4      '       d   \        # V P                  p\        WP                  P                  4      '       g    V P                  P                  V4      pS! W P                  VP                  4      #   \        \        3 d
    \        u # i ; irA   )	r5   r0   r   rB   r	  rC   rI   r   r   r   r   rB   r"  s   && r;   lop_complex_binary_op.<locals>.lop_complex  s{    a!!.#8ee!UU\\**&EEMM!$ hh11 	* &%%&s   B B"!B"c                    < V P                   p\        WP                   P                  4      '       g   V P                   P                  V4      pS! W!P                  V P                  4      # rA   )rB   r5   r	  rC   r   r0  s   && r;   rop_complex_binary_op.<locals>.rop_complex  sF    ee!UU\\**a Ahh11r=   rd   )r%  r!  r*  r-  r1  r4  r"  r&  s   ff    @@r;   
_binary_opr6     s.    =.22
 {77r=   c                   <   a  ] tR tRt o R tR t]! ]4      tRtV t	R# )ivmpf_constanti$  c                (    \        V 4      pWn        V# rA   )r   _f)rD   frJ   s   && r;   rE   ivmpf_constant.__new__%  s    3xr=   c                    V P                   P                  ^ ,          pV P                  V\        4      pV P                  V\        4      pW#3# r   )rB   _precr:  r
   r   )rJ   r9   rL   rM   s   &   r;   	_get_mpi_ivmpf_constant._get_mpi_)  s;    xx~~a GGD+&GGD-(tr=   )r:  N)
r   r   r   r   rE   r?  r   rH   r   r   r   s   @r;   r8  r8  $  s     
 YEr=   r8  c                      a  ] tR tRt o R tRR ltR tRR lt]R 4       t	R t
R	 t]! R
 ]
4      t]! R ]4      tR tR tR tR tRR ltR tR tR tR tR tR tR tR tR tR tR tR R ltRt V t!R# )!MPIntervalContexti0  c                X   \        R \        3/ 4      V n        \        R\        3/ 4      V n        V P                  V P                  3V n        \        R\        3/ 4      V n        ^5.V n        V P                  ^54       V P                  \        V P                  .;V P                  n        ;V P                  n        V P                  n        V ;V P                  n        ;V P                  n        V P                  n        RV n        \        P                  ! V 4       V P!                  4        R# )r?   r   r8  FN)typer?   r   r   mpcr	  r8  	_constantr>  	_set_precr   _ctxdatarB   r   r1   __init___init_builtinsrB   s   &r;   rI  MPIntervalContext.__init__2  s    w"-w"-ggsww'
-/@"ED	bHKQTVYV_V_G```!1CGG4D8;;;CGGK#''+
$$S)r=   Nc                P    Vf   V P                  V4      # V P                  W34      # rA   )r   )rB   rL   rM   s   &&&r;   _mpiMPIntervalContext._mpi?  s%    9771:wwu~r=   c                   V P                  ^4      V n        V P                  ^ 4      V n        V P                  R4      V n        V P                  ) V n        V P                  R4      V n        V P                  ^ ^4      V n        V P                  \        P                  \        P                  4      V n        V P                  \        P                  4      V n        V P                  \        P                  \        P                   4      V n        V P                  \        P$                  \        P&                  4      V n        V P                  \        P*                  \        P,                  4      V n        V P                  \        P0                  4      V n        V P                  \        P4                  \        P6                  4      V n        V P                  \        P:                  \        P<                  4      V n        V P                  \        P@                  \        PB                  4      V n"        V P                  \        PF                  \        PH                  4      V n%        V PJ                  V n&        V PO                  R 4      V n(        V PO                  \        PR                  4      V n*        V PO                  \        PV                  4      V n,        V PO                  \        PZ                  4      V n.        V PO                  \        P^                  4      V n0        V PO                  \        Pb                  4      V n2        V PO                  \        Pf                  4      V n4        V PO                  \        Pj                  4      V n6        V PO                  \        Pn                  4      V n8        V PO                  \        Pr                  4      V n:        V PO                  \        Pv                  4      V n<        R# )r   infnanc                 $    ^ \         ^V ,
          ^3# r   )r   )r9   rnds   &&r;   <lambda>2MPIntervalContext._init_builtins.<locals>.<lambda>W  s    1gqvq2Ir=   N)=r   onerh   rQ  ninfrR  rE  j_wrap_mpi_functionr   mpi_expr+   expmpi_sqrtsqrtmpi_logr,   lnmpi_cosmpci_coscosmpi_sinmpci_sinsinmpi_tantan	mpi_gamma
mpci_gammagammampi_loggammampci_loggammaloggamma
mpi_rgammampci_rgammargammampi_factorialmpci_factorial	factorialfacrF  epsmpf_pipimpf_eempf_ln2ln2mpf_ln10ln10mpf_phiphi	mpf_eulereulermpf_catalancatalanmpf_glaisherglaishermpf_khinchinkhinchinmpf_twinprime	twinprimerK  s   &r;   rJ   MPIntervalContext._init_builtinsD  sb   ''!*771:''%.GG8''%.!((G))%..9''u~~F((G((G((7**5??E<L<LM	--e.@.@%BUBUV++E,<,<e>O>OP
..u/B/BEDXDXY---- IJu||,ekk*--.==0--.MM%//2	mmE$5$56}}U%7%78}}U%7%78e&9&9:r=   c                   a aa V VV3R  lpV# )c                   < V'       d%   VP                  R SP                  ^ ,          4      pMSP                  ^ ,          pSP                  V 4      p \        V R4      '       d#   SP	                  S! V P
                  V4      4      # \        V R4      '       d#   SP                  S! V P                  V4      4      # \        h)r9   rH   r   )	getr>  rC   r4   rp   rH   r   r   rI   )r8   kwargsr9   rB   r!  r%  s   &, r;   g/MPIntervalContext._wrap_mpi_function.<locals>.gd  s    zz&#))A,7yy|AAq'""||F177D$9::q(##||Iahh$=>>r=   rd   )rB   r%  r!  r  s   fff r;   rZ  $MPIntervalContext._wrap_mpi_functionc  s    
	 r=   c                B   a V'       d   V3R  lpMSp\        WV4       R# )c                    < V P                   pV Uu. uF
  qC! V4      NK  	  ppV P                  p V ;P                  ^
,          un        S! V .VO5/ VB pWPn        V5# u upi   YPn        i ; i)
   )rC   r9   )rB   r   r  rC   rL   r9   retvalr;  s   &*,    r;   	f_wrapped2MPIntervalContext._wrap_specfun.<locals>.f_wrappedt  sm    ++,01Dq
D1xx$HHNHs4T4V4F#Hw 2  $Hs   A%A$ $A,N)setattr)rD   namer;  wrapr  s   &&f& r;   _wrap_specfunMPIntervalContext._wrap_specfunq  s    	 I9%r=   c                j    \        ^\        V4      4      V P                  ^ &   \        V4      V n        R# )r   N)maxrQ   r>  r   _dpsrB   r   s   &&r;   rG  MPIntervalContext._set_prec  s$    1c!f~		!q>r=   c                j    \        V4      V P                  ^ &   \        ^\        V4      4      V n        R# r   N)r   r>  r  rQ   r  r  s   &&r;   _set_dpsMPIntervalContext._set_dps  s$    "1~		!q#a&>r=   c                (    V P                   ^ ,          # r   )r>  rK  s   &r;   rU  MPIntervalContext.<lambda>  s    		!r=   c                    V P                   # rA   )r  rK  s   &r;   rU  r    s    sxxr=   c                <    \        V P                  4      pWn        V# rA   )r   r   rH   rB   rw   rL   s   && r;   rp   MPIntervalContext.make_mpf  s    Lr=   c                <    \        V P                  4      pWn        V# rA   )r   rE  r   r  s   && r;   r   MPIntervalContext.make_mpc  s    Lr=   c                    Vw  r#\         P                  ! W#V P                  \        4      p\         P                  ! W#V P                  \        4      pV P                  WE34      # rA   )r   r   r9   r
   r   rp   )rB   pqpqrL   rM   s   &&    r;   _mpqMPIntervalContext._mpq  sJ    chh<chh>||QF##r=   c                   \        WP                  V P                  34      '       d   V# \        WP                  4      '       d   V5# \        V\        4      '       g   \        VR 4      '       dH   V P                  VP                  4      pV P                  VP                  4      pV P                  W#4      # \        V\        4      '       d'   \        WP                  4      pV P                  V4      # \        VR4      '       d   VP                  w  rVM Vw  rV\        VR4      '       d   VP                  ^ ,          pM\!        WPP                  \"        4      p\        VR4      '       d   VP                  ^,          pM\!        W`P                  \$        4      pV\&        8X  g   V\&        8X  d   \(        p\*        p\-        WV4      '       g   Q R4       hV P                  WV34      #   \        \        3 d    T;rV Li ; i)_mpc_rH   z"endpoints must be properly ordered)r5   r   rE  rF  r[   r4   rC   re   ri   r   r"   r9   rp   rH   r   rI   r<   r
   r   r   r   r   r   )rB   r8   r   r   rw   rL   rM   s   &&     r;   rC   MPIntervalContext.convert  s   a''377+,,Ha''2Ia!!WQ%8%8QVV$BQVV$B772>!a$$Q)A<<?"1g77DAq q'""GGAJ HHk:q'""GGAJ HHm<9T	AAa||AAA|||QF## z* 	As   G% %G<;G<c                n   V P                  V4      p\        VR 4      '       d#   \        P                  ! VP                  V3/ VB # \        VR4      '       d^   \        P                  ! VP
                  ^ ,          V3/ VB p\        P                  ! VP
                  ^,          V3/ VB pRV: RV: R2# R# )rH   r   r   r   r   N)rC   r4   r   
mpi_to_strrH   r   )rB   r8   r   r  r   r   s   &&&,  r;   nstrMPIntervalContext.nstr  s    KKN1g##AGGQ9&991h!!!((1+q;F;B!!!((1+q;F;B$&++  r=   c                   V P                  V4      p\        WP                  4      '       dF   \        V P	                  VP
                  4      V P	                  VP                  4      4      ^,           # \        P                  ! VP                  4      w  r#Vw  rErgV'       d	   Wg,           # V\        8X  d   V P                  # V\        8X  d   V P                  # V P                  # r   )rC   r5   rE  r  magre   ri   r   r   rH   r   rX  r   rR  rQ  rB   r8   rL   rM   signmanr\  bcs   &&      r;   r  MPIntervalContext.mag  s    KKNa!!swwqvv81<<}}QWW%36M:88O977Nwwr=   c                    R # r  rd   rB   r8   s   &&r;   isnanMPIntervalContext.isnan  s    r=   c                    WP                   8H  # rA   )rQ  r  s   &&r;   isinfMPIntervalContext.isinf  s    GG|r=   c                    V P                  V4      pVP                  w  r#W#8X  d   Vw  rErgV'       d   V^ 8  # V\        8H  # R# r  )rC   rH   r   r  s   &&      r;   isintMPIntervalContext.isint  sB    KKNww6!"Dsax:r=   c                    V P                  V4      P                  w  r4\        P                  ! W24      p\        P                  ! WB4      pV P	                  W434      # rA   )rC   rH   r   	mpf_shiftrp   )rB   r8   r   rL   rM   s   &&&  r;   ldexpMPIntervalContext.ldexp  sD    {{1~##OOA!OOA!||QE""r=   c                J    \        V P                  V4      4      P                  # rA   )absrC   rL   r  s   &&r;   absminMPIntervalContext.absmin      3;;q>"$$$r=   c                J    \        V P                  V4      4      P                  # rA   )r  rC   rM   r  s   &&r;   absmaxMPIntervalContext.absmax  r  r=   c                    V P                  V4      P                  pV P                  V4      P                  pV P                  \        P                  ! WV P
                  4      4      # rA   )rC   rH   rp   r   	mpi_atan2r9   )rB   r   r8   s   &&&r;   atan2MPIntervalContext.atan2  sF    KKN  KKN  ||EOOA9::r=   c                z   \        V\        P                  4      '       d   VR 3# \        V\        4      '       d.   Vw  r#V P	                  V4      V P	                  V4      ,          R3# V P                  V4      p\        WP                  4      '       d   VR3# \        WP                  4      '       d   VR3# \        h)ZRC)r5   r   r   tupler   rC   rE  rI   )rB   r8   r  r  s   &&  r;   _convert_param MPIntervalContext._convert_param  s    a))c6MaDAGGAJ+S11KKNa!!c6Ma!!c6Mr=   c                \    \        WP                  4      ;'       g    \        V\        4      # rA   )r5   r   r   rB   zs   &&r;   _is_real_typeMPIntervalContext._is_real_type  s     !WW%AAAy)AAr=   c                ,    \        WP                  4      # rA   )r5   rE  r  s   &&r;   _is_complex_type"MPIntervalContext._is_complex_type  s    !WW%%r=   c                f   \        V4      p\        V4      p\        WV,           4      p	V P                  ;r^ p V F  qWM,          V,           ,          pK  	  V	 F  qWM,          V,           ,          pK  	  V^,          qV,          qV,          qV,          p
V^ 8X  d   V
# W8  g   Ko  V P                  hr   )listrangerW  NoConvergence)rB   r  r  typescoeffsr  maxtermsr  numdenr   r   kis   &&&&&&&,      r;   hypsumMPIntervalContext.hypsum	  s    fAhAcl	!,!S	!,!SFAFAFAFAAv |'''r=   rd   rA   )   )ip  )"r   r   r   r   rI  rN  rJ  rZ  classmethodr  rG  r  r   r9   dpsrp   r   r  rC   r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   r   s   @r;   rB  rB  0  s     
;> & & "" ,i8D
'
2C

$$B,#%%;
B&( (r=   rB  )Ooperator r   libmp.backendr   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   matrices.matricesr0   r~   ctx_baser1   objectrE   r   r<   r?   r   r6  __add____radd____sub____rsub____mul____rmul____div____rdiv____pow____rpow____truediv____rtruediv__r8  rB  numbersComplexregisterRealImportErrorrd   r=   r;   <module>r     s     %            '5> )nno6F o6b[6F [6z%8N @J'S[?\ <u~u}en?I'S[?\ <u~u}en?I'S[?\ <u~u}en?I'S[?\ <u~u}en?I'S[?\ <u~u}enMM 5#5MM 5#5
 U 
 i(+ i(d	OOU#LL%  		s   *:G& &G10G1