
    [hwD                     h    S SK 7  S rS rS rS rS rS rS rS	 rS
 r	S r
S rS rS rS rS rg)    )*c                  4   S[         l        [        S5      [        SS5      :X  d   e[        S5      [        SS5      :w  d   e[        S5      [        SS5      :w  a   e[        SS5      [        SS5      :X  d   e[        [        S5      5      S:X  d   e[	        [        S5      5      S:X  d   e[        SS	5      n SU ;   d   eSU ;   d   eS	U ;   d   eS
U ;  d   eSU ;  d   e[        SS	5      U ;   d   e[        SS5      U ;   d   e[        S
S5      U ;  d   e[        SS5      U ;  d   e[        [
        * [
        5      n[        SS5      U;   d   e[        S[
        5      U;   d   e[        SS5      [        SS5      ;   d   eS	[        [
        * S5      ;  d   eg )N         z0.1z1[0.099999999999999991673, 0.10000000000000000555]z2mpi('0.099999999999999992', '0.10000000000000001')   gg@r         @   
   )ivdpsmpistrreprinf)uws     R/var/www/auris/envauris/lib/python3.13/site-packages/mpmath/tests/test_interval.pytest_interval_identityr      s   BFq6SAYq6SQZA#a)#$$r1:R###s5z?QQQQE
SSSSB
A7N76M66M6q==a<<r1:??q!9>>tQ<q   sC=!!!SD#Ar1:??q#;!q!9Ar
"""S#q\!"!    c                  &   [        [        S5      5      [        S5      :X  d   e[        [        S5      5      [        S5      :X  d   e[        [        SS5      5      [        [        SS5      5      :X  d   e[        [        R                  S5      5      [        S5      :X  d   e[        [        R                  SS5      5      [        S5      :X  d   e[        [        R                  SS5      5      [        [        R                  SS5      5      :X  d   eg )Nr
   g      
@   y      @      @)r	   r
   )r   r   )hashr   r   mpc r   r   test_interval_hashr      s    A<47"""D	?d4j(((Aa>T#a(^+++q	?d1g%%%qT
***uU#$RVVE%-@(AAAAr   c                  
   S[         l        [        S5      [        SS5      -   [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        S5      [        SS	5      -   [        S[        S
5      5      :X  d   eSS[        S5      -  -  n U R                  Ss=:  a  U R
                  :  d   e   e[        S5      [        S5      -  n [         =R                  S-  sl        [         R                  S5      n[         =R                  S-  sl        U R                  Us=:  a  U R
                  :  d   e   e[        S5      [        S[        5      -  (       d   e[        SS5      [        -  [        SS5      :X  d   e[        S5      [        -  S:X  d   e[        S5      S-  [        [        * [        5      :X  d   e[        [        5      S-  [        [        * [        5      :X  d   e[        S5      [        -  [        [        * [        5      :X  d   eS[        S[        5      -  [        SS5      :X  d   e[        [        SS5      [        SS5      -  S-  5      S:X  d   e[        SS5      S-  [        SS5      :X  d   e[        SS5      R                  S:X  d   eS[         l        [        [         R                  5      nS[         l        U7nUR                  UR                  :  d   eUR
                  UR
                  :  d   e[        [         R                  5      nX"7:X  d   e[        [        SS5      5      [        SS5      :X  d   e[        [        SS5      5      [        SS5      :X  d   e[        [        SS5      5      [        SS5      :X  d   e[        [        SS5      5      [        SS5      :X  d   e[        S5      [        SS5      -  [        S5      :X  d   e[        SS5      [        S5      -  [        S5      :X  d   e[        SS5      R                  S:X  d   e[        SS5      [        SS5      -
  [        SS5      :X  d   e[        [        * S5      [        S[        5      -
  [        [        * S5      :X  d   e[        [        * S5      [        [        * [        5      -
  [        [        * [        5      :X  d   e[        S[        5      [        [        * S5      -
  [        S[        5      :X  d   eg )Nr   r   r
   r   r      r	   r   gJz5z1.0000000000000002      ?2   iz0[-166.66666666666668561, -166.66666666666665719]@      r         )r   r   r   mpfabsqrtr   r   midpiabsdelta)xsqr)   r*   s       r   test_interval_arithmeticr2   #   s   BFq6C!HAa(((q!9a<3q!9$$$q6C5M!SC0D,E%FFFF	QQZA33=QSS===A#c(AFFaKF	BFFaKF33>acc>>>q6C3Kq!9s?c!Qi'''q6C<1q6A:cT3'''s8a<3tS>)))q6C<3tS>)))s1c{?c!Sk)))Bc#sm+q01:; ; ;q!9>SBZ'''q8<<1BFBEE
ABF	
A33993399BEE
A7N7s2ay>S1X%%%s3qz?c#aj(((s2ay>S1X%%%s2d|C
***q6C!HA&&&q8c!fA&&&q8>>Qq8c!Ah#b*,,,tA;Qs#sC4{222tA;cT#&#sd3-777q:SD#s2c{222r   c                     [        SS5      [        -  [        [        * S5      :X  d   e[        SS5      [        * -  [        S[        5      :X  d   e[        SS5      [        -  [        S[        5      :X  d   e[        SS5      [        S[        5      -  [        S[        5      :X  d   e[        SS5      [        -  [        [        * [        5      :X  d   e[        SS5      [        S[        5      -  [        [        * [        5      :X  d   e[        SS5      [        [        * [        5      -  [        [        * [        5      :X  d   e[        [        * S5      [        SS5      -  [        [        * S5      :X  d   e[        [        * S5      [        SS5      -  [        [        * S5      -  (       d   e[        [        * S5      [        [        * [        5      -  [        [        * [        5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        S	S
5      [        SS	5      -  [        SS5      :X  d   e[        [        [        5      S-  [        [        * [        5      :X  d   e[        [        * [        * 5      S-  [        [        * [        5      :X  d   e[        S5      [        [        * S	5      -  [        [        * [        5      :X  d   e[        S5      [        S[        5      -  [        [        * [        5      :X  d   e[        S[        5      [        S5      -  [        [        * [        5      :X  d   e[        [        * S	5      [        S5      -  [        [        * [        5      :X  d   eg )Nr   r   r	   r   i   it   r   r
   r&   r!   r   r   r   r   r   r   test_interval_mulr7   N   s   r1:sC4|+++r1:As+++q!9s?c!Sk)))q!9s1c{"c!Sk111r1:sC4~---r1:As#sC4~555r1:SD#&#sdC.888tQ<#a)#sC4|333tQ<#a)#c3$l222tQ<#sdC.(CcN:::r!9SR[ CSM111q8c"Qi3r!9,,,sC=1SD#...tcT?Q#sdC.000q6CQK3tC=000q6C3K3tC=000r#;Q3tC=000tA;Q3tC=000r   c                     [        S5      S-  [        SS5      :X  d   e[        S5      S-  [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        S	S5      S-  [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        S
5      S-  [        SS5      :X  d   e[        S5      S-  [        SS5      :X  d   e[        S
5      S	-  [        SS5      :X  d   e[        S5      S	-  [        SS5      :X  d   e[        SS5      [        -  [        SS5      :X  d   e[        SS5      [        * -  [        S[        5      :X  d   e[        S[        5      [        -  [        S[        5      :X  d   e[        S[        5      [        * -  [        S[        5      :X  d   e[        S[        5      [        -  [        S[        5      :X  d   e[        S[        5      [        * -  [        SS5      :X  d   e[        SS5      S-  [        SS5      :X  d   e[        SS5      S-  S:X  d   e[        SS5      [        S5      -  [        SS5      :X  d   eg )Nr
   r   	   r&   r	   r   r   ir   r         ?      пg      ?r6   r   r   r   test_interval_powr=   c   sz   q619Aq	!!!r7A:Q"""r1:q=C1I%%%r2;>SAY&&&r2;>Sb\)))r1:q=CQK'''r1:q=C1I%%%r1:q=C1I%%%q6R<3tT?***r7b=Cu----q6R<3vv....r7b=C////q!9s1ay(((q!9As+++q#;#Q,,,q#;3$#a+---q#;#Q,,,q#;3$#a)+++q!9>SAY&&&q!9>Qq8s1vQq)))r   c                  >    [        S5      S-  [        S5      :X  d   eg )Nr   r"   r   )r   r   r   r   test_interval_sqrtr?   z   s    q6S=CF"""r   c                  x   [        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        S[        5      :X  d   e[        [        [        5      [        [        [        5      -  [        S[        5      :X  d   e[        [        [        5      [        S[        5      -  [        S[        5      :X  d   e[        [        [        5      [        SS5      -  [        [        [        5      :X  d   e[        S[        5      [        S[        5      -  [        S[        5      :X  d   e[        S[        5      [        SS5      -  [        S[        5      :X  d   e[        S[        5      [        SS5      -  [        S[        5      :X  d   e[        S[        5      [        S[        5      -  [        S[        5      :X  d   e[        SS5      [        S[        5      -  [        SS5      :X  d   e[        SS5      [        S[        5      -  [        S	S
5      :X  d   e[        [        * S5      [        S[        5      -  [        [        * S
5      :X  d   e[        [        * [        5      [        S[        5      -  [        [        * [        5      :X  d   e[        S[        5      [        S[        5      -  [        S[        5      :X  d   e[        S	[        5      [        S[        5      -  [        S[        5      :X  d   e[        SS5      [        [        [        5      -  [        SS5      :X  d   e[        SS5      [        [        [        5      -  [        SS5      :X  d   e[        SS5      [        [        [        5      -  [        SS5      :X  d   e[        [        * S5      [        [        [        5      -  [        [        * S5      :X  d   e[        [        * S5      [        [        [        5      -  [        [        * S5      :X  d   e[        [        * [        5      [        [        [        5      -  [        [        * [        5      :X  d   e[        S	[        5      [        [        [        5      -  [        S[        5      :X  d   e[        S[        5      [        [        [        5      -  [        S[        5      :X  d   e[        S[        5      [        [        [        5      -  [        S[        5      :X  d   e[        [        [        5      [        [        [        5      -  [        S[        5      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * [        75      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        [        * S5      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        S[        75      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        SS5      :X  d   e[        SS5      [        SS5      -  [        [        * [        5      :X  d   e[        SS5      [        SS5      -  [        [        * [        5      :X  d   eg )Nr"   r	   r   r   r'   r   r;         i        r<   r   r   r:   g       g      @g       @g      g       @g       g      g      ?      ?r6   r   r   r   test_interval_divrF   }   s
   sA;R#sC4666q!9s1ay C3K///sC=3sC=(C3K777sC=3q#;&#a+555sC=3q!9$C555q#;Q$As333q#;Q"c!Sk111q#;Q"c!Sk111q#;Q$As333r1:As#s2qz111r1:C%R444tQ<#c3-'3tR=888tS>CSM)S#s^;;;q#;S#&#a+555r3<#c3-'3sC=888r1:C%Q222q!9s3}$Aq	111q!9s3}$Aq	111tQ<#c3-'3tQ<777tQ<#c3-'3tQ<777tS>CSM)S#s^;;;r3<#c3-'3q#;666q#;S#&#a+555q#;S#&#a+555sC=3sC=(C3K777r1:Aq	!S#t_444q!9s1ay CcTN222r1:Aq	!S#s^333tUc!Qi'3tU+;;;;sA;Q"c#tn444sA;Q"c#tn444r4=3q!9$SD$777r4=3q!9$SD$777r1:B$SD3$777q!9s2s|#sC4#666r1:B$SD3$777tUc"cl*c3$o===sA;R%cTC4888sA;R%cTC4888r4=3r3<'3tcT?:::r4=3r3<'3tcT?:::r1:B
"c3$o555q!9s2qz!S#s^333r1:B
"c#tn444tUc"aj(CsdO;;;sA;R#sC4666sA;R#sC4666r4=3r1:%S3$777r4=3r1:%S3$777r1:C#s4~555q!9s3{"c#sm333r1:C#s4~555tUc#qk)Su-====sA;S!$C555sA;S!$C555r4=3sA;&#dD/999r4=3sA;&#dD/999r1:B%T3777q!9s2t}$D#666r1:B%S#666tUc"dm+s5#>>>sA;R&#dE*::::sA;R&#dE*::::r4=3r4=(CcN:::r4=3r4=(CcN:::q!9s1ay CcN222q!9s1ay CcN222r   c                     S[         l        [         R                  n [         R                  n[         R                  n[         R
                  nU " [        S5      5      S:X  d   eU" [        S5      5      S:X  d   eU " [        SS5      5      [        SS5      :X  d   eU" [        SS5      5      [        SS5      :X  d   eU " [        SS5      5      [        SS	5      :X  d   eU" [        SS5      5      [        S
S5      :X  d   eU" [        SS5      5      [        SS5      :X  d   eU " [        SS5      5      [        SS5      :X  d   eU " [        SS5      5      [        SS5      :X  d   eU " [        SS5      5      [        SS5      :X  d   eU" [        SS5      5      [        SS5      :X  d   eU" [        SS5      5      [        SS5      :X  d   e[        SS5      U" [        SS5      5      ;   d   e[        SS5      U" [        SS5      5      ;   d   eU " [        SS5      5      (       d   eU " [        SS5      5      [        SS5      :X  d   eU " [        SS5      5      [        SS5      :X  d   e[        SS5      U" [        SS5      5      ;   d   eU" [        SS5      5      [        SS 5      :X  d   eU" [        SS5      5      [        S!S"5      :X  d   eS#[         l        SS$S%-  -  [        S5      -   nS& H  nU[         l        SU" S[        U5      -  5      ;   d   eSU" SS$S%-  -  [        U5      -  5      ;   d   eSU " S'[        U5      -  5      ;   d   eSU " U[        U5      -  5      ;   d   eSU " S[        U5      -  5      ;   d   eSU " SS$S%-  -  [        U5      -  5      ;   a  M   e   S[         l        U " [        S[        5      5      [        SS5      :X  d   eU" [        S[        5      5      [        SS5      :X  d   eU " [        [        * S5      5      [        SS5      :X  d   eU" [        [        * S5      5      [        SS5      :X  d   eU" [        SS5      5      n[        UR                  5      R                  [        R	                  S5      5      (       d   e[        UR                  5      R                  [        R	                  S5      5      (       d   e[         R                  [        SS5      5      n[        UR                  5      R                  [        R                  S5      5      (       d   e[        UR                  5      R                  [        R                  S5      5      (       d   e[        S(S)S5       H  n[         R                  U[         R
                  -  5      n	SU	;   d   eU	S:  d   eU	S:w  d   e[         R                  US-   [         R
                  -  5      n	SU	;   d   eU	S:  d   eU	S:w  a  M   e   [        S*S+S5       H  n[         R                  U[         R
                  -  5      n	SU	;   d   eU	S::  d   eU(       a  U	S:w  d   e[         R                  US-   [         R
                  -  5      n	SU	;   d   eU	S::  d   eU	S:w  a  M   e   [        S*S)5       H  n[         R                  US-   [         R
                  -  5      n	U	R                  Ss=:  a  U	R                  :  d   e   e[         R                  U[         R
                  -  5      n	U(       d  M  U	R                  Ss=:  a  U	R                  :  a  M   e   e   g ),Nr   r   r	   g(J?rE   g	T?r   grSW&ڿg(J?g	T?r   g&?r   r"         ?gO?g	TgKt?g0.++g0.;      @r   g_tg$r   g      @gJkp'?gI<l?g&?gF?gݹ7gb~;sֿg4gV
Nɓ7   r   r#   )r   (   P   g      @r      irA   )r   r   cossintanr-   r   r   r(   r)   aempr*   cotrange)
rN   rO   rP   r-   r   pr   vnr0   s
             r   test_interval_cos_sinrX      sN   BF
&&C
&&C
&&C	Bs1v;!s1v;!s1Qx=C 6<<<<s1Qx=C#89999s1Qx=C 68NOOOOs1Qx=C 6<<<<s1Sz?c"8#>>>>s2qz?c"8#>>>>s2s|$:C @@@@s2s|$;S AAAAs2ay>S!79NOOOOs2c{s#9;QRRRR%'?@CBvDWWWW(*BCs3wW]K^G____s1c{s3{s#:<STTTTs1c{s#9;QRRRR%'=>#c!SkBRRRRs3{s#:<STTTTs1c{s#:<STTTTBF	"b&3s8AC#b'	N"""C"b&R())))CB((((C#b'	N"""C#b'	N"""C"b&R())))  BFs1Sz?c"Qi'''s1Sz?c"Qi'''sC4{s2ay(((sC4{s2ay(((CAJAqss8;;rvvc{####qss8;;rvvay!!!!
s3qzAqss8;;rvvay!!!!qss8;;rvvc{####2a]FF1RUU7OQwwBwwBwwFFAcE255=!QwwBwwBww  2a]FF1RUU7OAvvAvv6M6FFAcE255=!AvvAvvAvv  2a[FFAcE255=!ssQ}}}}FF1RUU7O133=QSS= = = r   c                     S[         l        S[        l        [         R                  SS5      S:X  d   e[         R                  SS5      S:w  d   e[         R                  SS5      S:w  d   eS[         R                  SS/SS/5      ;   d   eS	[         R                  SS/SS/5      ;  d   e[         R                  SS5      S
-   S:X  d   e[         R                  SS/SS/5      S-   S-   [         R                  SS/SS/5      :X  d   e[         R                  SS/SS/5      S-  [         R                  SS/SS/5      :X  d   e[         R                  SS/SS/5      S-  [         R                  SS/SS/5      :X  d   e[         R                  SS/SS/5      S-  [         R                  SS/SS/5      :X  d   e[         R	                  S5      R                  [        R	                  S5      5      (       d   e[         R                  S5      R                  [        R                  S5      5      (       d   e[         R                  SS5      [         R                  SS5      -  R                  [        R                  SS5      [        R                  SS5      -  5      (       d   eS
[         R                  S5      S-  ;   d   eS
[         R                  S5      S-  ;   d   e[        [         R                  S5      5      S:X  d   e[        [         R                  [        5      5      [        :X  d   e[        [         R                  SS5      5      S:X  d   e[        [         R                  S5      5      S:X  d   e[        [         R                  SS5      5      S:X  d   e[        [         R                  SSS/5      5      [         R                  SS/5      :X  d   e[        [         R                  SSS/5      5      [         R                  SS/5      :X  d   e[        [         R                  SS/SS/5      5      [         R                  SS/5      :X  d   e[        [         R                  SS/SS/5      5      [         R                  SS/5      :X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  SS5      S-  S:X  d   e[         R                  S5      R                  [        R                  S5      5      (       d   e[         R                  S5      R                  [        R                  S5      5      (       d   e[         R                  S5      R                  [        R                  S5      5      (       d   e[         R                  S5      R                  [        R                  S5      5      (       d   eg )Nr   r   r
          @      @y       @      @      ?      @r	   r   y       @      @y              ?y              @r   r!   rA   y               @rB   r;   r   r   r"   r   r&         y            (@y      G      "@y     ]      ^y     ^@     y      ?      пy              )r   r   rR   r   exprQ   logr(   r.   r   rN   rO   r   r   r   test_interval_complexr`     s-   BFBF66!A;$66!A;$66!A;$2661Q%1&&&&rvvqeQqE****66!A;t###661Q%1"2%1qe)<<<<661Q%1"bffaUAa5&9999661Q%1#rvvr"gqe'<<<<661Q%1#rvvqeRG'<<<<66$<??266$<((((66$<??266$<((((FF1QK266#a=(,,RVVAa[BFF3qM-IJJJJ"&&*#$$$"&&*#$$$rvvay>Qrvvc{s"""rvva{q   rvvay>Qrvva{q   rvva12661Q%=000rvvaA BFFAa5M111rvvqeQrF#$"v666rvvqeRG$%277766!A;!q   66!A;!%%%66!A;!y(((66!A;!y(((66!A;!y(((66!A;!y(((66!A;2.00066!A;2.00066!9<<q	""""66!9<<q	""""66$<??266$<((((66$<??266$<((((r   c                  N   S[         l        S[        l        [        R                  S5      S:X  d   e[        R                  S5      S:X  d   e[        R                  SS/5      S:X  d   e[        R                  S5      R	                  [
        5      (       d   e[        R                  S5      R	                  [        R                  S5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S	5      5      (       d   eUR                  R	                  [         R                  S
5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S5      5      (       d   eUR                  R	                  [         R                  S
5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S5      5      (       d   eUR                  R	                  [         R                  S5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S5      5      (       d   eUR                  R	                  [         R                  S5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S5      5      (       d   eUR                  R	                  [         R                  S5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S5      5      (       d   eUR                  R	                  [         R                  S5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R                  S5      5      (       d   eUR                  R	                  [         R                  S5      5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R
                  * 5      (       d   eUR                  R	                  [         R
                  5      (       d   e[        R                  SS/SS/5      n [        R                  U 5      nUR                  R	                  [         R
                  * 5      (       d   eUR                  R	                  [         R
                  5      (       d   eg )Nr   r
   r   r&   rZ   r   r   r   y            @y             @r	   r[   r   y      ?      @y      ?       r;   y      ?      y       @      y            y             y            )	rR   r   r   argrQ   r-   r   r)   r*   )zts     r   test_interval_complex_argre   9  s   BFBF66!9>>66!9>>661Q%=A66":==66$<??266$<((((
2w!uA
q	A3366"&&-    3366"&&-    
1vqeA
q	A3366"&&,3366"&&-    
!uaUA
q	A3366"&&,3366"&&,
!ubVA
q	A3366"&&,3366"&&,
!ubWA
q	A3366"&&,3366"&&,
1vr"gA
q	A3366"&&-    3366"&&,
2w2wA
q	A3366"&&-    3366"&&-    
2w1vA
q	A3366255&>>>3366"%%===
1vr!fA
q	A3366255&>>>3366"%%===r   c                     S[         l        [         R                  SS/5      n U R                  S5      b   eU R                  S5      b   eU R                  S5      b   eU R                  S5      SL d   eU R                  S5      SL d   e[         R                  S5      n U R                  S5      S	L d   eU R                  S
5      S	L d   eU R                  S5      S	L d   eU R                  S5      SL d   eU R                  S5      SL d   eU R                  [         R                  SS/5      5      b   eU R                  [         R                  SS/5      5      b   eg )Nr   r	   r   rH   gGz @FgGz?rI   Tg     @g@g5^I@gˡE@g     @)r   r   r(   rQ   )r0   s    r   test_interval_aerg   f  s=   BF
!uA447??449447??44:44:
sA44944	?d"""44	?d"""44;%44;%44E{#$,,,44I'(000r   c                     S=[         l        n [        SS5      n[         R                  XSSS9S:X  d   e[         R                  XSSSS	9S
:X  d   e[         R                  XSS9S:X  d   e[         R                  XSSS9S:X  d   e[         R                  XSSS9S:X  d   e[        SS5      n[         R                  XSS9S:X  d   e[         R                  [         R	                  [        S5      5      U SSS9S:X  d   e[         R                  [        SS5      U SS9S:X  d   e[         R
                  n[         R                  [         R                  [        S5      5      U SS9S:X  d   eS[         l        g )Nr%   r	   r   	plusminusr!   )mode	error_dps
1.5 +- 0.5F)rj   
use_spacesrk   z1.5+-0.5percent)rj   z1.5 (33.33%)brackets)rj   rm   z	[1.0,2.0])<>)rj   ro   z
<1.0, 2.0>z5.2582327113062393041z5.2582327113062749951diffz5.2582327113062[393041, 749951]z*0.54030230586813971740093660744[2955,3053]1e1231e129z[1.0e+123, 1.0e+129]z5000.1z-3.2797365856787867069110487[0926, 1191]e+2171r   )r   r   r   nstrrN   r^   )rW   r0   r^   s      r   test_interval_nstrrv   w  s_   OBFQAq	A771kQ77<GGG771keq7IZWWW771i7(N:::771jU7;{JJJ771jJ7?<OOO#%<=A771f7%)JJJJ77266#a&>16e7DHtttt773w(!&79=SSSS
&&C77266#h-(!&79=llllBFr   c                     S[         l        [         R                  S5      [        [	        S5      [	        S5      5      :X  d   e[        SS5      [         R                  S5      ;   d   e[         R                  S5      [        SS5      :X  d   e[         R                  S	5      [        S
S5      :X  d   e[         R                  S5      [        SS5      :X  d   e[         R                  S5      [        SS5      :X  d   eg )Nr   rl   z1.0z2.0r	   r   z'1.5 (33.33333333333333333333333333333%)z[1, 2]z1[2, 3]r\   r]   z1.[23,46]e-8z1.23e-8z1.46e-8z12[3.4,5.9]e4z123.4e+4z125.9e4)r   r   convertr   r(   r   r   r   test_mpi_from_strry     s    BF::l#s3u:s5z'BBBBq!9

#LMMMM::h3q!9,,,::i CBK///::n%Y	)BBBB::o&#j)*DDDDr   c                  	   S[         l        S[        l        [        R                  S5      S:X  d   e[        R	                  S5      S:X  d   e[        R	                  S5      S:X  d   e[        R	                  S5      S:X  d   e[        R	                  S5      S:X  d   e[        R                  S5      [        * [        /:X  d   e[        R                  S5      S:X  d   e[        R                  S5      S:X  d   e[        R                  S5      S:X  d   eS[        R                  S5      ;   d   e[        R                  S5      S:X  d   e[        R                  S5      S:X  d   eS	[        R                  S5      ;   d   e[        R                  SS/SS
/5      [        R                  SS/SS/5      [        R                  SS/SS
/5      [        R                  SS/SS/5      [        R                  SS/SS
/5      [        R                  SS/SS
/5      [        R                  SS/SS/5      /n U  GHx  n[         R                  [         R                  UR                  UR                  5      5      [         R                  [         R                  UR                  UR                  5      5      [         R                  [         R                  UR                  UR                  5      5      [         R                  [         R                  UR                  UR                  5      5      /nSUR                  ;   aA  U[         R                  UR                  5      [         R                  UR                  5      /-  n[        U Vs/ s H  o3R                  PM     sn5      n[!        U Vs/ s H  o3R                  PM     sn5      n[        U Vs/ s H  o3R                  PM     sn5      n[!        U Vs/ s H  o3R                  PM     sn5      n[        R                  U5      nUR                  R#                  U5      (       d   eUR                  R#                  U5      (       d   eUR                  R#                  U5      (       d   eUR                  R#                  U5      (       a  GMy   e   g s  snf s  snf s  snf s  snf )Nr   r   r	   r   r
   r!   gkﴑ[r'   g9B.?r   r;   r   r&   r   )rR   r   r   rgammafacgammar   loggammar   r)   cr*   dimagminrealmaxrQ   )	xsr0   ysymin_realmax_realmin_imagmax_imagrc   s	            r   test_interval_gammar     sy   BFBF99Q<166!9>>66!9>>66!9>>66!9>>88A;C4*$$$88A;!88A;!88A;!!RXXd^333;;q>Q;;q>Q!R[[^333
&&!A!u

&&!A2w

&&!A1v

&&!A1v

&&!A1v

&&"R!A

&&"R"R
!
#B kk"&&QSS/*kk"&&QSS/*kk"&&QSS/*kk"&&QSS/*, ;2;;qss#R[[%566B+1+,+1+,+1+,+1+,KKNssvvhssvvhssvvhssvvh  ,+++s   R2
)R7
R<
3S
c            
         S[         l        S[        l        SSSSS[        [	        S5      5      44 H  u  p[        X5      n[        UR                  5      [        U5      :X  d   e[        UR                  5      [        U 5      :X  d   e[        UR                  5      [        U5      :X  d   e[        UR                  5      [        U 5      :X  d   e[        UR                  5      [        U5      :X  a  M   e   g )Nr   )g       r   )rD   r"   )rE   r	   )-infg     4@r   r   )
rR   r   r   floatr+   r   intr*   r)   complex)r)   r*   rs      r   test_interval_conversionsr     s    BFBFJ&%Q.!9;I133x3q6!!!QSSzU1X%%%QSSzU1X%%%qss|wqz)))qss|wqz)));r   N)mpmathr   r   r2   r7   r=   r?   rF   rX   r`   re   rg   rv   ry   r   r   r   r   r   <module>r      s]    #0B)3V1**.#D3LK!Z')R+Z1""E( T
*r   