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� sdYh6. � �d � S r SSKrSSKr SSKrSS jr\R " 5 R 5 r\R \l \R \l \R \l S\R \R ' S rS rS rS rS rS rS rS rS rS rS rS r g! \ a Sr N�f = f)a� Python implementations of some algorithms for use by longobject.c. The goal is to provide asymptotically faster algorithms that can be used for operations on integers with many digits. In those cases, the performance overhead of the Python implementation is not significant since the asymptotic behavior is what dominates runtime. Functions provided by this module should be considered private and not part of any public API. Note: for ease of maintainability, please prefer clear code and avoid "micro-optimizations". This module will only be imported and used for integers with a huge number of digits. Saving a few microseconds with tricky or non-obvious code is not worth it. For people looking for maximum performance, they should use something like gmpy2.� Nc � � [ 5 n[ 5 nU 1nU( a{ UR 5 n X; d X:: a M# UR U 5 U S- nUR U5 UR U5 U S- ( a UR US- 5 U( a M{ 0 nU( d U$ [ [ U5 5 n [ U 5 n U( a [ SU 5 X- X�' U Hq n U S- U; a! U( a [ SU 5 X�S- U- X�' M- U S- nX�- n U( a [ SU 5 X� X� - n X�:w a U( a [ S5 X�- n X�U ' Ms U$ )N� zpow atz * base atz square atz and * base)�set�pop�add�iter�sorted�next�print)�w�base� more_than�show�seen�need�ws�lo�d�it�first�this�hi�sqs �./opt/alt/python313/lib64/python3.13/_pylong.py�compute_powersr 3 s: � � �5�D� �5�D� ��B� � �F�F�H�� �9��� � ���� � �!�V�� ���� � ���r� � �q�5� �F�F�2��6�N� �"� �A� ��� �f�T�l� �B� ��H�E� � �h�� ��}�A�H��� �!�8�q�=���k�4�(��q��k�D�(�A�G����B���B���k�4�(� ���� �B��x���*�+�� ���d�G�' �( �H� r c � ^^^^� SSK Jm SmUUUU4S jm[ R " [ 5 U R 5 n[ UT" S5 T5 mU S: a SnU * n OSnT" X5 nU( a U* nSSS5 U$ ! , ( d f W$ = f) z6Asymptotically fast conversion of an 'int' to Decimal.r )�Decimal�� c �| >� UT:: a T" U 5 $ US- nX- nU SU- S- - nT" XB5 T" X1U- 5 TU - - $ �Nr � ) �nr �w2r r �BITLIM�D�inner�w2pows ����r r' � int_to_decimal.<locals>.innery sV �� � ��;��Q�4�K� �!�V�� �W�� �1��7�a�-� ���R�}�u�R�R�� 0�5��9� <�<�<r � TFN)�decimalr � localcontext�_unbounded_dec_context� bit_lengthr )r# �nbits�negate�resultr% r& r' r( s @@@@r �int_to_decimalr2 g s� �� � %� �F�=� =� � � � 4� 5�� � ��� �u�a��d�F�3�� �q�5��F���A��F��q� �� � �W�F� 6� �M� 6� 5� �M�s �AA>�> B c �p ^^^� U R 5 nUS:� a [ b [ [ U 5 5 $ SmUUU4S jm[ US- S- 5 n[ UST5 mTR 5 H u p#X2- TU' M U S: a U * n SnOS nT" X5 nUS S :X a U ( a UR S 5 nXE- $ ) z?Asymptotically fast conversion of an 'int' to a decimal string.i�� i� c � >� UT:: a [ U 5 $ US- n[ U TU 5 u p4T" X1U- 5 T" XB5 R U5 - $ r! )�str�divmod�zfill)r# r r$ r r �DIGLIMr' �pow10s ���r r' �$int_to_decimal_string.<locals>.inner� sQ �� � ��;��q�6�M� �!�V����5��9�%����R�R�� �5��=�#6�#6�r�#:�:�:r g�y�PD�?r � r �-� �0)r. �_decimalr5 r2 �intr �items�lstrip) r# r �k�v�sign�sr8 r' r9 s @@@r �int_to_decimal_stringrG � s� �� � � � ��A��7�{�x�+� �>�!�$�%�%� �F�;� �A�"� "�Q� &�'�A� �1�a�� (�E�� � � ����6��a�� ��1�u� �B������ �a� �A���t�s�{�q� �H�H�S�M�� �8�Or c �p ^ ^^^� SmUUU U4S jm[ [ T 5 ST5 mT" S[ T 5 5 $ )z6Asymptotically fast conversion of a 'str' to an 'int'.i c �~ >� X- T:: a [ TX 5 $ X- S- S- nT" X!5 T" X5 TX- - X- - - $ r! )r@ )�a�b�midr8 r' rF �w5pows ����r r' � _str_to_int_inner.<locals>.inner� sW �� � �5�F�?��q��v�;� ��u�q�y�Q� ���c� ��!�M�E�!�'�N�2���!�"� #r r; r )r �len)rF r8 r' rM s `@@@r �_str_to_int_innerrP � s9 �� � �F�#� #� �3�q�6�1�f� -�E� ��C��F� �r c �X � U R 5 R SS5 n [ U 5 $ )zkAsymptotically fast version of PyLong_FromString(), conversion of a string of decimal digits into an 'int'.�_r= )�rstrip�replacerP )rF s r �int_from_stringrU � s' � � ��� ���3��#�A� �Q� � r c � � [ R " SU 5 nU( d [ S5 e[ UR S5 5 nUR S5 S:X a U* nU$ )zBAsymptotically fast version of decimal string to 'int' conversion.z\s*([+-]?)([0-9_]+)\s*z&invalid literal for int() with base 10r* r r< )�re�match� ValueErrorrU �group)rF �mrD s r � str_to_intr\ � sR � � ���*�A�.�A� ��A�B�B������ �#�A��w�w�q�z�S�� �B�� �Hr i� c �( � U R 5 U- [ :: a [ X5 $ US- nU( a U S- n US- nUS- nUS- nSU- S- nX- X- pv[ X- X- U- XXt5 u p�[ X�U- XXt5 u p�U( a U S- n X�- U - U 4$ )a2 Divide a 2n-bit nonnegative integer a by an n-bit positive integer b, using a recursive divide-and-conquer algorithm. Inputs: n is a positive integer b is a positive integer with exactly n bits a is a nonnegative integer such that a < 2**n * b Output: (q, r) such that a = b*q+r and 0 <= r < b. r )r. � _DIV_LIMITr6 �_div3n2n) rJ rK r# �pad�half_n�mask�b1�b2�q1�r�q2s r �_div2n1nrh � s� � � �|�|�~���Z�'��a�|�� �a�%�C� � �a��� �a��� �Q��� �!�V�F� ��K�1� �D� �[�!�(�� �Q�V�a�k�T� 1�1�"� E�E�B� �Q�D��!�� 4�E�B� � �a��� �<�"� �a� � r c � � X- U:X a SU- S- XU- - U- pvO[ XU5 u pgXu- U- Xd- - nUS: a US- nXr- nUS: a M Xg4$ )zAHelper function for _div2n1n; not intended to be called directly.r r )rh )�a12�a3rK rc rd r# �qrf s r r_ r_ sn � � �x�2�~��Q��!�|�S�!�G�_�r� 1�1����#��� ��"���� �A� �a�%� �Q��� ��� �a�%� �4�Kr c � ^^^� S/U R 5 T- S- T- - mUUU4S jmU ( a T" U S[ T5 5 T$ )a2 Decompose non-negative int a into base 2**n Input: a is a non-negative integer Output: List of the digits of a in base 2**n in little-endian order, meaning the most significant digit is last. The most significant digit is guaranteed to be non-zero. If a is 0 then the output is an empty list. r r c �z >� US- U:X a U TU' g X- S- nX1- T - nX- nXU- - nT" XaU5 T" XSU5 g r! r" ) �x�L�RrL �shift�upper�lower�a_digitsr' r# s ���r r' �_int2digits.<locals>.inner. sW �� � �q�5�A�:��H�Q�K� ��u��l����A� ��� ���e�^�$�� �e�� � �e�!� r )r. rO )rJ r# ru r' s `@@r � _int2digitsrw sE �� � �s�q�|�|�~��)�A�-�!�3�4�H� � � �a��C��M�"� �Or c �N ^ ^^� U UU4S jmT ( a T" S[ T 5 5 $ S$ )zxCombine base-2**n digits into an int. This function is the inverse of `_int2digits`. For more details, see _int2digits. c �d >� U S- U:X a TU $ X- S- nX - T- nT" X!5 U- T" X5 - $ r! r" )rp rq rL rr �digitsr' r# s ���r r' �_digits2int.<locals>.innerC sF �� � �q�5�A�:��!�9� ��u��l����A� ���c� ��&�%��-�7�7r r )rO )rz r# r' s ``@r � _digits2intr| > s" �� � 8� %+�5��C��K� �1��1r c �� � UR 5 n[ X5 nSn/ n[ U5 H' n[ XB- U- X5 u ptUR U5 M) UR 5 [ XR5 nX�4$ )zWDivide a non-negative integer a by a positive integer b, giving quotient and remainder.r )r. rw �reversedrh �append�reverser| ) rJ rK r# ru rf �q_digits�a_digit�q_digitrl s r � _divmod_posr� M sr � � � � ��A��1� �H� �A��H��H�%�� �q�v�� 0�!�7� ������ � &� �����H� �A� �4�Kr c � � US:X a [ eUS: a [ U * U* 5 u p#X#* 4$ U S: a [ U ) U5 u p#U) X) - 4$ [ X5 $ )zyAsymptotically fast replacement for divmod, for 'int'. Its time complexity is O(n**1.58), where n = #bits(a) + #bits(b). r )�ZeroDivisionError� int_divmodr� )rJ rK rl rf s r r� r� ^ se � � �A�v� � � �Q���1�"�q�b�!����"�u� � �Q���1�"�a� ����r�1�r�6�z���1� � r )F) �__doc__rW r+ r? � ImportErrorr � getcontext�copyr- �MAX_PREC�prec�MAX_EMAX�Emax�MIN_EMIN�Emin�traps�Inexactr2 rG rP rU r\ r^ rh r_ rw r| r� r� r" r r �<module>r� s� �� >� � ���B, �\ !�+�+�-�2�2�4� � %� .� .� � � %� .� .� � � %� .� .� � �01� � � �W�_�_� -�%�N+�Z �6 � �" � � �< � �> 2� �" !��W � ��H��s �B$ �$B/�.B/
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