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..	Parent	-	drwxr-xr-x	2026-04-10 04:18:08	-
__phello__	Folder	-	0755	2026-04-10 04:18:08
__pycache__	Folder	-	0755	2026-04-10 04:18:08
asyncio	Folder	-	0755	2026-04-10 04:18:08
collections	Folder	-	0755	2026-04-10 04:18:08
concurrent	Folder	-	0755	2026-04-10 04:18:08
ctypes	Folder	-	0755	2026-04-10 04:18:08
curses	Folder	-	0755	2026-04-10 04:18:08
dbm	Folder	-	0755	2026-04-10 04:18:08
email	Folder	-	0755	2026-04-10 04:18:08
encodings	Folder	-	0755	2026-04-10 04:18:08
html	Folder	-	0755	2026-04-10 04:18:08
http	Folder	-	0755	2026-04-10 04:18:08
importlib	Folder	-	0755	2026-04-10 04:18:08
json	Folder	-	0755	2026-04-10 04:18:08
lib-dynload	Folder	-	0755	2026-04-10 04:18:08
logging	Folder	-	0755	2026-04-10 04:18:08
multiprocessing	Folder	-	0755	2026-04-10 04:18:08
pydoc_data	Folder	-	0755	2026-04-10 04:18:08
re	Folder	-	0755	2026-04-10 04:18:08
sqlite3	Folder	-	0755	2026-04-10 04:18:08
test	Folder	-	0755	2026-04-10 04:18:08
tomllib	Folder	-	0755	2026-04-10 04:18:08
unittest	Folder	-	0755	2026-04-10 04:18:08
urllib	Folder	-	0755	2026-04-10 04:18:08
venv	Folder	-	0755	2026-04-10 04:18:08
wsgiref	Folder	-	0755	2026-04-10 04:18:08
xml	Folder	-	0755	2026-04-10 04:18:08
xmlrpc	Folder	-	0755	2026-04-10 04:18:08
zipfile	Folder	-	0755	2026-04-10 04:18:08
zoneinfo	Folder	-	0755	2026-04-10 04:18:08
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LICENSE.txt	File	13.61 KB	0644	2026-03-03 12:15:18
__future__.py	File	5.1 KB	0644	2026-03-03 12:15:18
__hello__.py	File	227 B	0644	2026-03-03 12:15:18
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dataclasses.py	File	60.31 KB	0644	2026-03-03 12:15:18
datetime.py	File	268 B	0644	2026-03-03 12:15:18
decimal.py	File	320 B	0644	2026-03-03 12:15:18
difflib.py	File	81.36 KB	0644	2026-03-03 12:15:18
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fractions.py	File	37.17 KB	0644	2026-03-03 12:15:18
ftplib.py	File	33.92 KB	0644	2026-03-03 12:15:18
functools.py	File	37.23 KB	0644	2026-03-03 12:15:18
genericpath.py	File	5.44 KB	0644	2026-03-03 12:15:18
getopt.py	File	7.31 KB	0644	2026-03-03 12:15:18
getpass.py	File	5.85 KB	0644	2026-03-03 12:15:18
gettext.py	File	21.24 KB	0644	2026-03-03 12:15:18
glob.py	File	8.53 KB	0644	2026-03-03 12:15:18
graphlib.py	File	9.43 KB	0644	2026-03-03 12:15:18
gzip.py	File	24.28 KB	0644	2026-03-03 12:15:18
hashlib.py	File	9.13 KB	0644	2026-03-03 12:15:18
heapq.py	File	22.48 KB	0644	2026-03-03 12:15:18
hmac.py	File	7.54 KB	0644	2026-03-03 12:15:18
imaplib.py	File	52.43 KB	0644	2026-03-03 12:15:18
imghdr.py	File	4.29 KB	0644	2026-03-03 12:15:18
inspect.py	File	122.48 KB	0644	2026-03-03 12:15:18
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ipaddress.py	File	76.46 KB	0644	2026-03-03 12:15:18
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linecache.py	File	5.52 KB	0644	2026-03-03 12:15:18
locale.py	File	76.72 KB	0644	2026-03-03 12:15:18
lzma.py	File	12.97 KB	0644	2026-03-03 12:15:18
mailbox.py	File	77.06 KB	0644	2026-03-03 12:15:18
mailcap.py	File	9.11 KB	0644	2026-03-03 12:15:18
mimetypes.py	File	22.35 KB	0644	2026-03-03 12:15:18
modulefinder.py	File	23.14 KB	0644	2026-03-03 12:15:18
netrc.py	File	6.76 KB	0644	2026-03-03 12:15:18
nntplib.py	File	40.12 KB	0644	2026-03-03 12:15:18
ntpath.py	File	29.32 KB	0644	2026-03-03 12:15:18
nturl2path.py	File	2.82 KB	0644	2026-03-03 12:15:18
numbers.py	File	11.2 KB	0644	2026-03-03 12:15:18
opcode.py	File	12.87 KB	0644	2026-03-03 12:15:18
operator.py	File	10.71 KB	0644	2026-03-03 12:15:18
optparse.py	File	58.95 KB	0644	2026-03-03 12:15:18
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pathlib.py	File	49.95 KB	0644	2026-03-03 12:15:18
pdb.py	File	67.83 KB	0755	2026-03-03 12:15:18
pickle.py	File	63.38 KB	0644	2026-03-03 12:15:18
pickletools.py	File	91.66 KB	0644	2026-03-03 12:15:18
pipes.py	File	8.77 KB	0644	2026-03-03 12:15:18
pkgutil.py	File	17.85 KB	0644	2026-03-03 12:15:18
platform.py	File	42.32 KB	0755	2026-03-03 12:15:18
plistlib.py	File	27.91 KB	0644	2026-03-03 12:15:18
poplib.py	File	13.83 KB	0644	2026-03-03 12:15:18
posixpath.py	File	17.21 KB	0644	2026-03-03 12:15:18
pprint.py	File	23.59 KB	0644	2026-03-03 12:15:18
profile.py	File	22.55 KB	0755	2026-03-03 12:15:18
pstats.py	File	28.6 KB	0644	2026-03-03 12:15:18
pty.py	File	5.99 KB	0644	2026-03-03 12:15:18
py_compile.py	File	7.69 KB	0644	2026-03-03 12:15:18
pyclbr.py	File	11.13 KB	0644	2026-03-03 12:15:18
pydoc.py	File	110.44 KB	0755	2026-03-03 12:15:18
queue.py	File	11.23 KB	0644	2026-03-03 12:15:18
quopri.py	File	7.01 KB	0755	2026-03-03 12:15:18
random.py	File	33.87 KB	0644	2026-03-03 12:15:18
reprlib.py	File	6.42 KB	0644	2026-03-03 12:15:18
rlcompleter.py	File	7.64 KB	0644	2026-03-03 12:15:18
runpy.py	File	12.6 KB	0644	2026-03-03 12:15:18
sched.py	File	6.2 KB	0644	2026-03-03 12:15:18
secrets.py	File	1.94 KB	0644	2026-03-03 12:15:18
selectors.py	File	19.21 KB	0644	2026-03-03 12:15:18
shelve.py	File	8.36 KB	0644	2026-03-03 12:15:18
shlex.py	File	13.04 KB	0644	2026-03-03 12:15:18
shutil.py	File	56.76 KB	0644	2026-03-03 12:15:18
signal.py	File	2.44 KB	0644	2026-03-03 12:15:18
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smtplib.py	File	42.51 KB	0755	2026-03-03 12:15:18
sndhdr.py	File	7.27 KB	0644	2026-03-03 12:15:18
socket.py	File	36.53 KB	0644	2026-03-03 12:15:18
socketserver.py	File	27.2 KB	0644	2026-03-03 12:15:18
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sre_constants.py	File	232 B	0644	2026-03-03 12:15:18
sre_parse.py	File	229 B	0644	2026-03-03 12:15:18
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statistics.py	File	49.05 KB	0644	2026-03-03 12:15:18
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subprocess.py	File	86.65 KB	0644	2026-03-03 12:15:18
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zipimport.py	File	27.47 KB	0644	2026-03-03 12:15:18

"""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."""

import re
import decimal

def int_to_decimal(n):
    """Asymptotically fast conversion of an 'int' to Decimal."""

# Function due to Tim Peters.  See GH issue #90716 for details.
    # https://github.com/python/cpython/issues/90716
    #
    # The implementation in longobject.c of base conversion algorithms
    # between power-of-2 and non-power-of-2 bases are quadratic time.
    # This function implements a divide-and-conquer algorithm that is
    # faster for large numbers.  Builds an equal decimal.Decimal in a
    # "clever" recursive way.  If we want a string representation, we
    # apply str to _that_.

D = decimal.Decimal
    D2 = D(2)

BITLIM = 128

mem = {}

def w2pow(w):
        """Return D(2)**w and store the result. Also possibly save some
        intermediate results. In context, these are likely to be reused
        across various levels of the conversion to Decimal."""
        if (result := mem.get(w)) is None:
            if w <= BITLIM:
                result = D2**w
            elif w - 1 in mem:
                result = (t := mem[w - 1]) + t
            else:
                w2 = w >> 1
                # If w happens to be odd, w-w2 is one larger then w2
                # now. Recurse on the smaller first (w2), so that it's
                # in the cache and the larger (w-w2) can be handled by
                # the cheaper `w-1 in mem` branch instead.
                result = w2pow(w2) * w2pow(w - w2)
            mem[w] = result
        return result

def inner(n, w):
        if w <= BITLIM:
            return D(n)
        w2 = w >> 1
        hi = n >> w2
        lo = n - (hi << w2)
        return inner(lo, w2) + inner(hi, w - w2) * w2pow(w2)

with decimal.localcontext() as ctx:
        ctx.prec = decimal.MAX_PREC
        ctx.Emax = decimal.MAX_EMAX
        ctx.Emin = decimal.MIN_EMIN
        ctx.traps[decimal.Inexact] = 1

if n < 0:
            negate = True
            n = -n
        else:
            negate = False
        result = inner(n, n.bit_length())
        if negate:
            result = -result
    return result

def int_to_decimal_string(n):
    """Asymptotically fast conversion of an 'int' to a decimal string."""
    return str(int_to_decimal(n))

def _str_to_int_inner(s):
    """Asymptotically fast conversion of a 'str' to an 'int'."""

# Function due to Bjorn Martinsson.  See GH issue #90716 for details.
    # https://github.com/python/cpython/issues/90716
    #
    # The implementation in longobject.c of base conversion algorithms
    # between power-of-2 and non-power-of-2 bases are quadratic time.
    # This function implements a divide-and-conquer algorithm making use
    # of Python's built in big int multiplication. Since Python uses the
    # Karatsuba algorithm for multiplication, the time complexity
    # of this function is O(len(s)**1.58).

DIGLIM = 2048

mem = {}

def w5pow(w):
        """Return 5**w and store the result.
        Also possibly save some intermediate results. In context, these
        are likely to be reused across various levels of the conversion
        to 'int'.
        """
        if (result := mem.get(w)) is None:
            if w <= DIGLIM:
                result = 5**w
            elif w - 1 in mem:
                result = mem[w - 1] * 5
            else:
                w2 = w >> 1
                # If w happens to be odd, w-w2 is one larger then w2
                # now. Recurse on the smaller first (w2), so that it's
                # in the cache and the larger (w-w2) can be handled by
                # the cheaper `w-1 in mem` branch instead.
                result = w5pow(w2) * w5pow(w - w2)
            mem[w] = result
        return result

def inner(a, b):
        if b - a <= DIGLIM:
            return int(s[a:b])
        mid = (a + b + 1) >> 1
        return inner(mid, b) + ((inner(a, mid) * w5pow(b - mid)) << (b - mid))

return inner(0, len(s))

def int_from_string(s):
    """Asymptotically fast version of PyLong_FromString(), conversion
    of a string of decimal digits into an 'int'."""
    # PyLong_FromString() has already removed leading +/-, checked for invalid
    # use of underscore characters, checked that string consists of only digits
    # and underscores, and stripped leading whitespace.  The input can still
    # contain underscores and have trailing whitespace.
    s = s.rstrip().replace('_', '')
    return _str_to_int_inner(s)

def str_to_int(s):
    """Asymptotically fast version of decimal string to 'int' conversion."""
    # FIXME: this doesn't support the full syntax that int() supports.
    m = re.match(r'\s*([+-]?)([0-9_]+)\s*', s)
    if not m:
        raise ValueError('invalid literal for int() with base 10')
    v = int_from_string(m.group(2))
    if m.group(1) == '-':
        v = -v
    return v

# Fast integer division, based on code from Mark Dickinson, fast_div.py
# GH-47701. Additional refinements and optimizations by Bjorn Martinsson.  The
# algorithm is due to Burnikel and Ziegler, in their paper "Fast Recursive
# Division".

_DIV_LIMIT = 4000

def _div2n1n(a, b, n):
    """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.

"""
    if a.bit_length() - n <= _DIV_LIMIT:
        return divmod(a, b)
    pad = n & 1
    if pad:
        a <<= 1
        b <<= 1
        n += 1
    half_n = n >> 1
    mask = (1 << half_n) - 1
    b1, b2 = b >> half_n, b & mask
    q1, r = _div3n2n(a >> n, (a >> half_n) & mask, b, b1, b2, half_n)
    q2, r = _div3n2n(r, a & mask, b, b1, b2, half_n)
    if pad:
        r >>= 1
    return q1 << half_n | q2, r

def _div3n2n(a12, a3, b, b1, b2, n):
    """Helper function for _div2n1n; not intended to be called directly."""
    if a12 >> n == b1:
        q, r = (1 << n) - 1, a12 - (b1 << n) + b1
    else:
        q, r = _div2n1n(a12, b1, n)
    r = (r << n | a3) - q * b2
    while r < 0:
        q -= 1
        r += b
    return q, r

def _int2digits(a, n):
    """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.

"""
    a_digits = [0] * ((a.bit_length() + n - 1) // n)

def inner(x, L, R):
        if L + 1 == R:
            a_digits[L] = x
            return
        mid = (L + R) >> 1
        shift = (mid - L) * n
        upper = x >> shift
        lower = x ^ (upper << shift)
        inner(lower, L, mid)
        inner(upper, mid, R)

if a:
        inner(a, 0, len(a_digits))
    return a_digits

def _digits2int(digits, n):
    """Combine base-2**n digits into an int. This function is the
    inverse of `_int2digits`. For more details, see _int2digits.
    """

def inner(L, R):
        if L + 1 == R:
            return digits[L]
        mid = (L + R) >> 1
        shift = (mid - L) * n
        return (inner(mid, R) << shift) + inner(L, mid)

return inner(0, len(digits)) if digits else 0

def _divmod_pos(a, b):
    """Divide a non-negative integer a by a positive integer b, giving
    quotient and remainder."""
    # Use grade-school algorithm in base 2**n, n = nbits(b)
    n = b.bit_length()
    a_digits = _int2digits(a, n)

r = 0
    q_digits = []
    for a_digit in reversed(a_digits):
        q_digit, r = _div2n1n((r << n) + a_digit, b, n)
        q_digits.append(q_digit)
    q_digits.reverse()
    q = _digits2int(q_digits, n)
    return q, r

def int_divmod(a, b):
    """Asymptotically fast replacement for divmod, for 'int'.
    Its time complexity is O(n**1.58), where n = #bits(a) + #bits(b).
    """
    if b == 0:
        raise ZeroDivisionError
    elif b < 0:
        q, r = int_divmod(-a, -b)
        return q, -r
    elif a < 0:
        q, r = int_divmod(~a, b)
        return ~q, b + ~r
    else:
        return _divmod_pos(a, b)

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