# Python 3.5: 552961
# Serhiy's patch: 504243
# using bits: 546250
# using bits and better log2(10) approxiation: 483424

import math

PyLong_SHIFT = 30
_PyLong_DECIMAL_SHIFT = 9
_PyLong_DECIMAL_BASE = 10 ** _PyLong_DECIMAL_SHIFT

def exact_decimalbase_digits(x):
    digits = 0
    while x > _PyLong_DECIMAL_BASE:
        digits += 1
        x //= _PyLong_DECIMAL_BASE
    return digits

def size(x):
    return (x.bit_length() + PyLong_SHIFT - 1) // PyLong_SHIFT

def math_decimalbase_digits(x):
    return 1 + math.floor(math.log2(x) / math.log2(_PyLong_DECIMAL_BASE))

def old_decimalbase_digits(x):
    bits = size(x) * PyLong_SHIFT
    return 1 + bits // (3 * _PyLong_DECIMAL_SHIFT)

def new_decimalbase_digits(x):
    # Serhiy's patch (issue #25402)
    digits = size(x)
    d = (33 * _PyLong_DECIMAL_SHIFT) // (10 * PyLong_SHIFT - 33 * _PyLong_DECIMAL_SHIFT)
    return 1 + digits + digits // d

def new_decimalbase_digits(x):
    # better estimation: use number of bits, not number of 30-bit digits
    bits = x.bit_length()
    # log2(10) = 3.321928094887362
    # approximate to 3 (lower-bound)
    return 1 + bits // (3 * _PyLong_DECIMAL_SHIFT)

def new_decimalbase_digits(x):
    # better estimation: use number of bits, not number of 30-bit digits
    bits = x.bit_length()
    # log2(10) = 3.321928094887362
    # approximate to 33219 / 10000 (lower-bound)
    return bits * 10000 // (33219 * _PyLong_DECIMAL_SHIFT)

total_old = 0
total_new = 0

def numbers():
    yield from range(1, 1500)
    for digits in range(1, 1500):
        x = 10 ** digits
        yield x -1
        yield x
        yield x +1
    for bits in range(1, 1500):
        x = 2 ** bits
        yield x -1
        yield x
        yield x +1

for x in numbers():
    exact = exact_decimalbase_digits(x)
    old = old_decimalbase_digits(x)
    assert old >= exact, (x, exact, old, size(x))

    new = new_decimalbase_digits(x)
    assert new >= exact, x
    assert old >= new, x
    total_old += old
    total_new += new

print("Total old: %s" % total_old)
print("Total new: %s" % total_new)