Class _Log10Memoize

Lib/_pydecimal.py:5831–5864

Class to compute, store, and allow retrieval of, digits of the constant log(10) = 2.302585.... This constant is needed by Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.

    return _div_nearest(f_log_ten + log_d, 100)

class _Log10Memoize(object):
    """Class to compute, store, and allow retrieval of, digits of the
    constant log(10) = 2.302585....  This constant is needed by
    Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__."""
    def __init__(self):
        self.digits = "23025850929940456840179914546843642076011014886"

    def getdigits(self, p):
        """Given an integer p >= 0, return floor(10**p)*log(10).

        For example, self.getdigits(3) returns 2302.
        """
        # digits are stored as a string, for quick conversion to
        # integer in the case that we've already computed enough
        # digits; the stored digits should always be correct
        # (truncated, not rounded to nearest).
        if p < 0:
            raise ValueError("p should be nonnegative")

        if p >= len(self.digits):
            # compute p+3, p+6, p+9, ... digits; continue until at
            # least one of the extra digits is nonzero
            extra = 3
            while True:
                # compute p+extra digits, correct to within 1ulp
                M = 10**(p+extra+2)
                digits = str(_div_nearest(_ilog(10*M, M), 100))
                if digits[-extra:] != '0'*extra:
                    break
                extra += 3
            # keep all reliable digits so far; remove trailing zeros
            # and next nonzero digit
            self.digits = digits.rstrip('0')[:-1]
        return int(self.digits[:p+1])

_log10_digits = _Log10Memoize().getdigits