Function _dpower

Lib/_pydecimal.py:5941–5981

Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: 10**(p-1) <= c <= 10**p, and (c-1)*10**e < x**y < (c+1)*10**e in other words, c*10**e is an approximation to x**y with p digits

(xc, xe, yc, ye, p)

    return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3

def _dpower(xc, xe, yc, ye, p):
    """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and
    y = yc*10**ye, compute x**y.  Returns a pair of integers (c, e) such that:

      10**(p-1) <= c <= 10**p, and
      (c-1)*10**e < x**y < (c+1)*10**e

    in other words, c*10**e is an approximation to x**y with p digits
    of precision, and with an error in c of at most 1.  (This is
    almost, but not quite, the same as the error being < 1ulp: when c
    == 10**(p-1) we can only guarantee error < 10ulp.)

    We assume that: x is positive and not equal to 1, and y is nonzero.
    """

    # Find b such that 10**(b-1) <= |y| <= 10**b
    b = len(str(abs(yc))) + ye

    # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point
    lxc = _dlog(xc, xe, p+b+1)

    # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1)
    shift = ye-b
    if shift >= 0:
        pc = lxc*yc*10**shift
    else:
        pc = _div_nearest(lxc*yc, 10**-shift)

    if pc == 0:
        # we prefer a result that isn't exactly 1; this makes it
        # easier to compute a correctly rounded result in __pow__
        if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1:
            coeff, exp = 10**(p-1)+1, 1-p
        else:
            coeff, exp = 10**p-1, -p
    else:
        coeff, exp = _dexp(pc, -(p+1), p+1)
        coeff = _div_nearest(coeff, 10)
        exp += 1

    return coeff, exp

def _log10_lb(c, correction = {
        '1': 100, '2': 70, '3': 53, '4': 40, '5': 31,