NAME
    power - evaluate a numerical power to specified accuracy

SYNOPSIS
    power(x, y, [, eps])

TYPES
    x		number
    x		number
    eps		nonzero real, defaults to epsilon()

    return	number

DESCRIPTION
    For real or complex x and y, power(x,y,eps) returns a real or
    complex number for which the real and imaginary parts are multiples
    of epsilon differing from the true real and imaginary parts of the
    principal y-th power of x by less than 0.75 * abs(eps), usually by
    less than 0.5 * abs(eps).  If the principal y-th power of x is a
    multiple of eps, it will be returned exactly.

    If y is a large integer but x^y is not large, and accuracy
    represented by eps is all that is required, power(x,y,eps) may be
    considerably faster than appr(x^y, eps, 24), the difference between
    the two results being probably at most abs(eps).

EXAMPLE
    > print power(1.2345, 10, 1e-5), power(1.2345, 10, 1e-10)
    8.22074 8.2207405646

    > print power(1+3i, 3, 1e-5), power(1 + 3i, 2+ 1i, 1e-5)
    -26-18i -2.50593-1.39445i

    > print power(1+ 1e-30, 1e30, 1e-20)
    2.71828182845904523536

    > print power(1i, 1i, 1e-20)
    .20787957635076190855

    > print power(exp(1, 1e-20), pi(1e-20) * 1i/2, 1e-20)
    1i

LIMITS
    If x = 0, y in power(x,y,eps) has to have positive real part,
    except in the case of y = 0; power(0, 0, eps) is the multiple of
    eps nearest 1.

    eps > 0

LIBRARY
    void powervalue(VALUE *x, VALUE *y, VALUE *eps, VALUE *result)
    NUMBER *qpower(NUMBER *x, NUMBER *y, NUMBER *eps)
    COMPLEX *cpower(COMPLEX *x, COMPLEX *y, NUMBER *eps)

SEE ALSO
    root