static public BigDecimal log(final Rational r, final MathContext mc) {
        /* the value is undefined if x is negative.
         */
        if (r.compareTo(Rational.ZERO) <= 0) {
            throw new ArithmeticException("Cannot take log of negative " + r.toString());
        } else if (r.compareTo(Rational.ONE) == 0) {
            return BigDecimal.ZERO;
        } else {
            /* log(r+epsr) = log(r)+epsr/r. Convert the precision to an absolute error in the result.
             * eps contains the required absolute error of the result, epsr/r.
             */
            double eps = prec2err(Math.log(r.doubleValue()), mc.getPrecision());
            /* Convert this further into a requirement of the relative precision in r, given that
             * epsr/r is also the relative precision of r. Add one safety digit.
             */
            MathContext mcloc = new MathContext(1 + err2prec(eps));
            final BigDecimal resul = log(r.BigDecimalValue(mcloc));
            return resul.round(mc);
        }
    }
static public BigDecimal log(final Rational r, final MathContext mc) {
        
        if (r.compareTo(Rational.ZERO) <= 0) {
            throw new ArithmeticException("Cannot take log of negative " + r.toString());
        } else if (r.compareTo(Rational.ONE) == 0) {
            return BigDecimal.ZERO;
        } else {
            
            double eps = prec2err(Math.log(r.doubleValue()), mc.getPrecision());
            
            MathContext mcloc = new MathContext(1 + err2prec(eps));
            final BigDecimal resul = log(r.BigDecimalValue(mcloc));
            return resul.round(mc);
        }
    }
static public BigDecimal log ( final Rational r , final MathContext mc ) { /* the value is undefined if x is negative.
         */ if ( r . compareTo ( Rational . ZERO ) <= 0 ) { throw new ArithmeticException ( "Cannot take log of negative " + r . toString ( ) ) ; } else if ( r . compareTo ( Rational . ONE ) == 0 ) { return BigDecimal . ZERO ; } else { /* log(r+epsr) = log(r)+epsr/r. Convert the precision to an absolute error in the result.
             * eps contains the required absolute error of the result, epsr/r.
             */ double eps = prec2err ( Math . log ( r . doubleValue ( ) ) , mc . getPrecision ( ) ) ; /* Convert this further into a requirement of the relative precision in r, given that
             * epsr/r is also the relative precision of r. Add one safety digit.
             */ MathContext mcloc = new MathContext ( 1 + err2prec ( eps ) ) ; final BigDecimal resul = log ( r . BigDecimalValue ( mcloc ) ) ; return resul . round ( mc ) ; } }
The natural logarithm.

@param r  The main argument, a strictly positive value.
@param mc The requirements on the precision.
@return ln(r).
The natural logarithm .