Если вы хотите поддерживать произвольно большие целые числа, просто небезопасно делать
Math.log(bigInteger.doubleValue());
, потому что это не удастся, если аргумент превысит диапазон double (примерно 2 ^ 1024 или 10 ^ 308,т. е. более 300 десятичных цифр).
Вот мой собственный класс, который предоставляет методы
double logBigInteger(BigInteger val);
double logBigDecimal(BigDecimal val);
BigDecimal expBig(double exponent);
BigDecimal powBig(double a, double b);
Они работают безопасно, даже когда BigDecimal / BigInteger слишком велики (или слишком малы), чтобы бытьпредставляется как тип double.
/**
* Provides some mathematical operations on BigDecimal and BigInteger
*/
public class BigMath {
protected static final double LOG2 = Math.log(2.0);
protected static final double LOG10 = Math.log(10.0);
// numbers greater than 10^MAX_DIGITS_10 or e^MAX_DIGITS_EXP are considered unsafe ('too big') for floating point operations
protected static final int MAX_DIGITS_EXP = 677;
protected static final int MAX_DIGITS_10 = 294; // ~ MAX_DIGITS_EXP/LN(10)
protected static final int MAX_DIGITS_2 = 977; // ~ MAX_DIGITS_EXP/LN(2)
/**
* Computes the natural logarithm of a BigInteger.
*
* Works for really big integers (practically unlimited), even when the argument
* falls outside the <tt>double</tt> range
*
* Returns Nan if argument is negative, NEGATIVE_INFINITY if zero.
*
* @param val Argument
* @return Natural logarithm, as in <tt>Math.log()</tt>
*/
public static double logBigInteger(BigInteger val) {
if (val.signum() < 1)
return val.signum() < 0 ? Double.NaN : Double.NEGATIVE_INFINITY;
int blex = val.bitLength() - MAX_DIGITS_2; // any value in 60..1023 works ok here
if (blex > 0)
val = val.shiftRight(blex);
double res = Math.log(val.doubleValue());
return blex > 0 ? res + blex * LOG2 : res;
}
/**
* Computes the natural logarithm of a BigDecimal.
*
* Works for really big (or really small) arguments, even outside the double range.
*
* Returns Nan if argument is negative, NEGATIVE_INFINITY if zero.
*
* @param val Argument
* @return Natural logarithm, as in <tt>Math.log()</tt>
*/
public static double logBigDecimal(BigDecimal val) {
if (val.signum() < 1)
return val.signum() < 0 ? Double.NaN : Double.NEGATIVE_INFINITY;
int digits = val.precision() - val.scale();
if (digits < MAX_DIGITS_10 && digits > -MAX_DIGITS_10)
return Math.log(val.doubleValue());
else
return logBigInteger(val.unscaledValue()) - val.scale() * LOG10;
}
/**
* Computes the exponential function, returning a BigDecimal (precision ~ 16).
*
* Works for very big and very small exponents, even when the result
* falls outside the double range
*
* @param exponent Any finite value (infinite or Nan throws IllegalArgumentException)
* @return The value of e (base of the natural logarithms) raised to the given exponent, as in <tt>Math.exp()</tt>
*/
public static BigDecimal expBig(double exponent) {
if (!Double.isFinite(exponent))
throw new IllegalArgumentException("Infinite not accepted: " + exponent);
// e^b = e^(b2+c) = e^b2 2^t with e^c = 2^t
double bc = MAX_DIGITS_EXP;
if (exponent < bc && exponent > -bc)
return new BigDecimal(Math.exp(exponent), MathContext.DECIMAL64);
boolean neg = false;
if (exponent < 0) {
neg = true;
exponent = -exponent;
}
double b2 = bc;
double c = exponent - bc;
int t = (int) Math.ceil(c / LOG10);
c = t * LOG10;
b2 = exponent - c;
if (neg) {
b2 = -b2;
t = -t;
}
return new BigDecimal(Math.exp(b2), MathContext.DECIMAL64).movePointRight(t);
}
/**
* Same as Math.pow(a,b) but returns a BigDecimal (precision ~ 16).
*
* Works even for outputs that fall outside the <tt>double</tt> range
*
* The only limit is that b * log(a) does not overflow the double range
*
* @param a Base. Should be non-negative
* @param b Exponent. Should be finite (and non-negative if base is zero)
* @return Returns the value of the first argument raised to the power of the second argument.
*/
public static BigDecimal powBig(double a, double b) {
if (!(Double.isFinite(a) && Double.isFinite(b)))
throw new IllegalArgumentException(Double.isFinite(b) ? "base not finite: a=" + a : "exponent not finite: b=" + b);
if (b == 0)
return BigDecimal.ONE;
if (b == 1)
return BigDecimal.valueOf(a);
if (a == 0) {
if (b >= 0)
return BigDecimal.ZERO;
else
throw new IllegalArgumentException("0**negative = infinite");
}
if (a < 0) {
throw new IllegalArgumentException("negative base a=" + a);
}
double x = b * Math.log(a);
if (Math.abs(x) < MAX_DIGITS_EXP)
return BigDecimal.valueOf(Math.pow(a, b));
else
return expBig(x);
}
}