java.lang.Object

@Beta
public final class LongMath
extends Object

A class for arithmetic on values of type long. Where possible, methods are defined and named analogously to their BigInteger counterparts.

The implementations of many methods in this class are based on material from Henry S. Warren, Jr.'s Hacker's Delight, (Addison Wesley, 2002).

Similar functionality for int and for BigInteger can be found in IntMath and BigIntegerMath respectively. For other common operations on long values, see Longs.

Since:
11.0
Author:
Louis Wasserman

Method Summary
static long binomial(int n, int k)
Returns n choose k, also known as the binomial coefficient of n and k, or Long.MAX_VALUE if the result does not fit in a long.
static long checkedAdd(long a, long b)
Returns the sum of a and b, provided it does not overflow.
static long checkedMultiply(long a, long b)
Returns the product of a and b, provided it does not overflow.
static long checkedPow(long b, int k)
Returns the b to the kth power, provided it does not overflow.
static long checkedSubtract(long a, long b)
Returns the difference of a and b, provided it does not overflow.
static long divide(long p, long q, RoundingMode mode)
Returns the result of dividing p by q, rounding using the specified RoundingMode.
static long factorial(int n)
Returns n!, that is, the product of the first n positive integers, 1 if n == 0, or Long.MAX_VALUE if the result does not fit in a long.
static long gcd(long a, long b)
Returns the greatest common divisor of a, b.
static boolean isPowerOfTwo(long x)
Returns true if x represents a power of two.
static int log10(long x, RoundingMode mode)
Returns the base-10 logarithm of x, rounded according to the specified rounding mode.
static int log2(long x, RoundingMode mode)
Returns the base-2 logarithm of x, rounded according to the specified rounding mode.
static int mod(long x, int m)
Returns x mod m.
static long mod(long x, long m)
Returns x mod m.
static long pow(long b, int k)
Returns b to the kth power.
static long sqrt(long x, RoundingMode mode)
Returns the square root of x, rounded with the specified rounding mode.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

### isPowerOfTwo

public static boolean isPowerOfTwo(long x)
Returns true if x represents a power of two.

This differs from Long.bitCount(x) == 1, because Long.bitCount(Long.MIN_VALUE) == 1, but Long.MIN_VALUE is not a power of two.

### log2

public static int log2(long x,
RoundingMode mode)
Returns the base-2 logarithm of x, rounded according to the specified rounding mode.

Throws:
IllegalArgumentException - if x <= 0
ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not a power of two

### log10

public static int log10(long x,
RoundingMode mode)
Returns the base-10 logarithm of x, rounded according to the specified rounding mode.

Throws:
IllegalArgumentException - if x <= 0
ArithmeticException - if mode is RoundingMode.UNNECESSARY and x is not a power of ten

### pow

public static long pow(long b,
int k)
Returns b to the kth power. Even if the result overflows, it will be equal to BigInteger.valueOf(b).pow(k).longValue(). This implementation runs in O(log k) time.

Throws:
IllegalArgumentException - if k < 0

### sqrt

public static long sqrt(long x,
RoundingMode mode)
Returns the square root of x, rounded with the specified rounding mode.

Throws:
IllegalArgumentException - if x < 0
ArithmeticException - if mode is RoundingMode.UNNECESSARY and sqrt(x) is not an integer

### divide

public static long divide(long p,
long q,
RoundingMode mode)
Returns the result of dividing p by q, rounding using the specified RoundingMode.

Throws:
ArithmeticException - if q == 0, or if mode == UNNECESSARY and a is not an integer multiple of b

### mod

public static int mod(long x,
int m)
Returns x mod m. This differs from x % m in that it always returns a non-negative result.

For example:

mod(7, 4) == 3
mod(-7, 4) == 1
mod(-1, 4) == 3
mod(-8, 4) == 0
mod(8, 4) == 0

Throws:
ArithmeticException - if m <= 0

### mod

public static long mod(long x,
long m)
Returns x mod m. This differs from x % m in that it always returns a non-negative result.

For example:

mod(7, 4) == 3
mod(-7, 4) == 1
mod(-1, 4) == 3
mod(-8, 4) == 0
mod(8, 4) == 0

Throws:
ArithmeticException - if m <= 0

### gcd

public static long gcd(long a,
long b)
Returns the greatest common divisor of a, b. Returns 0 if a == 0 && b == 0.

Throws:
IllegalArgumentException - if a < 0 or b < 0

long b)
Returns the sum of a and b, provided it does not overflow.

Throws:
ArithmeticException - if a + b overflows in signed long arithmetic

### checkedSubtract

public static long checkedSubtract(long a,
long b)
Returns the difference of a and b, provided it does not overflow.

Throws:
ArithmeticException - if a - b overflows in signed long arithmetic

### checkedMultiply

public static long checkedMultiply(long a,
long b)
Returns the product of a and b, provided it does not overflow.

Throws:
ArithmeticException - if a * b overflows in signed long arithmetic

### checkedPow

public static long checkedPow(long b,
int k)
Returns the b to the kth power, provided it does not overflow.

Throws:
ArithmeticException - if b to the kth power overflows in signed long arithmetic

### factorial

public static long factorial(int n)
Returns n!, that is, the product of the first n positive integers, 1 if n == 0, or Long.MAX_VALUE if the result does not fit in a long.

Throws:
IllegalArgumentException - if n < 0

### binomial

public static long binomial(int n,
int k)
Returns n choose k, also known as the binomial coefficient of n and k, or Long.MAX_VALUE if the result does not fit in a long.

Throws:
IllegalArgumentException - if n < 0, k < 0, or k > n