@GwtCompatible(emulated=true) public final class IntMath extends Object
A class for arithmetic on values of type int
. 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 long
and for BigInteger
can be found in LongMath
and BigIntegerMath
respectively. For other common operations on int
values, see Ints
.
Modifier and Type | Method and Description |
---|---|
static int |
binomial(int n,
int k)
Returns
n choose k , also known as the binomial coefficient of n and k , or Integer.MAX_VALUE if the result does not fit in an int . |
static int |
checkedAdd(int a,
int b)
Returns the sum of
a and b , provided it does not overflow. |
static int |
checkedMultiply(int a,
int b)
Returns the product of
a and b , provided it does not overflow. |
static int |
checkedPow(int b,
int k)
Returns the
b to the k th power, provided it does not overflow. |
static int |
checkedSubtract(int a,
int b)
Returns the difference of
a and b , provided it does not overflow. |
static int |
divide(int p,
int q,
RoundingMode mode)
Returns the result of dividing
p by q , rounding using the specified RoundingMode . |
static int |
factorial(int n)
Returns
n! , that is, the product of the first n positive integers, 1 if n == 0 , or Integer.MAX_VALUE if the result does not fit in a int . |
static int |
gcd(int a,
int b)
Returns the greatest common divisor of
a, b . |
static boolean |
isPowerOfTwo(int x)
Returns
true if x represents a power of two. |
static int |
log10(int x,
RoundingMode mode)
Returns the base-10 logarithm of
x , rounded according to the specified rounding mode. |
static int |
log2(int x,
RoundingMode mode)
Returns the base-2 logarithm of
x , rounded according to the specified rounding mode. |
static int |
mean(int x,
int y)
Returns the arithmetic mean of
x and y , rounded towards negative infinity. |
static int |
mod(int x,
int m)
Returns
x mod m , a non-negative value less than m . |
static int |
pow(int b,
int k)
Returns
b to the k th power. |
static int |
sqrt(int x,
RoundingMode mode)
Returns the square root of
x , rounded with the specified rounding mode. |
public static boolean isPowerOfTwo(int x)
Returns true
if x
represents a power of two.
This differs from Integer.bitCount(x) == 1
, because Integer.bitCount(Integer.MIN_VALUE) == 1
, but Integer.MIN_VALUE
is not a power of two.
public static int log2(int x, RoundingMode mode)
Returns the base-2 logarithm of x
, rounded according to the specified rounding mode.
IllegalArgumentException
- if x <= 0
ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not a power of two@GwtIncompatible(value="need BigIntegerMath to adequately test") public static int log10(int x, RoundingMode mode)
Returns the base-10 logarithm of x
, rounded according to the specified rounding mode.
IllegalArgumentException
- if x <= 0
ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not a power of ten@GwtIncompatible(value="failing tests") public static int pow(int b, int k)
Returns b
to the k
th power. Even if the result overflows, it will be equal to BigInteger.valueOf(b).pow(k).intValue()
. This implementation runs in O(log k)
time.
Compare checkedPow(int, int)
, which throws an ArithmeticException
upon overflow.
IllegalArgumentException
- if k < 0
@GwtIncompatible(value="need BigIntegerMath to adequately test") public static int sqrt(int x, RoundingMode mode)
Returns the square root of x
, rounded with the specified rounding mode.
IllegalArgumentException
- if x < 0
ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and sqrt(x)
is not an integerpublic static int divide(int p, int q, RoundingMode mode)
Returns the result of dividing p
by q
, rounding using the specified RoundingMode
.
ArithmeticException
- if q == 0
, or if mode == UNNECESSARY
and a
is not an integer multiple of b
public static int mod(int x, int m)
Returns x mod m
, a non-negative value less than m
. This differs from x % m
, which might be negative.
For example:
mod(7, 4) == 3
mod(-7, 4) == 1
mod(-1, 4) == 3
mod(-8, 4) == 0
mod(8, 4) == 0
ArithmeticException
- if m <= 0
public static int gcd(int a, int b)
Returns the greatest common divisor of a, b
. Returns 0
if a == 0 && b == 0
.
IllegalArgumentException
- if a < 0
or b < 0
public static int checkedAdd(int a, int b)
Returns the sum of a
and b
, provided it does not overflow.
ArithmeticException
- if a + b
overflows in signed int
arithmeticpublic static int checkedSubtract(int a, int b)
Returns the difference of a
and b
, provided it does not overflow.
ArithmeticException
- if a - b
overflows in signed int
arithmeticpublic static int checkedMultiply(int a, int b)
Returns the product of a
and b
, provided it does not overflow.
ArithmeticException
- if a * b
overflows in signed int
arithmeticpublic static int checkedPow(int b, int k)
Returns the b
to the k
th power, provided it does not overflow.
pow(int, int)
may be faster, but does not check for overflow.
ArithmeticException
- if b
to the k
th power overflows in signed int
arithmeticpublic static int factorial(int n)
Returns n!
, that is, the product of the first n
positive integers, 1
if n == 0
, or Integer.MAX_VALUE
if the result does not fit in a int
.
IllegalArgumentException
- if n < 0
@GwtIncompatible(value="need BigIntegerMath to adequately test") public static int binomial(int n, int k)
Returns n
choose k
, also known as the binomial coefficient of n
and k
, or Integer.MAX_VALUE
if the result does not fit in an int
.
IllegalArgumentException
- if n < 0
, k < 0
or k > n
public static int mean(int x, int y)
Returns the arithmetic mean of x
and y
, rounded towards negative infinity. This method is overflow resilient.