Package com.google.common.math
Class IntMath
- java.lang.Object
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- com.google.common.math.IntMath
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@GwtCompatible(emulated=true) public final class IntMath extends java.lang.Object
A class for arithmetic on values of typeint
. Where possible, methods are defined and named analogously to theirBigInteger
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 forBigInteger
can be found inLongMath
andBigIntegerMath
respectively. For other common operations onint
values, seeInts
.- Since:
- 11.0
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Field Summary
Fields Modifier and Type Field Description (package private) static int[]
biggestBinomials
private static int[]
factorials
(package private) static int
FLOOR_SQRT_MAX_INT
(package private) static int[]
halfPowersOf10
(package private) static int
MAX_POWER_OF_SQRT2_UNSIGNED
The biggest half power of two that can fit in an unsigned int.(package private) static int
MAX_SIGNED_POWER_OF_TWO
(package private) static byte[]
maxLog10ForLeadingZeros
(package private) static int[]
powersOf10
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Constructor Summary
Constructors Modifier Constructor Description private
IntMath()
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Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static int
binomial(int n, int k)
Returnsn
choosek
, also known as the binomial coefficient ofn
andk
, orInteger.MAX_VALUE
if the result does not fit in anint
.static int
ceilingPowerOfTwo(int x)
Returns the smallest power of two greater than or equal tox
.static int
checkedAdd(int a, int b)
Returns the sum ofa
andb
, provided it does not overflow.static int
checkedMultiply(int a, int b)
Returns the product ofa
andb
, provided it does not overflow.static int
checkedPow(int b, int k)
Returns theb
to thek
th power, provided it does not overflow.static int
checkedSubtract(int a, int b)
Returns the difference ofa
andb
, provided it does not overflow.static int
divide(int p, int q, java.math.RoundingMode mode)
Returns the result of dividingp
byq
, rounding using the specifiedRoundingMode
.static int
factorial(int n)
Returnsn!
, that is, the product of the firstn
positive integers,1
ifn == 0
, orInteger.MAX_VALUE
if the result does not fit in aint
.static int
floorPowerOfTwo(int x)
Returns the largest power of two less than or equal tox
.static int
gcd(int a, int b)
Returns the greatest common divisor ofa, b
.static boolean
isPowerOfTwo(int x)
Returnstrue
ifx
represents a power of two.static boolean
isPrime(int n)
Returnstrue
ifn
is a prime number: an integer greater than one that cannot be factored into a product of smaller positive integers.(package private) static int
lessThanBranchFree(int x, int y)
Returns 1 ifx < y
as unsigned integers, and 0 otherwise.static int
log10(int x, java.math.RoundingMode mode)
Returns the base-10 logarithm ofx
, rounded according to the specified rounding mode.private static int
log10Floor(int x)
static int
log2(int x, java.math.RoundingMode mode)
Returns the base-2 logarithm ofx
, rounded according to the specified rounding mode.static int
mean(int x, int y)
Returns the arithmetic mean ofx
andy
, rounded towards negative infinity.static int
mod(int x, int m)
Returnsx mod m
, a non-negative value less thanm
.static int
pow(int b, int k)
Returnsb
to thek
th power.static int
saturatedAdd(int a, int b)
Returns the sum ofa
andb
unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.static int
saturatedMultiply(int a, int b)
Returns the product ofa
andb
unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.static int
saturatedPow(int b, int k)
Returns theb
to thek
th power, unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.static int
saturatedSubtract(int a, int b)
Returns the difference ofa
andb
unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.static int
sqrt(int x, java.math.RoundingMode mode)
Returns the square root ofx
, rounded with the specified rounding mode.private static int
sqrtFloor(int x)
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Field Detail
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MAX_SIGNED_POWER_OF_TWO
static final int MAX_SIGNED_POWER_OF_TWO
- See Also:
- Constant Field Values
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MAX_POWER_OF_SQRT2_UNSIGNED
static final int MAX_POWER_OF_SQRT2_UNSIGNED
The biggest half power of two that can fit in an unsigned int.- See Also:
- Constant Field Values
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maxLog10ForLeadingZeros
static final byte[] maxLog10ForLeadingZeros
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powersOf10
static final int[] powersOf10
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halfPowersOf10
static final int[] halfPowersOf10
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FLOOR_SQRT_MAX_INT
static final int FLOOR_SQRT_MAX_INT
- See Also:
- Constant Field Values
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factorials
private static final int[] factorials
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biggestBinomials
static int[] biggestBinomials
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Method Detail
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ceilingPowerOfTwo
@Beta public static int ceilingPowerOfTwo(int x)
Returns the smallest power of two greater than or equal tox
. This is equivalent tocheckedPow(2, log2(x, CEILING))
.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
java.lang.ArithmeticException
- of the next-higher power of two is not representable as anint
, i.e. whenx > 2^30
- Since:
- 20.0
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floorPowerOfTwo
@Beta public static int floorPowerOfTwo(int x)
Returns the largest power of two less than or equal tox
. This is equivalent tocheckedPow(2, log2(x, FLOOR))
.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
- Since:
- 20.0
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isPowerOfTwo
public static boolean isPowerOfTwo(int x)
Returnstrue
ifx
represents a power of two.This differs from
Integer.bitCount(x) == 1
, becauseInteger.bitCount(Integer.MIN_VALUE) == 1
, butInteger.MIN_VALUE
is not a power of two.
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lessThanBranchFree
static int lessThanBranchFree(int x, int y)
Returns 1 ifx < y
as unsigned integers, and 0 otherwise. Assumes that x - y fits into a signed int. The implementation is branch-free, and benchmarks suggest it is measurably (if narrowly) faster than the straightforward ternary expression.
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log2
public static int log2(int x, java.math.RoundingMode mode)
Returns the base-2 logarithm ofx
, rounded according to the specified rounding mode.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not a power of two
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log10
@GwtIncompatible public static int log10(int x, java.math.RoundingMode mode)
Returns the base-10 logarithm ofx
, rounded according to the specified rounding mode.- Throws:
java.lang.IllegalArgumentException
- ifx <= 0
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not a power of ten
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log10Floor
private static int log10Floor(int x)
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pow
@GwtIncompatible public static int pow(int b, int k)
Returnsb
to thek
th power. Even if the result overflows, it will be equal toBigInteger.valueOf(b).pow(k).intValue()
. This implementation runs inO(log k)
time.Compare
checkedPow(int, int)
, which throws anArithmeticException
upon overflow.- Throws:
java.lang.IllegalArgumentException
- ifk < 0
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sqrt
@GwtIncompatible public static int sqrt(int x, java.math.RoundingMode mode)
Returns the square root ofx
, rounded with the specified rounding mode.- Throws:
java.lang.IllegalArgumentException
- ifx < 0
java.lang.ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andsqrt(x)
is not an integer
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sqrtFloor
private static int sqrtFloor(int x)
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divide
public static int divide(int p, int q, java.math.RoundingMode mode)
Returns the result of dividingp
byq
, rounding using the specifiedRoundingMode
.- Throws:
java.lang.ArithmeticException
- ifq == 0
, or ifmode == UNNECESSARY
anda
is not an integer multiple ofb
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mod
public static int mod(int x, int m)
Returnsx mod m
, a non-negative value less thanm
. This differs fromx % 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
- Throws:
java.lang.ArithmeticException
- ifm <= 0
- See Also:
- Remainder Operator
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gcd
public static int gcd(int a, int b)
Returns the greatest common divisor ofa, b
. Returns0
ifa == 0 && b == 0
.- Throws:
java.lang.IllegalArgumentException
- ifa < 0
orb < 0
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checkedAdd
public static int checkedAdd(int a, int b)
Returns the sum ofa
andb
, provided it does not overflow.- Throws:
java.lang.ArithmeticException
- ifa + b
overflows in signedint
arithmetic
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checkedSubtract
public static int checkedSubtract(int a, int b)
Returns the difference ofa
andb
, provided it does not overflow.- Throws:
java.lang.ArithmeticException
- ifa - b
overflows in signedint
arithmetic
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checkedMultiply
public static int checkedMultiply(int a, int b)
Returns the product ofa
andb
, provided it does not overflow.- Throws:
java.lang.ArithmeticException
- ifa * b
overflows in signedint
arithmetic
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checkedPow
public static int checkedPow(int b, int k)
Returns theb
to thek
th power, provided it does not overflow.pow(int, int)
may be faster, but does not check for overflow.- Throws:
java.lang.ArithmeticException
- ifb
to thek
th power overflows in signedint
arithmetic
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saturatedAdd
@Beta public static int saturatedAdd(int a, int b)
Returns the sum ofa
andb
unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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saturatedSubtract
@Beta public static int saturatedSubtract(int a, int b)
Returns the difference ofa
andb
unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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saturatedMultiply
@Beta public static int saturatedMultiply(int a, int b)
Returns the product ofa
andb
unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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saturatedPow
@Beta public static int saturatedPow(int b, int k)
Returns theb
to thek
th power, unless it would overflow or underflow in which caseInteger.MAX_VALUE
orInteger.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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factorial
public static int factorial(int n)
Returnsn!
, that is, the product of the firstn
positive integers,1
ifn == 0
, orInteger.MAX_VALUE
if the result does not fit in aint
.- Throws:
java.lang.IllegalArgumentException
- ifn < 0
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binomial
public static int binomial(int n, int k)
Returnsn
choosek
, also known as the binomial coefficient ofn
andk
, orInteger.MAX_VALUE
if the result does not fit in anint
.- Throws:
java.lang.IllegalArgumentException
- ifn < 0
,k < 0
ork > n
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mean
public static int mean(int x, int y)
Returns the arithmetic mean ofx
andy
, rounded towards negative infinity. This method is overflow resilient.- Since:
- 14.0
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isPrime
@GwtIncompatible @Beta public static boolean isPrime(int n)
Returnstrue
ifn
is a prime number: an integer greater than one that cannot be factored into a product of smaller positive integers. Returnsfalse
ifn
is zero, one, or a composite number (one which can be factored into smaller positive integers).To test larger numbers, use
LongMath.isPrime(long)
orBigInteger.isProbablePrime(int)
.- Throws:
java.lang.IllegalArgumentException
- ifn
is negative- Since:
- 20.0
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