Class LongMath
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
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Nested Class Summary
Nested Classes -
Field Summary
FieldsModifier and TypeFieldDescription(package private) static final int[]
(package private) static final int[]
(package private) static final long[]
(package private) static final long
(package private) static final long[]
(package private) static final long
The biggest half power of two that fits into an unsigned long(package private) static final long
(package private) static final byte[]
private static final long[][]
(package private) static final long[]
private static final int
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionstatic long
binomial
(int n, int k) Returnsn
choosek
, also known as the binomial coefficient ofn
andk
, orLong.MAX_VALUE
if the result does not fit in along
.static long
ceilingPowerOfTwo
(long x) Returns the smallest power of two greater than or equal tox
.static long
checkedAdd
(long a, long b) Returns the sum ofa
andb
, provided it does not overflow.static long
checkedMultiply
(long a, long b) Returns the product ofa
andb
, provided it does not overflow.static long
checkedPow
(long b, int k) Returns theb
to thek
th power, provided it does not overflow.static long
checkedSubtract
(long a, long b) Returns the difference ofa
andb
, provided it does not overflow.static long
divide
(long p, long q, RoundingMode mode) Returns the result of dividingp
byq
, rounding using the specifiedRoundingMode
.static long
factorial
(int n) Returnsn!
, that is, the product of the firstn
positive integers,1
ifn == 0
, orLong.MAX_VALUE
if the result does not fit in along
.(package private) static boolean
fitsInInt
(long x) static long
floorPowerOfTwo
(long x) Returns the largest power of two less than or equal tox
.static long
gcd
(long a, long b) Returns the greatest common divisor ofa, b
.static boolean
isPowerOfTwo
(long x) Returnstrue
ifx
represents a power of two.static boolean
isPrime
(long 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
(long x, long y) Returns 1 ifx < y
as unsigned longs, and 0 otherwise.static int
log10
(long x, RoundingMode mode) Returns the base-10 logarithm ofx
, rounded according to the specified rounding mode.(package private) static int
log10Floor
(long x) static int
log2
(long x, RoundingMode mode) Returns the base-2 logarithm ofx
, rounded according to the specified rounding mode.static long
mean
(long x, long y) Returns the arithmetic mean ofx
andy
, rounded toward negative infinity.static int
mod
(long x, int m) Returnsx mod m
, a non-negative value less thanm
.static long
mod
(long x, long m) Returnsx mod m
, a non-negative value less thanm
.(package private) static long
multiplyFraction
(long x, long numerator, long denominator) Returns (x * numerator / denominator), which is assumed to come out to an integral value.static long
pow
(long b, int k) Returnsb
to thek
th power.static double
roundToDouble
(long x, RoundingMode mode) Returnsx
, rounded to adouble
with the specified rounding mode.static long
saturatedAdd
(long a, long b) Returns the sum ofa
andb
unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.static long
saturatedMultiply
(long a, long b) Returns the product ofa
andb
unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.static long
saturatedPow
(long b, int k) Returns theb
to thek
th power, unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.static long
saturatedSubtract
(long a, long b) Returns the difference ofa
andb
unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.static long
sqrt
(long x, RoundingMode mode) Returns the square root ofx
, rounded with the specified rounding mode.
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Field Details
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MAX_SIGNED_POWER_OF_TWO
static final long MAX_SIGNED_POWER_OF_TWO- See Also:
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MAX_POWER_OF_SQRT2_UNSIGNED
static final long MAX_POWER_OF_SQRT2_UNSIGNEDThe biggest half power of two that fits into an unsigned long- See Also:
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maxLog10ForLeadingZeros
static final byte[] maxLog10ForLeadingZeros -
powersOf10
static final long[] powersOf10 -
halfPowersOf10
static final long[] halfPowersOf10 -
FLOOR_SQRT_MAX_LONG
static final long FLOOR_SQRT_MAX_LONG- See Also:
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factorials
static final long[] factorials -
biggestBinomials
static final int[] biggestBinomials -
biggestSimpleBinomials
static final int[] biggestSimpleBinomials -
SIEVE_30
private static final int SIEVE_30- See Also:
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millerRabinBaseSets
private static final long[][] millerRabinBaseSets
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Constructor Details
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LongMath
private LongMath()
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Method Details
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ceilingPowerOfTwo
public static long ceilingPowerOfTwo(long x) Returns the smallest power of two greater than or equal tox
. This is equivalent tocheckedPow(2, log2(x, CEILING))
.- Throws:
IllegalArgumentException
- ifx <= 0
ArithmeticException
- of the next-higher power of two is not representable as along
, i.e. whenx > 2^62
- Since:
- 20.0
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floorPowerOfTwo
public static long floorPowerOfTwo(long x) Returns the largest power of two less than or equal tox
. This is equivalent tocheckedPow(2, log2(x, FLOOR))
.- Throws:
IllegalArgumentException
- ifx <= 0
- Since:
- 20.0
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isPowerOfTwo
public static boolean isPowerOfTwo(long x) Returnstrue
ifx
represents a power of two.This differs from
Long.bitCount(x) == 1
, becauseLong.bitCount(Long.MIN_VALUE) == 1
, butLong.MIN_VALUE
is not a power of two. -
lessThanBranchFree
static int lessThanBranchFree(long x, long y) Returns 1 ifx < y
as unsigned longs, and 0 otherwise. Assumes that x - y fits into a signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster than the straightforward ternary expression. -
log2
Returns the base-2 logarithm ofx
, rounded according to the specified rounding mode.- Throws:
IllegalArgumentException
- ifx <= 0
ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not a power of two
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log10
Returns the base-10 logarithm ofx
, rounded according to the specified rounding mode.- Throws:
IllegalArgumentException
- ifx <= 0
ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not a power of ten
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log10Floor
static int log10Floor(long x) -
pow
public static long pow(long b, int k) Returnsb
to thek
th power. Even if the result overflows, it will be equal toBigInteger.valueOf(b).pow(k).longValue()
. This implementation runs inO(log k)
time.- Throws:
IllegalArgumentException
- ifk < 0
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sqrt
Returns the square root ofx
, rounded with the specified rounding mode.- Throws:
IllegalArgumentException
- ifx < 0
ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andsqrt(x)
is not an integer
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divide
Returns the result of dividingp
byq
, rounding using the specifiedRoundingMode
.- Throws:
ArithmeticException
- ifq == 0
, or ifmode == UNNECESSARY
anda
is not an integer multiple ofb
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mod
public static int mod(long 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:
ArithmeticException
- ifm <= 0
- See Also:
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mod
public static long mod(long x, long 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:
ArithmeticException
- ifm <= 0
- See Also:
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gcd
public static long gcd(long a, long b) Returns the greatest common divisor ofa, b
. Returns0
ifa == 0 && b == 0
.- Throws:
IllegalArgumentException
- ifa < 0
orb < 0
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checkedAdd
public static long checkedAdd(long a, long b) Returns the sum ofa
andb
, provided it does not overflow.- Throws:
ArithmeticException
- ifa + b
overflows in signedlong
arithmetic
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checkedSubtract
public static long checkedSubtract(long a, long b) Returns the difference ofa
andb
, provided it does not overflow.- Throws:
ArithmeticException
- ifa - b
overflows in signedlong
arithmetic
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checkedMultiply
public static long checkedMultiply(long a, long b) Returns the product ofa
andb
, provided it does not overflow.- Throws:
ArithmeticException
- ifa * b
overflows in signedlong
arithmetic
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checkedPow
public static long checkedPow(long b, int k) Returns theb
to thek
th power, provided it does not overflow.- Throws:
ArithmeticException
- ifb
to thek
th power overflows in signedlong
arithmetic
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saturatedAdd
public static long saturatedAdd(long a, long b) Returns the sum ofa
andb
unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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saturatedSubtract
public static long saturatedSubtract(long a, long b) Returns the difference ofa
andb
unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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saturatedMultiply
public static long saturatedMultiply(long a, long b) Returns the product ofa
andb
unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.- Since:
- 20.0
-
saturatedPow
public static long saturatedPow(long b, int k) Returns theb
to thek
th power, unless it would overflow or underflow in which caseLong.MAX_VALUE
orLong.MIN_VALUE
is returned, respectively.- Since:
- 20.0
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factorial
public static long factorial(int n) Returnsn!
, that is, the product of the firstn
positive integers,1
ifn == 0
, orLong.MAX_VALUE
if the result does not fit in along
.- Throws:
IllegalArgumentException
- ifn < 0
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binomial
public static long binomial(int n, int k) Returnsn
choosek
, also known as the binomial coefficient ofn
andk
, orLong.MAX_VALUE
if the result does not fit in along
.- Throws:
IllegalArgumentException
- ifn < 0
,k < 0
, ork > n
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multiplyFraction
static long multiplyFraction(long x, long numerator, long denominator) Returns (x * numerator / denominator), which is assumed to come out to an integral value. -
fitsInInt
static boolean fitsInInt(long x) -
mean
public static long mean(long x, long y) Returns the arithmetic mean ofx
andy
, rounded toward negative infinity. This method is resilient to overflow.- Since:
- 14.0
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isPrime
public static boolean isPrime(long 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
BigInteger.isProbablePrime(int)
.- Throws:
IllegalArgumentException
- ifn
is negative- Since:
- 20.0
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roundToDouble
Returnsx
, rounded to adouble
with the specified rounding mode. Ifx
is precisely representable as adouble
, itsdouble
value will be returned; otherwise, the rounding will choose between the two nearest representable values withmode
.For the case of
RoundingMode.HALF_EVEN
, this implementation uses the IEEE 754 default rounding mode: if the two nearest representable values are equally near, the one with the least significant bit zero is chosen. (In such cases, both of the nearest representable values are even integers; this method returns the one that is a multiple of a greater power of two.)- Throws:
ArithmeticException
- ifmode
isRoundingMode.UNNECESSARY
andx
is not precisely representable as adouble
- Since:
- 30.0
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