@GwtCompatible(emulated=true) public final class LongMath extends java.lang.Object
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
.
Modifier and Type | Field and Description |
---|---|
(package private) static int[] |
biggestBinomials |
(package private) static int[] |
biggestSimpleBinomials |
(package private) static long[] |
factorials |
(package private) static long |
FLOOR_SQRT_MAX_LONG |
(package private) static long[] |
halfPowersOf10 |
(package private) static long |
MAX_POWER_OF_SQRT2_UNSIGNED
The biggest half power of two that fits into an unsigned long
|
(package private) static byte[] |
maxLog10ForLeadingZeros |
(package private) static long[] |
powersOf10 |
Modifier | Constructor and Description |
---|---|
private |
LongMath() |
Modifier and Type | Method and Description |
---|---|
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 k th 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,
java.math.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 . |
(package private) static boolean |
fitsInInt(long x) |
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. |
(package private) static int |
lessThanBranchFree(long x,
long y)
Returns 1 if
x < y as unsigned longs, and 0 otherwise. |
static int |
log10(long x,
java.math.RoundingMode mode)
Returns the base-10 logarithm of
x , rounded according to the specified rounding mode. |
(package private) static int |
log10Floor(long x) |
static int |
log2(long x,
java.math.RoundingMode mode)
Returns the base-2 logarithm of
x , rounded according to the specified rounding mode. |
static long |
mean(long x,
long y)
Returns the arithmetic mean of
x and y , rounded toward
negative infinity. |
static int |
mod(long x,
int m)
Returns
x mod m , a non-negative value less than m . |
static long |
mod(long x,
long m)
Returns
x mod m , a non-negative value less than m . |
(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)
Returns
b to the k th power. |
static long |
sqrt(long x,
java.math.RoundingMode mode)
Returns the square root of
x , rounded with the specified rounding mode. |
static final long MAX_POWER_OF_SQRT2_UNSIGNED
static final byte[] maxLog10ForLeadingZeros
@GwtIncompatible(value="TODO") static final long[] powersOf10
@GwtIncompatible(value="TODO") static final long[] halfPowersOf10
static final long FLOOR_SQRT_MAX_LONG
static final long[] factorials
static final int[] biggestBinomials
static final int[] biggestSimpleBinomials
public static boolean isPowerOfTwo(long x)
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.
static int lessThanBranchFree(long x, long y)
x < 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.public static int log2(long x, java.math.RoundingMode mode)
x
, rounded according to the specified rounding mode.java.lang.IllegalArgumentException
- if x <= 0
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not a power of two@GwtIncompatible(value="TODO") public static int log10(long x, java.math.RoundingMode mode)
x
, rounded according to the specified rounding mode.java.lang.IllegalArgumentException
- if x <= 0
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and x
is not a power of ten@GwtIncompatible(value="TODO") static int log10Floor(long x)
@GwtIncompatible(value="TODO") public static long pow(long b, int k)
b
to the k
th 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.java.lang.IllegalArgumentException
- if k < 0
@GwtIncompatible(value="TODO") public static long sqrt(long x, java.math.RoundingMode mode)
x
, rounded with the specified rounding mode.java.lang.IllegalArgumentException
- if x < 0
java.lang.ArithmeticException
- if mode
is RoundingMode.UNNECESSARY
and
sqrt(x)
is not an integer@GwtIncompatible(value="TODO") public static long divide(long p, long q, java.math.RoundingMode mode)
p
by q
, rounding using the specified
RoundingMode
.java.lang.ArithmeticException
- if q == 0
, or if mode == UNNECESSARY
and a
is not an integer multiple of b
@GwtIncompatible(value="TODO") public static int mod(long x, int m)
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
java.lang.ArithmeticException
- if m <= 0
@GwtIncompatible(value="TODO") public static long mod(long x, long m)
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
java.lang.ArithmeticException
- if m <= 0
public static long gcd(long a, long b)
a, b
. Returns 0
if
a == 0 && b == 0
.java.lang.IllegalArgumentException
- if a < 0
or b < 0
@GwtIncompatible(value="TODO") public static long checkedAdd(long a, long b)
a
and b
, provided it does not overflow.java.lang.ArithmeticException
- if a + b
overflows in signed long
arithmetic@GwtIncompatible(value="TODO") public static long checkedSubtract(long a, long b)
a
and b
, provided it does not overflow.java.lang.ArithmeticException
- if a - b
overflows in signed long
arithmetic@GwtIncompatible(value="TODO") public static long checkedMultiply(long a, long b)
a
and b
, provided it does not overflow.java.lang.ArithmeticException
- if a * b
overflows in signed long
arithmetic@GwtIncompatible(value="TODO") public static long checkedPow(long b, int k)
b
to the k
th power, provided it does not overflow.java.lang.ArithmeticException
- if b
to the k
th power overflows in signed
long
arithmetic@GwtIncompatible(value="TODO") public static long factorial(int n)
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
.java.lang.IllegalArgumentException
- if n < 0
public static long binomial(int n, int k)
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
.java.lang.IllegalArgumentException
- if n < 0
, k < 0
, or k > n
static long multiplyFraction(long x, long numerator, long denominator)
static boolean fitsInInt(long x)
public static long mean(long x, long y)
x
and y
, rounded toward
negative infinity. This method is resilient to overflow.