The class
StrictMath
contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.
To help ensure portability of Java programs, the definitions of some of the numeric functions in this package require that they produce the same results as certain published algorithms. These algorithms are available from the well-known network library netlib as the package "Freely Distributable Math Library," fdlibm. These algorithms, which are written in the C programming language, are then to be understood to be transliterated into Java and executed with all floating-point and integer operations following the rules of Java arithmetic. The following transformations are used in the transliteration:
double in C is expressed using Java platform methods that perform bit-wise conversions from double to long and long to double.int values in C are mapped to signed int values in Java with updates to operations to replicate unsigned semantics where the results on the same textual operation would differ. For example, >> shifts on unsigned C values are replaced with >>> shifts on signed Java values. Sized comparisons on unsigned C values (<, <=, >, >=) are replaced with semantically equivalent calls to compareUnsigned.The Java math library is defined with respect to fdlibm version 5.3. Where fdlibm provides more than one definition for a function (such as acos), use the "IEEE 754 core function" version (residing in a file whose name begins with the letter e). The methods which require fdlibm semantics are sin, cos, tan, asin, acos, atan, exp, log, log10, cbrt, atan2, pow, sinh, cosh, tanh, hypot, expm1, and log1p.
The platform uses signed two's complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int or long and overflow errors need to be detected, the methods whose names end with Exact throw an ArithmeticException when the results overflow.
The
Math
class discusses how the shared quality of implementation criteria for selected
Math
and
StrictMath
methods
relate to the IEEE 754 recommended operations.
Fields
static final double
The double value that is closer than any other to e, the base of the natural logarithms.
static final double
The double value that is closer than any other to pi (π), the ratio of the circumference of a circle to its diameter.
static final double
The double value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius.
static double
Returns the absolute value of a double value.
static float
Returns the absolute value of a float value.
static int
Returns the absolute value of an int value.
static long
Returns the absolute value of a long value.
static int
Returns the mathematical absolute value of an int value if it is exactly representable as an int, throwing ArithmeticException if the result overflows the positive int range.
static long
Returns the mathematical absolute value of an long value if it is exactly representable as an long, throwing ArithmeticException if the result overflows the positive long range.
static double
Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi.
static int
Returns the sum of its arguments, throwing an exception if the result overflows an int.
static long
Returns the sum of its arguments, throwing an exception if the result overflows a long.
static double
Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2.
static double
Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2.
static double
atan2(double y, double x)
Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta).
static double
Returns the cube root of a double value.
static double
Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer.
static int
Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient.
static long
Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient.
static long
Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient.
static int
Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient.
static long
Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient.
static int
Returns the ceiling modulus of the int arguments.
static int
Returns the ceiling modulus of the long and int arguments.
static long
Returns the ceiling modulus of the long arguments.
static double
clamp(double value, double min, double max)
Clamps the value to fit between min and max.
static float
clamp(float value, float min, float max)
Clamps the value to fit between min and max.
static int
clamp(long value, int min, int max)
Clamps the value to fit between min and max.
static long
clamp(long value, long min, long max)
Clamps the value to fit between min and max.
static double
Returns the first floating-point argument with the sign of the second floating-point argument.
static float
Returns the first floating-point argument with the sign of the second floating-point argument.
static double
Returns the trigonometric cosine of an angle.
static double
Returns the hyperbolic cosine of a double value.
static int
Returns the argument decremented by one, throwing an exception if the result overflows an int.
static long
Returns the argument decremented by one, throwing an exception if the result overflows a long.
static int
Returns the quotient of the arguments, throwing an exception if the result overflows an int.
static long
Returns the quotient of the arguments, throwing an exception if the result overflows a long.
static double
Returns Euler's number e raised to the power of a double value.
static double
static double
Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer.
static int
Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
static long
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.
static long
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.
static int
Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
static long
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.
static int
Returns the floor modulus of the int arguments.
static int
Returns the floor modulus of the long and int arguments.
static long
Returns the floor modulus of the long arguments.
static double
fma(double a, double b, double c)
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest double.
static float
fma(float a, float b, float c)
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest float.
static int
Returns the unbiased exponent used in the representation of a double.
static int
Returns the unbiased exponent used in the representation of a float.
static double
hypot(double x, double y)
Returns sqrt(x2 +y2) without intermediate overflow or underflow.
static double
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.
static int
Returns the argument incremented by one, throwing an exception if the result overflows an int.
static long
Returns the argument incremented by one, throwing an exception if the result overflows a long.
static double
Returns the natural logarithm (base e) of a double value.
static double
Returns the base 10 logarithm of a double value.
static double
Returns the natural logarithm of the sum of the argument and 1.
static double
Returns the greater of two double values.
static float
Returns the greater of two float values.
static int
Returns the greater of two int values.
static long
Returns the greater of two long values.
static double
Returns the smaller of two double values.
static float
Returns the smaller of two float values.
static int
Returns the smaller of two int values.
static long
Returns the smaller of two long values.
static int
Returns the product of the arguments, throwing an exception if the result overflows an int.
static long
Returns the product of the arguments, throwing an exception if the result overflows a long.
static long
Returns the product of the arguments, throwing an exception if the result overflows a long.
static long
Returns the exact mathematical product of the arguments.
static long
Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors.
static int
Returns the negation of the argument, throwing an exception if the result overflows an int.
static long
Returns the negation of the argument, throwing an exception if the result overflows a long.
static double
Returns the floating-point number adjacent to the first argument in the direction of the second argument.
static float
Returns the floating-point number adjacent to the first argument in the direction of the second argument.
static double
Returns the floating-point value adjacent to d in the direction of negative infinity.
static float
Returns the floating-point value adjacent to f in the direction of negative infinity.
static double
Returns the floating-point value adjacent to d in the direction of positive infinity.
static float
Returns the floating-point value adjacent to f in the direction of positive infinity.
static double
Returns the value of the first argument raised to the power of the second argument.
static double
Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0.
static double
Returns the double value that is closest in value to the argument and is equal to a mathematical integer.
static long
Returns the closest long to the argument, with ties rounding to positive infinity.
static int
Returns the closest int to the argument, with ties rounding to positive infinity.
static double
scalb(double d, int scaleFactor)
Returns d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply.
static float
scalb(float f, int scaleFactor)
Returns f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply.
static double
Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.
static float
Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.
static double
Returns the trigonometric sine of an angle.
static double
Returns the hyperbolic sine of a double value.
static double
Returns the correctly rounded positive square root of a double value.
static int
Returns the difference of the arguments, throwing an exception if the result overflows an int.
static long
Returns the difference of the arguments, throwing an exception if the result overflows a long.
static double
Returns the trigonometric tangent of an angle.
static double
Returns the hyperbolic tangent of a double value.
static double
Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
static int
Returns the value of the long argument, throwing an exception if the value overflows an int.
static double
Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
static double
Returns the size of an ulp of the argument.
static float
Returns the size of an ulp of the argument.
static long
Returns as a long the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, waitpublic static final double E
The double value that is closer than any other to e, the base of the natural logarithms.
public static final double PI
The double value that is closer than any other to pi (π), the ratio of the circumference of a circle to its diameter.
public static final double TAU
The double value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius.
public static double sin(double a)
Returns the trigonometric sine of an angle. Special cases:
a - an angle, in radians.
public static double cos(double a)
Returns the trigonometric cosine of an angle. Special cases:
1.0.a - an angle, in radians.
public static double tan(double a)
Returns the trigonometric tangent of an angle. Special cases:
a - an angle, in radians.
public static double asin(double a)
Returns the arc sine of a value; the returned angle is in the range -
pi/2 through
pi/2. Special cases:
a - the value whose arc sine is to be returned.
public static double acos(double a)
Returns the arc cosine of a value; the returned angle is in the range 0.0 through
pi. Special case:
1.0, the result is positive zero.a - the value whose arc cosine is to be returned.
public static double atan(double a)
Returns the arc tangent of a value; the returned angle is in the range -
pi/2 through
pi/2. Special cases:
a - the value whose arc tangent is to be returned.
public static double toRadians(double angdeg)
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.
angdeg - an angle, in degrees
angdeg in radians.
public static double toDegrees(double angrad)
Converts an angle measured in radians to an approximately equivalent angle measured in degrees. The conversion from radians to degrees is generally inexact; users should not expect cos(toRadians(90.0)) to exactly equal 0.0.
angrad - an angle, in radians
angrad in degrees.
public static double exp(double a)
Returns Euler's number
eraised to the power of a
double
value. Special cases:
1.0.a - the exponent to raise e to.
a, where e is the base of the natural logarithms.
public static double log(double a)
Returns the natural logarithm (base
e) of a
double
value. Special cases:
1.0, then the result is positive zero.a - a value
a, the natural logarithm of a.
public static double log10(double a)
Returns the base 10 logarithm of a
double
value. Special cases:
1.0 (100), then the result is positive zero.a - a value
a.
public static double sqrt(double a)
Returns the correctly rounded positive square root of a
double
value. Special cases:
Otherwise, the result is the
double
value closest to the true mathematical square root of the argument value.
a - a value.
a.
public static double cbrt(double a)
Returns the cube root of a
double
value. For positive finite
x
,
cbrt(-x) == -cbrt(x)
; that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:
a - a value.
a.
public static double IEEEremainder(double f1, double f2)
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to
f1 - f2
×
n, where
nis the mathematical integer closest to the exact mathematical value of the quotient
f1/f2
, and if two mathematical integers are equally close to
f1/f2
, then
nis the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:
f1 - the dividend.
f2 - the divisor.
f1 is divided by f2.
public static double ceil(double a)
Returns the smallest (closest to negative infinity)
double
value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:
Note that the value of
StrictMath.ceil(x)
is exactly the value of
-StrictMath.floor(-x)
.
a - a value.
public static double floor(double a)
Returns the largest (closest to positive infinity)
double
value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:
a - a value.
public static double rint(double a)
Returns the
double
value that is closest in value to the argument and is equal to a mathematical integer. If two
double
values that are mathematical integers are equally close to the value of the argument, the result is the integer value that is even. Special cases:
a - a value.
a that is equal to a mathematical integer.
public static double atan2(double y, double x)
Returns the angle
thetafrom the conversion of rectangular coordinates (
x
,
y
) to polar coordinates (r,
theta). This method computes the phase
thetaby computing an arc tangent of
y/x
in the range of -
pito
pi. Special cases:
double value closest to pi.double value closest to -pi.double value closest to pi/2.double value closest to -pi/2.double value closest to pi/4.double value closest to 3*pi/4.double value closest to -pi/4.double value closest to -3*pi/4.atan2 is equal to:
y - the ordinate coordinate
x - the abscissa coordinate
public static double pow(double a, double b)
Returns the value of the first argument raised to the power of the second argument. Special cases:
double value.(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil or, equivalently, a fixed point of the method floor. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)
pow operation for ±1.0 raised to an infinite power. This method treats such cases as indeterminate and specifies a NaN is returned. The IEEE 754 specification treats the infinite power as a large integer (large-magnitude floating-point numbers are numerically integers, specifically even integers) and therefore specifies 1.0 be returned.
a - base.
b - the exponent.
ab.
public static int round(float a)
Returns the closest
int
to the argument, with ties rounding to positive infinity.
Special cases:
Integer.MIN_VALUE, the result is equal to the value of Integer.MIN_VALUE.Integer.MAX_VALUE, the result is equal to the value of Integer.MAX_VALUE.a - a floating-point value to be rounded to an integer.
int value.
public static long round(double a)
Returns the closest
long
to the argument, with ties rounding to positive infinity.
Special cases:
Long.MIN_VALUE, the result is equal to the value of Long.MIN_VALUE.Long.MAX_VALUE, the result is equal to the value of Long.MAX_VALUE.a - a floating-point value to be rounded to a long.
long value.
public static double random()
Returns a
double
value with a positive sign, greater than or equal to
0.0
and less than
1.0
. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.
When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression
new java.util.Random()
This new pseudorandom-number generator is used thereafter for all calls to this method and is used nowhere else.
This method is properly synchronized to allow correct use by more than one thread. However, if many threads need to generate pseudorandom numbers at a great rate, it may reduce contention for each thread to have its own pseudorandom-number generator.
double greater than or equal to 0.0 and less than 1.0.
public static int addExact(int x, int y)
Returns the sum of its arguments, throwing an exception if the result overflows an int.
x - the first value
y - the second value
ArithmeticException - if the result overflows an int
public static long addExact(long x, long y)
Returns the sum of its arguments, throwing an exception if the result overflows a long.
x - the first value
y - the second value
ArithmeticException - if the result overflows a long
public static int subtractExact(int x, int y)
Returns the difference of the arguments, throwing an exception if the result overflows an int.
x - the first value
y - the second value to subtract from the first
ArithmeticException - if the result overflows an int
public static long subtractExact(long x, long y)
Returns the difference of the arguments, throwing an exception if the result overflows a long.
x - the first value
y - the second value to subtract from the first
ArithmeticException - if the result overflows a long
public static int multiplyExact(int x, int y)
Returns the product of the arguments, throwing an exception if the result overflows an int.
x - the first value
y - the second value
ArithmeticException - if the result overflows an int
public static long multiplyExact(long x, int y)
Returns the product of the arguments, throwing an exception if the result overflows a long.
x - the first value
y - the second value
ArithmeticException - if the result overflows a long
public static long multiplyExact(long x, long y)
Returns the product of the arguments, throwing an exception if the result overflows a long.
x - the first value
y - the second value
ArithmeticException - if the result overflows a long
public static int divideExact(int x, int y)
Returns the quotient of the arguments, throwing an exception if the result overflows an
int
. Such overflow occurs in this method if
x
is
Integer.MIN_VALUE
and
y
is
-1
. In contrast, if
Integer.MIN_VALUE / -1
were evaluated directly, the result would be
Integer.MIN_VALUE
and no exception would be thrown.
If y is zero, an ArithmeticException is thrown (JLS 15.17.2).
The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".
x - the dividend
y - the divisor
x / y
ArithmeticException - if y is zero or the quotient overflows an int
public static long divideExact(long x, long y)
Returns the quotient of the arguments, throwing an exception if the result overflows a
long
. Such overflow occurs in this method if
x
is
Long.MIN_VALUE
and
y
is
-1
. In contrast, if
Long.MIN_VALUE / -1
were evaluated directly, the result would be
Long.MIN_VALUE
and no exception would be thrown.
If y is zero, an ArithmeticException is thrown (JLS 15.17.2).
The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".
x - the dividend
y - the divisor
x / y
ArithmeticException - if y is zero or the quotient overflows a long
public static int floorDivExact(int x, int y)
Returns the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient. This method is identical to
floorDiv(int,int)
except that it throws an
ArithmeticException
when the dividend is
Integer.MIN_VALUEand the divisor is
-1
instead of ignoring the integer overflow and returning
Integer.MIN_VALUE
.
The floor modulus method floorMod(int,int) is a suitable counterpart both for this method and for the floorDiv(int,int) method.
See Math.floorDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
int value that is less than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero, or the dividend x is Integer.MIN_VALUE and the divisor y is -1.
public static long floorDivExact(long x, long y)
Returns the largest (closest to positive infinity)
long
value that is less than or equal to the algebraic quotient. This method is identical to
floorDiv(long,long)
except that it throws an
ArithmeticException
when the dividend is
Long.MIN_VALUEand the divisor is
-1
instead of ignoring the integer overflow and returning
Long.MIN_VALUE
.
The floor modulus method floorMod(long,long) is a suitable counterpart both for this method and for the floorDiv(long,long) method.
For examples, see Math.floorDiv.
x - the dividend
y - the divisor
long value that is less than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero, or the dividend x is Long.MIN_VALUE and the divisor y is -1.
public static int ceilDivExact(int x, int y)
Returns the smallest (closest to negative infinity)
int
value that is greater than or equal to the algebraic quotient. This method is identical to
ceilDiv(int,int)
except that it throws an
ArithmeticException
when the dividend is
Integer.MIN_VALUEand the divisor is
-1
instead of ignoring the integer overflow and returning
Integer.MIN_VALUE
.
The ceil modulus method ceilMod(int,int) is a suitable counterpart both for this method and for the ceilDiv(int,int) method.
See Math.ceilDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
int value that is greater than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero, or the dividend x is Integer.MIN_VALUE and the divisor y is -1.
public static long ceilDivExact(long x, long y)
Returns the smallest (closest to negative infinity)
long
value that is greater than or equal to the algebraic quotient. This method is identical to
ceilDiv(long,long)
except that it throws an
ArithmeticException
when the dividend is
Long.MIN_VALUEand the divisor is
-1
instead of ignoring the integer overflow and returning
Long.MIN_VALUE
.
The ceil modulus method ceilMod(long,long) is a suitable counterpart both for this method and for the ceilDiv(long,long) method.
For examples, see Math.ceilDiv.
x - the dividend
y - the divisor
long value that is greater than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero, or the dividend x is Long.MIN_VALUE and the divisor y is -1.
public static int incrementExact(int a)
Returns the argument incremented by one, throwing an exception if the result overflows an
int
. The overflow only occurs for
the maximum value.
a - the value to increment
ArithmeticException - if the result overflows an int
public static long incrementExact(long a)
Returns the argument incremented by one, throwing an exception if the result overflows a
long
. The overflow only occurs for
the maximum value.
a - the value to increment
ArithmeticException - if the result overflows a long
public static int decrementExact(int a)
Returns the argument decremented by one, throwing an exception if the result overflows an
int
. The overflow only occurs for
the minimum value.
a - the value to decrement
ArithmeticException - if the result overflows an int
public static long decrementExact(long a)
Returns the argument decremented by one, throwing an exception if the result overflows a
long
. The overflow only occurs for
the minimum value.
a - the value to decrement
ArithmeticException - if the result overflows a long
public static int negateExact(int a)
Returns the negation of the argument, throwing an exception if the result overflows an
int
. The overflow only occurs for
the minimum value.
a - the value to negate
ArithmeticException - if the result overflows an int
public static long negateExact(long a)
Returns the negation of the argument, throwing an exception if the result overflows a
long
. The overflow only occurs for
the minimum value.
a - the value to negate
ArithmeticException - if the result overflows a long
public static int toIntExact(long value)
Returns the value of the long argument, throwing an exception if the value overflows an int.
value - the long value
ArithmeticException - if the argument overflows an int
public static long multiplyFull(int x, int y)
Returns the exact mathematical product of the arguments.
x - the first value
y - the second value
public static long multiplyHigh(long x, long y)
Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors.
x - the first value
y - the second value
public static long unsignedMultiplyHigh(long x, long y)
Returns as a long the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.
x - the first value
y - the second value
public static int floorDiv(int x, int y)
Returns the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is
Integer.MIN_VALUEand the divisor is
-1
, then integer overflow occurs and the result is equal to
Integer.MIN_VALUE
.
See Math.floorDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
int value that is less than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero
public static long floorDiv(long x, int y)
Returns the largest (closest to positive infinity)
long
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is
Long.MIN_VALUEand the divisor is
-1
, then integer overflow occurs and the result is equal to
Long.MIN_VALUE
.
See Math.floorDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
long value that is less than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero
public static long floorDiv(long x, long y)
Returns the largest (closest to positive infinity)
long
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is
Long.MIN_VALUEand the divisor is
-1
, then integer overflow occurs and the result is equal to
Long.MIN_VALUE
.
See Math.floorDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
long value that is less than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero
public static int floorMod(int x, int y)
Returns the floor modulus of the
int
arguments.
The floor modulus is r = x - (floorDiv(x, y) * y), has the same sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
floorDiv(x, y) * y + floorMod(x, y) == xSee Math.floorMod for examples and a comparison to the % operator.
x - the dividend
y - the divisor
x - (floorDiv(x, y) * y)
ArithmeticException - if the divisor y is zero
public static int floorMod(long x, int y)
Returns the floor modulus of the
long
and
int
arguments.
The floor modulus is r = x - (floorDiv(x, y) * y), has the same sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
floorDiv(x, y) * y + floorMod(x, y) == xSee Math.floorMod for examples and a comparison to the % operator.
x - the dividend
y - the divisor
x - (floorDiv(x, y) * y)
ArithmeticException - if the divisor y is zero
public static long floorMod(long x, long y)
Returns the floor modulus of the
long
arguments.
The floor modulus is r = x - (floorDiv(x, y) * y), has the same sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
floorDiv(x, y) * y + floorMod(x, y) == xSee Math.floorMod for examples and a comparison to the % operator.
x - the dividend
y - the divisor
x - (floorDiv(x, y) * y)
ArithmeticException - if the divisor y is zero
public static int ceilDiv(int x, int y)
Returns the smallest (closest to negative infinity)
int
value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is
Integer.MIN_VALUEand the divisor is
-1
, then integer overflow occurs and the result is equal to
Integer.MIN_VALUE
.
See Math.ceilDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
int value that is greater than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero
public static long ceilDiv(long x, int y)
Returns the smallest (closest to negative infinity)
long
value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is
Long.MIN_VALUEand the divisor is
-1
, then integer overflow occurs and the result is equal to
Long.MIN_VALUE
.
See Math.ceilDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
long value that is greater than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero
public static long ceilDiv(long x, long y)
Returns the smallest (closest to negative infinity)
long
value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is
Long.MIN_VALUEand the divisor is
-1
, then integer overflow occurs and the result is equal to
Long.MIN_VALUE
.
See Math.ceilDiv for examples and a comparison to the integer division / operator.
x - the dividend
y - the divisor
long value that is greater than or equal to the algebraic quotient.
ArithmeticException - if the divisor y is zero
public static int ceilMod(int x, int y)
Returns the ceiling modulus of the
int
arguments.
The ceiling modulus is r = x - (ceilDiv(x, y) * y), has the opposite sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between ceilDiv and ceilMod is such that:
ceilDiv(x, y) * y + ceilMod(x, y) == xSee Math.ceilMod for examples and a comparison to the % operator.
x - the dividend
y - the divisor
x - (ceilDiv(x, y) * y)
ArithmeticException - if the divisor y is zero
public static int ceilMod(long x, int y)
Returns the ceiling modulus of the
long
and
int
arguments.
The ceiling modulus is r = x - (ceilDiv(x, y) * y), has the opposite sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between ceilDiv and ceilMod is such that:
ceilDiv(x, y) * y + ceilMod(x, y) == xSee Math.ceilMod for examples and a comparison to the % operator.
x - the dividend
y - the divisor
x - (ceilDiv(x, y) * y)
ArithmeticException - if the divisor y is zero
public static long ceilMod(long x, long y)
Returns the ceiling modulus of the
long
arguments.
The ceiling modulus is r = x - (ceilDiv(x, y) * y), has the opposite sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between ceilDiv and ceilMod is such that:
ceilDiv(x, y) * y + ceilMod(x, y) == xSee Math.ceilMod for examples and a comparison to the % operator.
x - the dividend
y - the divisor
x - (ceilDiv(x, y) * y)
ArithmeticException - if the divisor y is zero
public static int abs(int a)
Returns the absolute value of an
int
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.
Note that if the argument is equal to the value of Integer.MIN_VALUE, the most negative representable int value, the result is that same value, which is negative. In contrast, the absExact(int) method throws an ArithmeticException for this value.
a - the argument whose absolute value is to be determined.
public static int absExact(int a)
Returns the mathematical absolute value of an
int
value if it is exactly representable as an
int
, throwing
ArithmeticException
if the result overflows the positive
int
range.
Since the range of two's complement integers is asymmetric with one additional negative value (JLS 4.2.1), the mathematical absolute value of Integer.MIN_VALUE overflows the positive int range, so an exception is thrown for that argument.
a - the argument whose absolute value is to be determined
ArithmeticException - if the argument is Integer.MIN_VALUE
public static long abs(long a)
Returns the absolute value of a
long
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.
Note that if the argument is equal to the value of Long.MIN_VALUE, the most negative representable long value, the result is that same value, which is negative. In contrast, the absExact(long) method throws an ArithmeticException for this value.
a - the argument whose absolute value is to be determined.
public static long absExact(long a)
Returns the mathematical absolute value of an
long
value if it is exactly representable as an
long
, throwing
ArithmeticException
if the result overflows the positive
long
range.
Since the range of two's complement integers is asymmetric with one additional negative value (JLS 4.2.1), the mathematical absolute value of Long.MIN_VALUE overflows the positive long range, so an exception is thrown for that argument.
a - the argument whose absolute value is to be determined
ArithmeticException - if the argument is Long.MIN_VALUE
public static float abs(float a)
Returns the absolute value of a
float
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
float with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:
Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))
a - the argument whose absolute value is to be determined
public static double abs(double a)
Returns the absolute value of a
double
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
double with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:
Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)
a - the argument whose absolute value is to be determined
public static int max(int a, int b)
Returns the greater of two
int
values. That is, the result is the argument closer to the value of
Integer.MAX_VALUE
. If the arguments have the same value, the result is that same value.
a - an argument.
b - another argument.
a and b.
public static long max(long a, long b)
Returns the greater of two
long
values. That is, the result is the argument closer to the value of
Long.MAX_VALUE
. If the arguments have the same value, the result is that same value.
a - an argument.
b - another argument.
a and b.
public static float max(float a, float b)
Returns the greater of two float values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.
a - an argument.
b - another argument.
a and b.
public static double max(double a, double b)
Returns the greater of two double values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.
a - an argument.
b - another argument.
a and b.
public static int min(int a, int b)
Returns the smaller of two
int
values. That is, the result the argument closer to the value of
Integer.MIN_VALUE
. If the arguments have the same value, the result is that same value.
a - an argument.
b - another argument.
a and b.
public static long min(long a, long b)
Returns the smaller of two
long
values. That is, the result is the argument closer to the value of
Long.MIN_VALUE
. If the arguments have the same value, the result is that same value.
a - an argument.
b - another argument.
a and b.
public static float min(float a, float b)
Returns the smaller of two float values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.
a - an argument.
b - another argument.
a and b.
public static double min(double a, double b)
Returns the smaller of two double values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.
a - an argument.
b - another argument.
a and b.
public static int clamp(long value, int min, int max)
Clamps the value to fit between min and max. If the value is less than
min
, then
min
is returned. If the value is greater than
max
, then
max
is returned. Otherwise, the original value is returned.
While the original value of type long may not fit into the int type, the bounds have the int type, so the result always fits the int type. This allows to use method to safely cast long value to int with saturation.
value - value to clamp
min - minimal allowed value
max - maximal allowed value
min..max interval
IllegalArgumentException - if min > max
public static long clamp(long value, long min, long max)
Clamps the value to fit between min and max. If the value is less than min, then min is returned. If the value is greater than max, then max is returned. Otherwise, the original value is returned.
value - value to clamp
min - minimal allowed value
max - maximal allowed value
min..max interval
IllegalArgumentException - if min > max
public static double clamp(double value, double min, double max)
Clamps the value to fit between min and max. If the value is less than
min
, then
min
is returned. If the value is greater than
max
, then
max
is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN.
Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. E.g., clamp(-0.0, 0.0, 1.0) returns 0.0.
value - value to clamp
min - minimal allowed value
max - maximal allowed value
min..max interval
IllegalArgumentException - if either of min and max arguments is NaN, or min > max, or min is +0.0, and max is -0.0.
public static float clamp(float value, float min, float max)
Clamps the value to fit between min and max. If the value is less than
min
, then
min
is returned. If the value is greater than
max
, then
max
is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN.
Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. E.g., clamp(-0.0f, 0.0f, 1.0f) returns 0.0f.
value - value to clamp
min - minimal allowed value
max - maximal allowed value
min..max interval
IllegalArgumentException - if either of min and max arguments is NaN, or min > max, or min is +0.0f, and max is -0.0f.
public static double fma(double a, double b, double c)
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest
double
. The rounding is done using the
round to nearest even rounding mode. In contrast, if
a * b + c
is evaluated as a regular floating-point expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.
Special cases:
Note that fusedMac(a, 1.0, c) returns the same result as (a + c). However, fusedMac(a, b, +0.0) does not always return the same result as (a * b) since fusedMac(-0.0, +0.0, +0.0) is +0.0 while (-0.0 * +0.0) is -0.0; fusedMac(a, b, -0.0) is equivalent to (a * b) however.
a - a value
b - a value
c - a value
double value
public static float fma(float a, float b, float c)
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest
float
. The rounding is done using the
round to nearest even rounding mode. In contrast, if
a * b + c
is evaluated as a regular floating-point expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.
Special cases:
Note that fma(a, 1.0f, c) returns the same result as (a + c). However, fma(a, b, +0.0f) does not always return the same result as (a * b) since fma(-0.0f, +0.0f, +0.0f) is +0.0f while (-0.0f * +0.0f) is -0.0f; fma(a, b, -0.0f) is equivalent to (a * b) however.
a - a value
b - a value
c - a value
float value
public static double ulp(double d)
Returns the size of an ulp of the argument. An ulp, unit in the last place, of a
double
value is the positive distance between this floating-point value and the
double
value next larger in magnitude. Note that for non-NaN
x,
ulp(-x) == ulp(x)
.
Special Cases:
Double.MIN_VALUE.Double.MAX_VALUE, then the result is equal to 2971.d - the floating-point value whose ulp is to be returned
public static float ulp(float f)
Returns the size of an ulp of the argument. An ulp, unit in the last place, of a
float
value is the positive distance between this floating-point value and the
float
value next larger in magnitude. Note that for non-NaN
x,
ulp(-x) == ulp(x)
.
Special Cases:
Float.MIN_VALUE.Float.MAX_VALUE, then the result is equal to 2104.f - the floating-point value whose ulp is to be returned
public static double signum(double d)
Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.
Special Cases:
d - the floating-point value whose signum is to be returned
public static float signum(float f)
Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.
Special Cases:
f - the floating-point value whose signum is to be returned
public static double sinh(double x)
Returns the hyperbolic sine of a
double
value. The hyperbolic sine of
xis defined to be (
ex - e-x)/2 where
eis
Euler's number.
Special cases:
x - The number whose hyperbolic sine is to be returned.
x.
public static double cosh(double x)
Returns the hyperbolic cosine of a
double
value. The hyperbolic cosine of
xis defined to be (
ex + e-x)/2 where
eis
Euler's number.
Special cases:
1.0.x - The number whose hyperbolic cosine is to be returned.
x.
public static double tanh(double x)
Returns the hyperbolic tangent of a
double
value. The hyperbolic tangent of
xis defined to be (
ex - e-x)/(
ex + e-x), in other words,
sinh(x)/
cosh(x). Note that the absolute value of the exact tanh is always less than 1.
Special cases:
+1.0.-1.0.x - The number whose hyperbolic tangent is to be returned.
x.
public static double hypot(double x, double y)
Returns sqrt(
x2+
y2) without intermediate overflow or underflow.
Special cases:
x - a value
y - a value
public static double expm1(double x)
Returns
ex-1. Note that for values of
xnear 0, the exact sum of
expm1(x)
+ 1 is much closer to the true result of
exthan
exp(x)
.
Special cases:
x - the exponent to raise e to in the computation of ex -1.
x - 1.
public static double log1p(double x)
Returns the natural logarithm of the sum of the argument and 1. Note that for small values
x
, the result of
log1p(x)
is much closer to the true result of ln(1 +
x
) than the floating-point evaluation of
log(1.0+x)
.
Special cases:
x - a value
x + 1), the natural log of x + 1
public static double copySign(double magnitude, double sign)
Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign argument is always treated as if it were positive.
magnitude - the parameter providing the magnitude of the result
sign - the parameter providing the sign of the result
magnitude and the sign of sign.
public static float copySign(float magnitude, float sign)
Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign argument is always treated as if it were positive.
magnitude - the parameter providing the magnitude of the result
sign - the parameter providing the sign of the result
magnitude and the sign of sign.
public static int getExponent(float f)
Returns the unbiased exponent used in the representation of a
float
. Special cases:
Float.MAX_EXPONENT + 1.Float.MIN_EXPONENT -1.f - a float value
public static int getExponent(double d)
Returns the unbiased exponent used in the representation of a
double
. Special cases:
Double.MAX_EXPONENT + 1.Double.MIN_EXPONENT -1.d - a double value
public static double nextAfter(double start, double direction)
Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal the second argument is returned.
Special cases:
direction is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).start is ±Double.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.start is infinite and direction has a value such that the result should have a smaller magnitude, Double.MAX_VALUE with the same sign as start is returned.start is equal to ± Double.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.start - starting floating-point value
direction - value indicating which of start's neighbors or start should be returned
start in the direction of direction.
public static float nextAfter(float start, double direction)
Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal a value equivalent to the second argument is returned.
Special cases:
direction is returned.start is ±Float.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.start is infinite and direction has a value such that the result should have a smaller magnitude, Float.MAX_VALUE with the same sign as start is returned.start is equal to ± Float.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.start - starting floating-point value
direction - value indicating which of start's neighbors or start should be returned
start in the direction of direction.
public static double nextUp(double d)
Returns the floating-point value adjacent to
d
in the direction of positive infinity. This method is semantically equivalent to
nextAfter(d, Double.POSITIVE_INFINITY)
; however, a
nextUp
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
Double.MIN_VALUEd - starting floating-point value
public static float nextUp(float f)
Returns the floating-point value adjacent to
f
in the direction of positive infinity. This method is semantically equivalent to
nextAfter(f, Float.POSITIVE_INFINITY)
; however, a
nextUp
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
Float.MIN_VALUEf - starting floating-point value
public static double nextDown(double d)
Returns the floating-point value adjacent to
d
in the direction of negative infinity. This method is semantically equivalent to
nextAfter(d, Double.NEGATIVE_INFINITY)
; however, a
nextDown
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
-Double.MIN_VALUEd - starting floating-point value
public static float nextDown(float f)
Returns the floating-point value adjacent to
f
in the direction of negative infinity. This method is semantically equivalent to
nextAfter(f, Float.NEGATIVE_INFINITY)
; however, a
nextDown
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
-Float.MIN_VALUEf - starting floating-point value
public static double scalb(double d, int scaleFactor)
Returns
d
× 2
scaleFactor
rounded as if performed by a single correctly rounded floating-point multiply. If the exponent of the result is between
Double.MIN_EXPONENT
and
Double.MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger than
Double.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when
scalb(x, n)
is subnormal,
scalb(scalb(x, n), -n)
may not equal
x. When the result is non-NaN, the result has the same sign as
d
.
Special cases:
d - number to be scaled by a power of two.
scaleFactor - power of 2 used to scale d
d × 2scaleFactor
public static float scalb(float f, int scaleFactor)
Returns
f
× 2
scaleFactor
rounded as if performed by a single correctly rounded floating-point multiply. If the exponent of the result is between
Float.MIN_EXPONENT
and
Float.MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger than
Float.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when
scalb(x, n)
is subnormal,
scalb(scalb(x, n), -n)
may not equal
x. When the result is non-NaN, the result has the same sign as
f
.
Special cases:
f - number to be scaled by a power of two.
scaleFactor - power of 2 used to scale f
f × 2scaleFactor
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