Class Math
 java.lang.Object

 java.lang.Math
public final class Math extends Object
The class Math
contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.
Unlike some of the numeric methods of class StrictMath
, all implementations of the equivalent functions of class Math
are not defined to return the bitforbit same results. This relaxation permits betterperforming implementations where strict reproducibility is not required.
By default many of the Math
methods simply call the equivalent method in StrictMath
for their implementation. Code generators are encouraged to use platformspecific native libraries or microprocessor instructions, where available, to provide higherperformance implementations of Math
methods. Such higherperformance implementations still must conform to the specification for Math
.
The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floatingpoint Math
methods is measured in terms of ulps, units in the last place. For a given floatingpoint format, an ulp of a specific real number value is the distance between the two floatingpoint values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worstcase error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floatingpoint number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floatingpoint approximation can be; however, it is impractical for many floatingpoint methods to be correctly rounded. Instead, for the Math
class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floatingpoint values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semimonotonic: whenever the mathematical function is nondecreasing, so is the floatingpoint approximation, likewise, whenever the mathematical function is nonincreasing, so is the floatingpoint approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.
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 addExact
, subtractExact
, multiplyExact
, and toIntExact
throw an ArithmeticException
when the results overflow. For other arithmetic operations such as divide, absolute value, increment by one, decrement by one, and negation, overflow occurs only with a specific minimum or maximum value and should be checked against the minimum or maximum as appropriate.
 Since:
 1.0
Field Summary
Modifier and Type  Field  Description 

static double  E  The 
static double  PI  The 
Method Summary
Modifier and Type  Method  Description 

static double  abs(double a)  Returns the absolute value of a 
static float  abs(float a)  Returns the absolute value of a 
static int  abs(int a)  Returns the absolute value of an 
static long  abs(long a)  Returns the absolute value of a 
static double  acos(double a)  Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. 
static int  addExact(int x,
int y)  Returns the sum of its arguments, throwing an exception if the result overflows an 
static long  addExact(long x,
long y)  Returns the sum of its arguments, throwing an exception if the result overflows a 
static double  asin(double a)  Returns the arc sine of a value; the returned angle is in the range pi/2 through pi/2. 
static double  atan(double a)  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 ( 
static double  cbrt(double a)  Returns the cube root of a 
static double  ceil(double a)  Returns the smallest (closest to negative infinity) 
static double  copySign(double magnitude,
double sign)  Returns the first floatingpoint argument with the sign of the second floatingpoint argument. 
static float  copySign(float magnitude,
float sign)  Returns the first floatingpoint argument with the sign of the second floatingpoint argument. 
static double  cos(double a)  Returns the trigonometric cosine of an angle. 
static double  cosh(double x)  Returns the hyperbolic cosine of a 
static int  decrementExact(int a)  Returns the argument decremented by one, throwing an exception if the result overflows an 
static long  decrementExact(long a)  Returns the argument decremented by one, throwing an exception if the result overflows a 
static double  exp(double a)  Returns Euler's number e raised to the power of a 
static double  expm1(double x)  Returns e^{x} 1. 
static double  floor(double a)  Returns the largest (closest to positive infinity) 
static int  floorDiv(int x,
int y)  Returns the largest (closest to positive infinity) 
static long  floorDiv(long x,
int y)  Returns the largest (closest to positive infinity) 
static long  floorDiv(long x,
long y)  Returns the largest (closest to positive infinity) 
static int  floorMod(int x,
int y)  Returns the floor modulus of the 
static int  floorMod(long x,
int y)  Returns the floor modulus of the 
static long  floorMod(long x,
long y)  Returns the floor modulus of the 
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 
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 
static int  getExponent(double d)  Returns the unbiased exponent used in the representation of a 
static int  getExponent(float f)  Returns the unbiased exponent used in the representation of a 
static double  hypot(double x,
double y)  Returns sqrt(x^{2} +y^{2}) without intermediate overflow or underflow. 
static double  IEEEremainder(double f1,
double f2)  Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. 
static int  incrementExact(int a)  Returns the argument incremented by one, throwing an exception if the result overflows an 
static long  incrementExact(long a)  Returns the argument incremented by one, throwing an exception if the result overflows a 
static double  log(double a)  Returns the natural logarithm (base e) of a 
static double  log10(double a)  Returns the base 10 logarithm of a 
static double  log1p(double x)  Returns the natural logarithm of the sum of the argument and 1. 
static double  max(double a,
double b)  Returns the greater of two 
static float  max(float a,
float b)  Returns the greater of two 
static int  max(int a,
int b)  Returns the greater of two 
static long  max(long a,
long b)  Returns the greater of two 
static double  min(double a,
double b)  Returns the smaller of two 
static float  min(float a,
float b)  Returns the smaller of two 
static int  min(int a,
int b)  Returns the smaller of two 
static long  min(long a,
long b)  Returns the smaller of two 
static int  multiplyExact(int x,
int y)  Returns the product of the arguments, throwing an exception if the result overflows an 
static long  multiplyExact(long x,
int y)  Returns the product of the arguments, throwing an exception if the result overflows a 
static long  multiplyExact(long x,
long y)  Returns the product of the arguments, throwing an exception if the result overflows a 
static long  multiplyFull(int x,
int y)  Returns the exact mathematical product of the arguments. 
static long  multiplyHigh(long x,
long y)  Returns as a 
static int  negateExact(int a)  Returns the negation of the argument, throwing an exception if the result overflows an 
static long  negateExact(long a)  Returns the negation of the argument, throwing an exception if the result overflows a 
static double  nextAfter(double start,
double direction)  Returns the floatingpoint number adjacent to the first argument in the direction of the second argument. 
static float  nextAfter(float start,
double direction)  Returns the floatingpoint number adjacent to the first argument in the direction of the second argument. 
static double  nextDown(double d)  Returns the floatingpoint value adjacent to 
static float  nextDown(float f)  Returns the floatingpoint value adjacent to 
static double  nextUp(double d)  Returns the floatingpoint value adjacent to 
static float  nextUp(float f)  Returns the floatingpoint value adjacent to 
static double  pow(double a,
double b)  Returns the value of the first argument raised to the power of the second argument. 
static double  random()  Returns a 
static double  rint(double a)  Returns the 
static long  round(double a)  Returns the closest 
static int  round(float a)  Returns the closest 
static double  scalb(double d,
int scaleFactor)  Returns 
static float  scalb(float f,
int scaleFactor)  Returns 
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. 
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. 
static double  sin(double a)  Returns the trigonometric sine of an angle. 
static double  sinh(double x)  Returns the hyperbolic sine of a 
static double  sqrt(double a)  Returns the correctly rounded positive square root of a 
static int  subtractExact(int x,
int y)  Returns the difference of the arguments, throwing an exception if the result overflows an 
static long  subtractExact(long x,
long y)  Returns the difference of the arguments, throwing an exception if the result overflows a 
static double  tan(double a)  Returns the trigonometric tangent of an angle. 
static double  tanh(double x)  Returns the hyperbolic tangent of a 
static double  toDegrees(double angrad)  Converts an angle measured in radians to an approximately equivalent angle measured in degrees. 
static int  toIntExact(long value)  Returns the value of the 
static double  toRadians(double angdeg)  Converts an angle measured in degrees to an approximately equivalent angle measured in radians. 
static double  ulp(double d)  Returns the size of an ulp of the argument. 
static float  ulp(float f)  Returns the size of an ulp of the argument. 
Methods declared in class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Field Detail
E
public static final double E
The double
value that is closer than any other to e, the base of the natural logarithms.
 See Also:
 Constant Field Values
PI
public static final double PI
The double
value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.
 See Also:
 Constant Field Values
Method Detail
sin
public static double sin(double a)
Returns the trigonometric sine of an angle. Special cases:
 If the argument is NaN or an infinity, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 an angle, in radians.  Returns:
 the sine of the argument.
cos
public static double cos(double a)
Returns the trigonometric cosine of an angle. Special cases:
 If the argument is NaN or an infinity, then the result is NaN.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 an angle, in radians.  Returns:
 the cosine of the argument.
tan
public static double tan(double a)
Returns the trigonometric tangent of an angle. Special cases:
 If the argument is NaN or an infinity, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 an angle, in radians.  Returns:
 the tangent of the argument.
asin
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:
 If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 the value whose arc sine is to be returned.  Returns:
 the arc sine of the argument.
acos
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:
 If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 the value whose arc cosine is to be returned.  Returns:
 the arc cosine of the argument.
atan
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:
 If the argument is NaN, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 the value whose arc tangent is to be returned.  Returns:
 the arc tangent of the argument.
toRadians
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.
 Parameters:

angdeg
 an angle, in degrees  Returns:
 the measurement of the angle
angdeg
in radians.  Since:
 1.2
toDegrees
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
.
 Parameters:

angrad
 an angle, in radians  Returns:
 the measurement of the angle
angrad
in degrees.  Since:
 1.2
exp
public static double exp(double a)
Returns Euler's number e raised to the power of a double
value. Special cases:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is negative infinity, then the result is positive zero.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 the exponent to raise e to.  Returns:
 the value e^{a}, where e is the base of the natural logarithms.
log
public static double log(double a)
Returns the natural logarithm (base e) of a double
value. Special cases:
 If the argument is NaN or less than zero, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is positive zero or negative zero, then the result is negative infinity.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 a value  Returns:
 the value ln
a
, the natural logarithm ofa
.
log10
public static double log10(double a)
Returns the base 10 logarithm of a double
value. Special cases:
 If the argument is NaN or less than zero, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is positive zero or negative zero, then the result is negative infinity.
 If the argument is equal to 10^{n} for integer n, then the result is n.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 a value  Returns:
 the base 10 logarithm of
a
.  Since:
 1.5
sqrt
public static double sqrt(double a)
Returns the correctly rounded positive square root of a double
value. Special cases:
 If the argument is NaN or less than zero, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is positive zero or negative zero, then the result is the same as the argument.
double
value closest to the true mathematical square root of the argument value.  Parameters:

a
 a value.  Returns:
 the positive square root of
a
. If the argument is NaN or less than zero, the result is NaN.
cbrt
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:
 If the argument is NaN, then the result is NaN.
 If the argument is infinite, then the result is an infinity with the same sign as the argument.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result.
 Parameters:

a
 a value.  Returns:
 the cube root of
a
.  Since:
 1.5
IEEEremainder
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 n is 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 n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:
 If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN.
 If the first argument is finite and the second argument is infinite, then the result is the same as the first argument.
 Parameters:

f1
 the dividend. 
f2
 the divisor.  Returns:
 the remainder when
f1
is divided byf2
.
ceil
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:
 If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
 If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
 If the argument value is less than zero but greater than 1.0, then the result is negative zero.
Math.ceil(x)
is exactly the value of Math.floor(x)
.  Parameters:

a
 a value.  Returns:
 the smallest (closest to negative infinity) floatingpoint value that is greater than or equal to the argument and is equal to a mathematical integer.
floor
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:
 If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
 If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
 Parameters:

a
 a value.  Returns:
 the largest (closest to positive infinity) floatingpoint value that less than or equal to the argument and is equal to a mathematical integer.
rint
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, the result is the integer value that is even. Special cases:
 If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
 If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
 Parameters:

a
 adouble
value.  Returns:
 the closest floatingpoint value to
a
that is equal to a mathematical integer.
atan2
public static double atan2(double y, double x)
Returns the angle theta from the conversion of rectangular coordinates (x
, y
) to polar coordinates (r, theta). This method computes the phase theta by computing an arc tangent of y/x
in the range of pi to pi. Special cases:
 If either argument is NaN, then the result is NaN.
 If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
 If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
 If the first argument is positive zero and the second argument is negative, or the first argument is positive and finite and the second argument is negative infinity, then the result is the
double
value closest to pi.  If the first argument is negative zero and the second argument is negative, or the first argument is negative and finite and the second argument is negative infinity, then the result is the
double
value closest to pi.  If the first argument is positive and the second argument is positive zero or negative zero, or the first argument is positive infinity and the second argument is finite, then the result is the
double
value closest to pi/2.  If the first argument is negative and the second argument is positive zero or negative zero, or the first argument is negative infinity and the second argument is finite, then the result is the
double
value closest to pi/2.  If both arguments are positive infinity, then the result is the
double
value closest to pi/4.  If the first argument is positive infinity and the second argument is negative infinity, then the result is the
double
value closest to 3*pi/4.  If the first argument is negative infinity and the second argument is positive infinity, then the result is the
double
value closest to pi/4.  If both arguments are negative infinity, then the result is the
double
value closest to 3*pi/4.
The computed result must be within 2 ulps of the exact result. Results must be semimonotonic.
 Parameters:

y
 the ordinate coordinate 
x
 the abscissa coordinate  Returns:
 the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.
pow
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:
 If the second argument is positive or negative zero, then the result is 1.0.
 If the second argument is 1.0, then the result is the same as the first argument.
 If the second argument is NaN, then the result is NaN.
 If the first argument is NaN and the second argument is nonzero, then the result is NaN.
 If
 the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or
 the absolute value of the first argument is less than 1 and the second argument is negative infinity,
 If
 the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
 the absolute value of the first argument is less than 1 and the second argument is positive infinity,
 If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
 If
 the first argument is positive zero and the second argument is greater than zero, or
 the first argument is positive infinity and the second argument is less than zero,
 If
 the first argument is positive zero and the second argument is less than zero, or
 the first argument is positive infinity and the second argument is greater than zero,
 If
 the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
 the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
 If
 the first argument is negative zero and the second argument is a positive finite odd integer, or
 the first argument is negative infinity and the second argument is a negative finite odd integer,
 If
 the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
 the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
 If
 the first argument is negative zero and the second argument is a negative finite odd integer, or
 the first argument is negative infinity and the second argument is a positive finite odd integer,
 If the first argument is finite and less than zero
 if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
 if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
 if the second argument is finite and not an integer, then the result is NaN.
 If both arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as a
double
value.
(In the foregoing descriptions, a floatingpoint 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 oneargument method if and only if the result of applying the method to the value is equal to the value.)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

a
 the base. 
b
 the exponent.  Returns:
 the value
a
^{b}.
round
public static int round(float a)
Returns the closest int
to the argument, with ties rounding to positive infinity.
Special cases:
 If the argument is NaN, the result is 0.
 If the argument is negative infinity or any value less than or equal to the value of
Integer.MIN_VALUE
, the result is equal to the value ofInteger.MIN_VALUE
.  If the argument is positive infinity or any value greater than or equal to the value of
Integer.MAX_VALUE
, the result is equal to the value ofInteger.MAX_VALUE
.
 Parameters:

a
 a floatingpoint value to be rounded to an integer.  Returns:
 the value of the argument rounded to the nearest
int
value.  See Also:

Integer.MAX_VALUE
,Integer.MIN_VALUE
round
public static long round(double a)
Returns the closest long
to the argument, with ties rounding to positive infinity.
Special cases:
 If the argument is NaN, the result is 0.
 If the argument is negative infinity or any value less than or equal to the value of
Long.MIN_VALUE
, the result is equal to the value ofLong.MIN_VALUE
.  If the argument is positive infinity or any value greater than or equal to the value of
Long.MAX_VALUE
, the result is equal to the value ofLong.MAX_VALUE
.
 Parameters:

a
 a floatingpoint value to be rounded to along
.  Returns:
 the value of the argument rounded to the nearest
long
value.  See Also:

Long.MAX_VALUE
,Long.MIN_VALUE
random
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 pseudorandomnumber generator, exactly as if by the expression
new java.util.Random()This new pseudorandomnumber 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 pseudorandomnumber generator.
 API Note:
 As the largest
double
value less than1.0
isMath.nextDown(1.0)
, a valuex
in the closed range[x1,x2]
wherex1<=x2
may be defined by the statementsdouble f = Math.random()/Math.nextDown(1.0); double x = x1*(1.0  f) + x2*f;
 Returns:
 a pseudorandom
double
greater than or equal to0.0
and less than1.0
.  See Also:

nextDown(double)
,Random.nextDouble()
addExact
public static int addExact(int x, int y)
Returns the sum of its arguments, throwing an exception if the result overflows an int
.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows an int  Since:
 1.8
addExact
public static long addExact(long x, long y)
Returns the sum of its arguments, throwing an exception if the result overflows a long
.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 1.8
subtractExact
public static int subtractExact(int x, int y)
Returns the difference of the arguments, throwing an exception if the result overflows an int
.
 Parameters:

x
 the first value 
y
 the second value to subtract from the first  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows an int  Since:
 1.8
subtractExact
public static long subtractExact(long x, long y)
Returns the difference of the arguments, throwing an exception if the result overflows a long
.
 Parameters:

x
 the first value 
y
 the second value to subtract from the first  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 1.8
multiplyExact
public static int multiplyExact(int x, int y)
Returns the product of the arguments, throwing an exception if the result overflows an int
.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows an int  Since:
 1.8
multiplyExact
public static long multiplyExact(long x, int y)
Returns the product of the arguments, throwing an exception if the result overflows a long
.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 9
multiplyExact
public static long multiplyExact(long x, long y)
Returns the product of the arguments, throwing an exception if the result overflows a long
.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 1.8
incrementExact
public static int incrementExact(int a)
Returns the argument incremented by one, throwing an exception if the result overflows an int
.
 Parameters:

a
 the value to increment  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows an int  Since:
 1.8
incrementExact
public static long incrementExact(long a)
Returns the argument incremented by one, throwing an exception if the result overflows a long
.
 Parameters:

a
 the value to increment  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 1.8
decrementExact
public static int decrementExact(int a)
Returns the argument decremented by one, throwing an exception if the result overflows an int
.
 Parameters:

a
 the value to decrement  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows an int  Since:
 1.8
decrementExact
public static long decrementExact(long a)
Returns the argument decremented by one, throwing an exception if the result overflows a long
.
 Parameters:

a
 the value to decrement  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 1.8
negateExact
public static int negateExact(int a)
Returns the negation of the argument, throwing an exception if the result overflows an int
.
 Parameters:

a
 the value to negate  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows an int  Since:
 1.8
negateExact
public static long negateExact(long a)
Returns the negation of the argument, throwing an exception if the result overflows a long
.
 Parameters:

a
 the value to negate  Returns:
 the result
 Throws:

ArithmeticException
 if the result overflows a long  Since:
 1.8
toIntExact
public static int toIntExact(long value)
Returns the value of the long
argument; throwing an exception if the value overflows an int
.
 Parameters:

value
 the long value  Returns:
 the argument as an int
 Throws:

ArithmeticException
 if theargument
overflows an int  Since:
 1.8
multiplyFull
public static long multiplyFull(int x, int y)
Returns the exact mathematical product of the arguments.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Since:
 9
multiplyHigh
public static long multiplyHigh(long x, long y)
Returns as a long
the most significant 64 bits of the 128bit product of two 64bit factors.
 Parameters:

x
 the first value 
y
 the second value  Returns:
 the result
 Since:
 9
floorDiv
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 the Integer.MIN_VALUE and the divisor is 1
, then integer overflow occurs and the result is equal to Integer.MIN_VALUE
.
Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is negative.
 If the signs of the arguments are the same, the results of
floorDiv
and the/
operator are the same.
For example,floorDiv(4, 3) == 1
and(4 / 3) == 1
.  If the signs of the arguments are different, the quotient is negative and
floorDiv
returns the integer less than or equal to the quotient and the/
operator returns the integer closest to zero.
For example,floorDiv(4, 3) == 2
, whereas(4 / 3) == 1
.
 Parameters:

x
 the dividend 
y
 the divisor  Returns:
 the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient.  Throws:

ArithmeticException
 if the divisory
is zero  Since:
 1.8
 See Also:

floorMod(int, int)
,floor(double)
floorDiv
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 the Long.MIN_VALUE and the divisor is 1
, then integer overflow occurs and the result is equal to Long.MIN_VALUE
.
Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is negative.
For examples, see floorDiv(int, int)
.
 Parameters:

x
 the dividend 
y
 the divisor  Returns:
 the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient.  Throws:

ArithmeticException
 if the divisory
is zero  Since:
 9
 See Also:

floorMod(long, int)
,floor(double)
floorDiv
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 the Long.MIN_VALUE and the divisor is 1
, then integer overflow occurs and the result is equal to Long.MIN_VALUE
.
Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is negative.
For examples, see floorDiv(int, int)
.
 Parameters:

x
 the dividend 
y
 the divisor  Returns:
 the largest (closest to positive infinity)
long
value that is less than or equal to the algebraic quotient.  Throws:

ArithmeticException
 if the divisory
is zero  Since:
 1.8
 See Also:

floorMod(long, long)
,floor(double)
floorMod
public static int floorMod(int x, int y)
Returns the floor modulus of the int
arguments.
The floor modulus is x  (floorDiv(x, y) * y)
, has the same sign as the divisor y
, 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) == x
The difference in values between floorMod
and the %
operator is due to the difference between floorDiv
that returns the integer less than or equal to the quotient and the /
operator that returns the integer closest to zero.
Examples:
 If the signs of the arguments are the same, the results of
floorMod
and the%
operator are the same.

floorMod(4, 3) == 1
; and(4 % 3) == 1

 If the signs of the arguments are different, the results differ from the
%
operator.

floorMod(+4, 3) == 2
; and(+4 % 3) == +1

floorMod(4, +3) == +2
; and(4 % +3) == 1

floorMod(4, 3) == 1
; and(4 % 3) == 1

If the signs of arguments are unknown and a positive modulus is needed it can be computed as (floorMod(x, y) + abs(y)) % abs(y)
.
 Parameters:

x
 the dividend 
y
 the divisor  Returns:
 the floor modulus
x  (floorDiv(x, y) * y)
 Throws:

ArithmeticException
 if the divisory
is zero  Since:
 1.8
 See Also:
floorDiv(int, int)
floorMod
public static int floorMod(long x, int y)
Returns the floor modulus of the long
and int
arguments.
The floor modulus is x  (floorDiv(x, y) * y)
, has the same sign as the divisor y
, 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) == x
For examples, see floorMod(int, int)
.
 Parameters:

x
 the dividend 
y
 the divisor  Returns:
 the floor modulus
x  (floorDiv(x, y) * y)
 Throws:

ArithmeticException
 if the divisory
is zero  Since:
 9
 See Also:
floorDiv(long, int)
floorMod
public static long floorMod(long x, long y)
Returns the floor modulus of the long
arguments.
The floor modulus is x  (floorDiv(x, y) * y)
, has the same sign as the divisor y
, 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) == x
For examples, see floorMod(int, int)
.
 Parameters:

x
 the dividend 
y
 the divisor  Returns:
 the floor modulus
x  (floorDiv(x, y) * y)
 Throws:

ArithmeticException
 if the divisory
is zero  Since:
 1.8
 See Also:
floorDiv(long, long)
abs
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.
 Parameters:

a
 the argument whose absolute value is to be determined  Returns:
 the absolute value of the argument.
abs
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.
 Parameters:

a
 the argument whose absolute value is to be determined  Returns:
 the absolute value of the argument.
abs
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:
 If the argument is positive zero or negative zero, the result is positive zero.
 If the argument is infinite, the result is positive infinity.
 If the argument is NaN, the result is NaN.
 API Note:
 As implied by the above, one valid implementation of this method is given by the expression below which computes a
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))
 Parameters:

a
 the argument whose absolute value is to be determined  Returns:
 the absolute value of the argument.
abs
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:
 If the argument is positive zero or negative zero, the result is positive zero.
 If the argument is infinite, the result is positive infinity.
 If the argument is NaN, the result is NaN.
 API Note:
 As implied by the above, one valid implementation of this method is given by the expression below which computes a
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)
 Parameters:

a
 the argument whose absolute value is to be determined  Returns:
 the absolute value of the argument.
max
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the larger of
a
andb
.
max
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the larger of
a
andb
.
max
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the larger of
a
andb
.
max
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the larger of
a
andb
.
min
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the smaller of
a
andb
.
min
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the smaller of
a
andb
.
min
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the smaller of
a
andb
.
min
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.
 Parameters:

a
 an argument. 
b
 another argument.  Returns:
 the smaller of
a
andb
.
fma
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 floatingpoint expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.
Special cases:
 If any argument is NaN, the result is NaN.
 If one of the first two arguments is infinite and the other is zero, the result is NaN.
 If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.
Note that fma(a, 1.0, c)
returns the same result as (a + c
). However, fma(a, b, +0.0)
does not always return the same result as (a * b
) since fma(0.0, +0.0, +0.0)
is +0.0
while (0.0 * +0.0
) is 0.0
; fma(a, b, 0.0)
is equivalent to (a * b
) however.
 API Note:
 This method corresponds to the fusedMultiplyAdd operation defined in IEEE 7542008.
 Parameters:

a
 a value 
b
 a value 
c
 a value  Returns:
 (a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest
double
value  Since:
 9
fma
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 floatingpoint expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.
Special cases:
 If any argument is NaN, the result is NaN.
 If one of the first two arguments is infinite and the other is zero, the result is NaN.
 If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.
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.
 API Note:
 This method corresponds to the fusedMultiplyAdd operation defined in IEEE 7542008.
 Parameters:

a
 a value 
b
 a value 
c
 a value  Returns:
 (a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest
float
value  Since:
 9
ulp
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 floatingpoint value and the
double
value next larger in magnitude. Note that for nonNaN x, ulp(x) == ulp(x)
.
Special Cases:
 If the argument is NaN, then the result is NaN.
 If the argument is positive or negative infinity, then the result is positive infinity.
 If the argument is positive or negative zero, then the result is
Double.MIN_VALUE
.  If the argument is ±
Double.MAX_VALUE
, then the result is equal to 2^{971}.
 Parameters:

d
 the floatingpoint value whose ulp is to be returned  Returns:
 the size of an ulp of the argument
 Since:
 1.5
ulp
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 floatingpoint value and the
float
value next larger in magnitude. Note that for nonNaN x, ulp(x) == ulp(x)
.
Special Cases:
 If the argument is NaN, then the result is NaN.
 If the argument is positive or negative infinity, then the result is positive infinity.
 If the argument is positive or negative zero, then the result is
Float.MIN_VALUE
.  If the argument is ±
Float.MAX_VALUE
, then the result is equal to 2^{104}.
 Parameters:

f
 the floatingpoint value whose ulp is to be returned  Returns:
 the size of an ulp of the argument
 Since:
 1.5
signum
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:
 If the argument is NaN, then the result is NaN.
 If the argument is positive zero or negative zero, then the result is the same as the argument.
 Parameters:

d
 the floatingpoint value whose signum is to be returned  Returns:
 the signum function of the argument
 Since:
 1.5
signum
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:
 If the argument is NaN, then the result is NaN.
 If the argument is positive zero or negative zero, then the result is the same as the argument.
 Parameters:

f
 the floatingpoint value whose signum is to be returned  Returns:
 the signum function of the argument
 Since:
 1.5
sinh
public static double sinh(double x)
Returns the hyperbolic sine of a double
value. The hyperbolic sine of x is defined to be (e^{x}  e^{x})/2 where e is Euler's number.
Special cases:
 If the argument is NaN, then the result is NaN.
 If the argument is infinite, then the result is an infinity with the same sign as the argument.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 2.5 ulps of the exact result.
 Parameters:

x
 The number whose hyperbolic sine is to be returned.  Returns:
 The hyperbolic sine of
x
.  Since:
 1.5
cosh
public static double cosh(double x)
Returns the hyperbolic cosine of a double
value. The hyperbolic cosine of x is defined to be (e^{x} + e^{x})/2 where e is Euler's number.
Special cases:
 If the argument is NaN, then the result is NaN.
 If the argument is infinite, then the result is positive infinity.
 If the argument is zero, then the result is
1.0
.
The computed result must be within 2.5 ulps of the exact result.
 Parameters:

x
 The number whose hyperbolic cosine is to be returned.  Returns:
 The hyperbolic cosine of
x
.  Since:
 1.5
tanh
public static double tanh(double x)
Returns the hyperbolic tangent of a double
value. The hyperbolic tangent of x is defined to be (e^{x}  e^{x})/(e^{x} + 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:
 If the argument is NaN, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
 If the argument is positive infinity, then the result is
+1.0
.  If the argument is negative infinity, then the result is
1.0
.
The computed result must be within 2.5 ulps of the exact result. The result of tanh
for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0
should be returned.
 Parameters:

x
 The number whose hyperbolic tangent is to be returned.  Returns:
 The hyperbolic tangent of
x
.  Since:
 1.5
hypot
public static double hypot(double x, double y)
Returns sqrt(x^{2} +y^{2}) without intermediate overflow or underflow.
Special cases:
 If either argument is infinite, then the result is positive infinity.
 If either argument is NaN and neither argument is infinite, then the result is NaN.
The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semimonotonic in the other parameter.
 Parameters:

x
 a value 
y
 a value  Returns:
 sqrt(x^{2} +y^{2}) without intermediate overflow or underflow
 Since:
 1.5
expm1
public static double expm1(double x)
Returns e^{x} 1. Note that for values of x near 0, the exact sum of expm1(x)
+ 1 is much closer to the true result of e^{x} than exp(x)
.
Special cases:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is negative infinity, then the result is 1.0.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic. The result of expm1
for any finite input must be greater than or equal to 1.0
. Note that once the exact result of e^{x}  1 is within 1/2 ulp of the limit value 1, 1.0
should be returned.
 Parameters:

x
 the exponent to raise e to in the computation of e^{x} 1.  Returns:
 the value e^{x}  1.
 Since:
 1.5
log1p
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 floatingpoint evaluation of log(1.0+x)
.
Special cases:
 If the argument is NaN or less than 1, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is negative one, then the result is negative infinity.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
 Parameters:

x
 a value  Returns:
 the value ln(
x
+ 1), the natural log ofx
+ 1  Since:
 1.5
copySign
public static double copySign(double magnitude, double sign)
Returns the first floatingpoint argument with the sign of the second floatingpoint argument. Note that unlike the StrictMath.copySign
method, this method does not require NaN sign
arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
 Parameters:

magnitude
 the parameter providing the magnitude of the result 
sign
 the parameter providing the sign of the result  Returns:
 a value with the magnitude of
magnitude
and the sign ofsign
.  Since:
 1.6
copySign
public static float copySign(float magnitude, float sign)
Returns the first floatingpoint argument with the sign of the second floatingpoint argument. Note that unlike the StrictMath.copySign
method, this method does not require NaN sign
arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
 Parameters:

magnitude
 the parameter providing the magnitude of the result 
sign
 the parameter providing the sign of the result  Returns:
 a value with the magnitude of
magnitude
and the sign ofsign
.  Since:
 1.6
getExponent
public static int getExponent(float f)
Returns the unbiased exponent used in the representation of a float
. Special cases:
 If the argument is NaN or infinite, then the result is
Float.MAX_EXPONENT
+ 1.  If the argument is zero or subnormal, then the result is
Float.MIN_EXPONENT
1.
 Parameters:

f
 afloat
value  Returns:
 the unbiased exponent of the argument
 Since:
 1.6
getExponent
public static int getExponent(double d)
Returns the unbiased exponent used in the representation of a double
. Special cases:
 If the argument is NaN or infinite, then the result is
Double.MAX_EXPONENT
+ 1.  If the argument is zero or subnormal, then the result is
Double.MIN_EXPONENT
1.
 Parameters:

d
 adouble
value  Returns:
 the unbiased exponent of the argument
 Since:
 1.6
nextAfter
public static double nextAfter(double start, double direction)
Returns the floatingpoint 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:
 If either argument is a NaN, then NaN is returned.
 If both arguments are signed zeros,
direction
is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).  If
start
is ±Double.MIN_VALUE
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned.  If
start
is infinite anddirection
has a value such that the result should have a smaller magnitude,Double.MAX_VALUE
with the same sign asstart
is returned.  If
start
is equal to ±Double.MAX_VALUE
anddirection
has a value such that the result should have a larger magnitude, an infinity with same sign asstart
is returned.
 Parameters:

start
 starting floatingpoint value 
direction
 value indicating which ofstart
's neighbors orstart
should be returned  Returns:
 The floatingpoint number adjacent to
start
in the direction ofdirection
.  Since:
 1.6
nextAfter
public static float nextAfter(float start, double direction)
Returns the floatingpoint 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:
 If either argument is a NaN, then NaN is returned.
 If both arguments are signed zeros, a value equivalent to
direction
is returned.  If
start
is ±Float.MIN_VALUE
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned.  If
start
is infinite anddirection
has a value such that the result should have a smaller magnitude,Float.MAX_VALUE
with the same sign asstart
is returned.  If
start
is equal to ±Float.MAX_VALUE
anddirection
has a value such that the result should have a larger magnitude, an infinity with same sign asstart
is returned.
 Parameters:

start
 starting floatingpoint value 
direction
 value indicating which ofstart
's neighbors orstart
should be returned  Returns:
 The floatingpoint number adjacent to
start
in the direction ofdirection
.  Since:
 1.6
nextUp
public static double nextUp(double d)
Returns the floatingpoint 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:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, the result is positive infinity.
 If the argument is zero, the result is
Double.MIN_VALUE
 Parameters:

d
 starting floatingpoint value  Returns:
 The adjacent floatingpoint value closer to positive infinity.
 Since:
 1.6
nextUp
public static float nextUp(float f)
Returns the floatingpoint 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:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, the result is positive infinity.
 If the argument is zero, the result is
Float.MIN_VALUE
 Parameters:

f
 starting floatingpoint value  Returns:
 The adjacent floatingpoint value closer to positive infinity.
 Since:
 1.6
nextDown
public static double nextDown(double d)
Returns the floatingpoint 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:
 If the argument is NaN, the result is NaN.
 If the argument is negative infinity, the result is negative infinity.
 If the argument is zero, the result is
Double.MIN_VALUE
 Parameters:

d
 starting floatingpoint value  Returns:
 The adjacent floatingpoint value closer to negative infinity.
 Since:
 1.8
nextDown
public static float nextDown(float f)
Returns the floatingpoint 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:
 If the argument is NaN, the result is NaN.
 If the argument is negative infinity, the result is negative infinity.
 If the argument is zero, the result is
Float.MIN_VALUE
 Parameters:

f
 starting floatingpoint value  Returns:
 The adjacent floatingpoint value closer to negative infinity.
 Since:
 1.8
scalb
public static double scalb(double d, int scaleFactor)
Returns d
× 2^{scaleFactor} rounded as if performed by a single correctly rounded floatingpoint multiply to a member of the double value set. See the Java Language Specification for a discussion of floatingpoint value sets. 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 nonNaN, the result has the same sign as d
.
Special cases:
 If the first argument is NaN, NaN is returned.
 If the first argument is infinite, then an infinity of the same sign is returned.
 If the first argument is zero, then a zero of the same sign is returned.
 Parameters:

d
 number to be scaled by a power of two. 
scaleFactor
 power of 2 used to scaled
 Returns:

d
× 2^{scaleFactor}  Since:
 1.6
scalb
public static float scalb(float f, int scaleFactor)
Returns f
× 2^{scaleFactor} rounded as if performed by a single correctly rounded floatingpoint multiply to a member of the float value set. See the Java Language Specification for a discussion of floatingpoint value sets. 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 nonNaN, the result has the same sign as f
.
Special cases:
 If the first argument is NaN, NaN is returned.
 If the first argument is infinite, then an infinity of the same sign is returned.
 If the first argument is zero, then a zero of the same sign is returned.
 Parameters:

f
 number to be scaled by a power of two. 
scaleFactor
 power of 2 used to scalef
 Returns:

f
× 2^{scaleFactor}  Since:
 1.6