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java.lang
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
difference
between the two floatingpoint values
bracketing
closest to
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,
number
the exact result should be
returned as the computed result;
returned;
otherwise, either of the two floatingpoint
values which bracket
numbers closest to
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.

Since:

JDK1.0
Field Summary

static double 
E
The double value that is closer than any other to
e
, the base of the natural logarithms. 
static double 
PI
The double value that is closer than any other to
pi
, the ratio of the circumference of a circle to its diameter. 
Method Summary

static double 
abs
(double a)
Returns the absolute value of a double value. 
static float 
abs
(float a)
Returns the absolute value of a float value. 
static int 
abs
(int a)
Returns the absolute value of an int value. 
static long 
abs
(long a)
Returns the absolute value of a long value. 
static double 
acos
(double a)
Returns the arc cosine of an angle, in the range of 0.0 through
pi
. 
static double 
asin
(double a)
Returns the arc sine of an angle, in the range of 
pi
/2 through
pi
/2. 
static double 
atan
(double a)
Returns the arc tangent of an angle, in the range of 
pi
/2 through
pi
/2. 
static double 
atan2
(double y, double x)
Converts rectangular coordinates (x, y) to polar (r,
theta
). 
static double 
cbrt
ceil
(double a)
Returns the
cube root of
smallest (closest to negative infinity) double value that is not less than the argument and is equal to
a
double value.
mathematical integer.

static double

ceil
(double a)
Returns the largest (closest to positive infinity) double value that is not greater than the argument and is equal to a mathematical integer.

static double 
cos
(double a)
Returns the trigonometric cosine of an angle. 
static double

cosh
(double x)
Returns the hyperbolic cosine of a double value.

static double 
exp
(double a)
Returns Euler's number
e
raised to the power of a double value. 
static double

expm1
(double x)
Returns
e
^{
x
}
1.

static double 
floor
(double a)
Returns the largest (closest to positive infinity) double value that is not greater than the argument and is equal to a mathematical integer. 
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 double 
log
(double a)
Returns the natural logarithm (base
e
) of a double value. 
static double

log10
(double a)
Returns the base 10 logarithm of a double value.

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 double values. 
static float 
max
(float a, float b)
Returns the greater of two float values. 
static int 
max
(int a, int b)
Returns the greater of two int values. 
static long 
max
(long a, long b)
Returns the greater of two long values. 
static double 
min
(double a, double b)
Returns the smaller of two double values. 
static float 
min
(float a, float b)
Returns the smaller of two float values. 
static int 
min
(int a, int b)
Returns the smaller of two int values. 
static long 
min
(long a, long b)
Returns the smaller of two long values. 
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 double value with a positive sign, greater than or equal to 0.0 and less than 1.0. 
static double 
rint
(double a)
Returns the double value that is closest in value to the argument and is equal to a mathematical integer. 
static long 
round
(double a)
Returns the closest long to the argument. 
static int 
round
(float a)
Returns the closest int to the argument. 
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 double value.

static double 
sqrt
(double a)
Returns the correctly rounded positive square root of a double value. 
static double 
tan
(double a)
Returns the trigonometric tangent of an angle. 
static double

tanh
(double x)
Returns the hyperbolic tangent of a double value.

static double 
toDegrees
(double angrad)
Converts an angle measured in radians to an approximately equivalent angle measured in degrees. 
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 inherited from class java.lang.
Object

clone
,
equals
,
finalize
,
getClass
,
hashCode
,
notify
,
notifyAll
,
toString
,
wait
,
wait
,
wait

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
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
A
result must be within 1 ulp of the
exact
correctly rounded
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
A
result must be within 1 ulp of the
exact
correctly rounded
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
A
result must be within 1 ulp of the
exact
correctly rounded
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 an angle, in the range of 
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
A
result must be within 1 ulp of the
exact
correctly rounded
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 an angle, in the range of 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
A
result must be within 1 ulp of the
exact
correctly rounded
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 an angle, in the range of 
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
A
result must be within 1 ulp of the
exact
correctly rounded
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
A
result must be within 1 ulp of the
exact
correctly rounded
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
A
result must be within 1 ulp of the
exact
correctly rounded
result. Results must be semimonotonic.


Parameters:

a  a
value
number greater than 0.0.

Returns:

the value ln a, the natural logarithm of a.
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.
Otherwise, the result is the 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 by f2.
ceil
public static double ceil(double a)

Returns the
largest
smallest
(closest to
positive
negative
infinity) double value that is not
greater
less
than 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.
Note that the value of Math.ceil(x) is exactly the value of Math.floor(x).


Parameters:

a  a value.

Returns:

the
largest
smallest
(closest to
positive
negative
infinity) floatingpoint value that is not
greater
less
than 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 not greater than 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
smallest
largest
(closest to
negative
positive
infinity) floatingpoint value that is not
less
greater
than 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  a double value.

Returns:

the closest floatingpoint value to a that is equal to a mathematical integer.
atan2
public static double atan2(double y,
double x)

Converts rectangular coordinates (x, y) to polar (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
A
result must be within 2 ulps of the
exact
correctly rounded
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,
then the result is positive 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,
then the result is positive zero. 
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,
then the result is positive 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,
then the result is positive infinity. 
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,
then the result is positive zero. 
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,
then the result is negative zero. 
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,
then the result is positive infinity. 
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,
then the result is negative infinity. 
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
A
result must be within 1 ulp of the
exact
correctly rounded
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. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to type int. In other words, the result is equal to the value of the expression:
(int)Math.floor(a + 0.5f)
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 of Integer.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 of Integer.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. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to type long. In other words, the result is equal to the value of the expression:
(long)Math.floor(a + 0.5d)
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 of Long.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 of Long.MAX_VALUE.


Parameters:

a  a floatingpoint value to be rounded to a long.

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.


Returns:

a pseudorandom double greater than or equal to 0.0 and less than 1.0.

See Also:

Random.nextDouble()
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.

See Also:

Integer.MIN_VALUE
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.

See Also:

Long.MIN_VALUE
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.
In other words, the result is the same as the value of the expression:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(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.
In other words, the result is the same as the value of the expression:
Double.longBitsToDouble((Double.doubleToLongBits(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 and b.

See Also:

Long.MAX_VALUE
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 and b.

See Also:

Long.MAX_VALUE
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 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 and b.
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 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 and b.
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 and b.

See Also:

Long.MIN_VALUE
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 and b.

See Also:

Long.MIN_VALUE
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 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 and b.
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 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 and b.
ulp
public static double ulp (double d)

Returns the size of an ulp of the argument. An ulp 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 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.
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 evaulation 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 of x + 1