public final class Math extends Object
Math
contains methods for performing basic
numeric operations such as the elementary exponential, logarithm,
square root, and trigonometric functions.
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.
Modifier and Type  Field and Description 

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. 
Modifier and Type  Method and Description 

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 a value; the returned angle is in the
range 0.0 through pi.

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 (
x , y ) to polar
coordinates (r, theta). 
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. 
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 
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. 
static int 
getExponent(double d)
Returns the unbiased exponent used in the representation of a
double . 
static int 
getExponent(float f)
Returns the unbiased exponent used in the representation of a
float . 
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 
random()
Returns a
double value with a positive sign, greater
than or equal to 0.0 and less than 1.0 . 
static long 
round(double a)
Returns the closest
long to the argument, with ties
rounding up. 
static int 
round(float a)
Returns the closest
int to the argument, with ties
rounding up. 
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 
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 
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.

public static final double E
double
value that is closer than any other to
e, the base of the natural logarithms.public static final double PI
double
value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter.public static double abs(double a)
double
value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Special cases:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
a
 the argument whose absolute value is to be determinedpublic static float abs(float a)
float
value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Special cases:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
a
 the argument whose absolute value is to be determinedpublic static int abs(int a)
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.
a
 the argument whose absolute value is to be determinedpublic static long abs(long 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.
a
 the argument whose absolute value is to be determinedpublic static double acos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the value whose arc cosine is to be returned.public static double asin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the value whose arc sine is to be returned.public static double atan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the value whose arc tangent is to be returned.public static double atan2(double y, double x)
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:
double
value closest to pi.
double
value closest to pi.
double
value closest to pi/2.
double
value closest to pi/2.
double
value closest to pi/4.
double
value closest to 3*pi/4.
double
value
closest to pi/4.
double
value closest to 3*pi/4.The computed result must be within 2 ulps of the exact result. Results must be semimonotonic.
y
 the ordinate coordinatex
 the abscissa coordinatepublic static double ceil(double a)
double
value that is greater than or equal to the
argument and is equal to a mathematical integer. Special cases:
Math.ceil(x)
is exactly the
value of Math.floor(x)
.a
 a value.public static double copySign(double magnitude, double sign)
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.magnitude
 the parameter providing the magnitude of the resultsign
 the parameter providing the sign of the resultmagnitude
and the sign of sign
.public static float copySign(float magnitude, float sign)
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.magnitude
 the parameter providing the magnitude of the resultsign
 the parameter providing the sign of the resultmagnitude
and the sign of sign
.public static double cos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 an angle, in radians.public static double floor(double a)
double
value that is less than or equal to the
argument and is equal to a mathematical integer. Special cases:
a
 a value.public static int getExponent(double d)
double
. Special cases:
Double.MAX_EXPONENT
+ 1.
Double.MIN_EXPONENT
1.
d
 a double
valuepublic static int getExponent(float f)
float
. Special cases:
Float.MAX_EXPONENT
+ 1.
Float.MIN_EXPONENT
1.
f
 a float
valuepublic static double max(double a, double b)
double
values. That
is, the result is the argument closer to positive infinity. If
the arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other negative zero, the
result is positive zero.a
 an argument.b
 another argument.a
and b
.public static float max(float a, float b)
float
values. That is,
the result is the argument closer to positive infinity. If the
arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other negative zero, the
result is positive zero.a
 an argument.b
 another argument.a
and b
.public static int max(int a, int b)
int
values. That is, the
result is the argument closer to the value of
Integer.MAX_VALUE
. If the arguments have the same value,
the result is that same value.a
 an argument.b
 another argument.a
and b
.public static long max(long a, long b)
long
values. That is, the
result is the argument closer to the value of
Long.MAX_VALUE
. If the arguments have the same value,
the result is that same value.a
 an argument.b
 another argument.a
and b
.public static double min(double a, double b)
double
values. That
is, the result is the value closer to negative infinity. If the
arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other is negative zero, the
result is negative zero.a
 an argument.b
 another argument.a
and b
.public static float min(float a, float b)
float
values. That is,
the result is the value closer to negative infinity. If the
arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If
one argument is positive zero and the other is negative zero,
the result is negative zero.a
 an argument.b
 another argument.a
and b
.public static int min(int a, int b)
int
values. That is,
the result the argument closer to the value of
Integer.MIN_VALUE
. If the arguments have the same
value, the result is that same value.a
 an argument.b
 another argument.a
and b
.public static long min(long a, long b)
long
values. That is,
the result is the argument closer to the value of
Long.MIN_VALUE
. If the arguments have the same
value, the result is that same value.a
 an argument.b
 another argument.a
and b
.public static double random()
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.
double
greater than or equal
to 0.0
and less than 1.0
.Random.nextDouble()
public static long round(double a)
long
to the argument, with ties
rounding up.
Special cases:
Long.MIN_VALUE
, the result is
equal to the value of Long.MIN_VALUE
.
Long.MAX_VALUE
, the result is
equal to the value of Long.MAX_VALUE
.a
 a floatingpoint value to be rounded to a
long
.long
value.Long.MAX_VALUE
,
Long.MIN_VALUE
public static int round(float a)
int
to the argument, with ties
rounding up.
Special cases:
Integer.MIN_VALUE
, the result is
equal to the value of Integer.MIN_VALUE
.
Integer.MAX_VALUE
, the result is
equal to the value of Integer.MAX_VALUE
.a
 a floatingpoint value to be rounded to an integer.int
value.Integer.MAX_VALUE
,
Integer.MIN_VALUE
public static double signum(double d)
Special Cases:
d
 the floatingpoint value whose signum is to be returnedpublic static float signum(float f)
Special Cases:
f
 the floatingpoint value whose signum is to be returnedpublic static double sin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 an angle, in radians.public static double sqrt(double a)
double
value.
Special cases:
double
value closest to
the true mathematical square root of the argument value.a
 a value.a
.
If the argument is NaN or less than zero, the result is NaN.public static double tan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 an angle, in radians.public static double toDegrees(double angrad)
cos(toRadians(90.0))
to exactly
equal 0.0
.angrad
 an angle, in radiansangrad
in degrees.public static double toRadians(double angdeg)
angdeg
 an angle, in degreesangdeg
in radians.Copyright (c) 2014, Oracle and/or its affiliates. All Rights Reserved. Use of this specification is subject to license terms.