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
platform-specific native libraries or microprocessor instructions,
where available, to provide higher-performance implementations of
Math
methods. Such higher-performance
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 floating-point Math
methods is
measured in terms of ulps, units in the last place. For a
given floating-point format, an ulp of a
specific real number value is the distance between the two
floating-point 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 worst-case
error at any argument. If a method always has an error less than
0.5 ulps, the method always returns the floating-point number
nearest the exact result; such a method is correctly
rounded. A correctly rounded method is generally the best a
floating-point approximation can be; however, it is impractical for
many floating-point 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 floating-point 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
semi-monotonic: whenever the mathematical function is
non-decreasing, so is the floating-point approximation, likewise,
whenever the mathematical function is non-increasing, so is the
floating-point 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 floating-point argument with the sign of the
second floating-point argument.
|
static float |
copySign(float magnitude,
float sign)
Returns the first floating-point argument with the sign of the
second floating-point 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 semi-monotonic.
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 semi-monotonic.
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 semi-monotonic.
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 semi-monotonic.
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 semi-monotonic.
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 pseudorandom-number generator, exactly as if by the expression
new java.util.Random()
This new pseudorandom-number generator is used thereafter for
all calls to this method and is used nowhere else.
This method is properly synchronized to allow correct use by more than one thread. However, if many threads need to generate pseudorandom numbers at a great rate, it may reduce contention for each thread to have its own pseudorandom-number generator.
double
greater than or equal
to 0.0
and less than 1.0
.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 floating-point 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 floating-point 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 floating-point value whose signum is to be returnedpublic static float signum(float f)
Special Cases:
f
- the floating-point 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 semi-monotonic.
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 semi-monotonic.
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.