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java.lang.Object  +java.lang.Math
Untamed: 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 difference between the two floatingpoint values
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 the exact result should be returned; otherwise, either of
the two floatingpoint numbers closest to the exact result may be
returned. Besides accuracy at individual arguments, maintaining
proper relations between the method at different arguments is also
important. Therefore, 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.
Field Summary  
static double 
E
Enabled: The double value that is closer than any other to
e, the base of the natural logarithms. 
private static long 
negativeZeroDoubleBits

private static long 
negativeZeroFloatBits

static double 
PI
Enabled: The double value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter. 
private static Random 
randomNumberGenerator

Constructor Summary  
private 
Math()
Don't let anyone instantiate this class. 
Method Summary  
static double 
abs(double a)
Enabled: Returns the absolute value of a double value. 
static float 
abs(float a)
Enabled: Returns the absolute value of a float value. 
static int 
abs(int a)
Enabled: Returns the absolute value of an int value. 
static long 
abs(long a)
Enabled: Returns the absolute value of a long value. 
static double 
acos(double a)
Enabled: Returns the arc cosine of an angle, in the range of 0.0 through pi. 
static double 
asin(double a)
Enabled: Returns the arc sine of an angle, in the range of pi/2 through pi/2. 
static double 
atan(double a)
Enabled: Returns the arc tangent of an angle, in the range of pi/2 through pi/2. 
static double 
atan2(double y,
double x)
Enabled: Converts rectangular coordinates ( x , y )
to polar (r, theta). 
static double 
ceil(double a)
Enabled: Returns the smallest (closest to negative infinity) double value that is not less than the argument and is
equal to a mathematical integer. 
static double 
cos(double a)
Enabled: Returns the trigonometric cosine of an angle. 
static double 
exp(double a)
Enabled: Returns Euler's number e raised to the power of a double value. 
static double 
floor(double a)
Enabled: 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 
IEEEremainder(double f1,
double f2)
Enabled: Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. 
private static void 
initRNG()

static double 
log(double a)
Enabled: Returns the natural logarithm (base e) of a double
value. 
static double 
max(double a,
double b)
Enabled: Returns the greater of two double values. 
static float 
max(float a,
float b)
Enabled: Returns the greater of two float values. 
static int 
max(int a,
int b)
Enabled: Returns the greater of two int values. 
static long 
max(long a,
long b)
Enabled: Returns the greater of two long values. 
static double 
min(double a,
double b)
Enabled: Returns the smaller of two double values. 
static float 
min(float a,
float b)
Enabled: Returns the smaller of two float values. 
static int 
min(int a,
int b)
Enabled: Returns the smaller of two int values. 
static long 
min(long a,
long b)
Enabled: Returns the smaller of two long values. 
static double 
pow(double a,
double b)
Enabled: Returns of value of the first argument raised to the power of the second argument. 
static double 
random()
Enabled: 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)
Enabled: Returns the double value that is closest in value
to the argument and is equal to a mathematical integer. 
static long 
round(double a)
Enabled: Returns the closest long to the argument. 
static int 
round(float a)
Enabled: Returns the closest int to the argument. 
static double 
sin(double a)
Enabled: Returns the trigonometric sine of an angle. 
static double 
sqrt(double a)
Enabled: Returns the correctly rounded positive square root of a double value. 
static double 
tan(double a)
Enabled: Returns the trigonometric tangent of an angle. 
static double 
toDegrees(double angrad)
Enabled: Converts an angle measured in radians to an approximately equivalent angle measured in degrees. 
static double 
toRadians(double angdeg)
Enabled: Converts an angle measured in degrees to an approximately equivalent angle measured in radians. 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Field Detail 
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.
private static Random randomNumberGenerator
private static long negativeZeroFloatBits
private static long negativeZeroDoubleBits
Constructor Detail 
private Math()
Method Detail 
public static double sin(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 an angle, in radians.
public static double cos(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 an angle, in radians.
public static double tan(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 an angle, in radians.
public static double asin(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 the value whose arc sine is to be returned.
public static double acos(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 the value whose arc cosine is to be returned.
public static double atan(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 the value whose arc tangent is to be returned.
public static double toRadians(double angdeg)
angdeg
 an angle, in degrees
angdeg
in radians.public static double toDegrees(double angrad)
cos(toRadians(90.0))
to exactly
equal 0.0
.
angrad
 an angle, in radians
angrad
in degrees.public static double exp(double a)
double
value. Special cases:
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 the exponent to raise e to.
public static double log(double a)
double
value. Special cases:
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 a number greater than 0.0
.
a
, the natural logarithm of
a
.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 IEEEremainder(double f1, double f2)
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:
f1
 the dividend.f2
 the divisor.
f1
is divided by
f2
.public static double ceil(double a)
double
value that is not less than 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 floor(double a)
double
value that is not greater than the argument and
is equal to a mathematical integer. Special cases:
a
 a value.
public static double rint(double a)
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:
a
 a double
value.
a
that is
equal to a mathematical integer.public static double atan2(double y, double x)
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:
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.A result must be within 2 ulps of the correctly rounded result. Results must be semimonotonic.
y
 the ordinate coordinatex
 the abscissa coordinate
public static double pow(double a, double b)
(In the foregoing descriptions, a floatingpoint value is
considered to be an integer if and only if it is 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.)
A result must be within 1 ulp of the correctly rounded result. Results must be semimonotonic.
a
 the base.b
 the exponent.
a^{b}
.public static int round(float a)
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:
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.java.lang.Integer#MAX_VALUE
,
java.lang.Integer#MIN_VALUE
public static long round(double a)
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:
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.java.lang.Long#MAX_VALUE
,
java.lang.Long#MIN_VALUE
private static void initRNG()
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
This new pseudorandomnumber generator is used thereafter for all calls to this method and is used nowhere else.new java.util.Random
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
.java.util.Random#nextDouble()
public 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 determined
java.lang.Integer#MIN_VALUE
public 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 determined
java.lang.Long#MIN_VALUE
public 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 determined
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 determined
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
.java.lang.Long#MAX_VALUE
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
.java.lang.Long#MAX_VALUE
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 the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other negative zero, the
result is positive zero.
a
 an argument.b
 another argument.
a
and b
.public static double max(double a, double b)
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.
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
.java.lang.Long#MIN_VALUE
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
.java.lang.Long#MIN_VALUE
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 the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If
one argument is positive zero and the other is negative zero,
the result is negative zero.
a
 an argument.b
 another argument.
a
and b.
public static double min(double a, double b)
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.
a
 an argument.b
 another argument.
a
and b
.


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