java.lang
Class Math
java.lang.Object java.lang.Math
 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. 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 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  ceil(double a) 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) Returns the trigonometric cosine of an angle. 
static double  exp(double a) Returns Euler's number e raised to the power of a double value. 
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  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  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  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. 
Field Detail 
E
public static final double E
 The
double
value that is closer than any other to e, the base of the natural alogarithms.
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.
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.

 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.

 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.

 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.

 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.

 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.

 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.
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 equal0.0
. 
 Parameters:
angrad
 an angle, in radians Returns:
 the measurement of the angle
angrad
in degrees.
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.

 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.

 Parameters:
a
 a number greater than0.0
. Returns:
 the value ln
a
, the natural logarithm ofa
.
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.
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 quotientf1/f2
, and if two mathematical integers are equally close tof1/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 not 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.
Math.ceil(x)
is exactly the value ofMath.floor(x)
. 
 Parameters:
a
 a value. Returns:
 the smallest (closest to negative infinity) floatingpoint value that is not 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 largest (closest to positive infinity) floatingpoint value that is not 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 twodouble
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)
 Converts rectangular coordinates (
x
,y
) to polar (r, theta). This method computes the phase theta by computing an arc tangent ofy/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.

 Parameters:
y
 the ordinate coordinatex
 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.
ceil
or, equivalently, a fixed point of the methodfloor
. 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. 
 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 typeint
. 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 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.
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 typelong
. 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 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.
random
public static double random()
 Returns a
double
value with a positive sign, greater than or equal to0.0
and less than1.0
. 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. 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.new java.util.Random

 Returns:
 a pseudorandom
double
greater than or equal to0.0
and less than1.0
.
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 ofInteger.MIN_VALUE
, the most negative representableint
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 ofLong.MIN_VALUE
, the most negative representablelong
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.
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.
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 ofInteger.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 ofLong.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 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 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 ofInteger.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 ofLong.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 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 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
.
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