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java.lang
Class Math


java.lang.Object
  extended by 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 bit-for-bit same results. This relaxation permits better-performing 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 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 difference between the two floating-point 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 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, number the exact result should be returned as the computed result; returned; otherwise, either of the two floating-point 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 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.

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
 

Field Detail

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
Method Detail

sin


public static double sin(double a)
Returns the trigonometric sine of an angle. Special cases:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed A result must be within 1 ulp of the exact correctly rounded result. Results must be semi-monotonic.

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:

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

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: 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:

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:

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: 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) floating-point 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:

Parameters:
a - a value.
Returns:
the smallest largest (closest to negative positive infinity) floating-point 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:

Parameters:
a - a double value.
Returns:
the closest floating-point 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:

The computed A result must be within 2 ulps of the exact correctly rounded result. Results must be semi-monotonic.

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:

(In the foregoing descriptions, a floating-point 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 one-argument 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 semi-monotonic.

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:

Parameters:
a - a floating-point 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:

Parameters:
a - a floating-point 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 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.

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: 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: 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 floating-point value and the double value next larger in magnitude. Note that for non-NaN x , ulp(- x ) == ulp( x ).

Special Cases:

Parameters:
d - the floating-point 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 floating-point value and the float value next larger in magnitude. Note that for non-NaN x , ulp(- x ) == ulp( x ).

Special Cases:

Parameters:
f - the floating-point 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:

Parameters:
d - the floating-point 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:

Parameters:
f - the floating-point 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:

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:

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:

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:

The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic 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:

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. 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 floating-point evaulation of log(1.0+x).

Special cases:

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
x - a value
Returns:
the value ln(x + 1), the natural log of x + 1