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*java.lang.Math* *Math* The class Math contains methods for performing basic
 nu

public final class Math
  extends    |java.lang.Object|

|java.lang.Math_Description|
|java.lang.Math_Fields|
|java.lang.Math_Constructors|
|java.lang.Math_Methods|

================================================================================

*java.lang.Math_Fields*
|double_java.lang.Math.E|
|double_java.lang.Math.PI|

*java.lang.Math_Methods*
|java.lang.Math.abs(double)|Returns the absolute value of a double value.
|java.lang.Math.abs(float)|Returns the absolute value of a float value.
|java.lang.Math.abs(int)|Returns the absolute value of an int value.
|java.lang.Math.abs(long)|Returns the absolute value of a long value.
|java.lang.Math.acos(double)|Returns the arc cosine of an angle, in the range o
|java.lang.Math.asin(double)|Returns the arc sine of an angle, in the range of 
|java.lang.Math.atan(double)|Returns the arc tangent of an angle, in the range 
|java.lang.Math.atan2(double,double)|Converts rectangular coordinates (x,y)  to
|java.lang.Math.cbrt(double)|Returns the cube root of a double value.
|java.lang.Math.ceil(double)|Returns the smallest (closest to negative infinity
|java.lang.Math.cos(double)|Returns the trigonometric cosine of an angle.
|java.lang.Math.cosh(double)|Returns the hyperbolic cosine of a double value.
|java.lang.Math.exp(double)|Returns Euler's number e raised to the power of a  
|java.lang.Math.expm1(double)|Returns ex-1.
|java.lang.Math.floor(double)|Returns the largest (closest to positive infinity
|java.lang.Math.hypot(double,double)|Returns sqrt(x2+y2)  without intermediate 
|java.lang.Math.IEEEremainder(double,double)|Computes the remainder operation o
|java.lang.Math.log(double)|Returns the natural logarithm (base e) of a double 
|java.lang.Math.log10(double)|Returns the base 10 logarithm of a double value.
|java.lang.Math.log1p(double)|Returns the natural logarithm of the sum of the a
|java.lang.Math.max(double,double)|Returns the greater of two double values.
|java.lang.Math.max(float,float)|Returns the greater of two float values.
|java.lang.Math.max(int,int)|Returns the greater of two int values.
|java.lang.Math.max(long,long)|Returns the greater of two long values.
|java.lang.Math.min(double,double)|Returns the smaller of two double values.
|java.lang.Math.min(float,float)|Returns the smaller of two float values.
|java.lang.Math.min(int,int)|Returns the smaller of two int values.
|java.lang.Math.min(long,long)|Returns the smaller of two long values.
|java.lang.Math.pow(double,double)|Returns the value of the first argument rais
|java.lang.Math.random()|Returns a double value with a positive sign, greater  
|java.lang.Math.rint(double)|Returns the double value that is closest in value 
|java.lang.Math.round(double)|Returns the closest long to the argument.
|java.lang.Math.round(float)|Returns the closest int to the argument.
|java.lang.Math.signum(double)|Returns the signum function of the argument; zer
|java.lang.Math.signum(float)|Returns the signum function of the argument; zero
|java.lang.Math.sin(double)|Returns the trigonometric sine of an angle.
|java.lang.Math.sinh(double)|Returns the hyperbolic sine of a double value.
|java.lang.Math.sqrt(double)|Returns the correctly rounded positive square root
|java.lang.Math.tan(double)|Returns the trigonometric tangent of an angle.
|java.lang.Math.tanh(double)|Returns the hyperbolic tangent of a double value.
|java.lang.Math.toDegrees(double)|Converts an angle measured in radians to an a
|java.lang.Math.toRadians(double)|Converts an angle measured in degrees to an a
|java.lang.Math.ulp(double)|Returns the size of an ulp of the argument.
|java.lang.Math.ulp(float)|Returns the size of an ulp of the argument.

*java.lang.Math_Description*

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 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. 


*double_java.lang.Math.E*

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 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. 


*double_java.lang.Math.PI*

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 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. 



*java.lang.Math.abs(double)*

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. In 
other words, the result is the same as the value of the expression: 
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1) 

    a - the argument whose absolute value is to be determined 

    Returns: the absolute value of the argument. 
*java.lang.Math.abs(float)*

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. In 
other words, the result is the same as the value of the expression: 

Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a)) 

    a - the argument whose absolute value is to be determined 

    Returns: the absolute value of the argument. 
*java.lang.Math.abs(int)*

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. 

    a - the argument whose absolute value is to be determined 

    Returns: the absolute value of the argument. 
*java.lang.Math.abs(long)*

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. 

    a - the argument whose absolute value is to be determined 

    Returns: the absolute value of the argument. 
*java.lang.Math.acos(double)*

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. 

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. 

    Returns: the arc cosine of the argument. 
*java.lang.Math.asin(double)*

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. 

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. 

    Returns: the arc sine of the argument. 
*java.lang.Math.atan(double)*

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. 

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. 

    Returns: the arc tangent of the argument. 
*java.lang.Math.atan2(double,double)*

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: 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. 

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

    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. 
*java.lang.Math.cbrt(double)*

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: 



If the argument is NaN, then the result is NaN. 

If the argument is infinite, then the result is an infinity with the same sign 
as the argument. 

If the argument is zero, then the result is a zero with the same sign as the 
argument. 



The computed result must be within 1 ulp of the exact result. 

    a - a value. 

    Returns: the cube root of a. 
*java.lang.Math.ceil(double)*

public 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. 
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. Note that the value of Math.ceil(x) is 
exactly the value of -Math.floor(-x). 

    a - a value. 

    Returns: the smallest (closest to negative infinity) floating-point value that is 
             greater than or equal to the argument and is equal to a 
             mathematical integer. 
*java.lang.Math.cos(double)*

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. 

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

    a - an angle, in radians. 

    Returns: the cosine of the argument. 
*java.lang.Math.cosh(double)*

public static double cosh(double x)

Returns the hyperbolic cosine of a double value. The hyperbolic cosine of x is 
defined to be (ex+e-x)/2 where e is Euler's number(|java.lang.Math|) . 

Special cases: 

If the argument is NaN, then the result is NaN. 

If the argument is infinite, then the result is positive infinity. 

If the argument is zero, then the result is 1.0. 



The computed result must be within 2.5 ulps of the exact result. 

    x - The number whose hyperbolic cosine is to be returned. 

    Returns: The hyperbolic cosine of x. 
*java.lang.Math.exp(double)*

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. 

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

    a - the exponent to raise e to. 

    Returns: the value ea, where e is the base of the natural logarithms. 
*java.lang.Math.expm1(double)*

public static double expm1(double x)

Returns ex-1. Note that for values of x near 0, the exact sum of expm1(x)+1 is 
much closer to the true result of ex than exp(x). 

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 -1.0. 

If the argument is zero, then the result is a zero with the same sign as the 
argument. 



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 ex-1 is within 1/2 ulp of 
the limit value -1, -1.0 should be returned. 

    x - the exponent to raise e to in the computation of ex-1. 

    Returns: the value ex-1. 
*java.lang.Math.floor(double)*

public 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. 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. 

    a - a value. 

    Returns: the largest (closest to positive infinity) floating-point value that less than 
             or equal to the argument and is equal to a mathematical integer. 
*java.lang.Math.hypot(double,double)*

public static double hypot(
  double x,
  double y)

Returns sqrt(x2+y2) without intermediate overflow or underflow. 

Special cases: 

If either argument is infinite, then the result is positive infinity. 

If either argument is NaN and neither argument is infinite, then the result is 
NaN. 



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. 

    x - a value 
    y - a value 

    Returns: sqrt(x2+y2) without intermediate overflow or underflow 
*java.lang.Math.IEEEremainder(double,double)*

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-f2n, 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: 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. 

    f1 - the dividend. 
    f2 - the divisor. 

    Returns: the remainder when f1 is divided by f2. 
*java.lang.Math.log(double)*

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. 

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

    a - a value 

    Returns: the value lna, the natural logarithm of a. 
*java.lang.Math.log10(double)*

public static double log10(double a)

Returns the base 10 logarithm 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. If the argument is equal to 10n for integer n, then the result is n. 

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

    a - a value 

    Returns: the base 10 logarithm of a. 
*java.lang.Math.log1p(double)*

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 evaluation of log(1.0+x). 

Special cases: 



If the argument is NaN or less than -1, then the result is NaN. 

If the argument is positive infinity, then the result is positive infinity. 

If the argument is negative one, then the result is negative infinity. 

If the argument is zero, then the result is a zero with the same sign as the 
argument. 



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

    x - a value 

    Returns: the value ln(x+1), the natural log of x+1 
*java.lang.Math.max(double,double)*

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 
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. 

    Returns: the larger of a and b. 
*java.lang.Math.max(float,float)*

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 
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. 

    Returns: the larger of a and b. 
*java.lang.Math.max(int,int)*

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. 

    a - an argument. 
    b - another argument. 

    Returns: the larger of a and b. 
*java.lang.Math.max(long,long)*

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. 

    a - an argument. 
    b - another argument. 

    Returns: the larger of a and b. 
*java.lang.Math.min(double,double)*

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 
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. 

    Returns: the smaller of a and b. 
*java.lang.Math.min(float,float)*

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 
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. 

    Returns: the smaller of a and b. 
*java.lang.Math.min(int,int)*

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. 

    a - an argument. 
    b - another argument. 

    Returns: the smaller of a and b. 
*java.lang.Math.min(long,long)*

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. 

    a - an argument. 
    b - another argument. 

    Returns: the smaller of a and b. 
*java.lang.Math.pow(double,double)*

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, 

then the result is positive 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, 

then the result is positive zero. 

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, 

then the result is positive 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, 

then the result is positive infinity. 

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, 

then the result is positive zero. 

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, 

then the result is negative zero. 

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, 

then the result is positive infinity. 

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, 

then the result is negative infinity. 

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. 

(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 
<tt>ceil</tt>(|java.lang.Math|) or, equivalently, a fixed point of the method 
<tt>floor</tt>(|java.lang.Math|) . 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 result must be within 1 ulp of the exact result. Results must be 
semi-monotonic. 

    a - the base. 
    b - the exponent. 

    Returns: the value ab. 
*java.lang.Math.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. 
*java.lang.Math.rint(double)*

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: 
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. 

    a - a double value. 

    Returns: the closest floating-point value to a that is equal to a mathematical integer. 
*java.lang.Math.round(double)*

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: 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 of Long.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 of Long.MAX_VALUE. 

    a - a floating-point value to be rounded to a long. 

    Returns: the value of the argument rounded to the nearest long value. 
*java.lang.Math.round(float)*

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: 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 of Integer.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 of 
Integer.MAX_VALUE. 

    a - a floating-point value to be rounded to an integer. 

    Returns: the value of the argument rounded to the nearest int value. 
*java.lang.Math.signum(double)*

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: 

If the argument is NaN, then the result is NaN. If the argument is positive 
zero or negative zero, then the result is the same as the argument. 

    d - the floating-point value whose signum is to be returned 

    Returns: the signum function of the argument 
*java.lang.Math.signum(float)*

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: 

If the argument is NaN, then the result is NaN. If the argument is positive 
zero or negative zero, then the result is the same as the argument. 

    f - the floating-point value whose signum is to be returned 

    Returns: the signum function of the argument 
*java.lang.Math.sin(double)*

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. 

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

    a - an angle, in radians. 

    Returns: the sine of the argument. 
*java.lang.Math.sinh(double)*

public static double sinh(double x)

Returns the hyperbolic sine of a double value. The hyperbolic sine of x is 
defined to be (ex-e-x)/2 where e is Euler's number(|java.lang.Math|) . 

Special cases: 

If the argument is NaN, then the result is NaN. 

If the argument is infinite, then the result is an infinity with the same sign 
as the argument. 

If the argument is zero, then the result is a zero with the same sign as the 
argument. 



The computed result must be within 2.5 ulps of the exact result. 

    x - The number whose hyperbolic sine is to be returned. 

    Returns: The hyperbolic sine of x. 
*java.lang.Math.sqrt(double)*

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. Otherwise, the result is the double value closest to the true 
mathematical square root of the argument value. 

    a - a value. 

    Returns: the positive square root of a. If the argument is NaN or less than zero, the 
             result is NaN. 
*java.lang.Math.tan(double)*

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. 

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

    a - an angle, in radians. 

    Returns: the tangent of the argument. 
*java.lang.Math.tanh(double)*

public static double tanh(double x)

Returns the hyperbolic tangent of a double value. The hyperbolic tangent of x 
is defined to be (ex-e-x)/(ex+e-x), in other words, 
sinh(<i>x</i>)(|java.lang.Math|) / cosh(<i>x</i>)(|java.lang.Math|) . Note that 
the absolute value of the exact tanh is always less than 1. 

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. 

If the argument is positive infinity, then the result is +1.0. 

If the argument is negative infinity, then the result is -1.0. 



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. 

    x - The number whose hyperbolic tangent is to be returned. 

    Returns: The hyperbolic tangent of x. 
*java.lang.Math.toDegrees(double)*

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. 

    angrad - an angle, in radians 

    Returns: the measurement of the angle angrad in degrees. 
*java.lang.Math.toRadians(double)*

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. 

    angdeg - an angle, in degrees 

    Returns: the measurement of the angle angdeg in radians. 
*java.lang.Math.ulp(double)*

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: 

If the argument is NaN, then the result is NaN. If the argument is positive or 
negative infinity, then the result is positive infinity. If the argument is 
positive or negative zero, then the result is Double.MIN_VALUE. If the argument 
is Double.MAX_VALUE, then the result is equal to 2971. 

    d - the floating-point value whose ulp is to be returned 

    Returns: the size of an ulp of the argument 
*java.lang.Math.ulp(float)*

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: 

If the argument is NaN, then the result is NaN. If the argument is positive or 
negative infinity, then the result is positive infinity. If the argument is 
positive or negative zero, then the result is Float.MIN_VALUE. If the argument 
is Float.MAX_VALUE, then the result is equal to 2104. 

    f - the floating-point value whose ulp is to be returned 

    Returns: the size of an ulp of the argument