[JAVA API] java.lang.Math

java.lang

Class Math

• java.lang.Object
• • 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 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.

  Since:

  JDK1.0

• • Field Summary

    Fields 

    Modifier and Type	Field and Description
    static double	E The double value that is closer than any other to e, the base of the natural logarithms.
    static double	PI The double value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

  • Method Summary

    Methods 

    Modifier and Type	Method and Description
    static double	abs(double a) Returns the absolute value of a double value.
    static float	abs(float a) Returns the absolute value of a float value.
    static int	abs(int a) Returns the absolute value of an int value.
    static long	abs(long a) Returns the absolute value of a long value.
    static double	acos(double a) Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi.
    static double	asin(double a) Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2.
    static double	atan(double a) Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2.
    static double	atan2(double y, double x) Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta).
    static double	cbrt(double a) Returns the cube root of a double value.
    static double	ceil(double a) Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer.
    static double	copySign(double magnitude, double sign) Returns the first floating-point argument with the sign of the second floating-point argument.
    static float	copySign(float magnitude, float sign) Returns the first floating-point argument with the sign of the second floating-point argument.
    static double	cos(double a) Returns the trigonometric cosine of an angle.
    static double	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 ex -1.
    static double	floor(double a) Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer.
    static int	getExponent(double d) Returns the unbiased exponent used in the representation of a double.
    static int	getExponent(float f) Returns the unbiased exponent used in the representation of a float.
    static double	hypot(double x, double y) Returns sqrt(x2 +y2) 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	nextAfter(double start, double direction) Returns the floating-point number adjacent to the first argument in the direction of the second argument.
    static float	nextAfter(float start, double direction) Returns the floating-point number adjacent to the first argument in the direction of the second argument.
    static double	nextUp(double d) Returns the floating-point value adjacent to d in the direction of positive infinity.
    static float	nextUp(float f) Returns the floating-point value adjacent to f in the direction of positive infinity.
    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, with ties rounding up.
    static int	round(float a) Returns the closest int to the argument, with ties rounding up.
    static double	scalb(double d, int scaleFactor) Return d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set.
    static float	scalb(float f, int scaleFactor) Return f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set.
    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