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.

Constant Summary

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

Public Method Summary

static double
IEEEremainder(double f1, double f2)
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.
static long
abs(long a)
Returns the absolute value of a long value.
static int
abs(int a)
Returns the absolute value of an int value.
static float
abs(float a)
Returns the absolute value of a float value.
static double
abs(double a)
Returns the absolute value of a double 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 int
addExact(int x, int y)
Returns the sum of its arguments, throwing an exception if the result overflows an int.
static long
addExact(long x, long y)
Returns the sum of its arguments, throwing an exception if the result overflows a long.
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 (xy) 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 float
copySign(float magnitude, float sign)
Returns the first floating-point argument with the sign of the second floating-point argument.
static double
copySign(double magnitude, double 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 long
decrementExact(long a)
Returns the argument decremented by one, throwing an exception if the result overflows a long.
static int
decrementExact(int a)
Returns the argument decremented by one, throwing an exception if the result overflows an int.
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
floorDiv(int x, int y)
Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
static long
floorDiv(long x, long y)
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.
static long
floorMod(long x, long y)
Returns the floor modulus of the long arguments.
static int
floorMod(int x, int y)
Returns the floor modulus of the int arguments.
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 int
incrementExact(int a)
Returns the argument incremented by one, throwing an exception if the result overflows an int.
static long
incrementExact(long a)
Returns the argument incremented by one, throwing an exception if the result overflows a long.
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 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 float
max(float a, float b)
Returns the greater of two float values.
static double
max(double a, double b)
Returns the greater of two double values.
static float
min(float a, float b)
Returns the smaller of two float values.
static double
min(double a, double b)
Returns the smaller of two double values.
static int