CLDC 8 (b75)
java.lang

## Class 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.

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, CLDC 1.0
• ### 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 (xy) to polar coordinates (r, theta).
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 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 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 random()
Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0.
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 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 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 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

• #### 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.
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.
• #### 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.
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 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.
• #### 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.
• #### acos

public static double acos(double a)
Returns the arc cosine of a value; the returned angle is in the range 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.

Parameters:
a - the value whose arc cosine is to be returned.
Returns:
the arc cosine of the argument.
• #### asin

public static double asin(double a)
Returns the arc sine of a value; the returned angle is in the range -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.

Parameters:
a - the value whose arc sine is to be returned.
Returns:
the arc sine of the argument.
• #### atan

public static double atan(double a)
Returns the arc tangent of a value; the returned angle is in the range -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.

Parameters:
a - the value whose arc tangent is to be returned.
Returns:
the arc tangent of the argument.
• #### atan2

public static double atan2(double y,
double x)
Returns the angle theta from the conversion of rectangular coordinates (xy) to polar coordinates (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.

Parameters:
y - the ordinate coordinate
x - the abscissa coordinate
Returns:
the theta component of the point (rtheta) in polar coordinates that corresponds to the point (xy) in Cartesian coordinates.
• #### ceil

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).
Parameters:
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.
• #### copySign

public static double copySign(double magnitude,
double sign)
Returns the first floating-point argument with the sign of the second floating-point argument. Note that this method does not require NaN sign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
Parameters:
magnitude - the parameter providing the magnitude of the result
sign - the parameter providing the sign of the result
Returns:
a value with the magnitude of magnitude and the sign of sign.
Since:
1.6
• #### copySign

public static float copySign(float magnitude,
float sign)
Returns the first floating-point argument with the sign of the second floating-point argument. Note that this method does not require NaN sign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
Parameters:
magnitude - the parameter providing the magnitude of the result
sign - the parameter providing the sign of the result
Returns:
a value with the magnitude of magnitude and the sign of sign.
Since:
1.6
• #### 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.

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

Parameters:
a - an angle, in radians.
Returns:
the cosine of the argument.
• #### floor

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.
Parameters:
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.
• #### getExponent

public static int getExponent(double d)
Returns the unbiased exponent used in the representation of a double. Special cases:
Parameters:
d - a double value
Returns:
the unbiased exponent of the argument
Since:
1.6
• #### getExponent

public static int getExponent(float f)
Returns the unbiased exponent used in the representation of a float. Special cases:
Parameters:
f - a float value
Returns:
the unbiased exponent of the argument
Since:
1.6
• #### 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 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 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.
Parameters:
a - an argument.
b - another argument.
Returns:
the larger of a and b.
• #### 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.
• #### 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.
• #### 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 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 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.
Parameters:
a - an argument.
b - another argument.
Returns:
the smaller 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.
• #### 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.
• #### 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()
• #### round

public static long round(double a)
Returns the closest long to the argument, with ties rounding up.

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.
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
• #### round

public static int round(float a)
Returns the closest int to the argument, with ties rounding up.

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.
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
• #### 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:

• 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.
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:

• 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.
Parameters:
f - the floating-point value whose signum is to be returned
Returns:
the signum function of the argument
Since:
1.5
• #### 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.

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

Parameters:
a - an angle, in radians.
Returns:
the sine of the argument.
• #### 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.
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.
• #### 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.

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

Parameters:
a - an angle, in radians.
Returns:
the tangent of the argument.
• #### 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
• #### 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
CLDC 8 (b75)
10-February-2014 08:32

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