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## Class XMath

• public final class XMath
extends Object
This class provides advanced mathematical functions.
• ### 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

All 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 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 cos(double a)
Returns the trigonometric cosine of an angle.
static double exp(double a)
Returns Euler's number e raised to the power of a double value.
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 double limit(double value, double min, double max)
Limits a value between two others: If value is lower than min, returns min. If value is greater than max, returns max. Otherwise, returns value.
static float limit(float value, float min, float max)
Limits a value between two others: If value is lower than min, returns min. If value is greater than max, returns max. Otherwise, returns value.
static int limit(int value, int min, int max)
Limits a value between two others: If value is lower than min, returns min. If value is greater than max, returns max. Otherwise, returns value.
static long limit(long value, long min, long max)
Limits a value between two others: If value is lower than min, returns min. If value is greater than max, returns max. Otherwise, returns value.
static double log(double a)
Returns the natural logarithm (base e) of a double value.
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 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.
Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
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.
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.
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.
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.
Long.MIN_VALUE
• #### 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.
• #### 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.
• #### 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.
• #### exp

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.
Parameters:
a - the exponent to raise e to.
Returns:
the value ea, where e is the base of the natural logarithms.
• #### 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.
• #### limit

public static double limit(double value,
double min,
double max)
Limits a value between two others:
1. If value is lower than min, returns min.
2. If value is greater than max, returns max.
3. Otherwise, returns value.
Parameters:
value - the value to limit
min - the lower bound
max - the upper bound
Returns:
the limited value
Throws:
IllegalArgumentException - if min is greater than max
• #### limit

public static float limit(float value,
float min,
float max)
Limits a value between two others:
1. If value is lower than min, returns min.
2. If value is greater than max, returns max.
3. Otherwise, returns value.
Parameters:
value - the value to limit
min - the lower bound
max - the upper bound
Returns:
the limited value
Throws:
IllegalArgumentException - if min is greater than max
• #### limit

public static int limit(int value,
int min,
int max)
Limits a value between two others:
1. If value is lower than min, returns min.
2. If value is greater than max, returns max.
3. Otherwise, returns value.
Parameters:
value - the value to limit
min - the lower bound
max - the upper bound
Returns:
the limited value
Throws:
IllegalArgumentException - if min is greater than max
• #### limit

public static long limit(long value,
long min,
long max)
Limits a value between two others:
1. If value is lower than min, returns min.
2. If value is greater than max, returns max.
3. Otherwise, returns value.
Parameters:
value - the value to limit
min - the lower bound
max - the upper bound
Returns:
the limited value
Throws:
IllegalArgumentException - if min is greater than max
• #### log

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.

Parameters:
a - the value whose the natural logarithm is to be returned
Returns:
the value ln a
• #### 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.
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.
Long.MAX_VALUE
• #### 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.
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.
Long.MIN_VALUE
• #### 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:
• 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 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 result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a - the base.
b - the exponent.
Returns:
the value ab.
• #### 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

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: