FastMath

java.lang.Object
- net.jafama.FastMath

```
public final class FastMath
extends Object
```
Class providing math treatments that: - are meant to be faster than java.lang.Math class equivalents (if any), - are still somehow accurate and robust (handling of NaN and such), - do not (or not directly) generate objects at run time (no "new"). Other than optimized treatments, a valuable feature of this class is the presence of angles normalization methods, derived from those used in java.lang.Math (for which, sadly, no API is provided, letting everyone with the terrible responsibility of writing their own ones). Non-redefined methods Math methods are also available, for easy replacement, even though for some of them, such as for incrementExact, you might want to stick to Math versions to benefit from eventual JVM intrinsics. Use of look-up tables: around 1 Mo total, and initialized lazily or on first call to initTables(). Depending on JVM, or JVM options, these treatments can actually be slower than Math ones. In particular, they can be slower if not optimized by the JIT, which you can see with -Xint JVM option. Another cause of slowness can be cache-misses on look-up tables. Also, look-up tables initialization typically takes multiple hundreds of milliseconds (and is about twice slower in J6 than in J5, and in J7 than in J6, possibly due to intrinsifications preventing optimizations such as use of hardware sqrt, and Math delegating to StrictMath with JIT optimizations not yet up during class load). As a result, you might want to make these treatments not use tables, and delegate to corresponding Math methods, when they are available in the lowest supported Java version, by using the appropriate property (see below). Methods with same signature than Math ones, are meant to return "good" approximations on all range. Methods terminating with "Fast" are meant to return "good" approximation on a reduced range only. Methods terminating with "Quick" are meant to be quick, but do not return a good approximation, and might only work on a reduced range. Properties: - jafama.usejdk (boolean, default is false): If true, for redefined methods, as well as their "Fast" or "Quick" terminated counterparts, instead of using redefined computations, delegating to Math, when available in required Java version. - jafama.fastlog (boolean, default is false): If true, using redefined computations for log(double) and log10(double), else they delegate to Math.log(double) and Math.log10(double). False by default because Math.log(double) and Math.log10(double) seem usually fast (redefined log(double) might be even faster, but is less accurate). - jafama.fastsqrt (boolean, default is false): If true, using redefined computation for sqrt(double), else it delegates to Math.sqrt(double). False by default because Math.sqrt(double) seems usually fast.

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`E` Closest double approximation of e.
`static double`	`PI` Closest double approximation of pi, which is inferior to mathematical pi: pi ~= 3.14159265358979323846...
`static double`	`PI_SUP` High double approximation of pi, which is further from pi than the low approximation PI: pi ~= 3.14159265358979323846...

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`abs(double a)`
`static float`	`abs(float a)`
`static int`	`abs(int value)`
`static long`	`abs(long value)`
`static double`	`acos(double value)`
`static double`	`acosh(double value)` Some properties of acosh(x) = log(x + sqrt(x^2 - 1)): 1) defined on [1,+Infinity[ 2) result in ]0,+Infinity[ (by convention, since cosh(x) = cosh(-x)) 3) acosh(1) = 0 4) acosh(1+epsilon) ~= log(1 + sqrt(2epsilon)) ~= sqrt(2epsilon) 5) lim(acosh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
`static double`	`acosh1p(double value)` Much more accurate than acosh(1+value), for arguments (and results) close to zero.
`static double`	`acosInRange(double value)` If value is not NaN and is outside [-1,1] range, closest value in this range is used.
`static int`	`addBounded(int a, int b)`
`static long`	`addBounded(long a, long b)`
`static int`	`addExact(int a, int b)`
`static long`	`addExact(long a, long b)`
`static double`	`asin(double value)`
`static double`	`asinh(double value)` Some properties of asinh(x) = log(x + sqrt(x^2 + 1)) 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) asinh(x) = -asinh(-x) (implies asinh(0) = 0) 4) asinh(epsilon) ~= epsilon 5) lim(asinh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
`static double`	`asinInRange(double value)` If value is not NaN and is outside [-1,1] range, closest value in this range is used.
`static double`	`atan(double value)`
`static double`	`atan2(double y, double x)` For special values for which multiple conventions could be adopted, behaves like Math.atan2(double,double).
`static double`	`atanh(double value)` Some properties of atanh(x) = log((1+x)/(1-x))/2: 1) defined on ]-1,1[ 2) result in ]-Infinity,+Infinity[ 3) atanh(-1) = -Infinity (by continuity) 4) atanh(1) = +Infinity (by continuity) 5) atanh(epsilon) ~= epsilon 6) lim(atanh(x),x->1) = +Infinity
`static double`	`cbrt(double value)`
`static double`	`ceil(double value)`
`static float`	`ceil(float value)`
`static double`	`copySign(double magnitude, double sign)` A sign of NaN can be interpreted as positive or negative.
`static float`	`copySign(float magnitude, float sign)` A sign of NaN can be interpreted as positive or negative.
`static double`	`cos(double angle)`
`static double`	`cosh(double value)` Some properties of cosh(x) = (exp(x)+exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in [1,+Infinity[ 3) cosh(0) = 1 4) cosh(x) = cosh(-x) 5) lim(cosh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e.
`static double`	`coshm1(double value)` Much more accurate than cosh(value)-1, for arguments (and results) close to zero.
`static double`	`cosQuick(double angle)` Quick cos, with accuracy of about 1.6e-3 (PI/) for \|angle\| < 6588397.0 (Integer.MAX_VALUE * (2*PI/)), and no accuracy at all for larger values.
`static int`	`decrementBounded(int value)`
`static long`	`decrementBounded(long value)`
`static int`	`decrementExact(int value)`
`static long`	`decrementExact(long value)`
`static double`	`exp(double value)`
`static double`	`expm1(double value)` Much more accurate than exp(value)-1, for arguments (and results) close to zero.
`static double`	`expQuick(double value)` Quick exp, with a max relative error of about 2.94e-2 for \|value\| < 700.0 or so, and no accuracy at all outside this range.
`static double`	`floor(double value)`
`static float`	`floor(float value)`
`static int`	`floorDiv(int x, int y)` Returns the largest int <= dividend/divisor.
`static long`	`floorDiv(long x, int y)` Returns the largest long <= dividend/divisor.
`static long`	`floorDiv(long x, long y)` Returns the largest long <= dividend/divisor.
`static int`	`floorMod(int x, int y)` Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[.
`static int`	`floorMod(long x, int y)` Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[.
`static long`	`floorMod(long x, long y)` Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[.
`static int`	`getExponent(double value)`
`static int`	`getExponent(float value)`
`static double`	`hypot(double x, double y)`
`static double`	`hypot(double x, double y, double z)`
`static double`	`IEEEremainder(double f1, double f2)`
`static int`	`incrementBounded(int value)`
`static long`	`incrementBounded(long value)`
`static int`	`incrementExact(int value)`
`static long`	`incrementExact(long value)`
`static void`	`initTables()` Ensures that all look-up tables are initialized - otherwise they are initialized lazily.
`static double`	`invSqrtQuick(double value)` Quick inverse of square root, with a max relative error of about 3.44e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range.
`static boolean`	`isInClockwiseDomain(double startAngRad, double angSpanRad, double angRad)` NB: Since 2Math.PI < 2PI, a span of 2*Math.PI does not mean full angular range.
`static boolean`	`isNaNOrInfinite(double value)`
`static boolean`	`isNaNOrInfinite(float value)`
`static double`	`log(double value)`
`static double`	`log10(double value)`
`static double`	`log1p(double value)` Much more accurate than log(1+value), for arguments (and results) close to zero.
`static int`	`log2(int value)`
`static int`	`log2(long value)`
`static double`	`logQuick(double value)` Quick log, with a max relative error of about 1.9e-3 for values in ]Double.MIN_NORMAL,+Infinity[, and worse accuracy outside this range.
`static double`	`max(double a, double b)`
`static float`	`max(float a, float b)`
`static int`	`max(int a, int b)`
`static long`	`max(long a, long b)`
`static double`	`min(double a, double b)`
`static float`	`min(float a, float b)`
`static int`	`min(int a, int b)`
`static long`	`min(long a, long b)`
`static int`	`multiplyBounded(int a, int b)`
`static long`	`multiplyBounded(long a, int b)`
`static long`	`multiplyBounded(long a, long b)`
`static int`	`multiplyExact(int a, int b)`
`static long`	`multiplyExact(long a, int b)`
`static long`	`multiplyExact(long a, long b)`
`static long`	`multiplyFull(int x, int y)`
`static long`	`multiplyHigh(long x, long y)`
`static int`	`negateBounded(int value)`
`static long`	`negateBounded(long value)`
`static int`	`negateExact(int value)`
`static long`	`negateExact(long value)`
`static double`	`nextAfter(double start, double direction)` If both arguments are +-0.0, direction is returned.
`static float`	`nextAfter(float start, double direction)` If both arguments are +-0.0(f), (float)direction is returned.
`static double`	`nextDown(double start)` Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
`static float`	`nextDown(float start)` Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
`static double`	`nextUp(double start)` Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
`static float`	`nextUp(float start)` Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
`static double`	`normalizeMinusHalfPiHalfPi(double angle)`
`static double`	`normalizeMinusHalfPiHalfPiFast(double angle)` Not accurate for large values.
`static double`	`normalizeMinusPiPi(double angle)`
`static double`	`normalizeMinusPiPiFast(double angle)` Not accurate for large values.
`static double`	`normalizeZeroTwoPi(double angle)`
`static double`	`normalizeZeroTwoPiFast(double angle)` Not accurate for large values.
`static double`	`pow(double value, double power)` 1e-13ish accuracy or better on whole double range.
`static double`	`pow2(double value)`
`static float`	`pow2(float value)`
`static int`	`pow2(int value)`
`static long`	`pow2(long value)`
`static double`	`pow3(double value)`
`static float`	`pow3(float value)`
`static int`	`pow3(int value)`
`static long`	`pow3(long value)`
`static double`	`powFast(double value, int power)` This treatment is somehow accurate for low values of \|power\|, and for \|power*getExponent(value)\| < 1023 or so (to stay away from double extreme magnitudes (large and small)).
`static double`	`powQuick(double value, double power)` Quick pow, with a max relative error of about 1e-2 for value >= Double.MIN_NORMAL and 1e-10 < \|value^power\| < 1e10, of about 6e-2 for value >= Double.MIN_NORMAL and 1e-40 < \|value^power\| < 1e40, and worse accuracy otherwise.
`static double`	`random()`
`static double`	`remainder(double dividend, double divisor)` Returns dividend - divisor * n, where n is the mathematical integer closest to dividend/divisor.
`static double`	`rint(double value)`
`static float`	`rint(float value)`
`static long`	`round(double value)` Might have different semantics than Math.round(double), see bugs 6430675 and 8010430.
`static int`	`round(float value)` Might have different semantics than Math.round(float), see bugs 6430675 and 8010430.
`static long`	`roundEven(double value)`
`static int`	`roundEven(float value)`
`static double`	`scalb(double value, int scaleFactor)` Precision may be lost if the result is subnormal.
`static float`	`scalb(float value, int scaleFactor)` Precision may be lost if the result is subnormal.
`static long`	`signFromBit(double value)`
`static int`	`signFromBit(float value)`
`static double`	`signum(double value)`
`static float`	`signum(float value)`
`static double`	`sin(double angle)`
`static double`	`sinAndCos(double angle, DoubleWrapper cosine)` Computes sine and cosine together.
`static double`	`sinh(double value)` Some properties of sinh(x) = (exp(x)-exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) sinh(x) = -sinh(-x) (implies sinh(0) = 0) 4) sinh(epsilon) ~= epsilon 5) lim(sinh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e.
`static double`	`sinhAndCosh(double value, DoubleWrapper hcosine)` Computes hyperbolic sine and hyperbolic cosine together.
`static double`	`sinQuick(double angle)` Quick sin, with accuracy of about 1.6e-3 (PI/) for \|angle\| < 6588395.0 (Integer.MAX_VALUE * (2*PI/) - 2) (- 2 due to removing PI/2 before using cosine tab), and no accuracy at all for larger values.
`static double`	`sqrt(double value)`
`static double`	`sqrtQuick(double value)` Quick sqrt, with with a max relative error of about 3.41e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range.
`static int`	`subtractBounded(int a, int b)`
`static long`	`subtractBounded(long a, long b)`
`static int`	`subtractExact(int a, int b)`
`static long`	`subtractExact(long a, long b)`
`static double`	`tan(double angle)` Can have very bad relative error near +-PI/2, but of the same magnitude than the relative delta between StrictMath.tan(PI/2) and StrictMath.tan(nextDown(PI/2)).
`static double`	`tanh(double value)` Some properties of tanh(x) = sinh(x)/cosh(x) = (exp(2x)-1)/(exp(2x)+1): 1) defined on ]-Infinity,+Infinity[ 2) result in ]-1,1[ 3) tanh(x) = -tanh(-x) (implies tanh(0) = 0) 4) tanh(epsilon) ~= epsilon 5) lim(tanh(x),x->+Infinity) = 1 6) reaches 1 (double loss of precision) for x = 19.061547465398498
`static double`	`toDegrees(boolean sign, int degrees, int minutes, double seconds)`
`static double`	`toDegrees(double angrad)` Gives same result as Math.toDegrees for some particular values like Math.PI/2, Math.PI or 2*Math.PI, but is faster (no division).
`static boolean`	`toDMS(double angrad, IntWrapper degrees, IntWrapper minutes, DoubleWrapper seconds)`
`static int`	`toInt(long value)`
`static int`	`toIntExact(long value)`
`static double`	`toRadians(boolean sign, int degrees, int minutes, double seconds)`
`static double`	`toRadians(double angdeg)` Gives same result as Math.toRadians for some particular values like 90.0, 180.0 or 360.0, but is faster (no division).
`static double`	`toRange(double min, double max, double value)`
`static float`	`toRange(float min, float max, float value)`
`static int`	`toRange(int min, int max, int value)`
`static long`	`toRange(long min, long max, long value)`
`static double`	`twoPow(int power)` Returns the exact result, provided it's in double range, i.e.
`static double`	`ulp(double value)` The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
`static float`	`ulp(float value)` The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - E
```
public static final double E
```
    Closest double approximation of e.
    
    See Also:
    
    Constant Field Values
  - PI
```
public static final double PI
```
    Closest double approximation of pi, which is inferior to mathematical pi: pi ~= 3.14159265358979323846... PI ~= 3.141592653589793
    
    See Also:
    
    Constant Field Values
  - PI_SUP
```
public static final double PI_SUP
```
    High double approximation of pi, which is further from pi than the low approximation PI: pi ~= 3.14159265358979323846... PI ~= 3.141592653589793 PI_SUP ~= 3.1415926535897936
- Method Detail
  - sin
```
public static double sin(double angle)
```
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle sine.
  - sinQuick
```
public static double sinQuick(double angle)
```
    Quick sin, with accuracy of about 1.6e-3 (PI/) for |angle| < 6588395.0 (Integer.MAX_VALUE * (2*PI/) - 2) (- 2 due to removing PI/2 before using cosine tab), and no accuracy at all for larger values.
    
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle sine.
  - cos
```
public static double cos(double angle)
```
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle cosine.
  - cosQuick
```
public static double cosQuick(double angle)
```
    Quick cos, with accuracy of about 1.6e-3 (PI/) for |angle| < 6588397.0 (Integer.MAX_VALUE * (2*PI/)), and no accuracy at all for larger values.
    
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle cosine.
  - sinAndCos
```
public static double sinAndCos(double angle,
                               DoubleWrapper cosine)
```
    Computes sine and cosine together.
    
    Parameters:
    
    angle - Angle in radians.
    
    cosine - (out) Angle cosine.
    
    Returns:
    
    Angle sine.
  - tan
```
public static double tan(double angle)
```
    Can have very bad relative error near +-PI/2, but of the same magnitude than the relative delta between StrictMath.tan(PI/2) and StrictMath.tan(nextDown(PI/2)).
    
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle tangent.
  - asin
```
public static double asin(double value)
```
    Parameters:
    
    value - Value in [-1,1].
    
    Returns:
    
    Value arcsine, in radians, in [-PI/2,PI/2].
  - asinInRange
```
public static double asinInRange(double value)
```
    If value is not NaN and is outside [-1,1] range, closest value in this range is used.
    
    Parameters:
    
    value - Value in [-1,1].
    
    Returns:
    
    Value arcsine, in radians, in [-PI/2,PI/2].
  - acos
```
public static double acos(double value)
```
    Parameters:
    
    value - Value in [-1,1].
    
    Returns:
    
    Value arccosine, in radians, in [0,PI].
  - acosInRange
```
public static double acosInRange(double value)
```
    If value is not NaN and is outside [-1,1] range, closest value in this range is used.
    
    Parameters:
    
    value - Value in [-1,1].
    
    Returns:
    
    Value arccosine, in radians, in [0,PI].
  - atan
```
public static double atan(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value arctangent, in radians, in [-PI/2,PI/2].
  - atan2
```
public static double atan2(double y,
                           double x)
```
    For special values for which multiple conventions could be adopted, behaves like Math.atan2(double,double).
    
    Parameters:
    
    y - Coordinate on y axis.
    
    x - Coordinate on x axis.
    
    Returns:
    
    Angle from x axis positive side to (x,y) position, in radians, in [-PI,PI]. Angle measure is positive when going from x axis to y axis (positive sides).
  - toRadians
```
public static double toRadians(double angdeg)
```
    Gives same result as Math.toRadians for some particular values like 90.0, 180.0 or 360.0, but is faster (no division).
    
    Parameters:
    
    angdeg - Angle value in degrees.
    
    Returns:
    
    Angle value in radians.
  - toDegrees
```
public static double toDegrees(double angrad)
```
    Gives same result as Math.toDegrees for some particular values like Math.PI/2, Math.PI or 2*Math.PI, but is faster (no division).
    
    Parameters:
    
    angrad - Angle value in radians.
    
    Returns:
    
    Angle value in degrees.
  - toRadians
```
public static double toRadians(boolean sign,
                               int degrees,
                               int minutes,
                               double seconds)
```
    Parameters:
    
    sign - Sign of the angle: true for positive, false for negative.
    
    degrees - Degrees, in [0,180].
    
    minutes - Minutes, in [0,59].
    
    seconds - Seconds, in [0.0,60.0[.
    
    Returns:
    
    Angle in radians.
  - toDegrees
```
public static double toDegrees(boolean sign,
                               int degrees,
                               int minutes,
                               double seconds)
```
    Parameters:
    
    sign - Sign of the angle: true for positive, false for negative.
    
    degrees - Degrees, in [0,180].
    
    minutes - Minutes, in [0,59].
    
    seconds - Seconds, in [0.0,60.0[.
    
    Returns:
    
    Angle in degrees.
  - toDMS
```
public static boolean toDMS(double angrad,
                            IntWrapper degrees,
                            IntWrapper minutes,
                            DoubleWrapper seconds)
```
    Parameters:
    
    angrad - Angle in radians.
    
    degrees - (out) Degrees, in [0,180].
    
    minutes - (out) Minutes, in [0,59].
    
    seconds - (out) Seconds, in [0.0,60.0[.
    
    Returns:
    
    true if the resulting angle in [-180deg,180deg] is positive, false if it is negative.
  - isInClockwiseDomain
```
public static boolean isInClockwiseDomain(double startAngRad,
                                          double angSpanRad,
                                          double angRad)
```
    NB: Since 2*Math.PI < 2*PI, a span of 2*Math.PI does not mean full angular range. ex.: isInClockwiseDomain(0.0, 2*Math.PI, -1e-20) returns false. ---> For full angular range, use a span > 2*Math.PI, like 2*PI_SUP constant of this class.
    
    Parameters:
    
    startAngRad - An angle, in radians.
    
    angSpanRad - An angular span, >= 0.0, in radians.
    
    angRad - An angle, in radians.
    
    Returns:
    
    true if angRad is in the clockwise angular domain going from startAngRad, over angSpanRad, extremities included, false otherwise.
  - sinh
```
public static double sinh(double value)
```
    Some properties of sinh(x) = (exp(x)-exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) sinh(x) = -sinh(-x) (implies sinh(0) = 0) 4) sinh(epsilon) ~= epsilon 5) lim(sinh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e. a bit further than exp(x)
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic sine.
  - cosh
```
public static double cosh(double value)
```
    Some properties of cosh(x) = (exp(x)+exp(-x))/2: 1) defined on ]-Infinity,+Infinity[ 2) result in [1,+Infinity[ 3) cosh(0) = 1 4) cosh(x) = cosh(-x) 5) lim(cosh(x),x->+Infinity) = +Infinity (y increasing exponentially faster than x) 6) reaches +Infinity (double overflow) for x >= 710.475860073944, i.e. a bit further than exp(x)
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic cosine.
  - coshm1
```
public static double coshm1(double value)
```
    Much more accurate than cosh(value)-1, for arguments (and results) close to zero. coshm1(-0.0) = -0.0, for homogeneity with acosh1p(-0.0) = -0.0.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic cosine, minus 1.
  - sinhAndCosh
```
public static double sinhAndCosh(double value,
                                 DoubleWrapper hcosine)
```
    Computes hyperbolic sine and hyperbolic cosine together.
    
    Parameters:
    
    value - A double value.
    
    hcosine - (out) Value hyperbolic cosine.
    
    Returns:
    
    Value hyperbolic sine.
  - tanh
```
public static double tanh(double value)
```
    Some properties of tanh(x) = sinh(x)/cosh(x) = (exp(2*x)-1)/(exp(2*x)+1): 1) defined on ]-Infinity,+Infinity[ 2) result in ]-1,1[ 3) tanh(x) = -tanh(-x) (implies tanh(0) = 0) 4) tanh(epsilon) ~= epsilon 5) lim(tanh(x),x->+Infinity) = 1 6) reaches 1 (double loss of precision) for x = 19.061547465398498
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic tangent.
  - asinh
```
public static double asinh(double value)
```
    Some properties of asinh(x) = log(x + sqrt(x^2 + 1)) 1) defined on ]-Infinity,+Infinity[ 2) result in ]-Infinity,+Infinity[ 3) asinh(x) = -asinh(-x) (implies asinh(0) = 0) 4) asinh(epsilon) ~= epsilon 5) lim(asinh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic arcsine.
  - acosh
```
public static double acosh(double value)
```
    Some properties of acosh(x) = log(x + sqrt(x^2 - 1)): 1) defined on [1,+Infinity[ 2) result in ]0,+Infinity[ (by convention, since cosh(x) = cosh(-x)) 3) acosh(1) = 0 4) acosh(1+epsilon) ~= log(1 + sqrt(2*epsilon)) ~= sqrt(2*epsilon) 5) lim(acosh(x),x->+Infinity) = +Infinity (y increasing logarithmically slower than x)
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic arccosine.
  - acosh1p
```
public static double acosh1p(double value)
```
    Much more accurate than acosh(1+value), for arguments (and results) close to zero. acosh1p(-0.0) = -0.0, for homogeneity with sqrt(-0.0) = -0.0, which looks about the same near 0.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Hyperbolic arccosine of (1+value).
  - atanh
```
public static double atanh(double value)
```
    Some properties of atanh(x) = log((1+x)/(1-x))/2: 1) defined on ]-1,1[ 2) result in ]-Infinity,+Infinity[ 3) atanh(-1) = -Infinity (by continuity) 4) atanh(1) = +Infinity (by continuity) 5) atanh(epsilon) ~= epsilon 6) lim(atanh(x),x->1) = +Infinity
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value hyperbolic arctangent.
  - exp
```
public static double exp(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    e^value.
  - expQuick
```
public static double expQuick(double value)
```
    Quick exp, with a max relative error of about 2.94e-2 for |value| < 700.0 or so, and no accuracy at all outside this range. Derived from a note by Nicol N. Schraudolph, IDSIA, 1998.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    e^value.
  - expm1
```
public static double expm1(double value)
```
    Much more accurate than exp(value)-1, for arguments (and results) close to zero.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    e^value-1.
  - log
```
public static double log(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value logarithm (base e).
  - logQuick
```
public static double logQuick(double value)
```
    Quick log, with a max relative error of about 1.9e-3 for values in ]Double.MIN_NORMAL,+Infinity[, and worse accuracy outside this range.
    
    Parameters:
    
    value - A double value, in ]0,+Infinity[ (strictly positive and finite).
    
    Returns:
    
    Value logarithm (base e).
  - log10
```
public static double log10(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value logarithm (base 10).
  - log1p
```
public static double log1p(double value)
```
    Much more accurate than log(1+value), for arguments (and results) close to zero.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Logarithm (base e) of (1+value).
  - pow
```
public static double pow(double value,
                         double power)
```
    1e-13ish accuracy or better on whole double range.
    
    Parameters:
    
    value - A double value.
    
    power - A power.
    
    Returns:
    
    value^power.
  - powQuick
```
public static double powQuick(double value,
                              double power)
```
    Quick pow, with a max relative error of about 1e-2 for value >= Double.MIN_NORMAL and 1e-10 < |value^power| < 1e10, of about 6e-2 for value >= Double.MIN_NORMAL and 1e-40 < |value^power| < 1e40, and worse accuracy otherwise.
    
    Parameters:
    
    value - A double value, in ]0,+Infinity[ (strictly positive and finite).
    
    power - A double value.
    
    Returns:
    
    value^power.
  - powFast
```
public static double powFast(double value,
                             int power)
```
    This treatment is somehow accurate for low values of |power|, and for |power*getExponent(value)| < 1023 or so (to stay away from double extreme magnitudes (large and small)).
    
    Parameters:
    
    value - A double value.
    
    power - A power.
    
    Returns:
    
    value^power.
  - pow2
```
public static float pow2(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    value*value.
  - pow2
```
public static double pow2(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    value*value.
  - pow3
```
public static float pow3(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    value*value*value.
  - pow3
```
public static double pow3(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    value*value*value.
  - sqrt
```
public static double sqrt(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value square root.
  - sqrtQuick
```
public static double sqrtQuick(double value)
```
    Quick sqrt, with with a max relative error of about 3.41e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value square root.
  - invSqrtQuick
```
public static double invSqrtQuick(double value)
```
    Quick inverse of square root, with a max relative error of about 3.44e-2 for values in [Double.MIN_NORMAL,Double.MAX_VALUE], and worse accuracy outside this range. This implementation uses zero step of Newton's method. Here are the max relative errors on [Double.MIN_NORMAL,Double.MAX_VALUE] depending on number of steps, if you want to copy-paste this code and use your own number: n=0: about 3.44e-2 n=1: about 1.75e-3 n=2: about 4.6e-6 n=3: about 3.17e-11 n=4: about 3.92e-16 n=5: about 3.03e-16
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Inverse of value square root.
  - cbrt
```
public static double cbrt(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value cubic root.
  - hypot
```
public static double hypot(double x,
                           double y)
```
    Returns:
    
    sqrt(x^2+y^2) without intermediate overflow or underflow.
  - hypot
```
public static double hypot(double x,
                           double y,
                           double z)
```
    Returns:
    
    sqrt(x^2+y^2+z^2) without intermediate overflow or underflow.
  - floor
```
public static float floor(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    Floor of value.
  - floor
```
public static double floor(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Floor of value.
  - ceil
```
public static float ceil(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    Ceiling of value.
  - ceil
```
public static double ceil(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Ceiling of value.
  - round
```
public static int round(float value)
```
    Might have different semantics than Math.round(float), see bugs 6430675 and 8010430.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value rounded to nearest int, choosing superior int in case two are equally close (i.e. rounding-up).
  - round
```
public static long round(double value)
```
    Might have different semantics than Math.round(double), see bugs 6430675 and 8010430.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value rounded to nearest long, choosing superior long in case two are equally close (i.e. rounding-up).
  - roundEven
```
public static int roundEven(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    Value rounded to nearest int, choosing even int in case two are equally close.
  - roundEven
```
public static long roundEven(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value rounded to nearest long, choosing even long in case two are equally close.
  - rint
```
public static float rint(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    The float mathematical integer closest to the specified value, choosing even one if two are equally close, or respectively NaN, +-Infinity or +-0.0f if the value is any of these.
  - rint
```
public static double rint(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    The double mathematical integer closest to the specified value, choosing even one if two are equally close, or respectively NaN, +-Infinity or +-0.0 if the value is any of these.
  - toRange
```
public static float toRange(float min,
                            float max,
                            float value)
```
    Parameters:
    
    min - A float value.
    
    max - A float value.
    
    value - A float value.
    
    Returns:
    
    min if value < min, max if value > max, value otherwise.
  - toRange
```
public static double toRange(double min,
                             double max,
                             double value)
```
    Parameters:
    
    min - A double value.
    
    max - A double value.
    
    value - A double value.
    
    Returns:
    
    min if value < min, max if value > max, value otherwise.
  - remainder
```
public static double remainder(double dividend,
                               double divisor)
```
    Returns dividend - divisor * n, where n is the mathematical integer closest to dividend/divisor. If dividend/divisor is equally close to surrounding integers, we choose n to be the integer of smallest magnitude, which makes this treatment differ from Math.IEEEremainder(double,double), where n is chosen to be the even integer. Note that the choice of n is not done considering the double approximation of dividend/divisor, because it could cause result to be outside [-|divisor|/2,|divisor|/2] range. The practical effect is that if multiple results would be possible, we always choose the result that is the closest to (and has the same sign as) the dividend. Ex. : - for (-3.0,2.0), this method returns -1.0, whereas Math.IEEEremainder returns 1.0. - for (-5.0,2.0), both this method and Math.IEEEremainder return -1.0. If the remainder is zero, its sign is the same as the sign of the first argument. 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. NB: - Modulo operator (%) returns a value in ]-|divisor|,|divisor|[, which sign is the same as dividend. - As for modulo operator, the sign of the divisor has no effect on the result. - On some architecture, % operator has been observed to return NaN for some subnormal values of divisor, when dividend exponent is 1023, which impacts the correctness of this method.
    
    Parameters:
    
    dividend - Dividend.
    
    divisor - Divisor.
    
    Returns:
    
    Remainder of dividend/divisor, i.e. a value in [-|divisor|/2,|divisor|/2].
  - normalizeMinusPiPi
```
public static double normalizeMinusPiPi(double angle)
```
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    The same angle, in radians, but in [-PI,PI].
  - normalizeMinusPiPiFast
```
public static double normalizeMinusPiPiFast(double angle)
```
    Not accurate for large values.
    
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    The same angle, in radians, but in [-PI,PI].
  - normalizeZeroTwoPi
```
public static double normalizeZeroTwoPi(double angle)
```
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    The same angle, in radians, but in [0,2*PI].
  - normalizeZeroTwoPiFast
```
public static double normalizeZeroTwoPiFast(double angle)
```
    Not accurate for large values.
    
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    The same angle, in radians, but in [0,2*PI].
  - normalizeMinusHalfPiHalfPi
```
public static double normalizeMinusHalfPiHalfPi(double angle)
```
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle value modulo PI, in radians, in [-PI/2,PI/2].
  - normalizeMinusHalfPiHalfPiFast
```
public static double normalizeMinusHalfPiHalfPiFast(double angle)
```
    Not accurate for large values.
    
    Parameters:
    
    angle - Angle in radians.
    
    Returns:
    
    Angle value modulo PI, in radians, in [-PI/2,PI/2].
  - isNaNOrInfinite
```
public static boolean isNaNOrInfinite(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    true if the specified value is NaN or +-Infinity, false otherwise.
  - isNaNOrInfinite
```
public static boolean isNaNOrInfinite(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    true if the specified value is NaN or +-Infinity, false otherwise.
  - getExponent
```
public static int getExponent(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    Value unbiased exponent.
  - getExponent
```
public static int getExponent(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    Value unbiased exponent.
  - signum
```
public static float signum(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    -1.0f if the specified value is < 0, 1.0f if it is > 0, and the value itself if it is NaN or +-0.0f.
  - signum
```
public static double signum(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    -1.0 if the specified value is < 0, 1.0 if it is > 0, and the value itself if it is NaN or +-0.0.
  - signFromBit
```
public static int signFromBit(float value)
```
    Parameters:
    
    value - A float value.
    
    Returns:
    
    -1 if sign bit is 1, 1 if sign bit is 0.
  - signFromBit
```
public static long signFromBit(double value)
```
    Parameters:
    
    value - A double value.
    
    Returns:
    
    -1 if sign bit is 1, 1 if sign bit is 0.
  - copySign
```
public static float copySign(float magnitude,
                             float sign)
```
    A sign of NaN can be interpreted as positive or negative.
    
    Parameters:
    
    magnitude - A float value.
    
    sign - A float value.
    
    Returns:
    
    A value with the magnitude of the first argument, and the sign of the second argument.
  - copySign
```
public static double copySign(double magnitude,
                              double sign)
```
    A sign of NaN can be interpreted as positive or negative.
    
    Parameters:
    
    magnitude - A double value.
    
    sign - A double value.
    
    Returns:
    
    A value with the magnitude of the first argument, and the sign of the second argument.
  - ulp
```
public static float ulp(float value)
```
    The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
    
    Parameters:
    
    value - A float value.
    
    Returns:
    
    The size of an ulp of the specified value, or Float.MIN_VALUE if it is +-0.0f, or +Infinity if it is +-Infinity, or NaN if it is NaN.
  - ulp
```
public static double ulp(double value)
```
    The ULP (Unit in the Last Place) is the distance to the next value larger in magnitude.
    
    Parameters:
    
    value - A double value.
    
    Returns:
    
    The size of an ulp of the specified value, or Double.MIN_VALUE if it is +-0.0, or +Infinity if it is +-Infinity, or NaN if it is NaN.
  - nextAfter
```
public static float nextAfter(float start,
                              double direction)
```
    If both arguments are +-0.0(f), (float)direction is returned. If both arguments are +Infinity or -Infinity, respectively +Infinity or -Infinity is returned.
    
    Parameters:
    
    start - A float value.
    
    direction - A double value.
    
    Returns:
    
    The float adjacent to start towards direction, considering that +(-)Float.MIN_VALUE is adjacent to +(-)0.0f, and that +(-)Float.MAX_VALUE is adjacent to +(-)Infinity, or NaN if any argument is NaN.
  - nextAfter
```
public static double nextAfter(double start,
                               double direction)
```
    If both arguments are +-0.0, direction is returned. If both arguments are +Infinity or -Infinity, respectively +Infinity or -Infinity is returned.
    
    Parameters:
    
    start - A double value.
    
    direction - A double value.
    
    Returns:
    
    The double adjacent to start towards direction, considering that +(-)Double.MIN_VALUE is adjacent to +(-)0.0, and that +(-)Double.MAX_VALUE is adjacent to +(-)Infinity, or NaN if any argument is NaN.
  - nextDown
```
public static float nextDown(float start)
```
    Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
  - nextDown
```
public static double nextDown(double start)
```
    Semantically equivalent to nextAfter(start,Double.NEGATIVE_INFINITY).
  - nextUp
```
public static float nextUp(float start)
```
    Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
  - nextUp
```
public static double nextUp(double start)
```
    Semantically equivalent to nextAfter(start,Double.POSITIVE_INFINITY).
  - scalb
```
public static float scalb(float value,
                          int scaleFactor)
```
    Precision may be lost if the result is subnormal.
    
    Parameters:
    
    value - A float value.
    
    scaleFactor - An int value.
    
    Returns:
    
    value * 2^scaleFactor, or a value equivalent to the specified one if it is NaN, +-Infinity or +-0.0f.
  - scalb
```
public static double scalb(double value,
                           int scaleFactor)
```
    Precision may be lost if the result is subnormal.
    
    Parameters:
    
    value - A double value.
    
    scaleFactor - An int value.
    
    Returns:
    
    value * 2^scaleFactor, or a value equivalent to the specified one if it is NaN, +-Infinity or +-0.0.
  - abs
```
public static float abs(float a)
```
  - abs
```
public static double abs(double a)
```
  - min
```
public static float min(float a,
                        float b)
```
  - min
```
public static double min(double a,
                         double b)
```
  - max
```
public static float max(float a,
                        float b)
```
  - max
```
public static double max(double a,
                         double b)
```
  - IEEEremainder
```
public static double IEEEremainder(double f1,
                                   double f2)
```
  - random
```
public static double random()
```
  - initTables
```
public static void initTables()
```
    Ensures that all look-up tables are initialized - otherwise they are initialized lazily.
  - log2
```
public static int log2(int value)
```
    Parameters:
    
    value - An integer value in [1,Integer.MAX_VALUE].
    
    Returns:
    
    The integer part of the logarithm, in base 2, of the specified value, i.e. a result in [0,30]
    
    Throws:
    
    IllegalArgumentException - if the specified value is <= 0.
  - log2
```
public static int log2(long value)
```
    Parameters:
    
    value - An integer value in [1,Long.MAX_VALUE].
    
    Returns:
    
    The integer part of the logarithm, in base 2, of the specified value, i.e. a result in [0,62]
    
    Throws:
    
    IllegalArgumentException - if the specified value is <= 0.
  - twoPow
```
public static double twoPow(int power)
```
    Returns the exact result, provided it's in double range, i.e. if power is in [-1074,1023].
    
    Parameters:
    
    power - An int power.
    
    Returns:
    
    2^power as a double, or +-Infinity in case of overflow.
  - pow2
```
public static int pow2(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    value*value.
  - pow2
```
public static long pow2(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    value*value.
  - pow3
```
public static int pow3(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    value*value*value.
  - pow3
```
public static long pow3(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    value*value*value.
  - abs
```
public static int abs(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The absolute value, except if value is Integer.MIN_VALUE, for which it returns Integer.MIN_VALUE.
  - abs
```
public static long abs(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The absolute value, except if value is Long.MIN_VALUE, for which it returns Long.MIN_VALUE.
  - toIntExact
```
public static int toIntExact(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The specified value as int.
    
    Throws:
    
    ArithmeticException - if the specified value is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
  - toInt
```
public static int toInt(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The closest int value in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
  - toRange
```
public static int toRange(int min,
                          int max,
                          int value)
```
    Parameters:
    
    min - An int value.
    
    max - An int value.
    
    value - An int value.
    
    Returns:
    
    minValue if value < minValue, maxValue if value > maxValue, value otherwise.
  - toRange
```
public static long toRange(long min,
                           long max,
                           long value)
```
    Parameters:
    
    min - A long value.
    
    max - A long value.
    
    value - A long value.
    
    Returns:
    
    min if value < min, max if value > max, value otherwise.
  - incrementExact
```
public static int incrementExact(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The argument incremented by one.
    
    Throws:
    
    ArithmeticException - if the mathematical result is not in int range.
  - incrementExact
```
public static long incrementExact(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The argument incremented by one.
    
    Throws:
    
    ArithmeticException - if the mathematical result is not in long range.
  - incrementBounded
```
public static int incrementBounded(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The argument incremented by one, or the argument if the mathematical result is not in int range.
  - incrementBounded
```
public static long incrementBounded(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The argument incremented by one, or the argument if the mathematical result is not in long range.
  - decrementExact
```
public static int decrementExact(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The argument decremented by one.
    
    Throws:
    
    ArithmeticException - if the mathematical result is not in int range.
  - decrementExact
```
public static long decrementExact(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The argument decremented by one.
    
    Throws:
    
    ArithmeticException - if the mathematical result is not in long range.
  - decrementBounded
```
public static int decrementBounded(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The argument decremented by one, or the argument if the mathematical result is not in int range.
  - decrementBounded
```
public static long decrementBounded(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The argument decremented by one, or the argument if the mathematical result is not in long range.
  - negateExact
```
public static int negateExact(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The argument negated.
    
    Throws:
    
    ArithmeticException - if the mathematical result is not in int range.
  - negateExact
```
public static long negateExact(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The argument negated.
    
    Throws:
    
    ArithmeticException - if the mathematical result is not in long range.
  - negateBounded
```
public static int negateBounded(int value)
```
    Parameters:
    
    value - An int value.
    
    Returns:
    
    The argument negated, or Integer.MAX_VALUE if the argument is Integer.MIN_VALUE.
  - negateBounded
```
public static long negateBounded(long value)
```
    Parameters:
    
    value - A long value.
    
    Returns:
    
    The argument negated, or Long.MAX_VALUE if the argument is Long.MIN_VALUE.
  - addExact
```
public static int addExact(int a,
                           int b)
```
    Parameters:
    
    a - An int value.
    
    b - An int value.
    
    Returns:
    
    The mathematical result of a+b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a+b is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
  - addExact
```
public static long addExact(long a,
                            long b)
```
    Parameters:
    
    a - A long value.
    
    b - A long value.
    
    Returns:
    
    The mathematical result of a+b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a+b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
  - addBounded
```
public static int addBounded(int a,
                             int b)
```
    Parameters:
    
    a - An int value.
    
    b - An int value.
    
    Returns:
    
    The int value of [Integer.MIN_VALUE,Integer.MAX_VALUE] range which is the closest to mathematical result of a+b.
  - addBounded
```
public static long addBounded(long a,
                              long b)
```
    Parameters:
    
    a - A long value.
    
    b - A long value.
    
    Returns:
    
    The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a+b.
  - subtractExact
```
public static int subtractExact(int a,
                                int b)
```
    Parameters:
    
    a - An int value.
    
    b - An int value.
    
    Returns:
    
    The mathematical result of a-b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a-b is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
  - subtractExact
```
public static long subtractExact(long a,
                                 long b)
```
    Parameters:
    
    a - A long value.
    
    b - A long value.
    
    Returns:
    
    The mathematical result of a-b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a-b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
  - subtractBounded
```
public static int subtractBounded(int a,
                                  int b)
```
    Parameters:
    
    a - An int value.
    
    b - An int value.
    
    Returns:
    
    The int value of [Integer.MIN_VALUE,Integer.MAX_VALUE] range which is the closest to mathematical result of a-b.
  - subtractBounded
```
public static long subtractBounded(long a,
                                   long b)
```
    Parameters:
    
    a - A long value.
    
    b - A long value.
    
    Returns:
    
    The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a-b.
  - multiplyExact
```
public static int multiplyExact(int a,
                                int b)
```
    Parameters:
    
    a - An int value.
    
    b - An int value.
    
    Returns:
    
    The mathematical result of a*b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a*b is not in [Integer.MIN_VALUE,Integer.MAX_VALUE] range.
  - multiplyExact
```
public static long multiplyExact(long a,
                                 int b)
```
    Parameters:
    
    a - A long value.
    
    b - An int value.
    
    Returns:
    
    The mathematical result of a*b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a*b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
  - multiplyExact
```
public static long multiplyExact(long a,
                                 long b)
```
    Parameters:
    
    a - A long value.
    
    b - A long value.
    
    Returns:
    
    The mathematical result of a*b.
    
    Throws:
    
    ArithmeticException - if the mathematical result of a*b is not in [Long.MIN_VALUE,Long.MAX_VALUE] range.
  - multiplyBounded
```
public static int multiplyBounded(int a,
                                  int b)
```
    Parameters:
    
    a - An int value.
    
    b - An int value.
    
    Returns:
    
    The int value of [Integer.MIN_VALUE,Integer.MAX_VALUE] range which is the closest to mathematical result of a*b.
  - multiplyBounded
```
public static long multiplyBounded(long a,
                                   int b)
```
    Parameters:
    
    a - A long value.
    
    b - An int value.
    
    Returns:
    
    The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a*b.
  - multiplyBounded
```
public static long multiplyBounded(long a,
                                   long b)
```
    Parameters:
    
    a - A long value.
    
    b - A long value.
    
    Returns:
    
    The long value of [Long.MIN_VALUE,Long.MAX_VALUE] range which is the closest to mathematical result of a*b.
  - multiplyFull
```
public static long multiplyFull(int x,
                                int y)
```
    Parameters:
    
    x - An int value.
    
    y - An int value.
    
    Returns:
    
    The mathematical product as a long.
  - multiplyHigh
```
public static long multiplyHigh(long x,
                                long y)
```
    Parameters:
    
    x - A long value.
    
    y - A long value.
    
    Returns:
    
    The most significant 64 bits of the 128-bit product of two 64-bit factors.
  - floorDiv
```
public static int floorDiv(int x,
                           int y)
```
    Returns the largest int <= dividend/divisor. Unlike "/" operator, which rounds towards 0, this division rounds towards -Infinity (which give different result when the exact result is negative).
    
    Parameters:
    
    x - The dividend.
    
    y - The divisor.
    
    Returns:
    
    The largest int <= dividend/divisor, unless dividend is Integer.MIN_VALUE and divisor is -1, in which case Integer.MIN_VALUE is returned.
    
    Throws:
    
    ArithmeticException - if the divisor is zero.
  - floorDiv
```
public static long floorDiv(long x,
                            int y)
```
    Returns the largest long <= dividend/divisor. Unlike "/" operator, which rounds towards 0, this division rounds towards -Infinity (which give different result when the exact result is negative).
    
    Parameters:
    
    x - The dividend.
    
    y - The divisor.
    
    Returns:
    
    The largest long <= dividend/divisor, unless dividend is Long.MIN_VALUE and divisor is -1, in which case Long.MIN_VALUE is returned.
    
    Throws:
    
    ArithmeticException - if the divisor is zero.
  - floorDiv
```
public static long floorDiv(long x,
                            long y)
```
    Returns the largest long <= dividend/divisor. Unlike "/" operator, which rounds towards 0, this division rounds towards -Infinity (which give different result when the exact result is negative).
    
    Parameters:
    
    x - The dividend.
    
    y - The divisor.
    
    Returns:
    
    The largest long <= dividend/divisor, unless dividend is Long.MIN_VALUE and divisor is -1, in which case Long.MIN_VALUE is returned.
    
    Throws:
    
    ArithmeticException - if the divisor is zero.
  - floorMod
```
public static int floorMod(int x,
                           int y)
```
    Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[. The relationship between floorMod and floorDiv is the same than between "%" and "/".
    
    Parameters:
    
    x - The dividend.
    
    y - The divisor.
    
    Returns:
    
    The floor modulus, i.e. "x - (floorDiv(x, y) * y)".
    
    Throws:
    
    ArithmeticException - if the divisor is zero.
  - floorMod
```
public static int floorMod(long x,
                           int y)
```
    Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[. The relationship between floorMod and floorDiv is the same than between "%" and "/".
    
    Parameters:
    
    x - The dividend.
    
    y - The divisor.
    
    Returns:
    
    The floor modulus, i.e. "x - (floorDiv(x, y) * y)".
    
    Throws:
    
    ArithmeticException - if the divisor is zero.
  - floorMod
```
public static long floorMod(long x,
                            long y)
```
    Returns the floor modulus, which is "x - floorDiv(x,y) * y", has the same sign as y, and is in ]-abs(y),abs(y)[. The relationship between floorMod and floorDiv is the same than between "%" and "/".
    
    Parameters:
    
    x - The dividend.
    
    y - The divisor.
    
    Returns:
    
    The floor modulus, i.e. "x - (floorDiv(x, y) * y)".
    
    Throws:
    
    ArithmeticException - if the divisor is zero.
  - min
```
public static int min(int a,
                      int b)
```
  - min
```
public static long min(long a,
                       long b)
```
  - max
```
public static int max(int a,
                      int b)
```
  - max
```
public static long max(long a,
                       long b)
```

Class FastMath

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

E

PI

PI_SUP

Method Detail

sin

sinQuick

cos

cosQuick

sinAndCos

tan

asin

asinInRange

acos

acosInRange

atan

atan2

toRadians

toDegrees

toRadians

toDegrees

toDMS

isInClockwiseDomain

sinh

cosh

coshm1

sinhAndCosh

tanh

asinh

acosh

acosh1p

atanh

exp

expQuick

expm1

log

logQuick

log10

log1p

pow

powQuick

powFast

pow2

pow2

pow3

pow3

sqrt

sqrtQuick

invSqrtQuick

cbrt

hypot

hypot

floor

floor

ceil

ceil

round

round

roundEven

roundEven

rint

rint

toRange

toRange

remainder

normalizeMinusPiPi

normalizeMinusPiPiFast

normalizeZeroTwoPi

normalizeZeroTwoPiFast

normalizeMinusHalfPiHalfPi

normalizeMinusHalfPiHalfPiFast

isNaNOrInfinite

isNaNOrInfinite

getExponent

getExponent

signum