FastMath (Commons Math 2.2 API)

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org.apache.commons.math.util
Class FastMath

java.lang.Object
  org.apache.commons.math.util.FastMath

public class FastMath
extends Object
extends Object

Faster, more accurate, portable alternative to StrictMath.

Additionally implements the following methods not found in StrictMath:

The following methods are found in StrictMath since 1.6 only

Since:: 2.2
Version:: $Revision: 1074294 $ $Date: 2011-02-24 22:18:59 +0100 (jeu. 24 fÃ©vr. 2011) $

Field Summary
`static double`	`E` Napier's constant e, base of the natural logarithm.
`static double`	`PI` Archimede's constant PI, ratio of circle circumference to diameter.

Method Summary
`static double`	`abs(double x)` Absolute value.
`static float`	`abs(float x)` Absolute value.
`static int`	`abs(int x)` Absolute value.
`static long`	`abs(long x)` Absolute value.
`static double`	`acos(double x)` Compute the arc cosine of a number.
`static double`	`acosh(double a)` Compute the inverse hyperbolic cosine of a number.
`static double`	`asin(double x)` Compute the arc sine of a number.
`static double`	`asinh(double a)` Compute the inverse hyperbolic sine of a number.
`static double`	`atan(double x)` Arctangent function
`static double`	`atan2(double y, double x)` Two arguments arctangent function
`static double`	`atanh(double a)` Compute the inverse hyperbolic tangent of a number.
`static double`	`cbrt(double x)` Compute the cubic root of a number.
`static double`	`ceil(double x)` Get the smallest whole number larger than x.
`static double`	`copySign(double magnitude, double sign)` Returns the first argument with the sign of the second argument.
`static float`	`copySign(float magnitude, float sign)` Returns the first argument with the sign of the second argument.
`static double`	`cos(double x)` Cosine function
`static double`	`cosh(double x)` Compute the hyperbolic cosine of a number.
`static double`	`exp(double x)` Exponential function.
`static double`	`expm1(double x)` Compute exp(x) - 1
`static double`	`floor(double x)` Get the largest whole number smaller than x.
`static int`	`getExponent(double d)` Return the exponent of a double number, removing the bias.
`static int`	`getExponent(float f)` Return the exponent of a float number, removing the bias.
`static double`	`hypot(double x, double y)` Returns the hypotenuse of a triangle with sides `x` and `y` - sqrt(x² +y²) avoiding intermediate overflow or underflow.
`static double`	`IEEEremainder(double dividend, double divisor)` Computes the remainder as prescribed by the IEEE 754 standard.
`static double`	`log(double x)` Natural logarithm.
`static double`	`log10(double x)` Compute the base 10 logarithm.
`static double`	`log1p(double x)` Compute log(1 + x).
`static double`	`max(double a, double b)` Compute the maximum of two values
`static float`	`max(float a, float b)` Compute the maximum of two values
`static int`	`max(int a, int b)` Compute the maximum of two values
`static long`	`max(long a, long b)` Compute the maximum of two values
`static double`	`min(double a, double b)` Compute the minimum of two values
`static float`	`min(float a, float b)` Compute the minimum of two values
`static int`	`min(int a, int b)` Compute the minimum of two values
`static long`	`min(long a, long b)` Compute the minimum of two values
`static double`	`nextAfter(double d, double direction)` Get the next machine representable number after a number, moving in the direction of another number.
`static float`	`nextAfter(float f, double direction)` Get the next machine representable number after a number, moving in the direction of another number.
`static double`	`nextUp(double a)` Compute next number towards positive infinity.
`static float`	`nextUp(float a)` Compute next number towards positive infinity.
`static double`	`pow(double x, double y)` Power function.
`static double`	`random()` Returns a pseudo-random number between 0.0 and 1.0.
`static double`	`rint(double x)` Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
`static long`	`round(double x)` Get the closest long to x.
`static int`	`round(float x)` Get the closest int to x.
`static double`	`scalb(double d, int n)` Multiply a double number by a power of 2.
`static float`	`scalb(float f, int n)` Multiply a float number by a power of 2.
`static double`	`signum(double a)` Compute the signum of a number.
`static float`	`signum(float a)` Compute the signum of a number.
`static double`	`sin(double x)` Sine function.
`static double`	`sinh(double x)` Compute the hyperbolic sine of a number.
`static double`	`sqrt(double a)` Compute the square root of a number.
`static double`	`tan(double x)` Tangent function
`static double`	`tanh(double x)` Compute the hyperbolic tangent of a number.
`static double`	`toDegrees(double x)` Convert radians to degrees, with error of less than 0.5 ULP
`static double`	`toRadians(double x)` Convert degrees to radians, with error of less than 0.5 ULP
`static double`	`ulp(double x)` Compute least significant bit (Unit in Last Position) for a number.
`static float`	`ulp(float x)` Compute least significant bit (Unit in Last Position) for a number.

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

Field Detail

PI

public static final double PI

Archimede's constant PI, ratio of circle circumference to diameter.

See Also:: Constant Field Values

E

public static final double E

Napier's constant e, base of the natural logarithm.

See Also:: Constant Field Values

Method Detail

sqrt

public static double sqrt(double a)

Compute the square root of a number.

Note: this implementation currently delegates to Math.sqrt(double)

Parameters:: a - number on which evaluation is done
Returns:: square root of a

cosh

public static double cosh(double x)

Compute the hyperbolic cosine of a number.

Parameters:: x - number on which evaluation is done
Returns:: hyperbolic cosine of x

sinh

public static double sinh(double x)

Compute the hyperbolic sine of a number.

Parameters:: x - number on which evaluation is done
Returns:: hyperbolic sine of x

tanh

public static double tanh(double x)

Compute the hyperbolic tangent of a number.

Parameters:: x - number on which evaluation is done
Returns:: hyperbolic tangent of x

acosh

public static double acosh(double a)

Compute the inverse hyperbolic cosine of a number.

Parameters:: a - number on which evaluation is done
Returns:: inverse hyperbolic cosine of a

asinh

public static double asinh(double a)

Compute the inverse hyperbolic sine of a number.

Parameters:: a - number on which evaluation is done
Returns:: inverse hyperbolic sine of a

atanh

public static double atanh(double a)

Compute the inverse hyperbolic tangent of a number.

Parameters:: a - number on which evaluation is done
Returns:: inverse hyperbolic tangent of a

signum

public static double signum(double a)

Compute the signum of a number. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise

Parameters:: a - number on which evaluation is done
Returns:: -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

signum

public static float signum(float a)

Compute the signum of a number. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise

Parameters:: a - number on which evaluation is done
Returns:: -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

nextUp

public static double nextUp(double a)

Compute next number towards positive infinity.

Parameters:: a - number to which neighbor should be computed
Returns:: neighbor of a towards positive infinity

nextUp

public static float nextUp(float a)

Compute next number towards positive infinity.

Parameters:: a - number to which neighbor should be computed
Returns:: neighbor of a towards positive infinity

random

public static double random()

Returns a pseudo-random number between 0.0 and 1.0.

Note: this implementation currently delegates to Math.random()

Returns:: a random number between 0.0 and 1.0

exp

public static double exp(double x)

Exponential function. Computes exp(x), function result is nearly rounded. It will be correctly rounded to the theoretical value for 99.9% of input values, otherwise it will have a 1 UPL error. Method: Lookup intVal = exp(int(x)) Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 ); Compute z as the exponential of the remaining bits by a polynomial minus one exp(x) = intVal * fracVal * (1 + z) Accuracy: Calculation is done with 63 bits of precision, so result should be correctly rounded for 99.9% of input values, with less than 1 ULP error otherwise.

Parameters:: x - a double
Returns:: double e^x

expm1

public static double expm1(double x)

Compute exp(x) - 1

Parameters:: x - number to compute shifted exponential
Returns:: exp(x) - 1

log

public static double log(double x)

Natural logarithm.

Parameters:: x - a double
Returns:: log(x)

log1p

public static double log1p(double x)

Compute log(1 + x).

Parameters:: x - a number
Returns:: log(1 + x)

log10

public static double log10(double x)

Compute the base 10 logarithm.

Parameters:: x - a number
Returns:: log10(x)

pow

public static double pow(double x,
                         double y)

Power function. Compute x^y.

Parameters:: x - a double; y - a double
Returns:: double

sin

public static double sin(double x)

Sine function.

Parameters:: x - a number
Returns:: sin(x)

cos

public static double cos(double x)

Cosine function

Parameters:: x - a number
Returns:: cos(x)

tan

public static double tan(double x)

Tangent function

Parameters:: x - a number
Returns:: tan(x)

atan

public static double atan(double x)

Arctangent function

Parameters:: x - a number
Returns:: atan(x)

atan2

public static double atan2(double y,
                           double x)

Two arguments arctangent function

Parameters:: y - ordinate; x - abscissa
Returns:: phase angle of point (x,y) between -PI and PI

asin

public static double asin(double x)

Compute the arc sine of a number.

Parameters:: x - number on which evaluation is done
Returns:: arc sine of x

acos

public static double acos(double x)

Compute the arc cosine of a number.

Parameters:: x - number on which evaluation is done
Returns:: arc cosine of x

cbrt

public static double cbrt(double x)

Compute the cubic root of a number.

Parameters:: x - number on which evaluation is done
Returns:: cubic root of x

toRadians

public static double toRadians(double x)

Convert degrees to radians, with error of less than 0.5 ULP

Parameters:: x - angle in degrees
Returns:: x converted into radians

toDegrees

public static double toDegrees(double x)

Convert radians to degrees, with error of less than 0.5 ULP

Parameters:: x - angle in radians
Returns:: x converted into degrees

abs

public static int abs(int x)

Absolute value.

Parameters:: x - number from which absolute value is requested
Returns:: abs(x)

abs

public static long abs(long x)

Absolute value.

Parameters:: x - number from which absolute value is requested
Returns:: abs(x)

abs

public static float abs(float x)

Absolute value.

Parameters:: x - number from which absolute value is requested
Returns:: abs(x)

abs

public static double abs(double x)

Absolute value.

Parameters:: x - number from which absolute value is requested
Returns:: abs(x)

ulp

public static double ulp(double x)

Compute least significant bit (Unit in Last Position) for a number.

Parameters:: x - number from which ulp is requested
Returns:: ulp(x)

ulp

public static float ulp(float x)

Compute least significant bit (Unit in Last Position) for a number.

Parameters:: x - number from which ulp is requested
Returns:: ulp(x)

scalb

public static double scalb(double d,
                           int n)

Multiply a double number by a power of 2.

Parameters:: d - number to multiply; n - power of 2
Returns:: d × 2ⁿ

scalb

public static float scalb(float f,
                          int n)

Multiply a float number by a power of 2.

Parameters:: f - number to multiply; n - power of 2
Returns:: f × 2ⁿ

nextAfter

public static double nextAfter(double d,
                               double direction)

Get the next machine representable number after a number, moving in the direction of another number.

The ordering is as follows (increasing):

-INFINITY
-MAX_VALUE
-MIN_VALUE
-0.0
+0.0
+MIN_VALUE
+MAX_VALUE
+INFINITY

If arguments compare equal, then the second argument is returned.

If direction is greater than d, the smallest machine representable number strictly greater than d is returned; if less, then the largest representable number strictly less than d is returned.

If d is infinite and direction does not bring it back to finite numbers, it is returned unchanged.

Parameters:: d - base number; direction - (the only important thing is whether direction is greater or smaller than d)
Returns:: the next machine representable number in the specified direction

nextAfter

public static float nextAfter(float f,
                              double direction)

Get the next machine representable number after a number, moving in the direction of another number.

The ordering is as follows (increasing):

-INFINITY
-MAX_VALUE
-MIN_VALUE
-0.0
+0.0
+MIN_VALUE
+MAX_VALUE
+INFINITY

If arguments compare equal, then the second argument is returned.

If direction is greater than f, the smallest machine representable number strictly greater than f is returned; if less, then the largest representable number strictly less than f is returned.

If f is infinite and direction does not bring it back to finite numbers, it is returned unchanged.

Parameters:: f - base number; direction - (the only important thing is whether direction is greater or smaller than f)
Returns:: the next machine representable number in the specified direction

floor

public static double floor(double x)

Get the largest whole number smaller than x.

Parameters:: x - number from which floor is requested
Returns:: a double number f such that f is an integer f <= x < f + 1.0

ceil

public static double ceil(double x)

Get the smallest whole number larger than x.

Parameters:: x - number from which ceil is requested
Returns:: a double number c such that c is an integer c - 1.0 < x <= c

rint

public static double rint(double x)

Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.

Parameters:: x - number from which nearest whole number is requested
Returns:: a double number r such that r is an integer r - 0.5 <= x <= r + 0.5

round

public static long round(double x)

Get the closest long to x.

Parameters:: x - number from which closest long is requested
Returns:: closest long to x

round

public static int round(float x)

Get the closest int to x.

Parameters:: x - number from which closest int is requested
Returns:: closest int to x

min

public static int min(int a,
                      int b)

Compute the minimum of two values

Parameters:: a - first value; b - second value
Returns:: a if a is lesser or equal to b, b otherwise

min

public static long min(long a,
                       long b)

Compute the minimum of two values

Parameters:: a - first value; b - second value
Returns:: a if a is lesser or equal to b, b otherwise

min

public static float min(float a,
                        float b)

Compute the minimum of two values

Parameters:: a - first value; b - second value
Returns:: a if a is lesser or equal to b, b otherwise

min

public static double min(double a,
                         double b)

Compute the minimum of two values

Parameters:: a - first value; b - second value
Returns:: a if a is lesser or equal to b, b otherwise

max

public static int max(int a,
                      int b)

Compute the maximum of two values

Parameters:: a - first value; b - second value
Returns:: b if a is lesser or equal to b, a otherwise

max

public static long max(long a,
                       long b)

Compute the maximum of two values

Parameters:: a - first value; b - second value
Returns:: b if a is lesser or equal to b, a otherwise

max

public static float max(float a,
                        float b)

Compute the maximum of two values

Parameters:: a - first value; b - second value
Returns:: b if a is lesser or equal to b, a otherwise

max

public static double max(double a,
                         double b)

Compute the maximum of two values

Parameters:: a - first value; b - second value
Returns:: b if a is lesser or equal to b, a otherwise

hypot

public static double hypot(double x,
                           double y)

Returns the hypotenuse of a triangle with sides x and y - sqrt(x² +y²)
avoiding intermediate overflow or underflow.

If either argument is infinite, then the result is positive infinity.
else, if either argument is NaN then the result is NaN.

Parameters:: x - a value; y - a value
Returns:: sqrt(x² +y²)

IEEEremainder

public static double IEEEremainder(double dividend,
                                   double divisor)

Computes the remainder as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to x - y*n where n is the mathematical integer closest to the exact mathematical value of the quotient x/y. If two mathematical integers are equally close to x/y then n is the integer that is even.

If either operand is NaN, the result is NaN.
If the result is not NaN, the sign of the result equals the sign of the dividend.
If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.
If the dividend is finite and the divisor is an infinity, the result equals the dividend.
If the dividend is a zero and the divisor is finite, the result equals the dividend.

Note: this implementation currently delegates to StrictMath.IEEEremainder(double, double)

Parameters:: dividend - the number to be divided; divisor - the number by which to divide
Returns:: the remainder, rounded

copySign

public static double copySign(double magnitude,
                              double sign)

Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.

Parameters:: magnitude - the value to return; sign - the sign for the returned value
Returns:: the magnitude with the same sign as the sign argument

copySign

public static float copySign(float magnitude,
                             float sign)

Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.

Parameters:: magnitude - the value to return; sign - the sign for the returned value
Returns:: the magnitude with the same sign as the sign argument

getExponent

public static int getExponent(double d)

Return the exponent of a double number, removing the bias.

For double numbers of the form 2^x, the unbiased exponent is exactly x.

Parameters:: d - number from which exponent is requested
Returns:: exponent for d in IEEE754 representation, without bias

getExponent

public static int getExponent(float f)

Return the exponent of a float number, removing the bias.

For float numbers of the form 2^x, the unbiased exponent is exactly x.

Parameters:: f - number from which exponent is requested
Returns:: exponent for d in IEEE754 representation, without bias

Overview

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PREV CLASS NEXT CLASS

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SUMMARY: NESTED | FIELD | CONSTR | METHOD

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org.apache.commons.math.util Class FastMath

PI

E

sqrt

cosh

sinh

tanh

acosh

asinh

atanh

signum

signum

nextUp

nextUp

random

exp

expm1

log

log1p

log10

pow

sin

cos

tan

atan

atan2

asin

acos

cbrt

toRadians

toDegrees

abs

abs

abs

abs

ulp

ulp

scalb

scalb

nextAfter

nextAfter

floor

ceil

rint

round

round

min

min

min

min

max

max

max

max

hypot

IEEEremainder

copySign

copySign

getExponent

getExponent

org.apache.commons.math.util
Class FastMath