Static Public Member Functions
static double	sqrt (final double a)

static double	cosh (double x)

static double	sinh (double x)

static double	tanh (double x)

static double	acosh (final double a)

static double	asinh (double a)

static double	atanh (double a)

static double	signum (final double a)

static float	signum (final float a)

static double	nextUp (final double a)

static float	nextUp (final float a)

static double	random ()

static double	exp (double x)

static double	expm1 (double x)

static double	log (final double x)

static double	log1p (final double x)

static double	log10 (final double x)

static double	pow (double x, double y)

static double	sin (double x)

static double	cos (double x)

static double	tan (double x)

static double	atan (double x)

static double	atan2 (double y, double x)

static double	asin (double x)

static double	acos (double x)

static double	cbrt (double x)

static double	toRadians (double x)

static double	toDegrees (double x)

static int	abs (final int x)

static long	abs (final long x)

static float	abs (final float x)

static double	abs (double x)

static double	ulp (double x)

static float	ulp (float x)

static double	scalb (final double d, final int n)

static float	scalb (final float f, final int n)

static double	nextAfter (double d, double direction)

static float	nextAfter (final float f, final double direction)

static double	floor (double x)

static double	ceil (double x)

static double	rint (double x)

static long	round (double x)

static int	round (final float x)

static int	min (final int a, final int b)

static long	min (final long a, final long b)

static float	min (final float a, final float b)

static double	min (final double a, final double b)

static int	max (final int a, final int b)

static long	max (final long a, final long b)

static float	max (final float a, final float b)

static double	max (final double a, final double b)

static double	hypot (final double x, final double y)

static double	IEEEremainder (double dividend, double divisor)

static double	copySign (double magnitude, double sign)

static float	copySign (float magnitude, float sign)

static int	getExponent (final double d)

static int	getExponent (final float f)

Static Public Attributes
static final double	PI = 105414357.0 / 33554432.0 + 1.984187159361080883e-9

static final double	E = 2850325.0 / 1048576.0 + 8.254840070411028747e-8

static final double	SAFE_MIN = 0x1.0p-1022

Detailed Description

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

Member Function Documentation

static int sprites.maths.FastMath.abs ( final int x )

static

Absolute value.

Parameters

x	number from which absolute value is requested

Returns: abs(x)

static long sprites.maths.FastMath.abs ( final long x )

static

Absolute value.

Parameters

x	number from which absolute value is requested

Returns: abs(x)

static float sprites.maths.FastMath.abs ( final float x )

static

Absolute value.

Parameters

x	number from which absolute value is requested

Returns: abs(x)

static double sprites.maths.FastMath.abs ( double x )

static

Absolute value.

Parameters

x	number from which absolute value is requested

Returns: abs(x)

static double sprites.maths.FastMath.acos ( double x )

static

Compute the arc cosine of a number.

Parameters

x	number on which evaluation is done

Returns: arc cosine of x

static double sprites.maths.FastMath.acosh ( final double a )

static

Compute the inverse hyperbolic cosine of a number.

Parameters

a	number on which evaluation is done

Returns: inverse hyperbolic cosine of a

static double sprites.maths.FastMath.asin ( double x )

static

Compute the arc sine of a number.

Parameters

x	number on which evaluation is done

Returns: arc sine of x

static double sprites.maths.FastMath.asinh ( double a )

static

Compute the inverse hyperbolic sine of a number.

Parameters

a	number on which evaluation is done

Returns: inverse hyperbolic sine of a

static double sprites.maths.FastMath.atan ( double x )

static

Arctangent function

Parameters

x a number

Returns: atan(x)

static double sprites.maths.FastMath.atan2	(	double	y,
		double	x
	)

static

Two arguments arctangent function

Parameters

y	ordinate
x	abscissa

Returns: phase angle of point (x,y) between
-PI

and
PI

static double sprites.maths.FastMath.atanh ( double a )

static

Compute the inverse hyperbolic tangent of a number.

Parameters

a	number on which evaluation is done

Returns: inverse hyperbolic tangent of a

static double sprites.maths.FastMath.cbrt ( double x )

static

Compute the cubic root of a number.

Parameters

x	number on which evaluation is done

Returns: cubic root of x

static double sprites.maths.FastMath.ceil ( double x )

static

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

static double sprites.maths.FastMath.copySign	(	double	magnitude,
		double	sign
	)

static

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

static float sprites.maths.FastMath.copySign	(	float	magnitude,
		float	sign
	)

static

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

static double sprites.maths.FastMath.cos ( double x )

static

Cosine function

Parameters

x a number

Returns: cos(x)

static double sprites.maths.FastMath.cosh ( double x )

static

Compute the hyperbolic cosine of a number.

Parameters

x	number on which evaluation is done

Returns: hyperbolic cosine of x

static double sprites.maths.FastMath.exp ( double x )

static

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

static double sprites.maths.FastMath.expm1 ( double x )

static

Compute exp(x) - 1

Parameters

x	number to compute shifted exponential

Returns: exp(x) - 1

static double sprites.maths.FastMath.floor ( double x )

static

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

static int sprites.maths.FastMath.getExponent ( final double d )

static

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

static int sprites.maths.FastMath.getExponent ( final float f )

static

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

static double sprites.maths.FastMath.hypot	(	final double	x,
		final double	y
	)

static

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)

static double sprites.maths.FastMath.IEEEremainder	(	double	dividend,
		double	divisor
	)

static

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

Parameters

dividend	the number to be divided
divisor	the number by which to divide

Returns: the remainder, rounded

static double sprites.maths.FastMath.log ( final double x )

static

Natural logarithm.

Parameters

x a double

Returns: log(x)

static double sprites.maths.FastMath.log10 ( final double x )

static

Compute the base 10 logarithm.

Parameters

x a number

Returns: log10(x)

static double sprites.maths.FastMath.log1p ( final double x )

static

Compute log(1 + x).

Parameters

x a number

Returns: log(1 + x)

static int sprites.maths.FastMath.max	(	final int	a,
		final int	b
	)

static

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

static long sprites.maths.FastMath.max	(	final long	a,
		final long	b
	)

static

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

static float sprites.maths.FastMath.max	(	final float	a,
		final float	b
	)

static

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

static double sprites.maths.FastMath.max	(	final double	a,
		final double	b
	)

static

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

static int sprites.maths.FastMath.min	(	final int	a,
		final int	b
	)

static

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

static long sprites.maths.FastMath.min	(	final long	a,
		final long	b
	)

static

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

static float sprites.maths.FastMath.min	(	final float	a,
		final float	b
	)

static

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

static double sprites.maths.FastMath.min	(	final double	a,
		final double	b
	)

static

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

static double sprites.maths.FastMath.nextAfter	(	double	d,
		double	direction
	)

static

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

static float sprites.maths.FastMath.nextAfter	(	final float	f,
		final double	direction
	)

static

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

static double sprites.maths.FastMath.nextUp ( final double a )

static

Compute next number towards positive infinity.

Parameters

a	number to which neighbor should be computed

Returns: neighbor of a towards positive infinity

static float sprites.maths.FastMath.nextUp ( final float a )

static

Compute next number towards positive infinity.

Parameters

a	number to which neighbor should be computed

Returns: neighbor of a towards positive infinity

static double sprites.maths.FastMath.pow	(	double	x,
		double	y
	)

static

Power function. Compute x^y.

Parameters

x	a double
y	a double

Returns: double

static double sprites.maths.FastMath.random ( )

static

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

static double sprites.maths.FastMath.rint ( double x )

static

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

static long sprites.maths.FastMath.round ( double x )

static

Get the closest long to x.

Parameters

x	number from which closest long is requested

Returns: closest long to x

static int sprites.maths.FastMath.round ( final float x )

static

Get the closest int to x.

Parameters

x	number from which closest int is requested

Returns: closest int to x

static double sprites.maths.FastMath.scalb	(	final double	d,
		final int	n
	)

static

Multiply a double number by a power of 2.

Parameters

d	number to multiply
n	power of 2

Returns: d × 2ⁿ

static float sprites.maths.FastMath.scalb	(	final float	f,
		final int	n
	)

static

Multiply a float number by a power of 2.

Parameters

f	number to multiply
n	power of 2

Returns: f × 2ⁿ

static double sprites.maths.FastMath.signum ( final double a )

static

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

static float sprites.maths.FastMath.signum ( final float a )

static

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

static double sprites.maths.FastMath.sin ( double x )

static

Sine function.

Parameters

x a number

Returns: sin(x)

static double sprites.maths.FastMath.sinh ( double x )

static

Compute the hyperbolic sine of a number.

Parameters

x	number on which evaluation is done

Returns: hyperbolic sine of x

static double sprites.maths.FastMath.sqrt ( final double a )

static

Compute the square root of a number.

Note: this implementation currently delegates to Math#sqrt

Parameters

a	number on which evaluation is done

Returns: square root of a

static double sprites.maths.FastMath.tan ( double x )

static

Tangent function

Parameters

x a number

Returns: tan(x)

static double sprites.maths.FastMath.tanh ( double x )

static

Compute the hyperbolic tangent of a number.

Parameters

x	number on which evaluation is done

Returns: hyperbolic tangent of x

static double sprites.maths.FastMath.toDegrees ( double x )

static

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

Parameters

x	angle in radians

Returns: x converted into degrees

static double sprites.maths.FastMath.toRadians ( double x )

static

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

Parameters

x	angle in degrees

Returns: x converted into radians

static double sprites.maths.FastMath.ulp ( double x )

static

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

Parameters

x	number from which ulp is requested

Returns: ulp(x)

static float sprites.maths.FastMath.ulp ( float x )

static

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

Parameters

x	number from which ulp is requested

Returns: ulp(x)

Member Data Documentation

final double sprites.maths.FastMath.E = 2850325.0 / 1048576.0 + 8.254840070411028747e-8

static

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

final double sprites.maths.FastMath.PI = 105414357.0 / 33554432.0 + 1.984187159361080883e-9

static

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

final double sprites.maths.FastMath.SAFE_MIN = 0x1.0p-1022

static

Safe minimum, such that 1 / SAFE_MIN does not overflow.

In IEEE 754 arithmetic, this is also the smallest normalized number 2^-1022.

The documentation for this class was generated from the following file:

/Users/peter/git/sprites-repos/Sprites 4P/src/sprites/maths/FastMath.java

d	base number
direction	(the only important thing is whether direction is greater or smaller than d )

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

Member Data Documentation