fpmath.FPMath Class Reference

List of all members.

Static Public Member Functions
static int	abs (int fp)
static int	add (int fpA, int fpB)
static int	atan (int fp)
static int	atan2 (int fpY, int fpX)
static int	ceil (int fp)
static int	cos (int fp)
static int	div (int fpA, int fpB)
static int	exp (int fp)
static int	floor (int fp)
static int	fraction (int fp)
static int	log (int fp)
static int	max (int fpA, int fpB)
static int	min (int fpA, int fpB)
static int	mul (int fpA, int fpB)
static int	pow (int fpBase, int fpPower)
static int	round (int fp)
static int	roundToInt (int fp)
static int	sin (int fp)
static int	sqrt (int fp)
static int	sub (int fpA, int fpB)
static int	toFP (int integer)
static int	toInt (int fp)
static int	toFP (String s) throws NumberFormatException
static String	toString (int fp)
Static Public Attributes
static final int	EPSILON = 1
static final int	MAX_VALUE = 0x7FFFFFFF
static final int	MIN_VALUE = 0x80000000

---

Detailed Description

16.16 Fixed Point Math libray using 16-bit, 32-bit and 64-bit integer arithmetic and look-up tables.

Please note that:

• This documentation denotes fixed point numbers as FP ints to distinguish them from integer numbers. However FP int are in fact plain int primitives.
• Its good programming practice to start all FP int variable and attribute names with 'f' or 'fp' to distinguish them from integer ints.
• Usage of Java built-in integer aritmetic operators (+, -, *, /, %, &, |, ^, <<, >>, >>>) for fixed point calculations should be kept to a minimum. Use the methods offered here instead.
• Built-in Java comparison operators (<, <=, ==, !=, >=, >) may be used to compare FP ints to other FP ints, but not to compare FP ints to other integer ints.
• All methods presented in this class are defined as static for performance reasons.
• The worst-case error of each method is mentioned in its description and is measured in EPSILONs, the smallest positive non-zero number a FP int can have.
• The internal look-up tables are stored hard-coded and have been thoroughly optimized for size, resulting in a total of 560 bytes.
• Non-linear monotic functions are NOT guaranteed to produce monotonic FP intresults, but will never differ more than the wost-case error of these methods.

The source code license:

Copyright (c) 2005-2011, Giliam de Carpentier. All rights reserved.

Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.
  
  
• Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.
  

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Author:

Giliam de Carpentier

---

Member Function Documentation

static int fpmath.FPMath.abs

(

int

fp

)

[static]

Returns the absolute value of the specified FP int as a FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fp	The FP int value.

Returns:

A FP int containing the absolute value.

static int fpmath.FPMath.add	(	int	fpA,
		int	fpB
	)		[static]

Returns the result of the addition of the two specified FP int parameters as a FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fpA	First FP int parameter.
fpB	Second FP int parameter.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.atan

(

int

fp

)

[static]

Returns the inverse tangent of the specified FP int parameter as a FP int.

The result is specified in 1/65536ths of a full rotation and is returned in the range of 0.0 through 0.25 and 0.75 through 1.0-EPSILON.

Maximum deviation from definition: 2 EPSILON.

Parameters:

fp	The FP int containing the tangent.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.atan2	(	int	fpY,
		int	fpX
	)		[static]

Returns the polar angle from the cartesian input vector, specified as an y-component FP int and x-component FP int, as a FP int.

The result is specified in 1/65536ths of a full rotation and is returned in the range of 0.0 through (1.0-EPSILON).

Maximum deviation from definition: 2 EPSILON.

Parameters:

fpY	The FP int containing the Y-component.
fpX	The FP int containing the X-component.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.ceil

(

int

fp

)

[static]

Returns the smallest integer that is equal or greater than specified FP int as a FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fp	The FP int value.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.cos

(

int

fp

)

[static]

Returns the cosine of the specified angle FP int parameter as a FP int.

Maximum deviation from definition: 2 EPSILON.

Parameters:

fp	The FP int containing the angle. This should be specified in 1/65536ths of a full rotation.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.div	(	int	fpA,
		int	fpB
	)		[static]

Returns the result of the division of the first specified FP int parameter by the second specified FP int parameter as a (rounded down) FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fpA	First FP int parameter.
fpB	Second FP int parameter.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.exp

(

int

fp

)

[static]

Returns the Euler's number e raised to the power of the specified FP int parameter as a FP int. Results greater than MAX_VALUE are clamped to MAX_VALUE.

Maximum deviation from definition:

• power FP int < -1 : 1 EPSILON
• -1 <= power FP int < 0 : 2 EPSILON
• power FP int >= 0 : Returned FP int * 2^-14 EPSILON

Parameters:

fp	The FP int containing the power.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.floor

(

int

fp

)

[static]

Returns the largest integer that is equal or smaller than specified FP int as a FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fp	The FP int value.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.fraction

(

int

fp

)

[static]

Returns the fraction of the specified FP int in 1/65536ths as in int integer.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fp	FP int parameter.

Returns:

A int containing the fraction in 1/65536ths.

static int fpmath.FPMath.log

(

int

fp

)

[static]

Returns the natural logaritm (base Euler's number e) of the specified FP int parameter as a FP int. All non-positive parameters return MIN_VALUE.

Maximum deviation from definition: 4 EPSILON.

Parameters:

fp	The FP int containing the input number.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.max	(	int	fpA,
		int	fpB
	)		[static]

Returns the larger of the two specified FP ints.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fpA	The first FP int value.
fpB	The second FP int value.

Returns:

A FP int containing the largest value of the two.

static int fpmath.FPMath.min	(	int	fpA,
		int	fpB
	)		[static]

Return the smaller of the two specified FP ints.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fpA	The first FP int value.
fpB	The second FP int value.

Returns:

A FP int containing the smallest value of the two.

static int fpmath.FPMath.mul	(	int	fpA,
		int	fpB
	)		[static]

Returns the result of the multiplication the two specified FP int parameters as a (rounded down) FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fpA	First FP int parameter.
fpB	Second FP int parameter.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.pow	(	int	fpBase,
		int	fpPower
	)		[static]

Returns the base specified by the first FP int parameter raised to the power specified by the second FP int parameter as a FP int. However, all negative bases return 0.

Maximum deviation from definition: Depends on both parameters.

Parameters:

fpBase	The FP int containing the base.
fpPower	The FP int containing the power.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.round

(

int

fp

)

[static]

Returns the integer closest to the specified FP int as a FP int.

Maximum deviation from definition: 0

Parameters:

fp	The FP int value.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.roundToInt

(

int

fp

)

[static]

Returns the integer closest to the specified FP int as a int integer.

Maximum deviation from definition: 0

Parameters:

fp	The FP int value.

Returns:

A int integer containing the result of this calculation.

static int fpmath.FPMath.sin

(

int

fp

)

[static]

Returns the sine of the specified angle FP parameter as a FP int.

Maximum deviation from definition: 2 EPSILON.

Parameters:

fp	The FP int containing the angle. This should be specified in 1/65536ths of a full rotation.

Returns:

This FP int containing the result of this calculation.

static int fpmath.FPMath.sqrt

(

int

fp

)

[static]

Returns the square root of the specified FP parameter as a FP int. Negative parameters return 0.

Maximum deviation from definition: 1 EPSILON.

Parameters:

fp	The FP int containing the input number.

Returns:

This FP int containing the result of this calculation.

static int fpmath.FPMath.sub	(	int	fpA,
		int	fpB
	)		[static]

Returns the result of the substraction of the second specified FP int parameter from the first specified FP parameter as a FP int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fpA	First FP int parameter.
fpB	Second FP int parameter.

Returns:

A FP int containing the result of this calculation.

static int fpmath.FPMath.toFP

(

int

integer

)

[static]

Returns the FP int representation of the integer specified by the int integer.

Maximum deviation from definition: 0 EPSILON.

Parameters:

integer

The integer value.

Returns:

A FP int containing the specified integer value.

static int fpmath.FPMath.toFP

(

String

s

)

throws NumberFormatException [static]

Returns the FP int value representing the floating point number indicated by the String parameter. Does not support floating point E notations.

Maximum deviation from definition: 0.5 EPSILON.

Parameters:

s	String containing a floating point number.

Returns:

This FP int containing the closest 16.16 fixed point to the specified floating point number.

static int fpmath.FPMath.toInt

(

int

fp

)

[static]

Returns the largest integer number smaller than the specified FP int as a int.

Maximum deviation from definition: 0 EPSILON.

Parameters:

fp	The FP int value.

Returns:

An int containing the integer value.

static String fpmath.FPMath.toString

(

int

fp

)

[static]

Returns a String containing a floating point number representation of the specified FP int number.

Parameters:

fp	The FP int containing the input number.

Returns:

A String representation of this FP int.

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Member Data Documentation

final int fpmath.FPMath.EPSILON = 1 [static]

A FP int constant holding the smallest positive non-zero value a FP int can have, 2^-16.

final int fpmath.FPMath.MAX_VALUE = 0x7FFFFFFF [static]

A FP int constant holding the maximum value a FP int can have, 2¹⁵ - 2^-16.

final int fpmath.FPMath.MIN_VALUE = 0x80000000 [static]

A FP int constant holding the miminum value a FP int can have, -2¹⁵.

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

• FPMath.java