Functions to handle fixed point integer math. More...

#include <fxfixed.h>

Static Public Member Functions
static Fixed32 BURGER_INLINE	FromInt (Int32 iInput)
	Convert an Int32 into a Fixed32 value.
static Fixed32 BURGER_INLINE	FromFloatFloor (float fInput)
	Convert a single float to a Fixed32 using floor().
static Fixed32 BURGER_INLINE	FromFloat (float fInput)
	Convert a single float to a Fixed32 using round to zero.
static Fixed32 BURGER_INLINE	FromFloatCeil (float fInput)
	Convert a single float to a Fixed32 using ceil().
static Fixed32 BURGER_INLINE	FromFloatNearest (float fInput)
	Convert a single float to a Fixed32 using round to nearest.
static void BURGER_INLINE	FromFloatFloor (Fixed32 *pOutput, float fInput)
	Convert a single float to a Fixed32 using floor().
static void BURGER_INLINE	FromFloat (Fixed32 *pOutput, float fInput)
	Convert a single float to a Fixed32 using round to zero.
static void BURGER_INLINE	FromFloatCeil (Fixed32 *pOutput, float fInput)
	Convert a single float to a Fixed32 using ceil().
static void BURGER_INLINE	FromFloatNearest (Fixed32 *pOutput, float fInput)
	Convert a single float to a Fixed32 using round to nearest.
static Fixed32 BURGER_API	FromIntSaturate (Int32 iInput)
	Convert an Int32 into a Fixed32 value with saturation.
static Fixed32 BURGER_INLINE	Abs (Fixed32 fInput)
	Get the absolute value of a 16.16 fixed point value...
static Fixed32 BURGER_API	SqrtFromInt (Word32 uInput)
	Get the square root of an integer.
static Fixed32 BURGER_API	SqrtFromFixed (Fixed32 fInput)
	Get the square root of a Fixed32.
static Fixed32 BURGER_INLINE	Multiply (Fixed32 fInputMulA, Fixed32 fInputMulB)
	Multiply two 16.16 fixed point numbers.
static Fixed32 BURGER_INLINE	Divide (Fixed32 fInputNumerator, Fixed32 fInputDenominator)
	Divide two 16.16 fixed point numbers.
static Fixed32 BURGER_INLINE	Reciprocal (Fixed32 fInput)
	Return the reciprocal of a fixed point number.
static Fixed32 BURGER_API	MultiplySaturate (Fixed32 fInputMulA, Fixed32 fInputMulB)
	Multiply two 16.16 fixed point numbers with saturation.
static Fixed32 BURGER_API	DivideSaturate (Fixed32 fInputNumerator, Fixed32 fInputDenominator)
	Divide a 16.16 fixed point number with saturation.
static Fixed32 BURGER_API	CrossProduct2DSign (Fixed32 fInputX1, Fixed32 fInputY1, Fixed32 fInputX2, Fixed32 fInputY2)
	Return the sign of the result of a 2D cross product.
static Fixed32 BURGER_API	ATan2 (Fixed32 fInput1, Fixed32 fInput2)
	Get the arctangent from the slope of two signed integers.

Detailed Description

Functions to handle fixed point integer math.

Not all modern computers have floating point support in hardware, so to get fractional values, a 16.16 integer format is used.

How it works is simple. The upper 16 bits are treated as a 16 bit whole integer while the lower 16 bits represent the numerator of the fraction x/65536. Using this method, 1.5f is represented at 0x18000.

These routines will make it easy to perform conversion of numbers to this numeric type and to handle the most common mathematical operations with 1/65536th precision.

Many of these functions are inline or written in assembly language for speed.

See also:: Fixed32, Frac32 or Int32

Member Function Documentation

Burger::FixedMath::Abs ( Fixed32 fInput ) [inline, static]

Get the absolute value of a 16.16 fixed point value...

Without branching, calculate the absolute value of a Fixed32..

Parameters:

fInput

Value to get the absolute value of.

Returns:: The absolute value of fInput.

See also:: Burger::IntMath::Abs(Int32)

Fixed32 BURGER_API Burger::FixedMath::ATan2	(	Fixed32	fInput1,
		Fixed32	fInput2
	)			`[static]`

Get the arctangent from the slope of two signed integers.

Taking two integers of like type (Two Fixed32, Int32 or Frac32) determine the atan2 value of the slope and return it as a Fixed32 in the range of - Burger::PiFixed32 to Burger::PiFixed32

Parameters:

	fInput1	Numerator for the atan2 calculation
	fInput2	Denominator for the atan2 calculation

Returns:: Fixed32 atan2 value of range +\- Burger::PiFixed32

Fixed32 BURGER_API Burger::FixedMath::CrossProduct2DSign	(	Fixed32	fInputX1,
		Fixed32	fInputY1,
		Fixed32	fInputX2,
		Fixed32	fInputY2
	)			`[static]`

Return the sign of the result of a 2D cross product.

For the calculation to determine if a point is on the front or back of a line, a cross product is done and only whether if the result is greater or equal to zero is all that matters.

To perform this operation efficiently on 32 bit CPUs, the values are multiplied to make 64 bit results, the values are subtracted and only the upper 32 bits are returned and the caller only tests the sign of the result to get the decision if the point is in front or behind a line.

Parameters:

	fInputX1	X coordinate of the first 2D point.
	fInputY1	Y coordinate of the first 2D point.
	fInputX2	X coordinate of the second 2D point.
	fInputY2	Y coordinate of the second 2D point.

Returns:: The sign of the formula (X1*Y2)-(X2*Y1)

Note:: The value returned is the upper 32 bits, or simply put, the integer part of the Fixed32 result. It's not recommended to act on the value unless the integer part is all that's required.

Burger::FixedMath::Divide	(	Fixed32	fInputNumerator,
		Fixed32	fInputDenominator
	)			`[inline, static]`

Divide two 16.16 fixed point numbers.

Divide a 16.16 fixed point number by another 16.16 fixed point number without saturation or checking for division by zero..

Parameters:

	fInputNumerator	Signed value to divide
	fInputDenominator	Signed value to divide with

Returns:: Result of fInputNumerator / fInputDenominator without saturation

Note:: This is a dangerous routine. A divide by zero or an overflow can cause an exception error! Use at your own risk!

See also:: Burger::FixedMath::DivideSaturate(Fixed32,Fixed32)

Fixed32 BURGER_API Burger::FixedMath::DivideSaturate	(	Fixed32	fInputNumerator,
		Fixed32	fInputDenominator
	)			`[static]`

Divide a 16.16 fixed point number with saturation.

Perform a signed division of two 32-bit fixed point numbers and return the fixed point result. If the answer exceeds the range allowable for a Fixed32 value, it will be saturated to the minimum and maximum bounds. Division by zero will return positive or negative maximums.

Parameters:

	fInputNumerator	Value to divide
	fInputDenominator	Value to divide with

Returns:: Result of fInputNumerator / fInputDenominator with saturation.

See also:: Burger::FixedMath::Divide(Fixed32,Fixed32)

Int32 Burger::FixedMath::FromFloat ( float fInput ) [inline, static]

Convert a single float to a Fixed32 using round to zero.

Convert a single precision floating point number to a Fixed32 using the round to zero fractional truncation

Parameters:

fInput

A valid single precision floating point number.

Returns:: a Fixed32 equivalent value after applying round to zero on the floating point number.

void Burger::FixedMath::FromFloat	(	Fixed32 *	pOutput,
		float	fInput
	)			`[inline, static]`

Convert a single float to a Fixed32 using round to zero.

Convert a single precision floating point number to a Fixed32 using the round to zero fractional truncation and store it to memory

Parameters:

	pOutput	A valid pointer to a Fixed32 to receive the result.
	fInput	A valid single precision floating point number.

void Burger::FixedMath::FromFloatCeil	(	Fixed32 *	pOutput,
		float	fInput
	)			`[inline, static]`

Convert a single float to a Fixed32 using ceil().

Convert a single precision floating point number to a Fixed32 using the ceil() form of fractional truncation and store it to memory

Parameters:

	pOutput	A valid pointer to a Fixed32 to receive the result.
	fInput	A valid single precision floating point number.

Int32 Burger::FixedMath::FromFloatCeil ( float fInput ) [inline, static]

Convert a single float to a Fixed32 using ceil().

Convert a single precision floating point number to a Fixed32 using the ceil() form of fractional truncation

Parameters:

fInput

A valid single precision floating point number.

Returns:: a Fixed32 equivalent value after applying ceil() on the floating point number.

void Burger::FixedMath::FromFloatFloor	(	Fixed32 *	pOutput,
		float	fInput
	)			`[inline, static]`

Convert a single float to a Fixed32 using floor().

Convert a single precision floating point number to a Fixed32 using the floor() form of fractional truncation and store it to memory

Parameters:

	pOutput	A valid pointer to a Fixed32 to receive the result.
	fInput	A valid single precision floating point number.

Int32 Burger::FixedMath::FromFloatFloor ( float fInput ) [inline, static]

Convert a single float to a Fixed32 using floor().

Convert a single precision floating point number to a Fixed32 using the floor() form of fractional truncation

Parameters:

fInput

A valid single precision floating point number.

Returns:: a Fixed32 equivalent value after applying floor() on the floating point number.

Int32 Burger::FixedMath::FromFloatNearest ( float fInput ) [inline, static]

Convert a single float to a Fixed32 using round to nearest.

Convert a single precision floating point number to a Fixed32 using the round to nearest fractional truncation

Parameters:

fInput

A valid single precision floating point number.

Returns:: a Fixed32 equivalent value after applying round to nearest on the floating point number.

void Burger::FixedMath::FromFloatNearest	(	Fixed32 *	pOutput,
		float	fInput
	)			`[inline, static]`

Convert a single float to a Fixed32 using round to nearest.

Convert a single precision floating point number to a Fixed32 using the round to nearest fractional truncation and store it to memory

Parameters:

	pOutput	A valid pointer to a Fixed32 to receive the result.
	fInput	A valid single precision floating point number.

Burger::FixedMath::FromInt ( Int32 iInput ) [inline, static]

Convert an Int32 into a Fixed32 value.

Convert an integer into a fixed point number. No bounds checking is performed so values that exceed 32767 or are less than -32768 will yield undefined results.

Parameters:

iInput

Integer to convert

Returns:: Result of the conversion without saturation

See also:: Burger::FixedMath::FromIntSaturate(Int32)

Fixed32 BURGER_API Burger::FixedMath::FromIntSaturate ( Int32 iInput ) [static]

Convert an Int32 into a Fixed32 value with saturation.

Convert an integer into a fixed point number. Bounds checking is performed so values that exceed 32767 or are less than -32768 will yield max and min values..

Examples of clamping:

0x8000 -> 0x7FFFFFFF
0xFEEDBEEF -> 0x80000000

Parameters:

iInput

Integer to convert

Returns:: Result of the conversion with saturation

See also:: Burger::FixedMath::FromInt(Int32)

Burger::FixedMath::Multiply	(	Fixed32	fInputMulA,
		Fixed32	fInputMulB
	)			`[inline, static]`

Multiply two 16.16 fixed point numbers.

Perform a signed multiplication of two 32-bit fixed point numbers and return the fixed point result. No error checking is performed, so overflow or underflow conditions yield undefined results.

Parameters:

	fInputMulA	First signed value to multiply
	fInputMulB	Second signed value to multiply

Returns:: Result of fInputMulA * fInputMulB without bounds checking

See also:: Burger::FixedMath::MultiplySaturate(Fixed32,Fixed32)

Fixed32 BURGER_API Burger::FixedMath::MultiplySaturate	(	Fixed32	fInputMulA,
		Fixed32	fInputMulB
	)			`[static]`

Multiply two 16.16 fixed point numbers with saturation.

Perform a signed multiplication of two 32-bit fixed point numbers and return the fixed point result. If the value exceeds the range allowable for a Fixed32 value, it will be saturated to the minimum and maximum bounds.

Parameters:

	fInputMulA	First signed value to multiply
	fInputMulB	Second signed value to multiply

Returns:: Result of fInputMulA * fInputMulB with saturation.

See also:: Burger::FixedMath::Multiply(Fixed32,Fixed32)

Burger::FixedMath::Reciprocal ( Fixed32 fInput ) [inline, static]

Return the reciprocal of a fixed point number.

Divide a 16.16 fixed point number by 1.0f in fixed point. If the input value is negative epsilon (0xFFFFFFFF), return 0x8000000. If the input is equal to 0 or positive epsilon (0x1), then return 0x7ffffff. This has the effect of saturating the output and leaving no output as undefined.

Parameters:

fInput

Fixed32 value to convert to a reciprocal.

Returns:: Result of 1.0f / fInput with saturation

Note:: It's not recommended to input epsilon or 0 due to saturation.

See also:: Burger::FixedMath::DivideSaturate(Fixed32,Fixed32)

Fixed32 BURGER_API Burger::FixedMath::SqrtFromFixed ( Fixed32 fInput ) [static]

Get the square root of a Fixed32.

Return the square root of a Fixed32 and return the Fixed32 result. The maximum value is 255.998 (256) for the square root of 0x7FFFFFFF. This routine is 100% accurate.

Negative numbers will return zero for the result.

Parameters:

fInput

Value to return the square root of.

Returns:: Return the square root as a Fixed32.

See also:: Burger::IntMath::SqrtFromFixed(Fixed32) or Burger::FixedMath::SqrtFromInt(Word32)

Fixed32 BURGER_API Burger::FixedMath::SqrtFromInt ( Word32 uInput ) [static]

Get the square root of an integer.

Return the square root of an integer. The maximum value is 46341 for the square root of 0x7FFFFFFF. This routine is 100% accurate.

Parameters:

uInput

Value to return the square root of.

Returns:: Return the square root as a Fixed32.

See also:: Burger::IntMath::SqrtFromInt(Word32) or Burger::FixedMath::SqrtFromFixed(Fixed32)

Burger::FixedMath Class Reference

Static Public Member Functions

Detailed Description

Member Function Documentation