fp_math.h File Reference

Detailed Description

Design Philosophy

These utility functions are can be used for fixed point decimal math.

q24_8 has 24 bits of signed integer and 8 bits of decimal. The integer range is from -8388608 to 8388607 and the smallest decimal resolution is 1/256.

q16_16 and q8_24 typedefs are also provided, but function macros aren't. Use with caution if more decimal precision is required.

vec_q24_8 is a vector type for q24_8. Fixed point vector math functions are provided and start with 'fpv.'

Usage

No initialization or deinitialization is required.

Example

q24_8 a = TO_FX(6);
q24_8 b = TO_FX_FRAC(1, 2);
q24_8 c = ADD_FX(a, b);
printf("%f\n", fixToFloat(c)); // prints 6.500000

Go to the source code of this file.

Data Structures
struct	vec_q24_8
	A 2D vector with q24_8 numbers. More...

Macros
#define	FRAC_BITS   8
	8 fractional bits for q24_8
#define	Q24_8_DECI_MASK   ((1 << FRAC_BITS) - 1)
	A mask for the fractional part of a q24_8.
#define	Q24_8_WHOLE_MASK   (~Q24_8_DECI_MASK)
	A mask for the integer part of a q24_8.
#define	Q16_16_FRAC_BITS   16
	8 fractional bits for q16_16
#define	Q16_16_DECI_MASK   ((1 << Q16_16_FRAC_BITS) - 1)
	A mask for the fractional part of a q16_16.
#define	Q16_16_WHOLE_MASK   (~Q16_16_DECI_MASK)
	A mask for the integer part of a q16_16.
#define	Q8_24_FRAC_BITS   24
	8 fractional bits for q8_24
#define	Q8_24_DECI_MASK   ((1 << Q8_24_FRAC_BITS) - 1)
	A mask for the fractional part of a q8_24.
#define	Q8_24_WHOLE_MASK   (~Q8_24_DECI_MASK)
	A mask for the integer part of a q8_24.
#define	FP_MATH_DEFINES
#define	TO_FX_QN(in, fracBits)
	Convert an integer to a fixed point type with N fractional bits.
#define	FROM_FX_QN(in, fracBits)
	Convert a fixed point type with N fractional bits to an integer.
#define	ADD_FX_QN(a, b, fracBits)
	Add two fixed point type with N fractional bits numbers together.
#define	SUB_FX_QN(a, b, fracBits)
	Subtract a fixed point type with N fractional bits from another.
#define	MUL_FX_QN(a, b, fracBits)
	Multiply two fixed point type with N fractional bits.
#define	DIV_FX_QN(a, b, fracBits)
	Divide a fixed point type with N fractional bits by another.
#define	FLOOR_FX_QN(a, fracBits)
	Find the floor of a fixed point type with N fractional bits.
#define	TO_FX_FRAC_QN(num, denom, fracBits)
	Convert an integer fraction to fixed point type with N fractional bits.
#define	TO_FX(in)
	Convert an integer to a q24_8.
#define	FROM_FX(in)
	Convert a q24_8 to an integer.
#define	ADD_FX(a, b)
	Add two q24_8 numbers together.
#define	SUB_FX(a, b)
	Subtract a q24_8 from another.
#define	MUL_FX(a, b)
	Multiply two q24_8.
#define	DIV_FX(a, b)
	Divide a q24_8 by another.
#define	FLOOR_FX(a)
	Find the floor of a q24_8.
#define	TO_FX_FRAC(num, denom)
	Convert an integer fraction to q24_8.

Typedefs
typedef int16_t	q8_8
	8 bits integer, 8 bits fraction
typedef int32_t	q24_8
	24 bits integer, 8 bits fraction
typedef int32_t	q16_16
	16 bits integer, 16 bits fraction
typedef int32_t	q8_24
	8 bits integer, 24 bits fraction
typedef uint16_t	uq8_8
	unsigned 8 bits integer, 8 bits fraction
typedef uint32_t	uq24_8
	unsigned 24 bits integer, 8 bits fraction
typedef uint32_t	uq16_16
	unsigned 16 bits integer, 16 bits fraction
typedef uint32_t	uq8_24
	unsigned 8 bits integer, 24 bits fraction

Functions
void	fastNormVec (q24_8 *xp, q24_8 *yp)
	Quickly normalize a q24_8 vector, in-place.
vec_q24_8	fpvAdd (vec_q24_8 a, vec_q24_8 b)
	Add two vectors.
vec_q24_8	fpvSub (vec_q24_8 a, vec_q24_8 b)
	Subtract two vectors.
vec_q24_8	fpvMulSc (vec_q24_8 vec, q24_8 scalar)
	Multiply a vector by a scalar.
vec_q24_8	fpvDivSc (vec_q24_8 vec, q24_8 scalar)
	Divide a vector by a scalar.
q24_8	fpvDot (vec_q24_8 a, vec_q24_8 b)
	Compute the dot product of two vectors.
q24_8	fpvSqMag (vec_q24_8 a)
	Compute the squared magnitude of a vector.
vec_q24_8	fpvNorm (vec_q24_8 vec)
	Normalize and return a vector.
float	fixToFloat (q24_8 fx)
	Convert a q24_8 to floating point.

---

Data Structure Documentation

vec_q24_8

struct vec_q24_8

Data Fields
q24_8	x	The X component of the vector.
q24_8	y	The Y component of the vector.

Macro Definition Documentation

FRAC_BITS

#define FRAC_BITS   8

8 fractional bits for q24_8

Q24_8_DECI_MASK

#define Q24_8_DECI_MASK   ((1 << FRAC_BITS) - 1)

A mask for the fractional part of a q24_8.

Q24_8_WHOLE_MASK

#define Q24_8_WHOLE_MASK   (~Q24_8_DECI_MASK)

A mask for the integer part of a q24_8.

Q16_16_FRAC_BITS

#define Q16_16_FRAC_BITS   16

8 fractional bits for q16_16

Q16_16_DECI_MASK

#define Q16_16_DECI_MASK   ((1 << Q16_16_FRAC_BITS) - 1)

A mask for the fractional part of a q16_16.

Q16_16_WHOLE_MASK

#define Q16_16_WHOLE_MASK   (~Q16_16_DECI_MASK)

A mask for the integer part of a q16_16.

Q8_24_FRAC_BITS

#define Q8_24_FRAC_BITS   24

8 fractional bits for q8_24

Q8_24_DECI_MASK

#define Q8_24_DECI_MASK   ((1 << Q8_24_FRAC_BITS) - 1)

A mask for the fractional part of a q8_24.

Q8_24_WHOLE_MASK

#define Q8_24_WHOLE_MASK   (~Q8_24_DECI_MASK)

A mask for the integer part of a q8_24.

FP_MATH_DEFINES

#define FP_MATH_DEFINES

TO_FX_QN

#define TO_FX_QN	(		in,
			fracBits )

Value:

((in) * (1 << (fracBits)))

Convert an integer to a fixed point type with N fractional bits.

Parameters

in	The integer to convert to a fixed point type with N fractional bits

Returns

A fixed point type with N fractional bits

FROM_FX_QN

#define FROM_FX_QN	(		in,
			fracBits )

Value:

((in) >> (fracBits))

Convert a fixed point type with N fractional bits to an integer.

Parameters

in	The fixed point type with N fractional bits to convert to integer

Returns

An integer

ADD_FX_QN

#define ADD_FX_QN	(		a,
			b,
			fracBits )

Value:

((a) + (b))

Add two fixed point type with N fractional bits numbers together.

Parameters

a	An operand
b	The other operand

Returns

The sum

SUB_FX_QN

#define SUB_FX_QN	(		a,
			b,
			fracBits )

Value:

((a) - (b))

Subtract a fixed point type with N fractional bits from another.

Parameters

a	The number to subtract from
b	The number to subtract

Returns

The difference

MUL_FX_QN

#define MUL_FX_QN	(		a,
			b,
			fracBits )

Value:

(((a) * (b)) >> (fracBits))

Multiply two fixed point type with N fractional bits.

Parameters

a	An operand
b	The other operand

Returns

The result

DIV_FX_QN

#define DIV_FX_QN	(		a,
			b,
			fracBits )

Value:

(((a) << (fracBits)) / (b))

Divide a fixed point type with N fractional bits by another.

Parameters

a	The numerator
b	The denominator

Returns

The result

FLOOR_FX_QN

#define FLOOR_FX_QN	(		a,
			fracBits )

Value:

((a) & (~((1 << (fracBits)) - 1)))

Find the floor of a fixed point type with N fractional bits.

Parameters

a	The number to floor

Returns

The floor of the input

TO_FX_FRAC_QN

#define TO_FX_FRAC_QN	(		num,
			denom,
			fracBits )

Value:

DIV_FX(num, denom)

Convert an integer fraction to fixed point type with N fractional bits.

Parameters

num	The numerator
denom	The denominator

Returns

The fraction in fixed point type with N fractional bits

TO_FX

#define TO_FX

(

in

)

Value:

TO_FX_QN(in, FRAC_BITS)

Convert an integer to a q24_8.

Parameters

in	The integer to convert to q24_8

Returns

A q24_8

FROM_FX

#define FROM_FX

(

in

)

Value:

FROM_FX_QN(in, FRAC_BITS)

Convert a q24_8 to an integer.

Parameters

in	The q24_8 to convert to integer

Returns

An integer

ADD_FX

#define ADD_FX	(		a,
			b )

Value:

ADD_FX_QN(a, b, FRAC_BITS)

Add two q24_8 numbers together.

Parameters

a	An operand
b	The other operand

Returns

The sum

SUB_FX

#define SUB_FX	(		a,
			b )

Value:

SUB_FX_QN(a, b, FRAC_BITS)

Subtract a q24_8 from another.

Parameters

a	The number to subtract from
b	The number to subtract

Returns

The difference

MUL_FX

#define MUL_FX	(		a,
			b )

Value:

MUL_FX_QN(a, b, FRAC_BITS)

Multiply two q24_8.

Parameters

a	An operand
b	The other operand

Returns

The result

DIV_FX

#define DIV_FX	(		a,
			b )

Value:

DIV_FX_QN(a, b, FRAC_BITS)

Divide a q24_8 by another.

Parameters

a	The numerator
b	The denominator

Returns

The result

FLOOR_FX

#define FLOOR_FX

(

a

)

Value:

FLOOR_FX_QN(a, FRAC_BITS)

Find the floor of a q24_8.

Parameters

a	The number to floor

Returns

The floor of the input

TO_FX_FRAC

#define TO_FX_FRAC	(		num,
			denom )

Value:

TO_FX_FRAC_QN(num, denom, FRAC_BITS)

Convert an integer fraction to q24_8.

Parameters

num	The numerator
denom	The denominator

Returns

The fraction in q24_8

Typedef Documentation

q8_8

typedef int16_t q8_8

8 bits integer, 8 bits fraction

q24_8

typedef int32_t q24_8

24 bits integer, 8 bits fraction

q16_16

typedef int32_t q16_16

16 bits integer, 16 bits fraction

q8_24

typedef int32_t q8_24

8 bits integer, 24 bits fraction

uq8_8

typedef uint16_t uq8_8

unsigned 8 bits integer, 8 bits fraction

uq24_8

typedef uint32_t uq24_8

unsigned 24 bits integer, 8 bits fraction

uq16_16

typedef uint32_t uq16_16

unsigned 16 bits integer, 16 bits fraction

uq8_24

typedef uint32_t uq8_24

unsigned 8 bits integer, 24 bits fraction

Function Documentation

fastNormVec()

void fastNormVec	(	q24_8 *	xp,
		q24_8 *	yp )

Quickly normalize a q24_8 vector, in-place.

Parameters

xp	The X component of the vector, normalized in-place
yp	The Y component of the vector, normalized in-place

fpvAdd()

vec_q24_8 fpvAdd	(	vec_q24_8	a,
		vec_q24_8	b )

Add two vectors.

Parameters

a	A vector to add
b	The other vector to add

Returns

The sum of the two input vectors

fpvSub()

vec_q24_8 fpvSub	(	vec_q24_8	a,
		vec_q24_8	b )

Subtract two vectors.

Parameters

a	A vector to subtract from
b	The other vector to subtract

Returns

The difference between the two input vectors

fpvMulSc()

vec_q24_8 fpvMulSc	(	vec_q24_8	vec,
		q24_8	scalar )

Multiply a vector by a scalar.

Parameters

vec	A vector multiply
scalar	A scalar to multiply the vector by

Returns

The scaled vector

fpvDivSc()

vec_q24_8 fpvDivSc	(	vec_q24_8	vec,
		q24_8	scalar )

Divide a vector by a scalar.

Parameters

vec	A vector divide
scalar	A scalar to divide the vector by

Returns

The scaled vector

fpvDot()

q24_8 fpvDot	(	vec_q24_8	a,
		vec_q24_8	b )

Compute the dot product of two vectors.

Parameters

a	A vector to dot
b	The other vector to dot

Returns

The dot product of the two vectors

fpvSqMag()

q24_8 fpvSqMag

(

vec_q24_8

a

)

Compute the squared magnitude of a vector.

Parameters

a	The vector to compute the squared magnitude of

Returns

The squared magnitude of the vector

fpvNorm()

vec_q24_8 fpvNorm

(

vec_q24_8

vec

)

Normalize and return a vector.

Parameters

vec	The vector to normalize

Returns

The normalized vector

fixToFloat()

float fixToFloat

(

q24_8

fx

)

Convert a q24_8 to floating point.

Parameters

fx	Fixed point input

Returns

Floating point output