Fixed-point math

Signed fixed-point types and a generic recursive filter. More...

Data Structures
union	Fixed_S16_3
	Fixed-point number with 1 sign bit, 12 integer bits and 3 fraction bits. More...
union	Fixed_S32_16
	Fixed-point number with 1 sign bit, 15 integer bits and 16 fraction bits. More...
union	Fixed_S64_32
	Fixed-point number with 1 sign bit, 31 integer bits and 32 fraction bits. More...
struct	Fixed_S16_3.__unnamed102__
struct	Fixed_S32_16.__unnamed104__
struct	Fixed_S64_32.__unnamed106__

Macros
#define	Fixed_S16_3(raw)   ((Fixed_S16_3){.raw_value = (raw)})
	Make a Fixed_S16_3 from its raw value.
#define	FIXED_S16_3_PRECISION   3
	Number of fraction bits of Fixed_S16_3.
#define	FIXED_S16_3_FACTOR   (1 << FIXED_S16_3_PRECISION)
	Scale factor of Fixed_S16_3.
#define	FIXED_S16_3_ZERO   ((Fixed_S16_3){.integer = 0, .fraction = 0})
	Fixed_S16_3 zero.
#define	FIXED_S16_3_ONE   ((Fixed_S16_3){.integer = 1, .fraction = 0})
	Fixed_S16_3 one.
#define	FIXED_S16_3_HALF   ((Fixed_S16_3){.raw_value = FIXED_S16_3_ONE.raw_value / 2})
	Fixed_S16_3 one half.
#define	Fixed_S32_16(raw)   ((Fixed_S32_16){.raw_value = (raw)})
	Make a Fixed_S32_16 from its raw value.
#define	FIXED_S32_16_PRECISION   16
	Number of fraction bits of Fixed_S32_16.
#define	FIXED_S32_16_ONE   ((Fixed_S32_16){.integer = 1, .fraction = 0})
	Fixed_S32_16 one.
#define	FIXED_S32_16_ZERO   ((Fixed_S32_16){.integer = 0, .fraction = 0})
	Fixed_S32_16 zero.
#define	FIXED_S64_32_PRECISION   32
	Number of fraction bits of Fixed_S64_32.
#define	FIXED_S64_32_ONE   ((Fixed_S64_32){.integer = 1, .fraction = 0})
	Fixed_S64_32 one.
#define	FIXED_S64_32_ZERO   ((Fixed_S64_32){.integer = 0, .fraction = 0})
	Fixed_S64_32 zero.
#define	FIXED_S64_32_FROM_RAW(raw)   ((Fixed_S64_32){.raw_value = (raw)})
	Make a Fixed_S64_32 from its raw value.
#define	FIXED_S64_32_FROM_INT(x)   ((Fixed_S64_32){.integer = x, .fraction = 0})
	Make a Fixed_S64_32 from an integer.
#define	FIXED_S64_32_TO_INT(x)   (x.integer)
	Get the integer part of a Fixed_S64_32, rounded towards negative infinity.

Typedefs
typedef Fixed_S32_16	Fixed_S32_16Return
	Alias of Fixed_S32_16 for function return types.

Functions
static __inline__ Fixed_S16_3	Fixed_S16_3_mul (Fixed_S16_3 a, Fixed_S16_3 b)
	Multiply two Fixed_S16_3 values.
static __inline__ Fixed_S16_3	Fixed_S16_3_add (Fixed_S16_3 a, Fixed_S16_3 b)
	Add two Fixed_S16_3 values.
static __inline__ Fixed_S16_3	Fixed_S16_3_sub (Fixed_S16_3 a, Fixed_S16_3 b)
	Subtract two Fixed_S16_3 values.
static __inline__ Fixed_S16_3	Fixed_S16_3_add3 (Fixed_S16_3 a, Fixed_S16_3 b, Fixed_S16_3 c)
	Add three Fixed_S16_3 values.
static __inline__ bool	Fixed_S16_3_equal (Fixed_S16_3 a, Fixed_S16_3 b)
	Compare two Fixed_S16_3 values.
static __inline__ int16_t	Fixed_S16_3_rounded_int (Fixed_S16_3 a)
	Round a Fixed_S16_3 value to the nearest integer, halves away from zero.
static __inline__ Fixed_S32_16	Fixed_S32_16_mul (Fixed_S32_16 a, Fixed_S32_16 b)
	Multiply two Fixed_S32_16 values.
static __inline__ Fixed_S32_16	Fixed_S32_16_add (Fixed_S32_16 a, Fixed_S32_16 b)
	Add two Fixed_S32_16 values.
static __inline__ Fixed_S32_16	Fixed_S32_16_add3 (Fixed_S32_16 a, Fixed_S32_16 b, Fixed_S32_16 c)
	Add three Fixed_S32_16 values.
static __inline__ Fixed_S32_16	Fixed_S32_16_sub (Fixed_S32_16 a, Fixed_S32_16 b)
	Subtract two Fixed_S32_16 values.
static __inline__ Fixed_S64_32	Fixed_S64_32_mul (Fixed_S64_32 a, Fixed_S64_32 b)
	Multiply two Fixed_S64_32 values.
static __inline__ Fixed_S64_32	Fixed_S64_32_add (Fixed_S64_32 a, Fixed_S64_32 b)
	Add two Fixed_S64_32 values.
static __inline__ Fixed_S64_32	Fixed_S64_32_add3 (Fixed_S64_32 a, Fixed_S64_32 b, Fixed_S64_32 c)
	Add three Fixed_S64_32 values.
static __inline__ Fixed_S64_32	Fixed_S64_32_sub (Fixed_S64_32 a, Fixed_S64_32 b)
	Subtract two Fixed_S64_32 values.
static __inline__ Fixed_S16_3	Fixed_S16_3_S32_16_mul (Fixed_S16_3 a, Fixed_S32_16 b)
	Multiply a Fixed_S16_3 by a Fixed_S32_16.
Fixed_S64_32	math_fixed_recursive_filter (Fixed_S64_32 x, int num_input_coefficients, int num_output_coefficients, const Fixed_S64_32 *cb, const Fixed_S64_32 *ca, Fixed_S64_32 *state_x, Fixed_S64_32 *state_y)
	Run a value through an Nth order linear recursive (IIR) filter.

Detailed Description

Signed fixed-point types and a generic recursive filter.

In every type the fraction is unsigned and adds to the integer part, so -1.125 in Fixed_S16_3 is stored as integer -2 and fraction 7 (-2 + 7 * 0.125), and 1.125 as integer 1 and fraction 1. This keeps raw_value a plain two's complement number, so values can be added and multiplied directly.

Fixed_S16_3 a = Fixed_S16_3(12);  // 1.5
Fixed_S16_3 b = FIXED_S16_3_ONE;
int16_t r = Fixed_S16_3_rounded_int(Fixed_S16_3_add(a, b));  // 3

---

Data Structure Documentation

Fixed_S16_3

union Fixed_S16_3

Fixed-point number with 1 sign bit, 12 integer bits and 3 fraction bits.

Data Fields
struct Fixed_S16_3.__unnamed102__	__unnamed__
int16_t	raw_value	Value scaled by 8.

Fixed_S32_16

union Fixed_S32_16

Fixed-point number with 1 sign bit, 15 integer bits and 16 fraction bits.

Data Fields
struct Fixed_S32_16.__unnamed104__	__unnamed__
int32_t	raw_value	Value scaled by 65536.

Fixed_S64_32

union Fixed_S64_32

Fixed-point number with 1 sign bit, 31 integer bits and 32 fraction bits.

Data Fields
struct Fixed_S64_32.__unnamed106__	__unnamed__
int64_t	raw_value	Value scaled by 2^32.

Fixed_S16_3.__unnamed102__

struct Fixed_S16_3.__unnamed102__

Data Fields
uint16_t	fraction: 3	Fraction, in eighths.
int16_t	integer: 13	Integer part, rounded towards negative infinity.

Fixed_S32_16.__unnamed104__

struct Fixed_S32_16.__unnamed104__

Data Fields
uint16_t	fraction: 16	Fraction, in 1/65536 units.
int16_t	integer: 16	Integer part, rounded towards negative infinity.

Fixed_S64_32.__unnamed106__

struct Fixed_S64_32.__unnamed106__

Data Fields
uint32_t	fraction: 32	Fraction, in 1/2^32 units.
int32_t	integer: 32	Integer part, rounded towards negative infinity.

Macro Definition Documentation

Fixed_S16_3

#define Fixed_S16_3

(

raw

)

((Fixed_S16_3){.raw_value = (raw)})

Make a Fixed_S16_3 from its raw value.

Parameters

raw	Value scaled by 8.

FIXED_S16_3_FACTOR

#define FIXED_S16_3_FACTOR   (1 << FIXED_S16_3_PRECISION)

Scale factor of Fixed_S16_3.

FIXED_S16_3_HALF

#define FIXED_S16_3_HALF   ((Fixed_S16_3){.raw_value = FIXED_S16_3_ONE.raw_value / 2})

Fixed_S16_3 one half.

FIXED_S16_3_ONE

#define FIXED_S16_3_ONE   ((Fixed_S16_3){.integer = 1, .fraction = 0})

Fixed_S16_3 one.

FIXED_S16_3_PRECISION

#define FIXED_S16_3_PRECISION   3

Number of fraction bits of Fixed_S16_3.

FIXED_S16_3_ZERO

#define FIXED_S16_3_ZERO   ((Fixed_S16_3){.integer = 0, .fraction = 0})

Fixed_S16_3 zero.

Fixed_S32_16

#define Fixed_S32_16

(

raw

)

((Fixed_S32_16){.raw_value = (raw)})

Make a Fixed_S32_16 from its raw value.

Parameters

raw	Value scaled by 65536.

FIXED_S32_16_ONE

#define FIXED_S32_16_ONE   ((Fixed_S32_16){.integer = 1, .fraction = 0})

Fixed_S32_16 one.

FIXED_S32_16_PRECISION

#define FIXED_S32_16_PRECISION   16

Number of fraction bits of Fixed_S32_16.

FIXED_S32_16_ZERO

#define FIXED_S32_16_ZERO   ((Fixed_S32_16){.integer = 0, .fraction = 0})

Fixed_S32_16 zero.

FIXED_S64_32_FROM_INT

#define FIXED_S64_32_FROM_INT

(

x

)

((Fixed_S64_32){.integer = x, .fraction = 0})

Make a Fixed_S64_32 from an integer.

Parameters

x

Integer.

FIXED_S64_32_FROM_RAW

#define FIXED_S64_32_FROM_RAW

(

raw

)

((Fixed_S64_32){.raw_value = (raw)})

Make a Fixed_S64_32 from its raw value.

Parameters

raw	Value scaled by 2^32.

FIXED_S64_32_ONE

#define FIXED_S64_32_ONE   ((Fixed_S64_32){.integer = 1, .fraction = 0})

Fixed_S64_32 one.

FIXED_S64_32_PRECISION

#define FIXED_S64_32_PRECISION   32

Number of fraction bits of Fixed_S64_32.

FIXED_S64_32_TO_INT

#define FIXED_S64_32_TO_INT

(

x

)

(x.integer)

Get the integer part of a Fixed_S64_32, rounded towards negative infinity.

Parameters

x

Value.

FIXED_S64_32_ZERO

#define FIXED_S64_32_ZERO   ((Fixed_S64_32){.integer = 0, .fraction = 0})

Fixed_S64_32 zero.

Typedef Documentation

Fixed_S32_16Return

typedef Fixed_S32_16 Fixed_S32_16Return

Alias of Fixed_S32_16 for function return types.

Avoids the function-like Fixed_S32_16() macro expanding in function pointer declarations.

Function Documentation

Fixed_S16_3_add()

static __inline__ Fixed_S16_3 Fixed_S16_3_add ( Fixed_S16_3  a, Fixed_S16_3  b  )

static

Add two Fixed_S16_3 values.

Parameters

a	First term.
b	Second term.

Returns

Sum.

References Fixed_S16_3, and Fixed_S16_3::raw_value.

Fixed_S16_3_add3()

static __inline__ Fixed_S16_3 Fixed_S16_3_add3 ( Fixed_S16_3  a, Fixed_S16_3  b, Fixed_S16_3  c  )

static

Add three Fixed_S16_3 values.

Parameters

a	First term.
b	Second term.
c	Third term.

Returns

Sum.

References Fixed_S16_3, and Fixed_S16_3::raw_value.

Fixed_S16_3_equal()

static __inline__ bool Fixed_S16_3_equal ( Fixed_S16_3  a, Fixed_S16_3  b  )

static

Compare two Fixed_S16_3 values.

Parameters

a	First value.
b	Second value.

Returns

true if equal.

References Fixed_S16_3::raw_value.

Fixed_S16_3_mul()

static __inline__ Fixed_S16_3 Fixed_S16_3_mul ( Fixed_S16_3  a, Fixed_S16_3  b  )

static

Multiply two Fixed_S16_3 values.

Parameters

a	First factor.
b	Second factor.

Returns

Product, truncated.

References Fixed_S16_3, FIXED_S16_3_PRECISION, and Fixed_S16_3::raw_value.

Fixed_S16_3_rounded_int()

static __inline__ int16_t Fixed_S16_3_rounded_int ( Fixed_S16_3  a )

static

Round a Fixed_S16_3 value to the nearest integer, halves away from zero.

Parameters

a

Value.

Returns

Rounded value.

References FIXED_S16_3_FACTOR, FIXED_S16_3_HALF, and Fixed_S16_3::raw_value.

Fixed_S16_3_S32_16_mul()

static __inline__ Fixed_S16_3 Fixed_S16_3_S32_16_mul ( Fixed_S16_3  a, Fixed_S32_16  b  )

static

Multiply a Fixed_S16_3 by a Fixed_S32_16.

Parameters

a	First factor.
b	Second factor.

Returns

Product, as a Fixed_S16_3.

References Fixed_S16_3, FIXED_S32_16_PRECISION, Fixed_S16_3::raw_value, and Fixed_S32_16::raw_value.

Fixed_S16_3_sub()

static __inline__ Fixed_S16_3 Fixed_S16_3_sub ( Fixed_S16_3  a, Fixed_S16_3  b  )

static

Subtract two Fixed_S16_3 values.

Parameters

a	Minuend.
b	Subtrahend.

Returns

a - b.

References Fixed_S16_3, and Fixed_S16_3::raw_value.

Fixed_S32_16_add()

static __inline__ Fixed_S32_16 Fixed_S32_16_add ( Fixed_S32_16  a, Fixed_S32_16  b  )

static

Add two Fixed_S32_16 values.

Parameters

a	First term.
b	Second term.

Returns

Sum.

References Fixed_S32_16, and Fixed_S32_16::raw_value.

Fixed_S32_16_add3()

static __inline__ Fixed_S32_16 Fixed_S32_16_add3 ( Fixed_S32_16  a, Fixed_S32_16  b, Fixed_S32_16  c  )

static

Add three Fixed_S32_16 values.

Parameters

a	First term.
b	Second term.
c	Third term.

Returns

Sum.

References Fixed_S32_16, and Fixed_S32_16::raw_value.

Fixed_S32_16_mul()

static __inline__ Fixed_S32_16 Fixed_S32_16_mul ( Fixed_S32_16  a, Fixed_S32_16  b  )

static

Multiply two Fixed_S32_16 values.

Parameters

a	First factor.
b	Second factor.

Returns

Product, truncated.

References FIXED_S32_16_PRECISION, and Fixed_S32_16::raw_value.

Fixed_S32_16_sub()

static __inline__ Fixed_S32_16 Fixed_S32_16_sub ( Fixed_S32_16  a, Fixed_S32_16  b  )

static

Subtract two Fixed_S32_16 values.

Parameters

a	Minuend.
b	Subtrahend.

Returns

a - b.

References Fixed_S32_16, and Fixed_S32_16::raw_value.

Fixed_S64_32_add()

static __inline__ Fixed_S64_32 Fixed_S64_32_add ( Fixed_S64_32  a, Fixed_S64_32  b  )

static

Add two Fixed_S64_32 values.

Parameters

a	First term.
b	Second term.

Returns

Sum.

References FIXED_S64_32_FROM_RAW, and Fixed_S64_32::raw_value.

Fixed_S64_32_add3()

static __inline__ Fixed_S64_32 Fixed_S64_32_add3 ( Fixed_S64_32  a, Fixed_S64_32  b, Fixed_S64_32  c  )

static

Add three Fixed_S64_32 values.

Parameters

a	First term.
b	Second term.
c	Third term.

Returns

Sum.

References FIXED_S64_32_FROM_RAW, and Fixed_S64_32::raw_value.

Fixed_S64_32_mul()

static __inline__ Fixed_S64_32 Fixed_S64_32_mul ( Fixed_S64_32  a, Fixed_S64_32  b  )

static

Multiply two Fixed_S64_32 values.

Parameters

a	First factor.
b	Second factor.

Returns

Product.

References Fixed_S64_32::raw_value.

Fixed_S64_32_sub()

static __inline__ Fixed_S64_32 Fixed_S64_32_sub ( Fixed_S64_32  a, Fixed_S64_32  b  )

static

Subtract two Fixed_S64_32 values.

Parameters

a	Minuend.
b	Subtrahend.

Returns

a - b.

References FIXED_S64_32_FROM_RAW, and Fixed_S64_32::raw_value.

math_fixed_recursive_filter()

Fixed_S64_32 math_fixed_recursive_filter	(	Fixed_S64_32	x,
		int	num_input_coefficients,
		int	num_output_coefficients,
		const Fixed_S64_32 *	cb,
		const Fixed_S64_32 *	ca,
		Fixed_S64_32 *	state_x,
		Fixed_S64_32 *	state_y
	)

Run a value through an Nth order linear recursive (IIR) filter.

Computes y[n] = sum(cb[i] * x[n - i]) - sum(ca[i] * y[n - 1 - i]), a generalization of the digital biquad filter.

Parameters

	x	Next input value, x[n].
	num_input_coefficients	Number of input taps, at least 1.
	num_output_coefficients	Number of output taps.
	cb	Input coefficients, num_input_coefficients entries.
	ca	Output coefficients, num_output_coefficients entries.
[in,out]	state_x	History of x, num_input_coefficients entries, kept between calls.
[in,out]	state_y	History of y, num_output_coefficients entries, kept between calls.

Returns

Filtered value, y[n].