Fixed point datatypes

Data Structures
struct	fixed_storage_type< M, F, s, bool >
	Storage type for a fixed point number. More...
struct	fixed_storage_type< M, F, true, test64(M, F, 1)>
	Storage type for a fixed point number representable on int64. More...
struct	fixed_storage_type< M, F, false, test64(M, F, 0)>
	Storage type for a fixed point number representable on uint64. More...
struct	fixed_storage_type< M, F, true, test32(M, F, 1)>
	Storage type for a fixed point number representable on int32. More...
struct	fixed_storage_type< M, F, false, test32(M, F, 0)>
	Storage type for a fixed point number representable on uint32. More...
struct	fixed_storage_type< M, F, true, test16(M, F, 1)>
	Storage type for a fixed point number representable on int16. More...
struct	fixed_storage_type< M, F, false, test16(M, F, 0)>
	Storage type for a fixed point number representable on uint16. More...
struct	fixed_storage_type< M, F, true, test8(M, F, 1)>
	Storage type for a fixed point number representable on int8. More...
struct	fixed_storage_type< M, F, false, test8(M, F, 0)>
	Storage type for a fixed point number representable on uint8. More...
struct	Q< M, F, S, T >
	Fixed point template. More...
struct	Q< M, F, true, int64_t >
	Signed fixed point datatypes on 64 bits. More...
struct	Q< M, F, false, uint64_t >
	Unsigned fixed point datatypes on 64 bits. More...
struct	Q< M, F, true, int32_t >
	Signed fixed point datatypes on 32 bits. More...
struct	Q< M, F, false, uint32_t >
	Unsigned fixed point datatypes on 32 bits. More...
struct	Q< M, F, true, int16_t >
	Signed fixed point datatypes on 16 bits. More...
struct	Q< M, F, false, uint16_t >
	Unsigned fixed point datatypes on 16 bits. More...
struct	Q< M, F, true, int8_t >
	Signed fixed point datatypes on 8 bits. More...
struct	Q< M, F, false, uint8_t >
	Unsigned fixed point datatypes on 8 bits. More...
struct	FixedCastShift< M, FD, FS, S,(FD >FS)>
	Changed fractional representation of a fixed point number using a shift. More...
struct	FixedCastShift< M, FD, FS, S,(FD< FS)>
	Changed fractional representation of a fixed point number using a shift. More...
struct	Accumulate< MD, MS, F, S, bool >
	Accumulation without saturation. More...
struct	Accumulate< MD, MS, F, S, true >
	Accumulation without saturation. More...

Typedefs
using	Q63 = Q< 0, 63 >
	Q63 datatype.
using	Q31 = Q< 0, 31 >
	Q31 datatype.
using	Q15 = Q< 0, 15 >
	Q15 datatype.
using	Q7 = Q< 0, 7 >
	Q7 datatype.

Functions
constexpr bool	test64 (const int M, const int F, const int S)
	Function to identify the template for fixed number representable on 64 bits.
constexpr bool	test32 (const int M, const int F, const int S)
	Function to identify the template for fixed number representable on 32 bits.
constexpr bool	test16 (const int M, const int F, const int S)
	Function to identify the template for fixed number representable on 16 bits.
constexpr bool	test8 (const int M, const int F, const int S)
	Function to identify the template for fixed number representable on 8 bits.
constexpr Q63	operator""_q63 (long double x)
	q63 literal
constexpr Q31	operator""_q31 (long double x)
	q31 literal
constexpr Q15	operator""_q15 (long double x)
	q15 literal
constexpr Q7	operator""_q7 (long double x)
	q7 literal
template<int MA, int FA, int MB, int FB, bool SA, bool SB>
Q< MA+MB+1, FA+FB, SA||SB >	mult (const Q< MA, FA, SA > &a, const Q< MB, FB, SB > &b)
	Multiplication of two fixed point numbers A and B.
template<int M, int F, bool S>
Q< M, F, S >	operator+ (const Q< M, F, S > &a, const Q< M, F, S > &b)
	Add two fixed point numbers with saturation.
template<int M, int F, bool S>
Q< M, F, S >	operator- (const Q< M, F, S > &a, const Q< M, F, S > &b)
	Subtract two fixed point numbers with saturation.
template<int M, int F, bool S>
Q< M, F, S >	operator- (const Q< M, F, S > &a)
	Negate a fixed point number with saturation.
template<int M, int F, bool S>
Q< M, F, S >	add (const Q< M, F, S > &a, const Q< M, F, S > &b)
	Add two fixed point numbers without saturation.
template<int M, int F, bool S>
Q< M, F, S >	sub (const Q< M, F, S > &a, const Q< M, F, S > &b)
	Subtract two fixed point numbers without saturation.
template<int M, int F, int N, bool S>
Q< M, F, S >	operator>> (const Q< M, F, S > &a, std::integral_constant< int, N >) noexcept
	Shift right a fixed point number with a shift known at build time.
template<int M, int F, int N, bool S>
Q< M+N, F, S >	operator<< (const Q< M, F, S > &a, std::integral_constant< int, N >) noexcept
	Shift left a fixed point number with a shift known at build time.
template<int MD = 0, int MS, int F>
Q< MD, F, true >	saturate (const Q< MS, F, true > &src, typename std::enable_if<(MD< MS) &&((MD+F)< 31)>::type *=nullptr)
	Saturate a signed fixed point number.
template<int MD = 0, int MS, int F>
Q< MD, F, false >	saturate (const Q< MS, F, false > &src, typename std::enable_if<(MD< MS) &&((MD+F)< 31)>::type *=nullptr)
	Saturate an unsigned fixed point number.
template<int FD, int M, int FS, bool S>
Q< M, FD, S >	toFrac (const Q< M, FS, S > &src)
	Convert between different fractional part formats.
template<int MD, int MS, int F, bool S>
Q< MD, F, S >	accumulate (const Q< MD, F, S > &a, const Q< MS, F, S > &b)
	Accumulate without saturation.
Q7	operator* (const Q7 &a, const Q7 &b)
	Multiplication operator.
Q15	operator* (const Q15 &a, const Q15 &b)
	Multiplication operator.
Q31	operator* (const Q31 &a, const Q31 &b)
	Multiplication operator.
template<int M, int F>
bool	operator> (const Q< M, F > &a, const Q< M, F > &b)
	Greater-than comparison operator.
template<int M, int F>
bool	operator< (const Q< M, F > &a, const Q< M, F > &b)
	Less-than comparison operator.
template<int M, int F>
bool	operator>= (const Q< M, F > &a, const Q< M, F > &b)
	Greater-than-or-equal comparison operator.
template<int M, int F>
bool	operator<= (const Q< M, F > &a, const Q< M, F > &b)
	Less-than-or-equal comparison operator.
template<int M, int F>
bool	operator== (const Q< M, F > a, const Q< M, F > b)
	Equality operator.
template<int M, int F>
bool	operator!= (const Q< M, F > a, const Q< M, F > b)
	Inequality operator.
template<int M, int F, bool S>
Q< M, F, S >	operator/ (const Q< M, F, S > a, const int32_t b)
	Division operator.
template<int M, int F, bool S>
Q< M, F, S >	operator+ (const Q< M, F, S > &a)
	No op operator.

Description

---

Data Structure Documentation

arm_cmsis_dsp::fixed_storage_type

struct arm_cmsis_dsp::fixed_storage_type

template<int M, int F, bool s = true, bool = true>
struct arm_cmsis_dsp::fixed_storage_type< M, F, s, bool >

Storage type for a fixed point number.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part
s	signed or unsigned

arm_cmsis_dsp::fixed_storage_type< M, F, true, test64(M, F, 1)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test64(M, F, 1)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test64(M, F, 1)>

Storage type for a fixed point number representable on int64.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef int64_t	value_type
	Storage for the fixed point number.
typedef int64_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef int32_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, false, test64(M, F, 0)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test64(M, F, 0)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test64(M, F, 0)>

Storage type for a fixed point number representable on uint64.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef uint64_t	value_type
	Storage for the fixed point number.
typedef uint64_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef uint32_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, true, test32(M, F, 1)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test32(M, F, 1)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test32(M, F, 1)>

Storage type for a fixed point number representable on int32.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef int32_t	value_type
	Storage for the fixed point number.
typedef int64_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef int16_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, false, test32(M, F, 0)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test32(M, F, 0)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test32(M, F, 0)>

Storage type for a fixed point number representable on uint32.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef uint32_t	value_type
	Storage for the fixed point number.
typedef uint64_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef uint16_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, true, test16(M, F, 1)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test16(M, F, 1)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test16(M, F, 1)>

Storage type for a fixed point number representable on int16.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef int16_t	value_type
	Storage for the fixed point number.
typedef int32_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef int8_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, false, test16(M, F, 0)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test16(M, F, 0)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test16(M, F, 0)>

Storage type for a fixed point number representable on uint16.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef uint16_t	value_type
	Storage for the fixed point number.
typedef uint32_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef uint8_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, true, test8(M, F, 1)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test8(M, F, 1)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, true, test8(M, F, 1)>

Storage type for a fixed point number representable on int8.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef int8_t	value_type
	Storage for the fixed point number.
typedef int16_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef int8_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::fixed_storage_type< M, F, false, test8(M, F, 0)>

struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test8(M, F, 0)>

template<int M, int F>
struct arm_cmsis_dsp::fixed_storage_type< M, F, false, test8(M, F, 0)>

Storage type for a fixed point number representable on uint8.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
typedef uint8_t	value_type
	Storage for the fixed point number.
typedef uint16_t	wider_type
	Storage for the widening of this fixed point number datatype.
typedef uint8_t	narrow_type
	Storage for the narrowing of this fixed point number datatype.

arm_cmsis_dsp::Q

struct arm_cmsis_dsp::Q

template<int M, int F, bool S = true, typename T = typename fixed_storage_type<M,F,S>::value_type>
struct arm_cmsis_dsp::Q< M, F, S, T >

Fixed point template.

Template Parameters

M	Number of bits for mantissa (without sign bit)#
F	Number of bits for fractional part
S	Signed or unsigned
T	storage datatype

arm_cmsis_dsp::Q< M, F, true, int64_t >

struct arm_cmsis_dsp::Q< M, F, true, int64_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, true, int64_t >

Signed fixed point datatypes on 64 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, true >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, true >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
constexpr	Q (const Q< M, F, false > &other)
	Convert an unsigned fixed point to this fixed point.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Q &	operator+= (const Q other)
	this += other
Q &	operator-= (const Q other)
	this -= other
Static Public Member Functions
static constexpr value_type	convert (const float f)
	Convert a float to fixed point.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = true
	Is this number representation signed.
static constexpr value_type	maxVal = 0x7FFFFFFFFFFFFFFFLL
	Maximum representable positive value.
static constexpr value_type	minVal = 0x8000000000000000LL
	Minimum representable negative value.

Constructor & Destructor Documentation

Q() [1/2]

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Q() [2/2]

constexpr Q ( const Q< M, F, false > &  other )

inlineexplicitconstexpr

Convert an unsigned fixed point to this fixed point.

Parameters

other

The unsigned fixed point number

Some problem may occur since the unsigned may not be representable with the less bits required for the sign representation. This convertion is not saturating.

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, true, int64_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator+=()

Q & operator+= ( const Q< M, F, true, int64_t >  other )

inline

this += other

Parameters

other

the other fixed point

Returns

true if this += other

operator-=()

Q & operator-= ( const Q< M, F, true, int64_t >  other )

inline

this -= other

Parameters

other

the other fixed point

Returns

true if this += other

operator<()

bool operator< ( const Q< M, F, true, int64_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, true, int64_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, true, int64_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, true, int64_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, true, int64_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

arm_cmsis_dsp::Q< M, F, false, uint64_t >

struct arm_cmsis_dsp::Q< M, F, false, uint64_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, false, uint64_t >

Unsigned fixed point datatypes on 64 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, false >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, false >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Static Public Member Functions
static constexpr value_type	convert (const float f)
	Convert a float to fixed point.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = false
	Is this number representation signed.
static constexpr value_type	maxVal = 0xFFFFFFFFFFFFFFFFLL
	Maximum representable positive value.

Constructor & Destructor Documentation

Q()

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, false, uint64_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator<()

bool operator< ( const Q< M, F, false, uint64_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, false, uint64_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, false, uint64_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, false, uint64_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, false, uint64_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

arm_cmsis_dsp::Q< M, F, true, int32_t >

struct arm_cmsis_dsp::Q< M, F, true, int32_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, true, int32_t >

Signed fixed point datatypes on 32 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, true >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, true >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
constexpr	Q (const Q< M, F, false > &other)
	Convert an unsigned fixed point to this fixed point.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Q &	operator+= (const Q other)
	this += other
Q &	operator-= (const Q other)
	this -= other
Static Public Member Functions
static constexpr value_type	sat (const wider_type i)
	Saturate a wider type to the current type.
static constexpr value_type	convert (const float f)
	Convert a float to fixed point with saturation.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = true
	Is this number representation signed.
static constexpr value_type	maxVal = 0x7FFFFFFFL
	Maximum representable positive value.
static constexpr value_type	minVal = 0x80000000L
	Minimum representable negative value.

Constructor & Destructor Documentation

Q() [1/2]

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Q() [2/2]

constexpr Q ( const Q< M, F, false > &  other )

inlineexplicitconstexpr

Convert an unsigned fixed point to this fixed point.

Parameters

other

The unsigned fixed point number

Some problem may occur since the unsigned may not be representable with the less bits required for the sign representation. This convertion is not saturating.

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point with saturation.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, true, int32_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator+=()

Q & operator+= ( const Q< M, F, true, int32_t >  other )

inline

this += other

Parameters

other

the other fixed point

Returns

true if this += other

operator-=()

Q & operator-= ( const Q< M, F, true, int32_t >  other )

inline

this -= other

Parameters

other

the other fixed point

Returns

true if this += other

operator<()

bool operator< ( const Q< M, F, true, int32_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, true, int32_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, true, int32_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, true, int32_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, true, int32_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

sat()

static constexpr value_type sat ( const wider_type  i )

inlinestaticconstexpr

Saturate a wider type to the current type.

Parameters

i	the wider integer type

Returns

the saturated value

arm_cmsis_dsp::Q< M, F, false, uint32_t >

struct arm_cmsis_dsp::Q< M, F, false, uint32_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, false, uint32_t >

Unsigned fixed point datatypes on 32 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, false >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, false >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Static Public Member Functions
static constexpr value_type	sat (const wider_type i)
	Saturate a wider type to the current type.
static constexpr value_type	convert (const float f)
	Convert a float to fixed point with saturation.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = false
	Is this number representation signed.
static constexpr value_type	maxVal = 0xFFFFFFFFL
	Maximum representable positive value.

Constructor & Destructor Documentation

Q()

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point with saturation.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, false, uint32_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator<()

bool operator< ( const Q< M, F, false, uint32_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, false, uint32_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, false, uint32_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, false, uint32_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, false, uint32_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

sat()

static constexpr value_type sat ( const wider_type  i )

inlinestaticconstexpr

Saturate a wider type to the current type.

Parameters

i	the wider integer type

Returns

the saturated value

arm_cmsis_dsp::Q< M, F, true, int16_t >

struct arm_cmsis_dsp::Q< M, F, true, int16_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, true, int16_t >

Signed fixed point datatypes on 16 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, true >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, true >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
constexpr	Q (const Q< M, F, false > &other)
	Convert an unsigned fixed point to this fixed point.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Q &	operator+= (const Q other)
	this += other
Q &	operator-= (const Q other)
	this -= other
Static Public Member Functions
static constexpr value_type	sat (const wider_type i)
	Saturate a wider type to the current type.
static constexpr value_type	convert (const float f)
	Convert a float to fixed point with saturation.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = true
	Is this number representation signed.
static constexpr value_type	maxVal = 0x7FFF
	Maximum representable positive value.
static constexpr value_type	minVal = 0x8000
	Minimum representable negative value.

Constructor & Destructor Documentation

Q() [1/2]

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Q() [2/2]

constexpr Q ( const Q< M, F, false > &  other )

inlineexplicitconstexpr

Convert an unsigned fixed point to this fixed point.

Parameters

other

The unsigned fixed point number

Some problem may occur since the unsigned may not be representable with the less bits required for the sign representation. This convertion is not saturating.

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point with saturation.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, true, int16_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator+=()

Q & operator+= ( const Q< M, F, true, int16_t >  other )

inline

this += other

Parameters

other

the other fixed point

Returns

true if this += other

operator-=()

Q & operator-= ( const Q< M, F, true, int16_t >  other )

inline

this -= other

Parameters

other

the other fixed point

Returns

true if this += other

operator<()

bool operator< ( const Q< M, F, true, int16_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, true, int16_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, true, int16_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, true, int16_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, true, int16_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

sat()

static constexpr value_type sat ( const wider_type  i )

inlinestaticconstexpr

Saturate a wider type to the current type.

Parameters

i	the wider integer type

Returns

the saturated value

arm_cmsis_dsp::Q< M, F, false, uint16_t >

struct arm_cmsis_dsp::Q< M, F, false, uint16_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, false, uint16_t >

Unsigned fixed point datatypes on 16 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, false >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, false >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Q &	operator+= (const Q other)
	this += other
Static Public Member Functions
static constexpr value_type	sat (const wider_type i)
	Saturate a wider type to the current type.
static constexpr value_type	convert (const float f)
	Convert a float to fixed point with saturation.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = false
	Is this number representation signed.
static constexpr value_type	maxVal = 0xFFFF
	Maximum representable positive value.

Constructor & Destructor Documentation

Q()

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point with saturation.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, false, uint16_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator+=()

Q & operator+= ( const Q< M, F, false, uint16_t >  other )

inline

this += other

Parameters

other

the other fixed point

Returns

true if this += other

operator<()

bool operator< ( const Q< M, F, false, uint16_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, false, uint16_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, false, uint16_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, false, uint16_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, false, uint16_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

sat()

static constexpr value_type sat ( const wider_type  i )

inlinestaticconstexpr

Saturate a wider type to the current type.

Parameters

i	the wider integer type

Returns

the saturated value

arm_cmsis_dsp::Q< M, F, true, int8_t >

struct arm_cmsis_dsp::Q< M, F, true, int8_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, true, int8_t >

Signed fixed point datatypes on 8 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, true >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, true >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
constexpr	Q (const Q< M, F, false > &other)
	Convert an unsigned fixed point to this fixed point.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Q &	operator+= (const Q other)
	this += other
Q &	operator-= (const Q other)
	this -= other
Static Public Member Functions
static constexpr value_type	sat (const wider_type i)
	Saturate a wider type to the current type.
static constexpr value_type	convert (const float f)
	Convert a float to fixed point with saturation.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = true
	Is this number representation signed.
static constexpr value_type	maxVal = 0x7F
	Maximum representable positive value.
static constexpr value_type	minVal = 0x80
	Minimum representable negative value.

Constructor & Destructor Documentation

Q() [1/2]

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Q() [2/2]

constexpr Q ( const Q< M, F, false > &  other )

inlineexplicitconstexpr

Convert an unsigned fixed point to this fixed point.

Parameters

other

The unsigned fixed point number

Some problem may occur since the unsigned may not be representable with the less bits required for the sign representation. This convertion is not saturating.

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point with saturation.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, true, int8_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator+=()

Q & operator+= ( const Q< M, F, true, int8_t >  other )

inline

this += other

Parameters

other

the other fixed point

Returns

true if this += other

operator-=()

Q & operator-= ( const Q< M, F, true, int8_t >  other )

inline

this -= other

Parameters

other

the other fixed point

Returns

true if this += other

operator<()

bool operator< ( const Q< M, F, true, int8_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, true, int8_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, true, int8_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, true, int8_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, true, int8_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

sat()

static constexpr value_type sat ( const wider_type  i )

inlinestaticconstexpr

Saturate a wider type to the current type.

Parameters

i	the wider integer type

Returns

the saturated value

arm_cmsis_dsp::Q< M, F, false, uint8_t >

struct arm_cmsis_dsp::Q< M, F, false, uint8_t >

template<int M, int F>
struct arm_cmsis_dsp::Q< M, F, false, uint8_t >

Unsigned fixed point datatypes on 8 bits.

Template Parameters

M	Number of bits for mantissa (without sign bit)
F	Number of bits for fractional part

Public Types
using	value_type = typename fixed_storage_type< M, F, false >::value_type
	Storage type for the value.
using	wider_type = typename fixed_storage_type< M, F, false >::wider_type
	Storage type for the widening of the value.
Public Member Functions
constexpr	Q ()
	Create a new zero fixed point.
constexpr	Q (const value_type x)
	Create a new fixed point from a raw integer.
bool	operator== (const Q &b) const
	this == b
bool	operator!= (const Q &b) const
	this != b
bool	operator< (const Q &b) const
	this < b
bool	operator> (const Q &b) const
	this > b
bool	operator<= (const Q &b) const
	this <= b
bool	operator>= (const Q &b) const
	this >= b
Q &	operator+= (const Q other)
	this += other
Static Public Member Functions
static constexpr value_type	sat (const wider_type i)
	Saturate a wider type to the current type.
static constexpr value_type	convert (const float f)
	Convert a float to fixed point with saturation.
static constexpr Q	f (const float x)
	Create a new fixed point from a float.
static constexpr Q	one ()
	Fixed point number representing 1.
Data Fields
value_type	v
	Storage value.
Static Public Attributes
static constexpr int	fracBits = F
	Number of fractional bits.
static constexpr int	mantissaBits = M
	Number of mantissa bits (without sign bit)
static constexpr bool	isSigned = false
	Is this number representation signed.
static constexpr value_type	maxVal = 0xFF
	Maximum representable positive value.

Constructor & Destructor Documentation

Q()

constexpr Q ( const value_type  x )

inlineexplicitconstexpr

Create a new fixed point from a raw integer.

Parameters

x	the raw integer

Member Function Documentation

convert()

static constexpr value_type convert ( const float  f )

inlinestaticconstexpr

Convert a float to fixed point with saturation.

Parameters

f	float value

Returns

the fixed point value in the storage type

f()

static constexpr Q f ( const float  x )

inlinestaticconstexpr

Create a new fixed point from a float.

Parameters

x

the float

Returns

The fixed point representing the float value with saturation

one()

static constexpr Q one ( )

inlinestaticconstexpr

Fixed point number representing 1.

Returns

Fixed point representing 1

operator!=()

bool operator!= ( const Q< M, F, false, uint8_t > &  b ) const

inline

this != b

Parameters

b	the other fixed point

Returns

true if this != b

operator+=()

Q & operator+= ( const Q< M, F, false, uint8_t >  other )

inline

this += other

Parameters

other

the other fixed point

Returns

true if this += other

operator<()

bool operator< ( const Q< M, F, false, uint8_t > &  b ) const

inline

this < b

Parameters

b	the other fixed point

Returns

true if this < b

operator<=()

bool operator<= ( const Q< M, F, false, uint8_t > &  b ) const

inline

this <= b

Parameters

b	the other fixed point

Returns

true if this <= b

operator==()

bool operator== ( const Q< M, F, false, uint8_t > &  b ) const

inline

this == b

Parameters

b	the other fixed point

Returns

true if this == b

operator>()

bool operator> ( const Q< M, F, false, uint8_t > &  b ) const

inline

this > b

Parameters

b	the other fixed point

Returns

true if this > b

operator>=()

bool operator>= ( const Q< M, F, false, uint8_t > &  b ) const

inline

this >= b

Parameters

b	the other fixed point

Returns

true if this >= b

sat()

static constexpr value_type sat ( const wider_type  i )

inlinestaticconstexpr

Saturate a wider type to the current type.

Parameters

i	the wider integer type

Returns

the saturated value

arm_cmsis_dsp::FixedCastShift< M, FD, FS, S,(FD >FS)>

struct arm_cmsis_dsp::FixedCastShift< M, FD, FS, S,(FD >FS)>

template<int M, int FD, int FS, bool S>
struct arm_cmsis_dsp::FixedCastShift< M, FD, FS, S,(FD >FS)>

Changed fractional representation of a fixed point number using a shift.

Template Parameters

M	Number of mantissa bits for the fixed point number
FD	Number of fractional bits for the destination fixed point number
FS	Number of fractional bits for the source fixed point number
S	Is the fixed point number using a signed representation

Parameters

src	The fixed point number

Returns

return the fixed point number with different fractional part format

Only applies if FD > FS

arm_cmsis_dsp::FixedCastShift< M, FD, FS, S,(FD< FS)>

struct arm_cmsis_dsp::FixedCastShift< M, FD, FS, S,(FD< FS)>

template<int M, int FD, int FS, bool S>
struct arm_cmsis_dsp::FixedCastShift< M, FD, FS, S,(FD< FS)>

Changed fractional representation of a fixed point number using a shift.

Template Parameters

M	Number of mantissa bits for the fixed point number
FD	Number of fractional bits for the destination fixed point number
FS	Number of fractional bits for the source fixed point number
S	Is the fixed point number using a signed representation

Parameters

src	The fixed point number

Returns

return the fixed point number with different fractional part format

Only applies if FD < FS

arm_cmsis_dsp::Accumulate

struct arm_cmsis_dsp::Accumulate

template<int MD, int MS, int F, bool S, bool = true>
struct arm_cmsis_dsp::Accumulate< MD, MS, F, S, bool >

Accumulation without saturation.

Template Parameters

MD	Number of mantissa bits for the destination fixed point number
MS	Number of mantissa bits for the source fixed point number
F	Number of fractional bits for fixed point number
S	Is the fixed point number using a signed representation

arm_cmsis_dsp::Accumulate< MD, MS, F, S, true >

struct arm_cmsis_dsp::Accumulate< MD, MS, F, S, true >

template<int MD, int MS, int F, bool S>
struct arm_cmsis_dsp::Accumulate< MD, MS, F, S, true >

Accumulation without saturation.

Template Parameters

MD	Number of mantissa bits for the destination fixed point number
MS	Number of mantissa bits for the source fixed point number
F	Number of fractional bits for fixed point number
S	Is the fixed point number using a signed representation

Static Public Member Functions
static Q< MD, F, S >	acc (const Q< MD, F, S > &a, const Q< MS, F, S > &b)
	Accumulation without saturation.

Member Function Documentation

acc()

static Q< MD, F, S > acc ( const Q< MD, F, S > &  a, const Q< MS, F, S > &  b  )

inlinestatic

Accumulation without saturation.

Parameters

[in]	a	first fixed point number
[in]	b	second fixed point number

Returns

The sum of both fixed point number with more matissa bits.

Function Documentation

accumulate()

Q< MD, F, S > accumulate ( const Q< MD, F, S > &  a, const Q< MS, F, S > &  b  )

inline

Accumulate without saturation.

Parameters

[in]	a	First fixed point number
[in]	b	Second fixed point number

Template Parameters

MD	Number of mantissa bits for destination
MS	Number of mantissa bits fro source
F	Number of fractional bits
S	Is the representation signed

Returns

Sum of two numbers without saturation and using the destination number of mantissa bits

add()

Q< M, F, S > add ( const Q< M, F, S > &  a, const Q< M, F, S > &  b  )

inline

Add two fixed point numbers without saturation.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number
b	Second fixed point number

Returns

return the sum without saturation

mult()

Q< MA+MB+1, FA+FB, SA||SB > mult ( const Q< MA, FA, SA > &  a, const Q< MB, FB, SB > &  b  )

inline

Multiplication of two fixed point numbers A and B.

Template Parameters

MA	Number of mantissa bits for A
FA	Number of fractional bits for A
MB	Number of mantissa bits for B
FB	Number of fractional bits for B
SA	Is A using a signed representation
SB	Is B using a signed representation

Parameters

a	First fixed point number
b	Second fixed point number

Returns

return the product of the two fixed point (and use adapted type)

operator!=()

bool operator!= ( const Q< M, F >  a, const Q< M, F >  b  )

inline

Inequality operator.

Parameters

[in]	a	First value
[in]	b	Second value

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits

Returns

The result of the inequality

operator""_q15()

constexpr Q15 operator""_q15 ( long double  x )

constexpr

q15 literal

Parameters

x	long double value

Returns

Q15 value

You can write

Q15 b = 0.4_q15;

The float is converted to Q15 at build time.

operator""_q31()

constexpr Q31 operator""_q31 ( long double  x )

constexpr

q31 literal

Parameters

x	long double value

Returns

Q31 value

You can write

Q31 b = 0.4_q31;

The float is converted to Q31 at build time.

operator""_q63()

constexpr Q63 operator""_q63 ( long double  x )

constexpr

q63 literal

Parameters

x	long double value

Returns

Q63 value

You can write

Q63 b = 0.4_q63;

The float is converted to Q63 at build time.

operator""_q7()

constexpr Q7 operator""_q7 ( long double  x )

constexpr

q7 literal

Parameters

x	long double value

Returns

Q7 value

You can write

Q7 b = 0.4_q7;

The float is converted to Q7 at build time.

operator*() [1/3]

Q15 operator* ( const Q15 &  a, const Q15 &  b  )

inline

Multiplication operator.

Parameters

[in]	a	First value
[in]	b	Second value

Returns

The result of the multiplication with saturation

operator*() [2/3]

Q31 operator* ( const Q31 &  a, const Q31 &  b  )

inline

Multiplication operator.

Parameters

[in]	a	First value
[in]	b	Second value

Returns

The result of the multiplication with saturation

operator*() [3/3]

Q7 operator* ( const Q7 &  a, const Q7 &  b  )

inline

Multiplication operator.

Parameters

[in]	a	First value
[in]	b	Second value

Returns

The result of the multiplication with saturation

operator+() [1/2]

Q< M, F, S > operator+ ( const Q< M, F, S > &  a )

inline

No op operator.

Parameters

[in]

a

Fixed point number

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits
S	Is the representation signed

Returns

The result of the addition

operator+() [2/2]

Q< M, F, S > operator+ ( const Q< M, F, S > &  a, const Q< M, F, S > &  b  )

inline

Add two fixed point numbers with saturation.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number
b	Second fixed point number

Returns

return the sum with saturation (if supported by the datatype)

operator-() [1/2]

Q< M, F, S > operator- ( const Q< M, F, S > &  a )

inline

Negate a fixed point number with saturation.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number

Returns

return negation with saturation (if supported by the datatype)

operator-() [2/2]

Q< M, F, S > operator- ( const Q< M, F, S > &  a, const Q< M, F, S > &  b  )

inline

Subtract two fixed point numbers with saturation.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number
b	Second fixed point number

Returns

return the subtraction with saturation (if supported by the datatype)

operator/()

Q< M, F, S > operator/ ( const Q< M, F, S >  a, const int32_t  b  )

inline

Division operator.

Parameters

[in]	a	First fixed point value
[in]	b	Integer

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits
S	Is representation signed

Returns

The result of the division

operator<()

bool operator< ( const Q< M, F > &  a, const Q< M, F > &  b  )

inline

Less-than comparison operator.

Parameters

[in]	a	First value
[in]	b	Second value

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits

Returns

The result of the less-than comparison

operator<<()

Q< M+N, F, S > operator<< ( const Q< M, F, S > &  a, std::integral_constant< int, N >    )

inlinenoexcept

Shift left a fixed point number with a shift known at build time.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number

Returns

return the shifted fixed point number

operator<=()

bool operator<= ( const Q< M, F > &  a, const Q< M, F > &  b  )

inline

Less-than-or-equal comparison operator.

Parameters

[in]	a	First value
[in]	b	Second value

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits

Returns

The result of the less-than-or-equal comparison

operator==()

bool operator== ( const Q< M, F >  a, const Q< M, F >  b  )

inline

Equality operator.

Parameters

[in]	a	First value
[in]	b	Second value

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits

Returns

The result of the equality

operator>()

bool operator> ( const Q< M, F > &  a, const Q< M, F > &  b  )

inline

Greater-than comparison operator.

Parameters

[in]	a	First value
[in]	b	Second value

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits

Returns

The result of the greater-than comparison

operator>=()

bool operator>= ( const Q< M, F > &  a, const Q< M, F > &  b  )

inline

Greater-than-or-equal comparison operator.

Parameters

[in]	a	First value
[in]	b	Second value

Template Parameters

M	Number of mantissa bits
F	Number of fractional bits

Returns

The result of the greater-than-or-equal comparison

operator>>()

Q< M, F, S > operator>> ( const Q< M, F, S > &  a, std::integral_constant< int, N >    )

inlinenoexcept

Shift right a fixed point number with a shift known at build time.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number

Returns

return the shifted fixed point number

saturate() [1/2]

Q< MD, F, false > saturate ( const Q< MS, F, false > &  src, typename std::enable_if<(MD< MS) &&((MD+F)< 31)>::type *  = nullptr  )

inline

Saturate an unsigned fixed point number.

Template Parameters

MD	Number of mantissa bits for the destination fixed point number
MS	Number of mantissa bits for the source fixed point number
S	Is the fixed point number using a signed representation

Parameters

src	The fixed point number

Returns

return the saturated fixed point number

Only applies if the number is unsigned, the representation requires less than 31 bits (since there is no saturating instruction for 64 bits) and if destination has less mantissa bits.

If destination has more or equal number of mantissa bits then it does not make sense to saturate.

saturate() [2/2]

Q< MD, F, true > saturate ( const Q< MS, F, true > &  src, typename std::enable_if<(MD< MS) &&((MD+F)< 31)>::type *  = nullptr  )

inline

Saturate a signed fixed point number.

Template Parameters

MD	Number of mantissa bits for the destination fixed point number
MS	Number of mantissa bits for the source fixed point number
S	Is the fixed point number using a signed representation

Parameters

src	First fixed point number

Returns

return the saturated fixed point number

Only applies if the number is signed, the representation requires less than 32 bits (since there is no saturating instruction for 64 bits) and if destination has less mantissa bits.

If destination has more or equal number of mantissa bits then it does not make sense to saturate.

sub()

Q< M, F, S > sub ( const Q< M, F, S > &  a, const Q< M, F, S > &  b  )

inline

Subtract two fixed point numbers without saturation.

Template Parameters

M	Number of mantissa bits for the fixed point number
F	Number of fractional bits for the fixed point number
S	Is the fixed point number using a signed representation

Parameters

a	First fixed point number
b	Second fixed point number

Returns

return the subtraction without saturation

test16()

constexpr bool test16 ( const int  M, const int  F, const int  S  )

constexpr

Function to identify the template for fixed number representable on 16 bits.

Parameters

M	number of mantissa bit (without sign bit)
F	number of fractional bits
S	sign or unsigned

Returns

True if the template must be selected

test32()

constexpr bool test32 ( const int  M, const int  F, const int  S  )

constexpr

Function to identify the template for fixed number representable on 32 bits.

Parameters

M	number of mantissa bit (without sign bit)
F	number of fractional bits
S	sign or unsigned

Returns

True if the template must be selected

test64()

constexpr bool test64 ( const int  M, const int  F, const int  S  )

constexpr

Function to identify the template for fixed number representable on 64 bits.

Parameters

M	number of mantissa bit (without sign bit)
F	number of fractional bits
S	sign or unsigned

Returns

True if the template must be selected

test8()

constexpr bool test8 ( const int  M, const int  F, const int  S  )

constexpr

Function to identify the template for fixed number representable on 8 bits.

Parameters

M	number of mantissa bit (without sign bit)
F	number of fractional bits
S	sign or unsigned

Returns

True if the template must be selected

toFrac()

Q< M, FD, S > toFrac ( const Q< M, FS, S > &  src )

inline

Convert between different fractional part formats.

Template Parameters

M	Number of mantissa bits for the fixed point number
FD	Number of fractional bits for the destination fixed point number
FS	Number of fractional bits for the source fixed point number
S	Is the fixed point number using a signed representation

Parameters

src	The fixed point number

Returns

return the fixed point number with different fractional part format