API for the qFP16 Fixed-point math library. More...

Data Structures
struct	qFP16_Settings_t
	A Q16.16 fixed-point settings object. More...

Macros
#define	qFP16_Constant(x)
	A macro for defining a fixed-point constant value.

Typedefs
typedef int32_t	qFP16_t
	Fixed-point Q16.16 type with width of exactly 32 bits.

Functions
int	qFP16_SettingsSet (qFP16_Settings_t *const instance, qFP16_t min, qFP16_t max, uint8_t rounding, uint8_t saturate)
	Set settings for the fixed-point API.

void	qFP16_SettingsSelect (qFP16_Settings_t *const instance)
	Select the provided setting instance to perform fixed-point operations.

int	qFP16_FPToInt (const qFP16_t x)
	Returns the fixed-point value x converted to int.

qFP16_t	qFP16_IntToFP (const int x)
	Returns the int value x converted to fixed-point q16.16.

qFP16_t	qFP16_FloatToFP (const float x)
	Returns the float value x converted to fixed-point q16.16.

float	qFP16_FPToFloat (const qFP16_t x)
	Returns the fixed-point value x converted to float.

qFP16_t	qFP16_DoubleToFP (const double x)
	Returns the double value x converted to fixed-point q16.16.

double	qFP16_FPToDouble (const qFP16_t x)
	Returns the fixed-point value x converted to double.

qFP16_t	qFP16_Abs (const qFP16_t x)
	Returns the absolute value of x.

qFP16_t	qFP16_Floor (const qFP16_t x)
	Returns the largest integer value less than or equal to x.

qFP16_t	qFP16_Ceil (const qFP16_t x)
	Returns the smallest integer value greater than or equal to x.

qFP16_t	qFP16_Round (const qFP16_t x)
	Returns the nearest integer value of the fixed-point argument x.

qFP16_t	qFP16_Add (const qFP16_t X, const qFP16_t Y)
	Returns the fixed-point addition x + y.

qFP16_t	qFP16_Sub (const qFP16_t X, const qFP16_t Y)
	Returns the fixed-point subtraction x - y.

qFP16_t	qFP16_Mul (const qFP16_t x, const qFP16_t y)
	Returns the fixed-point product operation x * y.

qFP16_t	qFP16_Div (const qFP16_t x, const qFP16_t y)
	Returns the fixed-point division operation x / y.

qFP16_t	qFP16_Mod (const qFP16_t x, const qFP16_t y)
	Returns the fixed-point modulo operation x % y.

qFP16_t	qFP16_Sqrt (qFP16_t x)
	Returns the fixed-point square root of x.

qFP16_t	qFP16_Exp (qFP16_t x)
	Returns the fixed-point value of e raised to the xth power.

qFP16_t	qFP16_Log (qFP16_t x)
	Returns the fixed-point natural logarithm (base-e logarithm) of x.

qFP16_t	qFP16_Log2 (const qFP16_t x)
	Returns the fixed-point log base 2 of x.

qFP16_t	qFP16_RadToDeg (const qFP16_t x)
	Converts angle units from radians to degrees.

qFP16_t	qFP16_DegToRad (const qFP16_t x)
	Converts angle units from degrees to radians.

qFP16_t	qFP16_WrapToPi (qFP16_t x)
	Wrap the fixed-point angle in radians to [−pi pi].

qFP16_t	qFP16_WrapTo180 (qFP16_t x)
	Wrap the fixed-point angle in degrees to [−180 180].

qFP16_t	qFP16_Sin (qFP16_t x)
	Computes the fixed-point sine of the radian angle x.

qFP16_t	qFP16_Cos (qFP16_t x)
	Computes the fixed-point cosine of the radian angle x.

qFP16_t	qFP16_Tan (qFP16_t x)
	Computes the fixed-point tangent of the radian angle x.

qFP16_t	qFP16_Atan2 (const qFP16_t y, const qFP16_t x)
	Computes the fixed-point arc tangent in radians of y / x based on the signs of both values to determine the correct quadrant.

qFP16_t	qFP16_Atan (qFP16_t x)
	Computes the fixed-point arc tangent of x in radians.

qFP16_t	qFP16_Asin (qFP16_t x)
	Computes the fixed-point arc sine of x in radians.

qFP16_t	qFP16_Acos (qFP16_t x)
	Computes the fixed-point arc cosine of x in radians.

qFP16_t	qFP16_Cosh (qFP16_t x)
	Computes the fixed-point hyperbolic cosine of x.

qFP16_t	qFP16_Sinh (qFP16_t x)
	Computes the fixed-point hyperbolic sine of x.

qFP16_t	qFP16_Tanh (qFP16_t x)
	Computes the fixed-point hyperbolic tangent of x.

qFP16_t	qFP16_Polyval (const qFP16_t *const p, const size_t n, const qFP16_t x)
	Evaluates the fixed-point polynomial p at the point x. The argument p is a vector of length n+1 whose elements are the coefficients (in descending powers) of an nth-degree polynomial.

qFP16_t	qFP16_IPow (const qFP16_t x, const qFP16_t y)
	Returns x raised to the power of the integer part of y. (x^y)

qFP16_t	qFP16_Pow (const qFP16_t x, const qFP16_t y)
	Returns x raised to the power of y. (x^y)

char *	qFP16_FPToA (const qFP16_t num, char *str, int decimals)
	Converts the fixed-point value to a formatted string.

qFP16_t	qFP16_AToFP (const char *s)
	Parses the C string s, interpreting its content as a fixed-point (q16.16) number and returns its value as a qFP16_t. The function first discards as many whitespace characters (as in isspace) as necessary until the first non-whitespace character is found. Then, starting from this character, takes as many characters as possible that are valid following a syntax resembling that of floating point literals, and interprets them as a fixed-point numerical value. The rest of the string after the last valid character is ignored and has no effect on the behavior of this function.

Variables
const struct _qFP16_const_s	qFP16
	Fixed-point Q16.16 constants.

Detailed Description

API for the qFP16 Fixed-point math library.

For a brief description of this module, please read Fixed-Point Q16.16 library

Macro Definition Documentation

◆ qFP16_Constant

#define qFP16_Constant ( x )

A macro for defining a fixed-point constant value.

Note: You should only use this for constant values. For runtime-conversions use qFP16_IntToFP(), qFP16_FloatToFP() or qFP16_DoubleToFP() instead.

Parameters

[in] x A literal value

Returns: The literal argument x converted to fixed-point(qFP16_t).

Function Documentation

◆ qFP16_Abs()

qFP16_t qFP16_Abs ( const qFP16_t x )

Returns the absolute value of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns the absolute value of x.

◆ qFP16_Acos()

qFP16_t qFP16_Acos ( qFP16_t x )

Computes the fixed-point arc cosine of x in radians.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns arc cosine of x.

◆ qFP16_Add()

qFP16_t qFP16_Add	(	const qFP16_t	X,
		const qFP16_t	Y )

Returns the fixed-point addition x + y.

Parameters

[in]	X	The fixed-point(q16.16) value.
[in]	Y	The fixed-point(q16.16) value.

Returns: This function returns the addition operation x+y. qFP16.overflow when an operation overflow is detected.

◆ qFP16_Asin()

qFP16_t qFP16_Asin ( qFP16_t x )

Computes the fixed-point arc sine of x in radians.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns arc sine of x.

◆ qFP16_Atan()

qFP16_t qFP16_Atan ( qFP16_t x )

Computes the fixed-point arc tangent of x in radians.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns arc tangent of x.

◆ qFP16_Atan2()

qFP16_t qFP16_Atan2	(	const qFP16_t	y,
		const qFP16_t	x )

Computes the fixed-point arc tangent in radians of y / x based on the signs of both values to determine the correct quadrant.

Parameters

[in]	y	The fixed-point(q16.16) value representing an x-coordinate.
[in]	x	The fixed-point(q16.16) value representing an y-coordinate.

Returns: This function returns the principal arc tangent of y/x, in the interval [-pi,+pi] radians.

◆ qFP16_AToFP()

qFP16_t qFP16_AToFP ( const char * s )

Parses the C string s, interpreting its content as a fixed-point (q16.16) number and returns its value as a qFP16_t. The function first discards as many whitespace characters (as in isspace) as necessary until the first non-whitespace character is found. Then, starting from this character, takes as many characters as possible that are valid following a syntax resembling that of floating point literals, and interprets them as a fixed-point numerical value. The rest of the string after the last valid character is ignored and has no effect on the behavior of this function.

Parameters

[in] s The string beginning with the representation of a floating-point number.

Returns: On success, the function returns the converted floating point number as a fixed-point value. If no valid conversion could be performed, the function returns zero (0.0) or qFP16.overflow. If the converted value would be out of the range of representable values by a fixed-point Q16.16, the function returns qFP16.overflow .

◆ qFP16_Ceil()

qFP16_t qFP16_Ceil ( const qFP16_t x )

Returns the smallest integer value greater than or equal to x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns the smallest integral value not less than x.

◆ qFP16_Cos()

qFP16_t qFP16_Cos ( qFP16_t x )

Computes the fixed-point cosine of the radian angle x.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns cosine of x.

◆ qFP16_Cosh()

qFP16_t qFP16_Cosh ( qFP16_t x )

Computes the fixed-point hyperbolic cosine of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns hyperbolic cosine of x. If overflow detected returns qFP16.overflow. If the function saturates, returns QFP16_EXP_MAX or QFP16_EXP_MIN.

◆ qFP16_DegToRad()

qFP16_t qFP16_DegToRad ( const qFP16_t x )

Converts angle units from degrees to radians.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in degrees.

Returns: This function returns the angle converted in radians.

◆ qFP16_Div()

qFP16_t qFP16_Div	(	const qFP16_t	x,
		const qFP16_t	y )

Returns the fixed-point division operation x / y.

Parameters

[in]	x	The fixed-point(q16.16) value.
[in]	y	The fixed-point(q16.16) value.

Returns: This function returns the product operation x/y. qFP16.overflow when an operation overflow is detected.

◆ qFP16_DoubleToFP()

qFP16_t qFP16_DoubleToFP ( const double x )

Returns the double value x converted to fixed-point q16.16.

Parameters

[in] x The double precision floating-point value.

Returns: This function returns x converted to fixed-point q16.16.

◆ qFP16_Exp()

qFP16_t qFP16_Exp ( qFP16_t x )

Returns the fixed-point value of e raised to the xth power.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns the exponential value of x. qFP16.overflow when an operation overflow is detected.

◆ qFP16_FloatToFP()

qFP16_t qFP16_FloatToFP ( const float x )

Returns the float value x converted to fixed-point q16.16.

Parameters

[in] x The floating-point value.

Returns: This function returns x converted to fixed-point q16.16.

◆ qFP16_Floor()

qFP16_t qFP16_Floor ( const qFP16_t x )

Returns the largest integer value less than or equal to x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns the largest integral value not greater than x.

◆ qFP16_FPToA()

char * qFP16_FPToA	(	const qFP16_t	num,
		char *	str,
		int	decimals )

Converts the fixed-point value to a formatted string.

Parameters

[in]	num	The fixed-point(q16.16) value to be converted to string.
[in]	str	Array in memory where to store the resulting null-terminated string.
[in]	decimals	Number of decimals to show in the string representation.

Note: : Max decimal allowed = 5

Returns: A pointer to the resulting null-terminated string, same as parameter str

◆ qFP16_FPToDouble()

double qFP16_FPToDouble ( const qFP16_t x )

Returns the fixed-point value x converted to double.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns x converted to double.

◆ qFP16_FPToFloat()

float qFP16_FPToFloat ( const qFP16_t x )

Returns the fixed-point value x converted to float.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns x converted to float.

◆ qFP16_FPToInt()

int qFP16_FPToInt ( const qFP16_t x )

Returns the fixed-point value x converted to int.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns x converted to int.

◆ qFP16_IntToFP()

qFP16_t qFP16_IntToFP ( const int x )

Returns the int value x converted to fixed-point q16.16.

Parameters

[in] x The integer value.

Returns: This function returns x converted to fixed-point q16.16.

◆ qFP16_IPow()

qFP16_t qFP16_IPow	(	const qFP16_t	x,
		const qFP16_t	y )

Returns x raised to the power of the integer part of y. (x^y)

Parameters

[in]	x	The fixed-point(q16.16) base value.
[in]	y	The fixed-point(q16.16) power value. Only the integer part is taken

Returns: This function returns the result of raising x to the power y. qFP16.overflow when an operation overflow is detected.

◆ qFP16_Log()

qFP16_t qFP16_Log ( qFP16_t x )

Returns the fixed-point natural logarithm (base-e logarithm) of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns natural logarithm of x. For negative values returnsqFP16.overflow

◆ qFP16_Log2()

qFP16_t qFP16_Log2 ( const qFP16_t x )

Returns the fixed-point log base 2 of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns log base 2 of x. For negative values returns qFP16.overflow

◆ qFP16_Mod()

qFP16_t qFP16_Mod	(	const qFP16_t	x,
		const qFP16_t	y )

Returns the fixed-point modulo operation x % y.

Parameters

[in]	x	The fixed-point(q16.16) value.
[in]	y	The fixed-point(q16.16) value.

Returns: This function returns the modulo operation xy.

◆ qFP16_Mul()

qFP16_t qFP16_Mul	(	const qFP16_t	x,
		const qFP16_t	y )

Returns the fixed-point product operation x * y.

Parameters

[in]	x	The fixed-point(q16.16) value.
[in]	y	The fixed-point(q16.16) value.

Returns: This function returns the product operation x*y. qFP16.overflow when an operation overflow is detected.

◆ qFP16_Polyval()

qFP16_t qFP16_Polyval	(	const qFP16_t *const	p,
		const size_t	n,
		const qFP16_t	x )

Evaluates the fixed-point polynomial p at the point x. The argument p is a vector of length n+1 whose elements are the coefficients (in descending powers) of an nth-degree polynomial.

Parameters

[in]	p	Polynomial coefficients, specified as a fixed-point(q16.16) array.
[in]	n	The number of elements of the fixed-point array p.
[in]	x	The fixed-point(q16.16) value to evaluate the polynomial.

Returns: This function returns the polynomial evaluation p(x). If overflow detected returns qFP16.overflow.

◆ qFP16_Pow()

qFP16_t qFP16_Pow	(	const qFP16_t	x,
		const qFP16_t	y )

Returns x raised to the power of y. (x^y)

Parameters

[in]	x	The fixed-point(q16.16) base value.
[in]	y	The fixed-point(q16.16) power value.

Returns: This function returns the result of raising x to the power y. qFP16.overflow when an operation overflow is detected.

◆ qFP16_RadToDeg()

qFP16_t qFP16_RadToDeg ( const qFP16_t x )

Converts angle units from radians to degrees.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns the angle converted in degrees.

◆ qFP16_Round()

qFP16_t qFP16_Round ( const qFP16_t x )

Returns the nearest integer value of the fixed-point argument x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns the nearest integral value of x.

◆ qFP16_SettingsSelect()

void qFP16_SettingsSelect ( qFP16_Settings_t *const instance )

Select the provided setting instance to perform fixed-point operations.

Parameters

[in] instance A pointer to the fixed-point settings instance. Pass NULL to use the default settings.

Returns: none.

◆ qFP16_SettingsSet()

int qFP16_SettingsSet	(	qFP16_Settings_t *const	instance,
		qFP16_t	min,
		qFP16_t	max,
		uint8_t	rounding,
		uint8_t	saturate )

Set settings for the fixed-point API.

Parameters

[in]	instance	A pointer to the fixed-point settings instance
[in]	min	The minimal value allowed for the output.
[in]	max	The maximal value allowed for the output.
[in]	rounding	Enable rounding mode.
[in]	saturate	Enable saturation mode.

Returns: 1 on success, otherwise return 0.

◆ qFP16_Sin()

qFP16_t qFP16_Sin ( qFP16_t x )

Computes the fixed-point sine of the radian angle x.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns sine of x.

◆ qFP16_Sinh()

qFP16_t qFP16_Sinh ( qFP16_t x )

Computes the fixed-point hyperbolic sine of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns hyperbolic sine of x. If overflow detected returns qFP16.overflow. If the function saturates, returns QFP16_EXP_MAX or QFP16_EXP_MIN.

◆ qFP16_Sqrt()

qFP16_t qFP16_Sqrt ( qFP16_t x )

Returns the fixed-point square root of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns the square root of x. For negative numbers, returns qFP16.overflow .

◆ qFP16_Sub()

qFP16_t qFP16_Sub	(	const qFP16_t	X,
		const qFP16_t	Y )

Returns the fixed-point subtraction x - y.

Parameters

[in]	X	The fixed-point(q16.16) value.
[in]	Y	The fixed-point(q16.16) value.

Returns: This function returns the subtraction operation x-y. qFP16.overflow when an operation overflow is detected.

◆ qFP16_Tan()

qFP16_t qFP16_Tan ( qFP16_t x )

Computes the fixed-point tangent of the radian angle x.

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns tangent of x.

◆ qFP16_Tanh()

qFP16_t qFP16_Tanh ( qFP16_t x )

Computes the fixed-point hyperbolic tangent of x.

Parameters

[in] x The fixed-point(q16.16) value.

Returns: This function returns hyperbolic tangent of x. If overflow detected returns qFP16.overflow. If the function saturates, returns QFP16_EXP_MAX or QFP16_EXP_MIN.

◆ qFP16_WrapTo180()

qFP16_t qFP16_WrapTo180 ( qFP16_t x )

Wrap the fixed-point angle in degrees to [−180 180].

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in degrees.

Returns: This function returns the wrapped angle in the range [−180, 180] of x.

◆ qFP16_WrapToPi()

qFP16_t qFP16_WrapToPi ( qFP16_t x )

Wrap the fixed-point angle in radians to [−pi pi].

Parameters

[in] x The fixed-point(q16.16) value representing an angle expressed in radians.

Returns: This function returns the wrapped angle in the range [−pi, pi] of x.

Data Structures

Macros

Typedefs

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ qFP16_Constant

Function Documentation

◆ qFP16_Abs()

◆ qFP16_Acos()

◆ qFP16_Add()

◆ qFP16_Asin()

◆ qFP16_Atan()

◆ qFP16_Atan2()

◆ qFP16_AToFP()

◆ qFP16_Ceil()

◆ qFP16_Cos()

◆ qFP16_Cosh()

◆ qFP16_DegToRad()

◆ qFP16_Div()

◆ qFP16_DoubleToFP()

◆ qFP16_Exp()

◆ qFP16_FloatToFP()

◆ qFP16_Floor()

◆ qFP16_FPToA()

◆ qFP16_FPToDouble()

◆ qFP16_FPToFloat()

◆ qFP16_FPToInt()

◆ qFP16_IntToFP()

◆ qFP16_IPow()

◆ qFP16_Log()

◆ qFP16_Log2()

◆ qFP16_Mod()

◆ qFP16_Mul()

◆ qFP16_Polyval()

◆ qFP16_Pow()

◆ qFP16_RadToDeg()

◆ qFP16_Round()

◆ qFP16_SettingsSelect()

◆ qFP16_SettingsSet()

◆ qFP16_Sin()

◆ qFP16_Sinh()

◆ qFP16_Sqrt()

◆ qFP16_Sub()

◆ qFP16_Tan()

◆ qFP16_Tanh()

◆ qFP16_WrapTo180()

◆ qFP16_WrapToPi()