fixmath.h File Reference

Fixed-point math library. More...

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Data Structures
struct	fx_rdiv_t

Typedefs
typedef int32_t	fixed_t

Functions
int	fx_clz (uint32_t word)
int	fx_ctz (uint32_t word)
int	fx_bitcount (uint32_t word)
fixed_t	fx_itox (int32_t ival, unsigned frac)
fixed_t	fx_ftox (float fval, unsigned frac)
fixed_t	fx_dtox (double dval, unsigned frac)
fixed_t	fx_xtox (fixed_t xval, unsigned frac1, unsigned frac2)
int32_t	fx_xtoi (fixed_t xval, unsigned frac)
float	fx_xtof (fixed_t xval, unsigned frac)
double	fx_xtod (fixed_t xval, unsigned frac)
int32_t	fx_roundx (fixed_t xval, unsigned frac)
int32_t	fx_ceilx (fixed_t xval, unsigned frac)
int32_t	fx_floorx (fixed_t xval, unsigned frac)
fixed_t	fx_addx (fixed_t x1, fixed_t x2)
fixed_t	fx_subx (fixed_t x1, fixed_t x2)
fixed_t	fx_mulx (fixed_t x1, fixed_t x2, unsigned frac)
fixed_t	fx_divx (fixed_t x1, fixed_t x2, unsigned frac)
fixed_t	fx_rdivx (fixed_t xval, const fx_rdiv_t *rdiv)
int	fx_itoa (char *str, int32_t val)
int	fx_xtoa (char *str, fixed_t xval, unsigned frac, unsigned digits)
fixed_t	fx_invx (fixed_t xval, unsigned frac, fx_rdiv_t *rdiv)
fixed_t	fx_sqrtx (fixed_t xval, unsigned frac)
fixed_t	fx_isqrtx (fixed_t xval, unsigned frac, fx_rdiv_t *rdiv)
fixed_t	fx_expx (fixed_t xval, unsigned frac)
fixed_t	fx_exp2x (fixed_t xval, unsigned frac)
fixed_t	fx_exp10x (fixed_t xval, unsigned frac)
fixed_t	fx_logx (fixed_t xval, unsigned frac)
fixed_t	fx_log2x (fixed_t xval, unsigned frac)
fixed_t	fx_log10x (fixed_t xval, unsigned frac)
fixed_t	fx_powx (fixed_t xval, unsigned xfrac, fixed_t yval, unsigned yfrac)
fixed_t	fx_sinx (fixed_t xval, unsigned frac)
fixed_t	fx_cosx (fixed_t xval, unsigned frac)

Detailed Description

Fixed-point math library.

Typedef Documentation

typedef int32_t fixed_t

The fixed-point data type.

Function Documentation

int fx_clz

(

uint32_t

word

)

Count the number of leading zeros in a 32-bit word. Note that fx_clz(0) is undefined.

Parameters

word	The source word.

Returns

The number of leading zeros.

int fx_ctz

(

uint32_t

word

)

Count the number of trailing zeros in a 32-bit word. Note that fx_ctz(0) is undefined.

Parameters

word	The source word.

Returns

The number of trailing zeros.

int fx_bitcount

(

uint32_t

word

)

Count the number of bits set in a 32-bit word.

Parameters

word	The source word.

Returns

The number of bits set.

fixed_t fx_itox	(	int32_t	ival,
		unsigned	frac
	)

Integer to fixed-point conversion.

Parameters

ival	Integer value.
frac	The number of fixed-point fractional bits desired.

Returns

The converted fixed-point number.

fixed_t fx_ftox	(	float	fval,
		unsigned	frac
	)

Single precision float to fixed-point conversion. The error is within 1 ulp.

Parameters

fval	Single-precision float value.
frac	The number of fixed-point fractional bits desired.

Returns

The converted fixed-point number.

Note

The fval argument may be evaluated twice.

fixed_t fx_dtox	(	double	dval,
		unsigned	frac
	)

Double precision float to fixed-point conversion. The error is within 1/2 ulp.

Parameters

dval	Double-precision float value.
frac	The number of fixed-point fractional bits desired.

Returns

The converted fixed-point number.

Note

The dval argument may be evaluated twice.

fixed_t fx_xtox	(	fixed_t	xval,
		unsigned	frac1,
		unsigned	frac2
	)

Fixed-point format conversion. The error is within 1/2 ulp.

Parameters

xval	Fixed-point value with frac1 fractional bits.
frac1	The number of fractional in original representation.
frac2	The number of fractional bits resired.

Returns

A fixed-point value with frac2 fractional bits.

Note

The frac1 and frac2 arguments may be evaluated twice.

int32_t fx_xtoi	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point to integer conversion.

This is equal to fx_floorx().

Parameters

xval	Fixed-point value.
frac	The number of fractional bits.

Returns

The integer part of xval, rounded towards -infinity.

float fx_xtof	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point to single precision float conversion. The error is within 1/2 ulp.

Parameters

xval	Fixed-point value.
frac	The number of fractional bits.

Returns

The converted floating-point number.

double fx_xtod	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point to double precision float conversion. The error is within 1/2 ulp.

Parameters

xval	Fixed-point value.
frac	The number of fractional bits.

Returns

The converted double-precision floating-point number.

int32_t fx_roundx	(	fixed_t	xval,
		unsigned	frac
	)

Round a fixed-point number to the nearest integer.

Parameters

xval	Fixed-point value.
frac	The number of fractional bits.

Returns

The value rounded to the nearest integer.

Note

The frac argument may be evaluated twice.

int32_t fx_ceilx	(	fixed_t	xval,
		unsigned	frac
	)

Round a fixed-point number up to the nearest integer.

Parameters

xval	Fixed-point value.
frac	The number of fractional bits in xval.

Returns

The value rounded to up to the nearest integer. The return value is int32_t and therefore has zero fractional bits.

Note

The frac argument may evaluated twice.

int32_t fx_floorx	(	fixed_t	xval,
		unsigned	frac
	)

Round a fixed-point number down to the nearest integer.

Parameters

xval	Fixed-point value.
frac	The number of fractional bits in xval.

Returns

The value rounded down to the nearest integer. The return value is int32_t and therefore has zero fractional bits.

fixed_t fx_addx	(	fixed_t	x1,
		fixed_t	x2
	)

Fixed-point addition. The terms must have the same number of fractional bits. This operation expands to a regular add operation.

Parameters

x1	First fixed-point term.
x2	Second fixed-point term.

Returns

The sum with the same number of fractional bits as the terms.

fixed_t fx_subx	(	fixed_t	x1,
		fixed_t	x2
	)

Fixed-point subtraction. The terms must have the same number of fractional bits. This operation expands to a regular add operation.

Parameters

x1	First fixed-point term.
x2	Second fixed-point term.

Returns

The difference with the same number of fractional bits as the terms.

fixed_t fx_mulx	(	fixed_t	x1,
		fixed_t	x2,
		unsigned	frac
	)

Fixed-point multiply. The error is within 1/2 ulp. The number of fraction bits in the result is f1 + f2 - frac, where f1 and f2 are the number of fraction bits of x1 and x2, respectively. Thus, if both f1 and f2 are equal to frac, the number of fraction bits in the result will also be frac.

Parameters

x1	First fixed-point factor.
x2	Second fixed-point factor.
frac	Number of fraction bits, see explaination above.

Returns

The multiplied result.

Note

The frac argument may be evaluated twice.

fixed_t fx_divx	(	fixed_t	x1,
		fixed_t	x2,
		unsigned	frac
	)

Fixed-point divide. The error is within 1/2 ulp. The number of fraction bits in the result is f1 - f2 + frac, where f1 and f2 are the number of fraction bits of x1 and x2, respectively. Thus, if both f1 and f2 are equal to frac, the number of fraction bits in the result will also be frac.

Parameters

x1	Fixed-point numerator.
x2	Fixed-point denominator.
frac	Number of fraction bits, see explaination above.

Returns

The quotient result.

fixed_t fx_rdivx	(	fixed_t	xval,
		const fx_rdiv_t *	rdiv
	)

Fixed-point divide by reciprocal multiplication.

Parameters

xval	Fixed-point numerator.
rdiv	A reciprocal division factor, obtained from either fx_invx() or fx_isqrtx().

Returns

The quotient, with the same number of fractional bits as the numerator.

Note

The rdiv argument may be evaluated twice.

int fx_itoa	(	char *	str,
		int32_t	val
	)

Integer to ASCII string conversion.

Parameters

str	The string buffer to use. It must be long enough to hold the string value, i.e. at least 12 bytes in the worst case.
val	The integral number to convert.

Returns

The length of the converted string. If str is NULL, a negative value is returned and errno is set to EINVAL.

int fx_xtoa	(	char *	str,
		fixed_t	xval,
		unsigned	frac,
		unsigned	digits
	)

Fixed-point to ASCII string conversion. The number is converted to the format [-]d.ddd[e+00]. If the precision (digits) is zero, no decimal point appears. If the exponent is zero, no exponent appears.

Parameters

str	The string buffer to use. It must be long enough to hold the string value, i.e. at least 8 + digits bytes.
xval	The fixed-point number to convert.
frac	The number of fractional bits.
digits	The number of digits to the right of the decimal point.

Returns

The length of the converted string. If str is NULL or frac is greater than 31, a negative value is returned and errno is set to EINVAL.

fixed_t fx_invx	(	fixed_t	xval,
		unsigned	frac,
		fx_rdiv_t *	rdiv
	)

Fixed-point inverse value. The error is within 4 ulp if frac is less than 31, 7 ulp otherwise. If the input is out-of-range (zero), then errno is set to EDOM.

Parameters

xval	A non-zero fixed-point value.
frac	The number of fractional bits.
rdiv	Optional reciprocal division multiplier.

Returns

The inverse value, i.e. 1/xval.

fixed_t fx_sqrtx	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point square root. The error is within 2 ulp if frac is less than 31, and within 4 ulp otherwise. If the input is out-of-range (negative), then errno is set to EDOM.

Parameters

xval	A non-zero fixed-point value.
frac	The number of fractional bits.

Returns

The square root value, i.e. sqrt(xval).

fixed_t fx_isqrtx	(	fixed_t	xval,
		unsigned	frac,
		fx_rdiv_t *	rdiv
	)

Fixed-point inverse square root. The error is within 2 ulp if frac is less than 31, and within 3 ulp otherwise. If the input is out-of-range (negative or zero), then errno is set to EDOM.

Parameters

xval	A non-zero fixed-point value.
frac	The number of fractional bits.
rdiv	Optional reciprocal division multiplier.

Returns

The inverse square root value, i.e. 1/sqrt(xval).

fixed_t fx_expx	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point natural exponential. The error is within 2 ulp. If frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The natural exponential of xval, i.e. exp(xval).

fixed_t fx_exp2x	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point base-2 exponential. The error is within 2 ulp. If frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The base-2 exponential of xval, i.e. 2**(xval).

fixed_t fx_exp10x	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point base-10 exponential. The error is within 2 ulp. If frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The base-10 exponential of xval, i.e. 10**(xval).

fixed_t fx_logx	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point natural logarithm. The error is within 2 ulp. If xval is negative or zero or frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The natural logarithm of xval, i.e. log(xval).

fixed_t fx_log2x	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point base-2 logarithm. The error is within 2 ulp. If xval is negative or zero or frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The base-2 logarithm of xval, i.e. log2(xval).

fixed_t fx_log10x	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point base-10 logarithm. The error is within 2 ulp. If xval is negative or zero or frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The base-10 logarithm of xval, i.e. log10(xval).

fixed_t fx_powx	(	fixed_t	xval,
		unsigned	xfrac,
		fixed_t	yval,
		unsigned	yfrac
	)

Fixed-point power function. The error is bounded by C₁ |yval| xval ^yval + C₂, where C₁ and C₂ are approximately 1 and 5 ulp, respectively. If either xfrac or yfrac is greater than 31, or xval is negative, or xval is zero and yval is negative, then errno is set to EDOM.

Parameters

xval	The base in fixed-point format.
xfrac	The number of fractional bits for the base.
yval	The exponent in fixed-point format.
yfrac	The number of fractional bits for the exponent.

Returns

xval raised to the power of yval. The number of fractional bits is xfrac.

fixed_t fx_sinx	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point sine. The error is within 3 ulp if frac is less than 31, and within 4 ulp otherwise. If frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The sine value of xval, i.e. sin(xval).

fixed_t fx_cosx	(	fixed_t	xval,
		unsigned	frac
	)

Fixed-point cosine. The error is within 3 ulp if frac is less than 31, and within 4 ulp otherwise. If frac is greater than 31, then errno is set to EDOM.

Parameters

xval	A fixed-point value.
frac	The number of fractional bits.

Returns

The cosine value of xval, i.e. cos(xval).