Macros
#define	FXTOA_ALL 0x1f

#define	FXTOA_ROUND 0x00

#define	FXTOA_TRUNC 0x80

#define	FXTOA_NTZ 0x40

#define	FXTOA_DOT 0x00

#define	FXTOA_COMMA 0x20

ASCII Conversions (not in ISO/IEC TR18037)
char *	hktoa (short accum x, char *buf, unsigned char mode)

char *	hrtoa (short fract x, char *buf, unsigned char mode)

char *	ktoa (accum x, char *buf, unsigned char mode)

char *	rtoa (fract x, char *buf, unsigned char mode)

char *	uhktoa (unsigned short accum x, char *buf, unsigned char mode)

char *	uhrtoa (unsigned short fract x, char *buf, unsigned char mode)

char *	uktoa (unsigned accum x, char *buf, unsigned char mode)

char *	urtoa (unsigned fract x, char *buf, unsigned char mode)

Absolute Value
short fract	abshr (short fract val)

fract	absr (fract val)

long fract	abslr (long fract val)

long long fract	absllr (long long fract val)

short accum	abshk (short accum val)

accum	absk (accum val)

long accum	abslk (long accum val)

long long accum	absllk (long long accum val)

Bit-Conversions to Integer
signed char	bitshr (short fract val)

unsigned char	bitsuhr (unsigned short fract val)

int	bitsr (fract val)

unsigned int	bitsur (unsigned fract val)

long	bitslr (long fract val)

unsigned long	bitsulr (unsigned long fract val)

long long	bitsllr (long long fract val)

unsigned long long	bitsullr (unsigned long long fract val)

int	bitshk (short accum val)

unsigned int	bitsuhk (unsigned short accum val)

long	bitsk (accum val)

unsigned long	bitsuk (unsigned accum val)

long long	bitslk (long accum val)

unsigned long long	bitsulk (unsigned long accum val)

long long	bitsllk (long long accum val)

unsigned long long	bitsullk (unsigned long long accum val)

Bit-Conversions to Fixed-Point
short fract	hrbits (signed char val)

unsigned short fract	uhrbits (unsigned char val)

fract	rbits (int val)

unsigned fract	urbits (unsigned int val)

long fract	lrbits (long val)

unsigned long fract	ulrbits (unsigned long val)

long long fract	llrbits (long long val)

unsigned long long fract	ullrbits (unsigned long long val)

short accum	hkbits (int val)

unsigned short accum	uhkbits (unsigned int val)

accum	kbits (long val)

unsigned accum	ukbits (unsigned long val)

long accum	lkbits (long long val)

unsigned long accum	ulkbits (unsigned long long val)

long long accum	llkbits (long long val)

unsigned long long accum	ullkbits (unsigned long long val)

Count Left-Shift
int	countlshr (short fract val)

int	countlsuhr (unsigned short fract val)

int	countlsr (fract val)

int	countlsur (unsigned fract val)

int	countlslr (long fract val)

int	countlsulr (unsigned long fract val)

int	countlsllr (long long fract val)

int	countlsullr (unsigned long long fract val)

int	countlshk (short accum val)

int	countlsuhk (unsigned short accum val)

int	countlsk (accum val)

int	countlsuk (unsigned accum val)

int	countlslk (long accum val)

int	countlsulk (unsigned long accum val)

int	countlsllk (long long accum val)

int	countlsullk (unsigned long long accum val)

Division
fract	rdivi (int num, int denom)

long fract	lrdivi (long int num, long int denom)

unsigned fract	urdivi (unsigned int num, unsigned int denom)

unsigned long fract	ulrdivi (unsigned long int num, unsigned long int denom)

Rounding
short fract	roundhr (short fract val, int bit)

unsigned short fract	rounduhr (unsigned short fract val, int bit)

fract	roundr (fract val, int bit)

unsigned fract	roundur (unsigned fract val, int bit)

long fract	roundlr (long fract val, int bit)

unsigned long fract	roundulr (unsigned long fract val, int bit)

long long fract	roundllr (long long fract val, int bit)

unsigned long long fract	roundullr (unsigned long long fract val, int bit)

short accum	roundhk (short accum val, int bit)

unsigned short accum	rounduhk (unsigned short accum val, int bit)

accum	roundk (accum val, int bit)

unsigned accum	rounduk (unsigned accum val, int bit)

long accum	roundlk (long accum val, int bit)

unsigned long accum	roundulk (unsigned long accum val, int bit)

long long accum	roundllk (long long accum val, int bit)

unsigned long long accum	roundullk (unsigned long long accum val, int bit)

Square Root and Transcendental Functions
accum	acosk (accum x)

unsigned accum	acosuk (unsigned accum x)

accum	asink (accum x)

unsigned accum	asinuk (unsigned accum x)

accum	atank (accum x)

unsigned accum	atanuk (unsigned accum x)

unsigned fract	atanur (unsigned fract x)

accum	exp2k (accum x)

unsigned accum	exp2uk (unsigned accum x)

unsigned fract	exp2m1ur (unsigned fract x)

accum	log2uk (unsigned accum x)

short accum	log2uhk (unsigned short accum x)

unsigned short fract	log21puhr (unsigned short fract x)

unsigned fract	log21pur (unsigned fract x)

accum	cospi2k (accum deg)

accum	sinpi2k (accum deg)

fract	sinuhk_deg (unsigned short accum deg)

fract	cosuhk_deg (unsigned short accum deg)

unsigned fract	sinpi2ur (unsigned fract x)

short accum	sqrthk (short accum radic)

short fract	sqrthr (short fract radic)

accum	sqrtk (accum radic)

long fract	sqrtlr (long fract radic)

fract	sqrtr (fract radic)

unsigned short accum	sqrtuhk (unsigned short accum radic)

unsigned short fract	sqrtuhr (unsigned short fract radic)

unsigned accum	sqrtuk (unsigned accum radic)

unsigned long fract	sqrtulr (unsigned long fract radic)

unsigned fract	sqrtur (unsigned fract radic)

Type-Generic Functions
type	absfx (type val)

int	countlsfx (type val)

type	roundfx (type val, int bit)

Functions reading from PROGMEM
static short fract	pgm_read_hr (const short fract *addr)

static unsigned short fract	pgm_read_uhr (const unsigned short fract *addr)

static fract	pgm_read_r (const fract *addr)

static unsigned fract	pgm_read_ur (const unsigned fract *addr)

static long fract	pgm_read_lr (const long fract *addr)

static unsigned long fract	pgm_read_ulr (const unsigned long fract *addr)

static long long fract	pgm_read_llr (const long long fract *addr)

static unsigned long long fract	pgm_read_ullr (const unsigned long long fract *addr)

static short accum	pgm_read_hk (const short accum *addr)

static unsigned short accum	pgm_read_uhk (const unsigned short accum *addr)

static accum	pgm_read_k (const accum *addr)

static unsigned accum	pgm_read_uk (const unsigned accum *addr)

static long accum	pgm_read_lk (const long accum *addr)

static unsigned long accum	pgm_read_ulk (const unsigned long accum *addr)

static long long accum	pgm_read_llk (const long long accum *addr)

static unsigned long long accum	pgm_read_ullk (const unsigned long long accum *addr)

Functions reading from PROGMEM_FAR
static short fract	pgm_read_hr_far (uint_farptr_t addr)

static unsigned short fract	pgm_read_uhr_far (uint_farptr_t addr)

static fract	pgm_read_r_far (uint_farptr_t addr)

static unsigned fract	pgm_read_ur_far (uint_farptr_t addr)

static long fract	pgm_read_lr_far (uint_farptr_t addr)

static unsigned long fract	pgm_read_ulr_far (uint_farptr_t addr)

static long long fract	pgm_read_llr_far (uint_farptr_t addr)

static unsigned long long fract	pgm_read_ullr_far (uint_farptr_t addr)

static short accum	pgm_read_hk_far (uint_farptr_t addr)

static unsigned short accum	pgm_read_uhk_far (uint_farptr_t addr)

static accum	pgm_read_k_far (uint_farptr_t addr)

static unsigned accum	pgm_read_uk_far (uint_farptr_t addr)

static long accum	pgm_read_lk_far (uint_farptr_t addr)

static unsigned long accum	pgm_read_ulk_far (uint_farptr_t addr)

static long long accum	pgm_read_llk_far (uint_farptr_t addr)

static unsigned long long accum	pgm_read_ullk_far (uint_farptr_t addr)

EEPROM Read Functions
short fract	eeprom_read_hr (const short fract *__p)

unsigned short fract	eeprom_read_uhr (const unsigned short fract *__p)

fract	eeprom_read_r (const fract *__p)

unsigned fract	eeprom_read_ur (const unsigned fract *__p)

long fract	eeprom_read_lr (const long fract *__p)

unsigned long fract	eeprom_read_ulr (const unsigned long fract *__p)

long long fract	eeprom_read_llr (const long long fract *__p)

unsigned long long fract	eeprom_read_ullr (const unsigned long long fract *__p)

short accum	eeprom_read_hk (const short accum *__p)

unsigned short accum	eeprom_read_uhk (const unsigned short accum *__p)

accum	eeprom_read_k (const accum *__p)

unsigned accum	eeprom_read_uk (const unsigned accum *__p)

long accum	eeprom_read_lk (const long accum *__p)

unsigned long accum	eeprom_read_ulk (const unsigned long accum *__p)

long long accum	eeprom_read_llk (const long long accum *__p)

unsigned long long accum	eeprom_read_ullk (const unsigned long long accum *__p)

EEPROM Write Functions
void	eeprom_write_hr (short fract *__p, short fract __value)

void	eeprom_write_uhr (unsigned short fract *__p, unsigned short fract __value)

void	eeprom_write_r (fract *__p, fract __value)

void	eeprom_write_ur (unsigned fract *__p, unsigned fract __value)

void	eeprom_write_lr (long fract *__p, long fract __value)

void	eeprom_write_ulr (unsigned long fract *__p, unsigned long fract __value)

void	eeprom_write_llr (long long fract *__p, long long fract __value)

void	eeprom_write_ullr (unsigned long long fract *__p, unsigned long long fract __value)

void	eeprom_write_hk (short accum *__p, short accum __value)

void	eeprom_write_uhk (unsigned short accum *__p, unsigned short accum __value)

void	eeprom_write_k (accum *__p, accum __value)

void	eeprom_write_uk (unsigned accum *__p, unsigned accum __value)

void	eeprom_write_lk (long accum *__p, long accum __value)

void	eeprom_write_ulk (unsigned long accum *__p, unsigned long accum __value)

void	eeprom_write_llk (long long accum *__p, long long accum __value)

void	eeprom_write_ullk (unsigned long long accum *__p, unsigned long long accum __value)

EEPROM Update Functions
void	eeprom_update_hr (short fract *__p, short fract __value)

void	eeprom_update_uhr (unsigned short fract *__p, unsigned short fract __value)

void	eeprom_update_r (fract *__p, fract __value)

void	eeprom_update_ur (unsigned fract *__p, unsigned fract __value)

void	eeprom_update_lr (long fract *__p, long fract __value)

void	eeprom_update_ulr (unsigned long fract *__p, unsigned long fract __value)

void	eeprom_update_llr (long long fract *__p, long long fract __value)

void	eeprom_update_ullr (unsigned long long fract *__p, unsigned long long fract __value)

void	eeprom_update_hk (short accum *__p, short accum __value)

void	eeprom_update_uhk (unsigned short accum *__p, unsigned short accum __value)

void	eeprom_update_k (accum *__p, accum __value)

void	eeprom_update_uk (unsigned accum *__p, unsigned accum __value)

void	eeprom_update_lk (long accum *__p, long accum __value)

void	eeprom_update_ulk (unsigned long accum *__p, unsigned long accum __value)

void	eeprom_update_llk (long long accum *__p, long long accum __value)

void	eeprom_update_ullk (unsigned long long accum *__p, unsigned long long accum __value)

Detailed Description

#include <stdfix.h>

As an extension, GNU C supports fixed-point types as defined in the N1169 draft of ISO/IEC DTR 18037.

Since: avr-gcc v4.8

Two groups of fixed-point data types are added:

The fract types and the accum types. The data value of a fract type has no integral part, hence values of a fract type are between -1.0 and +1.0.
The value range of an accum type depends on the number of integral bits in the data type.

Fixed-Point Type Layout
Const Suffix	Type	Size	Q-Format	Epsilon
`hr`	`short fract`	1	s.7	7.81·10^-3
`r`	`fract`	2	s.15	3.05·10^-5
`lr`	`long fract`	4	s.31	4.66·10^-10
`llr`	`long long fract`	8	s.63	1.08·10^-19
`hk`	`short accum`	2	s8.7	7.81·10^-3
`k`	`accum`	4	s16.15	3.05·10^-5
`lk`	`long accum`	8	s32.31	4.66·10^-10
`llk`	`long long accum`	8	s16.47	7.11·10^-15
`uhr`	`unsigned short fract`	1	0.8	3.91·10^-3
`ur`	`unsigned fract`	2	0.16	1.53·10^-5
`ulr`	`unsigned long fract`	4	0.32	2.33·10^-10
`ullr`	`unsigned long long fract`	8	0.64	5.42·10^-20
`uhk`	`unsigned short accum`	2	8.8	3.91·10^-3
`uk`	`unsigned accum`	4	16.16	1.53·10^-5
`ulk`	`unsigned long accum`	8	32.32	2.33·10^-10
`ullk`	`unsigned long long accum`	8	16.48	3.55·10^-15

Remarks

Upper case constant suffixes are also supported.
The long long fixed-point types are avr-gcc extensions.

Macro Definition Documentation

◆ FXTOA_ALL

#define FXTOA_ALL 0x1f

Include all significant digits in the result of a fixed-point to decimal ASCII conversion. The result has no trailing zeros.

To be used in the mode parameter of such a conversion. For details and examples, see uktoa().

Since: AVR-LibC v2.3

◆ FXTOA_COMMA

#define FXTOA_COMMA 0x20

The fixed-point to decimal ASCII conversion routines use a comma (,) for the decimal point.

For details and examples, see uktoa().

Since: AVR-LibC v2.3

◆ FXTOA_DOT

#define FXTOA_DOT 0x00

The fixed-point to decimal ASCII conversion routines use a dot (.) for the decimal point. This is the default, i.e. FXTOA_DOT can be omitted.

For details, and examples, see uktoa().

Since: AVR-LibC v2.3

◆ FXTOA_NTZ

#define FXTOA_NTZ 0x40

A flag to select that the result of a fixed-point to decimal ASCII conversion has no trailing zeros.

To be used in the mode parameter of such a conversion. For details and examples, see uktoa().

Since: AVR-LibC v2.3

◆ FXTOA_ROUND

#define FXTOA_ROUND 0x00

A flag to select rounding to nearest in a fixed-point to decimal ASCII conversion. Rounding mode is the default, i.e. FXTOA_ROUND can be omitted.

To be used in the mode parameter of such a conversion. For details and examples, see uktoa().

Since: AVR-LibC v2.3

◆ FXTOA_TRUNC

#define FXTOA_TRUNC 0x80

A flag to select truncation (rounding to zero) in a fixed-point to decimal ASCII conversion.

To be used in the mode parameter of such a conversion. For details and examples, see uktoa().

Since: AVR-LibC v2.3

Function Documentation

◆ absfx()

type absfx ( type val )

Computes the absolute value of fixed-point value val. When the result does not fit into the range of the return type, the result is saturated.

◆ abshk()

short accum abshk ( short accum val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ abshr()

short fract abshr ( short fract val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ absk()

accum absk ( accum val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ abslk()

long accum abslk ( long accum val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ absllk()

long long accum absllk ( long long accum val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ absllr()

long long fract absllr ( long long fract val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ abslr()

long fract abslr ( long fract val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ absr()

fract absr ( fract val )

Computes the absolute value of val. When the result does not fit into the range of the return type, the result is saturated.

◆ acosk()

accum acosk ( accum x )

Compute the arcus cosine of x. The returned value is in the range [0, π]. For invalid values of x the returned value is -65536 = kbits (0x80000000).

The absolute error is bounded by 5.5·10⁻⁵ ≈ 2^−14.1.

Since: AVR-LibC v2.3

◆ acosuk()

unsigned accum acosuk ( unsigned accum x )

Compute the arcus cosine of x. The returned value is in the range [0, π/2]. For invalid values of x the returned value is 32768 = ukbits (0x80000000).

The absolute error is bounded by 4.6·10⁻⁵ ≈ 2^−14.4.

Since: AVR-LibC v2.3

◆ asink()

accum asink ( accum x )

Compute the arcus sine of x. The returned value is in the range [−π/2, π/2]. For invalid values of x the returned value is -65536 = kbits (0x80000000).

The absolute error is bounded by 5.1·10⁻⁵ ≈ 2⁻¹⁴.

Since: AVR-LibC v2.3

◆ asinuk()

unsigned accum asinuk ( unsigned accum x )

Compute the arcus sine of x. The returned value is in the range [0, π/2]. For invalid values of x the returned value is 32768 = ukbits (0x80000000).

The absolute error is bounded by 4.5·10⁻⁵ ≈ 2^−14.4.

Since: AVR-LibC v2.3

◆ atank()

accum atank ( accum x )

Compute the arcus tangent of x. The returned value is in the range (−π/2, π/2≈1.5708).

Since: AVR-LibC v2.3

◆ atanuk()

unsigned accum atanuk ( unsigned accum x )

Compute the arcus tangent of x. The returned value is in the range [0, π/2≈1.5708).

Since: AVR-LibC v2.3

◆ atanur()

unsigned fract atanur ( unsigned fract x )

Compute the arcus tangent of x. The returned value is in the range [0, π/4≈0.7854].

The absolute error is bounded by 2.6·10⁻⁵ ≈ 2⁻¹⁵. The worst case execution time (WCET) is around 210 cycles when MUL is available, and around 1000 cycles when MUL is not available (measured with avr-gcc v15).

Since: AVR-LibC v2.3

◆ bitshk()

int bitshk ( short accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitshr()

signed char bitshr ( short fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsk()

long bitsk ( accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitslk()

long long bitslk ( long accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsllk()

long long bitsllk ( long long accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsllr()

long long bitsllr ( long long fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitslr()

long bitslr ( long fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsr()

int bitsr ( fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsuhk()

unsigned int bitsuhk ( unsigned short accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsuhr()

unsigned char bitsuhr ( unsigned short fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsuk()

unsigned long bitsuk ( unsigned accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsulk()

unsigned long long bitsulk ( unsigned long accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsullk()

unsigned long long bitsullk ( unsigned long long accum val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsullr()

unsigned long long bitsullr ( unsigned long long fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsulr()

unsigned long bitsulr ( unsigned long fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ bitsur()

unsigned int bitsur ( unsigned fract val )

Return an integer value of the same size and signedness, and with the same bit representation like val.

◆ cospi2k()

accum cospi2k ( accum deg )

Cosine of x·π/2 radians.

The absolute error is bounded by 4.6·10⁻⁵ ≈ 2^−14.4. The worst case execution time (WCET) is around 300 cycles when MUL is available, and around 1400 cycles when MUL is not available.

Since: AVR-LibC v2.3

◆ cosuhk_deg()

fract cosuhk_deg ( unsigned short accum deg )

Cosine of the angle deg where deg is specified in degrees, i.e. in the range [0°, 256°). The returned value is in the range (-1, +1), i.e. is never -1.

The absolute error is bounded by 6.5·10⁻⁵ ≈ 2^−13.9. The worst case execution time (WCET) is around 90 cycles.

Since: AVR-LibC v2.3

◆ countlsfx()

int countlsfx ( type val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlshk()

int countlshk ( short accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlshr()

int countlshr ( short fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsk()

int countlsk ( accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlslk()

int countlslk ( long accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsllk()

int countlsllk ( long long accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsllr()

int countlsllr ( long long fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlslr()

int countlslr ( long fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsr()

int countlsr ( fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsuhk()

int countlsuhk ( unsigned short accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsuhr()

int countlsuhr ( unsigned short fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsuk()

int countlsuk ( unsigned accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsulk()

int countlsulk ( unsigned long accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsullk()

int countlsullk ( unsigned long long accum val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsullr()

int countlsullr ( unsigned long long fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsulr()

int countlsulr ( unsigned long fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ countlsur()

int countlsur ( unsigned fract val )

If val is non-zero, the return value is the largest integer k for which the expression val << k does not overflow.
If val is zero, an integer value is returned that is at least as large as N - 1, where N is the total number of bits of the type of the argument.

◆ eeprom_read_hk()

short accum eeprom_read_hk ( const short accum * __p )

Read a short accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_hr()

short fract eeprom_read_hr ( const short fract * __p )

Read a short fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_k()

accum eeprom_read_k ( const accum * __p )

Read an accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_lk()

long accum eeprom_read_lk ( const long accum * __p )

Read a long accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_llk()

long long accum eeprom_read_llk ( const long long accum * __p )

Read a long long accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_llr()

long long fract eeprom_read_llr ( const long long fract * __p )

Read a long long fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_lr()

long fract eeprom_read_lr ( const long fract * __p )

Read a long fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_r()

fract eeprom_read_r ( const fract * __p )

Read a fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_uhk()

unsigned short accum eeprom_read_uhk ( const unsigned short accum * __p )

Read an unsigned short accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_uhr()

unsigned short fract eeprom_read_uhr ( const unsigned short fract * __p )

Read an unsigned short fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_uk()

unsigned accum eeprom_read_uk ( const unsigned accum * __p )

Read an unsigned accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_ulk()

unsigned long accum eeprom_read_ulk ( const unsigned long accum * __p )

Read an unsigned long accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_ullk()

unsigned long long accum eeprom_read_ullk ( const unsigned long long accum * __p )

Read an unsigned long long accum from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_ullr()

unsigned long long fract eeprom_read_ullr ( const unsigned long long fract * __p )

Read an unsigned long long fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_ulr()

unsigned long fract eeprom_read_ulr ( const unsigned long fract * __p )

Read an unsigned long fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_read_ur()

unsigned fract eeprom_read_ur ( const unsigned fract * __p )

Read an unsigned fract from EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_hk()

void eeprom_update_hk	(	short accum *	__p,
		short accum	__value
	)

Update a short accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_hr()

void eeprom_update_hr	(	short fract *	__p,
		short fract	__value
	)

Update a short fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_k()

void eeprom_update_k	(	accum *	__p,
		accum	__value
	)

Update an accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_lk()

void eeprom_update_lk	(	long accum *	__p,
		long accum	__value
	)

Update a long accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_llk()

void eeprom_update_llk	(	long long accum *	__p,
		long long accum	__value
	)

Update a long long accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_llr()

void eeprom_update_llr	(	long long fract *	__p,
		long long fract	__value
	)

Update a long long fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_lr()

void eeprom_update_lr	(	long fract *	__p,
		long fract	__value
	)

Update a long fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_r()

void eeprom_update_r	(	fract *	__p,
		fract	__value
	)

Update a fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_uhk()

void eeprom_update_uhk	(	unsigned short accum *	__p,
		unsigned short accum	__value
	)

Update an unsigned short accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_uhr()

void eeprom_update_uhr	(	unsigned short fract *	__p,
		unsigned short fract	__value
	)

Update an unsigned short fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_uk()

void eeprom_update_uk	(	unsigned accum *	__p,
		unsigned accum	__value
	)

Update an unsigned accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_ulk()

void eeprom_update_ulk	(	unsigned long accum *	__p,
		unsigned long accum	__value
	)

Update an unsigned long accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_ullk()

void eeprom_update_ullk	(	unsigned long long accum *	__p,
		unsigned long long accum	__value
	)

Update an unsigned long long accum at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_ullr()

void eeprom_update_ullr	(	unsigned long long fract *	__p,
		unsigned long long fract	__value
	)

Update an unsigned long long fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_ulr()

void eeprom_update_ulr	(	unsigned long fract *	__p,
		unsigned long fract	__value
	)

Update an unsigned long fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_update_ur()

void eeprom_update_ur	(	unsigned fract *	__p,
		unsigned fract	__value
	)

Update an unsigned fract at EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_hk()

void eeprom_write_hk	(	short accum *	__p,
		short accum	__value
	)

Write a short accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_hr()

void eeprom_write_hr	(	short fract *	__p,
		short fract	__value
	)

Write a short fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_k()

void eeprom_write_k	(	accum *	__p,
		accum	__value
	)

Write an accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_lk()

void eeprom_write_lk	(	long accum *	__p,
		long accum	__value
	)

Write a long accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_llk()

void eeprom_write_llk	(	long long accum *	__p,
		long long accum	__value
	)

Write a long long accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_llr()

void eeprom_write_llr	(	long long fract *	__p,
		long long fract	__value
	)

Write a long long fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_lr()

void eeprom_write_lr	(	long fract *	__p,
		long fract	__value
	)

Write a long fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_r()

void eeprom_write_r	(	fract *	__p,
		fract	__value
	)

Write a fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_uhk()

void eeprom_write_uhk	(	unsigned short accum *	__p,
		unsigned short accum	__value
	)

Write an unsigned short accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_uhr()

void eeprom_write_uhr	(	unsigned short fract *	__p,
		unsigned short fract	__value
	)

Write an unsigned short fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_uk()

void eeprom_write_uk	(	unsigned accum *	__p,
		unsigned accum	__value
	)

Write an unsigned accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_ulk()

void eeprom_write_ulk	(	unsigned long accum *	__p,
		unsigned long accum	__value
	)

Write an unsigned long accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_ullk()

void eeprom_write_ullk	(	unsigned long long accum *	__p,
		unsigned long long accum	__value
	)

Write an unsigned long long accum to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_ullr()

void eeprom_write_ullr	(	unsigned long long fract *	__p,
		unsigned long long fract	__value
	)

Write an unsigned long long fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_ulr()

void eeprom_write_ulr	(	unsigned long fract *	__p,
		unsigned long fract	__value
	)

Write an unsigned long fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ eeprom_write_ur()

void eeprom_write_ur	(	unsigned fract *	__p,
		unsigned fract	__value
	)

Write an unsigned fract to EEPROM address __p.

Since: AVR-LibC v2.3

◆ exp2k()

accum exp2k ( accum x )

Compute 2^x with saturation.

The WCET is at least the one of exp2m1ur().

Since: AVR-LibC v2.3

◆ exp2m1ur()

unsigned fract exp2m1ur ( unsigned fract x )

Compute 2^x − 1. The returned value is in the range [0, 1).

The absolute error is bounded by 2.2·10⁻⁵ ≈ 2^−15.4. The worst case execution time (WCET) is around 200 cycles when MUL is available, and around 1000 cycles when MUL is not available (measured with avr-gcc v15).

Since: AVR-LibC v2.3

◆ exp2uk()

unsigned accum exp2uk ( unsigned accum x )

Compute 2^x with saturation.

The WCET is at least the one of exp2m1ur().

Since: AVR-LibC v2.3

◆ hkbits()

short accum hkbits ( int val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ hktoa()

char * hktoa	(	short accum	x,
		char *	buf,
		unsigned char	mode
	)

Convert fixed-point value x to a decimal ASCII representation. The result is written to buf, and the user is responsible for providing enough memory in buf. Returns buf.

For the meaning of mode, and for the (maximal) number of character written by this function, see uktoa().

Since: AVR-LibC v2.3

◆ hrbits()

short fract hrbits ( signed char val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ hrtoa()

char * hrtoa	(	short fract	x,
		char *	buf,
		unsigned char	mode
	)

Convert fixed-point value x to a decimal ASCII representation. The result is written to buf, and the user is responsible for providing enough memory in buf. Returns buf.

For the meaning of mode, and for the (maximal) number of character written by this function, see uktoa().

Since: AVR-LibC v2.3

◆ kbits()

accum kbits ( long val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ ktoa()

char * ktoa	(	accum	x,
		char *	buf,
		unsigned char	mode
	)

Convert fixed-point value x to a decimal ASCII representation. The result is written to buf, and the user is responsible for providing enough memory in buf. Returns buf.

For the meaning of mode, and for the (maximal) number of character written by this function, see uktoa().

Since: AVR-LibC v2.3

◆ lkbits()

long accum lkbits ( long long val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ llkbits()

long long accum llkbits ( long long val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ llrbits()

long long fract llrbits ( long long val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ log21puhr()

unsigned short fract log21puhr ( unsigned short fract x )

Return log₂(1 + x), the logarithm to base 2 of the value 1 + x. The result is in the range [0, 1).

The absolute error is bounded by 4.3·10⁻³ ≈ 2^−7.5. The worst case execution time (WCET) is around 25 cycles when MUL is available, and around 340 cycles when MUL is not available.

Since: AVR-LibC v2.3

◆ log21pur()

unsigned fract log21pur ( unsigned fract x )

Return log₂(1 + x), the logarithm to base 2 of the value 1 + x. The result is in the range [0, 1).

The absolute error is bounded by 3·10⁻⁵ ≈ 2⁻¹⁵. The worst case execution time (WCET) is around 250 cycles when MUL is available, and around 1300 cycles when MUL is not available.

Since: AVR-LibC v2.3

◆ log2uhk()

short accum log2uhk ( unsigned short accum x )

Return log₂(x), the logarithm to base 2 of the value x. The returned value for x = 0 is -128.

The absolute error is bounded by 8·10⁻³ ≈ 2⁻⁷. The worst case execution time (WCET) is around 60 cycles plus the WCET of log21puhr().

Since: AVR-LibC v2.3

◆ log2uk()

accum log2uk ( unsigned accum x )

Returns log₂(x), the logarithm to base 2 of the value x. The returned value for x = 0 is -32768.

The absolute error is bounded by 4.5·10⁻⁵ ≈ 2^−14.5. The worst case execution time (WCET) is around 150 cycles more than the WCET of log21pur().

Since: AVR-LibC v2.3

◆ lrbits()

long fract lrbits ( long val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ lrdivi()

long fract lrdivi	(	long int	num,
		long int	denom
	)

The lrdivi() function computes the value of num/denom and returns the result of the long fract type. The return value is rounded towards zero, and is saturated on overflow. If denom is zero, the behavior is undefined.

Since: AVR-LibC v2.3

◆ pgm_read_hk()

static short accum pgm_read_hk ( const short accum * addr )

inlinestatic

Read a short accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_hk_far()

static short accum pgm_read_hk_far ( uint_farptr_t addr )

inlinestatic

Read a short accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_hr()

static short fract pgm_read_hr ( const short fract * addr )

inlinestatic

Read a short fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_hr_far()

static short fract pgm_read_hr_far ( uint_farptr_t addr )

inlinestatic

Read a short fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_k()

static accum pgm_read_k ( const accum * addr )

inlinestatic

Read an accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_k_far()

static accum pgm_read_k_far ( uint_farptr_t addr )

inlinestatic

Read an accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_lk()

static long accum pgm_read_lk ( const long accum * addr )

inlinestatic

Read a long accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_lk_far()

static long accum pgm_read_lk_far ( uint_farptr_t addr )

inlinestatic

Read a long accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_llk()

static long long accum pgm_read_llk ( const long long accum * addr )

inlinestatic

Read a long long accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_llk_far()

static long long accum pgm_read_llk_far ( uint_farptr_t addr )

inlinestatic

Read a long long accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_llr()

static long long fract pgm_read_llr ( const long long fract * addr )

inlinestatic

Read a long long fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_llr_far()

static long long fract pgm_read_llr_far ( uint_farptr_t addr )

inlinestatic

Read a long long fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_lr()

static long fract pgm_read_lr ( const long fract * addr )

inlinestatic

Read a long fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_lr_far()

static long fract pgm_read_lr_far ( uint_farptr_t addr )

inlinestatic

Read a long fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_r()

static fract pgm_read_r ( const fract * addr )

inlinestatic

Read a fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_r_far()

static fract pgm_read_r_far ( uint_farptr_t addr )

inlinestatic

Read a fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_uhk()

static unsigned short accum pgm_read_uhk ( const unsigned short accum * addr )

inlinestatic

Read an unsigned short accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_uhk_far()

static unsigned short accum pgm_read_uhk_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned short accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_uhr()

static unsigned short fract pgm_read_uhr ( const unsigned short fract * addr )

inlinestatic

Read an unsigned short fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_uhr_far()

static unsigned short fract pgm_read_uhr_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned short fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_uk()

static unsigned accum pgm_read_uk ( const unsigned accum * addr )

inlinestatic

Read an unsigned accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_uk_far()

static unsigned accum pgm_read_uk_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ulk()

static unsigned long accum pgm_read_ulk ( const unsigned long accum * addr )

inlinestatic

Read an unsigned long accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ulk_far()

static unsigned long accum pgm_read_ulk_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned long accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ullk()

static unsigned long long accum pgm_read_ullk ( const unsigned long long accum * addr )

inlinestatic

Read an unsigned long long accum from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ullk_far()

static unsigned long long accum pgm_read_ullk_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned long long accum from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ullr()

static unsigned long long fract pgm_read_ullr ( const unsigned long long fract * addr )

inlinestatic

Read an unsigned long long fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ullr_far()

static unsigned long long fract pgm_read_ullr_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned long long fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ulr()

static unsigned long fract pgm_read_ulr ( const unsigned long fract * addr )

inlinestatic

Read an unsigned long fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ulr_far()

static unsigned long fract pgm_read_ulr_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned long fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ur()

static unsigned fract pgm_read_ur ( const unsigned fract * addr )

inlinestatic

Read an unsigned fract from 16-bit address addr. The address is in the lower 64 KiB of program memory.

Since: AVR-LibC v2.3

◆ pgm_read_ur_far()

static unsigned fract pgm_read_ur_far ( uint_farptr_t addr )

inlinestatic

Read an unsigned fract from far address addr. The address is in the program memory.

Since: AVR-LibC v2.3

◆ rbits()

fract rbits ( int val )

Return a fixed-point value of the same size and signedness, and with the same bit representation like val.

◆ rdivi()

fract rdivi	(	int	num,
		int	denom
	)

The rdivi() function computes the value num/denom and returns the result of the fract type. The return value is rounded towards zero, and is saturated on overflow. If denom is zero, the behavior is undefined.

Since: AVR-LibC v2.3