<stdfix.h>: ISO/IEC TR 18037 Fixed-Point Arithmetic

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 fract	sqrthr (short fract radic)
unsigned short fract	sqrtuhr (unsigned short 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)

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
hr	short fract	1	s.7
r	fract	2	s.15
lr	long fract	4	s.31
llr	long long fract	8	s.63
hk	short accum	2	s8.7
k	accum	4	s16.15
lk	long accum	8	s32.31
llk	long long accum	8	s16.47
uhr	unsigned short fract	1	0.8
ur	unsigned fract	2	0.16
ulr	unsigned long fract	4	0.32
ullr	unsigned long long fract	8	0.64
uhk	unsigned short accum	2	8.8
uk	unsigned accum	4	16.16
ulk	unsigned long accum	8	32.32
ullk	unsigned long long accum	8	16.48

Remarks

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

See also some benchmarks.

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.

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

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

roundfx()

type roundfx	(	type	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundhk()

short accum roundhk	(	short accum	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundhr()

short fract roundhr	(	short fract	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

roundk()

accum roundk	(	accum	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundlk()

long accum roundlk	(	long accum	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundllk()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundllr()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

roundlr()

long fract roundlr	(	long fract	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

roundr()

fract roundr	(	fract	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

rounduhk()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

rounduhr()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

rounduk()

unsigned accum rounduk	(	unsigned accum	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundulk()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundullk()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

As an extension, bit may be in the range −IBIT < bit < FBIT. For example, bit = −1 rounds to an even value.

roundullr()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

roundulr()

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

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

roundur()

unsigned fract roundur	(	unsigned fract	val,
		int	bit
	)

Round val to bit fractional bits. When the result does not fit into the range of the return type, the result is saturated.

rtoa()

char * rtoa	(	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

sinpi2k()

accum sinpi2k

(

accum

deg

)

Sine 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

sinpi2ur()

unsigned fract sinpi2ur

(

unsigned fract

x

)

Sine of x·π/2 radians. The returned value is in the range [0, 1).

The absolute error is bounded by 2.9·10⁻⁵ ≈ 2⁻¹⁵. The worst case execution time (WCET) is around 260 cycles when MUL is available, and around 1400 cycles when MUL is not available.

Since

AVR-LibC v2.3

sinuhk_deg()

fract sinuhk_deg

(

unsigned short accum

deg

)

Sine 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 70 cycles.

Since

AVR-LibC v2.3

sqrthr()

short fract sqrthr

(

short fract

radic

)

Square root of the value radic rounded down.

Since

AVR-LibC v2.3

sqrtuhr()

unsigned short fract sqrtuhr

(

unsigned short fract

radic

)

Square root of the value radic rounded down. The result is in the range [0, 1).

The absolute error is in the range [−3.9·10⁻³ ≈ 2⁻⁸, 0]. The worst case execution time (WCET) is around 120 cycles.

Since

AVR-LibC v2.3

sqrtur()

unsigned fract sqrtur

(

unsigned fract

radic

)

Square root of the value radic. The result is in the range [0, 1).

The absolute error is in the range [−1.5·10⁻⁵ ≈ 2⁻¹⁶, 0]. The worst case execution time (WCET) is around 320 cycles.

Since

AVR-LibC v2.3

uhkbits()

unsigned short accum uhkbits

(

unsigned int

val

)

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

uhktoa()

char * uhktoa	(	unsigned 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

uhrbits()

unsigned short fract uhrbits

(

unsigned char

val

)

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

uhrtoa()

char * uhrtoa	(	unsigned 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

ukbits()

unsigned accum ukbits

(

unsigned long

val

)

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

uktoa()

char * uktoa	(	unsigned 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.

The format of the output is controlled by the mode parameter. It is composed from the format flags below together with Digs, the number of fractional digits. The mode is the ORed result from Digs and a combination of FXTOA_ALL, FXTOA_ROUND or FXTOA_TRUNC, FXTOA_DOT or FXTOA_COMMA, and FXTOA_NTZ, like in:

uktoa (x, buf, FXTOA_ROUND | FXTOA_NTZ | Digs);

• Supported values for Digs are in the range 0...30.

FXTOA_ALL

Include all significant digits. Digs will be ignored.

FXTOA_ROUND

Round to nearest for Digs fractional digits. Rounding for Digs ≥ 5 has no effect, i.e. for such Digs values the rounded result will be the same like the truncated result. Rounding mode is the default, i.e. FXTOA_ROUND can be omitted.

FXTOA_TRUNC

Like FXTOA_ALL, but truncate the result (round to zero) after Digs fractional digits.

FXTOA_NTZ

• With FXTOA_NTZ the result has no trailing zeros. When the result represents an integral value, then no decimal point and no fractional digits are present.
• Without FXTOA_NTZ and with FXTOA_ROUND or FXTOA_TRUNC, the result has the specified number of fractional digits.
• FXTOA_NTZ has no effect with FXTOA_ALL.
• FXTOA_NTZ has no effect on the required buffer size.

FXTOA_DOT

The decimal point is a dot (.). This is the default, i.e. FXTOA_DOT can be omitted.

FXTOA_COMMA

The decimal point is a comma (,).

Examples

Value	Mode	Result
1.8uk	0	"2"
1.8uk	1	"1.8"
1.8uk	2	"1.80"
1.8uk	3	"1.800"
1.8uk	FXTOA_NTZ | 0	"2"
1.8uk	FXTOA_NTZ | 1	"1.8"
1.8uk	FXTOA_NTZ | 2	"1.8"
1.8uk	FXTOA_NTZ | 3	"1.8"
1.8uk	FXTOA_TRUNC | FXTOA_COMMA | 0	"1"
1.8uk	FXTOA_TRUNC | FXTOA_COMMA | 1	"1,7"
1.8uk	FXTOA_TRUNC | FXTOA_COMMA | 2	"1,79"
1.8uk	FXTOA_TRUNC | FXTOA_COMMA | 3	"1,799"
1.8uk	FXTOA_ALL	"1.79998779296875"

The following table helps with providing enough memory in buf.

Notice that the required size of buf is independent of FXTOA_NTZ. This is the case since with FXTOA_NTZ the required buffer size may be larger that the size of the returned string.

Maximum Number of Bytes written to buf

Type	Function	FXTOA_ALL	All other Modes	Exact Maximal Value
unsigned accum	uktoa	23	7 + Digs	216−2−16	65535.9999847412109375
accum	ktoa	23	8 + Digs	216−2−15	65535.999969482421875
unsigned short accum	uhktoa	13	5 + Digs	28−2−8	255.99609375
short accum	hktoa	13	6 + Digs	28−2−7	255.9921875
unsigned fract	urtoa	19	3 + Digs	1−2−16	0.9999847412109375
fract	rtoa	19	4 + Digs	1−2−15	0.999969482421875
unsigned short fract	uhrtoa	11	3 + Digs	1−2−8	0.99609375
short fract	hrtoa	11	4 + Digs	1−2−7	0.9921875

Since

AVR-LibC v2.3

ulkbits()

unsigned long accum ulkbits

(

unsigned long long

val

)

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

ullkbits()

unsigned long long accum ullkbits

(

unsigned long long

val

)

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

ullrbits()

unsigned long long fract ullrbits

(

unsigned long long

val

)

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

ulrbits()

unsigned long fract ulrbits

(

unsigned long

val

)

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

ulrdivi()

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

The ulrdivi() function computes the value of num/denom and returns the result of the unsigned 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

urbits()

unsigned fract urbits

(

unsigned int

val

)

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

urdivi()

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

The urdivi() function computes the value num/denom and returns the result of the unsigned 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

urtoa()

char * urtoa	(	unsigned 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