maths.h File Reference

#include <stdint.h>
#include "globals.h"
#include "bit_shifts.h"

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Macros
#define	DIV_ROUND_DOWN   -1
	Rounding behavior: always round down.
#define	DIV_ROUND_UP   1
	Rounding behavior: always round up.
#define	DIV_ROUND_NEAREST   0
	Rounding behavior: round to nearest.
#define	DIV_ROUND_BEHAVIOR   DIV_ROUND_NEAREST
	Integer division rounding behavior.
#define	DIV_ROUND_CORRECT(d, t)   ((t)(((d)>>1U)+(t)DIV_ROUND_BEHAVIOR))
	Computes the denominator correction for rounding division based on our rounding behavior.
#define	DIV_ROUND_CLOSEST(n, d, t)
	Rounded integer division.
#define	UDIV_ROUND_CLOSEST(n, d, t)   ((t)((n) + DIV_ROUND_CORRECT(d, t))/(t)(d))
	Rounded unsigned integer division.
#define	IS_INTEGER(d)   ((d) == (int32_t)(d))
	Test whether the parameter is an integer or not.

Functions
uint8_t	random1to100 (void)
static uint32_t	div360 (uint32_t n)
	Optimised integer division by 360.
static uint32_t	percentage (uint8_t percent, uint32_t value)
	Integer based percentage calculation.
static uint16_t	halfPercentage (uint8_t percent, uint16_t value)
	Integer based half-percentage calculation.
static int16_t	nudge (int16_t min, int16_t max, int16_t value, int16_t nudgeAmount)
	Make one pass at correcting the value into the range [min, max)
static uint16_t	udiv_32_16 (uint32_t dividend, uint16_t divisor)
	Optimised division: uint32_t/uint16_t => uint16_t.
static uint16_t	udiv_32_16_closest (uint32_t dividend, uint16_t divisor)
	Same as udiv_32_16(), except this will round to nearest integer instead of truncating.
template<class T >
constexpr const T &	clamp (const T &v, const T &lo, const T &hi)
	clamps a given value between the minimum and maximum thresholds.
static uint16_t	LOW_PASS_FILTER (uint16_t input, uint8_t alpha, uint16_t prior)
	Simple low pass IIR filter 16-bit values.
static int16_t	LOW_PASS_FILTER (int16_t input, uint8_t alpha, int16_t prior)
	Simple low pass IIR filter for S16 values.
static uint16_t	div100 (uint16_t n)
	Performance optimised integer division by 100. I.e. same as n/100.
static int16_t	div100 (int16_t n)
	Performance optimised integer division by 100. I.e. same as n/100.
static uint32_t	div100 (uint32_t n)
	Performance optimised integer division by 100. I.e. same as n/100.
static int32_t	div100 (int32_t n)
	Performance optimised integer division by 100. I.e. same as n/100.

Macro Definition Documentation

IS_INTEGER

#define IS_INTEGER

(

d

)

((d) == (int32_t)(d))

Test whether the parameter is an integer or not.

Function Documentation

clamp()

template<class T >

constexpr const T & clamp ( const T &  v, const T &  lo, const T &  hi  )

constexpr

clamps a given value between the minimum and maximum thresholds.

Uses operator< to compare the values.

Template Parameters

T	Any type that supports operator<

Parameters

v	The value to clamp
lo	The minimum threshold
hi	The maximum threshold

Returns

if v compares less than lo, returns lo; otherwise if hi compares less than v, returns hi; otherwise returns v.

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div100() [1/4]

static int16_t div100 ( int16_t  n )

inlinestatic

Performance optimised integer division by 100. I.e. same as n/100.

Uses the rounding behaviour controlled by DIV_ROUND_BEHAVIOR

Parameters

n	Dividend to divide by 100

Returns

n/100, with rounding behavior applied

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div100() [2/4]

static int32_t div100 ( int32_t  n )

inlinestatic

Performance optimised integer division by 100. I.e. same as n/100.

Uses the rounding behaviour controlled by DIV_ROUND_BEHAVIOR

Parameters

n	Dividend to divide by 100

Returns

n/100, with rounding behavior applied

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div100() [3/4]

static uint16_t div100 ( uint16_t  n )

inlinestatic

Performance optimised integer division by 100. I.e. same as n/100.

Uses the rounding behaviour controlled by DIV_ROUND_BEHAVIOR

Parameters

n	Dividend to divide by 100

Returns

n/100, with rounding behavior applied

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div100() [4/4]

static uint32_t div100 ( uint32_t  n )

inlinestatic

Performance optimised integer division by 100. I.e. same as n/100.

Uses the rounding behaviour controlled by DIV_ROUND_BEHAVIOR

Parameters

n	Dividend to divide by 100

Returns

n/100, with rounding behavior applied

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div360()

static uint32_t div360 ( uint32_t  n )

inlinestatic

Optimised integer division by 360.

Parameters

n	The numerator (dividee) (an integer)

Returns

uint32_t

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halfPercentage()

static uint16_t halfPercentage ( uint8_t  percent, uint16_t  value  )

inlinestatic

Integer based half-percentage calculation.

Parameters

percent	The percent to calculate ([0, 100])
value	The value to operate on

Returns

uint16_t

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LOW_PASS_FILTER() [1/2]

static int16_t LOW_PASS_FILTER ( int16_t  input, uint8_t  alpha, int16_t  prior  )

inlinestatic

Simple low pass IIR filter for S16 values.

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LOW_PASS_FILTER() [2/2]

static uint16_t LOW_PASS_FILTER ( uint16_t  input, uint8_t  alpha, uint16_t  prior  )

inlinestatic

Simple low pass IIR filter 16-bit values.

This is effectively implementing the smooth filter from playground.arduino.cc/Main/Smooth But removes the use of floats and uses 8 bits of fixed precision.

Parameters

input	incoming unfiltered value
alpha	filter factor. 0=off, 255=full smoothing (0.00 to 0.99 in float, 0-99%)
prior	previous filtered value.

Returns

uint16_t The filtered input

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nudge()

static int16_t nudge ( int16_t  min, int16_t  max, int16_t  value, int16_t  nudgeAmount  )

inlinestatic

Make one pass at correcting the value into the range [min, max)

Parameters

min	Minimum value (inclusive)
max	Maximum value (exclusive)
value	Value to nudge
nudgeAmount	Amount to change value by

Returns

int16_t

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percentage()

static uint32_t percentage ( uint8_t  percent, uint32_t  value  )

inlinestatic

Integer based percentage calculation.

Parameters

percent	The percent to calculate ([0, 100])
value	The value to operate on

Returns

uint32_t

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random1to100()

uint8_t random1to100

(

void

)

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udiv_32_16()

static uint16_t udiv_32_16 ( uint32_t  dividend, uint16_t  divisor  )

inlinestatic

Optimised division: uint32_t/uint16_t => uint16_t.

Optimised division of unsigned 32-bit by unsigned 16-bit when it is known that the result fits into unsigned 16-bit.

~60% quicker than raw 32/32 => 32 division on ATMega

Note

Bad things will likely happen if the result doesn't fit into 16-bits.

Copied from https://stackoverflow.com/a/66593564

Parameters

dividend	The dividend (numerator)
divisor	The divisor (denominator)

Returns

uint16_t

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udiv_32_16_closest()

static uint16_t udiv_32_16_closest ( uint32_t  dividend, uint16_t  divisor  )

inlinestatic

Same as udiv_32_16(), except this will round to nearest integer instead of truncating.

Minor performance drop compared to non-rounding version.

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