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Using alternative methods for maths, saving ~8Kb with lights

fastled^2
Xose Pérez 6 years ago
parent
2a2579a7aa
commit
69ac57abb4
6 changed files with 768 additions and 8 deletions
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  1. +636
    -0
      code/espurna/libs/fs_math.c
  2. +116
    -0
      code/espurna/libs/fs_math.h
  3. +0
    -0
      code/espurna/libs/pwm.c
  4. +8
    -5
      code/espurna/light.ino
  5. +4
    -2
      code/espurna/sensors/EmonSensor.h
  6. +4
    -1
      code/espurna/sensors/V9261FSensor.h

+ 636
- 0
code/espurna/libs/fs_math.c View File

@ -0,0 +1,636 @@
/**
* This code is available at
* http://www.mindspring.com/~pfilandr/C/fs_math/
* and it is believed to be public domain.
*/
/* BEGIN fs_math.c */
#include "fs_math.h"
#include <float.h>
/*
** pi == (atan(1.0 / 3) + atan(1.0 / 2)) * 4
*/
static double fs_pi(void);
static long double fs_pil(void);
double fs_sqrt(double x)
{
int n;
double a, b;
if (x > 0 && DBL_MAX >= x) {
for (n = 0; x > 2; x /= 4) {
++n;
}
while (0.5 > x) {
--n;
x *= 4;
}
a = x;
b = (1 + x) / 2;
do {
x = b;
b = (a / x + x) / 2;
} while (x > b);
while (n > 0) {
x *= 2;
--n;
}
while (0 > n) {
x /= 2;
++n;
}
} else {
if (x != 0) {
x = DBL_MAX;
}
}
return x;
}
double fs_log(double x)
{
int n;
double a, b, c, epsilon;
static double A, B, C;
static int initialized;
if (x > 0 && DBL_MAX >= x) {
if (!initialized) {
initialized = 1;
A = fs_sqrt(2);
B = A / 2;
C = fs_log(A);
}
for (n = 0; x > A; x /= 2) {
++n;
}
while (B > x) {
--n;
x *= 2;
}
a = (x - 1) / (x + 1);
x = C * n + a;
c = a * a;
n = 1;
epsilon = DBL_EPSILON * x;
if (0 > a) {
if (epsilon > 0) {
epsilon = -epsilon;
}
do {
n += 2;
a *= c;
b = a / n;
x += b;
} while (epsilon > b);
} else {
if (0 > epsilon) {
epsilon = -epsilon;
}
do {
n += 2;
a *= c;
b = a / n;
x += b;
} while (b > epsilon);
}
x *= 2;
} else {
x = -DBL_MAX;
}
return x;
}
double fs_log10(double x)
{
static double log_10;
static int initialized;
if (!initialized) {
initialized = 1;
log_10 = fs_log(10);
}
return x > 0 && DBL_MAX >= x ? fs_log(x) / log_10 : fs_log(x);
}
double fs_exp(double x)
{
unsigned n, square;
double b, e;
static double x_max, x_min, epsilon;
static int initialized;
if (!initialized) {
initialized = 1;
x_max = fs_log(DBL_MAX);
x_min = fs_log(DBL_MIN);
epsilon = DBL_EPSILON / 4;
}
if (x_max >= x && x >= x_min) {
for (square = 0; x > 1; x /= 2) {
++square;
}
while (-1 > x) {
++square;
x /= 2;
}
e = b = n = 1;
do {
b /= n++;
b *= x;
e += b;
b /= n++;
b *= x;
e += b;
} while (b > epsilon);
while (square-- != 0) {
e *= e;
}
} else {
e = x > 0 ? DBL_MAX : 0;
}
return e;
}
double fs_modf(double value, double *iptr)
{
double a, b;
const double c = value;
if (0 > c) {
value = -value;
}
if (DBL_MAX >= value) {
for (*iptr = 0; value >= 1; value -= b) {
a = value / 2;
b = 1;
while (a >= b) {
b *= 2;
}
*iptr += b;
}
} else {
*iptr = value;
value = 0;
}
if (0 > c) {
*iptr = -*iptr;
value = -value;
}
return value;
}
double fs_fmod(double x, double y)
{
double a, b;
const double c = x;
if (0 > c) {
x = -x;
}
if (0 > y) {
y = -y;
}
if (y != 0 && DBL_MAX >= y && DBL_MAX >= x) {
while (x >= y) {
a = x / 2;
b = y;
while (a >= b) {
b *= 2;
}
x -= b;
}
} else {
x = 0;
}
return 0 > c ? -x : x;
}
double fs_pow(double x, double y)
{
double p = 0;
if (0 > x && fs_fmod(y, 1) == 0) {
if (fs_fmod(y, 2) == 0) {
p = fs_exp(fs_log(-x) * y);
} else {
p = -fs_exp(fs_log(-x) * y);
}
} else {
if (x != 0 || 0 >= y) {
p = fs_exp(fs_log( x) * y);
}
}
return p;
}
static double fs_pi(void)
{
unsigned n;
double a, b, epsilon;
static double p;
static int initialized;
if (!initialized) {
initialized = 1;
epsilon = DBL_EPSILON / 4;
n = 1;
a = 3;
do {
a /= 9;
b = a / n;
n += 2;
a /= 9;
b -= a / n;
n += 2;
p += b;
} while (b > epsilon);
epsilon = DBL_EPSILON / 2;
n = 1;
a = 2;
do {
a /= 4;
b = a / n;
n += 2;
a /= 4;
b -= a / n;
n += 2;
p += b;
} while (b > epsilon);
p *= 4;
}
return p;
}
double fs_cos(double x)
{
unsigned n;
int negative, sine;
double a, b, c;
static double pi, two_pi, half_pi, third_pi, epsilon;
static int initialized;
if (0 > x) {
x = -x;
}
if (DBL_MAX >= x) {
if (!initialized) {
initialized = 1;
pi = fs_pi();
two_pi = 2 * pi;
half_pi = pi / 2;
third_pi = pi / 3;
epsilon = DBL_EPSILON / 2;
}
if (x > two_pi) {
x = fs_fmod(x, two_pi);
}
if (x > pi) {
x = two_pi - x;
}
if (x > half_pi) {
x = pi - x;
negative = 1;
} else {
negative = 0;
}
if (x > third_pi) {
x = half_pi - x;
sine = 1;
} else {
sine = 0;
}
c = x * x;
x = n = 0;
a = 1;
do {
b = a;
a *= c;
a /= ++n;
a /= ++n;
b -= a;
a *= c;
a /= ++n;
a /= ++n;
x += b;
} while (b > epsilon);
if (sine) {
x = fs_sqrt((1 - x) * (1 + x));
}
if (negative) {
x = -x;
}
} else {
x = -DBL_MAX;
}
return x;
}
double fs_log2(double x)
{
static double log_2;
static int initialized;
if (!initialized) {
initialized = 1;
log_2 = fs_log(2);
}
return x > 0 && DBL_MAX >= x ? fs_log(x) / log_2 : fs_log(x);
}
double fs_exp2(double x)
{
static double log_2;
static int initialized;
if (!initialized) {
initialized = 1;
log_2 = fs_log(2);
}
return fs_exp(x * log_2);
}
long double fs_powl(long double x, long double y)
{
long double p;
if (0 > x && fs_fmodl(y, 1) == 0) {
if (fs_fmodl(y, 2) == 0) {
p = fs_expl(fs_logl(-x) * y);
} else {
p = -fs_expl(fs_logl(-x) * y);
}
} else {
if (x != 0 || 0 >= y) {
p = fs_expl(fs_logl( x) * y);
} else {
p = 0;
}
}
return p;
}
long double fs_sqrtl(long double x)
{
long int n;
long double a, b;
if (x > 0 && LDBL_MAX >= x) {
for (n = 0; x > 2; x /= 4) {
++n;
}
while (0.5 > x) {
--n;
x *= 4;
}
a = x;
b = (1 + x) / 2;
do {
x = b;
b = (a / x + x) / 2;
} while (x > b);
while (n > 0) {
x *= 2;
--n;
}
while (0 > n) {
x /= 2;
++n;
}
} else {
if (x != 0) {
x = LDBL_MAX;
}
}
return x;
}
long double fs_logl(long double x)
{
long int n;
long double a, b, c, epsilon;
static long double A, B, C;
static int initialized;
if (x > 0 && LDBL_MAX >= x) {
if (!initialized) {
initialized = 1;
B = 1.5;
do {
A = B;
B = 1 / A + A / 2;
} while (A > B);
B /= 2;
C = fs_logl(A);
}
for (n = 0; x > A; x /= 2) {
++n;
}
while (B > x) {
--n;
x *= 2;
}
a = (x - 1) / (x + 1);
x = C * n + a;
c = a * a;
n = 1;
epsilon = LDBL_EPSILON * x;
if (0 > a) {
if (epsilon > 0) {
epsilon = -epsilon;
}
do {
n += 2;
a *= c;
b = a / n;
x += b;
} while (epsilon > b);
} else {
if (0 > epsilon) {
epsilon = -epsilon;
}
do {
n += 2;
a *= c;
b = a / n;
x += b;
} while (b > epsilon);
}
x *= 2;
} else {
x = -LDBL_MAX;
}
return x;
}
long double fs_expl(long double x)
{
long unsigned n, square;
long double b, e;
static long double x_max, x_min, epsilon;
static int initialized;
if (!initialized) {
initialized = 1;
x_max = fs_logl(LDBL_MAX);
x_min = fs_logl(LDBL_MIN);
epsilon = LDBL_EPSILON / 4;
}
if (x_max >= x && x >= x_min) {
for (square = 0; x > 1; x /= 2) {
++square;
}
while (-1 > x) {
++square;
x /= 2;
}
e = b = n = 1;
do {
b /= n++;
b *= x;
e += b;
b /= n++;
b *= x;
e += b;
} while (b > epsilon);
while (square-- != 0) {
e *= e;
}
} else {
e = x > 0 ? LDBL_MAX : 0;
}
return e;
}
static long double fs_pil(void)
{
long unsigned n;
long double a, b, epsilon;
static long double p;
static int initialized;
if (!initialized) {
initialized = 1;
epsilon = LDBL_EPSILON / 4;
n = 1;
a = 3;
do {
a /= 9;
b = a / n;
n += 2;
a /= 9;
b -= a / n;
n += 2;
p += b;
} while (b > epsilon);
epsilon = LDBL_EPSILON / 2;
n = 1;
a = 2;
do {
a /= 4;
b = a / n;
n += 2;
a /= 4;
b -= a / n;
n += 2;
p += b;
} while (b > epsilon);
p *= 4;
}
return p;
}
long double fs_cosl(long double x)
{
long unsigned n;
int negative, sine;
long double a, b, c;
static long double pi, two_pi, half_pi, third_pi, epsilon;
static int initialized;
if (0 > x) {
x = -x;
}
if (LDBL_MAX >= x) {
if (!initialized) {
initialized = 1;
pi = fs_pil();
two_pi = 2 * pi;
half_pi = pi / 2;
third_pi = pi / 3;
epsilon = LDBL_EPSILON / 2;
}
if (x > two_pi) {
x = fs_fmodl(x, two_pi);
}
if (x > pi) {
x = two_pi - x;
}
if (x > half_pi) {
x = pi - x;
negative = 1;
} else {
negative = 0;
}
if (x > third_pi) {
x = half_pi - x;
sine = 1;
} else {
sine = 0;
}
c = x * x;
x = n = 0;
a = 1;
do {
b = a;
a *= c;
a /= ++n;
a /= ++n;
b -= a;
a *= c;
a /= ++n;
a /= ++n;
x += b;
} while (b > epsilon);
if (sine) {
x = fs_sqrtl((1 - x) * (1 + x));
}
if (negative) {
x = -x;
}
} else {
x = -LDBL_MAX;
}
return x;
}
long double fs_fmodl(long double x, long double y)
{
long double a, b;
const long double c = x;
if (0 > c) {
x = -x;
}
if (0 > y) {
y = -y;
}
if (y != 0 && LDBL_MAX >= y && LDBL_MAX >= x) {
while (x >= y) {
a = x / 2;
b = y;
while (a >= b) {
b *= 2;
}
x -= b;
}
} else {
x = 0;
}
return 0 > c ? -x : x;
}
/* END fs_math.c */

+ 116
- 0
code/espurna/libs/fs_math.h View File

@ -0,0 +1,116 @@
/**
* This code is available at
* http://www.mindspring.com/~pfilandr/C/fs_math/
* and it is believed to be public domain.
*/
/* BEGIN fs_math.h */
/*
** Portable freestanding code.
*/
#ifndef H_FS_MATH_H
#define H_FS_MATH_H
double fs_sqrt(double x);
double fs_log(double x);
double fs_log10(double x);
/*
** exp(x) = 1 + x + x^2/2! + x^3/3! + ...
*/
double fs_exp(double x);
double fs_modf(double value, double *iptr);
double fs_fmod(double x, double y);
double fs_pow(double x, double y);
double fs_cos(double x);
/*
** C99
*/
double fs_log2(double x);
double fs_exp2(double x);
long double fs_powl(long double x, long double y);
long double fs_sqrtl(long double x);
long double fs_logl(long double x);
long double fs_expl(long double x);
long double fs_cosl(long double x);
long double fs_fmodl(long double x, long double y);
#endif
/* END fs_math.h */
#if 0
/*
> > Anybody know where I can get some source code for a
> > reasonably fast double
> > precision square root algorithm in C.
> > I'm looking for one that is not IEEE
> > compliant as I am running on a Z/OS mainframe.
> >
> > I would love to use the standard library but
> > unfortunatly I'm using a
> > stripped down version of C that looses the the runtime library
> > (we have to write our own).
>
> long double Ssqrt(long double x)
> {
> long double a, b;
> size_t c;
size_t is a bug here.
c needs to be a signed type:
long c;
> if (x > 0) {
> c = 0;
> while (x > 4) {
> x /= 4;
> ++c;
> }
> while (1.0 / 4 > x) {
> x *= 4;
> --c;
> }
> a = x;
> b = ((4 > a) + a) / 2;
Not a bug, but should be:
b = (1 + a) / 2;
> do {
> x = b;
> b = (a / x + x) / 2;
> } while (x > b);
> if (c > 0) {
The above line is why c needs to be a signed type,
otherwise the decremented values of c, are greater than zero,
and the function won't work if the initial value of x
is less than 0.25
> while (c--) {
> x *= 2;
> }
> } else {
> while (c++) {
> x /= 2;
> }
> }
> }
> return x;
> }
>
> >
> > That algorithm was actually 4 times slower
> > then the one below, and more
> > code. It was accurate though.
> >
>
> Sorry Pete, I wasn't looking very carefully.
> When I converted your function
> to double precision it's was much quicker, the best I've seen yet.
*/
#endif

code/espurna/pwm.c → code/espurna/libs/pwm.c View File


+ 8
- 5
code/espurna/light.ino View File

@ -12,6 +12,10 @@ Copyright (C) 2016-2018 by Xose Pérez <xose dot perez at gmail dot com>
#include <ArduinoJson.h>
#include <vector>
extern "C" {
#include "libs/fs_math.h"
}
#if LIGHT_PROVIDER == LIGHT_PROVIDER_DIMMER
#define PWM_CHANNEL_NUM_MAX LIGHT_CHANNELS
extern "C" {
@ -288,19 +292,18 @@ void _fromKelvin(unsigned long kelvin, bool setMireds) {
return;
}
// Calculate colors
unsigned int red = (kelvin <= 66)
? LIGHT_MAX_VALUE
: 329.698727446 * pow((kelvin - 60), -0.1332047592);
: 329.698727446 * fs_pow((double) (kelvin - 60), -0.1332047592);
unsigned int green = (kelvin <= 66)
? 99.4708025861 * log(kelvin) - 161.1195681661
: 288.1221695283 * pow(kelvin, -0.0755148492);
? 99.4708025861 * fs_log(kelvin) - 161.1195681661
: 288.1221695283 * fs_pow((double) kelvin, -0.0755148492);
unsigned int blue = (kelvin >= 66)
? LIGHT_MAX_VALUE
: ((kelvin <= 19)
? 0
: 138.5177312231 * log(kelvin - 10) - 305.0447927307);
: 138.5177312231 * fs_log(kelvin - 10) - 305.0447927307);
_setRGBInputValue(red, green, blue);
}


+ 4
- 2
code/espurna/sensors/EmonSensor.h View File

@ -10,9 +10,11 @@
#undef I2C_SUPPORT
#define I2C_SUPPORT 1 // Explicitly request I2C support.
#include "Arduino.h"
#include "I2CSensor.h"
extern "C" {
#include "libs/fs_math.h"
}
class EmonSensor : public I2CSensor {
@ -197,7 +199,7 @@ class EmonSensor : public I2CSensor {
}
// Calculate current
double rms = _samples > 0 ? sqrt(sum / _samples) : 0;
double rms = _samples > 0 ? fs_sqrt(sum / _samples) : 0;
double current = _current_factor[channel] * rms;
current = (double) (int(current * _multiplier[channel]) - 1) / _multiplier[channel];
if (current < 0) current = 0;


+ 4
- 1
code/espurna/sensors/V9261FSensor.h View File

@ -9,6 +9,9 @@
#include "Arduino.h"
#include "BaseSensor.h"
extern "C" {
#include "libs/fs_math.h"
}
#include <SoftwareSerial.h>
@ -203,7 +206,7 @@ class V9261FSensor : public BaseSensor {
if (_voltage < 0) _voltage = 0;
if (_current < 0) _current = 0;
_apparent = sqrt(_reactive * _reactive + _active * _active);
_apparent = fs_sqrt(_reactive * _reactive + _active * _active);
}


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