Tasmota/sonoff/support_float.ino

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/*
support_float.ino - support for Sonoff-Tasmota
Copyright (C) 2019 Theo Arends
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
double FastPrecisePow(double a, double b)
{
// https://martin.ankerl.com/2012/01/25/optimized-approximative-pow-in-c-and-cpp/
// calculate approximation with fraction of the exponent
int e = abs((int)b);
union {
double d;
int x[2];
} u = { a };
u.x[1] = (int)((b - e) * (u.x[1] - 1072632447) + 1072632447);
u.x[0] = 0;
// exponentiation by squaring with the exponent's integer part
// double r = u.d makes everything much slower, not sure why
double r = 1.0;
while (e) {
if (e & 1) {
r *= a;
}
a *= a;
e >>= 1;
}
return r * u.d;
}
float FastPrecisePowf(const float x, const float y)
{
// return (float)(pow((double)x, (double)y));
return (float)FastPrecisePow(x, y);
}
double TaylorLog(double x)
{
// https://stackoverflow.com/questions/46879166/finding-the-natural-logarithm-of-a-number-using-taylor-series-in-c
if (x <= 0.0) { return NAN; }
double z = (x + 1) / (x - 1); // We start from power -1, to make sure we get the right power in each iteration;
double step = ((x - 1) * (x - 1)) / ((x + 1) * (x + 1)); // Store step to not have to calculate it each time
double totalValue = 0;
double powe = 1;
double y;
for (uint32_t count = 0; count < 10; count++) { // Experimental number of 10 iterations
z *= step;
y = (1 / powe) * z;
totalValue = totalValue + y;
powe = powe + 2;
}
totalValue *= 2;
/*
char logxs[33];
dtostrfd(x, 8, logxs);
double log1 = log(x);
char log1s[33];
dtostrfd(log1, 8, log1s);
char log2s[33];
dtostrfd(totalValue, 8, log2s);
AddLog_P2(LOG_LEVEL_DEBUG, PSTR("input %s, log %s, taylor %s"), logxs, log1s, log2s);
*/
return totalValue;
}
// All code adapted from: http://www.ganssle.com/approx.htm
/// ========================================
// The following code implements approximations to various trig functions.
//
// This is demo code to guide developers in implementing their own approximation
// software. This code is merely meant to illustrate algorithms.
inline float sinf(float x) { return sin_52(x); }
inline float cosf(float x) { return cos_52(x); }
inline float tanf(float x) { return tan_56(x); }
inline float atanf(float x) { return atan_66(x); }
inline float asinf(float x) { return asinf1(x); }
inline float acosf(float x) { return acosf1(x); }
inline float sqrtf(float x) { return sqrt1(x); }
inline float powf(float x, float y) { return FastPrecisePow(x, y); }
// Math constants we'll use
double const f_pi=3.1415926535897932384626433; // f_pi
double const f_twopi=2.0*f_pi; // f_pi times 2
double const f_two_over_pi= 2.0/f_pi; // 2/f_pi
double const f_halfpi=f_pi/2.0; // f_pi divided by 2
double const f_threehalfpi=3.0*f_pi/2.0; // f_pi times 3/2, used in tan routines
double const f_four_over_pi=4.0/f_pi; // 4/f_pi, used in tan routines
double const f_qtrpi=f_pi/4.0; // f_pi/4.0, used in tan routines
double const f_sixthpi=f_pi/6.0; // f_pi/6.0, used in atan routines
double const f_tansixthpi=tan(f_sixthpi); // tan(f_pi/6), used in atan routines
double const f_twelfthpi=f_pi/12.0; // f_pi/12.0, used in atan routines
double const f_tantwelfthpi=tan(f_twelfthpi); // tan(f_pi/12), used in atan routines
// *********************************************************
// ***
// *** Routines to compute sine and cosine to 5.2 digits
// *** of accuracy.
// ***
// *********************************************************
//
// cos_52s computes cosine (x)
//
// Accurate to about 5.2 decimal digits over the range [0, f_pi/2].
// The input argument is in radians.
//
// Algorithm:
// cos(x)= c1 + c2*x**2 + c3*x**4 + c4*x**6
// which is the same as:
// cos(x)= c1 + x**2(c2 + c3*x**2 + c4*x**4)
// cos(x)= c1 + x**2(c2 + x**2(c3 + c4*x**2))
//
float cos_52s(float x)
{
const float c1= 0.9999932946;
const float c2=-0.4999124376;
const float c3= 0.0414877472;
const float c4=-0.0012712095;
float x2; // The input argument squared
x2=x * x;
return (c1 + x2*(c2 + x2*(c3 + c4*x2)));
}
//
// This is the main cosine approximation "driver"
// It reduces the input argument's range to [0, f_pi/2],
// and then calls the approximator.
// See the notes for an explanation of the range reduction.
//
float cos_52(float x){
int quad; // what quadrant are we in?
x=fmodf(x, f_twopi); // Get rid of values > 2* f_pi
if(x<0)x=-x; // cos(-x) = cos(x)
quad=int(x * (float)f_two_over_pi); // Get quadrant # (0 to 3) we're in
switch (quad){
case 0: return cos_52s(x);
case 1: return -cos_52s((float)f_pi-x);
case 2: return -cos_52s(x-(float)f_pi);
case 3: return cos_52s((float)f_twopi-x);
}
}
//
// The sine is just cosine shifted a half-f_pi, so
// we'll adjust the argument and call the cosine approximation.
//
float sin_52(float x){
return cos_52((float)f_halfpi-x);
}
// *********************************************************
// ***
// *** Routines to compute tangent to 5.6 digits
// *** of accuracy.
// ***
// *********************************************************
//
// tan_56s computes tan(f_pi*x/4)
//
// Accurate to about 5.6 decimal digits over the range [0, f_pi/4].
// The input argument is in radians. Note that the function
// computes tan(f_pi*x/4), NOT tan(x); it's up to the range
// reduction algorithm that calls this to scale things properly.
//
// Algorithm:
// tan(x)= x(c1 + c2*x**2)/(c3 + x**2)
//
float tan_56s(float x)
{
const float c1=-3.16783027;
const float c2= 0.134516124;
const float c3=-4.033321984;
float x2; // The input argument squared
x2=x * x;
return (x*(c1 + c2 * x2)/(c3 + x2));
}
//
// This is the main tangent approximation "driver"
// It reduces the input argument's range to [0, f_pi/4],
// and then calls the approximator.
// See the notes for an explanation of the range reduction.
// Enter with positive angles only.
//
// WARNING: We do not test for the tangent approaching infinity,
// which it will at x=f_pi/2 and x=3*f_pi/2. If this is a problem
// in your application, take appropriate action.
//
float tan_56(float x){
int octant; // what octant are we in?
x=fmodf(x, (float)f_twopi); // Get rid of values >2 *f_pi
octant=int(x * (float)f_four_over_pi); // Get octant # (0 to 7)
switch (octant){
case 0: return tan_56s(x *(float)f_four_over_pi);
case 1: return 1.0f/tan_56s(((float)f_halfpi-x) *(float)f_four_over_pi);
case 2: return -1.0f/tan_56s((x-(float)f_halfpi) *(float)f_four_over_pi);
case 3: return - tan_56s(((float)f_pi-x) *(float)f_four_over_pi);
case 4: return tan_56s((x-(float)f_pi) *(float)f_four_over_pi);
case 5: return 1.0f/tan_56s(((float)f_threehalfpi-x)*(float)f_four_over_pi);
case 6: return -1.0f/tan_56s((x-(float)f_threehalfpi)*(float)f_four_over_pi);
case 7: return - tan_56s(((float)f_twopi-x) *(float)f_four_over_pi);
}
}
// *********************************************************
// ***
// *** Routines to compute arctangent to 6.6 digits
// *** of accuracy.
// ***
// *********************************************************
//
// atan_66s computes atan(x)
//
// Accurate to about 6.6 decimal digits over the range [0, f_pi/12].
//
// Algorithm:
// atan(x)= x(c1 + c2*x**2)/(c3 + x**2)
//
float atan_66s(float x)
{
const float c1=1.6867629106;
const float c2=0.4378497304;
const float c3=1.6867633134;
float x2; // The input argument squared
x2=x * x;
return (x*(c1 + x2*c2)/(c3 + x2));
}
//
// This is the main arctangent approximation "driver"
// It reduces the input argument's range to [0, f_pi/12],
// and then calls the approximator.
//
//
float atan_66(float x){
float y; // return from atan__s function
bool complement= false; // true if arg was >1
bool region= false; // true depending on region arg is in
bool sign= false; // true if arg was < 0
if (x <0 ){
x=-x;
sign=true; // arctan(-x)=-arctan(x)
}
if (x > 1.0){
x=1.0/x; // keep arg between 0 and 1
complement=true;
}
if (x > (float)f_tantwelfthpi){
x = (x-(float)f_tansixthpi)/(1+(float)f_tansixthpi*x); // reduce arg to under tan(f_pi/12)
region=true;
}
y=atan_66s(x); // run the approximation
if (region) y+=(float)f_sixthpi; // correct for region we're in
if (complement)y=(float)f_halfpi-y; // correct for 1/x if we did that
if (sign)y=-y; // correct for negative arg
return (y);
}
float asinf1(float x) {
float d = 1.0f - x*x;
if (d < 0.0f) { return nanf(""); }
return 2 * atan_66(x / (1 + sqrt1(d)));
}
float acosf1(float x) {
float d = 1.0f - x*x;
if (d < 0.0f) { return nanf(""); }
float y = asinf1(sqrt1(d));
if (x >= 0.0f) {
return y;
} else {
return (float)f_pi - y;
}
}
// https://www.codeproject.com/Articles/69941/Best-Square-Root-Method-Algorithm-Function-Precisi
float sqrt1(const float x)
{
union
{
int i;
float x;
} u;
u.x = x;
u.i = (1<<29) + (u.i >> 1) - (1<<22);
// Two Babylonian Steps (simplified from:)
// u.x = 0.5f * (u.x + x/u.x);
// u.x = 0.5f * (u.x + x/u.x);
u.x = u.x + x/u.x;
u.x = 0.25f*u.x + x/u.x;
return u.x;
}