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Tasmota/tasmota/support_float.ino

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/*
support_float.ino - Small floating point support for Tasmota
Copyright (C) 2020 Theo Arends and Stephan Hadinger
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/>.
*/
float fmodf(float x, float y)
{
// https://github.com/micropython/micropython/blob/master/lib/libm/fmodf.c
union {float f; uint32_t i;} ux = {x}, uy = {y};
int ex = ux.i>>23 & 0xff;
int ey = uy.i>>23 & 0xff;
uint32_t sx = ux.i & 0x80000000;
uint32_t i;
uint32_t uxi = ux.i;
if (uy.i<<1 == 0 || isnan(y) || ex == 0xff)
return (x*y)/(x*y);
if (uxi<<1 <= uy.i<<1) {
if (uxi<<1 == uy.i<<1)
return 0*x;
return x;
}
// normalize x and y
if (!ex) {
for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1);
uxi <<= -ex + 1;
} else {
uxi &= -1U >> 9;
uxi |= 1U << 23;
}
if (!ey) {
for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1);
uy.i <<= -ey + 1;
} else {
uy.i &= -1U >> 9;
uy.i |= 1U << 23;
}
// x mod y
for (; ex > ey; ex--) {
i = uxi - uy.i;
if (i >> 31 == 0) {
if (i == 0)
return 0*x;
uxi = i;
}
uxi <<= 1;
}
i = uxi - uy.i;
if (i >> 31 == 0) {
if (i == 0)
return 0*x;
uxi = i;
}
for (; uxi>>23 == 0; uxi <<= 1, ex--);
// scale result up
if (ex > 0) {
uxi -= 1U << 23;
uxi |= (uint32_t)ex << 23;
} else {
uxi >>= -ex + 1;
}
uxi |= sx;
ux.i = uxi;
return ux.f;
}
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; }
if (x == 1.0) { return 0; }
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;
for (uint32_t count = 0; count < 10; count++) { // Experimental number of 10 iterations
z *= step;
double 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_P(LOG_LEVEL_DEBUG, PSTR("input %s, log %s, taylor %s"), logxs, log1s, log2s);
*/
return totalValue;
}
// Following 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
float const f_180pi = 180 / f_pi; // 180 / pi for angles in degrees
// *******************************************************************
// ***
// *** 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 = x * x; // The input argument squared
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)
{
x = fmodf(x, f_twopi); // Get rid of values > 2* f_pi
if (x < 0) { x = -x; } // cos(-x) = cos(x)
int 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);
}
return 0.0; // Never reached. Fixes compiler warning
}
//
// 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 = x * x; // The input argument squared
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)
{
x = fmodf(x, (float)f_twopi); // Get rid of values >2 *f_pi
int 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);
}
return 0.0; // Never reached. Fixes compiler warning
}
// *******************************************************************
// ***
// *** 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 = x * x; // The input argument squared
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 NAN; }
return 2 * atan_66(x / (1 + sqrt1(d)));
}
float acosf1(float x)
{
float d = 1.0f - x * x;
if (d < 0.0f) { return NAN; }
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;
}
//
// changeUIntScale
// Change a value for range a..b to c..d, using only unsigned int math
//
// New version, you don't need the "to_min < to_max" precondition anymore
//
// PRE-CONDITIONS (if not satisfied, you may 'halt and catch fire')
// from_min < from_max (not checked)
// from_min <= num <= from-max (chacked)
// POST-CONDITIONS
// to_min <= result <= to_max
//
uint16_t changeUIntScale(uint16_t inum, uint16_t ifrom_min, uint16_t ifrom_max,
uint16_t ito_min, uint16_t ito_max) {
// guard-rails
if (ifrom_min >= ifrom_max) {
if (ito_min > ito_max) {
return ito_max;
} else {
return ito_min; // invalid input, return arbitrary value
}
}
// convert to uint31, it's more verbose but code is more compact
uint32_t num = inum;
uint32_t from_min = ifrom_min;
uint32_t from_max = ifrom_max;
uint32_t to_min = ito_min;
uint32_t to_max = ito_max;
// check source range
num = (num > from_max ? from_max : (num < from_min ? from_min : num));
// check to_* order
if (to_min > to_max) {
// reverse order
num = (from_max - num) + from_min;
to_min = ito_max;
to_max = ito_min;
}
uint32_t numerator = (num - from_min) * (to_max - to_min);
uint32_t result;
if (numerator >= 0x80000000L) {
// don't do rounding as it would create an overflow
result = numerator / (from_max - from_min) + to_min;
} else {
result = (((numerator * 2) / (from_max - from_min)) + 1) / 2 + to_min;
}
return (uint32_t) (result > to_max ? to_max : (result < to_min ? to_min : result));
}
// Force a float value between two ranges, and adds or substract the range until we fit
float ModulusRangef(float f, float a, float b) {
if (b <= a) { return a; } // inconsistent, do what we can
float range = b - a;
float x = f - a; // now range of x should be 0..range
x = fmodf(x, range); // actual range is now -range..range
if (x < 0.0f) { x += range; } // actual range is now 0..range
return x + a; // returns range a..b
}
// Compute a n-degree polynomial for value x and an array of coefficient (by increasing order)
// Ex:
// For factors = { f0, f1, f2, f3 }
// Returns : f0 + f1 x + f2 x^2, + f3 x^3
// Internally computed as : f0 + x (f1 + x (f2 + x f3))
float Polynomialf(const float *factors, uint32_t degree, float x) {
float r = 0.0f;
for (uint32_t i = degree - 1; i >= 0; i--) {
r = r * x + factors[i];
}
return r;
}
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