foc_utils.cpp

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#include "foc_utils.h"
 
 
// function approximating the sine calculation by using fixed size array
// uses a 65 element lookup table and interpolation
// thanks to @dekutree for his work on optimizing this
__attribute__((weak)) float _sin(float a){
  // 16bit integer array for sine lookup. interpolation is used for better precision
  // 16 bit precision on sine value, 8 bit fractional value for interpolation, 6bit LUT size
  // resulting precision compared to stdlib sine is 0.00006480 (RMS difference in range -PI,PI for 3217 steps)
  static uint16_t sine_array[65] = {0,804,1608,2411,3212,4011,4808,5602,6393,7180,7962,8740,9512,10279,11039,11793,12540,13279,14010,14733,15447,16151,16846,17531,18205,18868,19520,20160,20788,21403,22006,22595,23170,23732,24279,24812,25330,25833,26320,26791,27246,27684,28106,28511,28899,29269,29622,29957,30274,30572,30853,31114,31357,31581,31786,31972,32138,32286,32413,32522,32610,32679,32729,32758,32768};
  int32_t t1, t2;
  unsigned int i = (unsigned int)(a * (64*4*256.0f/_2PI));
  int frac = i & 0xff;
  i = (i >> 8) & 0xff;
  if (i < 64) {
    t1 = (int32_t)sine_array[i]; t2 = (int32_t)sine_array[i+1];
  }
  else if(i < 128) {
    t1 = (int32_t)sine_array[128 - i]; t2 = (int32_t)sine_array[127 - i];
  }
  else if(i < 192) {
    t1 = -(int32_t)sine_array[-128 + i]; t2 = -(int32_t)sine_array[-127 + i];
  }
  else {
    t1 = -(int32_t)sine_array[256 - i]; t2 = -(int32_t)sine_array[255 - i];
  }
  return (1.0f/32768.0f) * (t1 + (((t2 - t1) * frac) >> 8));
}
 
// function approximating cosine calculation by using fixed size array
// ~55us (float array)
// ~56us (int array)
// precision +-0.005
// it has to receive an angle in between 0 and 2PI
__attribute__((weak)) float _cos(float a){
  float a_sin = a + _PI_2;
  a_sin = a_sin > _2PI ? a_sin - _2PI : a_sin;
  return _sin(a_sin);
}
 
 
__attribute__((weak)) void _sincos(float a, float* s, float* c){
  *s = _sin(a);
  *c = _cos(a);
}
 
// fast_atan2 based on https://math.stackexchange.com/a/1105038/81278
// Via Odrive project
// https://github.com/odriverobotics/ODrive/blob/master/Firmware/MotorControl/utils.cpp
// This function is MIT licenced, copyright Oskar Weigl/Odrive Robotics
// The origin for Odrive atan2 is public domain. Thanks to Odrive for making
// it easy to borrow.
__attribute__((weak)) float _atan2(float y, float x) {
    // a := min (|x|, |y|) / max (|x|, |y|)
    float abs_y = fabsf(y);
    float abs_x = fabsf(x);
    // inject FLT_MIN in denominator to avoid division by zero
    float a = min(abs_x, abs_y) / (max(abs_x, abs_y));
    // s := a * a
    float s = a * a;
    // r := ((-0.0464964749 * s + 0.15931422) * s - 0.327622764) * s * a + a
    float r =
        ((-0.0464964749f * s + 0.15931422f) * s - 0.327622764f) * s * a + a;
    // if |y| > |x| then r := 1.57079637 - r
    if (abs_y > abs_x) r = 1.57079637f - r;
    // if x < 0 then r := 3.14159274 - r
    if (x < 0.0f) r = 3.14159274f - r;
    // if y < 0 then r := -r
    if (y < 0.0f) r = -r;
 
    return r;
  }
 
 
// normalizing radian angle to [0,2PI]
__attribute__((weak)) float _normalizeAngle(float angle){
  float a = fmod(angle, _2PI);
  return a >= 0 ? a : (a + _2PI);
}
 
// Electrical angle calculation
float _electricalAngle(float shaft_angle, int pole_pairs) {
  return (shaft_angle * pole_pairs);
}
 
// square root approximation function using
// https://reprap.org/forum/read.php?147,219210
// https://en.wikipedia.org/wiki/Fast_inverse_square_root
__attribute__((weak)) float _sqrtApprox(float number) {//low in fat
  union {
    float    f;
    uint32_t i;
  } y = { .f = number };
  y.i = 0x5f375a86 - ( y.i >> 1 );
  return number * y.f;
}