text: /**
   * @file lv_math.c
   *
   */
  
  /*********************
   *      INCLUDES
   *********************/
  #include "lv_math.h"
  #include <stdbool.h>
  #include <stdlib.h>
  #include <string.h>
  
  /*********************
   *      DEFINES
   *********************/
  
  /**********************
   *      TYPEDEFS
   **********************/
  
  /**********************
   *  STATIC PROTOTYPES
   **********************/
  
  /**********************
   *  STATIC VARIABLES
   **********************/
  static const int16_t sin0_90_table[] = {
      0,     572,   1144,  1715,  2286,  2856,  3425,  3993,  4560,  5126,  5690,  6252,  6813,  7371,  7927,  8481,
      9032,  9580,  10126, 10668, 11207, 11743, 12275, 12803, 13328, 13848, 14364, 14876, 15383, 15886, 16383, 16876,
      17364, 17846, 18323, 18794, 19260, 19720, 20173, 20621, 21062, 21497, 21925, 22347, 22762, 23170, 23571, 23964,
      24351, 24730, 25101, 25465, 25821, 26169, 26509, 26841, 27165, 27481, 27788, 28087, 28377, 28659, 28932, 29196,
      29451, 29697, 29934, 30162, 30381, 30591, 30791, 30982, 31163, 31335, 31498, 31650, 31794, 31927, 32051, 32165,
      32269, 32364, 32448, 32523, 32587, 32642, 32687, 32722, 32747, 32762, 32767
  };
  
  
  
  /**********************
   *      MACROS
   **********************/
  
  /**********************
   *   GLOBAL FUNCTIONS
   **********************/
  
  /**
   * Return with sinus of an angle
   * @param angle
   * @return sinus of 'angle'. sin(-90) = -32767, sin(90) = 32767
   */
  LV_ATTRIBUTE_FAST_MEM int16_t _lv_trigo_sin(int16_t angle)
  {
      int16_t ret = 0;
      angle       = angle % 360;
  
      if(angle < 0) angle = 360 + angle;
  
      if(angle < 90) {
          ret = sin0_90_table[angle];
      }
      else if(angle >= 90 && angle < 180) {
          angle = 180 - angle;
          ret   = sin0_90_table[angle];
      }
      else if(angle >= 180 && angle < 270) {
          angle = angle - 180;
          ret   = -sin0_90_table[angle];
      }
      else {   /*angle >=270*/
          angle = 360 - angle;
          ret   = -sin0_90_table[angle];
      }
  
      return ret;
  }
  
  /**
   * Calculate a value of a Cubic Bezier function.
   * @param t time in range of [0..LV_BEZIER_VAL_MAX]
   * @param u0 start values in range of [0..LV_BEZIER_VAL_MAX]
   * @param u1 control value 1 values in range of [0..LV_BEZIER_VAL_MAX]
   * @param u2 control value 2 in range of [0..LV_BEZIER_VAL_MAX]
   * @param u3 end values in range of [0..LV_BEZIER_VAL_MAX]
   * @return the value calculated from the given parameters in range of [0..LV_BEZIER_VAL_MAX]
   */
  int32_t _lv_bezier3(uint32_t t, int32_t u0, int32_t u1, int32_t u2, int32_t u3)
  {
      uint32_t t_rem  = 1024 - t;
      uint32_t t_rem2 = (t_rem * t_rem) >> 10;
      uint32_t t_rem3 = (t_rem2 * t_rem) >> 10;
      uint32_t t2     = (t * t) >> 10;
      uint32_t t3     = (t2 * t) >> 10;
  
      uint32_t v1 = ((uint32_t)t_rem3 * u0) >> 10;
      uint32_t v2 = ((uint32_t)3 * t_rem2 * t * u1) >> 20;
      uint32_t v3 = ((uint32_t)3 * t_rem * t2 * u2) >> 20;
      uint32_t v4 = ((uint32_t)t3 * u3) >> 10;
  
      return v1 + v2 + v3 + v4;
  }
  
  /**
   * Get the square root of a number
   * @param x integer which square root should be calculatoed
   * @param q store the result here. q->i: integer part, q->f: fractional part in 1/256 unit
   * @param mask: optional to skip some iterations if the magnitude of the root is known.
   * Set to 0x8000 by default.
   * If root < 16: mask = 0x80
   * If root < 256: mask = 0x800
   * Else: mask = 0x8000
   */
  LV_ATTRIBUTE_FAST_MEM void _lv_sqrt(uint32_t x, lv_sqrt_res_t * q, uint32_t mask)
  {
      x = x << 8; /*To get 4 bit precision. (sqrt(256) = 16 = 4 bit)*/
  
      uint32_t root = 0;
      uint32_t trial;
      // http://ww1.microchip.com/...en/AppNotes/91040a.pdf
      do {
          trial = root + mask;
          if((uint32_t)trial * trial <= x) root = trial;
          mask = mask >> 1;
      } while(mask);
  
      q->i = (uint32_t) root >> 4;
      q->f = (uint32_t)(root & 0xf) << 4;
  }
  
  
  /**
   * Calculate the atan2 of a vector.
   * @param x
   * @param y
   * @return the angle in degree calculated from the given parameters in range of [0..360]
   */
  uint16_t _lv_atan2(int x, int y)
  {
      // Fast XY vector to integer degree algorithm - Jan 2011 www.RomanBlack.com
      // Converts any XY values including 0 to a degree value that should be
      // within +/- 1 degree of the accurate value without needing
      // large slow trig functions like ArcTan() or ArcCos().
      // NOTE! at least one of the X or Y values must be non-zero!
      // This is the full version, for all 4 quadrants and will generate
      // the angle in integer degrees from 0-360.
      // Any values of X and Y are usable including negative values provided
      // they are between -1456 and 1456 so the 16bit multiply does not overflow.
  
      unsigned char negflag;
      unsigned char tempdegree;
      unsigned char comp;
      unsigned int degree;     // this will hold the result
      //signed int x;            // these hold the XY vector at the start
      //signed int y;            // (and they will be destroyed)
      unsigned int ux;
      unsigned int uy;
  
      // Save the sign flags then remove signs and get XY as unsigned ints
      negflag = 0;
      if(x < 0) {
          negflag += 0x01;    // x flag bit
          x = (0 - x);        // is now +
      }
      ux = x;                // copy to unsigned var before multiply
      if(y < 0) {
          negflag += 0x02;    // y flag bit
          y = (0 - y);        // is now +
      }
      uy = y;                // copy to unsigned var before multiply
  
      // 1. Calc the scaled "degrees"
      if(ux > uy) {
          degree = (uy * 45) / ux;   // degree result will be 0-45 range
          negflag += 0x10;    // octant flag bit
      }
      else {
          degree = (ux * 45) / uy;   // degree result will be 0-45 range
      }
  
      // 2. Compensate for the 4 degree error curve
      comp = 0;
      tempdegree = degree;    // use an unsigned char for speed!
      if(tempdegree > 22) {    // if top half of range
          if(tempdegree <= 44) comp++;
          if(tempdegree <= 41) comp++;
          if(tempdegree <= 37) comp++;
          if(tempdegree <= 32) comp++;  // max is 4 degrees compensated
      }
      else {   // else is lower half of range
          if(tempdegree >= 2) comp++;
          if(tempdegree >= 6) comp++;
          if(tempdegree >= 10) comp++;
          if(tempdegree >= 15) comp++;  // max is 4 degrees compensated
      }
      degree += comp;   // degree is now accurate to +/- 1 degree!
  
      // Invert degree if it was X>Y octant, makes 0-45 into 90-45
      if(negflag & 0x10) degree = (90 - degree);
  
      // 3. Degree is now 0-90 range for this quadrant,
      // need to invert it for whichever quadrant it was in
      if(negflag & 0x02) { // if -Y
          if(negflag & 0x01)   // if -Y -X
              degree = (180 + degree);
          else        // else is -Y +X
              degree = (180 - degree);
      }
      else {   // else is +Y
          if(negflag & 0x01)   // if +Y -X
              degree = (360 - degree);
      }
      return degree;
  }
  
  /**
   * Calculate the integer exponents.
   * @param base
   * @param power
   * @return base raised to the power exponent
   */
  int64_t _lv_pow(int64_t base, int8_t exp)
  {
      int64_t result = 1;
      while(exp) {
          if(exp & 1)
              result *= base;
          exp >>= 1;
          base *= base;
      }
  
      return result;
  }
  
  /**********************
   *   STATIC FUNCTIONS
   **********************/
  