/**
  * @file lv_math.c
  *
  */
 
 /*********************
  *      INCLUDES
  *********************/
 #include "lv_math.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]
  */
 uint32_t lv_bezier3(uint32_t t, uint32_t u0, uint32_t u1, uint32_t u2, uint32_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 = (t_rem3 * u0) >> 10;
     uint32_t v2 = (3 * t_rem2 * t * u1) >> 20;
     uint32_t v3 = (3 * t_rem * t2 * u2) >> 20;
     uint32_t v4 = (t3 * u3) >> 10;
 
     return v1 + v2 + v3 + v4;
 }
 
 /**
  * Get the square root of a number
  * @param x integer which square root should be calculated
  * @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(trial * trial <= x) root = trial;
         mask = mask >> 1;
     } while(mask);
 
     q->i = root >> 4;
     q->f = (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
     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;
 }
 
 /**
  * Get the mapped of a number given an input and output range
  * @param x integer which mapped value should be calculated
  * @param min_in min input range
  * @param max_in max input range
  * @param min_out max output range
  * @param max_out max output range
  * @return the mapped number
  */
 int32_t lv_map(int32_t x, int32_t min_in, int32_t max_in, int32_t min_out, int32_t max_out)
 {
     if(max_in >= min_in && x >= max_in) return max_out;
     if(max_in >= min_in && x <= min_in) return min_out;
 
     if(max_in <= min_in && x <= max_in) return max_out;
     if(max_in <= min_in && x >= min_in) return min_out;
 
     /**
      * The equation should be:
      *   ((x - min_in) * delta_out) / delta in) + min_out
      * To avoid rounding error reorder the operations:
      *   (x - min_in) * (delta_out / delta_min) + min_out
      */
 
     int32_t delta_in = max_in - min_in;
     int32_t delta_out = max_out - min_out;
 
     return ((x - min_in) * delta_out) / delta_in + min_out;
 }
 
 uint32_t lv_rand(uint32_t min, uint32_t max)
 {
     static uint32_t a = 0x1234ABCD; /*Seed*/
 
     /*Algorithm "xor" from p. 4 of Marsaglia, "Xorshift RNGs"*/
     uint32_t x = a;
     x ^= x << 13;
     x ^= x >> 17;
     x ^= x << 5;
     a = x;
 
     return (a % (max - min + 1)) + min;
 }
 
 /**********************
  *   STATIC FUNCTIONS
  **********************/

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