xref: /lvgl-3.4.0/src/misc/lv_math.c

/**
 * @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(x >= max_in) return max_out;
    if(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
 **********************/