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lvgl_cpp/lvgl/misc/lv_math.c

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/**
* @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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