mirror of
https://github.com/qmk/qmk_firmware.git
synced 2024-12-24 02:19:54 +00:00
270b39b2eb
* Spirals, Pinwheels, and Documentation....Oh My! * Spiral effect band thickness adjustments * Fixing animation spin directions
285 lines
7.5 KiB
C
285 lines
7.5 KiB
C
#ifndef __INC_LIB8TION_TRIG_H
|
|
#define __INC_LIB8TION_TRIG_H
|
|
|
|
///@ingroup lib8tion
|
|
|
|
///@defgroup Trig Fast trig functions
|
|
/// Fast 8 and 16-bit approximations of sin(x) and cos(x).
|
|
/// Don't use these approximations for calculating the
|
|
/// trajectory of a rocket to Mars, but they're great
|
|
/// for art projects and LED displays.
|
|
///
|
|
/// On Arduino/AVR, the 16-bit approximation is more than
|
|
/// 10X faster than floating point sin(x) and cos(x), while
|
|
/// the 8-bit approximation is more than 20X faster.
|
|
///@{
|
|
|
|
#if defined(__AVR__)
|
|
#define sin16 sin16_avr
|
|
#else
|
|
#define sin16 sin16_C
|
|
#endif
|
|
|
|
/// Fast 16-bit approximation of sin(x). This approximation never varies more than
|
|
/// 0.69% from the floating point value you'd get by doing
|
|
///
|
|
/// float s = sin(x) * 32767.0;
|
|
///
|
|
/// @param theta input angle from 0-65535
|
|
/// @returns sin of theta, value between -32767 to 32767.
|
|
LIB8STATIC int16_t sin16_avr( uint16_t theta )
|
|
{
|
|
static const uint8_t data[] =
|
|
{ 0, 0, 49, 0, 6393%256, 6393/256, 48, 0,
|
|
12539%256, 12539/256, 44, 0, 18204%256, 18204/256, 38, 0,
|
|
23170%256, 23170/256, 31, 0, 27245%256, 27245/256, 23, 0,
|
|
30273%256, 30273/256, 14, 0, 32137%256, 32137/256, 4 /*,0*/ };
|
|
|
|
uint16_t offset = (theta & 0x3FFF);
|
|
|
|
// AVR doesn't have a multi-bit shift instruction,
|
|
// so if we say "offset >>= 3", gcc makes a tiny loop.
|
|
// Inserting empty volatile statements between each
|
|
// bit shift forces gcc to unroll the loop.
|
|
offset >>= 1; // 0..8191
|
|
asm volatile("");
|
|
offset >>= 1; // 0..4095
|
|
asm volatile("");
|
|
offset >>= 1; // 0..2047
|
|
|
|
if( theta & 0x4000 ) offset = 2047 - offset;
|
|
|
|
uint8_t sectionX4;
|
|
sectionX4 = offset / 256;
|
|
sectionX4 *= 4;
|
|
|
|
uint8_t m;
|
|
|
|
union {
|
|
uint16_t b;
|
|
struct {
|
|
uint8_t blo;
|
|
uint8_t bhi;
|
|
};
|
|
} u;
|
|
|
|
//in effect u.b = blo + (256 * bhi);
|
|
u.blo = data[ sectionX4 ];
|
|
u.bhi = data[ sectionX4 + 1];
|
|
m = data[ sectionX4 + 2];
|
|
|
|
uint8_t secoffset8 = (uint8_t)(offset) / 2;
|
|
|
|
uint16_t mx = m * secoffset8;
|
|
|
|
int16_t y = mx + u.b;
|
|
if( theta & 0x8000 ) y = -y;
|
|
|
|
return y;
|
|
}
|
|
|
|
/// Fast 16-bit approximation of sin(x). This approximation never varies more than
|
|
/// 0.69% from the floating point value you'd get by doing
|
|
///
|
|
/// float s = sin(x) * 32767.0;
|
|
///
|
|
/// @param theta input angle from 0-65535
|
|
/// @returns sin of theta, value between -32767 to 32767.
|
|
LIB8STATIC int16_t sin16_C( uint16_t theta )
|
|
{
|
|
static const uint16_t base[] =
|
|
{ 0, 6393, 12539, 18204, 23170, 27245, 30273, 32137 };
|
|
static const uint8_t slope[] =
|
|
{ 49, 48, 44, 38, 31, 23, 14, 4 };
|
|
|
|
uint16_t offset = (theta & 0x3FFF) >> 3; // 0..2047
|
|
if( theta & 0x4000 ) offset = 2047 - offset;
|
|
|
|
uint8_t section = offset / 256; // 0..7
|
|
uint16_t b = base[section];
|
|
uint8_t m = slope[section];
|
|
|
|
uint8_t secoffset8 = (uint8_t)(offset) / 2;
|
|
|
|
uint16_t mx = m * secoffset8;
|
|
int16_t y = mx + b;
|
|
|
|
if( theta & 0x8000 ) y = -y;
|
|
|
|
return y;
|
|
}
|
|
|
|
|
|
/// Fast 16-bit approximation of cos(x). This approximation never varies more than
|
|
/// 0.69% from the floating point value you'd get by doing
|
|
///
|
|
/// float s = cos(x) * 32767.0;
|
|
///
|
|
/// @param theta input angle from 0-65535
|
|
/// @returns sin of theta, value between -32767 to 32767.
|
|
LIB8STATIC int16_t cos16( uint16_t theta)
|
|
{
|
|
return sin16( theta + 16384);
|
|
}
|
|
|
|
///////////////////////////////////////////////////////////////////////
|
|
|
|
// sin8 & cos8
|
|
// Fast 8-bit approximations of sin(x) & cos(x).
|
|
// Input angle is an unsigned int from 0-255.
|
|
// Output is an unsigned int from 0 to 255.
|
|
//
|
|
// This approximation can vary to to 2%
|
|
// from the floating point value you'd get by doing
|
|
// float s = (sin( x ) * 128.0) + 128;
|
|
//
|
|
// Don't use this approximation for calculating the
|
|
// "real" trigonometric calculations, but it's great
|
|
// for art projects and LED displays.
|
|
//
|
|
// On Arduino/AVR, this approximation is more than
|
|
// 20X faster than floating point sin(x) and cos(x)
|
|
|
|
#if defined(__AVR__) && !defined(LIB8_ATTINY)
|
|
#define sin8 sin8_avr
|
|
#else
|
|
#define sin8 sin8_C
|
|
#endif
|
|
|
|
|
|
static const uint8_t b_m16_interleave[8] = { 0, 49, 49, 41, 90, 27, 117, 10 };
|
|
|
|
/// Fast 8-bit approximation of sin(x). This approximation never varies more than
|
|
/// 2% from the floating point value you'd get by doing
|
|
///
|
|
/// float s = (sin(x) * 128.0) + 128;
|
|
///
|
|
/// @param theta input angle from 0-255
|
|
/// @returns sin of theta, value between 0 and 255
|
|
LIB8STATIC uint8_t sin8_avr( uint8_t theta)
|
|
{
|
|
uint8_t offset = theta;
|
|
|
|
asm volatile(
|
|
"sbrc %[theta],6 \n\t"
|
|
"com %[offset] \n\t"
|
|
: [theta] "+r" (theta), [offset] "+r" (offset)
|
|
);
|
|
|
|
offset &= 0x3F; // 0..63
|
|
|
|
uint8_t secoffset = offset & 0x0F; // 0..15
|
|
if( theta & 0x40) secoffset++;
|
|
|
|
uint8_t m16; uint8_t b;
|
|
|
|
uint8_t section = offset >> 4; // 0..3
|
|
uint8_t s2 = section * 2;
|
|
|
|
const uint8_t* p = b_m16_interleave;
|
|
p += s2;
|
|
b = *p;
|
|
p++;
|
|
m16 = *p;
|
|
|
|
uint8_t mx;
|
|
uint8_t xr1;
|
|
asm volatile(
|
|
"mul %[m16],%[secoffset] \n\t"
|
|
"mov %[mx],r0 \n\t"
|
|
"mov %[xr1],r1 \n\t"
|
|
"eor r1, r1 \n\t"
|
|
"swap %[mx] \n\t"
|
|
"andi %[mx],0x0F \n\t"
|
|
"swap %[xr1] \n\t"
|
|
"andi %[xr1], 0xF0 \n\t"
|
|
"or %[mx], %[xr1] \n\t"
|
|
: [mx] "=d" (mx), [xr1] "=d" (xr1)
|
|
: [m16] "d" (m16), [secoffset] "d" (secoffset)
|
|
);
|
|
|
|
int8_t y = mx + b;
|
|
if( theta & 0x80 ) y = -y;
|
|
|
|
y += 128;
|
|
|
|
return y;
|
|
}
|
|
|
|
|
|
/// Fast 8-bit approximation of sin(x). This approximation never varies more than
|
|
/// 2% from the floating point value you'd get by doing
|
|
///
|
|
/// float s = (sin(x) * 128.0) + 128;
|
|
///
|
|
/// @param theta input angle from 0-255
|
|
/// @returns sin of theta, value between 0 and 255
|
|
LIB8STATIC uint8_t sin8_C( uint8_t theta)
|
|
{
|
|
uint8_t offset = theta;
|
|
if( theta & 0x40 ) {
|
|
offset = (uint8_t)255 - offset;
|
|
}
|
|
offset &= 0x3F; // 0..63
|
|
|
|
uint8_t secoffset = offset & 0x0F; // 0..15
|
|
if( theta & 0x40) secoffset++;
|
|
|
|
uint8_t section = offset >> 4; // 0..3
|
|
uint8_t s2 = section * 2;
|
|
const uint8_t* p = b_m16_interleave;
|
|
p += s2;
|
|
uint8_t b = *p;
|
|
p++;
|
|
uint8_t m16 = *p;
|
|
|
|
uint8_t mx = (m16 * secoffset) >> 4;
|
|
|
|
int8_t y = mx + b;
|
|
if( theta & 0x80 ) y = -y;
|
|
|
|
y += 128;
|
|
|
|
return y;
|
|
}
|
|
|
|
/// Fast 8-bit approximation of cos(x). This approximation never varies more than
|
|
/// 2% from the floating point value you'd get by doing
|
|
///
|
|
/// float s = (cos(x) * 128.0) + 128;
|
|
///
|
|
/// @param theta input angle from 0-255
|
|
/// @returns sin of theta, value between 0 and 255
|
|
LIB8STATIC uint8_t cos8( uint8_t theta)
|
|
{
|
|
return sin8( theta + 64);
|
|
}
|
|
|
|
/// Fast 16-bit approximation of atan2(x).
|
|
/// @returns atan2, value between 0 and 255
|
|
LIB8STATIC uint8_t atan2_8(int16_t dy, int16_t dx)
|
|
{
|
|
if (dy == 0)
|
|
{
|
|
if (dx >= 0)
|
|
return 0;
|
|
else
|
|
return 128;
|
|
}
|
|
|
|
int16_t abs_y = dy > 0 ? dy : -dy;
|
|
int8_t a;
|
|
|
|
if (dx >= 0)
|
|
a = 32 - (32 * (dx - abs_y) / (dx + abs_y));
|
|
else
|
|
a = 96 - (32 * (dx + abs_y) / (abs_y - dx));
|
|
|
|
if (dy < 0)
|
|
return -a; // negate if in quad III or IV
|
|
return a;
|
|
}
|
|
|
|
///@}
|
|
#endif
|