summaryrefslogtreecommitdiff
path: root/lib/lib8tion/trig8.h
diff options
context:
space:
mode:
Diffstat (limited to 'lib/lib8tion/trig8.h')
-rw-r--r--lib/lib8tion/trig8.h284
1 files changed, 0 insertions, 284 deletions
diff --git a/lib/lib8tion/trig8.h b/lib/lib8tion/trig8.h
deleted file mode 100644
index cfba6373fb..0000000000
--- a/lib/lib8tion/trig8.h
+++ /dev/null
@@ -1,284 +0,0 @@
-#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
generated by cgit v1.2.3 (git 2.25.1) at 2025-04-27 07:27:04 +0000