269 lines
6.9 KiB
C
269 lines
6.9 KiB
C
#ifndef __INC_LIB8TION_TRIG_H
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#define __INC_LIB8TION_TRIG_H
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/// @file trig8.h
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/// Fast, efficient 8-bit trigonometry functions specifically
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/// designed for high-performance LED programming.
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/// @ingroup lib8tion
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/// @{
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/// @defgroup Trig Fast Trigonometry Functions
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/// Fast 8-bit and 16-bit approximations of sin(x) and cos(x).
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///
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/// Don't use these approximations for calculating the
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/// trajectory of a rocket to Mars, but they're great
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/// for art projects and LED displays.
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///
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/// On Arduino/AVR, the 16-bit approximation is more than
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/// 10X faster than floating point sin(x) and cos(x), while
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/// the 8-bit approximation is more than 20X faster.
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/// @{
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#if defined(__AVR__)
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/// Platform-independent alias of the fast sin implementation
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#define sin16 sin16_avr
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/// Fast 16-bit approximation of sin(x). This approximation never varies more than
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/// 0.69% from the floating point value you'd get by doing
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/// @code{.cpp}
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/// float s = sin(x) * 32767.0;
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/// @endcode
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///
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/// @param theta input angle from 0-65535
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/// @returns sin of theta, value between -32767 to 32767.
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LIB8STATIC int16_t sin16_avr( uint16_t theta )
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{
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static const uint8_t data[] =
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{ 0, 0, 49, 0, 6393%256, 6393/256, 48, 0,
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12539%256, 12539/256, 44, 0, 18204%256, 18204/256, 38, 0,
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23170%256, 23170/256, 31, 0, 27245%256, 27245/256, 23, 0,
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30273%256, 30273/256, 14, 0, 32137%256, 32137/256, 4 /*,0*/ };
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uint16_t offset = (theta & 0x3FFF);
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// AVR doesn't have a multi-bit shift instruction,
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// so if we say "offset >>= 3", gcc makes a tiny loop.
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// Inserting empty volatile statements between each
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// bit shift forces gcc to unroll the loop.
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offset >>= 1; // 0..8191
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asm volatile("");
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offset >>= 1; // 0..4095
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asm volatile("");
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offset >>= 1; // 0..2047
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if( theta & 0x4000 ) offset = 2047 - offset;
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uint8_t sectionX4;
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sectionX4 = offset / 256;
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sectionX4 *= 4;
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uint8_t m;
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union {
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uint16_t b;
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struct {
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uint8_t blo;
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uint8_t bhi;
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};
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} u;
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//in effect u.b = blo + (256 * bhi);
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u.blo = data[ sectionX4 ];
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u.bhi = data[ sectionX4 + 1];
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m = data[ sectionX4 + 2];
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uint8_t secoffset8 = (uint8_t)(offset) / 2;
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uint16_t mx = m * secoffset8;
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int16_t y = mx + u.b;
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if( theta & 0x8000 ) y = -y;
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return y;
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}
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#else
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/// Platform-independent alias of the fast sin implementation
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#define sin16 sin16_C
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/// Fast 16-bit approximation of sin(x). This approximation never varies more than
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/// 0.69% from the floating point value you'd get by doing
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/// @code{.cpp}
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/// float s = sin(x) * 32767.0;
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/// @endcode
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///
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/// @param theta input angle from 0-65535
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/// @returns sin of theta, value between -32767 to 32767.
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LIB8STATIC int16_t sin16_C( uint16_t theta )
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{
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static const uint16_t base[] =
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{ 0, 6393, 12539, 18204, 23170, 27245, 30273, 32137 };
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static const uint8_t slope[] =
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{ 49, 48, 44, 38, 31, 23, 14, 4 };
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uint16_t offset = (theta & 0x3FFF) >> 3; // 0..2047
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if( theta & 0x4000 ) offset = 2047 - offset;
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uint8_t section = offset / 256; // 0..7
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uint16_t b = base[section];
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uint8_t m = slope[section];
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uint8_t secoffset8 = (uint8_t)(offset) / 2;
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uint16_t mx = m * secoffset8;
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int16_t y = mx + b;
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if( theta & 0x8000 ) y = -y;
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return y;
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}
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#endif
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/// Fast 16-bit approximation of cos(x). This approximation never varies more than
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/// 0.69% from the floating point value you'd get by doing
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/// @code{.cpp}
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/// float s = cos(x) * 32767.0;
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/// @endcode
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///
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/// @param theta input angle from 0-65535
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/// @returns cos of theta, value between -32767 to 32767.
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LIB8STATIC int16_t cos16( uint16_t theta)
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{
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return sin16( theta + 16384);
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}
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///////////////////////////////////////////////////////////////////////
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// sin8() and cos8()
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// Fast 8-bit approximations of sin(x) & cos(x).
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/// Pre-calculated lookup table used in sin8() and cos8() functions
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const uint8_t b_m16_interleave[] = { 0, 49, 49, 41, 90, 27, 117, 10 };
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#if defined(__AVR__) && !defined(LIB8_ATTINY)
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/// Platform-independent alias of the fast sin implementation
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#define sin8 sin8_avr
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/// Fast 8-bit approximation of sin(x). This approximation never varies more than
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/// 2% from the floating point value you'd get by doing
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/// @code{.cpp}
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/// float s = (sin(x) * 128.0) + 128;
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/// @endcode
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///
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/// @param theta input angle from 0-255
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/// @returns sin of theta, value between 0 and 255
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LIB8STATIC uint8_t sin8_avr( uint8_t theta)
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{
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uint8_t offset = theta;
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asm volatile(
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"sbrc %[theta],6 \n\t"
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"com %[offset] \n\t"
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: [theta] "+r" (theta), [offset] "+r" (offset)
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);
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offset &= 0x3F; // 0..63
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uint8_t secoffset = offset & 0x0F; // 0..15
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if( theta & 0x40) ++secoffset;
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uint8_t m16; uint8_t b;
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uint8_t section = offset >> 4; // 0..3
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uint8_t s2 = section * 2;
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const uint8_t* p = b_m16_interleave;
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p += s2;
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b = *p;
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++p;
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m16 = *p;
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uint8_t mx;
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uint8_t xr1;
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asm volatile(
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"mul %[m16],%[secoffset] \n\t"
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"mov %[mx],r0 \n\t"
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"mov %[xr1],r1 \n\t"
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"eor r1, r1 \n\t"
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"swap %[mx] \n\t"
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"andi %[mx],0x0F \n\t"
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"swap %[xr1] \n\t"
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"andi %[xr1], 0xF0 \n\t"
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"or %[mx], %[xr1] \n\t"
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: [mx] "=d" (mx), [xr1] "=d" (xr1)
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: [m16] "d" (m16), [secoffset] "d" (secoffset)
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);
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int8_t y = mx + b;
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if( theta & 0x80 ) y = -y;
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y += 128;
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return y;
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}
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#else
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/// Platform-independent alias of the fast sin implementation
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#define sin8 sin8_C
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/// Fast 8-bit approximation of sin(x). This approximation never varies more than
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/// 2% from the floating point value you'd get by doing
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/// @code{.cpp}
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/// float s = (sin(x) * 128.0) + 128;
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/// @endcode
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///
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/// @param theta input angle from 0-255
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/// @returns sin of theta, value between 0 and 255
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LIB8STATIC uint8_t sin8_C( uint8_t theta)
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{
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uint8_t offset = theta;
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if( theta & 0x40 ) {
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offset = (uint8_t)255 - offset;
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}
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offset &= 0x3F; // 0..63
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uint8_t secoffset = offset & 0x0F; // 0..15
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if( theta & 0x40) ++secoffset;
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uint8_t section = offset >> 4; // 0..3
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uint8_t s2 = section * 2;
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const uint8_t* p = b_m16_interleave;
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p += s2;
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uint8_t b = *p;
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++p;
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uint8_t m16 = *p;
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uint8_t mx = (m16 * secoffset) >> 4;
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int8_t y = mx + b;
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if( theta & 0x80 ) y = -y;
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y += 128;
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return y;
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}
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#endif
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/// Fast 8-bit approximation of cos(x). This approximation never varies more than
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/// 2% from the floating point value you'd get by doing
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/// @code{.cpp}
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/// float s = (cos(x) * 128.0) + 128;
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/// @endcode
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///
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/// @param theta input angle from 0-255
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/// @returns cos of theta, value between 0 and 255
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LIB8STATIC uint8_t cos8( uint8_t theta)
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{
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return sin8( theta + 64);
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}
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/// @} Trig
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/// @} lib8tion
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#endif
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