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Fabian Schlenz
2020-07-17 18:55:06 +02:00
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#ifndef __INC_LIB8TION_MATH_H
#define __INC_LIB8TION_MATH_H
#include "scale8.h"
///@ingroup lib8tion
///@defgroup Math Basic math operations
/// Fast, efficient 8-bit math functions specifically
/// designed for high-performance LED programming.
///
/// Because of the AVR(Arduino) and ARM assembly language
/// implementations provided, using these functions often
/// results in smaller and faster code than the equivalent
/// program using plain "C" arithmetic and logic.
///@{
/// add one byte to another, saturating at 0xFF
/// @param i - first byte to add
/// @param j - second byte to add
/// @returns the sum of i & j, capped at 0xFF
LIB8STATIC_ALWAYS_INLINE uint8_t qadd8( uint8_t i, uint8_t j)
{
#if QADD8_C == 1
unsigned int t = i + j;
if( t > 255) t = 255;
return t;
#elif QADD8_AVRASM == 1
asm volatile(
/* First, add j to i, conditioning the C flag */
"add %0, %1 \n\t"
/* Now test the C flag.
If C is clear, we branch around a load of 0xFF into i.
If C is set, we go ahead and load 0xFF into i.
*/
"brcc L_%= \n\t"
"ldi %0, 0xFF \n\t"
"L_%=: "
: "+a" (i)
: "a" (j) );
return i;
#elif QADD8_ARM_DSP_ASM == 1
asm volatile( "uqadd8 %0, %0, %1" : "+r" (i) : "r" (j));
return i;
#else
#error "No implementation for qadd8 available."
#endif
}
/// Add one byte to another, saturating at 0x7F
/// @param i - first byte to add
/// @param j - second byte to add
/// @returns the sum of i & j, capped at 0xFF
LIB8STATIC_ALWAYS_INLINE int8_t qadd7( int8_t i, int8_t j)
{
#if QADD7_C == 1
int16_t t = i + j;
if( t > 127) t = 127;
return t;
#elif QADD7_AVRASM == 1
asm volatile(
/* First, add j to i, conditioning the V flag */
"add %0, %1 \n\t"
/* Now test the V flag.
If V is clear, we branch around a load of 0x7F into i.
If V is set, we go ahead and load 0x7F into i.
*/
"brvc L_%= \n\t"
"ldi %0, 0x7F \n\t"
"L_%=: "
: "+a" (i)
: "a" (j) );
return i;
#elif QADD7_ARM_DSP_ASM == 1
asm volatile( "qadd8 %0, %0, %1" : "+r" (i) : "r" (j));
return i;
#else
#error "No implementation for qadd7 available."
#endif
}
/// subtract one byte from another, saturating at 0x00
/// @returns i - j with a floor of 0
LIB8STATIC_ALWAYS_INLINE uint8_t qsub8( uint8_t i, uint8_t j)
{
#if QSUB8_C == 1
int t = i - j;
if( t < 0) t = 0;
return t;
#elif QSUB8_AVRASM == 1
asm volatile(
/* First, subtract j from i, conditioning the C flag */
"sub %0, %1 \n\t"
/* Now test the C flag.
If C is clear, we branch around a load of 0x00 into i.
If C is set, we go ahead and load 0x00 into i.
*/
"brcc L_%= \n\t"
"ldi %0, 0x00 \n\t"
"L_%=: "
: "+a" (i)
: "a" (j) );
return i;
#else
#error "No implementation for qsub8 available."
#endif
}
/// add one byte to another, with one byte result
LIB8STATIC_ALWAYS_INLINE uint8_t add8( uint8_t i, uint8_t j)
{
#if ADD8_C == 1
int t = i + j;
return t;
#elif ADD8_AVRASM == 1
// Add j to i, period.
asm volatile( "add %0, %1" : "+a" (i) : "a" (j));
return i;
#else
#error "No implementation for add8 available."
#endif
}
/// add one byte to another, with one byte result
LIB8STATIC_ALWAYS_INLINE uint16_t add8to16( uint8_t i, uint16_t j)
{
#if ADD8_C == 1
uint16_t t = i + j;
return t;
#elif ADD8_AVRASM == 1
// Add i(one byte) to j(two bytes)
asm volatile( "add %A[j], %[i] \n\t"
"adc %B[j], __zero_reg__ \n\t"
: [j] "+a" (j)
: [i] "a" (i)
);
return i;
#else
#error "No implementation for add8to16 available."
#endif
}
/// subtract one byte from another, 8-bit result
LIB8STATIC_ALWAYS_INLINE uint8_t sub8( uint8_t i, uint8_t j)
{
#if SUB8_C == 1
int t = i - j;
return t;
#elif SUB8_AVRASM == 1
// Subtract j from i, period.
asm volatile( "sub %0, %1" : "+a" (i) : "a" (j));
return i;
#else
#error "No implementation for sub8 available."
#endif
}
/// Calculate an integer average of two unsigned
/// 8-bit integer values (uint8_t).
/// Fractional results are rounded down, e.g. avg8(20,41) = 30
LIB8STATIC_ALWAYS_INLINE uint8_t avg8( uint8_t i, uint8_t j)
{
#if AVG8_C == 1
return (i + j) >> 1;
#elif AVG8_AVRASM == 1
asm volatile(
/* First, add j to i, 9th bit overflows into C flag */
"add %0, %1 \n\t"
/* Divide by two, moving C flag into high 8th bit */
"ror %0 \n\t"
: "+a" (i)
: "a" (j) );
return i;
#else
#error "No implementation for avg8 available."
#endif
}
/// Calculate an integer average of two unsigned
/// 16-bit integer values (uint16_t).
/// Fractional results are rounded down, e.g. avg16(20,41) = 30
LIB8STATIC_ALWAYS_INLINE uint16_t avg16( uint16_t i, uint16_t j)
{
#if AVG16_C == 1
return (uint32_t)((uint32_t)(i) + (uint32_t)(j)) >> 1;
#elif AVG16_AVRASM == 1
asm volatile(
/* First, add jLo (heh) to iLo, 9th bit overflows into C flag */
"add %A[i], %A[j] \n\t"
/* Now, add C + jHi to iHi, 17th bit overflows into C flag */
"adc %B[i], %B[j] \n\t"
/* Divide iHi by two, moving C flag into high 16th bit, old 9th bit now in C */
"ror %B[i] \n\t"
/* Divide iLo by two, moving C flag into high 8th bit */
"ror %A[i] \n\t"
: [i] "+a" (i)
: [j] "a" (j) );
return i;
#else
#error "No implementation for avg16 available."
#endif
}
/// Calculate an integer average of two signed 7-bit
/// integers (int8_t)
/// If the first argument is even, result is rounded down.
/// If the first argument is odd, result is result up.
LIB8STATIC_ALWAYS_INLINE int8_t avg7( int8_t i, int8_t j)
{
#if AVG7_C == 1
return ((i + j) >> 1) + (i & 0x1);
#elif AVG7_AVRASM == 1
asm volatile(
"asr %1 \n\t"
"asr %0 \n\t"
"adc %0, %1 \n\t"
: "+a" (i)
: "a" (j) );
return i;
#else
#error "No implementation for avg7 available."
#endif
}
/// Calculate an integer average of two signed 15-bit
/// integers (int16_t)
/// If the first argument is even, result is rounded down.
/// If the first argument is odd, result is result up.
LIB8STATIC_ALWAYS_INLINE int16_t avg15( int16_t i, int16_t j)
{
#if AVG15_C == 1
return ((int32_t)((int32_t)(i) + (int32_t)(j)) >> 1) + (i & 0x1);
#elif AVG15_AVRASM == 1
asm volatile(
/* first divide j by 2, throwing away lowest bit */
"asr %B[j] \n\t"
"ror %A[j] \n\t"
/* now divide i by 2, with lowest bit going into C */
"asr %B[i] \n\t"
"ror %A[i] \n\t"
/* add j + C to i */
"adc %A[i], %A[j] \n\t"
"adc %B[i], %B[j] \n\t"
: [i] "+a" (i)
: [j] "a" (j) );
return i;
#else
#error "No implementation for avg15 available."
#endif
}
/// Calculate the remainder of one unsigned 8-bit
/// value divided by anoter, aka A % M.
/// Implemented by repeated subtraction, which is
/// very compact, and very fast if A is 'probably'
/// less than M. If A is a large multiple of M,
/// the loop has to execute multiple times. However,
/// even in that case, the loop is only two
/// instructions long on AVR, i.e., quick.
LIB8STATIC_ALWAYS_INLINE uint8_t mod8( uint8_t a, uint8_t m)
{
#if defined(__AVR__)
asm volatile (
"L_%=: sub %[a],%[m] \n\t"
" brcc L_%= \n\t"
" add %[a],%[m] \n\t"
: [a] "+r" (a)
: [m] "r" (m)
);
#else
while( a >= m) a -= m;
#endif
return a;
}
/// Add two numbers, and calculate the modulo
/// of the sum and a third number, M.
/// In other words, it returns (A+B) % M.
/// It is designed as a compact mechanism for
/// incrementing a 'mode' switch and wrapping
/// around back to 'mode 0' when the switch
/// goes past the end of the available range.
/// e.g. if you have seven modes, this switches
/// to the next one and wraps around if needed:
/// mode = addmod8( mode, 1, 7);
///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance.
LIB8STATIC uint8_t addmod8( uint8_t a, uint8_t b, uint8_t m)
{
#if defined(__AVR__)
asm volatile (
" add %[a],%[b] \n\t"
"L_%=: sub %[a],%[m] \n\t"
" brcc L_%= \n\t"
" add %[a],%[m] \n\t"
: [a] "+r" (a)
: [b] "r" (b), [m] "r" (m)
);
#else
a += b;
while( a >= m) a -= m;
#endif
return a;
}
/// Subtract two numbers, and calculate the modulo
/// of the difference and a third number, M.
/// In other words, it returns (A-B) % M.
/// It is designed as a compact mechanism for
/// incrementing a 'mode' switch and wrapping
/// around back to 'mode 0' when the switch
/// goes past the end of the available range.
/// e.g. if you have seven modes, this switches
/// to the next one and wraps around if needed:
/// mode = addmod8( mode, 1, 7);
///LIB8STATIC_ALWAYS_INLINESee 'mod8' for notes on performance.
LIB8STATIC uint8_t submod8( uint8_t a, uint8_t b, uint8_t m)
{
#if defined(__AVR__)
asm volatile (
" sub %[a],%[b] \n\t"
"L_%=: sub %[a],%[m] \n\t"
" brcc L_%= \n\t"
" add %[a],%[m] \n\t"
: [a] "+r" (a)
: [b] "r" (b), [m] "r" (m)
);
#else
a -= b;
while( a >= m) a -= m;
#endif
return a;
}
/// 8x8 bit multiplication, with 8 bit result
LIB8STATIC_ALWAYS_INLINE uint8_t mul8( uint8_t i, uint8_t j)
{
#if MUL8_C == 1
return ((int)i * (int)(j) ) & 0xFF;
#elif MUL8_AVRASM == 1
asm volatile(
/* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */
"mul %0, %1 \n\t"
/* Extract the LOW 8-bits (r0) */
"mov %0, r0 \n\t"
/* Restore r1 to "0"; it's expected to always be that */
"clr __zero_reg__ \n\t"
: "+a" (i)
: "a" (j)
: "r0", "r1");
return i;
#else
#error "No implementation for mul8 available."
#endif
}
/// saturating 8x8 bit multiplication, with 8 bit result
/// @returns the product of i * j, capping at 0xFF
LIB8STATIC_ALWAYS_INLINE uint8_t qmul8( uint8_t i, uint8_t j)
{
#if QMUL8_C == 1
int p = ((int)i * (int)(j) );
if( p > 255) p = 255;
return p;
#elif QMUL8_AVRASM == 1
asm volatile(
/* Multiply 8-bit i * 8-bit j, giving 16-bit r1,r0 */
" mul %0, %1 \n\t"
/* If high byte of result is zero, all is well. */
" tst r1 \n\t"
" breq Lnospill_%= \n\t"
/* If high byte of result > 0, saturate low byte to 0xFF */
" ldi %0,0xFF \n\t"
" rjmp Ldone_%= \n\t"
"Lnospill_%=: \n\t"
/* Extract the LOW 8-bits (r0) */
" mov %0, r0 \n\t"
"Ldone_%=: \n\t"
/* Restore r1 to "0"; it's expected to always be that */
" clr __zero_reg__ \n\t"
: "+a" (i)
: "a" (j)
: "r0", "r1");
return i;
#else
#error "No implementation for qmul8 available."
#endif
}
/// take abs() of a signed 8-bit uint8_t
LIB8STATIC_ALWAYS_INLINE int8_t abs8( int8_t i)
{
#if ABS8_C == 1
if( i < 0) i = -i;
return i;
#elif ABS8_AVRASM == 1
asm volatile(
/* First, check the high bit, and prepare to skip if it's clear */
"sbrc %0, 7 \n"
/* Negate the value */
"neg %0 \n"
: "+r" (i) : "r" (i) );
return i;
#else
#error "No implementation for abs8 available."
#endif
}
/// square root for 16-bit integers
/// About three times faster and five times smaller
/// than Arduino's general sqrt on AVR.
LIB8STATIC uint8_t sqrt16(uint16_t x)
{
if( x <= 1) {
return x;
}
uint8_t low = 1; // lower bound
uint8_t hi, mid;
if( x > 7904) {
hi = 255;
} else {
hi = (x >> 5) + 8; // initial estimate for upper bound
}
do {
mid = (low + hi) >> 1;
if ((uint16_t)(mid * mid) > x) {
hi = mid - 1;
} else {
if( mid == 255) {
return 255;
}
low = mid + 1;
}
} while (hi >= low);
return low - 1;
}
/// blend a variable proproportion(0-255) of one byte to another
/// @param a - the starting byte value
/// @param b - the byte value to blend toward
/// @param amountOfB - the proportion (0-255) of b to blend
/// @returns a byte value between a and b, inclusive
#if (FASTLED_BLEND_FIXED == 1)
LIB8STATIC uint8_t blend8( uint8_t a, uint8_t b, uint8_t amountOfB)
{
#if BLEND8_C == 1
uint16_t partial;
uint8_t result;
uint8_t amountOfA = 255 - amountOfB;
partial = (a * amountOfA);
#if (FASTLED_SCALE8_FIXED == 1)
partial += a;
//partial = add8to16( a, partial);
#endif
partial += (b * amountOfB);
#if (FASTLED_SCALE8_FIXED == 1)
partial += b;
//partial = add8to16( b, partial);
#endif
result = partial >> 8;
return result;
#elif BLEND8_AVRASM == 1
uint16_t partial;
uint8_t result;
asm volatile (
/* partial = b * amountOfB */
" mul %[b], %[amountOfB] \n\t"
" movw %A[partial], r0 \n\t"
/* amountOfB (aka amountOfA) = 255 - amountOfB */
" com %[amountOfB] \n\t"
/* partial += a * amountOfB (aka amountOfA) */
" mul %[a], %[amountOfB] \n\t"
" add %A[partial], r0 \n\t"
" adc %B[partial], r1 \n\t"
" clr __zero_reg__ \n\t"
#if (FASTLED_SCALE8_FIXED == 1)
/* partial += a */
" add %A[partial], %[a] \n\t"
" adc %B[partial], __zero_reg__ \n\t"
// partial += b
" add %A[partial], %[b] \n\t"
" adc %B[partial], __zero_reg__ \n\t"
#endif
: [partial] "=r" (partial),
[amountOfB] "+a" (amountOfB)
: [a] "a" (a),
[b] "a" (b)
: "r0", "r1"
);
result = partial >> 8;
return result;
#else
#error "No implementation for blend8 available."
#endif
}
#else
LIB8STATIC uint8_t blend8( uint8_t a, uint8_t b, uint8_t amountOfB)
{
// This version loses precision in the integer math
// and can actually return results outside of the range
// from a to b. Its use is not recommended.
uint8_t result;
uint8_t amountOfA = 255 - amountOfB;
result = scale8_LEAVING_R1_DIRTY( a, amountOfA)
+ scale8_LEAVING_R1_DIRTY( b, amountOfB);
cleanup_R1();
return result;
}
#endif
///@}
#endif

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#ifndef __INC_LIB8TION_RANDOM_H
#define __INC_LIB8TION_RANDOM_H
///@ingroup lib8tion
///@defgroup Random Fast random number generators
/// Fast 8- and 16- bit unsigned random numbers.
/// Significantly faster than Arduino random(), but
/// also somewhat less random. You can add entropy.
///@{
// X(n+1) = (2053 * X(n)) + 13849)
#define FASTLED_RAND16_2053 ((uint16_t)(2053))
#define FASTLED_RAND16_13849 ((uint16_t)(13849))
/// random number seed
extern uint16_t rand16seed;// = RAND16_SEED;
/// Generate an 8-bit random number
LIB8STATIC uint8_t random8()
{
rand16seed = (rand16seed * FASTLED_RAND16_2053) + FASTLED_RAND16_13849;
// return the sum of the high and low bytes, for better
// mixing and non-sequential correlation
return (uint8_t)(((uint8_t)(rand16seed & 0xFF)) +
((uint8_t)(rand16seed >> 8)));
}
/// Generate a 16 bit random number
LIB8STATIC uint16_t random16()
{
rand16seed = (rand16seed * FASTLED_RAND16_2053) + FASTLED_RAND16_13849;
return rand16seed;
}
/// Generate an 8-bit random number between 0 and lim
/// @param lim the upper bound for the result
LIB8STATIC uint8_t random8(uint8_t lim)
{
uint8_t r = random8();
r = (r*lim) >> 8;
return r;
}
/// Generate an 8-bit random number in the given range
/// @param min the lower bound for the random number
/// @param lim the upper bound for the random number
LIB8STATIC uint8_t random8(uint8_t min, uint8_t lim)
{
uint8_t delta = lim - min;
uint8_t r = random8(delta) + min;
return r;
}
/// Generate an 16-bit random number between 0 and lim
/// @param lim the upper bound for the result
LIB8STATIC uint16_t random16( uint16_t lim)
{
uint16_t r = random16();
uint32_t p = (uint32_t)lim * (uint32_t)r;
r = p >> 16;
return r;
}
/// Generate an 16-bit random number in the given range
/// @param min the lower bound for the random number
/// @param lim the upper bound for the random number
LIB8STATIC uint16_t random16( uint16_t min, uint16_t lim)
{
uint16_t delta = lim - min;
uint16_t r = random16( delta) + min;
return r;
}
/// Set the 16-bit seed used for the random number generator
LIB8STATIC void random16_set_seed( uint16_t seed)
{
rand16seed = seed;
}
/// Get the current seed value for the random number generator
LIB8STATIC uint16_t random16_get_seed()
{
return rand16seed;
}
/// Add entropy into the random number generator
LIB8STATIC void random16_add_entropy( uint16_t entropy)
{
rand16seed += entropy;
}
///@}
#endif

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#ifndef __INC_LIB8TION_SCALE_H
#define __INC_LIB8TION_SCALE_H
///@ingroup lib8tion
///@defgroup Scaling Scaling functions
/// Fast, efficient 8-bit scaling functions specifically
/// designed for high-performance LED programming.
///
/// Because of the AVR(Arduino) and ARM assembly language
/// implementations provided, using these functions often
/// results in smaller and faster code than the equivalent
/// program using plain "C" arithmetic and logic.
///@{
/// scale one byte by a second one, which is treated as
/// the numerator of a fraction whose denominator is 256
/// In other words, it computes i * (scale / 256)
/// 4 clocks AVR with MUL, 2 clocks ARM
LIB8STATIC_ALWAYS_INLINE uint8_t scale8( uint8_t i, fract8 scale)
{
#if SCALE8_C == 1
#if (FASTLED_SCALE8_FIXED == 1)
return (((uint16_t)i) * (1+(uint16_t)(scale))) >> 8;
#else
return ((uint16_t)i * (uint16_t)(scale) ) >> 8;
#endif
#elif SCALE8_AVRASM == 1
#if defined(LIB8_ATTINY)
#if (FASTLED_SCALE8_FIXED == 1)
uint8_t work=i;
#else
uint8_t work=0;
#endif
uint8_t cnt=0x80;
asm volatile(
#if (FASTLED_SCALE8_FIXED == 1)
" inc %[scale] \n\t"
" breq DONE_%= \n\t"
" clr %[work] \n\t"
#endif
"LOOP_%=: \n\t"
/*" sbrc %[scale], 0 \n\t"
" add %[work], %[i] \n\t"
" ror %[work] \n\t"
" lsr %[scale] \n\t"
" clc \n\t"*/
" sbrc %[scale], 0 \n\t"
" add %[work], %[i] \n\t"
" ror %[work] \n\t"
" lsr %[scale] \n\t"
" lsr %[cnt] \n\t"
"brcc LOOP_%= \n\t"
"DONE_%=: \n\t"
: [work] "+r" (work), [cnt] "+r" (cnt)
: [scale] "r" (scale), [i] "r" (i)
:
);
return work;
#else
asm volatile(
#if (FASTLED_SCALE8_FIXED==1)
// Multiply 8-bit i * 8-bit scale, giving 16-bit r1,r0
"mul %0, %1 \n\t"
// Add i to r0, possibly setting the carry flag
"add r0, %0 \n\t"
// load the immediate 0 into i (note, this does _not_ touch any flags)
"ldi %0, 0x00 \n\t"
// walk and chew gum at the same time
"adc %0, r1 \n\t"
#else
/* Multiply 8-bit i * 8-bit scale, giving 16-bit r1,r0 */
"mul %0, %1 \n\t"
/* Move the high 8-bits of the product (r1) back to i */
"mov %0, r1 \n\t"
/* Restore r1 to "0"; it's expected to always be that */
#endif
"clr __zero_reg__ \n\t"
: "+a" (i) /* writes to i */
: "a" (scale) /* uses scale */
: "r0", "r1" /* clobbers r0, r1 */ );
/* Return the result */
return i;
#endif
#else
#error "No implementation for scale8 available."
#endif
}
/// The "video" version of scale8 guarantees that the output will
/// be only be zero if one or both of the inputs are zero. If both
/// inputs are non-zero, the output is guaranteed to be non-zero.
/// This makes for better 'video'/LED dimming, at the cost of
/// several additional cycles.
LIB8STATIC_ALWAYS_INLINE uint8_t scale8_video( uint8_t i, fract8 scale)
{
#if SCALE8_C == 1 || defined(LIB8_ATTINY)
uint8_t j = (((int)i * (int)scale) >> 8) + ((i&&scale)?1:0);
// uint8_t nonzeroscale = (scale != 0) ? 1 : 0;
// uint8_t j = (i == 0) ? 0 : (((int)i * (int)(scale) ) >> 8) + nonzeroscale;
return j;
#elif SCALE8_AVRASM == 1
uint8_t j=0;
asm volatile(
" tst %[i]\n\t"
" breq L_%=\n\t"
" mul %[i], %[scale]\n\t"
" mov %[j], r1\n\t"
" clr __zero_reg__\n\t"
" cpse %[scale], r1\n\t"
" subi %[j], 0xFF\n\t"
"L_%=: \n\t"
: [j] "+a" (j)
: [i] "a" (i), [scale] "a" (scale)
: "r0", "r1");
return j;
// uint8_t nonzeroscale = (scale != 0) ? 1 : 0;
// asm volatile(
// " tst %0 \n"
// " breq L_%= \n"
// " mul %0, %1 \n"
// " mov %0, r1 \n"
// " add %0, %2 \n"
// " clr __zero_reg__ \n"
// "L_%=: \n"
// : "+a" (i)
// : "a" (scale), "a" (nonzeroscale)
// : "r0", "r1");
// // Return the result
// return i;
#else
#error "No implementation for scale8_video available."
#endif
}
/// This version of scale8 does not clean up the R1 register on AVR
/// If you are doing several 'scale8's in a row, use this, and
/// then explicitly call cleanup_R1.
LIB8STATIC_ALWAYS_INLINE uint8_t scale8_LEAVING_R1_DIRTY( uint8_t i, fract8 scale)
{
#if SCALE8_C == 1
#if (FASTLED_SCALE8_FIXED == 1)
return (((uint16_t)i) * ((uint16_t)(scale)+1)) >> 8;
#else
return ((int)i * (int)(scale) ) >> 8;
#endif
#elif SCALE8_AVRASM == 1
asm volatile(
#if (FASTLED_SCALE8_FIXED==1)
// Multiply 8-bit i * 8-bit scale, giving 16-bit r1,r0
"mul %0, %1 \n\t"
// Add i to r0, possibly setting the carry flag
"add r0, %0 \n\t"
// load the immediate 0 into i (note, this does _not_ touch any flags)
"ldi %0, 0x00 \n\t"
// walk and chew gum at the same time
"adc %0, r1 \n\t"
#else
/* Multiply 8-bit i * 8-bit scale, giving 16-bit r1,r0 */
"mul %0, %1 \n\t"
/* Move the high 8-bits of the product (r1) back to i */
"mov %0, r1 \n\t"
#endif
/* R1 IS LEFT DIRTY HERE; YOU MUST ZERO IT OUT YOURSELF */
/* "clr __zero_reg__ \n\t" */
: "+a" (i) /* writes to i */
: "a" (scale) /* uses scale */
: "r0", "r1" /* clobbers r0, r1 */ );
// Return the result
return i;
#else
#error "No implementation for scale8_LEAVING_R1_DIRTY available."
#endif
}
/// In place modifying version of scale8, also this version of nscale8 does not
/// clean up the R1 register on AVR
/// If you are doing several 'scale8's in a row, use this, and
/// then explicitly call cleanup_R1.
LIB8STATIC_ALWAYS_INLINE void nscale8_LEAVING_R1_DIRTY( uint8_t& i, fract8 scale)
{
#if SCALE8_C == 1
#if (FASTLED_SCALE8_FIXED == 1)
i = (((uint16_t)i) * ((uint16_t)(scale)+1)) >> 8;
#else
i = ((int)i * (int)(scale) ) >> 8;
#endif
#elif SCALE8_AVRASM == 1
asm volatile(
#if (FASTLED_SCALE8_FIXED==1)
// Multiply 8-bit i * 8-bit scale, giving 16-bit r1,r0
"mul %0, %1 \n\t"
// Add i to r0, possibly setting the carry flag
"add r0, %0 \n\t"
// load the immediate 0 into i (note, this does _not_ touch any flags)
"ldi %0, 0x00 \n\t"
// walk and chew gum at the same time
"adc %0, r1 \n\t"
#else
/* Multiply 8-bit i * 8-bit scale, giving 16-bit r1,r0 */
"mul %0, %1 \n\t"
/* Move the high 8-bits of the product (r1) back to i */
"mov %0, r1 \n\t"
#endif
/* R1 IS LEFT DIRTY HERE; YOU MUST ZERO IT OUT YOURSELF */
/* "clr __zero_reg__ \n\t" */
: "+a" (i) /* writes to i */
: "a" (scale) /* uses scale */
: "r0", "r1" /* clobbers r0, r1 */ );
#else
#error "No implementation for nscale8_LEAVING_R1_DIRTY available."
#endif
}
/// This version of scale8_video does not clean up the R1 register on AVR
/// If you are doing several 'scale8_video's in a row, use this, and
/// then explicitly call cleanup_R1.
LIB8STATIC_ALWAYS_INLINE uint8_t scale8_video_LEAVING_R1_DIRTY( uint8_t i, fract8 scale)
{
#if SCALE8_C == 1 || defined(LIB8_ATTINY)
uint8_t j = (((int)i * (int)scale) >> 8) + ((i&&scale)?1:0);
// uint8_t nonzeroscale = (scale != 0) ? 1 : 0;
// uint8_t j = (i == 0) ? 0 : (((int)i * (int)(scale) ) >> 8) + nonzeroscale;
return j;
#elif SCALE8_AVRASM == 1
uint8_t j=0;
asm volatile(
" tst %[i]\n\t"
" breq L_%=\n\t"
" mul %[i], %[scale]\n\t"
" mov %[j], r1\n\t"
" breq L_%=\n\t"
" subi %[j], 0xFF\n\t"
"L_%=: \n\t"
: [j] "+a" (j)
: [i] "a" (i), [scale] "a" (scale)
: "r0", "r1");
return j;
// uint8_t nonzeroscale = (scale != 0) ? 1 : 0;
// asm volatile(
// " tst %0 \n"
// " breq L_%= \n"
// " mul %0, %1 \n"
// " mov %0, r1 \n"
// " add %0, %2 \n"
// " clr __zero_reg__ \n"
// "L_%=: \n"
// : "+a" (i)
// : "a" (scale), "a" (nonzeroscale)
// : "r0", "r1");
// // Return the result
// return i;
#else
#error "No implementation for scale8_video_LEAVING_R1_DIRTY available."
#endif
}
/// In place modifying version of scale8_video, also this version of nscale8_video
/// does not clean up the R1 register on AVR
/// If you are doing several 'scale8_video's in a row, use this, and
/// then explicitly call cleanup_R1.
LIB8STATIC_ALWAYS_INLINE void nscale8_video_LEAVING_R1_DIRTY( uint8_t & i, fract8 scale)
{
#if SCALE8_C == 1 || defined(LIB8_ATTINY)
i = (((int)i * (int)scale) >> 8) + ((i&&scale)?1:0);
#elif SCALE8_AVRASM == 1
asm volatile(
" tst %[i]\n\t"
" breq L_%=\n\t"
" mul %[i], %[scale]\n\t"
" mov %[i], r1\n\t"
" breq L_%=\n\t"
" subi %[i], 0xFF\n\t"
"L_%=: \n\t"
: [i] "+a" (i)
: [scale] "a" (scale)
: "r0", "r1");
#else
#error "No implementation for scale8_video_LEAVING_R1_DIRTY available."
#endif
}
/// Clean up the r1 register after a series of *LEAVING_R1_DIRTY calls
LIB8STATIC_ALWAYS_INLINE void cleanup_R1()
{
#if CLEANUP_R1_AVRASM == 1
// Restore r1 to "0"; it's expected to always be that
asm volatile( "clr __zero_reg__ \n\t" : : : "r1" );
#endif
}
/// scale three one byte values by a fourth one, which is treated as
/// the numerator of a fraction whose demominator is 256
/// In other words, it computes r,g,b * (scale / 256)
///
/// THIS FUNCTION ALWAYS MODIFIES ITS ARGUMENTS IN PLACE
LIB8STATIC void nscale8x3( uint8_t& r, uint8_t& g, uint8_t& b, fract8 scale)
{
#if SCALE8_C == 1
#if (FASTLED_SCALE8_FIXED == 1)
uint16_t scale_fixed = scale + 1;
r = (((uint16_t)r) * scale_fixed) >> 8;
g = (((uint16_t)g) * scale_fixed) >> 8;
b = (((uint16_t)b) * scale_fixed) >> 8;
#else
r = ((int)r * (int)(scale) ) >> 8;
g = ((int)g * (int)(scale) ) >> 8;
b = ((int)b * (int)(scale) ) >> 8;
#endif
#elif SCALE8_AVRASM == 1
r = scale8_LEAVING_R1_DIRTY(r, scale);
g = scale8_LEAVING_R1_DIRTY(g, scale);
b = scale8_LEAVING_R1_DIRTY(b, scale);
cleanup_R1();
#else
#error "No implementation for nscale8x3 available."
#endif
}
/// scale three one byte values by a fourth one, which is treated as
/// the numerator of a fraction whose demominator is 256
/// In other words, it computes r,g,b * (scale / 256), ensuring
/// that non-zero values passed in remain non zero, no matter how low the scale
/// argument.
///
/// THIS FUNCTION ALWAYS MODIFIES ITS ARGUMENTS IN PLACE
LIB8STATIC void nscale8x3_video( uint8_t& r, uint8_t& g, uint8_t& b, fract8 scale)
{
#if SCALE8_C == 1
uint8_t nonzeroscale = (scale != 0) ? 1 : 0;
r = (r == 0) ? 0 : (((int)r * (int)(scale) ) >> 8) + nonzeroscale;
g = (g == 0) ? 0 : (((int)g * (int)(scale) ) >> 8) + nonzeroscale;
b = (b == 0) ? 0 : (((int)b * (int)(scale) ) >> 8) + nonzeroscale;
#elif SCALE8_AVRASM == 1
nscale8_video_LEAVING_R1_DIRTY( r, scale);
nscale8_video_LEAVING_R1_DIRTY( g, scale);
nscale8_video_LEAVING_R1_DIRTY( b, scale);
cleanup_R1();
#else
#error "No implementation for nscale8x3 available."
#endif
}
/// scale two one byte values by a third one, which is treated as
/// the numerator of a fraction whose demominator is 256
/// In other words, it computes i,j * (scale / 256)
///
/// THIS FUNCTION ALWAYS MODIFIES ITS ARGUMENTS IN PLACE
LIB8STATIC void nscale8x2( uint8_t& i, uint8_t& j, fract8 scale)
{
#if SCALE8_C == 1
#if FASTLED_SCALE8_FIXED == 1
uint16_t scale_fixed = scale + 1;
i = (((uint16_t)i) * scale_fixed ) >> 8;
j = (((uint16_t)j) * scale_fixed ) >> 8;
#else
i = ((uint16_t)i * (uint16_t)(scale) ) >> 8;
j = ((uint16_t)j * (uint16_t)(scale) ) >> 8;
#endif
#elif SCALE8_AVRASM == 1
i = scale8_LEAVING_R1_DIRTY(i, scale);
j = scale8_LEAVING_R1_DIRTY(j, scale);
cleanup_R1();
#else
#error "No implementation for nscale8x2 available."
#endif
}
/// scale two one byte values by a third one, which is treated as
/// the numerator of a fraction whose demominator is 256
/// In other words, it computes i,j * (scale / 256), ensuring
/// that non-zero values passed in remain non zero, no matter how low the scale
/// argument.
///
/// THIS FUNCTION ALWAYS MODIFIES ITS ARGUMENTS IN PLACE
LIB8STATIC void nscale8x2_video( uint8_t& i, uint8_t& j, fract8 scale)
{
#if SCALE8_C == 1
uint8_t nonzeroscale = (scale != 0) ? 1 : 0;
i = (i == 0) ? 0 : (((int)i * (int)(scale) ) >> 8) + nonzeroscale;
j = (j == 0) ? 0 : (((int)j * (int)(scale) ) >> 8) + nonzeroscale;
#elif SCALE8_AVRASM == 1
nscale8_video_LEAVING_R1_DIRTY( i, scale);
nscale8_video_LEAVING_R1_DIRTY( j, scale);
cleanup_R1();
#else
#error "No implementation for nscale8x2 available."
#endif
}
/// scale a 16-bit unsigned value by an 8-bit value,
/// considered as numerator of a fraction whose denominator
/// is 256. In other words, it computes i * (scale / 256)
LIB8STATIC_ALWAYS_INLINE uint16_t scale16by8( uint16_t i, fract8 scale )
{
#if SCALE16BY8_C == 1
uint16_t result;
#if FASTLED_SCALE8_FIXED == 1
result = (i * (1+((uint16_t)scale))) >> 8;
#else
result = (i * scale) / 256;
#endif
return result;
#elif SCALE16BY8_AVRASM == 1
#if FASTLED_SCALE8_FIXED == 1
uint16_t result = 0;
asm volatile(
// result.A = HighByte( (i.A x scale) + i.A )
" mul %A[i], %[scale] \n\t"
" add r0, %A[i] \n\t"
// " adc r1, [zero] \n\t"
// " mov %A[result], r1 \n\t"
" adc %A[result], r1 \n\t"
// result.A-B += i.B x scale
" mul %B[i], %[scale] \n\t"
" add %A[result], r0 \n\t"
" adc %B[result], r1 \n\t"
// cleanup r1
" clr __zero_reg__ \n\t"
// result.A-B += i.B
" add %A[result], %B[i] \n\t"
" adc %B[result], __zero_reg__ \n\t"
: [result] "+r" (result)
: [i] "r" (i), [scale] "r" (scale)
: "r0", "r1"
);
return result;
#else
uint16_t result = 0;
asm volatile(
// result.A = HighByte(i.A x j )
" mul %A[i], %[scale] \n\t"
" mov %A[result], r1 \n\t"
//" clr %B[result] \n\t"
// result.A-B += i.B x j
" mul %B[i], %[scale] \n\t"
" add %A[result], r0 \n\t"
" adc %B[result], r1 \n\t"
// cleanup r1
" clr __zero_reg__ \n\t"
: [result] "+r" (result)
: [i] "r" (i), [scale] "r" (scale)
: "r0", "r1"
);
return result;
#endif
#else
#error "No implementation for scale16by8 available."
#endif
}
/// scale a 16-bit unsigned value by a 16-bit value,
/// considered as numerator of a fraction whose denominator
/// is 65536. In other words, it computes i * (scale / 65536)
LIB8STATIC uint16_t scale16( uint16_t i, fract16 scale )
{
#if SCALE16_C == 1
uint16_t result;
#if FASTLED_SCALE8_FIXED == 1
result = ((uint32_t)(i) * (1+(uint32_t)(scale))) / 65536;
#else
result = ((uint32_t)(i) * (uint32_t)(scale)) / 65536;
#endif
return result;
#elif SCALE16_AVRASM == 1
#if FASTLED_SCALE8_FIXED == 1
// implemented sort of like
// result = ((i * scale) + i ) / 65536
//
// why not like this, you may ask?
// result = (i * (scale+1)) / 65536
// the answer is that if scale is 65535, then scale+1
// will be zero, which is not what we want.
uint32_t result;
asm volatile(
// result.A-B = i.A x scale.A
" mul %A[i], %A[scale] \n\t"
// save results...
// basic idea:
//" mov %A[result], r0 \n\t"
//" mov %B[result], r1 \n\t"
// which can be written as...
" movw %A[result], r0 \n\t"
// Because we're going to add i.A-B to
// result.A-D, we DO need to keep both
// the r0 and r1 portions of the product
// UNlike in the 'unfixed scale8' version.
// So the movw here is needed.
: [result] "=r" (result)
: [i] "r" (i),
[scale] "r" (scale)
: "r0", "r1"
);
asm volatile(
// result.C-D = i.B x scale.B
" mul %B[i], %B[scale] \n\t"
//" mov %C[result], r0 \n\t"
//" mov %D[result], r1 \n\t"
" movw %C[result], r0 \n\t"
: [result] "+r" (result)
: [i] "r" (i),
[scale] "r" (scale)
: "r0", "r1"
);
const uint8_t zero = 0;
asm volatile(
// result.B-D += i.B x scale.A
" mul %B[i], %A[scale] \n\t"
" add %B[result], r0 \n\t"
" adc %C[result], r1 \n\t"
" adc %D[result], %[zero] \n\t"
// result.B-D += i.A x scale.B
" mul %A[i], %B[scale] \n\t"
" add %B[result], r0 \n\t"
" adc %C[result], r1 \n\t"
" adc %D[result], %[zero] \n\t"
// cleanup r1
" clr r1 \n\t"
: [result] "+r" (result)
: [i] "r" (i),
[scale] "r" (scale),
[zero] "r" (zero)
: "r0", "r1"
);
asm volatile(
// result.A-D += i.A-B
" add %A[result], %A[i] \n\t"
" adc %B[result], %B[i] \n\t"
" adc %C[result], %[zero] \n\t"
" adc %D[result], %[zero] \n\t"
: [result] "+r" (result)
: [i] "r" (i),
[zero] "r" (zero)
);
result = result >> 16;
return result;
#else
uint32_t result;
asm volatile(
// result.A-B = i.A x scale.A
" mul %A[i], %A[scale] \n\t"
// save results...
// basic idea:
//" mov %A[result], r0 \n\t"
//" mov %B[result], r1 \n\t"
// which can be written as...
" movw %A[result], r0 \n\t"
// We actually don't need to do anything with r0,
// as result.A is never used again here, so we
// could just move the high byte, but movw is
// one clock cycle, just like mov, so might as
// well, in case we want to use this code for
// a generic 16x16 multiply somewhere.
: [result] "=r" (result)
: [i] "r" (i),
[scale] "r" (scale)
: "r0", "r1"
);
asm volatile(
// result.C-D = i.B x scale.B
" mul %B[i], %B[scale] \n\t"
//" mov %C[result], r0 \n\t"
//" mov %D[result], r1 \n\t"
" movw %C[result], r0 \n\t"
: [result] "+r" (result)
: [i] "r" (i),
[scale] "r" (scale)
: "r0", "r1"
);
const uint8_t zero = 0;
asm volatile(
// result.B-D += i.B x scale.A
" mul %B[i], %A[scale] \n\t"
" add %B[result], r0 \n\t"
" adc %C[result], r1 \n\t"
" adc %D[result], %[zero] \n\t"
// result.B-D += i.A x scale.B
" mul %A[i], %B[scale] \n\t"
" add %B[result], r0 \n\t"
" adc %C[result], r1 \n\t"
" adc %D[result], %[zero] \n\t"
// cleanup r1
" clr r1 \n\t"
: [result] "+r" (result)
: [i] "r" (i),
[scale] "r" (scale),
[zero] "r" (zero)
: "r0", "r1"
);
result = result >> 16;
return result;
#endif
#else
#error "No implementation for scale16 available."
#endif
}
///@}
///@defgroup Dimming Dimming and brightening functions
///
/// Dimming and brightening functions
///
/// The eye does not respond in a linear way to light.
/// High speed PWM'd LEDs at 50% duty cycle appear far
/// brighter then the 'half as bright' you might expect.
///
/// If you want your midpoint brightness leve (128) to
/// appear half as bright as 'full' brightness (255), you
/// have to apply a 'dimming function'.
///@{
/// Adjust a scaling value for dimming
LIB8STATIC uint8_t dim8_raw( uint8_t x)
{
return scale8( x, x);
}
/// Adjust a scaling value for dimming for video (value will never go below 1)
LIB8STATIC uint8_t dim8_video( uint8_t x)
{
return scale8_video( x, x);
}
/// Linear version of the dimming function that halves for values < 128
LIB8STATIC uint8_t dim8_lin( uint8_t x )
{
if( x & 0x80 ) {
x = scale8( x, x);
} else {
x += 1;
x /= 2;
}
return x;
}
/// inverse of the dimming function, brighten a value
LIB8STATIC uint8_t brighten8_raw( uint8_t x)
{
uint8_t ix = 255 - x;
return 255 - scale8( ix, ix);
}
/// inverse of the dimming function, brighten a value
LIB8STATIC uint8_t brighten8_video( uint8_t x)
{
uint8_t ix = 255 - x;
return 255 - scale8_video( ix, ix);
}
/// inverse of the dimming function, brighten a value
LIB8STATIC uint8_t brighten8_lin( uint8_t x )
{
uint8_t ix = 255 - x;
if( ix & 0x80 ) {
ix = scale8( ix, ix);
} else {
ix += 1;
ix /= 2;
}
return 255 - ix;
}
///@}
#endif

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#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
const uint8_t b_m16_interleave[] = { 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);
}
///@}
#endif