diff options
Diffstat (limited to 'lib')
| -rw-r--r-- | lib/lib8tion/LICENSE | 20 | ||||
| -rw-r--r-- | lib/lib8tion/lib8tion.c | 242 | ||||
| -rw-r--r-- | lib/lib8tion/lib8tion.h | 934 | ||||
| -rw-r--r-- | lib/lib8tion/math8.h | 552 | ||||
| -rw-r--r-- | lib/lib8tion/random8.h | 94 | ||||
| -rw-r--r-- | lib/lib8tion/scale8.h | 542 | ||||
| -rw-r--r-- | lib/lib8tion/trig8.h | 259 |
7 files changed, 2643 insertions, 0 deletions
diff --git a/lib/lib8tion/LICENSE b/lib/lib8tion/LICENSE new file mode 100644 index 000000000..ebe476330 --- /dev/null +++ b/lib/lib8tion/LICENSE @@ -0,0 +1,20 @@ +The MIT License (MIT) + +Copyright (c) 2013 FastLED + +Permission is hereby granted, free of charge, to any person obtaining a copy of +this software and associated documentation files (the "Software"), to deal in +the Software without restriction, including without limitation the rights to +use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of +the Software, and to permit persons to whom the Software is furnished to do so, +subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS +FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR +COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER +IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN +CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/lib/lib8tion/lib8tion.c b/lib/lib8tion/lib8tion.c new file mode 100644 index 000000000..84b3e9c61 --- /dev/null +++ b/lib/lib8tion/lib8tion.c @@ -0,0 +1,242 @@ +#define FASTLED_INTERNAL +#include <stdint.h> + +#define RAND16_SEED 1337 +uint16_t rand16seed = RAND16_SEED; + + +// memset8, memcpy8, memmove8: +// optimized avr replacements for the standard "C" library +// routines memset, memcpy, and memmove. +// +// There are two techniques that make these routines +// faster than the standard avr-libc routines. +// First, the loops are unrolled 2X, meaning that +// the average loop overhead is cut in half. +// And second, the compare-and-branch at the bottom +// of each loop decrements the low byte of the +// counter, and if the carry is clear, it branches +// back up immediately. Only if the low byte math +// causes carry do we bother to decrement the high +// byte and check that result for carry as well. +// Results for a 100-byte buffer are 20-40% faster +// than standard avr-libc, at a cost of a few extra +// bytes of code. + +#if defined(__AVR__) +//__attribute__ ((noinline)) +void * memset8 ( void * ptr, uint8_t val, uint16_t num ) +{ + asm volatile( + " movw r26, %[ptr] \n\t" + " sbrs %A[num], 0 \n\t" + " rjmp Lseteven_%= \n\t" + " rjmp Lsetodd_%= \n\t" + "Lsetloop_%=: \n\t" + " st X+, %[val] \n\t" + "Lsetodd_%=: \n\t" + " st X+, %[val] \n\t" + "Lseteven_%=: \n\t" + " subi %A[num], 2 \n\t" + " brcc Lsetloop_%= \n\t" + " sbci %B[num], 0 \n\t" + " brcc Lsetloop_%= \n\t" + : [num] "+r" (num) + : [ptr] "r" (ptr), + [val] "r" (val) + : "memory" + ); + return ptr; +} + + + +//__attribute__ ((noinline)) +void * memcpy8 ( void * dst, const void* src, uint16_t num ) +{ + asm volatile( + " movw r30, %[src] \n\t" + " movw r26, %[dst] \n\t" + " sbrs %A[num], 0 \n\t" + " rjmp Lcpyeven_%= \n\t" + " rjmp Lcpyodd_%= \n\t" + "Lcpyloop_%=: \n\t" + " ld __tmp_reg__, Z+ \n\t" + " st X+, __tmp_reg__ \n\t" + "Lcpyodd_%=: \n\t" + " ld __tmp_reg__, Z+ \n\t" + " st X+, __tmp_reg__ \n\t" + "Lcpyeven_%=: \n\t" + " subi %A[num], 2 \n\t" + " brcc Lcpyloop_%= \n\t" + " sbci %B[num], 0 \n\t" + " brcc Lcpyloop_%= \n\t" + : [num] "+r" (num) + : [src] "r" (src), + [dst] "r" (dst) + : "memory" + ); + return dst; +} + +//__attribute__ ((noinline)) +void * memmove8 ( void * dst, const void* src, uint16_t num ) +{ + if( src > dst) { + // if src > dst then we can use the forward-stepping memcpy8 + return memcpy8( dst, src, num); + } else { + // if src < dst then we have to step backward: + dst = (char*)dst + num; + src = (char*)src + num; + asm volatile( + " movw r30, %[src] \n\t" + " movw r26, %[dst] \n\t" + " sbrs %A[num], 0 \n\t" + " rjmp Lmoveven_%= \n\t" + " rjmp Lmovodd_%= \n\t" + "Lmovloop_%=: \n\t" + " ld __tmp_reg__, -Z \n\t" + " st -X, __tmp_reg__ \n\t" + "Lmovodd_%=: \n\t" + " ld __tmp_reg__, -Z \n\t" + " st -X, __tmp_reg__ \n\t" + "Lmoveven_%=: \n\t" + " subi %A[num], 2 \n\t" + " brcc Lmovloop_%= \n\t" + " sbci %B[num], 0 \n\t" + " brcc Lmovloop_%= \n\t" + : [num] "+r" (num) + : [src] "r" (src), + [dst] "r" (dst) + : "memory" + ); + return dst; + } +} + +#endif /* AVR */ + + + + +#if 0 +// TEST / VERIFICATION CODE ONLY BELOW THIS POINT +#include <Arduino.h> +#include "lib8tion.h" + +void test1abs( int8_t i) +{ + Serial.print("abs("); Serial.print(i); Serial.print(") = "); + int8_t j = abs8(i); + Serial.print(j); Serial.println(" "); +} + +void testabs() +{ + delay(5000); + for( int8_t q = -128; q != 127; q++) { + test1abs(q); + } + for(;;){}; +} + + +void testmul8() +{ + delay(5000); + byte r, c; + + Serial.println("mul8:"); + for( r = 0; r <= 20; r += 1) { + Serial.print(r); Serial.print(" : "); + for( c = 0; c <= 20; c += 1) { + byte t; + t = mul8( r, c); + Serial.print(t); Serial.print(' '); + } + Serial.println(' '); + } + Serial.println("done."); + for(;;){}; +} + + +void testscale8() +{ + delay(5000); + byte r, c; + + Serial.println("scale8:"); + for( r = 0; r <= 240; r += 10) { + Serial.print(r); Serial.print(" : "); + for( c = 0; c <= 240; c += 10) { + byte t; + t = scale8( r, c); + Serial.print(t); Serial.print(' '); + } + Serial.println(' '); + } + + Serial.println(' '); + Serial.println("scale8_video:"); + + for( r = 0; r <= 100; r += 4) { + Serial.print(r); Serial.print(" : "); + for( c = 0; c <= 100; c += 4) { + byte t; + t = scale8_video( r, c); + Serial.print(t); Serial.print(' '); + } + Serial.println(' '); + } + + Serial.println("done."); + for(;;){}; +} + + + +void testqadd8() +{ + delay(5000); + byte r, c; + for( r = 0; r <= 240; r += 10) { + Serial.print(r); Serial.print(" : "); + for( c = 0; c <= 240; c += 10) { + byte t; + t = qadd8( r, c); + Serial.print(t); Serial.print(' '); + } + Serial.println(' '); + } + Serial.println("done."); + for(;;){}; +} + +void testnscale8x3() +{ + delay(5000); + byte r, g, b, sc; + for( byte z = 0; z < 10; z++) { + r = random8(); g = random8(); b = random8(); sc = random8(); + + Serial.print("nscale8x3_video( "); + Serial.print(r); Serial.print(", "); + Serial.print(g); Serial.print(", "); + Serial.print(b); Serial.print(", "); + Serial.print(sc); Serial.print(") = [ "); + + nscale8x3_video( r, g, b, sc); + + Serial.print(r); Serial.print(", "); + Serial.print(g); Serial.print(", "); + Serial.print(b); Serial.print("]"); + + Serial.println(' '); + } + Serial.println("done."); + for(;;){}; +} + +#endif diff --git a/lib/lib8tion/lib8tion.h b/lib/lib8tion/lib8tion.h new file mode 100644 index 000000000..d93c748e6 --- /dev/null +++ b/lib/lib8tion/lib8tion.h @@ -0,0 +1,934 @@ +#ifndef __INC_LIB8TION_H +#define __INC_LIB8TION_H + +/* + + 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. + + + Included are: + + + - Saturating unsigned 8-bit add and subtract. + Instead of wrapping around if an overflow occurs, + these routines just 'clamp' the output at a maxumum + of 255, or a minimum of 0. Useful for adding pixel + values. E.g., qadd8( 200, 100) = 255. + + qadd8( i, j) == MIN( (i + j), 0xFF ) + qsub8( i, j) == MAX( (i - j), 0 ) + + - Saturating signed 8-bit ("7-bit") add. + qadd7( i, j) == MIN( (i + j), 0x7F) + + + - Scaling (down) of unsigned 8- and 16- bit values. + Scaledown value is specified in 1/256ths. + scale8( i, sc) == (i * sc) / 256 + scale16by8( i, sc) == (i * sc) / 256 + + Example: scaling a 0-255 value down into a + range from 0-99: + downscaled = scale8( originalnumber, 100); + + A special version of scale8 is provided for scaling + LED brightness values, to make sure that they don't + accidentally scale down to total black at low + dimming levels, since that would look wrong: + scale8_video( i, sc) = ((i * sc) / 256) +? 1 + + Example: reducing an LED brightness by a + dimming factor: + new_bright = scale8_video( orig_bright, dimming); + + + - Fast 8- and 16- bit unsigned random numbers. + Significantly faster than Arduino random(), but + also somewhat less random. You can add entropy. + random8() == random from 0..255 + random8( n) == random from 0..(N-1) + random8( n, m) == random from N..(M-1) + + random16() == random from 0..65535 + random16( n) == random from 0..(N-1) + random16( n, m) == random from N..(M-1) + + random16_set_seed( k) == seed = k + random16_add_entropy( k) == seed += k + + + - Absolute value of a signed 8-bit value. + abs8( i) == abs( i) + + + - 8-bit math operations which return 8-bit values. + These are provided mostly for completeness, + not particularly for performance. + mul8( i, j) == (i * j) & 0xFF + add8( i, j) == (i + j) & 0xFF + sub8( i, j) == (i - j) & 0xFF + + + - Fast 16-bit approximations of sin and cos. + Input angle is a uint16_t from 0-65535. + Output is a signed int16_t from -32767 to 32767. + sin16( x) == sin( (x/32768.0) * pi) * 32767 + cos16( x) == cos( (x/32768.0) * pi) * 32767 + Accurate to more than 99% in all cases. + + - Fast 8-bit approximations of sin and cos. + Input angle is a uint8_t from 0-255. + Output is an UNsigned uint8_t from 0 to 255. + sin8( x) == (sin( (x/128.0) * pi) * 128) + 128 + cos8( x) == (cos( (x/128.0) * pi) * 128) + 128 + Accurate to within about 2%. + + + - Fast 8-bit "easing in/out" function. + ease8InOutCubic(x) == 3(x^i) - 2(x^3) + ease8InOutApprox(x) == + faster, rougher, approximation of cubic easing + ease8InOutQuad(x) == quadratic (vs cubic) easing + + - Cubic, Quadratic, and Triangle wave functions. + Input is a uint8_t representing phase withing the wave, + similar to how sin8 takes an angle 'theta'. + Output is a uint8_t representing the amplitude of + the wave at that point. + cubicwave8( x) + quadwave8( x) + triwave8( x) + + - Square root for 16-bit integers. About three times + faster and five times smaller than Arduino's built-in + generic 32-bit sqrt routine. + sqrt16( uint16_t x ) == sqrt( x) + + - Dimming and brightening functions for 8-bit + light values. + dim8_video( x) == scale8_video( x, x) + dim8_raw( x) == scale8( x, x) + dim8_lin( x) == (x<128) ? ((x+1)/2) : scale8(x,x) + brighten8_video( x) == 255 - dim8_video( 255 - x) + brighten8_raw( x) == 255 - dim8_raw( 255 - x) + brighten8_lin( x) == 255 - dim8_lin( 255 - x) + The dimming functions in particular are suitable + for making LED light output appear more 'linear'. + + + - Linear interpolation between two values, with the + fraction between them expressed as an 8- or 16-bit + fixed point fraction (fract8 or fract16). + lerp8by8( fromU8, toU8, fract8 ) + lerp16by8( fromU16, toU16, fract8 ) + lerp15by8( fromS16, toS16, fract8 ) + == from + (( to - from ) * fract8) / 256) + lerp16by16( fromU16, toU16, fract16 ) + == from + (( to - from ) * fract16) / 65536) + map8( in, rangeStart, rangeEnd) + == map( in, 0, 255, rangeStart, rangeEnd); + + - Optimized memmove, memcpy, and memset, that are + faster than standard avr-libc 1.8. + memmove8( dest, src, bytecount) + memcpy8( dest, src, bytecount) + memset8( buf, value, bytecount) + + - Beat generators which return sine or sawtooth + waves in a specified number of Beats Per Minute. + Sine wave beat generators can specify a low and + high range for the output. Sawtooth wave beat + generators always range 0-255 or 0-65535. + beatsin8( BPM, low8, high8) + = (sine(beatphase) * (high8-low8)) + low8 + beatsin16( BPM, low16, high16) + = (sine(beatphase) * (high16-low16)) + low16 + beatsin88( BPM88, low16, high16) + = (sine(beatphase) * (high16-low16)) + low16 + beat8( BPM) = 8-bit repeating sawtooth wave + beat16( BPM) = 16-bit repeating sawtooth wave + beat88( BPM88) = 16-bit repeating sawtooth wave + BPM is beats per minute in either simple form + e.g. 120, or Q8.8 fixed-point form. + BPM88 is beats per minute in ONLY Q8.8 fixed-point + form. + +Lib8tion is pronounced like 'libation': lie-BAY-shun + +*/ + + + +#include <stdint.h> + +#define LIB8STATIC __attribute__ ((unused)) static inline +#define LIB8STATIC_ALWAYS_INLINE __attribute__ ((always_inline)) static inline + +#if !defined(__AVR__) +#include <string.h> +// for memmove, memcpy, and memset if not defined here +#endif + +#if defined(__arm__) + +#if defined(FASTLED_TEENSY3) +// Can use Cortex M4 DSP instructions +#define QADD8_C 0 +#define QADD7_C 0 +#define QADD8_ARM_DSP_ASM 1 +#define QADD7_ARM_DSP_ASM 1 +#else +// Generic ARM +#define QADD8_C 1 +#define QADD7_C 1 +#endif + +#define QSUB8_C 1 +#define SCALE8_C 1 +#define SCALE16BY8_C 1 +#define SCALE16_C 1 +#define ABS8_C 1 +#define MUL8_C 1 +#define QMUL8_C 1 +#define ADD8_C 1 +#define SUB8_C 1 +#define EASE8_C 1 +#define AVG8_C 1 +#define AVG7_C 1 +#define AVG16_C 1 +#define AVG15_C 1 +#define BLEND8_C 1 + + +#elif defined(__AVR__) + +// AVR ATmega and friends Arduino + +#define QADD8_C 0 +#define QADD7_C 0 +#define QSUB8_C 0 +#define ABS8_C 0 +#define ADD8_C 0 +#define SUB8_C 0 +#define AVG8_C 0 +#define AVG7_C 0 +#define AVG16_C 0 +#define AVG15_C 0 + +#define QADD8_AVRASM 1 +#define QADD7_AVRASM 1 +#define QSUB8_AVRASM 1 +#define ABS8_AVRASM 1 +#define ADD8_AVRASM 1 +#define SUB8_AVRASM 1 +#define AVG8_AVRASM 1 +#define AVG7_AVRASM 1 +#define AVG16_AVRASM 1 +#define AVG15_AVRASM 1 + +// Note: these require hardware MUL instruction +// -- sorry, ATtiny! +#if !defined(LIB8_ATTINY) +#define SCALE8_C 0 +#define SCALE16BY8_C 0 +#define SCALE16_C 0 +#define MUL8_C 0 +#define QMUL8_C 0 +#define EASE8_C 0 +#define BLEND8_C 0 +#define SCALE8_AVRASM 1 +#define SCALE16BY8_AVRASM 1 +#define SCALE16_AVRASM 1 +#define MUL8_AVRASM 1 +#define QMUL8_AVRASM 1 +#define EASE8_AVRASM 1 +#define CLEANUP_R1_AVRASM 1 +#define BLEND8_AVRASM 1 +#else +// On ATtiny, we just use C implementations +#define SCALE8_C 1 +#define SCALE16BY8_C 1 +#define SCALE16_C 1 +#define MUL8_C 1 +#define QMUL8_C 1 +#define EASE8_C 1 +#define BLEND8_C 1 +#define SCALE8_AVRASM 0 +#define SCALE16BY8_AVRASM 0 +#define SCALE16_AVRASM 0 +#define MUL8_AVRASM 0 +#define QMUL8_AVRASM 0 +#define EASE8_AVRASM 0 +#define BLEND8_AVRASM 0 +#endif + +#else + +// unspecified architecture, so +// no ASM, everything in C +#define QADD8_C 1 +#define QADD7_C 1 +#define QSUB8_C 1 +#define SCALE8_C 1 +#define SCALE16BY8_C 1 +#define SCALE16_C 1 +#define ABS8_C 1 +#define MUL8_C 1 +#define QMUL8_C 1 +#define ADD8_C 1 +#define SUB8_C 1 +#define EASE8_C 1 +#define AVG8_C 1 +#define AVG7_C 1 +#define AVG16_C 1 +#define AVG15_C 1 +#define BLEND8_C 1 + +#endif + +///@defgroup lib8tion Fast math functions +///A variety of functions for working with numbers. +///@{ + + +/////////////////////////////////////////////////////////////////////// +// +// typdefs for fixed-point fractional types. +// +// sfract7 should be interpreted as signed 128ths. +// fract8 should be interpreted as unsigned 256ths. +// sfract15 should be interpreted as signed 32768ths. +// fract16 should be interpreted as unsigned 65536ths. +// +// Example: if a fract8 has the value "64", that should be interpreted +// as 64/256ths, or one-quarter. +// +// +// fract8 range is 0 to 0.99609375 +// in steps of 0.00390625 +// +// sfract7 range is -0.9921875 to 0.9921875 +// in steps of 0.0078125 +// +// fract16 range is 0 to 0.99998474121 +// in steps of 0.00001525878 +// +// sfract15 range is -0.99996948242 to 0.99996948242 +// in steps of 0.00003051757 +// + +/// ANSI unsigned short _Fract. range is 0 to 0.99609375 +/// in steps of 0.00390625 +typedef uint8_t fract8; ///< ANSI: unsigned short _Fract + +/// ANSI: signed short _Fract. range is -0.9921875 to 0.9921875 +/// in steps of 0.0078125 +typedef int8_t sfract7; ///< ANSI: signed short _Fract + +/// ANSI: unsigned _Fract. range is 0 to 0.99998474121 +/// in steps of 0.00001525878 +typedef uint16_t fract16; ///< ANSI: unsigned _Fract + +/// ANSI: signed _Fract. range is -0.99996948242 to 0.99996948242 +/// in steps of 0.00003051757 +typedef int16_t sfract15; ///< ANSI: signed _Fract + + +// accumXY types should be interpreted as X bits of integer, +// and Y bits of fraction. +// E.g., accum88 has 8 bits of int, 8 bits of fraction + +typedef uint16_t accum88; ///< ANSI: unsigned short _Accum. 8 bits int, 8 bits fraction +typedef int16_t saccum78; ///< ANSI: signed short _Accum. 7 bits int, 8 bits fraction +typedef uint32_t accum1616;///< ANSI: signed _Accum. 16 bits int, 16 bits fraction +typedef int32_t saccum1516;///< ANSI: signed _Accum. 15 bits int, 16 bits fraction +typedef uint16_t accum124; ///< no direct ANSI counterpart. 12 bits int, 4 bits fraction +typedef int32_t saccum114;///< no direct ANSI counterpart. 1 bit int, 14 bits fraction + + + +#include "math8.h" +#include "scale8.h" +#include "random8.h" +#include "trig8.h" + +/////////////////////////////////////////////////////////////////////// + + + + + + + +/////////////////////////////////////////////////////////////////////// +// +// float-to-fixed and fixed-to-float conversions +// +// Note that anything involving a 'float' on AVR will be slower. + +/// sfract15ToFloat: conversion from sfract15 fixed point to +/// IEEE754 32-bit float. +LIB8STATIC float sfract15ToFloat( sfract15 y) +{ + return y / 32768.0; +} + +/// conversion from IEEE754 float in the range (-1,1) +/// to 16-bit fixed point. Note that the extremes of +/// one and negative one are NOT representable. The +/// representable range is basically +LIB8STATIC sfract15 floatToSfract15( float f) +{ + return f * 32768.0; +} + + + +/////////////////////////////////////////////////////////////////////// +// +// memmove8, memcpy8, and memset8: +// alternatives to memmove, memcpy, and memset that are +// faster on AVR than standard avr-libc 1.8 + +#if defined(__AVR__) +void * memmove8( void * dst, const void * src, uint16_t num ); +void * memcpy8 ( void * dst, const void * src, uint16_t num ) __attribute__ ((noinline)); +void * memset8 ( void * ptr, uint8_t value, uint16_t num ) __attribute__ ((noinline)) ; +#else +// on non-AVR platforms, these names just call standard libc. +#define memmove8 memmove +#define memcpy8 memcpy +#define memset8 memset +#endif + + +/////////////////////////////////////////////////////////////////////// +// +// linear interpolation, such as could be used for Perlin noise, etc. +// + +// A note on the structure of the lerp functions: +// The cases for b>a and b<=a are handled separately for +// speed: without knowing the relative order of a and b, +// the value (a-b) might be overflow the width of a or b, +// and have to be promoted to a wider, slower type. +// To avoid that, we separate the two cases, and are able +// to do all the math in the same width as the arguments, +// which is much faster and smaller on AVR. + +/// linear interpolation between two unsigned 8-bit values, +/// with 8-bit fraction +LIB8STATIC uint8_t lerp8by8( uint8_t a, uint8_t b, fract8 frac) +{ + uint8_t result; + if( b > a) { + uint8_t delta = b - a; + uint8_t scaled = scale8( delta, frac); + result = a + scaled; + } else { + uint8_t delta = a - b; + uint8_t scaled = scale8( delta, frac); + result = a - scaled; + } + return result; +} + +/// linear interpolation between two unsigned 16-bit values, +/// with 16-bit fraction +LIB8STATIC uint16_t lerp16by16( uint16_t a, uint16_t b, fract16 frac) +{ + uint16_t result; + if( b > a ) { + uint16_t delta = b - a; + uint16_t scaled = scale16(delta, frac); + result = a + scaled; + } else { + uint16_t delta = a - b; + uint16_t scaled = scale16( delta, frac); + result = a - scaled; + } + return result; +} + +/// linear interpolation between two unsigned 16-bit values, +/// with 8-bit fraction +LIB8STATIC uint16_t lerp16by8( uint16_t a, uint16_t b, fract8 frac) +{ + uint16_t result; + if( b > a) { + uint16_t delta = b - a; + uint16_t scaled = scale16by8( delta, frac); + result = a + scaled; + } else { + uint16_t delta = a - b; + uint16_t scaled = scale16by8( delta, frac); + result = a - scaled; + } + return result; +} + +/// linear interpolation between two signed 15-bit values, +/// with 8-bit fraction +LIB8STATIC int16_t lerp15by8( int16_t a, int16_t b, fract8 frac) +{ + int16_t result; + if( b > a) { + uint16_t delta = b - a; + uint16_t scaled = scale16by8( delta, frac); + result = a + scaled; + } else { + uint16_t delta = a - b; + uint16_t scaled = scale16by8( delta, frac); + result = a - scaled; + } + return result; +} + +/// linear interpolation between two signed 15-bit values, +/// with 8-bit fraction +LIB8STATIC int16_t lerp15by16( int16_t a, int16_t b, fract16 frac) +{ + int16_t result; + if( b > a) { + uint16_t delta = b - a; + uint16_t scaled = scale16( delta, frac); + result = a + scaled; + } else { + uint16_t delta = a - b; + uint16_t scaled = scale16( delta, frac); + result = a - scaled; + } + return result; +} + +/// map8: map from one full-range 8-bit value into a narrower +/// range of 8-bit values, possibly a range of hues. +/// +/// E.g. map myValue into a hue in the range blue..purple..pink..red +/// hue = map8( myValue, HUE_BLUE, HUE_RED); +/// +/// Combines nicely with the waveform functions (like sin8, etc) +/// to produce continuous hue gradients back and forth: +/// +/// hue = map8( sin8( myValue), HUE_BLUE, HUE_RED); +/// +/// Mathematically simiar to lerp8by8, but arguments are more +/// like Arduino's "map"; this function is similar to +/// +/// map( in, 0, 255, rangeStart, rangeEnd) +/// +/// but faster and specifically designed for 8-bit values. +LIB8STATIC uint8_t map8( uint8_t in, uint8_t rangeStart, uint8_t rangeEnd) +{ + uint8_t rangeWidth = rangeEnd - rangeStart; + uint8_t out = scale8( in, rangeWidth); + out += rangeStart; + return out; +} + + +/////////////////////////////////////////////////////////////////////// +// +// easing functions; see http://easings.net +// + +/// ease8InOutQuad: 8-bit quadratic ease-in / ease-out function +/// Takes around 13 cycles on AVR +#if EASE8_C == 1 +LIB8STATIC uint8_t ease8InOutQuad( uint8_t i) +{ + uint8_t j = i; + if( j & 0x80 ) { + j = 255 - j; + } + uint8_t jj = scale8( j, j); + uint8_t jj2 = jj << 1; + if( i & 0x80 ) { + jj2 = 255 - jj2; + } + return jj2; +} + +#elif EASE8_AVRASM == 1 +// This AVR asm version of ease8InOutQuad preserves one more +// low-bit of precision than the C version, and is also slightly +// smaller and faster. +LIB8STATIC uint8_t ease8InOutQuad(uint8_t val) { + uint8_t j=val; + asm volatile ( + "sbrc %[val], 7 \n" + "com %[j] \n" + "mul %[j], %[j] \n" + "add r0, %[j] \n" + "ldi %[j], 0 \n" + "adc %[j], r1 \n" + "lsl r0 \n" // carry = high bit of low byte of mul product + "rol %[j] \n" // j = (j * 2) + carry // preserve add'l bit of precision + "sbrc %[val], 7 \n" + "com %[j] \n" + "clr __zero_reg__ \n" + : [j] "+&a" (j) + : [val] "a" (val) + : "r0", "r1" + ); + return j; +} + +#else +#error "No implementation for ease8InOutQuad available." +#endif + +/// ease16InOutQuad: 16-bit quadratic ease-in / ease-out function +// C implementation at this point +LIB8STATIC uint16_t ease16InOutQuad( uint16_t i) +{ + uint16_t j = i; + if( j & 0x8000 ) { + j = 65535 - j; + } + uint16_t jj = scale16( j, j); + uint16_t jj2 = jj << 1; + if( i & 0x8000 ) { + jj2 = 65535 - jj2; + } + return jj2; +} + + +/// ease8InOutCubic: 8-bit cubic ease-in / ease-out function +/// Takes around 18 cycles on AVR +LIB8STATIC fract8 ease8InOutCubic( fract8 i) +{ + uint8_t ii = scale8_LEAVING_R1_DIRTY( i, i); + uint8_t iii = scale8_LEAVING_R1_DIRTY( ii, i); + + uint16_t r1 = (3 * (uint16_t)(ii)) - ( 2 * (uint16_t)(iii)); + + /* the code generated for the above *'s automatically + cleans up R1, so there's no need to explicitily call + cleanup_R1(); */ + + uint8_t result = r1; + + // if we got "256", return 255: + if( r1 & 0x100 ) { + result = 255; + } + return result; +} + +/// ease8InOutApprox: fast, rough 8-bit ease-in/ease-out function +/// shaped approximately like 'ease8InOutCubic', +/// it's never off by more than a couple of percent +/// from the actual cubic S-curve, and it executes +/// more than twice as fast. Use when the cycles +/// are more important than visual smoothness. +/// Asm version takes around 7 cycles on AVR. + +#if EASE8_C == 1 +LIB8STATIC fract8 ease8InOutApprox( fract8 i) +{ + if( i < 64) { + // start with slope 0.5 + i /= 2; + } else if( i > (255 - 64)) { + // end with slope 0.5 + i = 255 - i; + i /= 2; + i = 255 - i; + } else { + // in the middle, use slope 192/128 = 1.5 + i -= 64; + i += (i / 2); + i += 32; + } + + return i; +} + +#elif EASE8_AVRASM == 1 +LIB8STATIC uint8_t ease8InOutApprox( fract8 i) +{ + // takes around 7 cycles on AVR + asm volatile ( + " subi %[i], 64 \n\t" + " cpi %[i], 128 \n\t" + " brcc Lshift_%= \n\t" + + // middle case + " mov __tmp_reg__, %[i] \n\t" + " lsr __tmp_reg__ \n\t" + " add %[i], __tmp_reg__ \n\t" + " subi %[i], 224 \n\t" + " rjmp Ldone_%= \n\t" + + // start or end case + "Lshift_%=: \n\t" + " lsr %[i] \n\t" + " subi %[i], 96 \n\t" + + "Ldone_%=: \n\t" + + : [i] "+&a" (i) + : + : "r0", "r1" + ); + return i; +} +#else +#error "No implementation for ease8 available." +#endif + + + +/// triwave8: triangle (sawtooth) wave generator. Useful for +/// turning a one-byte ever-increasing value into a +/// one-byte value that oscillates up and down. +/// +/// input output +/// 0..127 0..254 (positive slope) +/// 128..255 254..0 (negative slope) +/// +/// On AVR this function takes just three cycles. +/// +LIB8STATIC uint8_t triwave8(uint8_t in) +{ + if( in & 0x80) { + in = 255 - in; + } + uint8_t out = in << 1; + return out; +} + + +// quadwave8 and cubicwave8: S-shaped wave generators (like 'sine'). +// Useful for turning a one-byte 'counter' value into a +// one-byte oscillating value that moves smoothly up and down, +// with an 'acceleration' and 'deceleration' curve. +// +// These are even faster than 'sin8', and have +// slightly different curve shapes. +// + +/// quadwave8: quadratic waveform generator. Spends just a little more +/// time at the limits than 'sine' does. +LIB8STATIC uint8_t quadwave8(uint8_t in) +{ + return ease8InOutQuad( triwave8( in)); +} + +/// cubicwave8: cubic waveform generator. Spends visibly more time +/// at the limits than 'sine' does. +LIB8STATIC uint8_t cubicwave8(uint8_t in) +{ + return ease8InOutCubic( triwave8( in)); +} + +/// squarewave8: square wave generator. Useful for +/// turning a one-byte ever-increasing value +/// into a one-byte value that is either 0 or 255. +/// The width of the output 'pulse' is +/// determined by the pulsewidth argument: +/// +///~~~ +/// If pulsewidth is 255, output is always 255. +/// If pulsewidth < 255, then +/// if input < pulsewidth then output is 255 +/// if input >= pulsewidth then output is 0 +///~~~ +/// +/// the output looking like: +/// +///~~~ +/// 255 +--pulsewidth--+ +/// . | | +/// 0 0 +--------(256-pulsewidth)-------- +///~~~ +/// +/// @param in +/// @param pulsewidth +/// @returns square wave output +LIB8STATIC uint8_t squarewave8( uint8_t in, uint8_t pulsewidth) +{ + if( in < pulsewidth || (pulsewidth == 255)) { + return 255; + } else { + return 0; + } +} + + +// Beat generators - These functions produce waves at a given +// number of 'beats per minute'. Internally, they use +// the Arduino function 'millis' to track elapsed time. +// Accuracy is a bit better than one part in a thousand. +// +// beat8( BPM ) returns an 8-bit value that cycles 'BPM' times +// per minute, rising from 0 to 255, resetting to zero, +// rising up again, etc.. The output of this function +// is suitable for feeding directly into sin8, and cos8, +// triwave8, quadwave8, and cubicwave8. +// beat16( BPM ) returns a 16-bit value that cycles 'BPM' times +// per minute, rising from 0 to 65535, resetting to zero, +// rising up again, etc. The output of this function is +// suitable for feeding directly into sin16 and cos16. +// beat88( BPM88) is the same as beat16, except that the BPM88 argument +// MUST be in Q8.8 fixed point format, e.g. 120BPM must +// be specified as 120*256 = 30720. +// beatsin8( BPM, uint8_t low, uint8_t high) returns an 8-bit value that +// rises and falls in a sine wave, 'BPM' times per minute, +// between the values of 'low' and 'high'. +// beatsin16( BPM, uint16_t low, uint16_t high) returns a 16-bit value +// that rises and falls in a sine wave, 'BPM' times per +// minute, between the values of 'low' and 'high'. +// beatsin88( BPM88, ...) is the same as beatsin16, except that the +// BPM88 argument MUST be in Q8.8 fixed point format, +// e.g. 120BPM must be specified as 120*256 = 30720. +// +// BPM can be supplied two ways. The simpler way of specifying BPM is as +// a simple 8-bit integer from 1-255, (e.g., "120"). +// The more sophisticated way of specifying BPM allows for fractional +// "Q8.8" fixed point number (an 'accum88') with an 8-bit integer part and +// an 8-bit fractional part. The easiest way to construct this is to multiply +// a floating point BPM value (e.g. 120.3) by 256, (e.g. resulting in 30796 +// in this case), and pass that as the 16-bit BPM argument. +// "BPM88" MUST always be specified in Q8.8 format. +// +// Originally designed to make an entire animation project pulse with brightness. +// For that effect, add this line just above your existing call to "FastLED.show()": +// +// uint8_t bright = beatsin8( 60 /*BPM*/, 192 /*dimmest*/, 255 /*brightest*/ )); +// FastLED.setBrightness( bright ); +// FastLED.show(); +// +// The entire animation will now pulse between brightness 192 and 255 once per second. + + +// The beat generators need access to a millisecond counter. +// On Arduino, this is "millis()". On other platforms, you'll +// need to provide a function with this signature: +// uint32_t get_millisecond_timer(); +// that provides similar functionality. +// You can also force use of the get_millisecond_timer function +// by #defining USE_GET_MILLISECOND_TIMER. +#if (defined(ARDUINO) || defined(SPARK) || defined(FASTLED_HAS_MILLIS)) && !defined(USE_GET_MILLISECOND_TIMER) +// Forward declaration of Arduino function 'millis'. +//uint32_t millis(); +#define GET_MILLIS millis +#else +uint32_t get_millisecond_timer(void); +#define GET_MILLIS get_millisecond_timer +#endif + +// beat16 generates a 16-bit 'sawtooth' wave at a given BPM, +/// with BPM specified in Q8.8 fixed-point format; e.g. +/// for this function, 120 BPM MUST BE specified as +/// 120*256 = 30720. +/// If you just want to specify "120", use beat16 or beat8. +LIB8STATIC uint16_t beat88( accum88 beats_per_minute_88, uint32_t timebase) +{ + // BPM is 'beats per minute', or 'beats per 60000ms'. + // To avoid using the (slower) division operator, we + // want to convert 'beats per 60000ms' to 'beats per 65536ms', + // and then use a simple, fast bit-shift to divide by 65536. + // + // The ratio 65536:60000 is 279.620266667:256; we'll call it 280:256. + // The conversion is accurate to about 0.05%, more or less, + // e.g. if you ask for "120 BPM", you'll get about "119.93". + return (((GET_MILLIS()) - timebase) * beats_per_minute_88 * 280) >> 16; +} + +/// beat16 generates a 16-bit 'sawtooth' wave at a given BPM +LIB8STATIC uint16_t beat16( accum88 beats_per_minute, uint32_t timebase) +{ + // Convert simple 8-bit BPM's to full Q8.8 accum88's if needed + if( beats_per_minute < 256) beats_per_minute <<= 8; + return beat88(beats_per_minute, timebase); +} + +/// beat8 generates an 8-bit 'sawtooth' wave at a given BPM +LIB8STATIC uint8_t beat8( accum88 beats_per_minute, uint32_t timebase) +{ + return beat16( beats_per_minute, timebase) >> 8; +} + +/// beatsin88 generates a 16-bit sine wave at a given BPM, +/// that oscillates within a given range. +/// For this function, BPM MUST BE SPECIFIED as +/// a Q8.8 fixed-point value; e.g. 120BPM must be +/// specified as 120*256 = 30720. +/// If you just want to specify "120", use beatsin16 or beatsin8. +LIB8STATIC uint16_t beatsin88( accum88 beats_per_minute_88, uint16_t lowest, uint16_t highest, uint32_t timebase, uint16_t phase_offset) +{ + uint16_t beat = beat88( beats_per_minute_88, timebase); + uint16_t beatsin = (sin16( beat + phase_offset) + 32768); + uint16_t rangewidth = highest - lowest; + uint16_t scaledbeat = scale16( beatsin, rangewidth); + uint16_t result = lowest + scaledbeat; + return result; +} + +/// beatsin16 generates a 16-bit sine wave at a given BPM, +/// that oscillates within a given range. +LIB8STATIC uint16_t beatsin16(accum88 beats_per_minute, uint16_t lowest, uint16_t highest, uint32_t timebase, uint16_t phase_offset) +{ + uint16_t beat = beat16( beats_per_minute, timebase); + uint16_t beatsin = (sin16( beat + phase_offset) + 32768); + uint16_t rangewidth = highest - lowest; + uint16_t scaledbeat = scale16( beatsin, rangewidth); + uint16_t result = lowest + scaledbeat; + return result; +} + +/// beatsin8 generates an 8-bit sine wave at a given BPM, +/// that oscillates within a given range. +LIB8STATIC uint8_t beatsin8( accum88 beats_per_minute, uint8_t lowest, uint8_t highest, uint32_t timebase, uint8_t phase_offset) +{ + uint8_t beat = beat8( beats_per_minute, timebase); + uint8_t beatsin = sin8( beat + phase_offset); + uint8_t rangewidth = highest - lowest; + uint8_t scaledbeat = scale8( beatsin, rangewidth); + uint8_t result = lowest + scaledbeat; + return result; +} + + +/// Return the current seconds since boot in a 16-bit value. Used as part of the +/// "every N time-periods" mechanism +LIB8STATIC uint16_t seconds16(void) +{ + uint32_t ms = GET_MILLIS(); + uint16_t s16; + s16 = ms / 1000; + return s16; +} + +/// Return the current minutes since boot in a 16-bit value. Used as part of the +/// "every N time-periods" mechanism +LIB8STATIC uint16_t minutes16(void) +{ + uint32_t ms = GET_MILLIS(); + uint16_t m16; + m16 = (ms / (60000L)) & 0xFFFF; + return m16; +} + +/// Return the current hours since boot in an 8-bit value. Used as part of the +/// "every N time-periods" mechanism +LIB8STATIC uint8_t hours8(void) +{ + uint32_t ms = GET_MILLIS(); + uint8_t h8; + h8 = (ms / (3600000L)) & 0xFF; + return h8; +} + +///@} + +#endif diff --git a/lib/lib8tion/math8.h b/lib/lib8tion/math8.h new file mode 100644 index 000000000..8c6b6c227 --- /dev/null +++ b/lib/lib8tion/math8.h @@ -0,0 +1,552 @@ +#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 + uint16_t 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 + int16_t 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 + uint16_t 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 + int16_t 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 ((uint16_t)i * (uint16_t)(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 = ((uint16_t)i * (uint16_t)(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 diff --git a/lib/lib8tion/random8.h b/lib/lib8tion/random8.h new file mode 100644 index 000000000..7ee67cbb3 --- /dev/null +++ b/lib/lib8tion/random8.h @@ -0,0 +1,94 @@ +#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(void) +{ + 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(void) +{ + 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_max(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_min_max(uint8_t min, uint8_t lim) +{ + uint8_t delta = lim - min; + uint8_t r = random8_max(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_max(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_min_max( uint16_t min, uint16_t lim) +{ + uint16_t delta = lim - min; + uint16_t r = random16_max(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(void) +{ + return rand16seed; +} + +/// Add entropy into the random number generator +LIB8STATIC void random16_add_entropy(uint16_t entropy) +{ + rand16seed += entropy; +} + +///@} + +#endif diff --git a/lib/lib8tion/scale8.h b/lib/lib8tion/scale8.h new file mode 100644 index 000000000..9895fd4d7 --- /dev/null +++ b/lib/lib8tion/scale8.h @@ -0,0 +1,542 @@ +#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 +} + + +/// 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 +} + +/// Clean up the r1 register after a series of *LEAVING_R1_DIRTY calls +LIB8STATIC_ALWAYS_INLINE void cleanup_R1(void) +{ +#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 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 diff --git a/lib/lib8tion/trig8.h b/lib/lib8tion/trig8.h new file mode 100644 index 000000000..4907c6ff3 --- /dev/null +++ b/lib/lib8tion/trig8.h @@ -0,0 +1,259 @@ +#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 |