935 lines
28 KiB
C
935 lines
28 KiB
C
#ifndef __INC_LIB8TION_H
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#define __INC_LIB8TION_H
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/*
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Fast, efficient 8-bit math functions specifically
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designed for high-performance LED programming.
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Because of the AVR(Arduino) and ARM assembly language
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implementations provided, using these functions often
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results in smaller and faster code than the equivalent
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program using plain "C" arithmetic and logic.
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Included are:
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- Saturating unsigned 8-bit add and subtract.
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Instead of wrapping around if an overflow occurs,
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these routines just 'clamp' the output at a maxumum
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of 255, or a minimum of 0. Useful for adding pixel
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values. E.g., qadd8( 200, 100) = 255.
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qadd8( i, j) == MIN( (i + j), 0xFF )
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qsub8( i, j) == MAX( (i - j), 0 )
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- Saturating signed 8-bit ("7-bit") add.
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qadd7( i, j) == MIN( (i + j), 0x7F)
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- Scaling (down) of unsigned 8- and 16- bit values.
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Scaledown value is specified in 1/256ths.
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scale8( i, sc) == (i * sc) / 256
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scale16by8( i, sc) == (i * sc) / 256
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Example: scaling a 0-255 value down into a
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range from 0-99:
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downscaled = scale8( originalnumber, 100);
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A special version of scale8 is provided for scaling
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LED brightness values, to make sure that they don't
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accidentally scale down to total black at low
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dimming levels, since that would look wrong:
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scale8_video( i, sc) = ((i * sc) / 256) +? 1
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Example: reducing an LED brightness by a
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dimming factor:
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new_bright = scale8_video( orig_bright, dimming);
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- Fast 8- and 16- bit unsigned random numbers.
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Significantly faster than Arduino random(), but
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also somewhat less random. You can add entropy.
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random8() == random from 0..255
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random8( n) == random from 0..(N-1)
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random8( n, m) == random from N..(M-1)
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random16() == random from 0..65535
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random16( n) == random from 0..(N-1)
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random16( n, m) == random from N..(M-1)
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random16_set_seed( k) == seed = k
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random16_add_entropy( k) == seed += k
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- Absolute value of a signed 8-bit value.
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abs8( i) == abs( i)
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- 8-bit math operations which return 8-bit values.
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These are provided mostly for completeness,
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not particularly for performance.
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mul8( i, j) == (i * j) & 0xFF
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add8( i, j) == (i + j) & 0xFF
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sub8( i, j) == (i - j) & 0xFF
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- Fast 16-bit approximations of sin and cos.
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Input angle is a uint16_t from 0-65535.
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Output is a signed int16_t from -32767 to 32767.
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sin16( x) == sin( (x/32768.0) * pi) * 32767
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cos16( x) == cos( (x/32768.0) * pi) * 32767
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Accurate to more than 99% in all cases.
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- Fast 8-bit approximations of sin and cos.
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Input angle is a uint8_t from 0-255.
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Output is an UNsigned uint8_t from 0 to 255.
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sin8( x) == (sin( (x/128.0) * pi) * 128) + 128
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cos8( x) == (cos( (x/128.0) * pi) * 128) + 128
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Accurate to within about 2%.
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- Fast 8-bit "easing in/out" function.
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ease8InOutCubic(x) == 3(x^i) - 2(x^3)
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ease8InOutApprox(x) ==
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faster, rougher, approximation of cubic easing
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ease8InOutQuad(x) == quadratic (vs cubic) easing
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- Cubic, Quadratic, and Triangle wave functions.
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Input is a uint8_t representing phase withing the wave,
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similar to how sin8 takes an angle 'theta'.
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Output is a uint8_t representing the amplitude of
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the wave at that point.
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cubicwave8( x)
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quadwave8( x)
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triwave8( x)
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- Square root for 16-bit integers. About three times
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faster and five times smaller than Arduino's built-in
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generic 32-bit sqrt routine.
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sqrt16( uint16_t x ) == sqrt( x)
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- Dimming and brightening functions for 8-bit
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light values.
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dim8_video( x) == scale8_video( x, x)
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dim8_raw( x) == scale8( x, x)
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dim8_lin( x) == (x<128) ? ((x+1)/2) : scale8(x,x)
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brighten8_video( x) == 255 - dim8_video( 255 - x)
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brighten8_raw( x) == 255 - dim8_raw( 255 - x)
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brighten8_lin( x) == 255 - dim8_lin( 255 - x)
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The dimming functions in particular are suitable
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for making LED light output appear more 'linear'.
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- Linear interpolation between two values, with the
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fraction between them expressed as an 8- or 16-bit
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fixed point fraction (fract8 or fract16).
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lerp8by8( fromU8, toU8, fract8 )
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lerp16by8( fromU16, toU16, fract8 )
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lerp15by8( fromS16, toS16, fract8 )
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== from + (( to - from ) * fract8) / 256)
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lerp16by16( fromU16, toU16, fract16 )
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== from + (( to - from ) * fract16) / 65536)
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map8( in, rangeStart, rangeEnd)
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== map( in, 0, 255, rangeStart, rangeEnd);
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- Optimized memmove, memcpy, and memset, that are
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faster than standard avr-libc 1.8.
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memmove8( dest, src, bytecount)
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memcpy8( dest, src, bytecount)
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memset8( buf, value, bytecount)
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- Beat generators which return sine or sawtooth
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waves in a specified number of Beats Per Minute.
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Sine wave beat generators can specify a low and
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high range for the output. Sawtooth wave beat
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generators always range 0-255 or 0-65535.
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beatsin8( BPM, low8, high8)
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= (sine(beatphase) * (high8-low8)) + low8
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beatsin16( BPM, low16, high16)
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= (sine(beatphase) * (high16-low16)) + low16
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beatsin88( BPM88, low16, high16)
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= (sine(beatphase) * (high16-low16)) + low16
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beat8( BPM) = 8-bit repeating sawtooth wave
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beat16( BPM) = 16-bit repeating sawtooth wave
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beat88( BPM88) = 16-bit repeating sawtooth wave
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BPM is beats per minute in either simple form
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e.g. 120, or Q8.8 fixed-point form.
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BPM88 is beats per minute in ONLY Q8.8 fixed-point
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form.
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Lib8tion is pronounced like 'libation': lie-BAY-shun
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*/
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#include <stdint.h>
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#define LIB8STATIC static inline
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#define LIB8STATIC_ALWAYS_INLINE static inline
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#if !defined(__AVR__)
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#include <string.h>
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// for memmove, memcpy, and memset if not defined here
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#endif
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#if defined(__arm__)
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#if defined(FASTLED_TEENSY3)
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// Can use Cortex M4 DSP instructions
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#define QADD8_C 0
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#define QADD7_C 0
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#define QADD8_ARM_DSP_ASM 1
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#define QADD7_ARM_DSP_ASM 1
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#else
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// Generic ARM
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#define QADD8_C 1
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#define QADD7_C 1
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#endif
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#define QSUB8_C 1
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#define SCALE8_C 1
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#define SCALE16BY8_C 1
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#define SCALE16_C 1
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#define ABS8_C 1
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#define MUL8_C 1
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#define QMUL8_C 1
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#define ADD8_C 1
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#define SUB8_C 1
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#define EASE8_C 1
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#define AVG8_C 1
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#define AVG7_C 1
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#define AVG16_C 1
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#define AVG15_C 1
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#define BLEND8_C 1
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#elif defined(__AVR__)
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// AVR ATmega and friends Arduino
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#define QADD8_C 0
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#define QADD7_C 0
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#define QSUB8_C 0
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#define ABS8_C 0
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#define ADD8_C 0
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#define SUB8_C 0
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#define AVG8_C 0
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#define AVG7_C 0
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#define AVG16_C 0
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#define AVG15_C 0
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#define QADD8_AVRASM 1
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#define QADD7_AVRASM 1
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#define QSUB8_AVRASM 1
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#define ABS8_AVRASM 1
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#define ADD8_AVRASM 1
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#define SUB8_AVRASM 1
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#define AVG8_AVRASM 1
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#define AVG7_AVRASM 1
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#define AVG16_AVRASM 1
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#define AVG15_AVRASM 1
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// Note: these require hardware MUL instruction
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// -- sorry, ATtiny!
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#if !defined(LIB8_ATTINY)
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#define SCALE8_C 0
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#define SCALE16BY8_C 0
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#define SCALE16_C 0
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#define MUL8_C 0
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#define QMUL8_C 0
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#define EASE8_C 0
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#define BLEND8_C 0
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#define SCALE8_AVRASM 1
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#define SCALE16BY8_AVRASM 1
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#define SCALE16_AVRASM 1
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#define MUL8_AVRASM 1
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#define QMUL8_AVRASM 1
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#define EASE8_AVRASM 1
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#define CLEANUP_R1_AVRASM 1
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#define BLEND8_AVRASM 1
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#else
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// On ATtiny, we just use C implementations
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#define SCALE8_C 1
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#define SCALE16BY8_C 1
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#define SCALE16_C 1
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#define MUL8_C 1
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#define QMUL8_C 1
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#define EASE8_C 1
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#define BLEND8_C 1
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#define SCALE8_AVRASM 0
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#define SCALE16BY8_AVRASM 0
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#define SCALE16_AVRASM 0
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#define MUL8_AVRASM 0
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#define QMUL8_AVRASM 0
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#define EASE8_AVRASM 0
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#define BLEND8_AVRASM 0
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#endif
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#else
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// unspecified architecture, so
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// no ASM, everything in C
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#define QADD8_C 1
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#define QADD7_C 1
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#define QSUB8_C 1
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#define SCALE8_C 1
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#define SCALE16BY8_C 1
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#define SCALE16_C 1
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#define ABS8_C 1
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#define MUL8_C 1
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#define QMUL8_C 1
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#define ADD8_C 1
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#define SUB8_C 1
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#define EASE8_C 1
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#define AVG8_C 1
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#define AVG7_C 1
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#define AVG16_C 1
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#define AVG15_C 1
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#define BLEND8_C 1
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#endif
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///@defgroup lib8tion Fast math functions
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///A variety of functions for working with numbers.
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///@{
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///////////////////////////////////////////////////////////////////////
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//
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// typdefs for fixed-point fractional types.
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//
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// sfract7 should be interpreted as signed 128ths.
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// fract8 should be interpreted as unsigned 256ths.
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// sfract15 should be interpreted as signed 32768ths.
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// fract16 should be interpreted as unsigned 65536ths.
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//
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// Example: if a fract8 has the value "64", that should be interpreted
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// as 64/256ths, or one-quarter.
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//
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//
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// fract8 range is 0 to 0.99609375
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// in steps of 0.00390625
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//
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// sfract7 range is -0.9921875 to 0.9921875
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// in steps of 0.0078125
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//
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// fract16 range is 0 to 0.99998474121
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// in steps of 0.00001525878
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//
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// sfract15 range is -0.99996948242 to 0.99996948242
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// in steps of 0.00003051757
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//
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/// ANSI unsigned short _Fract. range is 0 to 0.99609375
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/// in steps of 0.00390625
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typedef uint8_t fract8; ///< ANSI: unsigned short _Fract
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/// ANSI: signed short _Fract. range is -0.9921875 to 0.9921875
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/// in steps of 0.0078125
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typedef int8_t sfract7; ///< ANSI: signed short _Fract
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/// ANSI: unsigned _Fract. range is 0 to 0.99998474121
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/// in steps of 0.00001525878
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typedef uint16_t fract16; ///< ANSI: unsigned _Fract
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/// ANSI: signed _Fract. range is -0.99996948242 to 0.99996948242
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/// in steps of 0.00003051757
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typedef int16_t sfract15; ///< ANSI: signed _Fract
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// accumXY types should be interpreted as X bits of integer,
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// and Y bits of fraction.
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// E.g., accum88 has 8 bits of int, 8 bits of fraction
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typedef uint16_t accum88; ///< ANSI: unsigned short _Accum. 8 bits int, 8 bits fraction
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typedef int16_t saccum78; ///< ANSI: signed short _Accum. 7 bits int, 8 bits fraction
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typedef uint32_t accum1616;///< ANSI: signed _Accum. 16 bits int, 16 bits fraction
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typedef int32_t saccum1516;///< ANSI: signed _Accum. 15 bits int, 16 bits fraction
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typedef uint16_t accum124; ///< no direct ANSI counterpart. 12 bits int, 4 bits fraction
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typedef int32_t saccum114;///< no direct ANSI counterpart. 1 bit int, 14 bits fraction
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#include "math8.h"
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#include "scale8.h"
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#include "random8.h"
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#include "trig8.h"
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///////////////////////////////////////////////////////////////////////
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///////////////////////////////////////////////////////////////////////
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//
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// float-to-fixed and fixed-to-float conversions
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//
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// Note that anything involving a 'float' on AVR will be slower.
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/// sfract15ToFloat: conversion from sfract15 fixed point to
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/// IEEE754 32-bit float.
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LIB8STATIC float sfract15ToFloat( sfract15 y)
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{
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return y / 32768.0;
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}
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/// conversion from IEEE754 float in the range (-1,1)
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/// to 16-bit fixed point. Note that the extremes of
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/// one and negative one are NOT representable. The
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/// representable range is basically
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LIB8STATIC sfract15 floatToSfract15( float f)
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{
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return f * 32768.0;
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}
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///////////////////////////////////////////////////////////////////////
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//
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// memmove8, memcpy8, and memset8:
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// alternatives to memmove, memcpy, and memset that are
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// faster on AVR than standard avr-libc 1.8
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#if defined(__AVR__)
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void * memmove8( void * dst, const void * src, uint16_t num );
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void * memcpy8 ( void * dst, const void * src, uint16_t num ) __attribute__ ((noinline));
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void * memset8 ( void * ptr, uint8_t value, uint16_t num ) __attribute__ ((noinline)) ;
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#else
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// on non-AVR platforms, these names just call standard libc.
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#define memmove8 memmove
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#define memcpy8 memcpy
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#define memset8 memset
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#endif
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///////////////////////////////////////////////////////////////////////
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//
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// linear interpolation, such as could be used for Perlin noise, etc.
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//
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// A note on the structure of the lerp functions:
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// The cases for b>a and b<=a are handled separately for
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// speed: without knowing the relative order of a and b,
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// the value (a-b) might be overflow the width of a or b,
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// and have to be promoted to a wider, slower type.
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// To avoid that, we separate the two cases, and are able
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// to do all the math in the same width as the arguments,
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// which is much faster and smaller on AVR.
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/// linear interpolation between two unsigned 8-bit values,
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/// with 8-bit fraction
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LIB8STATIC uint8_t lerp8by8( uint8_t a, uint8_t b, fract8 frac)
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{
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uint8_t result;
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if( b > a) {
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uint8_t delta = b - a;
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uint8_t scaled = scale8( delta, frac);
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result = a + scaled;
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} else {
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uint8_t delta = a - b;
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uint8_t scaled = scale8( delta, frac);
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result = a - scaled;
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}
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return result;
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}
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/// linear interpolation between two unsigned 16-bit values,
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/// with 16-bit fraction
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LIB8STATIC uint16_t lerp16by16( uint16_t a, uint16_t b, fract16 frac)
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{
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uint16_t result;
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if( b > a ) {
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uint16_t delta = b - a;
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uint16_t scaled = scale16(delta, frac);
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result = a + scaled;
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} else {
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uint16_t delta = a - b;
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uint16_t scaled = scale16( delta, frac);
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result = a - scaled;
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}
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return result;
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}
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/// linear interpolation between two unsigned 16-bit values,
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/// with 8-bit fraction
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LIB8STATIC uint16_t lerp16by8( uint16_t a, uint16_t b, fract8 frac)
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{
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uint16_t result;
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if( b > a) {
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uint16_t delta = b - a;
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uint16_t scaled = scale16by8( delta, frac);
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result = a + scaled;
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} else {
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uint16_t delta = a - b;
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uint16_t scaled = scale16by8( delta, frac);
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result = a - scaled;
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}
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return result;
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}
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/// linear interpolation between two signed 15-bit values,
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/// with 8-bit fraction
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LIB8STATIC int16_t lerp15by8( int16_t a, int16_t b, fract8 frac)
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{
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int16_t result;
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if( b > a) {
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uint16_t delta = b - a;
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uint16_t scaled = scale16by8( delta, frac);
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result = a + scaled;
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} else {
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uint16_t delta = a - b;
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uint16_t scaled = scale16by8( delta, frac);
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result = a - scaled;
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}
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return result;
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}
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/// linear interpolation between two signed 15-bit values,
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/// with 8-bit fraction
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LIB8STATIC int16_t lerp15by16( int16_t a, int16_t b, fract16 frac)
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{
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int16_t result;
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if( b > a) {
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uint16_t delta = b - a;
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uint16_t scaled = scale16( delta, frac);
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result = a + scaled;
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} else {
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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
|