lib8tion.h

/*
 * 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.
 */

#ifndef __INC_LIB8TION_H
#define __INC_LIB8TION_H

/*

 Fast, efficient 8-bit math functions specifically
 designed for high-performance LED programming.

 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);

 - 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>
#include <string.h>
#include <esp_timer.h>

#define LIB8STATIC               __attribute__ ((unused)) static inline
#define LIB8STATIC_ALWAYS_INLINE __attribute__ ((always_inline)) static inline

///@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

/// typedef for IEEE754 "binary32" float type internals
typedef union
{
    uint32_t i;
    float f;
    struct
    {
        uint32_t mantissa :23;
        uint32_t exponent :8;
        uint32_t signbit :1;
    };
    struct
    {
        uint32_t mant7 :7;
        uint32_t mant16 :16;
        uint32_t exp_ :8;
        uint32_t sb_ :1;
    };
    struct
    {
        uint32_t mant_lo8 :8;
        uint32_t mant_hi16_exp_lo1 :16;
        uint32_t sb_exphi7 :8;
    };
} IEEE754binary32_t;

#include "lib8tion/math8.h"
#include "lib8tion/scale8.h"
#include "lib8tion/random8.h"
#include "lib8tion/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;
}

///////////////////////////////////////////////////////////////////////
//
// 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
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;
}

/// 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(i, i);
    uint8_t iii = scale8(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.
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;
}

/// 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;
    return in << 1;
}

// 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)
{
    return in < pulsewidth || pulsewidth == 255 ? 255 : 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.

#define GET_MILLIS() (esp_timer_get_time() / 1000)

/// 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()
{
    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()
{
    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()
{
    uint32_t ms = GET_MILLIS();
    uint8_t h8;
    h8 = (ms / (3600000L)) & 0xFF;
    return h8;
}

/// Helper routine to divide a 32-bit value by 1024, returning
/// only the low 16 bits. You'd think this would be just
///   result = (in32 >> 10) & 0xFFFF;
/// and on ARM, that's what you want and all is well.
/// Used to convert millis to 'binary seconds' aka bseconds:
/// one bsecond == 1024 millis.
LIB8STATIC uint16_t div1024_32_16(uint32_t in32)
{
    uint16_t out16 = (in32 >> 10) & 0xFFFF;
    return out16;
}

/// bseconds16 returns the current time-since-boot in
/// "binary seconds", which are actually 1024/1000 of a
/// second long.
LIB8STATIC uint16_t bseconds16()
{
    uint32_t ms = GET_MILLIS();
    uint16_t s16;
    s16 = div1024_32_16(ms);
    return s16;
}

///@}

#endif