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import std/[algorithm, math, sugar]

type Note* = tuple
    len: float
    octave: float
    step: float
    vol: float

func n*(a, b, c, d: float = 1): Note =
    (a, b, c, d)

type ProcessedNote* = tuple
    start: float
    `end`: float
    octave: float
    step: float
    vol: float

func process*(music: var seq[ProcessedNote], notes: openArray[Note]; m_start: float, speed: float=1, gain:float = 1) =
    ## Adds a list of notes to the music list
    var start = m_start
    var t = start
    for note in notes:
        let vol = note[3]
        start = min(t, t + note[0] / speed)
        let `end` = max(t, t + note[0] / speed)
        music &= ((start, `end`, note[1], note[2], vol * gain))
        t = `end`

func bisect(music: openArray[ProcessedNote], x: (float, float)): int =
    ## Return the index where to insert item `x` in list `music`, assuming `music` is sorted.
    music.lowerBound(x, (m, key) => cmp((m[0], m[1]), key))


func freq(octave, step: float): float =
    ## Returns the frequency of a note
    55 * pow(2, (octave + step / 12 - 1))

func tone(f, t: float): float =
    ## Returns the intensity of a tone of frequency f sampled at time t
    # https://dsp.stackexchange.com/questions/46598/mathematical-equation-for-the-sound-wave-that-a-piano-makes
    # https://youtu.be/ogFAHvYatWs?t=254
    # return int(2**13*(1+square(t, 440*2**(math.floor(5*t)/12))))
    # Y = sum([math.sin(2 * i * math.pi * t * f) * math.exp(-0.0004 * 2 * math.pi * t * f) / 2**i for i in range(1, 4)])
    # Y += Y * Y * Y
    # Y *= 1 + 16 * t * math.exp(-6 * t)
    let w = 2 * PI * f
    var Y = 0.6 * math.sin(w * t) * math.exp(-0.001 * w * t)
    Y += 0.2 * math.sin(2 * w * t) * math.exp(-0.001 * w * t)
    Y += 0.05 * math.sin(3 * w * t) * math.exp(-0.001 * w * t)
    Y += Y * Y * Y
    Y *= 1 + 16 * t * math.exp(-6 * t)
    Y

const bias: float = pow(2.0, 28.0)
func at*(music: openArray[ProcessedNote], t: float): int32 =
    ## Returns the total intensity of music sampled at time t
    let i: int = music.bisect((t, pow(2.0, 31.0)))
    # This is actually pretty efficient ngl
    # Because people usually don't have that many overlapping notes
    var ret: float = 0
    # this `32` is flaky
    # maybe some notes are longer?
    for j in (max(i - 32, 0) ..< i):
        let m = music[j]
        if m[0] + m[1] > t:
            ret += m[4] * tone(freq(m[2], m[3]), t - m[0])
    int32(ret * bias)