1 files changed, 68 insertions, 0 deletions
diff --git a/musiclib.nim b/musiclib.nim
new file mode 100644
index 0000000..7050dd3
--- /dev/null
+++ b/musiclib.nim
@@ -0,0 +1,68 @@
+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)