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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)
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