import bisect
import math
import struct
import sys

# Number of times to sample each second
bitrate = 44100
music = []


def saw(x):
    """
    Sawtooth wave
    """
    return x / 2 / math.pi % 1


def freq(octave, step):
    """
    Returns the frequency of a note
    """
    return 55 * 2 ** (octave + step / 12 - 1)


def droplet(f, t):
    """
    Returns the intensity of the "droplet" waveform 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
    """
    w = 2 * math.pi * f
    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)
    return Y


def seething(f, t):
    """
    Returns the intensity of the "seething" waveform of frequency f sampled at time t
    """
    w = 2 * math.pi * f
    Y = 0.6 * math.sin(w * t) * math.exp(-0.0005 * w * t)
    Y += 0.1 * math.sin(0.99 * w * t) * math.exp(-0.0005 * w * t)
    Y += 0.1 * math.sin(1.01 * w * t) * math.exp(-0.0005 * w * t)
    Y += 0.2 * math.sin(2 * w * t) * math.exp(-0.0005 * w * t)
    Y += math.copysign(Y * Y, Y)
    Y *= 1 + 16 * t * math.exp(-6 * t)
    Y *= 0.5 * min(24 * t, 1)
    return Y


def honk(f, t):
    """
    Returns the intensity of the "honk" waveform of frequency f sampled at time t
    """
    w = 2 * math.pi * f
    Y = sum([(saw(i * w * t) / 3 + math.sin(i * w * t)) * math.exp(-0.002 * w * t) for i in range(1, 6)]) / 2
    Y = math.copysign(abs(Y) ** (1 / 2), Y)
    return Y


def at(t):
    """
    Returns the total intensity of music sampled at time t
    This is actually pretty efficient ngl
    Because people usually don't have that many overlapping notes
    """
    i = bisect.bisect(music, (t, 2**31))
    ret = 0
    for j in range(max(i - 32, 0), i):
        m = music[j]
        if m[1] > t and m[2] > 0:
            ret += m[4] * m[5](freq(m[2], m[3]), t - m[0])
    return int(2**28 * ret)


def process(notes, start, speed=1, gain=1, blend=0, waveform=droplet):
    """
    Adds a list of notes to the music list
    """
    t = start
    for note in notes:
        vol = 1
        if len(note) == 4:
            vol = note[3]
        start = min(t, t + note[0] / speed)
        end = max(t, t + note[0] / speed)
        music.append((start, end + 16 * int(blend), note[1], note[2], vol * gain, waveform))
        t = end


def play(start, end):
    """
    Print music from the start time to end time encoded in s32 to standard output
    """
    music.sort()
    for i in range(start * bitrate, end * bitrate):
        sys.stdout.buffer.write(struct.pack("i", at(i / bitrate)))