import bisect
import math
import struct
import sys

# Number of times to sample each second
bitrate = 44100

intro = [
    (1,3,3),
    (1,3,7),
    (1,3,10),
    (6,4,2),

    (1,3,1),
    (1,3,5),
    (1,3,8),
    (3,4,0),

    (1,2,11),
    (1,3,3),
    (1,3,6),
    (3,3,10),

    (1,2,8),
    (1,3,0),
    (1,3,3),
    (8,3,7),
]

melody = [
    (1,3,3),
    (1,3,7),
    (1,3,10),
    (1,4,2),
    (1,4,3),
    (1,4,7),
    (2,4,8),

    (1,3,1),
    (1,3,5),
    (1,3,8),
    (1,4,0),
    (1,4,1),
    (1,4,5),
    (2,4,8),

    (1,3,3),
    (1,3,7),
    (1,3,10),
    (1,4,2),
    (1,4,3),
    (1,4,10),
    (2,4,3),

    (1,3,1),
    (1,3,5),
    (1,3,8),
    (1,4,0),
    (1,4,10),
    (1,4,8),
    (2,4,10),


    (1,3,3),
    (1,3,7),
    (1,3,10),
    (1,4,2),
    (1,4,3),
    (1,4,7),
    (2,4,8),

    (1,3,1),
    (1,3,5),
    (1,3,8),
    (1,4,0),
    (1,4,1),
    (1,4,5),
    (2,4,1),

    (1,3,3),
    (1,3,7),
    (1,3,10),
    (1,4,2),
    (1,4,3),
    (1,4,10),
    (1,4,8),
    (1,4,7),

    (1,3,1),
    (1,3,5),
    (1,3,8),
    (1,4,0),
    (1,4,10),
    (1,4,8),
    (2,4,10),
]

bass = [
    (1,1,3),
    (1,1,10),
    (1,1,1),
    (1,1,8),
    (1,1,3),
    (1,2,3),
    (1,1,1),
    (1,1,10),
]

melody2 = [
    (1,0,0),
    (1,5,10),
    (1,5,8),
    (1,5,7),
    (1,5,8),
    (3,5,7,2),

    (1,5,3),
    (1,4,10),
    (6,5,1,2),

    (1/2,5,0,2),
    (1/2,5,1,2),
    (3,5,3,2),
    (1/2,5,10,2),
    (7/2,5,3,2),

    (8,0,0),

    (1,0,0),
    (1,5,3),
    (1,5,10),
    (1,5,10),
    (4/3,5,10),
    (4/3,5,8),
    (4/3,5,7),

    (1,0,0),
    (1,5,1),
    (1,5,8),
    (1,5,8),
    (4/3,5,8),
    (4/3,5,8),
    (4/3,5,10),

    (8,0,0),

    (1,0,0),
    (5,5,3,2),
    (2,5,10,2),
]

melody3 = [
    (1,0,0),
    (1,5,10),
    (1/2,5,8,2/3),
    (1/2,5,7,2/3),
    (1/4,5,8,1/2),
    (1/4,5,7,1/2),
    (1/4,5,8,1/2),
    (1/4,5,7,1/2),
    (1,5,8),
    (3,5,7,2),

    (1,5,3),
    (1,4,10),
    (1,5,1),
    (5,5,7,2),

    (1/2,5,7),
    (1/2,5,10),
    (1/4,5,7),
    (1/4,5,10),
    (1/4,5,7),
    (1/4,5,10),
    (1,6,3),
    (2,5,3,2),
    (1/2,6,3),
    (5/2,5,3,2),

    (1/2,5,10),
    (1/2,5,8),
    (1/2,5,7),
    (1/2,5,8),
    (1/2,5,7),
    (1/2,5,3),
    (1/2,4,10),
    (1/2,5,1),
    (1/2,5,0),
    (1/2,4,10),
    (1/2,4,8),
    (1/2,4,10),
    (1/2,5,3),
    (1/2,5,7),
    (1/2,5,3),
    (1/2,5,10),

    (4/3,5,7),
    (4/3,6,3),
    (4/3,6,3),
    (4/3,6,2),
    (4/3,5,10),
    (4/3,5,7),

    (3,5,5),
    (2,5,7),
    (2,5,8),
    (1,6,1),

    (1,5,3),
    (1,5,5),
    (2,5,7),
    (1,5,3),
    (1,5,8),
    (2,5,10),

    (3/2,6,0),
    (3/2,6,1),
    (5,6,3,2),
]

outro = [
    (1,3,3),
    (1,3,7),
    (1,3,10),
    (1,4,2),
    (1,4,3),
    (1,4,7),
    (2,4,8),

    (1,3,1),
    (1,3,5),
    (1,3,8),
    (1,4,0),
    (1,4,1),
    (1,4,5),
    (2,4,8),

    (1,2,11),
    (1,3,3),
    (1,3,6),
    (1,3,10),
    (1.5,3,11),
    (1.5,4,3),
    (3,4,8),

    (1.5,2,8),
    (1.5,3,0),
    (2,3,3),
    (16,3,7,2),
]

def process(notes, start, speed=1, gain=1):
    """
    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, note[1], note[2], vol * gain))
        t = end


# Process all lists of notes
music = []
process(intro, 0, 4)
process(melody, 8, 4)
process(melody, 24, 4)
process(bass, 24, gain=1.5)
process(bass, 32, gain=1.5)
process(melody, 40, 4)
process(melody2, 40, 4)
process(bass, 40, gain=1.5)
process(bass, 48, gain=1.5)
process(melody, 56, 4)
process(melody3, 56, 4)
process(bass, 56, gain=1.5)
process(bass, 64, gain=1.5)
process(outro, 72, 4)
music.sort()


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


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


# Print out music encoded in s16 to standard output
for i in range(0 * bitrate, 84 * bitrate):
    sys.stdout.buffer.write(struct.pack('i', at(i / bitrate)))