Graphing the density distribution of audio bit depth formats

bit-depth-density.py

import matplotlib.pyplot as plt
import numpy as np


def bits_to_unit(d, n):
    sign = (n >> (d - 1)) & 1
    mantissa = n & (2**(d - 1) - 1)
    return ((-1) ** sign) * (mantissa / (2 ** (d - 1)))

def bits_to_float32(n):
    sign = (n >> 31) & 1
    exponent = ((n >> 23) & (2 ** 8 - 1)) - (2 ** 7 - 1)
    mantissa = n & (2 ** 23 - 1)
    return ((-1) ** sign) * (1 + mantissa / (2 ** 23)) * (2 ** exponent)

stride = 2**12
bins = np.linspace(-4, 4, 2 ** 10)

dist24u = [bits_to_unit(24, n) for n in range(0, 2**24, stride)]
dist32u = [bits_to_unit(32, n) for n in range(0, 2**32, stride)]
dist32f = [bits_to_float32(n) for n in range(0, 2**32, stride)]

plt.style.use('dark_background')
plt.hist(
    [dist24u, dist32u, dist32f],
    bins,
    label=['24-bit Linear', '32-bit Linear', '32-bit Float'],
    color=['blue', 'red', 'white'],
    alpha=0.75,
    histtype="step",
)
plt.xlim(bins[0], bins[-1])

plt.yscale('log')
plt.xlabel('Amplitude')
plt.ylabel('Resolution')
plt.legend()
plt.title('Audio Bit Depth')

plt.show()