Rounding error when normalizing color intensity with float16

image_normalization.py

# Images have color pixels encoded as uint8. In computer
# vision and deep learning the images is represented with
# floatingpoints with value in the range [0,1]. This is
# obtained by dividing by 255, the highest color intensity.
# However, reduced precision training an inference become
# the new standard.
#
# What is the magnitude of the rouding error when normalizing
# an image by 255 rather than 256 (256=2^8)?

import numpy as np

colors_u8 = np.arange(1, 256).astype(np.uint8)

# FP32 precision
colors_fp32 = colors_u8.astype(np.float32)
colors_fp32_01_255 = colors_fp32 / 255
colors_fp32_01_256 = colors_fp32 / 256

# FP16 precsion
colors_fp16 = colors_u8.astype(np.float16)
colors_fp16_01_255 = colors_fp16 / 255
colors_fp16_01_256 = colors_fp16 / 256

# Diffenrece
relative_diff_255 = (colors_fp32_01_255 - colors_fp16_01_255).astype(np.float64) / colors_fp32_01_255
diff256 = colors_fp32_01_256 - colors_fp16_01_256

print("/255 relative error:", np.max(np.abs(relative_diff_255)))
print("/256 maximum erro:", np.max(np.abs(diff256)))

# >>> /255 relative error: 0.00042345138386973345
# >>> /256 maximum erro: 0.0

# The rounding error is below 0.05%