Double Quantization Scale Savings

Problem

Compute the storage bytes for quantization scales before and after double quantization: fp32 scales cost 4 bytes each, while double quantization stores each scale at second_bits and adds one fp32 second-level scale per second_block scales. Return [fp32_bytes, double_quant_bytes].

The signature is double_quant_scale_savings(num_scales, second_bits=8, second_block=256).

Hint

Double quantization treats the first-level scales as data and quantizes them again.

Test cases

case 1

in: [4096,8,256]

expected: [16384,4160]

case 2

in: [256,8,256]

expected: [1024,260]

case 3

in: [100,8,64]

expected: [400,108]

case 4

in: [0,8,256]

expected: [0,0]

case 5

in: [1,4,1]

expected: [4,4.5]

Starter codePython

import math
def double_quant_scale_savings(num_scales, second_bits=8, second_block=256):
    # Your code here
    pass

5 test cases · run your code against them in the editor