the interger bits and mantissa bits after log min max quantize

[zhangying0127]

I do not understand the log min max quantize quite well. can you explain which bits are interger part and which are mantissa part after log min max quantize? How can i get the interger representation of the quantized number? Thank you so much.

[aaron-xichen]

The log min max method actually first scales any float tensor to [0, 1], followed with normal linear quantization.

def linear_quantize(input, sf, bits):
    assert bits >= 1, bits
    if bits == 1:
        return torch.sign(input) - 1
    delta = math.pow(2.0, -sf)
    bound = math.pow(2.0, bits-1)
    min_val = - bound
    max_val = bound - 1
    rounded = torch.floor(input / delta + 0.5)

    clipped_value = torch.clamp(rounded, min_val, max_val) * delta
    return clipped_value

torch.clamp(rounded, min_val, max_val) is the integer representation.

[jeff830107]

Why do you say that the log_minmax method first scales any float tensor to [0,1] and followed with normal linear quantization? It seems that it is followed with the min_max_quantize() function, not the linear_quantize() function.

def log_minmax_quantize(input, bits):
    assert bits >= 1, bits
    if bits == 1:
        return torch.sign(input), 0.0, 0.0
    s = torch.sign(input)
    input0 = torch.log(torch.abs(input) + 1e-20)
    v = min_max_quantize(input0, bits)
    v = torch.exp(v) * s
    return v