Mapping Function:
Q = round(F/S + Z)
Notice that:
f = (Q - Z) * S
leadsto: f != F
with:
F = Float value
Q = Quantized value
f = Reconstructed float value
Scaling Factor: S Zero-Point: Z
S = (B - A) / (Bq - Aq)
Z = - ( (A / S) - Aq)
with:
A,B = Clipping Range
and, |Bq - Aq| <= (2**bitwidth - 1)
A, B are determined during Calibration which are by default the Max-Min, but could be obtained in several ways (e.g., Entropy Minimization, mean-square-error minimization, ...).
Given the floating matrices If, Wf, Of with Of = If x Wf and their corresponding integer version Ii, Wi, Oi.
Given the respective Scale Factors si, sw, so and the respective Zero Points zi, zw, zo.
The GEMM can be computed as:
Of = If x Wf
so*(Oi - zi) = si*sw*((Ii x Wi) - zi*Wi - zw*Ii)
However, in case of Symmetric Quantization (Zero Points are null):
Of = si*sw*(Ii x Wi)