# Namespace faiss::quantize_lut

namespace quantize_lut

Functions to quantize PQ floating-point Look Up Tables (LUT) to uint8, and biases to uint16. The accumulation is supposed to take place in uint16. The quantization coefficients are float (a, b) such that

``` original_value = quantized_value * a / b
```
The hardest part of the quantization is with multiple LUTs that need to be added up together. In that case, coefficient a has to be chosen so that the sum fits in a uint16 accumulator.

Functions

void round_uint8_per_column(float *tab, size_t n, size_t d, float *a_out = nullptr, float *b_out = nullptr)
void round_uint8_per_column_multi(float *tab, size_t m, size_t n, size_t d, float *a_out = nullptr, float *b_out = nullptr)
void quantize_LUT_and_bias(size_t nprobe, size_t M, size_t ksub, bool lut_is_3d, const float *LUT, const float *bias, uint8_t *LUTq, size_t M2, uint16_t *biasq, float *a_out = nullptr, float *b_out = nullptr)

LUT quantization to uint8 and bias to uint16.

(nprobe, M, ksub, lut_is_3d) determine the size of the the LUT

LUT input:

• 2D size (M, ksub): single matrix per probe (lut_is_3d=false)

• 3D size (nprobe, M, ksub): separate LUT per probe (lut_is_3d=true) bias input:

• nullptr: bias is 0

• size (nprobe): one bias per probe Output:

• LUTq uint8 version of the LUT (M size is rounded up to M2)

• biasq (or nullptr): uint16 version of the LUT

• a, b: scalars to approximate the true distance

void aq_quantize_LUT_and_bias(size_t nprobe, size_t M, size_t ksub, const float *LUT, const float *bias, size_t M_norm, int norm_scale, uint8_t *LUTq, size_t M2, uint16_t *biasq, float *a_out, float *b_out)
float aq_estimate_norm_scale(size_t M, size_t ksub, size_t M_norm, const float *LUT)