# llama.cpp clone with better CPU performance

[![License: MIT](https://img.shields.io/badge/license-MIT-blue.svg)](https://opensource.org/licenses/MIT)

## TL;DR

This repository is a clone of [llama.cpp](https://github.com/ggerganov/llama.cpp) with the following improvements
* Better implementation of CPU matrix multiplications (`AVX2` and `ARM_NEON`) for `fp16/fp32` and all k-, i-, and legacy `llama.cpp` quants, that leads to a significant improvement in prompt processing (PP) speed, typically in the range of 2X, but up to 4X for some quantization types. Token generation (TG) also benefits, but to a lesser extent due to TG being memory bound
* Faster CPU inference for MoE models with similar performance gains
* Implementation of the [Bitnet b1.58](https://huggingface.co/1bitLLM/bitnet_b1_58-3B) model for the CPU (`AVX2` and `ARM_NEON`) and GPU (`CUDA` and `Metal`). This implementation is much faster than the unmerged `llama.cpp` [PR-8151](https://github.com/ggerganov/llama.cpp/pull/8151)

If you are not already familiar with [llama.cpp](https://github.com/ggerganov/llama.cpp), it is better to start there. For those familiar with `llama.cpp`, everything here works the same as in `llama.cpp` (or at least the way `llama.cpp` worked when I last synced on Aug 12 2024).

Note that I have published some, but not all, of the code in this repository in a series of [llamafile](https://github.com/Mozilla-Ocho/llamafile) PRs ([394](https://github.com/Mozilla-Ocho/llamafile/pull/394), [405](https://github.com/Mozilla-Ocho/llamafile/pull/405), [428](https://github.com/Mozilla-Ocho/llamafile/pull/428), [435](https://github.com/Mozilla-Ocho/llamafile/pull/435), [453](https://github.com/Mozilla-Ocho/llamafile/pull/453), and [464](https://github.com/Mozilla-Ocho/llamafile/pull/464))

The implementation of matrix-matrix and matrix-vector multiplications is in a single C++ source file (`iqk_mul_mat.cpp`) with just two interface functions `iqk_mul_mat` (`fp16/fp32` and quantized matrix multiplications) and `iqk_mul_mat_moe` (as `iqk_mul_mat` but meant to be used for the FFN part of a MoE model). Under the hood `iqk_mul_mat_moe` uses the same implementation as `iqk_mul_mat`, with the only difference being where results are stored in memory. Bitnet quantization related stuff is in `iqk-quantize.cpp`.   

## Why?

Mostly out of curiosity:
* Justine Tunney's `tinyBLAS`, which she contributed to `llama.cpp` in [PR 6414](https://github.com/ggerganov/llama.cpp/pull/6414), only works for `Q4_0`, `Q8_0` and `fp16/bf16` models. In the surrounding discussion about possibly extending `tinyBLAS` to k- and i-quants, she felt that k-quants are [not amenable to block-tiling](https://github.com/ggerganov/llama.cpp/pull/6840#issuecomment-2072995387), which is required to improve performance. This statement piqued my curiosity, so here we are.
* Bitnet-1.58b has been one of the [most discussed topics](https://github.com/ggerganov/llama.cpp/issues/5761#issuecomment-2198380366) in the `llama.cpp` project, so eventually I decided to see how efficiently one can implement a ternary model

Curiosity aside, improved CPU performance may be (or may become) important in practice. According to The Register, 70% of AI inference [is done on the CPU of mobile phones](https://www.theregister.com/2024/05/30/arm_cortex_x925_ai_cores/?td=rt-3a), at least in the Android world (but I haven't come around to actually comparing performance on a phone). With ever increasing number of LLM model parameters, and with Meta's 400B model just released, the CPU may become the only viable option for people not willing (or not able to) rent/buy uber expensive GPU instances capable of running such models. Granted, one would need a pretty beefy computer to run a 400B model, and inference speed will be sluggish, but at least one will not need to spend the equivalent of a luxury apartment in the downtown of the city where I live to buy the GPU system capable of running the model.

## Performance comparison to llama.cpp

The results in the following tables are obtained with these parameters:
* Model is LLaMA-v3-8B for `AVX2` and LLaMA-v2-7B for `ARM_NEON`
* The `AVX2` CPU is a 16-core Ryzen-7950X
* The `ARM_NEON` CPU is M2-Max
* `tinyBLAS` is enabled in `llama.cpp`
* `llama.cpp` results are for `build: 081fe431 (3441)`, which was the current `llama.cpp` master branch when I pulled on July 23 2024.
* The projects are built without `CUDA` support, no `BLAS`, and Accelerate framework disabled

### Prompt processing

Here I set the number of threads to be equal to the number of (performance) cores of the CPU, so 16 threads for the Ryzen-7950X and 8 threads for the M2-Max. The following table summarizes the results. To not make the table too long, I have listed only quantized models containing predominantly one quantization type (i.e., excluded the `QX_K - Medium/Large` variants, which are typically a mix of `QX_K` and `Q(X+1)_K`, as well as `IQ2_S` and `IQ3_XS`).  

The command line to generate the benchmark data is
```
./bin/llama-bench -m $model -p 512 -n 0 -t $num_threads -ngl 0
```

| Quantization|       size | backend    | threads | t/s (llama.cpp)  | t/s (iqk_mul_mat)| Speedup |
| ----------- | ---------: | ---------- | ------: | ---------------: | ---------------: | ------: |
| 8B F16      |  14.96 GiB | AVX2       |      16 |    112.37 ± 0.40 |    131.27 ± 0.38 |  1.168  |
| 7B F16      |  12.55 GiB | NEON       |       8 |     90.28 ± 1.25 |     95.34 ± 0.15 |  1.056  |
| 8B Q8_0     |   7.95 GiB | AVX2       |      16 |    118.07 ± 0.53 |    134.00 ± 0.47 |  1.135  |
| 7B Q8_0     |   6.67 GiB | NEON       |       8 |     77.25 ± 1.81 |     94.14 ± 1.15 |  1.219  |
| 8B Q4_0     |   4.35 GiB | AVX2       |      16 |    104.46 ± 0.33 |    130.20 ± 0.29 |  1.246  |
| 7B Q4_0     |   3.57 GiB | NEON       |       8 |     65.46 ± 0.79 |     76.22 ± 0.71 |  1.164  |
| 8B Q4_1     |   4.77 GiB | AVX2       |      16 |     57.83 ± 0.24 |    160.69 ± 0.49 |  2.779  |
| 7B Q4_1     |   3.95 GiB | NEON       |       8 |     37.40 ± 0.50 |     65.83 ± 0.98 |  1.760  |
| 8B Q5_0     |   5.22 GiB | AVX2       |      16 |     53.50 ± 0.35 |    122.62 ± 0.48 |  2.292  |
| 7B Q5_0     |   4.34 GiB | NEON       |       8 |     29.31 ± 0.51 |     67.51 ± 1.17 |  2.303  |
| 8B Q5_1     |   5.64 GiB | AVX2       |      16 |     50.85 ± 0.36 |    147.15 ± 0.47 |  2.894  |
| 7B Q5_1     |   4.72 GiB | NEON       |       8 |     26.02 ± 0.37 |     58.49 ± 0.85 |  2.248  |
| 8B Q2_K_S   |   2.78 GiB | AVX2       |      16 |    110.11 ± 0.28 |    192.47 ± 1.35 |  1.748  |
| 7B Q2_K_S   |   2.16 GiB | NEON       |       8 |     35.44 ± 0.06 |     77.93 ± 1.64 |  2.199  |
| 8B Q3_K_S   |   3.41 GiB | AVX2       |      16 |     77.42 ± 0.36 |    181.64 ± 0.44 |  2.346  |
| 7B Q3_K_S   |   2.75 GiB | NEON       |       8 |     26.79 ± 0.03 |     59.38 ± 1.08 |  2.216  |
| 8B Q4_K_S   |   4.36 GiB | AVX2       |      16 |     98.92 ± 0.34 |    185.35 ± 0.39 |  1.874  |
| 7B Q4_K_S   |   3.59 GiB | NEON       |       8 |     46.55 ± 0.67 |     76.31 ± 0.38 |  1.639  |
| 8B Q5_K_S   |   5.21 GiB | AVX2       |      16 |     69.44 ± 0.31 |    179.62 ± 0.69 |  2.587  |
| 7B Q5_K_S   |   4.33 GiB | NEON       |       8 |     30.18 ± 0.23 |     65.34 ± 0.79 |  2.165  |
| 8B Q6_K     |   6.14 GiB | AVX2       |      16 |     74.89 ± 0.26 |    181.86 ± 0.55 |  2.428  |
| 7B Q6_K     |   5.15 GiB | NEON       |       8 |     28.12 ± 1.24 |     60.75 ± 1.15 |  2.160  |
| 8B IQ2_XXS  |   2.23 GiB | AVX2       |      16 |     42.57 ± 0.16 |    126.63 ± 0.55 |  2.975  |
| 7B IQ2_XXS  |   1.73 GiB | NEON       |       8 |     20.87 ± 0.20 |     64.29 ± 1.12 |  3.080  |
| 8B IQ2_XS   |   2.42 GiB | AVX2       |      16 |     46.45 ± 0.27 |    125.46 ± 0.43 |  2.701  |
| 7B IQ2_XS   |   1.89 GiB | NEON       |       8 |     22.77 ± 0.21 |     51.15 ± 0.24 |  2.246  |
| 8B IQ2_M    |   2.74 GiB | AVX2       |      16 |     40.76 ± 0.18 |    113.07 ± 0.48 |  2.774  |
| 7B IQ2_M    |   2.20 GiB | NEON       |       8 |     14.95 ± 0.26 |     44.87 ± 0.50 |  3.001  |
| 8B IQ3_XXS  |   3.04 GiB | AVX2       |      16 |     31.95 ± 0.20 |    109.86 ± 0.45 |  3.438  |
| 7B IQ3_XXS  |   2.41 GiB | NEON       |       8 |     14.40 ± 0.10 |     53.58 ± 0.85 |  3.721  |
| 8B IQ3_S    |   3.42 GiB | AVX2       |      16 |     28.04 ± 0.08 |     96.28 ± 0.45 |  3.434  |
| 7B IQ3_S    |   2.75 GiB | NEON       |       8 |     12.08 ± 0.30 |     49.72 ± 0.06 |  4.116  |
| 8B IQ4_XS   |   4.13 GiB | AVX2       |      16 |     68.98 ± 0.31 |    180.34 ± 0.55 |  2.614  |
| 7B IQ4_XS   |   3.37 GiB | NEON       |       8 |     40.67 ± 1.97 |     75.11 ± 1.97 |  1.847  |
| 8B IQ4_NL   |   4.35 GiB | AVX2       |      16 |     59.94 ± 0.21 |    129.06 ± 0.43 |  2.153  |
| 7B IQ4_NL   |   3.56 GiB | NEON       |       8 |     34.36 ± 0.81 |     76.02 ± 1.36 |  2.212  |

We see that `llama.cpp` achieves respectable performance for `fp16`, `Q8_0`, and `Q4_0`, being only up to 25% slower than this implementation. This is thanks to the use of Justine Tunney's `tinyBLAS`, which is utilized for these quantization types. For all other quants we observe performance gains in the `1.75X - 4X` range, which is not a small feat considering that the `ggml` matrix multiplication functions has been rewritten several times since `llama.cpp` was first published. Performance gains are larger for i-quants due to the higher quant unpacking cost (see discussion in "To tile or not to tile")

### Token generation

On the Ryzen-7950X TG is memory bound, and for many quantization types peak performance is achieved at just 4 threads. Hence, only results for 2 and 4 threads are shown for `AVX2`. The M2-Max has a much more capable memory subsystem and as a result performance keep increasing up to 8 threads. Thus, results are given for up to 8 threads for `ARM_NEON`.

The command line to generate the data was
```
./bin/llama-bench -m $model -p 0 -n 128 -t $num_threads -ngl 0
```

| Quantization|       size | backend    | threads | t/s (llama.cpp)  | t/s (iqk_mul_mat)| Speedup |
| ---------- | ---------: | ---------- | ------: | ---------------: | ---------------: | ------: |
| 8B F16     |  14.96 GiB | AVX2       |       1 |      2.20 ± 0.00 |      2.25 ± 0.00 |  1.023  |
|            |            |            |       2 |      3.63 ± 0.00 |      3.68 ± 0.00 |  1.014  |
|            |            |            |       4 |      4.20 ± 0.00 |      4.20 ± 0.00 |  1.000  |
| 7B F16     |  12.55 GiB | NEON       |       2 |      6.94 ± 0.27 |      7.40 ± 0.01 |  1.066  |
|            |            |            |       4 |      8.73 ± 0.01 |      8.83 ± 0.01 |  1.011  |
|            |            |            |       6 |      9.05 ± 0.02 |      9.05 ± 0.01 |  1.000  |
| 8B Q8_0    |   7.95 GiB | AVX2       |       2 |      5.03 ± 0.00 |      7.87 ± 0.00 |  1.565  |
|            |            |            |       4 |      7.40 ± 0.00 |      7.82 ± 0.00 |  1.057  |
| 7B Q8_0    |   6.67 GiB | NEON       |       2 |      8.29 ± 0.44 |     12.07 ± 0.10 |  1.456  |
|            |            |            |       4 |     13.53 ± 0.03 |     15.77 ± 0.08 |  1.166  |
|            |            |            |       8 |     16.24 ± 0.10 |     16.94 ± 0.04 |  1.043  |
| 8B Q4_0    |   4.35 GiB | AVX2       |       2 |      6.36 ± 0.00 |     10.28 ± 0.00 |  1.616  |
|            |            |            |       4 |     10.97 ± 0.06 |     13.55 ± 0.07 |  1.235  |
| 7B Q4_0    |   3.57 GiB | NEON       |       2 |      9.77 ± 0.02 |     13.69 ± 0.03 |  1.401  |
|            |            |            |       4 |     17.82 ± 0.06 |     23.98 ± 0.11 |  1.346  |
|            |            |            |       8 |     26.63 ± 0.41 |     29.86 ± 0.04 |  1.121  |
| 8B Q4_1    |   4.77 GiB | AVX2       |       2 |      5.11 ± 0.00 |     11.45 ± 0.00 |  2.241  |
|            |            |            |       4 |      9.08 ± 0.02 |     12.58 ± 0.00 |  1.385  |
| 7B Q4_1    |   3.95 GiB | NEON       |       2 |      9.11 ± 0.06 |     14.62 ± 0.04 |  1.605  |
|            |            |            |       4 |     17.04 ± 0.09 |     24.08 ± 0.28 |  1.413  |
|            |            |            |       8 |     25.26 ± 0.24 |     27.23 ± 0.14 |  1.078  |
| 8B Q5_0    |   5.22 GiB | AVX2       |       2 |      5.31 ± 0.01 |      8.30 ± 0.01 |  1.563  |
|            |            |            |       4 |      9.40 ± 0.01 |     11.47 ± 0.00 |  1.220  |
| 7B Q5_0    |   4.34 GiB | NEON       |       2 |      7.26 ± 0.06 |      7.52 ± 0.00 |  1.036  |
|            |            |            |       4 |     13.63 ± 0.18 |     14.16 ± 0.10 |  1.039  |
|            |            |            |       8 |     22.55 ± 0.35 |     24.34 ± 0.22 |  1.079  |
| 8B Q5_1    |   5.64 GiB | AVX2       |       2 |      4.52 ± 0.00 |      8.86 ± 0.00 |  1.960  |
|            |            |            |       4 |      7.72 ± 0.05 |     10.68 ± 0.03 |  1.383  |
| 7B Q5_1    |   4.72 GiB | NEON       |       2 |      6.51 ± 0.01 |      6.42 ± 0.03 |  0.986  |
|            |            |            |       4 |     12.26 ± 0.18 |     12.21 ± 0.14 |  0.996  |
|            |            |            |       8 |     20.33 ± 0.52 |     21.85 ± 0.22 |  1.075  |
| 8B Q2_K_S  |   2.78 GiB | AVX2       |       2 |     11.30 ± 0.00 |     13.06 ± 0.01 |  1.156  |
|            |            |            |       4 |     18.70 ± 0.00 |     19.04 ± 0.65 |  1.014  |
| 7B Q2_K_S  |   2.16 GiB | NEON       |       2 |      8.42 ± 0.05 |     11.97 ± 0.10 |  1.422  |
|            |            |            |       4 |     15.74 ± 0.01 |     22.09 ± 0.08 |  1.403  |
|            |            |            |       8 |     27.35 ± 0.05 |     38.32 ± 0.05 |  1.401  |
| 8B Q3_K_S  |   3.41 GiB | AVX2       |       2 |      8.58 ± 0.00 |     10.82 ± 0.00 |  1.261  |
|            |            |            |       4 |     15.26 ± 0.01 |     16.25 ± 0.01 |  1.065  |
| 7B Q3_K_S  |   2.75 GiB | NEON       |       2 |      6.40 ± 0.02 |      9.12 ± 0.09 |  1.425  |
|            |            |            |       4 |     12.17 ± 0.00 |     17.11 ± 0.03 |  1.406  |
|            |            |            |       8 |     22.04 ± 0.08 |     31.39 ± 0.31 |  1.424  |
| 8B Q4_K_S  |   4.36 GiB | AVX2       |       2 |      9.61 ± 0.00 |     10.72 ± 0.01 |  1.116  |
|            |            |            |       4 |     13.24 ± 0.31 |     13.28 ± 0.01 |  1.003  |
| 7B Q4_K_S  |   3.59 GiB | NEON       |       2 |     11.15 ± 0.05 |     12.93 ± 0.09 |  1.160  |
|            |            |            |       4 |     20.24 ± 0.16 |     23.49 ± 0.29 |  1.161  |
|            |            |            |       8 |     25.76 ± 0.07 |     28.31 ± 0.22 |  1.099  |
| 8B Q5_K_S  |   5.21 GiB | AVX2       |       2 |      7.45 ± 0.00 |      9.73 ± 0.00 |  1.306  |
|            |            |            |       4 |     11.05 ± 0.33 |     11.43 ± 0.02 |  1.034  |
| 7B Q5_K_S  |   4.33 GiB | NEON       |       2 |      7.20 ± 0.04 |      8.81 ± 0.04 |  1.224  |
|            |            |            |       4 |     13.62 ± 0.15 |     16.81 ± 0.16 |  1.234  |
|            |            |            |       8 |     20.56 ± 0.19 |     23.96 ± 0.14 |  1.165  |
| 8B Q6_K    |   6.14 GiB | AVX2       |       2 |      7.53 ± 0.00 |      9.42 ± 0.00 |  1.251  |
|            |            |            |       4 |      9.74 ± 0.00 |      9.97 ± 0.01 |  1.024  |
| 7B Q6_K    |   5.15 GiB | NEON       |       2 |      6.85 ± 0.04 |      8.30 ± 0.06 |  1.212  |
|            |            |            |       4 |     13.03 ± 0.05 |     15.47 ± 0.17 |  1.187  |
|            |            |            |       8 |     18.52 ± 0.07 |     20.67 ± 0.08 |  1.116  |
| 8B IQ2_XXS |   2.23 GiB | AVX2       |       2 |      5.33 ± 0.01 |      6.40 ± 0.00 |  1.201  |
|            |            |            |       4 |     10.06 ± 0.03 |     11.76 ± 0.03 |  1.169  |
| 7B IQ2_XXS |   1.73 GiB | NEON       |       2 |      5.07 ± 0.04 |      5.22 ± 0.05 |  1.030  |
|            |            |            |       4 |      9.63 ± 0.00 |      9.91 ± 0.07 |  1.029  |
|            |            |            |       8 |     17.40 ± 0.50 |     18.65 ± 0.22 |  1.072  |
| 8B IQ2_XS  |   2.42 GiB | AVX2       |       2 |      5.83 ± 0.00 |      6.55 ± 0.00 |  1.123  |
|            |            |            |       4 |     10.88 ± 0.09 |     12.07 ± 0.07 |  1.109  |
| 7B IQ2_XS  |   1.89 GiB | NEON       |       2 |      5.52 ± 0.01 |      5.60 ± 0.00 |  1.014  |
|            |            |            |       4 |     10.50 ± 0.01 |     11.15 ± 0.00 |  1.062  |
|            |            |            |       8 |     18.19 ± 1.30 |     20.94 ± 0.19 |  1.151  |
| 8B IQ2_M   |   2.74 GiB | AVX2       |       2 |      5.12 ± 0.01 |      5.17 ± 0.00 |  1.010  |
|            |            |            |       4 |      9.60 ± 0.28 |      9.68 ± 0.16 |  1.008  |
| 7B IQ2_M   |   2.20 GiB | NEON       |       2 |      3.73 ± 0.02 |      4.53 ± 0.00 |  1.214  |
|            |            |            |       4 |      7.14 ± 0.05 |      8.70 ± 0.06 |  1.218  |
|            |            |            |       8 |     11.99 ± 0.48 |     16.41 ± 0.05 |  1.369  |
| 8B IQ3_XXS |   3.04 GiB | AVX2       |       2 |      4.06 ± 0.01 |      5.00 ± 0.00 |  1.232  |
|            |            |            |       4 |      7.75 ± 0.02 |      9.13 ± 0.45 |  1.178  |
| 7B IQ3_XXS |   2.41 GiB | NEON       |       2 |      3.53 ± 0.00 |      3.82 ± 0.00 |  1.082  |
|            |            |            |       4 |      6.74 ± 0.04 |      7.42 ± 0.07 |  1.103  |
|            |            |            |       8 |     11.96 ± 0.40 |     13.19 ± 0.29 |  1.103  |
| 8B IQ3_S   |   3.42 GiB | AVX2       |       2 |      3.62 ± 0.00 |      4.06 ± 0.00 |  1.122  |
|            |            |            |       4 |      6.80 ± 0.01 |      7.62 ± 0.10 |  1.121  |
| 7B IQ3_S   |   2.75 GiB | NEON       |       2 |      2.96 ± 0.01 |      3.21 ± 0.03 |  1.084  |
|            |            |            |       4 |      5.68 ± 0.01 |      6.25 ± 0.05 |  1.100  |
|            |            |            |       8 |     10.32 ± 0.25 |     11.11 ± 0.37 |  1.077  |
| 8B IQ4_XS  |   4.13 GiB | AVX2       |       2 |      8.08 ± 0.00 |     11.35 ± 0.00 |  1.405  |
|            |            |            |       4 |     13.36 ± 0.72 |     14.32 ± 0.24 |  1.072  |
| 7B IQ4_XS  |   3.37 GiB | NEON       |       2 |      9.87 ± 0.03 |     12.06 ± 0.00 |  1.222  |
|            |            |            |       4 |     17.78 ± 0.23 |     22.06 ± 0.28 |  1.241  |
|            |            |            |       8 |     27.62 ± 0.09 |     29.70 ± 0.39 |  1.075  |
| 8B IQ4_NL  |   4.35 GiB | AVX2       |       2 |      5.52 ± 0.00 |     10.26 ± 0.00 |  1.859  |
|            |            |            |       4 |     10.78 ± 0.01 |     13.69 ± 0.08 |  1.270  |
| 7B IQ4_NL  |   3.56 GiB | NEON       |       2 |      8.32 ± 0.01 |     13.54 ± 0.01 |  1.627  |
|            |            |            |       4 |     15.89 ± 0.00 |     24.28 ± 0.29 |  1.528  |
|            |            |            |       8 |     26.56 ± 0.36 |     29.87 ± 0.08 |  1.125  |

Here gains are generally lower compared to PP due to TG performance being limited by memory bandwidth. Nevertheless, for some quants/architectures/threads the speedup is quite remarkable (e.g., almost a factor of 2 for `Q5_1` on `AVX2` with 2 threads).  

## MoE models

There is [PR-6840](https://github.com/ggerganov/llama.cpp/pull/6840) from Justine Tunney in `llama.cpp`, but it has not been merged since April 23, so I'll compare performance to the master branch for Mixtral-8x7B. As Mixtral8x7B quantization is quite a lengthy process, the following table shows data only for `Q4_K_S` (a commonly used k-quant, 4 bit), `Q5_0` (a legacy quant, 5 bit), and `IQ4_XXS` (a 3-bit i-quant)

| model        |       size | backend    | threads |     test |  t/s (llama.cpp) | t/s (iqk_mul_mat)| Speedup |
| ------------ | ---------: | ---------- | ------: | -------: | ---------------: | ---------------: | ------: |
| 8x7B Q4_K_S  |  48.75 GiB | AVX2       |      16 |    pp512 |     54.92 ± 0.23 |    102.94 ± 0.37 |  1.874  |
|              |            | NEON       |       8 |    pp512 |     23.54 ± 1.56 |     38.32 ± 0.54 |  1.628  |
|              |            | AVX2       |       4 |    tg128 |      7.80 ± 0.07 |      7.83 ± 0.09 |  1.004  |
|              |            | NEON       |       8 |    tg128 |     14.95 ± 0.25 |     15.28 ± 0.24 |  2.022  |
| 8x7B IQ3_XXS |  33.07 GiB | AVX2       |      16 |    pp512 |     17.58 ± 0.04 |     68.45 ± 0.22 |  3.894  |
|              |            | NEON       |       8 |    pp512 |      7.75 ± 0.04 |     34.67 ± 0.40 |  4.474  |
|              |            | AVX2       |       4 |    tg128 |      4.60 ± 0.01 |      5.45 ± 0.09 |  1.185  |
|              |            | AVX2       |       8 |    tg128 |      8.04 ± 0.65 |      9.83 ± 0.06 |  1.223  |
|              |            | AVX2       |      16 |    tg128 |     10.42 ± 0.01 |     10.57 ± 0.01 |  1.014  |
|              |            | NEON       |       8 |    tg128 |      6.19 ± 1.16 |      7.27 ± 0.14 |  1.174  |
| 8x7B Q5_0    |  59.11 GiB | AVX2       |      16 |    pp512 |     29.06 ± 0.43 |     62.67 ± 0.32 |  2.157  |
|              |            | NEON       |       8 |    pp512 |     15.17 ± 0.51 |     27.36 ± 1.03 |  1.804  |
|              |            | AVX2       |       4 |    tg128 |      5.44 ± 0.10 |      6.81 ± 0.06 |  1.252  |
|              |            | NEON       |       8 |    tg128 |     12.03 ± 0.77 |     12.41 ± 1.27 |  1.032  |


## Bitnet-1.58B

Two implementations are provided
* `IQ1_BN` - uses 1.625 bits-per-weight (bpw)
* `IQ2_BN` - uses 2.0 bpw

`IQ2_BN` is faster for PP (CPU and GPU, although the PP performance difference on CUDA is very minor). `IQ1_BN` can arrive at a higher TG performance on the Ryzen-7950X (given enough threads) because of the smaller model size, but it is always slower on the GPU and on the M2-Max CPU.

There is the unmerged [PR 8151](https://github.com/ggerganov/llama.cpp/pull/8151) in `llama.cpp` that implements Bitnet-1.58B for the CPU (`AVX` and `ARM_NEON`, no GPU implementation). The following table compares performance between this repo and `PR-8151` in `llama.cpp`. The CUDA results were obtained on an RTX-4080, the Metal results on a 30-core M2-Max GPU.

| model       |       size | backend    | threads |   test | t/s (llama.cpp)  | t/s (this repo)| Speedup |
| ----------- | ---------: | ---------- | ------: | -----: | ---------------: | -------------: | ------: |
| 3B - IQ1_BN | 729.64 MiB | AVX2       |      16 |  pp512 |    120.61 ± 0.48 | 423.19 ± 1.28  |  3.509  |
|             |            | NEON       |       8 |  pp512 |     46.64 ± 0.02 | 205.90 ± 0.88  |  4.415  |
|             |            | CUDA       |       8 |  pp512 |           -      | 10660 ± 170    |    -    |
|             |            | Metal      |       8 |  pp512 |           -      | 698.25 ± 1.91  |    -    |
|             |            | AVX2       |       2 |  tg128 |     15.79 ± 0.01 |  22.13 ± 0.02  |  1.402  |
|             |            | AVX2       |       4 |  tg128 |     28.64 ± 1.72 |  40.14 ± 0.04  |  1.402  |
|             |            | AVX2       |       8 |  tg128 |     48.91 ± 0.08 |  61.79 ± 0.09  |  1.263  |
|             |            | AVX2       |      16 |  tg128 |     57.73 ± 0.05 |  60.79 ± 0.05  |  1.053  |
|             |            | NEON       |       2 |  tg128 |     11.43 ± 0.04 |  16.87 ± 0.02  |  1.476  |
|             |            | NEON       |       4 |  tg128 |     21.11 ± 0.05 |  30.66 ± 0.11  |  1.452  |
|             |            | NEON       |       8 |  tg128 |     37.36 ± 0.07 |  55.21 ± 0.16  |  1.478  |
|             |            | CUDA       |       8 |  tg128 |           -      | 301.44 ± 0.12  |    -    |
|             |            | Metal      |       8 |  tg128 |           -      |  76.70 ± 0.07  |    -    |
| 3B - IQ2_BN | 873.65 MiB | AVX2       |      16 |  pp512 |    151.39 ± 0.35 | 540.82 ± 2.48  |  3.572  |
|             |            | NEON       |       8 |  pp512 |     46.54 ± 0.03 | 242.05 ± 0.34  |  5.201  |
|             |            | CUDA       |       8 |  pp512 |           -      | 10800 ± 160    |    -    |
|             |            | Metal      |       8 |  pp512 |           -      | 723.19 ± 0.53  |    -    |
|             |            | AVX2       |       2 |  tg128 |     18.93 ± 0.02 |  38.34 ± 0.08  |  2.026  |
|             |            | AVX2       |       4 |  tg128 |     34.54 ± 0.06 |  56.29 ± 0.07  |  1.630  |
|             |            | AVX2       |       8 |  tg128 |     52.97 ± 0.07 |  53.44 ± 0.08  |  1.009  |
|             |            | AVX2       |      16 |  tg128 |     51.84 ± 0.25 |  53.46 ± 0.07  |  1.031  |
|             |            | NEON       |       2 |  tg128 |     11.40 ± 0.02 |  32.01 ± 0.27  |  2.808  |
|             |            | NEON       |       4 |  tg128 |     20.99 ± 0.00 |  56.45 ± 0.11  |  2.689  |
|             |            | NEON       |       8 |  tg128 |     37.28 ± 0.08 |  89.77 ± 0.70  |  2.408  |
|             |            | CUDA       |       8 |  tg128 |           -      | 322.10 ± 0.07  |    -    |
|             |            | Metal      |       8 |  tg128 |           -      | 110.39 ± 0.13  |    -    |

We can make the following observations:
* For prompt processing this Bitnet-1.58b implementation is massively better than PR-8151 in `llama.cpp`, with gains between 3.4X and 5.2X!
* We get `PP-512 = 520 t/s` for the 2.0 bpw variant on the Ryzen-7950X, which costs less than $500. Hey, who needs a GPU?  
* For low number of threads (2), this implementation is also much faster than PR-8151 for TG, where speed gains are between 1.4X and 2.8X. As we become memory bound on the Ryzen-7950X, the speed advantage goes away there for sufficiently high number of threads. But on the M2-Max this implementation is 1.4X (1.625 bpw) or 2.4X faster even at 8 threads
* Looking at TG on the M2-Max, the GPU looks a bit like wasted silicon (90 vs 110 t/s for TG-128 and the 2.0 bpw variant). If the GPU transistors had been spent to double the M2 number of CPU cores (and all memory bandwidth is given to the CPU), the CPU would be wiping the floor with the GPU.
* I'm of course kidding with the above. Still, it seems there are massive inefficiencies in the `llama.cpp` Metal implementation that start showing up when matrix multiplications become very fast as is the case here. The difference between CPU and GPU prompt processing speed is typically at least a factor of 7 in favor of the GPU on the M2-Max, but it is only around a factor of 3 here.
* It is worth noting that one needs to offload the token embeddings tensor to the GPU, else performance on CUDA/Metal is significantly lower. Bitnet uses the same tensor for token embeddings and for output. Mainline `llama.cpp` currently puts the token embeddings tensor on the CPU, and this results in running the matrix multiplication with the output tensor on the CPU. This most likely affects other models as well (e.g., Gemma), but I haven't yet looked into this.

To reproduce these results:
* Clone https://huggingface.co/1bitLLM/bitnet_b1_58-3B
* Run `python3 --outtype f16 path_to_bitnet` to convert to GGUF
* Run `./bin/llama-quantize path_to_bitnet/ggml-model-f16.gguf quantized.gguf [iq1_bn | iq2_bn]`. Note: no imatrix is required (and, if you provide one, it is ignored)
* Caveat: only the 3B Bitnet variant works. The smaller Bitnet models contain tensors with number of columns that are not even a multiple of 32, so basically no `llama.cpp` quant will work for these.  

## To tile or not to tile

The common wisdom for efficient matrix multiplications is to use block tiling, and this is also used here for `fp16/fp32` matrices. But block tiling does not somehow magically reduce the amount of computation that needs to get done. Performance gains are simply due to the better utilization of memory caches. When dealing with quantized matrix multiplications, there is an additional factor that comes into play: the quantized data needs to be unpacked to 8-bit integers before being used in the matrix multiplication multiply-add operations. Depending on quantization type, this unpacking can represent a significant fraction of the overall computation cost. Hence, for best performance, one would want to reuse the unpacked quants as much as possible, thus spending some fraction of the available vector registers to hold the unpacked data. But when using block tiling, one also needs a certain number of vector registers for accumulating results. For instance, on `AVX2` (16 vector registers available), for `fp16/fp32` models best performance is achieved with `2 x 6` tiles (where the `2` refers to rows in the left matrix and is measured in units of the vector register size, so 16/8 floats for `fp16/fp32`, and `6` is for the number of columns in the right matrix). Unpacking quantized data works best when done in blocks of 128 or 256 quants so that, if we wanted to keep unpacked quants for 2 rows, we would need at least 8 vector registers, thus being left with less than 8 registers for result accumulation, so at best `2 x 3` tiles. In practice one needs addition vector registers for various constants that are typically needed for de-quantization, so that, at the end, it becomes better to use `1 x N` "tiles", i.e., a row-wise multiplication where each row in the left matrix is multiplied with `N` columns in the right matrix, thus reusing the unpacked data `N` times. This (i.e., amortizing de-quantization cost) is the main mechanism for seeding up quantized matrix multiplications. Having started with quantized matrices, and having gone from tiles to a row-wise implementation after some experimentation, I did try row-wise multiplication for float matrices first. Performance was not quite as good as for block-tiling, but I did get up to 90-95% of the speed of `tinyBLAS` that way before switching the `fp16/fp32` implementation to `2 x 6` (`AVX2`) or `5 x 5` (`AVX512` and `ARM_NEON`) block-tiles. But even for for `Q8_0 x Q8_0` multiplications, where there is basically no de-quantization cost, row-wise multiplication is faster than tiling (and hence this implemeintation beats `tinyBLAS`, which uses block-tiling also for `Q8_0`).

