# Compute-PI

## GPU acceleration

* Device Info
* Device name: GeForce GTX 770
* Warp size: 32
* multiProcessorCount: 8

* **Gnuplot** command

	> set title 'GPU acceleration'
	> set ylabel 'Speed up'
	> set xlabel 'number of threads'
	> set terminal png
	> set output 'xxx.png'
	> plot "SpeedUp.txt" with points pointtype 7 notitle

### Speed up for 12800000 slices



* 需注意設定的執行緒數量，會很明顯影響到提昇速率
* 當執行緒數量超過 6144 時，便不再有速率提昇，可參考 [**Amdahl's law**](https://zh.wikipedia.org/wiki/%E9%98%BF%E5%A7%86%E8%BE%BE%E5%B0%94%E5%AE%9A%E5%BE%8B)，固定負載下能平行計算的部份有限，因此速度提昇會趨近定值

### Error percentage form 1 to 20480000 slices


### Time cost for 400000000 slices

* **Baseline**: 2.999478(s)
* **OpenMP**
* **2** threads: 1.460224(s)
* **4** threads: 0.767469(s)
* **AVX**: 1.283873(s)
* **AVX + Loop unroll**: 1.169533(s)
* **6144 GPU threads** (threads per block = 256): 0.070991(s)

**Source of this article: https://hackmd.io/s/SyEgyhlA**