---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- prefix
- parallel
---

# threshold-prefix-or

4-bit parallel prefix OR operation. Computes running OR from MSB to each position. Used in leading-one detection and any-ones-above detection.

## Circuit

```
    x3      x2      x1      x0
     │       │       │       │
     ▼       ▼       ▼       ▼
   ┌───┐   ┌───┐   ┌───┐   ┌───┐
   │y3 │   │y2 │   │y1 │   │y0 │
   │>=1│   │>=1│   │>=1│   │>=1│
   └───┘   └───┘   └───┘   └───┘
     │       │       │       │
     ▼       ▼       ▼       ▼
   (x3)  (x3|x2) (x3|x2|x1) (all)
```

## Function

```
prefix_or(x3, x2, x1, x0) -> (y3, y2, y1, y0)

y3 = x3
y2 = x3 OR x2
y1 = x3 OR x2 OR x1
y0 = x3 OR x2 OR x1 OR x0
```

Each output yi is the OR of all inputs from x3 down to xi.

## Truth Table (selected)

| x3 x2 x1 x0 | y3 y2 y1 y0 | Meaning |
|-------------|-------------|---------|
| 0 0 0 0 | 0 0 0 0 | All zeros |
| 0 0 0 1 | 0 0 0 1 | Only LSB set |
| 0 0 1 0 | 0 0 1 1 | First one at pos 1 |
| 0 1 0 0 | 0 1 1 1 | First one at pos 2 |
| 1 0 0 0 | 1 1 1 1 | First one at MSB |
| 1 1 1 1 | 1 1 1 1 | All ones |
| 1 0 1 0 | 1 1 1 1 | Mixed pattern |

## Mechanism

**Single-layer parallel implementation:**

| Output | Condition | Weights | Bias |
|--------|-----------|---------|------|
| y3 | x3 >= 1 | [1,0,0,0] | -1 |
| y2 | x3 + x2 >= 1 | [1,1,0,0] | -1 |
| y1 | x3 + x2 + x1 >= 1 | [1,1,1,0] | -1 |
| y0 | x3 + x2 + x1 + x0 >= 1 | [1,1,1,1] | -1 |

All use bias -1 (fires when at least one relevant input is 1).

## Parameters

| | |
|---|---|
| Inputs | 4 |
| Outputs | 4 |
| Neurons | 4 |
| Layers | 1 |
| Parameters | 20 |
| Magnitude | 14 |

## Applications

- **Leading-one detection:** Transition from 0→1 in output marks MSB position
- **Any-bit-set prefix:** y_i = 1 means some bit from MSB to position i is set
- **Carry kill detection:** In adders, prefix-OR of "kill" signals

## Usage

```python
from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def prefix_or(x3, x2, x1, x0):
    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
    y3 = int((inp @ w['y3.weight'].T + w['y3.bias'] >= 0).item())
    y2 = int((inp @ w['y2.weight'].T + w['y2.bias'] >= 0).item())
    y1 = int((inp @ w['y1.weight'].T + w['y1.bias'] >= 0).item())
    y0 = int((inp @ w['y0.weight'].T + w['y0.bias'] >= 0).item())
    return y3, y2, y1, y0

print(prefix_or(0, 0, 1, 0))  # (0, 0, 1, 1)
print(prefix_or(1, 0, 0, 0))  # (1, 1, 1, 1)
```

## License

MIT