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license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- arithmetic
- divider
---
# threshold-divider
4-bit unsigned integer divider as threshold circuit using restoring division algorithm.
## Circuit
```
A[3:0] ──┐ (dividend, 0-15)
├──► Divider ──┬──► Q[3:0] (quotient)
B[3:0] ──┘ (divisor, 1-15) └──► R[3:0] (remainder)
A = Q × B + R, where R < B
```
## Algorithm (Restoring Division)
```
P = 0 (partial remainder)
for i = 3 downto 0:
P = (P << 1) | A[i] // shift in next dividend bit
diff = P - B
if diff >= 0: // P >= B
Q[i] = 1
P = diff // keep subtraction result
else:
Q[i] = 0 // restore P (don't subtract)
R = P (final remainder)
```
## Architecture
Each of 4 stages contains:
| Component | Function | Neurons |
|-----------|----------|---------|
| 4-bit Subtractor | P - B | 28 |
| 4× MUX | Select P or diff | 12 |
**Total: 160 neurons, 496 parameters, 8 layers**
## Example
```
13 ÷ 3:
Stage 3: P=0, shift in 1 → P=1, 1<3, Q[3]=0
Stage 2: P=1, shift in 1 → P=3, 3≥3, Q[2]=1, P=0
Stage 1: P=0, shift in 0 → P=0, 0<3, Q[1]=0
Stage 0: P=0, shift in 1 → P=1, 1<3, Q[0]=0
Result: Q=0100=4, R=0001=1
Verify: 4×3+1=13 ✓
```
## Usage
```python
from safetensors.torch import load_file
w = load_file('model.safetensors')
# Division by zero returns Q=15, R=0
# All 240 test cases verified (16 × 15 non-zero divisors)
```
## Files
```
threshold-divider/
├── model.safetensors
├── create_safetensors.py
├── config.json
└── README.md
```
## License
MIT
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