README.md

---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- bit-manipulation
- ffs
---

# threshold-ffs8

8-bit find first set (FFS). Returns the 1-indexed position of the least significant set bit. Returns 0 if no bits are set.

## Circuit

```
 x7  x6  x5  x4  x3  x2  x1  x0
  │   │   │   │   │   │   │   │
  └───┴───┴───┴───┴───┴───┴───┘
              │
              ▼
    ┌─────────────────────┐
    │  CTZ + 1 (if set)   │
    │  or 0 (if all zero) │
    └─────────────────────┘
              │
              ▼
      [f3, f2, f1, f0]
       (position 0-8)
```

## Function

```
ffs8(x7..x0) -> (f3, f2, f1, f0)

position = 8*f3 + 4*f2 + 2*f1 + f0

if input = 0: position = 0
if input != 0: position = CTZ(input) + 1
```

FFS is 1-indexed: the first bit (x0) is position 1, not 0.

## Truth Table (selected)

| Input (hex) | Binary | FFS | f3 f2 f1 f0 | Meaning |
|-------------|--------|:---:|-------------|---------|
| 0x00 | 00000000 | 0 | 0 0 0 0 | No bits set |
| 0x01 | 00000001 | 1 | 0 0 0 1 | Bit 0 is first |
| 0x02 | 00000010 | 2 | 0 0 1 0 | Bit 1 is first |
| 0x04 | 00000100 | 3 | 0 0 1 1 | Bit 2 is first |
| 0x08 | 00001000 | 4 | 0 1 0 0 | Bit 3 is first |
| 0x10 | 00010000 | 5 | 0 1 0 1 | Bit 4 is first |
| 0x20 | 00100000 | 6 | 0 1 1 0 | Bit 5 is first |
| 0x40 | 01000000 | 7 | 0 1 1 1 | Bit 6 is first |
| 0x80 | 10000000 | 8 | 1 0 0 0 | Bit 7 is first |
| 0xFF | 11111111 | 1 | 0 0 0 1 | Bit 0 is first |

## Relationship to CTZ

```
if (input == 0):
    FFS = 0
else:
    FFS = CTZ + 1
```

FFS and CTZ are closely related:
- CTZ returns 0-7 for positions, 8 for zero input
- FFS returns 1-8 for positions, 0 for zero input

## Mechanism

**Position detectors:** Same as CTZ - detect where first 1 appears from LSB

| Signal | Fires when |
|--------|------------|
| p0 | x0 = 1 |
| p1 | x0 = 0, x1 = 1 |
| p2 | x0 = x1 = 0, x2 = 1 |
| ... | ... |
| p7 | x0..x6 = 0, x7 = 1 |

**Output encoding:** Direct binary encoding of position + 1

- f0 = p0 OR p2 OR p4 OR p6 (positions 0,2,4,6 → FFS 1,3,5,7)
- f1 = p1 OR p2 OR p5 OR p6 (positions 1,2,5,6 → FFS 2,3,6,7)
- f2 = p3 OR p4 OR p5 OR p6 (positions 3,4,5,6 → FFS 4,5,6,7)
- f3 = p7 (position 7 → FFS 8)

## Parameters

| | |
|---|---|
| Inputs | 8 |
| Outputs | 4 |
| Neurons | 12 |
| Layers | 2 |
| Parameters | 76 |
| Magnitude | 48 |

## Usage

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

w = load_file('model.safetensors')

def ffs8(bits):
    # bits = [x0, x1, ..., x7] (LSB first)
    inp = torch.tensor([float(b) for b in bits])
    # ... (see model.py for full implementation)

# Examples
print(ffs8([1,0,0,0,0,0,0,0]))  # 1 (first bit set is position 0)
print(ffs8([0,0,1,0,0,0,0,0]))  # 3 (first bit set is position 2)
print(ffs8([0,0,0,0,0,0,0,0]))  # 0 (no bits set)
```

## Applications

- POSIX ffs() function implementation
- Finding available slots in bitmaps
- Scheduler ready queue processing
- Memory allocator free list management
- Interrupt priority handling

## Comparison: FFS vs CTZ vs CLZ

| Function | Zero input | Non-zero input | Index base |
|----------|------------|----------------|------------|
| FFS | 0 | 1 to 8 | 1-indexed |
| CTZ | 8 | 0 to 7 | 0-indexed |
| CLZ | 8 | 0 to 7 | 0-indexed from MSB |

## Files

```
threshold-ffs8/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md
```

## License

MIT