threshold-ctz4

4-bit count trailing zeros. Returns the number of consecutive zero bits starting from the LSB.

Function

ctz4(x3, x2, x1, x0) -> count (0-4)

• CTZ = 0 if x0 = 1 (no trailing zeros)
• CTZ = 1 if x0 = 0, x1 = 1
• CTZ = 2 if x0 = x1 = 0, x2 = 1
• CTZ = 3 if x0 = x1 = x2 = 0, x3 = 1
• CTZ = 4 if all bits are zero

Truth Table (selected rows)

Input	CTZ	Output
0001	0	000
0010	1	001
0100	2	010
1000	3	011
0000	4	100
0110	1	001
1100	2	010

Architecture

x3 x2 x1 x0
    │
    ▼
┌─────────────────────────────────┐
│ Layer 1: Prefix conditions      │
│ p0 = (x0=0)                     │
│ p01 = (x0=x1=0)                 │
│ p012 = (x0=x1=x2=0)             │
│ all_zero = (all=0)              │
└─────────────────────────────────┘
    │
    ▼
┌─────────────────────────────────┐
│ Layer 2: One-hot position       │
│ z1 = p0 AND x1                  │
│ z2 = p01 AND x2                 │
│ z3 = p012 AND x3                │
└─────────────────────────────────┘
    │
    ▼
┌─────────────────────────────────┐
│ Layer 3: Binary encoding        │
│ y2 = all_zero                   │
│ y1 = z2 OR z3                   │
│ y0 = z1 OR z3                   │
└─────────────────────────────────┘
    │
    ▼
  y2 y1 y0

Parameters

Inputs	4
Outputs	3
Neurons	10
Layers	3
Parameters	37
Magnitude	30

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

# ctz4(0,1,0,0) = 2 (binary 0100 has 2 trailing zeros)
# See model.py for full implementation

Applications

• Finding the lowest set bit position
• Efficient division by powers of 2
• Bit manipulation in cryptography
• Hardware priority encoders

License

MIT