threshold-ffs4

4-bit find first set (priority encoder). Returns 1-indexed position of the least significant set bit.

Function

ffs4(a3, a2, a1, a0) = position of first (least significant) 1 bit, 0 if no bits set

Truth Table (selected rows)

Input	First bit	Output (y2,y1,y0)
0000	none	000 (0)
0001	bit 0	001 (1)
0010	bit 1	010 (2)
0011	bit 0	001 (1)
0100	bit 2	011 (3)
1000	bit 3	100 (4)
1010	bit 1	010 (2)

Architecture

Layer 1: Priority detection
  has0 = a0 (bit 0 is set)
  has1_first = a1 AND NOT(a0)
  has2_first = a2 AND NOT(a1) AND NOT(a0)
  has3_first = a3 AND NOT(a2) AND NOT(a1) AND NOT(a0)

Layer 2: Binary encoding
  y0 = has0 OR has2_first (ffs is 1 or 3)
  y1 = has1_first OR has2_first (ffs is 2 or 3)
  y2 = has3_first (ffs is 4)

Parameters

Inputs	4
Outputs	3
Neurons	7
Layers	2
Parameters	35
Magnitude	22

Usage

from safetensors.torch import load_file
# See model.py for full implementation

# ffs4(1, 0, 1, 0) = [0, 1, 0] = 2 (bit 1 is first set)
# ffs4(0, 0, 0, 1) = [0, 0, 1] = 1 (bit 0 is first set)

License

MIT