threshold-overflowdetect

Detect signed addition overflow from sign bits of operands and result.

Function

overflow(a_sign, b_sign, sum_sign) = 1 if overflow occurred

In 2's complement addition, overflow occurs when:

• Two positive numbers produce a negative result
• Two negative numbers produce a positive result

Truth Table

a_sign	b_sign	sum_sign	overflow	meaning
0	0	0	0	pos + pos = pos (ok)
0	0	1	1	pos + pos = neg (OVERFLOW)
0	1	0	0	pos + neg = pos (ok)
0	1	1	0	pos + neg = neg (ok)
1	0	0	0	neg + pos = pos (ok)
1	0	1	0	neg + pos = neg (ok)
1	1	0	1	neg + neg = pos (OVERFLOW)
1	1	1	0	neg + neg = neg (ok)

Architecture

2-layer circuit detecting both overflow cases:

Layer 1:

• N1: detects positive overflow (0,0,1) - weights [-1,-1,+1], bias -1
• N2: detects negative overflow (1,1,0) - weights [+1,+1,-1], bias -2

Layer 2:

• OR gate: weights [1,1], bias -1

Parameters

Inputs	3
Outputs	1
Neurons	3
Layers	2
Parameters	11
Magnitude	12

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def overflow_detect(a_sign, b_sign, sum_sign):
    inp = torch.tensor([float(a_sign), float(b_sign), float(sum_sign)])
    n1 = int((inp @ w['layer1.n1.weight'].T + w['layer1.n1.bias'] >= 0).item())
    n2 = int((inp @ w['layer1.n2.weight'].T + w['layer1.n2.bias'] >= 0).item())
    hidden = torch.tensor([float(n1), float(n2)])
    return int((hidden @ w['layer2.weight'].T + w['layer2.bias'] >= 0).item())

# Example: 5 + 4 = 9, but in 4-bit signed: 0101 + 0100 = 1001 = -7
print(overflow_detect(0, 0, 1))  # 1 (overflow!)

# Example: -3 + 2 = -1 (no overflow)
print(overflow_detect(1, 0, 1))  # 0 (ok)

License

MIT