8-bit count leading zeros, magnitude 69

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-clz8
+
+8-bit count leading zeros.
+
+## Function
+
+clz8(a7, a6, a5, a4, a3, a2, a1, a0) = number of leading zeros from MSB (0-8)
+
+## Truth Table (selected rows)
+
+| Input | First 1 | CLZ | Output |
+|-------|---------|-----|--------|
+| 1xxxxxxx | bit 7 | 0 | 0000 |
+| 01xxxxxx | bit 6 | 1 | 0001 |
+| 001xxxxx | bit 5 | 2 | 0010 |
+| 0001xxxx | bit 4 | 3 | 0011 |
+| 00001xxx | bit 3 | 4 | 0100 |
+| 000001xx | bit 2 | 5 | 0101 |
+| 0000001x | bit 1 | 6 | 0110 |
+| 00000001 | bit 0 | 7 | 0111 |
+| 00000000 | none | 8 | 1000 |
+
+## Architecture
+
+```
+Layer 1: Priority detection from MSB (9 neurons)
+  has7 = a7 (MSB is set, clz=0)
+  has6_first = a6 AND NOT(a7) (clz=1)
+  has5_first = a5 AND NOT(a6) AND NOT(a7) (clz=2)
+  ...
+  has0_first = a0 AND NOT(a1..a7) (clz=7)
+  all_zero = NOT(any bit) (clz=8)
+
+Layer 2: Binary encoding (4 neurons)
+  y0 = has6_first OR has4_first OR has2_first OR has0_first
+  y1 = has5_first OR has4_first OR has1_first OR has0_first
+  y2 = has3_first OR has2_first OR has1_first OR has0_first
+  y3 = all_zero
+```
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 8 |
+| Outputs | 4 |
+| Neurons | 13 |
+| Layers | 2 |
+| Parameters | 117 |
+| Magnitude | 69 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+# See model.py for full implementation
+
+# clz8(1,0,0,0,0,0,0,0) = [0,0,0,0] = 0 (MSB set)
+# clz8(0,0,0,0,1,0,0,0) = [0,1,0,0] = 4 (four leading zeros)
+# clz8(0,0,0,0,0,0,0,0) = [1,0,0,0] = 8 (all zeros)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-clz8",
+  "description": "8-bit count leading zeros",
+  "inputs": 8,
+  "outputs": 4,
+  "neurons": 13,
+  "layers": 2,
+  "parameters": 117
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# Input order: [a7, a6, a5, a4, a3, a2, a1, a0] (a7 is MSB)
+# clz returns count of leading zeros (0-8)
+
+# Layer 1: Priority detection from MSB
+# has7: a7 is set (clz = 0)
+weights['has7.weight'] = torch.tensor([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['has7.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has6_first: a6 is first set from MSB (clz = 1)
+weights['has6_first.weight'] = torch.tensor([[-1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['has6_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has5_first: a5 is first set from MSB (clz = 2)
+weights['has5_first.weight'] = torch.tensor([[-1.0, -1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['has5_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has4_first: a4 is first set from MSB (clz = 3)
+weights['has4_first.weight'] = torch.tensor([[-1.0, -1.0, -1.0, 1.0, 0.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['has4_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has3_first: a3 is first set from MSB (clz = 4)
+weights['has3_first.weight'] = torch.tensor([[-1.0, -1.0, -1.0, -1.0, 1.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['has3_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has2_first: a2 is first set from MSB (clz = 5)
+weights['has2_first.weight'] = torch.tensor([[-1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 0.0, 0.0]], dtype=torch.float32)
+weights['has2_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has1_first: a1 is first set from MSB (clz = 6)
+weights['has1_first.weight'] = torch.tensor([[-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 0.0]], dtype=torch.float32)
+weights['has1_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# has0_first: a0 is first set from MSB (clz = 7)
+weights['has0_first.weight'] = torch.tensor([[-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0]], dtype=torch.float32)
+weights['has0_first.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# all_zero: no bits set (clz = 8)
+weights['all_zero.weight'] = torch.tensor([[-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0]], dtype=torch.float32)
+weights['all_zero.bias'] = torch.tensor([0.0], dtype=torch.float32)
+
+# Layer 2: Encode to binary (4 bits for 0-8)
+# Input order: [has7, has6_first, has5_first, has4_first, has3_first, has2_first, has1_first, has0_first, all_zero]
+# clz: 0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000
+
+# y0 (bit 0): clz is 1,3,5,7 (has6_first, has4_first, has2_first, has0_first)
+weights['y0.weight'] = torch.tensor([[0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0]], dtype=torch.float32)
+weights['y0.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y1 (bit 1): clz is 2,3,6,7 (has5_first, has4_first, has1_first, has0_first)
+weights['y1.weight'] = torch.tensor([[0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0]], dtype=torch.float32)
+weights['y1.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y2 (bit 2): clz is 4,5,6,7 (has3_first, has2_first, has1_first, has0_first)
+weights['y2.weight'] = torch.tensor([[0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0]], dtype=torch.float32)
+weights['y2.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y3 (bit 3): clz is 8 (all_zero)
+weights['y3.weight'] = torch.tensor([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]], dtype=torch.float32)
+weights['y3.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+# Verify
+def clz8(a7, a6, a5, a4, a3, a2, a1, a0):
+    inp = torch.tensor([float(a7), float(a6), float(a5), float(a4),
+                        float(a3), float(a2), float(a1), float(a0)])
+
+    # Layer 1
+    has7 = int((inp @ weights['has7.weight'].T + weights['has7.bias'] >= 0).item())
+    has6_first = int((inp @ weights['has6_first.weight'].T + weights['has6_first.bias'] >= 0).item())
+    has5_first = int((inp @ weights['has5_first.weight'].T + weights['has5_first.bias'] >= 0).item())
+    has4_first = int((inp @ weights['has4_first.weight'].T + weights['has4_first.bias'] >= 0).item())
+    has3_first = int((inp @ weights['has3_first.weight'].T + weights['has3_first.bias'] >= 0).item())
+    has2_first = int((inp @ weights['has2_first.weight'].T + weights['has2_first.bias'] >= 0).item())
+    has1_first = int((inp @ weights['has1_first.weight'].T + weights['has1_first.bias'] >= 0).item())
+    has0_first = int((inp @ weights['has0_first.weight'].T + weights['has0_first.bias'] >= 0).item())
+    all_zero = int((inp @ weights['all_zero.weight'].T + weights['all_zero.bias'] >= 0).item())
+
+    # Layer 2
+    l1 = torch.tensor([float(has7), float(has6_first), float(has5_first), float(has4_first),
+                       float(has3_first), float(has2_first), float(has1_first), float(has0_first),
+                       float(all_zero)])
+    y0 = int((l1 @ weights['y0.weight'].T + weights['y0.bias'] >= 0).item())
+    y1 = int((l1 @ weights['y1.weight'].T + weights['y1.bias'] >= 0).item())
+    y2 = int((l1 @ weights['y2.weight'].T + weights['y2.bias'] >= 0).item())
+    y3 = int((l1 @ weights['y3.weight'].T + weights['y3.bias'] >= 0).item())
+
+    return [y3, y2, y1, y0]
+
+print("Verifying clz8...")
+errors = 0
+for i in range(256):
+    bits = [(i >> j) & 1 for j in range(7, -1, -1)]
+    a7, a6, a5, a4, a3, a2, a1, a0 = bits
+
+    # Compute expected clz
+    expected_clz = 8
+    for j in range(8):
+        if bits[j]:
+            expected_clz = j
+            break
+
+    expected = [(expected_clz >> 3) & 1, (expected_clz >> 2) & 1,
+                (expected_clz >> 1) & 1, expected_clz & 1]
+    result = clz8(a7, a6, a5, a4, a3, a2, a1, a0)
+
+    if result != expected:
+        errors += 1
+        if errors <= 5:
+            print(f"ERROR: {bits} clz={expected_clz} -> {result}, expected {expected}")
+
+if errors == 0:
+    print("All 256 test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+
+mag = sum(t.abs().sum().item() for t in weights.values())
+print(f"Magnitude: {mag:.0f}")

model.py

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+import torch
+from safetensors.torch import load_file
+
+def load_model(path='model.safetensors'):
+    return load_file(path)
+
+def clz8(a7, a6, a5, a4, a3, a2, a1, a0, weights):
+    """8-bit count leading zeros. Returns 4-bit binary encoding of 0-8."""
+    inp = torch.tensor([float(a7), float(a6), float(a5), float(a4),
+                        float(a3), float(a2), float(a1), float(a0)])
+
+    # Layer 1: priority detection
+    has7 = int((inp @ weights['has7.weight'].T + weights['has7.bias'] >= 0).item())
+    has6_first = int((inp @ weights['has6_first.weight'].T + weights['has6_first.bias'] >= 0).item())
+    has5_first = int((inp @ weights['has5_first.weight'].T + weights['has5_first.bias'] >= 0).item())
+    has4_first = int((inp @ weights['has4_first.weight'].T + weights['has4_first.bias'] >= 0).item())
+    has3_first = int((inp @ weights['has3_first.weight'].T + weights['has3_first.bias'] >= 0).item())
+    has2_first = int((inp @ weights['has2_first.weight'].T + weights['has2_first.bias'] >= 0).item())
+    has1_first = int((inp @ weights['has1_first.weight'].T + weights['has1_first.bias'] >= 0).item())
+    has0_first = int((inp @ weights['has0_first.weight'].T + weights['has0_first.bias'] >= 0).item())
+    all_zero = int((inp @ weights['all_zero.weight'].T + weights['all_zero.bias'] >= 0).item())
+
+    # Layer 2: binary encoding
+    l1 = torch.tensor([float(has7), float(has6_first), float(has5_first), float(has4_first),
+                       float(has3_first), float(has2_first), float(has1_first), float(has0_first),
+                       float(all_zero)])
+    y0 = int((l1 @ weights['y0.weight'].T + weights['y0.bias'] >= 0).item())
+    y1 = int((l1 @ weights['y1.weight'].T + weights['y1.bias'] >= 0).item())
+    y2 = int((l1 @ weights['y2.weight'].T + weights['y2.bias'] >= 0).item())
+    y3 = int((l1 @ weights['y3.weight'].T + weights['y3.bias'] >= 0).item())
+
+    return [y3, y2, y1, y0]
+
+if __name__ == '__main__':
+    w = load_model()
+    print('clz8 examples:')
+    test_cases = [
+        (1, 0, 0, 0, 0, 0, 0, 0),  # 0 leading zeros
+        (0, 1, 0, 0, 0, 0, 0, 0),  # 1 leading zero
+        (0, 0, 0, 0, 1, 0, 0, 0),  # 4 leading zeros
+        (0, 0, 0, 0, 0, 0, 0, 1),  # 7 leading zeros
+        (0, 0, 0, 0, 0, 0, 0, 0),  # 8 leading zeros
+    ]
+    for bits in test_cases:
+        result = clz8(*bits, w)
+        clz_val = result[0]*8 + result[1]*4 + result[2]*2 + result[3]
+        print(f'  {bits} -> {result} = {clz_val}')