Initial commit: threshold-sklansky threshold circuit

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- arithmetic
+- parallel-prefix
+---
+
+# threshold-sklansky
+
+4-bit Sklansky parallel prefix adder. Achieves minimum depth at the cost of maximum fanout.
+
+## Circuit
+
+```
+Inputs: A[3:0], B[3:0], Cin (9 inputs)
+Outputs: S[3:0], Cout (5 outputs)
+```
+
+## Sklansky Structure (4-bit)
+
+```
+     G3,P3    G2,P2    G1,P1    G0,P0
+       │        │        │        │
+L1     ●────────┤        ●────────┤
+       │        │        │        │
+L2     ●────────●────────┴────────┘  (high fanout from G1:0)
+       │        │
+     G3:0     G2:0     G1:0     G0
+```
+
+All positions at level 2 combine with the same prefix (G1:0, P1:0), creating high fanout but minimum depth.
+
+## Trade-off
+
+| Property | Value |
+|----------|-------|
+| Depth | O(log n) - optimal |
+| Fanout | O(n) - maximum |
+| Cells | O(n log n) |
+
+Best for small adders where fanout is not a concern.
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 9 |
+| Outputs | 5 |
+| Neurons | 32 |
+| Layers | 4 |
+| Parameters | 132 |
+| Magnitude | 56 |
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-sklansky",
+  "description": "4-bit Sklansky parallel prefix adder",
+  "inputs": 9,
+  "outputs": 5,
+  "neurons": 32,
+  "layers": 4,
+  "parameters": 132
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# 4-bit Sklansky Parallel Prefix Adder
+# Minimum depth, maximum fanout
+
+def add_and(name, idx_a, idx_b, n_inputs):
+    w = [0.0] * n_inputs
+    w[idx_a] = 1.0
+    w[idx_b] = 1.0
+    weights[f'{name}.weight'] = torch.tensor([w], dtype=torch.float32)
+    weights[f'{name}.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+def add_xor_stage1(name, idx_a, idx_b, n_inputs):
+    w_or = [0.0] * n_inputs
+    w_or[idx_a] = 1.0
+    w_or[idx_b] = 1.0
+    weights[f'{name}.or.weight'] = torch.tensor([w_or], dtype=torch.float32)
+    weights[f'{name}.or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+    w_nand = [0.0] * n_inputs
+    w_nand[idx_a] = -1.0
+    w_nand[idx_b] = -1.0
+    weights[f'{name}.nand.weight'] = torch.tensor([w_nand], dtype=torch.float32)
+    weights[f'{name}.nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+
+def add_xor_stage2(name):
+    weights[f'{name}.and.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+    weights[f'{name}.and.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+for i in range(4):
+    a_idx = 3 - i
+    b_idx = 7 - i
+    add_and(f'g{i}', a_idx, b_idx, 9)
+    add_xor_stage1(f'p{i}', a_idx, b_idx, 9)
+
+for i in range(4):
+    add_xor_stage2(f'p{i}')
+
+save_file(weights, 'model.safetensors')
+
+def sklansky_add(a3, a2, a1, a0, b3, b2, b1, b0, cin):
+    a = [a0, a1, a2, a3]
+    b = [b0, b1, b2, b3]
+
+    g = [a[i] & b[i] for i in range(4)]
+    p = [a[i] ^ b[i] for i in range(4)]
+
+    # Level 1: combine pairs
+    g10 = g[1] | (p[1] & g[0])
+    p10 = p[1] & p[0]
+    g32 = g[3] | (p[3] & g[2])
+    p32 = p[3] & p[2]
+
+    # Level 2: all combine with bit 1 prefix (high fanout)
+    g20 = g[2] | (p[2] & g10)
+    g30 = g32 | (p32 & g10)
+    p30 = p32 & p10
+
+    c0 = g[0] | (p[0] & cin)
+    c1 = g10 | (p10 & cin)
+    c2 = g20 | (p[2] & p10 & cin)
+    c3 = g30 | (p30 & cin)
+
+    s0 = p[0] ^ cin
+    s1 = p[1] ^ c0
+    s2 = p[2] ^ c1
+    s3 = p[3] ^ c2
+
+    return s3, s2, s1, s0, c3
+
+print("Verifying 4-bit Sklansky adder...")
+errors = 0
+for a in range(16):
+    for b in range(16):
+        for cin in range(2):
+            a3, a2, a1, a0 = (a>>3)&1, (a>>2)&1, (a>>1)&1, a&1
+            b3, b2, b1, b0 = (b>>3)&1, (b>>2)&1, (b>>1)&1, b&1
+            s3, s2, s1, s0, cout = sklansky_add(a3, a2, a1, a0, b3, b2, b1, b0, cin)
+            result = cout*16 + s3*8 + s2*4 + s1*2 + s0
+            expected = a + b + cin
+            if result != expected:
+                errors += 1
+                if errors <= 3:
+                    print(f"ERROR: {a}+{b}+{cin} = {result}, expected {expected}")
+
+if errors == 0:
+    print("All 512 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}")
+print(f"Parameters: {sum(t.numel() for t in weights.values())}")