4-bit carry-save adder

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- arithmetic
+- adder
+---
+
+# threshold-carrysave-adder
+
+4-bit carry-save adder (CSA) as threshold circuit. Adds three 4-bit numbers producing a sum and carry vector, with no carry propagation delay.
+
+## Circuit
+
+```
+A[3:0] ──┐
+B[3:0] ──┼──► CSA ──┬──► S[3:0]    (sum)
+C[3:0] ──┘         └──► Cout[3:0] (carry)
+
+Final result: A + B + C = S + (Cout << 1)
+```
+
+## How It Works
+
+Each bit position computed independently (no ripple):
+
+```
+S[i]    = A[i] XOR B[i] XOR C[i]
+Cout[i] = MAJ(A[i], B[i], C[i])
+```
+
+The carry vector is shifted left by 1 before final addition.
+
+## Truth Table (per bit)
+
+| A | B | C | S | Cout |
+|---|---|---|---|------|
+| 0 | 0 | 0 | 0 | 0 |
+| 0 | 0 | 1 | 1 | 0 |
+| 0 | 1 | 0 | 1 | 0 |
+| 0 | 1 | 1 | 0 | 1 |
+| 1 | 0 | 0 | 1 | 0 |
+| 1 | 0 | 1 | 0 | 1 |
+| 1 | 1 | 0 | 0 | 1 |
+| 1 | 1 | 1 | 1 | 1 |
+
+## Architecture
+
+| Component | Count | Neurons |
+|-----------|-------|---------|
+| XOR3 (sum) | 4 | 28 |
+| MAJ3 (carry) | 4 | 4 |
+
+**Total: 32 neurons, 256 parameters, 3 layers**
+
+## Applications
+
+CSAs are fundamental building blocks in:
+- Fast multipliers (Wallace trees, Dadda trees)
+- Multi-operand addition
+- DSP circuits
+- Reducing 3 operands to 2 without carry propagation
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+
+w = load_file('model.safetensors')
+
+# Example: 15 + 15 + 15 = 45
+# S = 13 (1101), Cout = 7 (0111)
+# Result = 13 + (7 << 1) = 13 + 14 = 27... wait
+# Actually: S + 2*Cout = 13 + 14 = 27, but need final adder
+# CSA output needs one final ripple-carry add
+```
+
+## Files
+
+```
+threshold-carrysave-adder/
+├── model.safetensors
+├── create_safetensors.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-carrysave-adder",
+  "description": "4-bit carry-save adder as threshold circuit",
+  "inputs": 12,
+  "outputs": 8,
+  "neurons": 32,
+  "layers": 3,
+  "parameters": 256
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# 4-bit Carry-Save Adder
+# Inputs: a3,a2,a1,a0, b3,b2,b1,b0, c3,c2,c1,c0 (12 inputs)
+# Outputs: s3,s2,s1,s0, cout3,cout2,cout1,cout0 (8 outputs)
+#
+# For each bit i:
+#   s[i] = a[i] XOR b[i] XOR c[i]
+#   cout[i] = MAJ(a[i], b[i], c[i])
+#
+# No carry propagation - all bits computed in parallel
+
+def add_xor3(name, a_idx, b_idx, c_idx, total_inputs):
+    w1 = [0.0] * total_inputs
+    w1[a_idx] = 1.0
+    w1[b_idx] = 1.0
+    weights[f'{name}.xor1.or.weight'] = torch.tensor([w1], dtype=torch.float32)
+    weights[f'{name}.xor1.or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+    w2 = [0.0] * total_inputs
+    w2[a_idx] = -1.0
+    w2[b_idx] = -1.0
+    weights[f'{name}.xor1.nand.weight'] = torch.tensor([w2], dtype=torch.float32)
+    weights[f'{name}.xor1.nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+    weights[f'{name}.xor1.and.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+    weights[f'{name}.xor1.and.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+    weights[f'{name}.xor2.or.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+    weights[f'{name}.xor2.or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+    weights[f'{name}.xor2.nand.weight'] = torch.tensor([[-1.0, -1.0]], dtype=torch.float32)
+    weights[f'{name}.xor2.nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+    weights[f'{name}.xor2.and.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+    weights[f'{name}.xor2.and.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+    wc = [0.0] * total_inputs
+    wc[c_idx] = 1.0
+    weights[f'{name}.c_input.weight'] = torch.tensor([wc], dtype=torch.float32)
+    weights[f'{name}.c_input.bias'] = torch.tensor([0.0], dtype=torch.float32)
+
+def add_maj3(name, a_idx, b_idx, c_idx, total_inputs):
+    w = [0.0] * total_inputs
+    w[a_idx] = 1.0
+    w[b_idx] = 1.0
+    w[c_idx] = 1.0
+    weights[f'{name}.weight'] = torch.tensor([w], dtype=torch.float32)
+    weights[f'{name}.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+# Input indices: a3=0,a2=1,a1=2,a0=3, b3=4,b2=5,b1=6,b0=7, c3=8,c2=9,c1=10,c0=11
+
+for i in range(4):
+    a_idx = 3 - i
+    b_idx = 7 - i
+    c_idx = 11 - i
+    add_xor3(f's{i}', a_idx, b_idx, c_idx, 12)
+    add_maj3(f'cout{i}', a_idx, b_idx, c_idx, 12)
+
+save_file(weights, 'model.safetensors')
+
+def eval_xor(a, b):
+    or_out = int(a + b >= 1)
+    nand_out = int(-a - b + 1 >= 0)
+    return int(or_out + nand_out >= 2)
+
+def eval_xor3(a, b, c):
+    return eval_xor(eval_xor(a, b), c)
+
+def eval_maj3(a, b, c):
+    return int(a + b + c >= 2)
+
+def csa_4bit(a3, a2, a1, a0, b3, b2, b1, b0, c3, c2, c1, c0):
+    a = [a0, a1, a2, a3]
+    b = [b0, b1, b2, b3]
+    c = [c0, c1, c2, c3]
+    s = [eval_xor3(a[i], b[i], c[i]) for i in range(4)]
+    cout = [eval_maj3(a[i], b[i], c[i]) for i in range(4)]
+    return s[0], s[1], s[2], s[3], cout[0], cout[1], cout[2], cout[3]
+
+print("Verifying 4-bit Carry-Save Adder...")
+errors = 0
+for a in range(16):
+    for b in range(16):
+        for c in range(16):
+            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
+            c3, c2, c1, c0 = (c>>3)&1, (c>>2)&1, (c>>1)&1, c&1
+            s0, s1, s2, s3, cout0, cout1, cout2, cout3 = csa_4bit(
+                a3, a2, a1, a0, b3, b2, b1, b0, c3, c2, c1, c0)
+            s_val = s0 + (s1 << 1) + (s2 << 2) + (s3 << 3)
+            cout_val = cout0 + (cout1 << 1) + (cout2 << 2) + (cout3 << 3)
+            result = s_val + (cout_val << 1)
+            expected = a + b + c
+            if result != expected:
+                errors += 1
+                if errors <= 5:
+                    print(f"ERROR: {a}+{b}+{c} = {result}, expected {expected}")
+
+if errors == 0:
+    print("All 4096 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())}")