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Browse files- README.md +50 -0
- config.json +9 -0
- create_safetensors.py +94 -0
- model.safetensors +3 -0
README.md
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---
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license: mit
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tags:
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- pytorch
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- safetensors
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- threshold-logic
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- neuromorphic
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- arithmetic
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- multiplier
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---
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# threshold-dadda-tree
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2x2 Dadda tree multiplier. Uses height-reduction algorithm to minimize adder stages.
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## Circuit
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```
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Inputs: A[1:0], B[1:0] (4 inputs)
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Outputs: P[3:0] (4 outputs)
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P = A × B (unsigned)
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```
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## Dadda Algorithm
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Reduces partial product columns to heights in sequence: 2, 3, 4, 6, 9, 13...
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For 2x2, columns are already within limits, so minimal reduction needed.
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```
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A1·B0 A0·B0
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A1·B1 A0·B1
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─────────────────
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P3 P2 P1 P0
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```
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## Parameters
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| | |
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|---|---|
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| Inputs | 4 |
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| Outputs | 4 |
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| Neurons | 10 |
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| Layers | 3 |
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| Parameters | 44 |
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| Magnitude | 44 |
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## License
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MIT
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config.json
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{
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"name": "threshold-dadda-tree",
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"description": "2x2 Dadda tree multiplier",
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"inputs": 4,
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"outputs": 4,
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"neurons": 10,
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"layers": 3,
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"parameters": 44
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}
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create_safetensors.py
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import torch
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from safetensors.torch import save_file
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weights = {}
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# 2x2 Dadda Tree Multiplier
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# Inputs: A1,A0, B1,B0 (4 inputs)
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# Outputs: P3,P2,P1,P0 (4 outputs)
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#
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# Partial products:
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# A1B0 A0B0
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# A1B1 A0B1
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# ----------------
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# P3 P2 P1 P0
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#
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# Dadda reduces column heights to specific sequence: 2,2,3,4,6,9,13...
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# For 2x2, columns are already height 1 or 2, so minimal reduction needed.
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# Input indices: A1=0, A0=1, B1=2, B0=3
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def add_and(name, idx_a, idx_b, n_inputs):
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w = [0.0] * n_inputs
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w[idx_a] = 1.0
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w[idx_b] = 1.0
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weights[f'{name}.weight'] = torch.tensor([w], dtype=torch.float32)
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weights[f'{name}.bias'] = torch.tensor([-2.0], dtype=torch.float32)
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def add_xor_direct(name, n_prev):
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weights[f'{name}.or.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
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weights[f'{name}.or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
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weights[f'{name}.nand.weight'] = torch.tensor([[-1.0, -1.0]], dtype=torch.float32)
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weights[f'{name}.nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
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weights[f'{name}.and.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
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weights[f'{name}.and.bias'] = torch.tensor([-2.0], dtype=torch.float32)
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# Partial products (AND gates)
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add_and('pp00', 1, 3, 4) # A0 * B0 -> P0
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add_and('pp01', 1, 2, 4) # A0 * B1
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add_and('pp10', 0, 3, 4) # A1 * B0
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add_and('pp11', 0, 2, 4) # A1 * B1
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# Column 1 (weight 2): pp01 + pp10 -> half adder
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add_xor_direct('ha1_sum', 2)
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weights['ha1_carry.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
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weights['ha1_carry.bias'] = torch.tensor([-2.0], dtype=torch.float32)
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# Column 2 (weight 4): pp11 + carry from column 1 -> half adder
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add_xor_direct('ha2_sum', 2)
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weights['ha2_carry.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
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weights['ha2_carry.bias'] = torch.tensor([-2.0], dtype=torch.float32)
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save_file(weights, 'model.safetensors')
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def dadda_mult(a1, a0, b1, b0):
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pp00 = a0 & b0
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pp01 = a0 & b1
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pp10 = a1 & b0
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pp11 = a1 & b1
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p0 = pp00
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# Half adder for column 1
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p1 = pp01 ^ pp10
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c1 = pp01 & pp10
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# Half adder for column 2
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p2 = pp11 ^ c1
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c2 = pp11 & c1
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p3 = c2
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return p3, p2, p1, p0
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print("Verifying 2x2 Dadda tree multiplier...")
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errors = 0
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for a in range(4):
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for b in range(4):
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a1, a0 = (a >> 1) & 1, a & 1
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b1, b0 = (b >> 1) & 1, b & 1
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p3, p2, p1, p0 = dadda_mult(a1, a0, b1, b0)
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result = p3*8 + p2*4 + p1*2 + p0
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expected = a * b
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if result != expected:
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errors += 1
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print(f"ERROR: {a}*{b} = {result}, expected {expected}")
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if errors == 0:
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print("All 16 test cases passed!")
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else:
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print(f"FAILED: {errors} errors")
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mag = sum(t.abs().sum().item() for t in weights.values())
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print(f"Magnitude: {mag:.0f}")
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print(f"Parameters: {sum(t.numel() for t in weights.values())}")
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model.safetensors
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version https://git-lfs.github.com/spec/v1
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oid sha256:190502e4d427546b55862398447302774edfa455b6f96b24931d25603b3b4e0d
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size 1864
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