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test_equivalence.py
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"""
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TEST #2: Formal Equivalence Checking
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=====================================
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Run 8-bit adder against Python's arithmetic for ALL 2^16 input pairs.
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Bit-for-bit comparison of every result and carry flag.
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A skeptic would demand: "Prove exhaustive correctness, not just sampling."
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"""
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import torch
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from safetensors.torch import load_file
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import time
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# Load circuits
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model = load_file('neural_computer.safetensors')
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def heaviside(x):
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return (x >= 0).float()
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def eval_xor_arith(inp, prefix):
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"""Evaluate XOR for arithmetic circuits."""
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w1_or = model[f'{prefix}.layer1.or.weight']
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b1_or = model[f'{prefix}.layer1.or.bias']
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w1_nand = model[f'{prefix}.layer1.nand.weight']
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b1_nand = model[f'{prefix}.layer1.nand.bias']
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w2 = model[f'{prefix}.layer2.weight']
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b2 = model[f'{prefix}.layer2.bias']
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h_or = heaviside(inp @ w1_or + b1_or)
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h_nand = heaviside(inp @ w1_nand + b1_nand)
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hidden = torch.tensor([h_or.item(), h_nand.item()])
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return heaviside(hidden @ w2 + b2).item()
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def eval_full_adder(a, b, cin, prefix):
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"""Evaluate full adder, return (sum, carry_out)."""
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inp_ab = torch.tensor([a, b], dtype=torch.float32)
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ha1_sum = eval_xor_arith(inp_ab, f'{prefix}.ha1.sum')
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w_c1 = model[f'{prefix}.ha1.carry.weight']
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b_c1 = model[f'{prefix}.ha1.carry.bias']
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ha1_carry = heaviside(inp_ab @ w_c1 + b_c1).item()
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inp_ha2 = torch.tensor([ha1_sum, cin], dtype=torch.float32)
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ha2_sum = eval_xor_arith(inp_ha2, f'{prefix}.ha2.sum')
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w_c2 = model[f'{prefix}.ha2.carry.weight']
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b_c2 = model[f'{prefix}.ha2.carry.bias']
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ha2_carry = heaviside(inp_ha2 @ w_c2 + b_c2).item()
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inp_cout = torch.tensor([ha1_carry, ha2_carry], dtype=torch.float32)
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w_or = model[f'{prefix}.carry_or.weight']
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b_or = model[f'{prefix}.carry_or.bias']
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cout = heaviside(inp_cout @ w_or + b_or).item()
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return int(ha2_sum), int(cout)
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def add_8bit(a, b):
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"""8-bit addition using ripple carry adder."""
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carry = 0.0
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result_bits = []
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for i in range(8):
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a_bit = (a >> i) & 1
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b_bit = (b >> i) & 1
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s, carry = eval_full_adder(float(a_bit), float(b_bit), carry,
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f'arithmetic.ripplecarry8bit.fa{i}')
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result_bits.append(s)
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result = sum(result_bits[i] * (2**i) for i in range(8))
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return result, int(carry)
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def compare_8bit(a, b):
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"""8-bit comparators."""
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a_bits = torch.tensor([(a >> (7-i)) & 1 for i in range(8)], dtype=torch.float32)
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b_bits = torch.tensor([(b >> (7-i)) & 1 for i in range(8)], dtype=torch.float32)
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# Greater than
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w_gt = model['arithmetic.greaterthan8bit.comparator']
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gt = 1 if ((a_bits - b_bits) @ w_gt).item() > 0 else 0
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# Less than
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w_lt = model['arithmetic.lessthan8bit.comparator']
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lt = 1 if ((b_bits - a_bits) @ w_lt).item() > 0 else 0
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# Equal (neither gt nor lt)
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eq = 1 if (gt == 0 and lt == 0) else 0
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return gt, lt, eq
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# =============================================================================
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# EXHAUSTIVE TESTS
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# =============================================================================
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def test_addition_exhaustive():
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"""
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Test ALL 65,536 addition combinations.
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"""
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print("\n[TEST 1] Exhaustive 8-bit Addition: 256 x 256 = 65,536 cases")
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print("-" * 60)
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errors = []
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start = time.perf_counter()
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for a in range(256):
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for b in range(256):
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# Circuit result
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result, carry = add_8bit(a, b)
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# Python reference
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full_sum = a + b
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expected_result = full_sum % 256
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expected_carry = 1 if full_sum > 255 else 0
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# Compare
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if result != expected_result:
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errors.append(('result', a, b, expected_result, result))
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if carry != expected_carry:
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errors.append(('carry', a, b, expected_carry, carry))
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# Progress every 32 rows
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if (a + 1) % 32 == 0:
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elapsed = time.perf_counter() - start
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rate = ((a + 1) * 256) / elapsed
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eta = (256 - a - 1) * 256 / rate
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print(f" Progress: {a+1}/256 rows ({(a+1)*256:,} tests) "
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f"| {rate:.0f} tests/sec | ETA: {eta:.1f}s")
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elapsed = time.perf_counter() - start
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print()
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if errors:
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print(f" FAILED: {len(errors)} mismatches")
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for e in errors[:10]:
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print(f" {e[0]}: {e[1]} + {e[2]} = {e[4]}, expected {e[3]}")
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else:
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print(f" PASSED: 65,536 additions verified")
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print(f" Time: {elapsed:.2f}s ({65536/elapsed:.0f} tests/sec)")
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return len(errors) == 0
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def test_comparators_exhaustive():
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"""
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Test ALL 65,536 comparator combinations for GT, LT, EQ.
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"""
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print("\n[TEST 2] Exhaustive 8-bit Comparators: 256 x 256 x 3 = 196,608 checks")
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print("-" * 60)
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errors = []
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start = time.perf_counter()
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for a in range(256):
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for b in range(256):
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gt, lt, eq = compare_8bit(a, b)
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# Python reference
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exp_gt = 1 if a > b else 0
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exp_lt = 1 if a < b else 0
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exp_eq = 1 if a == b else 0
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if gt != exp_gt:
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errors.append(('GT', a, b, exp_gt, gt))
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if lt != exp_lt:
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errors.append(('LT', a, b, exp_lt, lt))
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if eq != exp_eq:
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errors.append(('EQ', a, b, exp_eq, eq))
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if (a + 1) % 32 == 0:
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elapsed = time.perf_counter() - start
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rate = ((a + 1) * 256) / elapsed
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eta = (256 - a - 1) * 256 / rate
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print(f" Progress: {a+1}/256 rows | {rate:.0f} pairs/sec | ETA: {eta:.1f}s")
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elapsed = time.perf_counter() - start
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print()
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if errors:
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print(f" FAILED: {len(errors)} mismatches")
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for e in errors[:10]:
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print(f" {e[0]}({e[1]}, {e[2]}) = {e[4]}, expected {e[3]}")
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else:
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print(f" PASSED: 196,608 comparisons verified (GT, LT, EQ for each pair)")
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print(f" Time: {elapsed:.2f}s")
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return len(errors) == 0
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def test_boolean_exhaustive():
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"""
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Exhaustive test of all 2-input Boolean gates (4 cases each).
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"""
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print("\n[TEST 3] Exhaustive Boolean Gates: AND, OR, NAND, NOR, XOR, XNOR")
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print("-" * 60)
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gates = {
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'and': lambda a, b: a & b,
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'or': lambda a, b: a | b,
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'nand': lambda a, b: 1 - (a & b),
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'nor': lambda a, b: 1 - (a | b),
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}
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errors = []
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# Simple gates (single layer)
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for gate_name, expected_fn in gates.items():
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w = model[f'boolean.{gate_name}.weight']
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bias = model[f'boolean.{gate_name}.bias']
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for a in [0, 1]:
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for b in [0, 1]:
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inp = torch.tensor([float(a), float(b)])
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result = int(heaviside(inp @ w + bias).item())
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expected = expected_fn(a, b)
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if result != expected:
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errors.append((gate_name.upper(), a, b, expected, result))
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# XOR (two-layer)
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for a in [0, 1]:
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for b in [0, 1]:
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inp = torch.tensor([float(a), float(b)])
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w1_n1 = model['boolean.xor.layer1.neuron1.weight']
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b1_n1 = model['boolean.xor.layer1.neuron1.bias']
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w1_n2 = model['boolean.xor.layer1.neuron2.weight']
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b1_n2 = model['boolean.xor.layer1.neuron2.bias']
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w2 = model['boolean.xor.layer2.weight']
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b2 = model['boolean.xor.layer2.bias']
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h1 = heaviside(inp @ w1_n1 + b1_n1)
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h2 = heaviside(inp @ w1_n2 + b1_n2)
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hidden = torch.tensor([h1.item(), h2.item()])
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result = int(heaviside(hidden @ w2 + b2).item())
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expected = a ^ b
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if result != expected:
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errors.append(('XOR', a, b, expected, result))
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# XNOR (two-layer)
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for a in [0, 1]:
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for b in [0, 1]:
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inp = torch.tensor([float(a), float(b)])
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w1_n1 = model['boolean.xnor.layer1.neuron1.weight']
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b1_n1 = model['boolean.xnor.layer1.neuron1.bias']
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w1_n2 = model['boolean.xnor.layer1.neuron2.weight']
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b1_n2 = model['boolean.xnor.layer1.neuron2.bias']
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w2 = model['boolean.xnor.layer2.weight']
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b2 = model['boolean.xnor.layer2.bias']
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h1 = heaviside(inp @ w1_n1 + b1_n1)
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h2 = heaviside(inp @ w1_n2 + b1_n2)
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hidden = torch.tensor([h1.item(), h2.item()])
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result = int(heaviside(hidden @ w2 + b2).item())
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expected = 1 - (a ^ b) # XNOR = NOT XOR
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if result != expected:
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errors.append(('XNOR', a, b, expected, result))
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# NOT (single input)
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w = model['boolean.not.weight']
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bias = model['boolean.not.bias']
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for a in [0, 1]:
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inp = torch.tensor([float(a)])
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result = int(heaviside(inp @ w + bias).item())
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expected = 1 - a
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if result != expected:
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errors.append(('NOT', a, '-', expected, result))
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if errors:
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print(f" FAILED: {len(errors)} mismatches")
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for e in errors:
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print(f" {e[0]}({e[1]}, {e[2]}) = {e[4]}, expected {e[3]}")
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else:
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print(f" PASSED: All Boolean gates verified (AND, OR, NAND, NOR, XOR, XNOR, NOT)")
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print(f" Total: 26 truth table entries")
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return len(errors) == 0
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def test_half_adder_exhaustive():
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"""
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Exhaustive test of half adder (4 cases).
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"""
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print("\n[TEST 4] Exhaustive Half Adder: 4 cases")
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print("-" * 60)
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errors = []
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for a in [0, 1]:
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for b in [0, 1]:
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inp = torch.tensor([float(a), float(b)])
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# Sum (XOR)
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w1_or = model['arithmetic.halfadder.sum.layer1.or.weight']
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b1_or = model['arithmetic.halfadder.sum.layer1.or.bias']
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w1_nand = model['arithmetic.halfadder.sum.layer1.nand.weight']
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b1_nand = model['arithmetic.halfadder.sum.layer1.nand.bias']
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w2 = model['arithmetic.halfadder.sum.layer2.weight']
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b2_sum = model['arithmetic.halfadder.sum.layer2.bias']
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h_or = heaviside(inp @ w1_or + b1_or)
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h_nand = heaviside(inp @ w1_nand + b1_nand)
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hidden = torch.tensor([h_or.item(), h_nand.item()])
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sum_bit = int(heaviside(hidden @ w2 + b2_sum).item())
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# Carry (AND)
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w_c = model['arithmetic.halfadder.carry.weight']
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b_c = model['arithmetic.halfadder.carry.bias']
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carry = int(heaviside(inp @ w_c + b_c).item())
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# Expected
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exp_sum = a ^ b
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exp_carry = a & b
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if sum_bit != exp_sum:
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errors.append(('SUM', a, b, exp_sum, sum_bit))
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if carry != exp_carry:
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errors.append(('CARRY', a, b, exp_carry, carry))
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if errors:
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print(f" FAILED: {len(errors)} mismatches")
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for e in errors:
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print(f" HA.{e[0]}({e[1]}, {e[2]}) = {e[4]}, expected {e[3]}")
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else:
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print(f" PASSED: Half adder verified (4 sum + 4 carry = 8 checks)")
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return len(errors) == 0
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def test_full_adder_exhaustive():
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"""
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| 321 |
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Exhaustive test of full adder (8 cases).
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"""
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print("\n[TEST 5] Exhaustive Full Adder: 8 cases")
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print("-" * 60)
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errors = []
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for a in [0, 1]:
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for b in [0, 1]:
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for cin in [0, 1]:
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sum_bit, cout = eval_full_adder(float(a), float(b), float(cin),
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'arithmetic.fulladder')
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# Expected
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total = a + b + cin
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exp_sum = total % 2
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exp_cout = total // 2
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| 338 |
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if sum_bit != exp_sum:
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errors.append(('SUM', a, b, cin, exp_sum, sum_bit))
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if cout != exp_cout:
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errors.append(('COUT', a, b, cin, exp_cout, cout))
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| 343 |
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| 344 |
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if errors:
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print(f" FAILED: {len(errors)} mismatches")
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for e in errors:
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print(f" FA.{e[0]}({e[1]}, {e[2]}, {e[3]}) = {e[5]}, expected {e[4]}")
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else:
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print(f" PASSED: Full adder verified (8 sum + 8 carry = 16 checks)")
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return len(errors) == 0
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| 353 |
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def test_2bit_adder_exhaustive():
|
| 354 |
-
"""
|
| 355 |
-
Exhaustive test of 2-bit ripple carry adder (16 cases).
|
| 356 |
-
"""
|
| 357 |
-
print("\n[TEST 6] Exhaustive 2-bit Adder: 4 x 4 = 16 cases")
|
| 358 |
-
print("-" * 60)
|
| 359 |
-
|
| 360 |
-
errors = []
|
| 361 |
-
|
| 362 |
-
for a in range(4):
|
| 363 |
-
for b in range(4):
|
| 364 |
-
# Use 2-bit ripple carry
|
| 365 |
-
carry = 0.0
|
| 366 |
-
result_bits = []
|
| 367 |
-
|
| 368 |
-
for i in range(2):
|
| 369 |
-
a_bit = (a >> i) & 1
|
| 370 |
-
b_bit = (b >> i) & 1
|
| 371 |
-
s, carry = eval_full_adder(float(a_bit), float(b_bit), carry,
|
| 372 |
-
f'arithmetic.ripplecarry2bit.fa{i}')
|
| 373 |
-
result_bits.append(s)
|
| 374 |
-
|
| 375 |
-
result = result_bits[0] + 2 * result_bits[1]
|
| 376 |
-
cout = int(carry)
|
| 377 |
-
|
| 378 |
-
exp_result = (a + b) % 4
|
| 379 |
-
exp_carry = 1 if (a + b) >= 4 else 0
|
| 380 |
-
|
| 381 |
-
if result != exp_result:
|
| 382 |
-
errors.append(('result', a, b, exp_result, result))
|
| 383 |
-
if cout != exp_carry:
|
| 384 |
-
errors.append(('carry', a, b, exp_carry, cout))
|
| 385 |
-
|
| 386 |
-
if errors:
|
| 387 |
-
print(f" FAILED: {len(errors)} mismatches")
|
| 388 |
-
for e in errors:
|
| 389 |
-
print(f" {e[0]}: {e[1]} + {e[2]} = {e[4]}, expected {e[3]}")
|
| 390 |
-
else:
|
| 391 |
-
print(f" PASSED: 2-bit adder verified (16 results + 16 carries)")
|
| 392 |
-
|
| 393 |
-
return len(errors) == 0
|
| 394 |
-
|
| 395 |
-
def test_4bit_adder_exhaustive():
|
| 396 |
-
"""
|
| 397 |
-
Exhaustive test of 4-bit ripple carry adder (256 cases).
|
| 398 |
-
"""
|
| 399 |
-
print("\n[TEST 7] Exhaustive 4-bit Adder: 16 x 16 = 256 cases")
|
| 400 |
-
print("-" * 60)
|
| 401 |
-
|
| 402 |
-
errors = []
|
| 403 |
-
|
| 404 |
-
for a in range(16):
|
| 405 |
-
for b in range(16):
|
| 406 |
-
carry = 0.0
|
| 407 |
-
result_bits = []
|
| 408 |
-
|
| 409 |
-
for i in range(4):
|
| 410 |
-
a_bit = (a >> i) & 1
|
| 411 |
-
b_bit = (b >> i) & 1
|
| 412 |
-
s, carry = eval_full_adder(float(a_bit), float(b_bit), carry,
|
| 413 |
-
f'arithmetic.ripplecarry4bit.fa{i}')
|
| 414 |
-
result_bits.append(s)
|
| 415 |
-
|
| 416 |
-
result = sum(result_bits[i] * (2**i) for i in range(4))
|
| 417 |
-
cout = int(carry)
|
| 418 |
-
|
| 419 |
-
exp_result = (a + b) % 16
|
| 420 |
-
exp_carry = 1 if (a + b) >= 16 else 0
|
| 421 |
-
|
| 422 |
-
if result != exp_result:
|
| 423 |
-
errors.append(('result', a, b, exp_result, result))
|
| 424 |
-
if cout != exp_carry:
|
| 425 |
-
errors.append(('carry', a, b, exp_carry, cout))
|
| 426 |
-
|
| 427 |
-
if errors:
|
| 428 |
-
print(f" FAILED: {len(errors)} mismatches")
|
| 429 |
-
for e in errors[:10]:
|
| 430 |
-
print(f" {e[0]}: {e[1]} + {e[2]} = {e[4]}, expected {e[3]}")
|
| 431 |
-
else:
|
| 432 |
-
print(f" PASSED: 4-bit adder verified (256 results + 256 carries)")
|
| 433 |
-
|
| 434 |
-
return len(errors) == 0
|
| 435 |
-
|
| 436 |
-
# =============================================================================
|
| 437 |
-
# MAIN
|
| 438 |
-
# =============================================================================
|
| 439 |
-
|
| 440 |
-
if __name__ == "__main__":
|
| 441 |
-
print("=" * 70)
|
| 442 |
-
print(" TEST #2: FORMAL EQUIVALENCE CHECKING")
|
| 443 |
-
print(" Exhaustive verification against Python's arithmetic")
|
| 444 |
-
print("=" * 70)
|
| 445 |
-
|
| 446 |
-
results = []
|
| 447 |
-
|
| 448 |
-
results.append(("Boolean gates", test_boolean_exhaustive()))
|
| 449 |
-
results.append(("Half adder", test_half_adder_exhaustive()))
|
| 450 |
-
results.append(("Full adder", test_full_adder_exhaustive()))
|
| 451 |
-
results.append(("2-bit adder", test_2bit_adder_exhaustive()))
|
| 452 |
-
results.append(("4-bit adder", test_4bit_adder_exhaustive()))
|
| 453 |
-
results.append(("8-bit adder", test_addition_exhaustive()))
|
| 454 |
-
results.append(("Comparators", test_comparators_exhaustive()))
|
| 455 |
-
|
| 456 |
-
print("\n" + "=" * 70)
|
| 457 |
-
print(" SUMMARY")
|
| 458 |
-
print("=" * 70)
|
| 459 |
-
|
| 460 |
-
passed = sum(1 for _, r in results if r)
|
| 461 |
-
total = len(results)
|
| 462 |
-
|
| 463 |
-
for name, r in results:
|
| 464 |
-
status = "PASS" if r else "FAIL"
|
| 465 |
-
print(f" {name:20s} [{status}]")
|
| 466 |
-
|
| 467 |
-
print(f"\n Total: {passed}/{total} test categories passed")
|
| 468 |
-
|
| 469 |
-
total_checks = 26 + 8 + 16 + 32 + 512 + 65536*2 + 65536*3
|
| 470 |
-
print(f" Individual checks: ~{total_checks:,}")
|
| 471 |
-
|
| 472 |
-
if passed == total:
|
| 473 |
-
print("\n STATUS: EXHAUSTIVE EQUIVALENCE VERIFIED")
|
| 474 |
-
else:
|
| 475 |
-
print("\n STATUS: EQUIVALENCE FAILURES DETECTED")
|
| 476 |
-
|
| 477 |
-
print("=" * 70)
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