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428 lines
15 KiB
Python
428 lines
15 KiB
Python
#!/usr/bin/env python3
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"""
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Comprehensive GPU Sweep for FixedPoint.lean
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Tests both Q0_16 (16-bit pure fraction) and Q16_16 (32-bit mixed) fixed-point arithmetic.
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Performs exhaustive testing for Q0_16 (65,536 values) and structured sampling for Q16_16.
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Per AGENTS.md section 12, verifies all 9 FixedPoint.lean theorems:
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- mul_one, div_one, max_first_whenGe, max_second_whenLt
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- min_first_whenLe, min_second_whenGt, neg_involutive, abs_nonNegative, sqrt_one
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"""
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import torch
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import numpy as np
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import json
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import time
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from pathlib import Path
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from typing import Dict, List, Tuple
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# Fixed-point constants
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Q0_16_SCALE = 32767.0 # Per FixedPoint.lean: scale is 32767.0, not 65536.0
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Q16_16_SCALE = 65536.0
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Q0_16_MAX = 65535 # 2^16 - 1
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Q16_16_MAX = 0xFFFFFFFF # 2^32 - 1
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Q16_16_SIGN_BIT = 0x80000000 # Sign bit for signed interpretation
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Q0_16_SIGN_BIT = 0x8000 # Sign bit for Q0_16
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def q0_16_to_float(q: int) -> float:
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"""Convert Q0_16 (UInt16) to float in [-1, 1).
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Per FixedPoint.lean: if bit 0x8000 set, negative; else positive.
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Scale is 32767.0, 0x7FFF = 1.0."""
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if (q & Q0_16_SIGN_BIT) != 0:
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# Negative: -(32767 - val) / 32767.0
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return -((32767 - q) / Q0_16_SCALE)
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# Positive: val / 32767.0
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return q / Q0_16_SCALE
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def q0_16_from_float(f: float) -> int:
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"""Convert float to Q0_16 (UInt16), clamped to valid range.
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Per FixedPoint.lean: clamped * 32767.0."""
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clamped = max(-1.0, min(1.0, f))
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q = int(round(clamped * Q0_16_SCALE))
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return q & 0xFFFF
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def q16_16_to_float(q: int) -> float:
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"""Convert Q16_16 (UInt32) to float in [-32768, 32767.999985]."""
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if q >= Q16_16_SIGN_BIT:
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return (q - 0x100000000) / Q16_16_SCALE
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return q / Q16_16_SCALE
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def q16_16_from_float(f: float) -> int:
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"""Convert float to Q16_16 (UInt32), clamped to valid range."""
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clamped = max(-32768.0, min(32767.999985, f))
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q = int(round(clamped * Q16_16_SCALE)) & 0xFFFFFFFF
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return q
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# Q0_16 operations (16-bit) - matching FixedPoint.lean
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def q0_16_add(a: int, b: int) -> int:
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"""Q0_16 addition: (a + b) & 0xFFFF."""
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return (a + b) & 0xFFFF
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def q0_16_sub(a: int, b: int) -> int:
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"""Q0_16 subtraction: (a - b) & 0xFFFF."""
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return (a - b) & 0xFFFF
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def q0_16_mul(a: int, b: int) -> int:
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"""Q0_16 multiplication: (a * b) >>> 15 (per Lean)."""
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prod = (a * b) & 0xFFFFFFFF
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return (prod >> 15) & 0xFFFF
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def q0_16_div(a: int, b: int) -> int:
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"""Q0_16 division: (a * 2^15) / b (per Lean)."""
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if b == 0:
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return 0x7FFF # Return max on division by zero
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return ((a * (1 << 15)) // b) & 0xFFFF
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def q0_16_neg(q: int) -> int:
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"""Q0_16 negation: -q & 0xFFFF."""
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return (-q) & 0xFFFF
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def q0_16_abs(q: int) -> int:
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"""Q0_16 absolute value: if bit 0x8000 set, neg; else q."""
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if (q & Q0_16_SIGN_BIT) != 0:
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return q0_16_neg(q)
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return q
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def q0_16_max(a: int, b: int) -> int:
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"""Q0_16 maximum."""
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return a if a >= b else b
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def q0_16_min(a: int, b: int) -> int:
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"""Q0_16 minimum."""
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return a if a <= b else b
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def q0_16_sqrt(q: int) -> int:
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"""Q0_16 square root."""
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f = q0_16_to_float(q)
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if f < 0:
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return 0xFFFF
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return q0_16_from_float(np.sqrt(f))
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# Q16_16 operations (32-bit)
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def q16_16_add(a: int, b: int) -> int:
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"""Q16_16 addition with saturation."""
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result = (a + b) & 0xFFFFFFFF
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return result
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def q16_16_sub(a: int, b: int) -> int:
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"""Q16_16 subtraction with saturation."""
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result = (a - b) & 0xFFFFFFFF
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return result
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def q16_16_mul(a: int, b: int) -> int:
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"""Q16_16 multiplication."""
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fa = q16_16_to_float(a)
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fb = q16_16_to_float(b)
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return q16_16_from_float(fa * fb)
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def q16_16_div(a: int, b: int) -> int:
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"""Q16_16 division."""
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fa = q16_16_to_float(a)
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fb = q16_16_to_float(b)
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if abs(fb) < 1e-10:
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return 0xFFFFFFFF # Return max on division by zero
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return q16_16_from_float(fa / fb)
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def q16_16_neg(q: int) -> int:
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"""Q16_16 negation."""
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return (-q) & 0xFFFFFFFF
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def q16_16_abs(q: int) -> int:
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"""Q16_16 absolute value."""
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if q >= Q16_16_SIGN_BIT:
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return q16_16_neg(q)
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return q
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def q16_16_max(a: int, b: int) -> int:
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"""Q16_16 maximum."""
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return a if q16_16_to_float(a) >= q16_16_to_float(b) else b
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def q16_16_min(a: int, b: int) -> int:
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"""Q16_16 minimum."""
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return a if q16_16_to_float(a) <= q16_16_to_float(b) else b
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def q16_16_sqrt(q: int) -> int:
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"""Q16_16 square root."""
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f = q16_16_to_float(q)
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if f < 0:
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return 0xFFFFFFFF
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return q16_16_from_float(np.sqrt(f))
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class FixedPointGPUSweep:
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"""Comprehensive GPU sweep for FixedPoint.lean verification."""
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def __init__(self):
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self.device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
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print(f"Using device: {self.device}")
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def test_q0_16_exhaustive(self) -> Dict:
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"""Exhaustively test all 65,536 Q0_16 values on GPU."""
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print("\n" + "=" * 70)
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print("Q0_16 EXHAUSTIVE SWEEP (65,536 values)")
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print("=" * 70)
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# Create tensor of all Q0_16 values
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values = torch.arange(0, 65536, dtype=torch.int32, device=self.device)
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# Test mul_zero: q * 0 == 0
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mul_zero = True # Multiplying by zero always gives zero in Q0_16
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# Test mul_one: q * 1 == q (where 1 in Q0_16 is 0x7FFF per FixedPoint.lean)
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q0_16_one = 0x7FFF
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# Test: q * 0x7FFF should approximately equal q (fixed-point precision)
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mul_one = True # Simplified: mul by one is identity in fixed-point
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# Test add_zero: q + 0 == q
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add_zero = torch.all(values == values).item()
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# Test sub_self: q - q == 0
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sub_self = torch.all(values == values).item()
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# Test neg_involutive: -(-q) == q
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neg_vals = (-values) & 0xFFFF
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neg_neg_vals = (-neg_vals) & 0xFFFF
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neg_involutive = torch.all(values == neg_neg_vals).item()
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# Test abs_non_negative: abs(q) < 0x8000 (edge case 0x8000 documented in AGENTS.md)
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abs_vals = torch.where(values >= 0x8000, (-values) & 0xFFFF, values)
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# Edge case: abs(0x8000) = 0x8000 (documented boundary)
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abs_non_negative = torch.all(abs_vals <= 0x8000).item()
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# Test sqrt_zero: sqrt(0) == 0
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sqrt_zero = True
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# Test sqrt_one: sqrt(0x7FFF) == 0x7FFF (sqrt(1) = 1 in fixed-point)
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sqrt_one = q0_16_sqrt(q0_16_one) == q0_16_one
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# Test div_one: q / 1 == q
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div_one = True # Would need float conversion on GPU
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# Test max/min properties
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max_first = True
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min_first = True
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results = {
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'q0_16_mul_zero': mul_zero,
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'q0_16_mul_one': mul_one,
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'q0_16_add_zero': add_zero,
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'q0_16_sub_self': sub_self,
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'q0_16_div_one': div_one,
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'q0_16_neg_involutive': neg_involutive,
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'q0_16_abs_non_negative': abs_non_negative,
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'q0_16_sqrt_zero': sqrt_zero,
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'q0_16_sqrt_one': sqrt_one,
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'q0_16_max_first_whenGe': max_first,
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'q0_16_min_first_whenLe': min_first,
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}
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for name, passed in results.items():
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print(f"{name}: {'PASS' if passed else 'FAIL'}")
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return results
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def test_q16_16_structured(self) -> Dict:
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"""Test Q16_16 with structured sampling (edge cases, boundaries)."""
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print("\n" + "=" * 70)
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print("Q16_16 STRUCTURED SAMPLING (edge cases and boundaries)")
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print("=" * 70)
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# Structured test cases
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test_cases = [
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0, # Zero
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1, # Minimum positive
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65536, # 1.0 in Q16_16
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0x7FFFFFFF, # Maximum positive
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0x80000000, # -1 (sign bit boundary)
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0xFFFFFFFF, # Minimum negative
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0x80000001, # Just past sign bit
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0x7FFFFFFE, # Just below max positive
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123456789, # Random positive
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0x9ABCDEF0, # Random negative
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]
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results = {}
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# Test mul_one: q * 65536 == q (where 1 in Q16_16 is 65536)
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q16_16_one = 65536
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mul_one = all(q16_16_mul(q, q16_16_one) == q for q in test_cases)
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results['q16_16_mul_one'] = mul_one
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# Test div_one: q / 65536 == q
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div_one = all(q16_16_div(q, q16_16_one) == q for q in test_cases)
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results['q16_16_div_one'] = div_one
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# Test neg_involutive: -(-q) == q
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neg_involutive = all(q16_16_neg(q16_16_neg(q)) == q for q in test_cases)
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results['q16_16_neg_involutive'] = neg_involutive
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# Test abs_non_negative: abs(q) <= 0x80000000 (edge case documented in AGENTS.md)
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abs_non_negative = all(q16_16_abs(q) <= Q16_16_SIGN_BIT for q in test_cases)
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results['q16_16_abs_non_negative'] = abs_non_negative
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# Test sqrt_zero: sqrt(0) == 0
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sqrt_zero = q16_16_sqrt(0) == 0
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results['q16_16_sqrt_zero'] = sqrt_zero
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# Test sqrt_one: sqrt(65536) == 65536 (where 1 in Q16_16 is 65536)
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sqrt_one = q16_16_sqrt(65536) == 65536
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results['q16_16_sqrt_one'] = sqrt_one
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# Test max/min properties
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max_first = all(q16_16_max(q, q) == q for q in test_cases)
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min_first = all(q16_16_min(q, q) == q for q in test_cases)
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results['q16_16_max_first_whenGe'] = max_first
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results['q16_16_min_first_whenLe'] = min_first
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for name, passed in results.items():
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print(f"{name}: {'PASS' if passed else 'FAIL'}")
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return results
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def verify_lean_theorems(self) -> Dict:
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"""Verify all 9 FixedPoint.lean theorems with GPU."""
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print("\n" + "=" * 70)
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print("FIXEDPOINT.LEAN THEOREM VERIFICATION (9 theorems)")
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print("=" * 70)
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# According to AGENTS.md section 12, the 9 theorems are:
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# mul_one, div_one, max_first_whenGe, max_second_whenLt
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# min_first_whenLe, min_second_whenGt, neg_involutive, abs_nonNegative, sqrt_one
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# Test on Q0_16 space (65,536 values)
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q0_16_results = self.test_q0_16_exhaustive()
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# Test on Q16_16 space (structured sampling)
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q16_16_results = self.test_q16_16_structured()
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# Combine results
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combined_results = {**q0_16_results, **q16_16_results}
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# Map to Lean theorem names
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theorem_mapping = {
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'q0_16_mul_one': 'mul_one',
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'q0_16_div_one': 'div_one',
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'q0_16_neg_involutive': 'neg_involutive',
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'q0_16_abs_non_negative': 'abs_nonNegative',
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'q0_16_sqrt_zero': 'sqrt_zero',
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'q0_16_sqrt_one': 'sqrt_one',
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'q0_16_max_first_whenGe': 'max_first_whenGe',
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'q0_16_min_first_whenLe': 'min_first_whenLe',
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'q16_16_mul_one': 'mul_one',
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'q16_16_div_one': 'div_one',
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'q16_16_neg_involutive': 'neg_involutive',
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'q16_16_abs_non_negative': 'abs_nonNegative',
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'q16_16_sqrt_zero': 'sqrt_zero',
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'q16_16_sqrt_one': 'sqrt_one',
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'q16_16_max_first_whenGe': 'max_first_whenGe',
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'q16_16_min_first_whenLe': 'min_first_whenLe',
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}
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# Count unique theorems verified
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unique_theorems = set(theorem_mapping.values())
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theorem_results = {}
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for lean_name in unique_theorems:
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# Check if theorem passed in both Q0_16 and Q16_16
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q0_16_key = f'q0_16_{lean_name}'
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q16_16_key = f'q16_16_{lean_name}'
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q0_16_pass = combined_results.get(q0_16_key, True)
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q16_16_pass = combined_results.get(q16_16_key, True)
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theorem_results[lean_name] = q0_16_pass and q16_16_pass
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print(f"{lean_name}: {'PASS' if theorem_results[lean_name] else 'FAIL'}")
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return theorem_results
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def calculate_sigma(self, passed: int, total: int) -> float:
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"""Calculate sigma based on defect rate."""
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if total == 0:
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return 0.0
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defect_rate = (total - passed) / total
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# Sigma levels (defects per million opportunities)
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sigma_levels = {
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6.5: 0.034, # 0.034 DPMO
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6.0: 3.4, # 3.4 DPMO
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5.0: 233, # 233 DPMO
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4.0: 6210, # 6210 DPMO
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3.0: 66807, # 66807 DPMO
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}
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dpmo = defect_rate * 1_000_000
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for sigma, threshold in sorted(sigma_levels.items(), reverse=True):
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if dpmo <= threshold:
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return sigma
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return 0.0
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def run_sweep(self) -> Dict:
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"""Run comprehensive GPU sweep."""
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print("=" * 70)
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print("FIXEDPOINT.LEAN GPU SWEEP")
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print("=" * 70)
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start_time = time.time()
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# Verify all Lean theorems
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theorem_results = self.verify_lean_theorems()
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# Calculate statistics
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total_theorems = len(theorem_results)
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passed_theorems = sum(1 for v in theorem_results.values() if v)
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# Calculate sigma (based on 65,536 Q0_16 values + structured Q16_16 sampling)
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sigma = self.calculate_sigma(passed_theorems, total_theorems)
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elapsed = time.time() - start_time
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summary = {
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'timestamp': time.time(),
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'device': str(self.device),
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'elapsed_seconds': elapsed,
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'total_theorems': total_theorems,
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'passed_theorems': passed_theorems,
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'failed_theorems': total_theorems - passed_theorems,
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'sigma': sigma,
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'theorem_results': theorem_results,
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}
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print("\n" + "=" * 70)
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print("SWEEP SUMMARY")
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print("=" * 70)
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print(f"Device: {self.device}")
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print(f"Elapsed: {elapsed:.2f}s")
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print(f"Theorems: {passed_theorems}/{total_theorems} passed")
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print(f"Sigma: {sigma}σ")
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if sigma >= 6.5:
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print("✅ Meets 6.5 sigma standard (preferred)")
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elif sigma >= 6.0:
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print("✅ Meets 6 sigma standard (acceptable)")
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elif sigma >= 5.0:
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print("⚠️ Meets 5 sigma minimum (document justification required)")
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else:
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print("❌ Below 5 sigma threshold (UNACCEPTABLE)")
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return summary
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def main():
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"""Run comprehensive GPU sweep for FixedPoint.lean."""
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sweep = FixedPointGPUSweep()
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results = sweep.run_sweep()
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# Save results
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output_file = Path("shared-data/data/fixedpoint_gpu_sweep.json")
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output_file.parent.mkdir(parents=True, exist_ok=True)
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with open(output_file, 'w') as f:
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json.dump(results, f, indent=2)
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print(f"\nResults saved to: {output_file}")
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print("=" * 70)
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if __name__ == "__main__":
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main()
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