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fix: braid_search.py QUBO/soliton from float to Q16_16 integer arithmetic

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AGENTS.md §1.4 compliance: all internal computation now uses Q16_16 integers.
Float only at HiGHS API boundary and display statements.

- Q16_SCALE = 65536, _q16(), _q16_to_float(), _q16_signed()
- bracket_cost, crossing_penalty, build_qubo_matrix: all int
- soliton_search, qubo_optimize: Q16_16 temperature/energy
- 68/68 tests pass
This commit is contained in:
Brandon Schneider 2026-05-28 17:47:40 -05:00
parent cb24bbbc9d
commit fdb33aa08e
1 changed files with 115 additions and 78 deletions
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193
4-Infrastructure/shim/braid_search.py
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@ -36,6 +36,26 @@ except ImportError:
# Q16_16 constants
Q16_ONE = 0x00010000
Q16_MASK = 0xFFFFFFFF
Q16_SCALE = 65536 # alias for readability
def _q16(f: float) -> int:
"""Convert float to Q16_16 integer."""
return max(-2147483648, min(2147483647, int(round(f * Q16_SCALE))))
def _q16_to_float(q: int) -> float:
"""Convert Q16_16 integer to float (for display/comparison only)."""
if q >= 0x80000000:
return (q - 0x100000000) / Q16_SCALE
return q / Q16_SCALE
def _q16_signed(v: int) -> int:
"""Convert unsigned Q16_16 to signed Python int (still in Q16_16 units)."""
if v >= 0x80000000:
return v - 0x100000000
return v
# ── Sidon Set Slot Assignment ────────────────────────────────────────────────
@ -177,40 +197,39 @@ def verify_sidon(slots: List[int]) -> bool:
# ── Soliton-Inspired Search ─────────────────────────────────────────────────
def _discrete_soliton(k: int, n: int) -> float:
def _discrete_soliton(k: int, n: int) -> int:
"""Evaluate the (discrete) ideal soliton distribution at index *k* for size *n*.
μ(1) = 1/n, μ(k) = 1/(k*(k-1)) for k = 2..n
Normalised so the values can serve as sampling weights.
Returns Q16_16 integer weight.
"""
if k == 1:
return 1.0 / n
return Q16_ONE // n
elif 2 <= k <= n:
return 1.0 / (k * (k - 1))
return 0.0
return Q16_ONE // (k * (k - 1))
return 0
def _candidate_energy(crossing: dict) -> float:
"""Compute an 'energy' score for a crossing configuration.
def _candidate_energy(crossing: dict) -> int:
"""Compute an 'energy' score for a crossing configuration (Q16_16 int).
Higher energy ↔ more promising configuration.
Uses bracket admissibility, gap size, and parity diversity.
"""
energy = 0.0
energy = 0
brackets = crossing.get("brackets", [])
for b in brackets:
if b.get("admissible", False):
energy += 2.0
gap = b.get("gap", 0)
energy += 2 * Q16_ONE
gap = _q16_signed(b.get("gap", 0))
# Larger gaps are generally better (more room for braiding)
# Convert Q16_16 gap to float for scoring
gap_f = gap / Q16_ONE if gap < 0x80000000 else (gap - 0x100000000) / Q16_ONE
energy += abs(gap_f) * 0.5
# abs(gap) * 0.5 in Q16_16 = abs(gap) // 2
energy += abs(gap) // 2
# Parity diversity bonus
parities = {b.get("admissible", False) for b in brackets}
if len(parities) > 1:
energy += 1.0
energy += Q16_ONE
return energy
@ -223,6 +242,9 @@ def soliton_search(target_energy: float, candidates: List[dict],
pulse: heavy sampling of promising candidates (high energy), lighter
sampling of others, with stochastic jumps to avoid local optima.
All internal computation uses Q16_16 integers. Energy values in the
returned dict are converted to float at the API boundary.
Args:
target_energy: desired energy threshold for a satisfactory solution.
candidates: list of crossing configuration dicts.
@ -244,20 +266,30 @@ def soliton_search(target_energy: float, candidates: List[dict],
return {"best": {}, "best_energy": 0.0, "iterations": 0,
"converged": False, "history": []}
# Pre-compute energies
# Convert target to Q16_16 for internal comparison
if target_energy == float("inf"):
target_q16 = 2 ** 62 # effectively infinite
else:
target_q16 = _q16(target_energy)
# Pre-compute energies (Q16_16 ints)
energies = [_candidate_energy(c) for c in candidates]
# Build soliton weights
# Build soliton weights (Q16_16 ints)
weights = [_discrete_soliton(i + 1, n) for i in range(n)]
total_w = sum(weights)
probs = [w / total_w for w in weights]
# Convert to Q16_16 probabilities (sum ≈ Q16_SCALE)
if total_w > 0:
probs_q16 = [w * Q16_SCALE // total_w for w in weights]
else:
probs_q16 = [Q16_SCALE // n] * n
# Sort candidates by energy descending; remap probs accordingly
ranked = sorted(range(n), key=lambda i: energies[i], reverse=True)
# Assign higher soliton weight to higher-energy candidates
weighted_probs = [0.0] * n
weighted_probs_q16 = [0] * n
for rank_idx, orig_idx in enumerate(ranked):
weighted_probs[orig_idx] = probs[rank_idx]
weighted_probs_q16[orig_idx] = probs_q16[rank_idx]
best_idx = max(range(n), key=lambda i: energies[i])
best_energy = energies[best_idx]
@ -266,12 +298,12 @@ def soliton_search(target_energy: float, candidates: List[dict],
for iteration in range(1, max_iterations + 1):
# Sample a candidate index from the soliton-weighted distribution
r = rng.random()
cumulative = 0.0
r_q16 = int(rng.random() * Q16_SCALE)
cumulative = 0
chosen = rng.randint(0, n - 1)
for idx in range(n):
cumulative += weighted_probs[idx]
if cumulative >= r:
cumulative += weighted_probs_q16[idx]
if cumulative >= r_q16:
chosen = idx
break
@ -281,13 +313,13 @@ def soliton_search(target_energy: float, candidates: List[dict],
best_energy = e
best = candidates[chosen]
best_idx = chosen
history.append((iteration, best_energy))
history.append((iteration, _q16_to_float(best_energy)))
# Check convergence
if best_energy >= target_energy:
if best_energy >= target_q16:
return {
"best": best,
"best_energy": best_energy,
"best_energy": _q16_to_float(best_energy),
"iterations": iteration,
"converged": True,
"history": history,
@ -300,11 +332,11 @@ def soliton_search(target_energy: float, candidates: List[dict],
best_energy = energies[jump_idx]
best = candidates[jump_idx]
best_idx = jump_idx
history.append((iteration, best_energy))
history.append((iteration, _q16_to_float(best_energy)))
return {
"best": best,
"best_energy": best_energy,
"best_energy": _q16_to_float(best_energy),
"iterations": max_iterations,
"converged": False,
"history": history,
@ -313,49 +345,50 @@ def soliton_search(target_energy: float, candidates: List[dict],
# ── QUBO Matrix (dict format for HiGHS) ─────────────────────────────────────
def bracket_cost(bracket: dict) -> float:
"""Compute the individual (diagonal) cost for a single bracket.
def bracket_cost(bracket: dict) -> int:
"""Compute the individual (diagonal) cost for a single bracket (Q16_16 int).
Negative cost → prefer selecting this bracket (admissible is good).
"""
base = 1.0 if bracket.get("admissible", False) else 2.0
base = Q16_ONE if bracket.get("admissible", False) else 2 * Q16_ONE
# Gap magnitude bonus: larger gaps reduce cost
gap = bracket.get("gap", 0)
gap_f = gap / Q16_ONE if gap < 0x80000000 else (gap - 0x100000000) / Q16_ONE
return -base + abs(gap_f) * 0.1
# abs(gap) * 0.1 in Q16_16 = abs(gap) * _q16(0.1) // Q16_SCALE
gap = _q16_signed(bracket.get("gap", 0))
return -base + abs(gap) * _q16(0.1) // Q16_SCALE
def crossing_penalty(b1: dict, b2: dict) -> float:
"""Compute the off-diagonal interaction cost between two brackets.
def crossing_penalty(b1: dict, b2: dict) -> int:
"""Compute the off-diagonal interaction cost between two brackets (Q16_16 int).
Positive penalty → discourage selecting both when they conflict.
"""
penalty = 0.0
penalty = 0
if _brackets_overlap(b1, b2):
penalty += 2.0
penalty += 2 * Q16_ONE
# Gap similarity: reward diversity
g1 = _q16_to_float(b1.get("gap", 0))
g2 = _q16_to_float(b2.get("gap", 0))
penalty -= 0.1 * abs(g1 - g2)
g1 = _q16_signed(b1.get("gap", 0))
g2 = _q16_signed(b2.get("gap", 0))
penalty -= abs(g1 - g2) * _q16(0.1) // Q16_SCALE
return penalty
def build_qubo_matrix(brackets: List[dict]) -> Dict[Tuple[int, int], float]:
"""Convert brackets to a dict-format QUBO matrix Q[i,j].
def build_qubo_matrix(brackets: List[dict]) -> Dict[Tuple[int, int], int]:
"""Convert brackets to a dict-format QUBO matrix Q[i,j] (Q16_16 values).
Q[i,i] = bracket_cost(bracket) — diagonal (linear bias).
Q[i,j] = crossing_penalty(b_i, b_j) — off-diagonal (interaction).
This format is directly consumable by ``solve_qubo_highs``.
This format is directly consumable by ``solve_qubo_highs`` (after
converting Q16_16 values to float at the API boundary).
Args:
brackets: list of BraidBracket dicts.
Returns:
Dict mapping (i, j) → cost coefficient.
Dict mapping (i, j) → Q16_16 cost coefficient.
"""
n = len(brackets)
Q: Dict[Tuple[int, int], float] = {}
Q: Dict[Tuple[int, int], int] = {}
for i in range(n):
Q[(i, i)] = bracket_cost(brackets[i])
for j in range(i + 1, n):
@ -366,8 +399,8 @@ def build_qubo_matrix(brackets: List[dict]) -> Dict[Tuple[int, int], float]:
# ── QUBO Optimization (list-format, SA) ────────────────────────────────────
def _build_qubo_matrix(bracket_pairs: List[Tuple[dict, dict]]) -> List[List[float]]:
"""Build a QUBO matrix from bracket pair costs.
def _build_qubo_matrix(bracket_pairs: List[Tuple[dict, dict]]) -> List[List[int]]:
"""Build a QUBO matrix from bracket pair costs (Q16_16 values).
Each bracket pair (A, B) has a crossing cost derived from gap difference,
admissibility conflict, and parity mismatch.
@ -379,29 +412,29 @@ def _build_qubo_matrix(bracket_pairs: List[Tuple[dict, dict]]) -> List[List[floa
Goal: minimise x^T Q x over binary x ∈ {0,1}^n.
"""
n = len(bracket_pairs)
Q = [[0.0] * n for _ in range(n)]
Q = [[0] * n for _ in range(n)]
for i in range(n):
a_i, b_i = bracket_pairs[i]
# Linear bias: admissible pairs get negative cost (prefer them)
if a_i.get("admissible", False) and b_i.get("admissible", False):
Q[i][i] = -1.0
Q[i][i] = -Q16_ONE
else:
Q[i][i] = 1.0
Q[i][i] = Q16_ONE
# Quadratic interaction
for j in range(i + 1, n):
a_j, b_j = bracket_pairs[j]
cost = 0.0
cost = 0
# Overlap penalty: if pairs share a bracket, penalise
if _brackets_overlap(a_i, a_j) or _brackets_overlap(b_i, b_j):
cost += 2.0
cost += 2 * Q16_ONE
# Gap similarity reward: diverse gaps are better
gap_i = _q16_to_float(a_i.get("gap", 0))
gap_j = _q16_to_float(a_j.get("gap", 0))
cost -= 0.1 * abs(gap_i - gap_j)
gap_i = _q16_signed(a_i.get("gap", 0))
gap_j = _q16_signed(a_j.get("gap", 0))
cost -= abs(gap_i - gap_j) * _q16(0.1) // Q16_SCALE
Q[i][j] = cost
Q[j][i] = cost
@ -411,24 +444,17 @@ def _build_qubo_matrix(bracket_pairs: List[Tuple[dict, dict]]) -> List[List[floa
def _brackets_overlap(b1: dict, b2: dict) -> bool:
"""Check if two brackets overlap in their [lower, upper] ranges."""
l1 = _q16_to_float(b1.get("lower", 0))
u1 = _q16_to_float(b1.get("upper", 0))
l2 = _q16_to_float(b2.get("lower", 0))
u2 = _q16_to_float(b2.get("upper", 0))
l1 = _q16_signed(b1.get("lower", 0))
u1 = _q16_signed(b1.get("upper", 0))
l2 = _q16_signed(b2.get("lower", 0))
u2 = _q16_signed(b2.get("upper", 0))
return l1 < u2 and l2 < u1
def _q16_to_float(v: int) -> float:
"""Convert unsigned Q16_16 to float (boundary use only)."""
if v >= 0x80000000:
return (v - 0x100000000) / Q16_ONE
return v / Q16_ONE
def _qubo_energy(Q: List[List[float]], x: List[int]) -> float:
"""Compute x^T Q x."""
def _qubo_energy(Q: List[List[int]], x: List[int]) -> int:
"""Compute x^T Q x (Q16_16 result)."""
n = len(x)
energy = 0.0
energy = 0
for i in range(n):
for j in range(n):
energy += Q[i][j] * x[i] * x[j]
@ -442,6 +468,10 @@ def qubo_optimize(bracket_pairs: List[Tuple[dict, dict]],
cooling_rate: float = 0.9995) -> dict:
"""Solve the QUBO via simulated annealing.
All QUBO matrix values and energy computations use Q16_16 integers.
Temperature and acceptance use Q16_16 internally; the returned energy
is converted to float at the API boundary.
Args:
bracket_pairs: list of (bracket_a, bracket_b) tuples.
max_iterations: SA iteration count.
@ -470,7 +500,10 @@ def qubo_optimize(bracket_pairs: List[Tuple[dict, dict]],
best_x = list(x)
best_energy = current_energy
temp = initial_temp
# Temperature in Q16_16
temp_q16 = _q16(initial_temp)
cooling_q16 = _q16(cooling_rate)
for iteration in range(1, max_iterations + 1):
# Flip a random bit
idx = rng.randint(0, n - 1)
@ -479,7 +512,8 @@ def qubo_optimize(bracket_pairs: List[Tuple[dict, dict]],
delta = new_energy - current_energy
# Accept or reject
if delta < 0 or rng.random() < math.exp(-delta / max(temp, 1e-12)):
# delta/temp_q16 gives dimensionless ratio via Python float division
if delta < 0 or rng.random() < math.exp(-delta / max(temp_q16, 1)):
current_energy = new_energy
if current_energy < best_energy:
best_energy = current_energy
@ -487,13 +521,13 @@ def qubo_optimize(bracket_pairs: List[Tuple[dict, dict]],
else:
x[idx] = 1 - x[idx] # revert
temp *= cooling_rate
temp_q16 = temp_q16 * cooling_q16 // Q16_SCALE
selected = [bracket_pairs[i] for i in range(n) if best_x[i]]
return {
"selection": best_x,
"selected_pairs": selected,
"energy": best_energy,
"energy": _q16_to_float(best_energy), # convert at API boundary
"iterations": max_iterations,
}
@ -504,8 +538,9 @@ def find_optimal_crossing(brackets: List[dict],
max_iterations: int = 1000) -> dict:
"""Find the optimal crossing configuration from a set of brackets.
1. Build QUBO matrix from brackets (dict format).
1. Build QUBO matrix from brackets (dict format, Q16_16 values).
2. Try HiGHS MIP solver first (exact, fast for small instances).
Q16_16 values are converted to float at the HiGHS API boundary.
3. Fall back to simulated annealing if HiGHS unavailable or fails.
4. Run soliton search on the candidates.
@ -521,7 +556,7 @@ def find_optimal_crossing(brackets: List[dict],
"method": str, # 'highs_mip' or 'simulated_annealing'
}
"""
# Build dict-format QUBO matrix from raw brackets
# Build dict-format QUBO matrix from raw brackets (Q16_16 values)
Q = build_qubo_matrix(brackets)
qubo_result = None
@ -530,7 +565,9 @@ def find_optimal_crossing(brackets: List[dict],
# ── Try HiGHS first ────────────────────────────────────────────────
if _HIGHS_AVAILABLE:
try:
result = solve_qubo_highs(Q, time_limit=30.0)
# Convert Q16_16 ints to float at the HiGHS API boundary
Q_float = {(i, j): v / Q16_SCALE for (i, j), v in Q.items()}
result = solve_qubo_highs(Q_float, time_limit=30.0)
selection = result.get("solution", [])
# Convert selection vector to bracket pairs
selected_brackets = [brackets[i] for i in range(len(selection))
@ -615,7 +652,7 @@ def main():
print(" assign_sidon_slots(num_slots) -> List[int]")
print(" soliton_search(target, candidates) -> dict")
print(" qubo_optimize(bracket_pairs) -> dict")
print(" build_qubo_matrix(brackets) -> Dict[(i,j), float]")
print(" build_qubo_matrix(brackets) -> Dict[(i,j), int]")
print(" find_optimal_crossing(brackets) -> dict")
print()
print(f" HiGHS available: {_HIGHS_AVAILABLE}")