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import operator
import re
from typing import List, Dict, Optional, Tuple
from dataclasses import dataclass, field
import numpy as np
# βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
# Data model
# βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
@dataclass
class QASMCircuit:
"""
Parsed representation of an OpenQASM 2.0 / 3.0 circuit.
Attributes
----------
n_qubits : total qubit count declared in qreg / qubit statements
n_cbits : total classical bit count declared in creg / bit statements
ops : list of gate dicts β each dict has keys:
'type' : 'gate'
'name' : lowercase gate name (aliases resolved)
'qubits' : list[int] β absolute qubit indices
'params' : list[float] β evaluated rotation angles
"""
n_qubits: int = 0
n_cbits: int = 0
ops: List[Dict] = field(default_factory=list)
def to_tuples(self) -> List[Tuple]:
"""
Convert ops to the tuple format expected by DenseSVSimulator.run_circuit:
(name, qubit0[, qubit1, ...][, param0, ...])
BUG FIX (original): the original returned
(name,) + tuple(qubits) + tuple(params)
which placed params *after* qubits, but run_circuit expects
params interleaved or trailing depending on gate type.
For the standard (name, qubit, param) convention used throughout
the simulator, this ordering is correct β preserved here but
documented explicitly so callers know what to expect.
"""
out = []
for op in self.ops:
row = (op['name'],) + tuple(op['qubits']) + tuple(op['params'])
out.append(row)
return out
def __iter__(self):
"""Duck-type as an iterable of the same tuples to_tuples() returns,
so a QASMCircuit works anywhere a plain circuit list is expected
(QuantumTranspiler.transpile, Chunk.run_chunk, ...) without the
caller having to remember to call .to_tuples() first. Verified this
was a real gap, not a hypothetical one: `for cmd in circuit` inside
QuantumTranspiler.transpile β reached via Chunk.run_chunk(circuit)
β raised `TypeError: 'QASMCircuit' object is not iterable` when
handed a QASMCircuit straight from QASMParser().parse(), instead of
circuit.to_tuples()."""
return iter(self.to_tuples())
# βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
# Parser
# βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
class QASMParser:
"""
Robust OpenQASM 2.0 / 3.0 parser.
Supported features
------------------
- qreg / creg (QASM 2.0)
- qubit / bit (QASM 3.0)
- Parametric gates: rx, ry, rz, p, u1, u2, u3, cp, crz, ...
- Compound parameter expressions: pi/2, sqrt(2), cos(0.3), ...
- Block comments /* ... */ and line comments // ...
- Gate aliases: cu1βcp, u1βp, toffoliβccx, cnotβcx, ...
- Range syntax q[0:3] expanded to individual qubits
- Bare register name (no index) resolved to qubit 0 of that register
- Silent fallback (0.0) for unparseable parameter expressions
"""
# ββ compiled regexes ββββββββββββββββββββββββββββββββββββββββββββ
_RE_BLOCK_CMT = re.compile(r'/\*.*?\*/', re.DOTALL)
_RE_LINE_CMT = re.compile(r'//[^\n]*')
_RE_INDEX = re.compile(r'\[(\d+)\]')
_RE_RANGE = re.compile(r'^([a-zA-Z_]\w*)\[(\d+):(\d+)\]$') # q[0:3]
_RE_QREG2 = re.compile(r'^qreg\s+([a-zA-Z_]\w*)\s*\[(\d+)\]')
_RE_CREG2 = re.compile(r'^creg\s+([a-zA-Z_]\w*)\s*\[(\d+)\]')
_RE_QREG3 = re.compile(r'^qubit(?:\s*\[(\d+)\])?\s+([a-zA-Z_]\w*)')
_RE_CREG3 = re.compile(r'^bit(?:\s*\[(\d+)\])?\s+([a-zA-Z_]\w*)')
_RE_GATE_HEAD = re.compile(r'^([a-zA-Z_]\w*)(?:\((.*)\))?$')
# QASM 3.0 `for <type> <var> in [start:end] {` β range is INCLUSIVE
# of `end` per the OpenQASM 3 spec (unlike this parser's own q[a:b]
# qubit-range syntax, which is exclusive β a separate feature).
_RE_FOR_HEAD = re.compile(
r'for\s+(?:\w+\s+)?(\w+)\s+in\s*\[\s*([^\]]+?)\s*:\s*([^\]]+?)\s*\]\s*\{')
_RE_BLOCK_HEAD = re.compile(r'\b(for|if|while|def|gate)\b[^{]*\{')
_RE_INT_DECL = re.compile(
r'(?:const\s+)?int(?:\s*\[\d+\])?\s+(\w+)\s*=\s*(-?\d+)\s*;')
# ββ gate name aliases ββββββββββββββββββββββββββββββββββββββββββββ
_ALIAS: Dict[str, str] = {
'cu1': 'cp',
'u1': 'p',
'toffoli': 'ccx',
'fredkin': 'cswap',
'cnot': 'cx',
'not': 'x',
'id': 'i',
'cx': 'cx', # explicit identity mappings for safety
'cz': 'cz',
'ccx': 'ccx',
}
# ββ gate names that only ever take one qubit βββββββββββββββββββββ
# Used to expand range syntax (q[0:3]) into one op per qubit instead
# of a single op with multiple qubits attached β see BUG FIX 3 note
# on parse(): the original fix resolved q[0:3] to the qubit list
# [0,1,2], but nothing expanded that list into separate applications
# for gates that are only ever single-qubit, so e.g. `h q[0:3]` ended
# up applying H to qubit 0 only, silently dropping qubits 1 and 2.
_SINGLE_QUBIT_GATES = frozenset((
'h', 'x', 'y', 'z', 's', 'sdg', 't', 'tdg', 'sx', 'id',
'rx', 'ry', 'rz', 'p', 'u1', 'u2', 'u3',
))
# ββ statements to skip entirely ββββββββββββββββββββββββββββββββββ
# BUG FIX (original): 'gate ' had a trailing space making it miss
# 'gate foo(...)' where the token is 'gate' followed by space.
# Using startswith on lowercased tokens is correct but the original
# also skipped 'def ' and 'for ' which are QASM 3.0 keywords β
# kept here for forward compatibility.
_SKIP = frozenset((
'openqasm', 'include', 'barrier', 'measure',
'reset', 'gate', 'def', 'if', 'for', 'while',
))
# ββ safe math environment for the AST-based expression evaluator ββββ
# No '__builtins__' entry and no raw 'np' module reference (either one
# would still be reachable via attribute access in a naive eval() β
# see _eval_ast_node's docstring for why this environment alone was
# never actually what made the old eval() call safe).
_MATH_ENV: Dict = {
'pi': np.pi,
'tau': 2.0 * np.pi,
'euler': np.e,
'sin': np.sin, 'cos': np.cos, 'tan': np.tan,
'sqrt': np.sqrt, 'exp': np.exp, 'log': np.log,
'asin': np.arcsin,'acos': np.arccos,'atan': np.arctan,
'arcsin': np.arcsin,'arccos': np.arccos,'arctan': np.arctan,
'abs': abs, 'round': round,
}
# ββ operators allowed in the AST expression evaluator ββββββββββββ
_BINOPS = {
ast.Add: operator.add, ast.Sub: operator.sub,
ast.Mult: operator.mul, ast.Div: operator.truediv,
ast.Pow: operator.pow, ast.Mod: operator.mod,
}
_UNARYOPS = {ast.UAdd: operator.pos, ast.USub: operator.neg}
# ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
# Public interface
# ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _find_matching_brace(self, s: str, open_idx: int) -> Optional[int]:
"""Return the index of the '}' matching s[open_idx] == '{', or None
if unbalanced. Counter-based β no regex, handles nesting correctly."""
depth = 0
for i in range(open_idx, len(s)):
if s[i] == '{':
depth += 1
elif s[i] == '}':
depth -= 1
if depth == 0:
return i
return None
def _collect_int_declarations(self, s: str) -> Dict[str, int]:
"""Map QASM3 `int n = 3;` / `const int n = 3;` declarations to their
literal value, so `for` bounds like `n-1` can be resolved."""
return {name: int(val) for name, val in self._RE_INT_DECL.findall(s)}
def _eval_ast_node(self, node, env: Dict):
"""
Evaluate a Python expression AST node against an explicit node-type
whitelist β never eval()/exec(). Only literals, +-*/%** arithmetic,
unary +/-, and Name/Call lookups restricted to `env` are handled;
anything else (Attribute, Subscript, comprehensions, lambda, ...)
falls through to the final `raise` and is rejected.
This exists because `eval(tok, {'__builtins__': {}})` β the
previous implementation β does NOT stop attribute/dunder traversal
of the live object graph: `().__class__.__bases__[0].__subclasses__()`
needs no builtin name at all, and from there any class loaded in
the process (including ones whose __globals__ reference `os`) is
reachable. Verified directly: that exact expression, passed as a
gate parameter through the public QASMParser.parse() entry point,
executed successfully and returned a real value before this fix.
An AST whitelist makes that structurally impossible β an
`ast.Attribute` node is never one of the cases handled below, so
`.` in an expression always ends in the rejection branch.
"""
if isinstance(node, ast.Expression):
return self._eval_ast_node(node.body, env)
if isinstance(node, ast.Constant) and isinstance(node.value, (int, float)):
return node.value
if isinstance(node, ast.BinOp) and type(node.op) in self._BINOPS:
return self._BINOPS[type(node.op)](
self._eval_ast_node(node.left, env),
self._eval_ast_node(node.right, env))
if isinstance(node, ast.UnaryOp) and type(node.op) in self._UNARYOPS:
return self._UNARYOPS[type(node.op)](self._eval_ast_node(node.operand, env))
if isinstance(node, ast.Name) and node.id in env and not callable(env[node.id]):
return env[node.id]
if (isinstance(node, ast.Call) and isinstance(node.func, ast.Name)
and node.func.id in env and callable(env[node.func.id])
and not node.keywords):
args = [self._eval_ast_node(a, env) for a in node.args]
return env[node.func.id](*args)
raise ValueError(f"disallowed expression node: {type(node).__name__}")
def _resolve_int_expr(self, expr: str, decls: Dict[str, int]) -> Optional[int]:
"""Resolve a `for`-bound expression (literal int, or a declared int
variable combined with +/-/*// arithmetic) to a concrete int.
Returns None if the expression isn't a safe, resolvable integer
expression β callers then treat the loop as unrollable-unresolved."""
expr = expr.strip()
for name, val in decls.items():
expr = re.sub(r'\b' + re.escape(name) + r'\b', str(val), expr)
try:
tree = ast.parse(expr, mode='eval')
return int(self._eval_ast_node(tree, {}))
except Exception:
return None
def _process_block_constructs(self, s: str) -> str:
"""
Pre-process `for` / `if` / `while` / `def` / `gate` blocks BEFORE the
statement-level `split(';')` in parse() ever sees them.
These are brace-delimited, not `;`-terminated, so leaving them for
the naive splitter corrupts whatever statement follows the block on
the same line (the closing '}' merges into the next real statement).
`gate` matters beyond QASM3: OpenQASM 2.0 exporters (e.g. Qiskit's
`qiskit.qasm2.dumps` for composite gates like `mcx`) emit a `gate
NAME params { ... }` definition on a single line, so this hits real
QASM2 circuits too, not just QASM3 control-flow syntax.
- `for <type> <var> in [start:end] { body }` with resolvable
integer bounds (literals, or `int`/`const int` variables declared
earlier in the source) is unrolled: `var` is substituted into
`body` for each value in range(start, end+1) β QASM3 `for`-ranges
are INCLUSIVE of the end bound (unlike this parser's own
exclusive `q[a:b]` qubit-range syntax).
- `for` loops with unresolvable bounds, and all `if`/`while`/`def`
blocks (no static execution β would need runtime classical bit
state), are simply removed, leaving the rest of the source intact.
- `gate` definitions are removed too β their body uses the gate's
own formal parameter names, not real qubit indices, so it can't
be executed directly; a later call site referencing that gate
name still falls through as an unrecognized gate (silent no-op,
same as any other unknown gate name elsewhere in this codebase),
but no longer corrupts the qubit/statement that follows it.
Runs as a search/replace loop rather than recursion: after an outer
block is unrolled, any inner (nested) blocks are duplicated as raw
text into the result and get picked up on a later iteration of the
same loop, so nesting is handled without extra bookkeeping.
"""
decls = self._collect_int_declarations(s)
while True:
m = self._RE_BLOCK_HEAD.search(s)
if not m:
break
keyword = m.group(1).lower()
open_brace = m.end() - 1
close_brace = self._find_matching_brace(s, open_brace)
if close_brace is None:
# Unbalanced braces β bail out rather than loop forever;
# leftover text falls through to the existing _SKIP path.
break
header = s[m.start():open_brace]
body = s[open_brace + 1:close_brace]
replacement = ''
if keyword == 'for':
fm = self._RE_FOR_HEAD.search(header + '{')
if fm:
var, start_e, end_e = fm.group(1), fm.group(2), fm.group(3)
start_v = self._resolve_int_expr(start_e, decls)
end_v = self._resolve_int_expr(end_e, decls)
if start_v is not None and end_v is not None:
var_re = re.compile(r'\b' + re.escape(var) + r'\b')
parts = [var_re.sub(str(i), body)
for i in range(start_v, end_v + 1)]
replacement = ' '.join(parts)
# unresolved `for`, and all `if`/`while`/`def` blocks, collapse
# to '' (replacement stays empty) β stripped, not corrupting.
s = s[:m.start()] + replacement + s[close_brace + 1:]
return s
def parse(self, qasm_str: str) -> QASMCircuit:
"""
Parse an OpenQASM 2.0 or 3.0 string into a QASMCircuit.
BUG FIX 1 (original): the original joined all lines with a single
space then split on ';'. Multi-line gate definitions (gate foo ...)
were not stripped before joining, causing 'gate foo ...' to appear
as a runnable instruction. Fixed by stripping comments *before*
joining and by using the frozenset _SKIP check on the first token.
BUG FIX 2 (original): bare register names (e.g. 'h q' instead of
'h q[0]') were silently dropped if the register had more than one
qubit, because qubit_map only stored 'name[0]' β 0 for size-1
registers. Fixed: bare names always map to qubit 0 of that register
regardless of register size.
BUG FIX 3 (original): range syntax q[0:3] was never handled β
such tokens fell through to the digit-extraction fallback which
returned only the last digit. Fixed in _resolve_qubits.
"""
qubit_map: Dict[str, int] = {}
cbit_map: Dict[str, int] = {}
n_qubits = 0
n_cbits = 0
ops: List[Dict] = []
# ββ strip comments βββββββββββββββββββββββββββββββββββββββββββ
cleaned = self._RE_BLOCK_CMT.sub(' ', qasm_str)
cleaned = self._RE_LINE_CMT.sub(' ', cleaned)
# ββ unroll for-loops / strip if-while-def blocks ββββββββββββββββ
# Must run before the ';'-split below: brace-delimited blocks are
# not single ';'-terminated statements, and left alone they corrupt
# whatever real statement follows them on the same line.
cleaned = self._process_block_constructs(cleaned)
# ββ split into statements βββββββββββββββββββββββββββββββββββββ
statements = [s.strip() for s in cleaned.split(';') if s.strip()]
for instr in statements:
# collapse internal whitespace runs to a single space
instr = re.sub(r'\s+', ' ', instr).strip()
if not instr:
continue
# first token (before any space or '(') for keyword detection
first_token = re.split(r'[\s(]', instr)[0].lower()
if first_token in self._SKIP:
continue
# ββ qreg (QASM 2.0) βββββββββββββββββββββββββββββββββββββ
m = self._RE_QREG2.match(instr)
if m:
reg_name, sz = m.group(1), int(m.group(2))
for i in range(sz):
qubit_map[f'{reg_name}[{i}]'] = n_qubits + i
qubit_map[reg_name] = n_qubits # bare name β first qubit
n_qubits += sz
continue
# ββ creg (QASM 2.0) βββββββββββββββββββββββββββββββββββββ
m = self._RE_CREG2.match(instr)
if m:
reg_name, sz = m.group(1), int(m.group(2))
for i in range(sz):
cbit_map[f'{reg_name}[{i}]'] = n_cbits + i
cbit_map[reg_name] = n_cbits
n_cbits += sz
continue
# ββ qubit (QASM 3.0) βββββββββββββββββββββββββββββββββββββ
m = self._RE_QREG3.match(instr)
if m:
sz_s, reg_name = m.group(1), m.group(2)
sz = int(sz_s) if sz_s else 1
for i in range(sz):
qubit_map[f'{reg_name}[{i}]'] = n_qubits + i
qubit_map[reg_name] = n_qubits
n_qubits += sz
continue
# ββ bit (QASM 3.0) βββββββββββββββββββββββββββββββββββββββ
m = self._RE_CREG3.match(instr)
if m:
sz_s, reg_name = m.group(1), m.group(2)
sz = int(sz_s) if sz_s else 1
for i in range(sz):
cbit_map[f'{reg_name}[{i}]'] = n_cbits + i
cbit_map[reg_name] = n_cbits
n_cbits += sz
continue
# ββ gate application βββββββββββββββββββββββββββββββββββββ
op = self._parse_gate(instr, qubit_map)
if op is not None:
if op['name'] in self._SINGLE_QUBIT_GATES and len(op['qubits']) > 1:
# range syntax on an inherently single-qubit gate
# (e.g. `h q[0:3]`) β expand into one op per qubit.
for q in op['qubits']:
ops.append({
'type': op['type'], 'name': op['name'],
'qubits': [q], 'params': list(op['params']),
})
n_qubits = max(n_qubits, q + 1)
else:
ops.append(op)
# update n_qubits from seen qubit indices
# (handles circuits without explicit qreg declarations)
if op['qubits']:
n_qubits = max(n_qubits, max(op['qubits']) + 1)
return QASMCircuit(n_qubits, n_cbits, ops)
def validate(self, circ: QASMCircuit) -> Tuple[bool, str]:
"""Light structural validation β does not verify gate semantics."""
if circ.n_qubits <= 0:
return False, 'n_qubits must be > 0.'
if not circ.ops:
return False, 'No gate operations found in circuit.'
# check for out-of-range qubit references
for i, op in enumerate(circ.ops):
for q in op.get('qubits', []):
if not (0 <= q < circ.n_qubits):
return False, (
f"Gate '{op['name']}' at op[{i}] references "
f"qubit {q} but n_qubits={circ.n_qubits}.")
return True, 'OK'
# ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
# Private helpers
# ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
def _parse_gate(self,
instr: str,
qubit_map: Dict[str, int]) -> Optional[Dict]:
"""
Parse a single gate instruction into an op dict.
BUG FIX 4 (original): the original code had two independent
code paths for extracting param_str β one using _RE_GATE_HEAD
and one rescanning for '(' β that could disagree, leaving
param_str as the group(2) of an earlier (shorter) match while
paren_start/paren_end referred to a different range. Unified
into a single pass that:
1. finds the parameter parentheses (balanced),
2. extracts everything before '(' as the gate name,
3. extracts everything after the closing ')' as the qubit list.
BUG FIX 5 (original): split_at was found by scanning for the
first space at depth==0 *in the whole instruction*, so for
rx(pi/2) q[0]
split_at was -1 (no space outside parens in 'rx(pi/2)') and
rest was '' β dropping the qubit entirely. Fixed by splitting
on the space after the closing ')'.
"""
instr = instr.strip()
# ββ locate parameter block '(...)' βββββββββββββββββββββββββββ
paren_open = instr.find('(')
paren_close = -1
param_str = ''
if paren_open != -1:
depth = 0
for idx in range(paren_open, len(instr)):
if instr[idx] == '(':
depth += 1
elif instr[idx] == ')':
depth -= 1
if depth == 0:
paren_close = idx
break
if paren_close == -1:
# Unbalanced parentheses β skip this instruction
return None
param_str = instr[paren_open + 1 : paren_close].strip()
# gate_head = everything before '(', qubit_part = everything after ')'
gate_head = instr[:paren_open].strip()
qubit_part = instr[paren_close + 1:].strip()
else:
# No parameters: split on first whitespace
parts = instr.split(None, 1)
gate_head = parts[0]
qubit_part = parts[1] if len(parts) > 1 else ''
gate_name_raw = gate_head.strip().lower()
if not gate_name_raw:
return None
gate_name = self._ALIAS.get(gate_name_raw, gate_name_raw)
# ββ parse parameters βββββββββββββββββββββββββββββββββββββββββ
params: List[float] = []
if param_str:
for tok in self._split_params(param_str):
tok = tok.strip()
if not tok:
continue
params.append(self._eval_param(tok))
# ββ resolve qubits βββββββββββββββββββββββββββββββββββββββββββ
qubits = self._resolve_qubits(
qubit_part.replace(' ', ''), qubit_map)
if not qubits:
return None
return {
'type': 'gate',
'name': gate_name,
'qubits': qubits,
'params': params,
}
def _eval_param(self, tok: str) -> float:
"""
Evaluate a parameter token to float via the AST whitelist evaluator
(_eval_ast_node) β never eval()/exec(). See _eval_ast_node's
docstring for why a raw eval() here was a real code-execution
vulnerability (attribute/dunder traversal bypasses
`{'__builtins__': {}}` entirely), fixed in this version.
Handles: numeric literals, pi, pi/2, sqrt(2), cos(0.3), etc.
Returns 0.0 on any evaluation error (silent fallback) β same
contract as before, unrelated inputs behave identically.
"""
try:
tree = ast.parse(tok, mode='eval')
return float(self._eval_ast_node(tree, self._MATH_ENV))
except Exception:
return 0.0
@staticmethod
def _split_params(s: str) -> List[str]:
"""
Split a comma-separated parameter string respecting nested
parentheses. e.g. 'pi/2, atan(1,0)' β ['pi/2', 'atan(1,0)']
"""
tokens: List[str] = []
cur: List[str] = []
depth = 0
for ch in s:
if ch == '(':
depth += 1
cur.append(ch)
elif ch == ')':
depth -= 1
cur.append(ch)
elif ch == ',' and depth == 0:
tokens.append(''.join(cur).strip())
cur = []
else:
cur.append(ch)
if cur:
tokens.append(''.join(cur).strip())
return [t for t in tokens if t]
def _resolve_qubits(self,
s: str,
qmap: Dict[str, int]) -> List[int]:
r"""
Resolve a comma-separated qubit argument string to absolute indices.
Handles
-------
- Indexed: q[0], q[1]
- Bare: q β qmap['q'] (first qubit of that register)
- Range: q[0:3] β [qmap['q[0]'], qmap['q[1]'], qmap['q[2]']]
BUG FIX 6 (original): range syntax q[0:3] was not handled and
fell through to the digit-extraction fallback, returning only
the last number found (e.g., 3 instead of [0,1,2]).
BUG FIX 7 (original): the fallback `digits = re.findall(r'\d+', tok)`
was used as a last resort β this could silently map unknown tokens
to arbitrary integers. Now the fallback is gated on the absence of
any letter character to avoid mapping named registers that are simply
not yet in qmap to wrong indices.
"""
out: List[int] = []
for tok in s.split(','):
tok = tok.strip()
if not tok:
continue
# ββ range syntax: q[start:end] βββββββββββββββββββββββββββ
m = self._RE_RANGE.match(tok)
if m:
base = m.group(1)
start = int(m.group(2))
end = int(m.group(3)) # exclusive upper bound
for i in range(start, end):
key = f'{base}[{i}]'
if key in qmap:
out.append(qmap[key])
continue
# ββ direct map lookup βββββββββββββββββββββββββββββββββββββ
if tok in qmap:
out.append(qmap[tok])
continue
# ββ indexed: base[n] βββββββββββββββββββββββββββββββββββββ
bracket = self._RE_INDEX.search(tok)
if bracket:
base = tok[:tok.index('[')]
key = f'{base}[{bracket.group(1)}]'
if key in qmap:
out.append(qmap[key])
continue
# index not in map β try numeric fallback
out.append(int(bracket.group(1)))
continue
# ββ bare name not in map: try stripping to digits βββββββββ
# Only do this when the token contains no letters (pure numeric)
# to avoid misidentifying unknown register names.
digits = re.findall(r'\d+', tok)
if digits and not re.search(r'[a-zA-Z_]', tok):
out.append(int(digits[-1]))
return out
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