tools/perf/pmu-events/metric.py - linux - Git at Google

 # SPDX-License-Identifier: (LGPL-2.1 OR BSD-2-Clause)
 """Parse or generate representations of perf metrics."""
 import ast
 import decimal
 import json
 import re
 from typing import Dict, List, Optional, Set, Tuple, Union


 class Expression:
   """Abstract base class of elements in a metric expression."""

   def ToPerfJson(self) -> str:
     """Returns a perf json file encoded representation."""
     raise NotImplementedError()

   def ToPython(self) -> str:
     """Returns a python expr parseable representation."""
     raise NotImplementedError()

   def Simplify(self):
     """Returns a simplified version of self."""
     raise NotImplementedError()

   def Equals(self, other) -> bool:
     """Returns true when two expressions are the same."""
     raise NotImplementedError()

   def Substitute(self, name: str, expression: 'Expression') -> 'Expression':
     raise NotImplementedError()

   def __str__(self) -> str:
     return self.ToPerfJson()

   def __or__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('|', self, other)

   def __ror__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('|', other, self)

   def __xor__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('^', self, other)

   def __and__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('&', self, other)

   def __rand__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('&', other, self)

   def __lt__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('<', self, other)

   def __gt__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('>', self, other)

   def __add__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('+', self, other)

   def __radd__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('+', other, self)

   def __sub__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('-', self, other)

   def __rsub__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('-', other, self)

   def __mul__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('*', self, other)

   def __rmul__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('*', other, self)

   def __truediv__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('/', self, other)

   def __rtruediv__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('/', other, self)

   def __mod__(self, other: Union[int, float, 'Expression']) -> 'Operator':
     return Operator('%', self, other)


 def _Constify(val: Union[bool, int, float, Expression]) -> Expression:
   """Used to ensure that the nodes in the expression tree are all Expression."""
   if isinstance(val, bool):
     return Constant(1 if val else 0)
   if isinstance(val, (int, float)):
     return Constant(val)
   return val


 # Simple lookup for operator precedence, used to avoid unnecessary
 # brackets. Precedence matches that of the simple expression parser
 # but differs from python where comparisons are lower precedence than
 # the bitwise &, ^, | but not the logical versions that the expression
 # parser doesn't have.
 _PRECEDENCE = {
     '|': 0,
     '^': 1,
     '&': 2,
     '<': 3,
     '>': 3,
     '+': 4,
     '-': 4,
     '*': 5,
     '/': 5,
     '%': 5,
 }


 class Operator(Expression):
   """Represents a binary operator in the parse tree."""

   def __init__(self, operator: str, lhs: Union[int, float, Expression],
                rhs: Union[int, float, Expression]):
     self.operator = operator
     self.lhs = _Constify(lhs)
     self.rhs = _Constify(rhs)

   def Bracket(self,
               other: Expression,
               other_str: str,
               rhs: bool = False) -> str:
     """If necessary brackets the given other value.

     If ``other`` is an operator then a bracket is necessary when
     this/self operator has higher precedence. Consider: '(a + b) * c',
     ``other_str`` will be 'a + b'. A bracket is necessary as without
     the bracket 'a + b * c' will evaluate 'b * c' first. However, '(a
     * b) + c' doesn't need a bracket as 'a * b' will always be
     evaluated first. For 'a / (b * c)' (ie the same precedence level
     operations) then we add the bracket to best match the original
     input, but not for '(a / b) * c' where the bracket is unnecessary.

     Args:
       other (Expression): is a lhs or rhs operator
       other_str (str): ``other`` in the appropriate string form
       rhs (bool):  is ``other`` on the RHS

     Returns:
       str: possibly bracketed other_str
     """
     if isinstance(other, Operator):
       if _PRECEDENCE.get(self.operator, -1) > _PRECEDENCE.get(
           other.operator, -1):
         return f'({other_str})'
       if rhs and _PRECEDENCE.get(self.operator, -1) == _PRECEDENCE.get(
           other.operator, -1):
         return f'({other_str})'
     return other_str

   def ToPerfJson(self):
     return (f'{self.Bracket(self.lhs, self.lhs.ToPerfJson())} {self.operator} '
             f'{self.Bracket(self.rhs, self.rhs.ToPerfJson(), True)}')

   def ToPython(self):
     return (f'{self.Bracket(self.lhs, self.lhs.ToPython())} {self.operator} '
             f'{self.Bracket(self.rhs, self.rhs.ToPython(), True)}')

   def Simplify(self) -> Expression:
     lhs = self.lhs.Simplify()
     rhs = self.rhs.Simplify()
     if isinstance(lhs, Constant) and isinstance(rhs, Constant):
       return Constant(ast.literal_eval(lhs + self.operator + rhs))

     if isinstance(self.lhs, Constant):
       if self.operator in ('+', '|') and lhs.value == '0':
         return rhs

       # Simplify multiplication by 0 except for the slot event which
       # is deliberately introduced using this pattern.
       if self.operator == '*' and lhs.value == '0' and (
           not isinstance(rhs, Event) or 'slots' not in rhs.name.lower()):
         return Constant(0)

       if self.operator == '*' and lhs.value == '1':
         return rhs

     if isinstance(rhs, Constant):
       if self.operator in ('+', '|') and rhs.value == '0':
         return lhs

       if self.operator == '*' and rhs.value == '0':
         return Constant(0)

       if self.operator == '*' and self.rhs.value == '1':
         return lhs

     return Operator(self.operator, lhs, rhs)

   def Equals(self, other: Expression) -> bool:
     if isinstance(other, Operator):
       return self.operator == other.operator and self.lhs.Equals(
           other.lhs) and self.rhs.Equals(other.rhs)
     return False

   def Substitute(self, name: str, expression: Expression) -> Expression:
     if self.Equals(expression):
       return Event(name)
     lhs = self.lhs.Substitute(name, expression)
     rhs = None
     if self.rhs:
       rhs = self.rhs.Substitute(name, expression)
     return Operator(self.operator, lhs, rhs)


 class Select(Expression):
   """Represents a select ternary in the parse tree."""

   def __init__(self, true_val: Union[int, float, Expression],
                cond: Union[int, float, Expression],
                false_val: Union[int, float, Expression]):
     self.true_val = _Constify(true_val)
     self.cond = _Constify(cond)
     self.false_val = _Constify(false_val)

   def ToPerfJson(self):
     true_str = self.true_val.ToPerfJson()
     cond_str = self.cond.ToPerfJson()
     false_str = self.false_val.ToPerfJson()
     return f'({true_str} if {cond_str} else {false_str})'

   def ToPython(self):
     return (f'Select({self.true_val.ToPython()}, {self.cond.ToPython()}, '
             f'{self.false_val.ToPython()})')

   def Simplify(self) -> Expression:
     cond = self.cond.Simplify()
     true_val = self.true_val.Simplify()
     false_val = self.false_val.Simplify()
     if isinstance(cond, Constant):
       return false_val if cond.value == '0' else true_val

     if true_val.Equals(false_val):
       return true_val

     return Select(true_val, cond, false_val)

   def Equals(self, other: Expression) -> bool:
     if isinstance(other, Select):
       return self.cond.Equals(other.cond) and self.false_val.Equals(
           other.false_val) and self.true_val.Equals(other.true_val)
     return False

   def Substitute(self, name: str, expression: Expression) -> Expression:
     if self.Equals(expression):
       return Event(name)
     true_val = self.true_val.Substitute(name, expression)
     cond = self.cond.Substitute(name, expression)
     false_val = self.false_val.Substitute(name, expression)
     return Select(true_val, cond, false_val)


 class Function(Expression):
   """A function in an expression like min, max, d_ratio."""

   def __init__(self,
                fn: str,
                lhs: Union[int, float, Expression],
                rhs: Optional[Union[int, float, Expression]] = None):
     self.fn = fn
     self.lhs = _Constify(lhs)
     self.rhs = _Constify(rhs)

   def ToPerfJson(self):
     if self.rhs:
       return f'{self.fn}({self.lhs.ToPerfJson()}, {self.rhs.ToPerfJson()})'
     return f'{self.fn}({self.lhs.ToPerfJson()})'

   def ToPython(self):
     if self.rhs:
       return f'{self.fn}({self.lhs.ToPython()}, {self.rhs.ToPython()})'
     return f'{self.fn}({self.lhs.ToPython()})'

   def Simplify(self) -> Expression:
     lhs = self.lhs.Simplify()
     rhs = self.rhs.Simplify() if self.rhs else None
     if isinstance(lhs, Constant) and isinstance(rhs, Constant):
       if self.fn == 'd_ratio':
         if rhs.value == '0':
           return Constant(0)
         Constant(ast.literal_eval(f'{lhs} / {rhs}'))
       return Constant(ast.literal_eval(f'{self.fn}({lhs}, {rhs})'))

     return Function(self.fn, lhs, rhs)

   def Equals(self, other: Expression) -> bool:
     if isinstance(other, Function):
       result = self.fn == other.fn and self.lhs.Equals(other.lhs)
       if self.rhs:
         result = result and self.rhs.Equals(other.rhs)
       return result
     return False

   def Substitute(self, name: str, expression: Expression) -> Expression:
     if self.Equals(expression):
       return Event(name)
     lhs = self.lhs.Substitute(name, expression)
     rhs = None
     if self.rhs:
       rhs = self.rhs.Substitute(name, expression)
     return Function(self.fn, lhs, rhs)


 def _FixEscapes(s: str) -> str:
   s = re.sub(r'([^\\]),', r'\1\\,', s)
   return re.sub(r'([^\\])=', r'\1\\=', s)


 class Event(Expression):
   """An event in an expression."""

   def __init__(self, name: str, legacy_name: str = ''):
     self.name = _FixEscapes(name)
     self.legacy_name = _FixEscapes(legacy_name)

   def ToPerfJson(self):
     result = re.sub('/', '@', self.name)
     return result

   def ToPython(self):
     return f'Event(r"{self.name}")'

   def Simplify(self) -> Expression:
     return self

   def Equals(self, other: Expression) -> bool:
     return isinstance(other, Event) and self.name == other.name

   def Substitute(self, name: str, expression: Expression) -> Expression:
     return self


 class Constant(Expression):
   """A constant within the expression tree."""

   def __init__(self, value: Union[float, str]):
     ctx = decimal.Context()
     ctx.prec = 20
     dec = ctx.create_decimal(repr(value) if isinstance(value, float) else value)
     self.value = dec.normalize().to_eng_string()
     self.value = self.value.replace('+', '')
     self.value = self.value.replace('E', 'e')

   def ToPerfJson(self):
     return self.value

   def ToPython(self):
     return f'Constant({self.value})'

   def Simplify(self) -> Expression:
     return self

   def Equals(self, other: Expression) -> bool:
     return isinstance(other, Constant) and self.value == other.value

   def Substitute(self, name: str, expression: Expression) -> Expression:
     return self


 class Literal(Expression):
   """A runtime literal within the expression tree."""

   def __init__(self, value: str):
     self.value = value

   def ToPerfJson(self):
     return self.value

   def ToPython(self):
     return f'Literal({self.value})'

   def Simplify(self) -> Expression:
     return self

   def Equals(self, other: Expression) -> bool:
     return isinstance(other, Literal) and self.value == other.value

   def Substitute(self, name: str, expression: Expression) -> Expression:
     return self


 def min(lhs: Union[int, float, Expression], rhs: Union[int, float,
                                                        Expression]) -> Function:
   # pylint: disable=redefined-builtin
   # pylint: disable=invalid-name
   return Function('min', lhs, rhs)


 def max(lhs: Union[int, float, Expression], rhs: Union[int, float,
                                                        Expression]) -> Function:
   # pylint: disable=redefined-builtin
   # pylint: disable=invalid-name
   return Function('max', lhs, rhs)


 def d_ratio(lhs: Union[int, float, Expression],
             rhs: Union[int, float, Expression]) -> Function:
   # pylint: disable=redefined-builtin
   # pylint: disable=invalid-name
   return Function('d_ratio', lhs, rhs)


 def source_count(event: Event) -> Function:
   # pylint: disable=redefined-builtin
   # pylint: disable=invalid-name
   return Function('source_count', event)


 def has_event(event: Event) -> Function:
   # pylint: disable=redefined-builtin
   # pylint: disable=invalid-name
   return Function('has_event', event)

 def strcmp_cpuid_str(cpuid: Event) -> Function:
   # pylint: disable=redefined-builtin
   # pylint: disable=invalid-name
   return Function('strcmp_cpuid_str', cpuid)

 class Metric:
   """An individual metric that will specifiable on the perf command line."""
   groups: Set[str]
   expr: Expression
   scale_unit: str
   constraint: bool

   def __init__(self,
                name: str,
                description: str,
                expr: Expression,
                scale_unit: str,
                constraint: bool = False):
     self.name = name
     self.description = description
     self.expr = expr.Simplify()
     # Workraound valid_only_metric hiding certain metrics based on unit.
     scale_unit = scale_unit.replace('/sec', ' per sec')
     if scale_unit[0].isdigit():
       self.scale_unit = scale_unit
     else:
       self.scale_unit = f'1{scale_unit}'
     self.constraint = constraint
     self.groups = set()

   def __lt__(self, other):
     """Sort order."""
     return self.name < other.name

   def AddToMetricGroup(self, group):
     """Callback used when being added to a MetricGroup."""
     self.groups.add(group.name)

   def Flatten(self) -> Set['Metric']:
     """Return a leaf metric."""
     return set([self])

   def ToPerfJson(self) -> Dict[str, str]:
     """Return as dictionary for Json generation."""
     result = {
         'MetricName': self.name,
         'MetricGroup': ';'.join(sorted(self.groups)),
         'BriefDescription': self.description,
         'MetricExpr': self.expr.ToPerfJson(),
         'ScaleUnit': self.scale_unit
     }
     if self.constraint:
       result['MetricConstraint'] = 'NO_NMI_WATCHDOG'

     return result


 class _MetricJsonEncoder(json.JSONEncoder):
   """Special handling for Metric objects."""

   def default(self, o):
     if isinstance(o, Metric):
       return o.ToPerfJson()
     return json.JSONEncoder.default(self, o)


 class MetricGroup:
   """A group of metrics.

   Metric groups may be specificd on the perf command line, but within
   the json they aren't encoded. Metrics may be in multiple groups
   which can facilitate arrangements similar to trees.
   """

   def __init__(self, name: str, metric_list: List[Union[Metric,
                                                         'MetricGroup']]):
     self.name = name
     self.metric_list = metric_list
     for metric in metric_list:
       metric.AddToMetricGroup(self)

   def AddToMetricGroup(self, group):
     """Callback used when a MetricGroup is added into another."""
     for metric in self.metric_list:
       metric.AddToMetricGroup(group)

   def Flatten(self) -> Set[Metric]:
     """Returns a set of all leaf metrics."""
     result = set()
     for x in self.metric_list:
       result = result.union(x.Flatten())

     return result

   def ToPerfJson(self) -> str:
     return json.dumps(sorted(self.Flatten()), indent=2, cls=_MetricJsonEncoder)

   def __str__(self) -> str:
     return self.ToPerfJson()


 class _RewriteIfExpToSelect(ast.NodeTransformer):
   """Transformer to convert if-else nodes to Select expressions."""

   def visit_IfExp(self, node):
     # pylint: disable=invalid-name
     self.generic_visit(node)
     call = ast.Call(
         func=ast.Name(id='Select', ctx=ast.Load()),
         args=[node.body, node.test, node.orelse],
         keywords=[])
     ast.copy_location(call, node.test)
     return call


 def ParsePerfJson(orig: str) -> Expression:
   """A simple json metric expression decoder.

   Converts a json encoded metric expression by way of python's ast and
   eval routine. First tokens are mapped to Event calls, then
   accidentally converted keywords or literals are mapped to their
   appropriate calls. Python's ast is used to match if-else that can't
   be handled via operator overloading. Finally the ast is evaluated.

   Args:
     orig (str): String to parse.

   Returns:
     Expression: The parsed string.
   """
   # pylint: disable=eval-used
   py = orig.strip()
   # First try to convert everything that looks like a string (event name) into Event(r"EVENT_NAME").
   # This isn't very selective so is followed up by converting some unwanted conversions back again
   py = re.sub(r'([a-zA-Z][^-+/\* \\\(\),]*(?:\\.[^-+/\* \\\(\),]*)*)',
               r'Event(r"\1")', py)
   # If it started with a # it should have been a literal, rather than an event name
   py = re.sub(r'#Event\(r"([^"]*)"\)', r'Literal("#\1")', py)
   # Convert accidentally converted hex constants ("0Event(r"xDEADBEEF)"") back to a constant,
   # but keep it wrapped in Event(), otherwise Python drops the 0x prefix and it gets interpreted as
   # a double by the Bison parser
   py = re.sub(r'0Event\(r"[xX]([0-9a-fA-F]*)"\)', r'Event("0x\1")', py)
   # Convert accidentally converted scientific notation constants back
   py = re.sub(r'([0-9]+)Event\(r"(e[0-9]+)"\)', r'\1\2', py)
   # Convert all the known keywords back from events to just the keyword
   keywords = ['if', 'else', 'min', 'max', 'd_ratio', 'source_count', 'has_event', 'strcmp_cpuid_str']
   for kw in keywords:
     py = re.sub(rf'Event\(r"{kw}"\)', kw, py)
   try:
     parsed = ast.parse(py, mode='eval')
   except SyntaxError as e:
     raise SyntaxError(f'Parsing expression:\n{orig}') from e
   _RewriteIfExpToSelect().visit(parsed)
   parsed = ast.fix_missing_locations(parsed)
   return _Constify(eval(compile(parsed, orig, 'eval')))


 def RewriteMetricsInTermsOfOthers(metrics: List[Tuple[str, str, Expression]]
                                   )-> Dict[Tuple[str, str], Expression]:
   """Shorten metrics by rewriting in terms of others.

   Args:
     metrics (list): pmus, metric names and their expressions.
   Returns:
     Dict: mapping from a pmu, metric name pair to a shortened expression.
   """
   updates: Dict[Tuple[str, str], Expression] = dict()
   for outer_pmu, outer_name, outer_expression in metrics:
     if outer_pmu is None:
       outer_pmu = 'cpu'
     updated = outer_expression
     while True:
       for inner_pmu, inner_name, inner_expression in metrics:
         if inner_pmu is None:
           inner_pmu = 'cpu'
         if inner_pmu.lower() != outer_pmu.lower():
           continue
         if inner_name.lower() == outer_name.lower():
           continue
         if (inner_pmu, inner_name) in updates:
           inner_expression = updates[(inner_pmu, inner_name)]
         updated = updated.Substitute(inner_name, inner_expression)
       if updated.Equals(outer_expression):
         break
       if (outer_pmu, outer_name) in updates and updated.Equals(updates[(outer_pmu, outer_name)]):
         break
       updates[(outer_pmu, outer_name)] = updated
   return updates
	# SPDX-License-Identifier: (LGPL-2.1 OR BSD-2-Clause)
	"""Parse or generate representations of perf metrics."""
	import ast
	import decimal
	import json
	import re
	from typing import Dict, List, Optional, Set, Tuple, Union


	class Expression:
	"""Abstract base class of elements in a metric expression."""

	def ToPerfJson(self) -> str:
	"""Returns a perf json file encoded representation."""
	raise NotImplementedError()

	def ToPython(self) -> str:
	"""Returns a python expr parseable representation."""
	raise NotImplementedError()

	def Simplify(self):
	"""Returns a simplified version of self."""
	raise NotImplementedError()

	def Equals(self, other) -> bool:
	"""Returns true when two expressions are the same."""
	raise NotImplementedError()

	def Substitute(self, name: str, expression: 'Expression') -> 'Expression':
	raise NotImplementedError()

	def __str__(self) -> str:
	return self.ToPerfJson()

	def __or__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('\|', self, other)

	def __ror__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('\|', other, self)

	def __xor__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('^', self, other)

	def __and__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('&', self, other)

	def __rand__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('&', other, self)

	def __lt__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('<', self, other)

	def __gt__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('>', self, other)

	def __add__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('+', self, other)

	def __radd__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('+', other, self)

	def __sub__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('-', self, other)

	def __rsub__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('-', other, self)

	def __mul__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('*', self, other)

	def __rmul__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('*', other, self)

	def __truediv__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('/', self, other)

	def __rtruediv__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('/', other, self)

	def __mod__(self, other: Union[int, float, 'Expression']) -> 'Operator':
	return Operator('%', self, other)


	def _Constify(val: Union[bool, int, float, Expression]) -> Expression:
	"""Used to ensure that the nodes in the expression tree are all Expression."""
	if isinstance(val, bool):
	return Constant(1 if val else 0)
	if isinstance(val, (int, float)):
	return Constant(val)
	return val


	# Simple lookup for operator precedence, used to avoid unnecessary
	# brackets. Precedence matches that of the simple expression parser
	# but differs from python where comparisons are lower precedence than
	# the bitwise &, ^, \| but not the logical versions that the expression
	# parser doesn't have.
	_PRECEDENCE = {
	'\|': 0,
	'^': 1,
	'&': 2,
	'<': 3,
	'>': 3,
	'+': 4,
	'-': 4,
	'*': 5,
	'/': 5,
	'%': 5,
	}


	class Operator(Expression):
	"""Represents a binary operator in the parse tree."""

	def __init__(self, operator: str, lhs: Union[int, float, Expression],
	rhs: Union[int, float, Expression]):
	self.operator = operator
	self.lhs = _Constify(lhs)
	self.rhs = _Constify(rhs)

	def Bracket(self,
	other: Expression,
	other_str: str,
	rhs: bool = False) -> str:
	"""If necessary brackets the given other value.

	If ``other`` is an operator then a bracket is necessary when
	this/self operator has higher precedence. Consider: '(a + b) * c',
	``other_str`` will be 'a + b'. A bracket is necessary as without
	the bracket 'a + b * c' will evaluate 'b * c' first. However, '(a
	* b) + c' doesn't need a bracket as 'a * b' will always be
	evaluated first. For 'a / (b * c)' (ie the same precedence level
	operations) then we add the bracket to best match the original
	input, but not for '(a / b) * c' where the bracket is unnecessary.

	Args:
	other (Expression): is a lhs or rhs operator
	other_str (str): ``other`` in the appropriate string form
	rhs (bool): is ``other`` on the RHS

	Returns:
	str: possibly bracketed other_str
	"""
	if isinstance(other, Operator):
	if _PRECEDENCE.get(self.operator, -1) > _PRECEDENCE.get(
	other.operator, -1):
	return f'({other_str})'
	if rhs and _PRECEDENCE.get(self.operator, -1) == _PRECEDENCE.get(
	other.operator, -1):
	return f'({other_str})'
	return other_str

	def ToPerfJson(self):
	return (f'{self.Bracket(self.lhs, self.lhs.ToPerfJson())} {self.operator} '
	f'{self.Bracket(self.rhs, self.rhs.ToPerfJson(), True)}')

	def ToPython(self):
	return (f'{self.Bracket(self.lhs, self.lhs.ToPython())} {self.operator} '
	f'{self.Bracket(self.rhs, self.rhs.ToPython(), True)}')

	def Simplify(self) -> Expression:
	lhs = self.lhs.Simplify()
	rhs = self.rhs.Simplify()
	if isinstance(lhs, Constant) and isinstance(rhs, Constant):
	return Constant(ast.literal_eval(lhs + self.operator + rhs))

	if isinstance(self.lhs, Constant):
	if self.operator in ('+', '\|') and lhs.value == '0':
	return rhs

	# Simplify multiplication by 0 except for the slot event which
	# is deliberately introduced using this pattern.
	if self.operator == '*' and lhs.value == '0' and (
	not isinstance(rhs, Event) or 'slots' not in rhs.name.lower()):
	return Constant(0)

	if self.operator == '*' and lhs.value == '1':
	return rhs

	if isinstance(rhs, Constant):
	if self.operator in ('+', '\|') and rhs.value == '0':
	return lhs

	if self.operator == '*' and rhs.value == '0':
	return Constant(0)

	if self.operator == '*' and self.rhs.value == '1':
	return lhs

	return Operator(self.operator, lhs, rhs)

	def Equals(self, other: Expression) -> bool:
	if isinstance(other, Operator):
	return self.operator == other.operator and self.lhs.Equals(
	other.lhs) and self.rhs.Equals(other.rhs)
	return False

	def Substitute(self, name: str, expression: Expression) -> Expression:
	if self.Equals(expression):
	return Event(name)
	lhs = self.lhs.Substitute(name, expression)
	rhs = None
	if self.rhs:
	rhs = self.rhs.Substitute(name, expression)
	return Operator(self.operator, lhs, rhs)


	class Select(Expression):
	"""Represents a select ternary in the parse tree."""

	def __init__(self, true_val: Union[int, float, Expression],
	cond: Union[int, float, Expression],
	false_val: Union[int, float, Expression]):
	self.true_val = _Constify(true_val)
	self.cond = _Constify(cond)
	self.false_val = _Constify(false_val)

	def ToPerfJson(self):
	true_str = self.true_val.ToPerfJson()
	cond_str = self.cond.ToPerfJson()
	false_str = self.false_val.ToPerfJson()
	return f'({true_str} if {cond_str} else {false_str})'

	def ToPython(self):
	return (f'Select({self.true_val.ToPython()}, {self.cond.ToPython()}, '
	f'{self.false_val.ToPython()})')

	def Simplify(self) -> Expression:
	cond = self.cond.Simplify()
	true_val = self.true_val.Simplify()
	false_val = self.false_val.Simplify()
	if isinstance(cond, Constant):
	return false_val if cond.value == '0' else true_val

	if true_val.Equals(false_val):
	return true_val

	return Select(true_val, cond, false_val)

	def Equals(self, other: Expression) -> bool:
	if isinstance(other, Select):
	return self.cond.Equals(other.cond) and self.false_val.Equals(
	other.false_val) and self.true_val.Equals(other.true_val)
	return False

	def Substitute(self, name: str, expression: Expression) -> Expression:
	if self.Equals(expression):
	return Event(name)
	true_val = self.true_val.Substitute(name, expression)
	cond = self.cond.Substitute(name, expression)
	false_val = self.false_val.Substitute(name, expression)
	return Select(true_val, cond, false_val)


	class Function(Expression):
	"""A function in an expression like min, max, d_ratio."""

	def __init__(self,
	fn: str,
	lhs: Union[int, float, Expression],
	rhs: Optional[Union[int, float, Expression]] = None):
	self.fn = fn
	self.lhs = _Constify(lhs)
	self.rhs = _Constify(rhs)

	def ToPerfJson(self):
	if self.rhs:
	return f'{self.fn}({self.lhs.ToPerfJson()}, {self.rhs.ToPerfJson()})'
	return f'{self.fn}({self.lhs.ToPerfJson()})'

	def ToPython(self):
	if self.rhs:
	return f'{self.fn}({self.lhs.ToPython()}, {self.rhs.ToPython()})'
	return f'{self.fn}({self.lhs.ToPython()})'

	def Simplify(self) -> Expression:
	lhs = self.lhs.Simplify()
	rhs = self.rhs.Simplify() if self.rhs else None
	if isinstance(lhs, Constant) and isinstance(rhs, Constant):
	if self.fn == 'd_ratio':
	if rhs.value == '0':
	return Constant(0)
	Constant(ast.literal_eval(f'{lhs} / {rhs}'))
	return Constant(ast.literal_eval(f'{self.fn}({lhs}, {rhs})'))

	return Function(self.fn, lhs, rhs)

	def Equals(self, other: Expression) -> bool:
	if isinstance(other, Function):
	result = self.fn == other.fn and self.lhs.Equals(other.lhs)
	if self.rhs:
	result = result and self.rhs.Equals(other.rhs)
	return result
	return False

	def Substitute(self, name: str, expression: Expression) -> Expression:
	if self.Equals(expression):
	return Event(name)
	lhs = self.lhs.Substitute(name, expression)
	rhs = None
	if self.rhs:
	rhs = self.rhs.Substitute(name, expression)
	return Function(self.fn, lhs, rhs)


	def _FixEscapes(s: str) -> str:
	s = re.sub(r'([^\\]),', r'\1\\,', s)
	return re.sub(r'([^\\])=', r'\1\\=', s)


	class Event(Expression):
	"""An event in an expression."""

	def __init__(self, name: str, legacy_name: str = ''):
	self.name = _FixEscapes(name)
	self.legacy_name = _FixEscapes(legacy_name)

	def ToPerfJson(self):
	result = re.sub('/', '@', self.name)
	return result

	def ToPython(self):
	return f'Event(r"{self.name}")'

	def Simplify(self) -> Expression:
	return self

	def Equals(self, other: Expression) -> bool:
	return isinstance(other, Event) and self.name == other.name

	def Substitute(self, name: str, expression: Expression) -> Expression:
	return self


	class Constant(Expression):
	"""A constant within the expression tree."""

	def __init__(self, value: Union[float, str]):
	ctx = decimal.Context()
	ctx.prec = 20
	dec = ctx.create_decimal(repr(value) if isinstance(value, float) else value)
	self.value = dec.normalize().to_eng_string()
	self.value = self.value.replace('+', '')
	self.value = self.value.replace('E', 'e')

	def ToPerfJson(self):
	return self.value

	def ToPython(self):
	return f'Constant({self.value})'

	def Simplify(self) -> Expression:
	return self

	def Equals(self, other: Expression) -> bool:
	return isinstance(other, Constant) and self.value == other.value

	def Substitute(self, name: str, expression: Expression) -> Expression:
	return self


	class Literal(Expression):
	"""A runtime literal within the expression tree."""

	def __init__(self, value: str):
	self.value = value

	def ToPerfJson(self):
	return self.value

	def ToPython(self):
	return f'Literal({self.value})'

	def Simplify(self) -> Expression:
	return self

	def Equals(self, other: Expression) -> bool:
	return isinstance(other, Literal) and self.value == other.value

	def Substitute(self, name: str, expression: Expression) -> Expression:
	return self


	def min(lhs: Union[int, float, Expression], rhs: Union[int, float,
	Expression]) -> Function:
	# pylint: disable=redefined-builtin
	# pylint: disable=invalid-name
	return Function('min', lhs, rhs)


	def max(lhs: Union[int, float, Expression], rhs: Union[int, float,
	Expression]) -> Function:
	# pylint: disable=redefined-builtin
	# pylint: disable=invalid-name
	return Function('max', lhs, rhs)


	def d_ratio(lhs: Union[int, float, Expression],
	rhs: Union[int, float, Expression]) -> Function:
	# pylint: disable=redefined-builtin
	# pylint: disable=invalid-name
	return Function('d_ratio', lhs, rhs)


	def source_count(event: Event) -> Function:
	# pylint: disable=redefined-builtin
	# pylint: disable=invalid-name
	return Function('source_count', event)


	def has_event(event: Event) -> Function:
	# pylint: disable=redefined-builtin
	# pylint: disable=invalid-name
	return Function('has_event', event)

	def strcmp_cpuid_str(cpuid: Event) -> Function:
	# pylint: disable=redefined-builtin
	# pylint: disable=invalid-name
	return Function('strcmp_cpuid_str', cpuid)

	class Metric:
	"""An individual metric that will specifiable on the perf command line."""
	groups: Set[str]
	expr: Expression
	scale_unit: str
	constraint: bool

	def __init__(self,
	name: str,
	description: str,
	expr: Expression,
	scale_unit: str,
	constraint: bool = False):
	self.name = name
	self.description = description
	self.expr = expr.Simplify()
	# Workraound valid_only_metric hiding certain metrics based on unit.
	scale_unit = scale_unit.replace('/sec', ' per sec')
	if scale_unit[0].isdigit():
	self.scale_unit = scale_unit
	else:
	self.scale_unit = f'1{scale_unit}'
	self.constraint = constraint
	self.groups = set()

	def __lt__(self, other):
	"""Sort order."""
	return self.name < other.name

	def AddToMetricGroup(self, group):
	"""Callback used when being added to a MetricGroup."""
	self.groups.add(group.name)

	def Flatten(self) -> Set['Metric']:
	"""Return a leaf metric."""
	return set([self])

	def ToPerfJson(self) -> Dict[str, str]:
	"""Return as dictionary for Json generation."""
	result = {
	'MetricName': self.name,
	'MetricGroup': ';'.join(sorted(self.groups)),
	'BriefDescription': self.description,
	'MetricExpr': self.expr.ToPerfJson(),
	'ScaleUnit': self.scale_unit
	}
	if self.constraint:
	result['MetricConstraint'] = 'NO_NMI_WATCHDOG'

	return result


	class _MetricJsonEncoder(json.JSONEncoder):
	"""Special handling for Metric objects."""

	def default(self, o):
	if isinstance(o, Metric):
	return o.ToPerfJson()
	return json.JSONEncoder.default(self, o)


	class MetricGroup:
	"""A group of metrics.

	Metric groups may be specificd on the perf command line, but within
	the json they aren't encoded. Metrics may be in multiple groups
	which can facilitate arrangements similar to trees.
	"""

	def __init__(self, name: str, metric_list: List[Union[Metric,
	'MetricGroup']]):
	self.name = name
	self.metric_list = metric_list
	for metric in metric_list:
	metric.AddToMetricGroup(self)

	def AddToMetricGroup(self, group):
	"""Callback used when a MetricGroup is added into another."""
	for metric in self.metric_list:
	metric.AddToMetricGroup(group)

	def Flatten(self) -> Set[Metric]:
	"""Returns a set of all leaf metrics."""
	result = set()
	for x in self.metric_list:
	result = result.union(x.Flatten())

	return result

	def ToPerfJson(self) -> str:
	return json.dumps(sorted(self.Flatten()), indent=2, cls=_MetricJsonEncoder)

	def __str__(self) -> str:
	return self.ToPerfJson()


	class _RewriteIfExpToSelect(ast.NodeTransformer):
	"""Transformer to convert if-else nodes to Select expressions."""

	def visit_IfExp(self, node):
	# pylint: disable=invalid-name
	self.generic_visit(node)
	call = ast.Call(
	func=ast.Name(id='Select', ctx=ast.Load()),
	args=[node.body, node.test, node.orelse],
	keywords=[])
	ast.copy_location(call, node.test)
	return call


	def ParsePerfJson(orig: str) -> Expression:
	"""A simple json metric expression decoder.

	Converts a json encoded metric expression by way of python's ast and
	eval routine. First tokens are mapped to Event calls, then
	accidentally converted keywords or literals are mapped to their
	appropriate calls. Python's ast is used to match if-else that can't
	be handled via operator overloading. Finally the ast is evaluated.

	Args:
	orig (str): String to parse.

	Returns:
	Expression: The parsed string.
	"""
	# pylint: disable=eval-used
	py = orig.strip()
	# First try to convert everything that looks like a string (event name) into Event(r"EVENT_NAME").
	# This isn't very selective so is followed up by converting some unwanted conversions back again
	py = re.sub(r'([a-zA-Z][^-+/\* \\\(\),](?:\\.[^-+/\ \\\(\),]))',
	r'Event(r"\1")', py)
	# If it started with a # it should have been a literal, rather than an event name
	py = re.sub(r'#Event\(r"([^"]*)"\)', r'Literal("#\1")', py)
	# Convert accidentally converted hex constants ("0Event(r"xDEADBEEF)"") back to a constant,
	# but keep it wrapped in Event(), otherwise Python drops the 0x prefix and it gets interpreted as
	# a double by the Bison parser
	py = re.sub(r'0Event\(r"[xX]([0-9a-fA-F]*)"\)', r'Event("0x\1")', py)
	# Convert accidentally converted scientific notation constants back
	py = re.sub(r'([0-9]+)Event\(r"(e[0-9]+)"\)', r'\1\2', py)
	# Convert all the known keywords back from events to just the keyword
	keywords = ['if', 'else', 'min', 'max', 'd_ratio', 'source_count', 'has_event', 'strcmp_cpuid_str']
	for kw in keywords:
	py = re.sub(rf'Event\(r"{kw}"\)', kw, py)
	try:
	parsed = ast.parse(py, mode='eval')
	except SyntaxError as e:
	raise SyntaxError(f'Parsing expression:\n{orig}') from e
	_RewriteIfExpToSelect().visit(parsed)
	parsed = ast.fix_missing_locations(parsed)
	return _Constify(eval(compile(parsed, orig, 'eval')))


	def RewriteMetricsInTermsOfOthers(metrics: List[Tuple[str, str, Expression]]
	)-> Dict[Tuple[str, str], Expression]:
	"""Shorten metrics by rewriting in terms of others.

	Args:
	metrics (list): pmus, metric names and their expressions.
	Returns:
	Dict: mapping from a pmu, metric name pair to a shortened expression.
	"""
	updates: Dict[Tuple[str, str], Expression] = dict()
	for outer_pmu, outer_name, outer_expression in metrics:
	if outer_pmu is None:
	outer_pmu = 'cpu'
	updated = outer_expression
	while True:
	for inner_pmu, inner_name, inner_expression in metrics:
	if inner_pmu is None:
	inner_pmu = 'cpu'
	if inner_pmu.lower() != outer_pmu.lower():
	continue
	if inner_name.lower() == outer_name.lower():
	continue
	if (inner_pmu, inner_name) in updates:
	inner_expression = updates[(inner_pmu, inner_name)]
	updated = updated.Substitute(inner_name, inner_expression)
	if updated.Equals(outer_expression):
	break
	if (outer_pmu, outer_name) in updates and updated.Equals(updates[(outer_pmu, outer_name)]):
	break
	updates[(outer_pmu, outer_name)] = updated
	return updates