text: ###################################################################
  #  Numexpr - Fast numerical array expression evaluator for NumPy.
  #
  #      License: MIT
  #      Author:  See AUTHORS.txt
  #
  #  See LICENSE.txt and LICENSES/*.txt for details about copyright and
  #  rights to use.
  ####################################################################
  
  import __future__
  import sys
  import numpy
  import threading
  
  is_cpu_amd_intel = False # DEPRECATION WARNING: WILL BE REMOVED IN FUTURE RELEASE
  from numexpr import interpreter, expressions, use_vml
  from numexpr.utils import CacheDict
  
  # Declare a double type that does not exist in Python space
  double = numpy.double
  if sys.version_info[0] < 3:
      int_ = int
      long_ = int
  else:
      int_ = numpy.int32
      long_ = numpy.int64
  
  typecode_to_kind = {'b': 'bool', 'i': 'int', 'l': 'long', 'f': 'float',
                      'd': 'double', 'c': 'complex', 's': 'bytes', 'n': 'none'}
  kind_to_typecode = {'bool': 'b', 'int': 'i', 'long': 'l', 'float': 'f',
                      'double': 'd', 'complex': 'c', 'bytes': 's', 'none': 'n'}
  type_to_typecode = {bool: 'b', int_: 'i', long_: 'l', float: 'f',
                      double: 'd', complex: 'c', bytes: 's'}
  type_to_kind = expressions.type_to_kind
  kind_to_type = expressions.kind_to_type
  default_type = kind_to_type[expressions.default_kind]
  
  # VML functions that are implemented in numexpr
  vml_functions = [
      "div",  # interp_body.cpp
      "inv",  # interp_body.cpp
      "pow",  # interp_body.cpp
      # Keep the rest of this list in sync with the ones listed in functions.hpp
      "sqrt",
      "sin",
      "cos",
      "tan",
      "arcsin",
      "arccos",
      "arctan",
      "sinh",
      "cosh",
      "tanh",
      "arcsinh",
      "arccosh",
      "arctanh",
      "log",
      "log1p",
      "log10",
      "exp",
      "expm1",
      "absolute",
      "conjugate",
      "arctan2",
      "fmod",
      "ceil",
      "floor"
      ]
  
  # Final addtions for Python 3 (mainly for PyTables needs)
  if sys.version_info[0] > 2:
      typecode_to_kind['s'] = 'str'
      kind_to_typecode['str'] = 's'
      type_to_typecode[str] = 's'
  
  scalar_constant_kinds = list(kind_to_typecode.keys())
  
  
  class ASTNode(object):
      """Abstract Syntax Tree node.
  
      Members:
  
      astType      -- type of node (op, constant, variable, raw, or alias)
      astKind      -- the type of the result (bool, float, etc.)
      value        -- value associated with this node.
                      An opcode, numerical value, a variable name, etc.
      children     -- the children below this node
      reg          -- the register assigned to the result for this node.
      """
      cmpnames = ['astType', 'astKind', 'value', 'children']
  
      def __init__(self, astType='generic', astKind='unknown',
                   value=None, children=()):
          object.__init__(self)
          self.astType = astType
          self.astKind = astKind
          self.value = value
          self.children = tuple(children)
          self.reg = None
  
      def __eq__(self, other):
          if self.astType == 'alias':
              self = self.value
          if other.astType == 'alias':
              other = other.value
          if not isinstance(other, ASTNode):
              return False
          for name in self.cmpnames:
              if getattr(self, name) != getattr(other, name):
                  return False
          return True
      
      def __lt__(self,other):
          # RAM: this is a fix for issue #88 whereby sorting on constants 
          # that may be of astKind == 'complex' but type(self.value) == int or float
          # Here we let NumPy sort as it will cast data properly for comparison 
          # when the Python built-ins will raise an error.
          if self.astType == 'constant':
              if self.astKind == other.astKind:
                  return numpy.array(self.value) < numpy.array(other.value)
              return self.astKind < other.astKind
          else:
              raise TypeError( 'Sorting not implemented for astType: %s'%self.astType )
  
      def __hash__(self):
          if self.astType == 'alias':
              self = self.value
          return hash((self.astType, self.astKind, self.value, self.children))
  
      def __str__(self):
          return 'AST(%s, %s, %s, %s, %s)' % (self.astType, self.astKind,
                                              self.value, self.children, self.reg)
  
      def __repr__(self):
          return '<AST object at %s>' % id(self)
  
      def key(self):
          return (self.astType, self.astKind, self.value, self.children)
  
      def typecode(self):
          return kind_to_typecode[self.astKind]
  
      def postorderWalk(self):
          for c in self.children:
              for w in c.postorderWalk():
                  yield w
          yield self
  
      def allOf(self, *astTypes):
          astTypes = set(astTypes)
          for w in self.postorderWalk():
              if w.astType in astTypes:
                  yield w
  
  
  def expressionToAST(ex):
      """Take an expression tree made out of expressions.ExpressionNode,
      and convert to an AST tree.
  
      This is necessary as ExpressionNode overrides many methods to act
      like a number.
      """
      return ASTNode(ex.astType, ex.astKind, ex.value,
                     [expressionToAST(c) for c in ex.children])
  
  
  def sigPerms(s):
      """Generate all possible signatures derived by upcasting the given
      signature.
      """
      codes = 'bilfdc'
      if not s:
          yield ''
      elif s[0] in codes:
          start = codes.index(s[0])
          for x in codes[start:]:
              for y in sigPerms(s[1:]):
                  yield x + y
      elif s[0] == 's':  # numbers shall not be cast to strings
          for y in sigPerms(s[1:]):
              yield 's' + y
      else:
          yield s
  
  
  def typeCompileAst(ast):
      """Assign appropiate types to each node in the AST.
  
      Will convert opcodes and functions to appropiate upcast version,
      and add "cast" ops if needed.
      """
      children = list(ast.children)
      if ast.astType == 'op':
          retsig = ast.typecode()
          basesig = ''.join(x.typecode() for x in list(ast.children))
          # Find some operation that will work on an acceptable casting of args.
          for sig in sigPerms(basesig):
              value = (ast.value + '_' + retsig + sig).encode('ascii')
              if value in interpreter.opcodes:
                  break
          else:
              for sig in sigPerms(basesig):
                  funcname = (ast.value + '_' + retsig + sig).encode('ascii')
                  if funcname in interpreter.funccodes:
                      value = ('func_%sn' % (retsig + sig)).encode('ascii')
                      children += [ASTNode('raw', 'none',
                                           interpreter.funccodes[funcname])]
                      break
              else:
                  raise NotImplementedError(
                      "couldn't find matching opcode for '%s'"
                      % (ast.value + '_' + retsig + basesig))
          # First just cast constants, then cast variables if necessary:
          for i, (have, want) in enumerate(zip(basesig, sig)):
              if have != want:
                  kind = typecode_to_kind[want]
                  if children[i].astType == 'constant':
                      children[i] = ASTNode('constant', kind, children[i].value)
                  else:
                      opname = "cast"
                      children[i] = ASTNode('op', kind, opname, [children[i]])
      else:
          value = ast.value
          children = ast.children
      return ASTNode(ast.astType, ast.astKind, value,
                     [typeCompileAst(c) for c in children])
  
  
  class Register(object):
      """Abstraction for a register in the VM.
  
      Members:
      node          -- the AST node this corresponds to
      temporary     -- True if this isn't an input or output
      immediate     -- not a register, but an immediate value
      n             -- the physical register number.
                       None if no number assigned yet.
      """
  
      def __init__(self, astnode, temporary=False):
          self.node = astnode
          self.temporary = temporary
          self.immediate = False
          self.n = None
  
      def __str__(self):
          if self.temporary:
              name = 'Temporary'
          else:
              name = 'Register'
          return '%s(%s, %s, %s)' % (name, self.node.astType,
                                     self.node.astKind, self.n,)
  
      def __repr__(self):
          return self.__str__()
  
  
  class Immediate(Register):
      """Representation of an immediate (integer) operand, instead of
      a register.
      """
  
      def __init__(self, astnode):
          Register.__init__(self, astnode)
          self.immediate = True
  
      def __str__(self):
          return 'Immediate(%d)' % (self.node.value,)
  
  
  def stringToExpression(s, types, context):
      """Given a string, convert it to a tree of ExpressionNode's.
      """
      old_ctx = expressions._context.get_current_context()
      try:
          expressions._context.set_new_context(context)
          # first compile to a code object to determine the names
          if context.get('truediv', False):
              flags = __future__.division.compiler_flag
          else:
              flags = 0
          c = compile(s, '<expr>', 'eval', flags)
          # make VariableNode's for the names
          names = {}
          for name in c.co_names:
              if name == "None":
                  names[name] = None
              elif name == "True":
                  names[name] = True
              elif name == "False":
                  names[name] = False
              else:
                  t = types.get(name, default_type)
                  names[name] = expressions.VariableNode(name, type_to_kind[t])
          names.update(expressions.functions)
          # now build the expression
          ex = eval(c, names)
          if expressions.isConstant(ex):
              ex = expressions.ConstantNode(ex, expressions.getKind(ex))
          elif not isinstance(ex, expressions.ExpressionNode):
              raise TypeError("unsupported expression type: %s" % type(ex))
      finally:
          expressions._context.set_new_context(old_ctx)
      return ex
  
  
  def isReduction(ast):
      prefixes = (b'sum_', b'prod_', b'min_', b'max_')
      return any(ast.value.startswith(p) for p in prefixes)
  
  
  def getInputOrder(ast, input_order=None):
      """Derive the input order of the variables in an expression.
      """
      variables = {}
      for a in ast.allOf('variable'):
          variables[a.value] = a
      variable_names = set(variables.keys())
  
      if input_order:
          if variable_names != set(input_order):
              raise ValueError(
                  "input names (%s) don't match those found in expression (%s)"
                  % (input_order, variable_names))
  
          ordered_names = input_order
      else:
          ordered_names = list(variable_names)
          ordered_names.sort()
      ordered_variables = [variables[v] for v in ordered_names]
      return ordered_variables
  
  
  def convertConstantToKind(x, kind):
      # Exception for 'float' types that will return the NumPy float32 type
      if kind == 'float':
          return numpy.float32(x)
      elif sys.version_info[0] >= 3 and isinstance(x,str):
          return x.encode('ascii')
      return kind_to_type[kind](x)
  
  
  def getConstants(ast):
      '''
      RAM: implemented magic method __lt__ for ASTNode to fix issues
      #88 and #209. The following test code works now, as does the test suite.
      import numexpr as ne
      a = 1 + 3j; b = 5.0
      ne.evaluate( 'a*2 + 15j - b' )
      '''
      constants_order = sorted( ast.allOf('constant') )
      constants = [convertConstantToKind(a.value, a.astKind)
                   for a in constants_order]
      return constants_order, constants
  
  
  def sortNodesByOrder(nodes, order):
      order_map = {}
      for i, (_, v, _) in enumerate(order):
          order_map[v] = i
      dec_nodes = [(order_map[n.value], n) for n in nodes]
      dec_nodes.sort()
      return [a[1] for a in dec_nodes]
  
  
  def assignLeafRegisters(inodes, registerMaker):
      """Assign new registers to each of the leaf nodes.
      """
      leafRegisters = {}
      for node in inodes:
          key = node.key()
          if key in leafRegisters:
              node.reg = leafRegisters[key]
          else:
              node.reg = leafRegisters[key] = registerMaker(node)
  
  
  def assignBranchRegisters(inodes, registerMaker):
      """Assign temporary registers to each of the branch nodes.
      """
      for node in inodes:
          node.reg = registerMaker(node, temporary=True)
  
  
  def collapseDuplicateSubtrees(ast):
      """Common subexpression elimination.
      """
      seen = {}
      aliases = []
      for a in ast.allOf('op'):
          if a in seen:
              target = seen[a]
              a.astType = 'alias'
              a.value = target
              a.children = ()
              aliases.append(a)
          else:
              seen[a] = a
      # Set values and registers so optimizeTemporariesAllocation
      # doesn't get confused
      for a in aliases:
          while a.value.astType == 'alias':
              a.value = a.value.value
      return aliases
  
  
  def optimizeTemporariesAllocation(ast):
      """Attempt to minimize the number of temporaries needed, by
      reusing old ones.
      """
      nodes = [n for n in ast.postorderWalk() if n.reg.temporary]
      users_of = dict((n.reg, set()) for n in nodes)
  
      node_regs = dict((n, set(c.reg for c in n.children if c.reg.temporary))
                       for n in nodes)
      if nodes and nodes[-1] is not ast:
          nodes_to_check = nodes + [ast]
      else:
          nodes_to_check = nodes
      for n in nodes_to_check:
          for c in n.children:
              if c.reg.temporary:
                  users_of[c.reg].add(n)
  
      unused = dict([(tc, set()) for tc in scalar_constant_kinds])
      for n in nodes:
          for c in n.children:
              reg = c.reg
              if reg.temporary:
                  users = users_of[reg]
                  users.discard(n)
                  if not users:
                      unused[reg.node.astKind].add(reg)
          if unused[n.astKind]:
              reg = unused[n.astKind].pop()
              users_of[reg] = users_of[n.reg]
              n.reg = reg
  
  
  def setOrderedRegisterNumbers(order, start):
      """Given an order of nodes, assign register numbers.
      """
      for i, node in enumerate(order):
          node.reg.n = start + i
      return start + len(order)
  
  
  def setRegisterNumbersForTemporaries(ast, start):
      """Assign register numbers for temporary registers, keeping track of
      aliases and handling immediate operands.
      """
      seen = 0
      signature = ''
      aliases = []
      for node in ast.postorderWalk():
          if node.astType == 'alias':
              aliases.append(node)
              node = node.value
          if node.reg.immediate:
              node.reg.n = node.value
              continue
          reg = node.reg
          if reg.n is None:
              reg.n = start + seen
              seen += 1
              signature += reg.node.typecode()
      for node in aliases:
          node.reg = node.value.reg
      return start + seen, signature
  
  
  def convertASTtoThreeAddrForm(ast):
      """Convert an AST to a three address form.
  
      Three address form is (op, reg1, reg2, reg3), where reg1 is the
      destination of the result of the instruction.
  
      I suppose this should be called three register form, but three
      address form is found in compiler theory.
      """
      return [(node.value, node.reg) + tuple([c.reg for c in node.children])
              for node in ast.allOf('op')]
  
  
  def compileThreeAddrForm(program):
      """Given a three address form of the program, compile it a string that
      the VM understands.
      """
  
      def nToChr(reg):
          if reg is None:
              return b'\xff'
          elif reg.n < 0:
              raise ValueError("negative value for register number %s" % reg.n)
          else:
              if sys.version_info[0] < 3:
                  return chr(reg.n)
              else:
                  # int.to_bytes is not available in Python < 3.2
                  #return reg.n.to_bytes(1, sys.byteorder)
                  return bytes([reg.n])
  
      def quadrupleToString(opcode, store, a1=None, a2=None):
          cop = chr(interpreter.opcodes[opcode]).encode('ascii')
          cs = nToChr(store)
          ca1 = nToChr(a1)
          ca2 = nToChr(a2)
          return cop + cs + ca1 + ca2
  
      def toString(args):
          while len(args) < 4:
              args += (None,)
          opcode, store, a1, a2 = args[:4]
          s = quadrupleToString(opcode, store, a1, a2)
          l = [s]
          args = args[4:]
          while args:
              s = quadrupleToString(b'noop', *args[:3])
              l.append(s)
              args = args[3:]
          return b''.join(l)
  
      prog_str = b''.join([toString(t) for t in program])
      return prog_str
  
  
  context_info = [
      ('optimization', ('none', 'moderate', 'aggressive'), 'aggressive'),
      ('truediv', (False, True, 'auto'), 'auto')
  ]
  
  
  def getContext(kwargs, frame_depth=1):
      d = kwargs.copy()
      context = {}
      for name, allowed, default in context_info:
          value = d.pop(name, default)
          if value in allowed:
              context[name] = value
          else:
              raise ValueError("'%s' must be one of %s" % (name, allowed))
  
      if d:
          raise ValueError("Unknown keyword argument '%s'" % d.popitem()[0])
      if context['truediv'] == 'auto':
          caller_globals = sys._getframe(frame_depth + 1).f_globals
          context['truediv'] = caller_globals.get('division', None) == __future__.division
  
      return context
  
  
  def precompile(ex, signature=(), context={}):
      """Compile the expression to an intermediate form.
      """
      types = dict(signature)
      input_order = [name for (name, type_) in signature]
  
      if isinstance(ex, str):
          ex = stringToExpression(ex, types, context)
  
      # the AST is like the expression, but the node objects don't have
      # any odd interpretations
  
      ast = expressionToAST(ex)
  
      if ex.astType != 'op':
          ast = ASTNode('op', value='copy', astKind=ex.astKind, children=(ast,))
  
      ast = typeCompileAst(ast)
  
      aliases = collapseDuplicateSubtrees(ast)
  
      assignLeafRegisters(ast.allOf('raw'), Immediate)
      assignLeafRegisters(ast.allOf('variable', 'constant'), Register)
      assignBranchRegisters(ast.allOf('op'), Register)
  
      # assign registers for aliases
      for a in aliases:
          a.reg = a.value.reg
  
      input_order = getInputOrder(ast, input_order)
      constants_order, constants = getConstants(ast)
  
      if isReduction(ast):
          ast.reg.temporary = False
  
      optimizeTemporariesAllocation(ast)
  
      ast.reg.temporary = False
      r_output = 0
      ast.reg.n = 0
  
      r_inputs = r_output + 1
      r_constants = setOrderedRegisterNumbers(input_order, r_inputs)
      r_temps = setOrderedRegisterNumbers(constants_order, r_constants)
      r_end, tempsig = setRegisterNumbersForTemporaries(ast, r_temps)
  
      threeAddrProgram = convertASTtoThreeAddrForm(ast)
      input_names = tuple([a.value for a in input_order])
      signature = ''.join(type_to_typecode[types.get(x, default_type)]
                          for x in input_names)
      return threeAddrProgram, signature, tempsig, constants, input_names
  
  
  def NumExpr(ex, signature=(), **kwargs):
      """
      Compile an expression built using E.<variable> variables to a function.
  
      ex can also be specified as a string "2*a+3*b".
  
      The order of the input variables and their types can be specified using the
      signature parameter, which is a list of (name, type) pairs.
  
      Returns a `NumExpr` object containing the compiled function.
      """
      # NumExpr can be called either directly by the end-user, in which case
      # kwargs need to be sanitized by getContext, or by evaluate,
      # in which case kwargs are in already sanitized.
      # In that case frame_depth is wrong (it should be 2) but it doesn't matter
      # since it will not be used (because truediv='auto' has already been
      # translated to either True or False).
  
      context = getContext(kwargs, frame_depth=1)
      threeAddrProgram, inputsig, tempsig, constants, input_names = precompile(ex, signature, context)
      program = compileThreeAddrForm(threeAddrProgram)
      return interpreter.NumExpr(inputsig.encode('ascii'),
                                 tempsig.encode('ascii'),
                                 program, constants, input_names)
  
  
  def disassemble(nex):
      """
      Given a NumExpr object, return a list which is the program disassembled.
      """
      rev_opcodes = {}
      for op in interpreter.opcodes:
          rev_opcodes[interpreter.opcodes[op]] = op
      r_constants = 1 + len(nex.signature)
      r_temps = r_constants + len(nex.constants)
  
      def getArg(pc, offset):
          if sys.version_info[0] < 3:
              arg = ord(nex.program[pc + offset])
              op = rev_opcodes.get(ord(nex.program[pc]))
          else:
              arg = nex.program[pc + offset]
              op = rev_opcodes.get(nex.program[pc])
          try:
              code = op.split(b'_')[1][offset - 1]
          except IndexError:
              return None
          if sys.version_info[0] > 2:
              # int.to_bytes is not available in Python < 3.2
              #code = code.to_bytes(1, sys.byteorder)
              code = bytes([code])
          if arg == 255:
              return None
          if code != b'n':
              if arg == 0:
                  return b'r0'
              elif arg < r_constants:
                  return ('r%d[%s]' % (arg, nex.input_names[arg - 1])).encode('ascii')
              elif arg < r_temps:
                  return ('c%d[%s]' % (arg, nex.constants[arg - r_constants])).encode('ascii')
              else:
                  return ('t%d' % (arg,)).encode('ascii')
          else:
              return arg
  
      source = []
      for pc in range(0, len(nex.program), 4):
          if sys.version_info[0] < 3:
              op = rev_opcodes.get(ord(nex.program[pc]))
          else:
              op = rev_opcodes.get(nex.program[pc])
          dest = getArg(pc, 1)
          arg1 = getArg(pc, 2)
          arg2 = getArg(pc, 3)
          source.append((op, dest, arg1, arg2))
      return source
  
  
  def getType(a):
      kind = a.dtype.kind
      if kind == 'b':
          return bool
      if kind in 'iu':
          if a.dtype.itemsize > 4:
              return long_  # ``long`` is for integers of more than 32 bits
          if kind == 'u' and a.dtype.itemsize == 4:
              return long_  # use ``long`` here as an ``int`` is not enough
          return int_
      if kind == 'f':
          if a.dtype.itemsize > 4:
              return double  # ``double`` is for floats of more than 32 bits
          return float
      if kind == 'c':
          return complex
      if kind == 'S':
          return bytes
      if kind == 'U':
          raise ValueError('NumExpr 2 does not support Unicode as a dtype.')
      raise ValueError("unknown type %s" % a.dtype.name)
  
  
  def getExprNames(text, context):
      ex = stringToExpression(text, {}, context)
      ast = expressionToAST(ex)
      input_order = getInputOrder(ast, None)
      #try to figure out if vml operations are used by expression
      if not use_vml:
          ex_uses_vml = False
      else:
          for node in ast.postorderWalk():
              if node.astType == 'op' and node.value in vml_functions:
                  ex_uses_vml = True
                  break
          else:
              ex_uses_vml = False
  
      return [a.value for a in input_order], ex_uses_vml
  
  
  def getArguments(names, local_dict=None, global_dict=None):
      """Get the arguments based on the names."""
      call_frame = sys._getframe(2)
  
      clear_local_dict = False
      if local_dict is None:
          local_dict = call_frame.f_locals
          clear_local_dict = True
      try:
          frame_globals = call_frame.f_globals
          if global_dict is None:
              global_dict = frame_globals
  
          # If `call_frame` is the top frame of the interpreter we can't clear its 
          # `local_dict`, because it is actually the `global_dict`.
          clear_local_dict = clear_local_dict and not frame_globals is local_dict
  
          arguments = []
          for name in names:
              try:
                  a = local_dict[name]
              except KeyError:
                  a = global_dict[name]
              arguments.append(numpy.asarray(a))
      finally:
          # If we generated local_dict via an explicit reference to f_locals,
          # clear the dict to prevent creating extra ref counts in the caller's scope
          # See https://github.com/pydata/numexpr/issues/310
          if clear_local_dict:
              local_dict.clear()
  
      return arguments
  
  
  # Dictionaries for caching variable names and compiled expressions
  _names_cache = CacheDict(256)
  _numexpr_cache = CacheDict(256)
  _numexpr_last = {}
  
  evaluate_lock = threading.Lock()
  
  def evaluate(ex, local_dict=None, global_dict=None,
               out=None, order='K', casting='safe', **kwargs):
      """Evaluate a simple array expression element-wise, using the new iterator.
  
      ex is a string forming an expression, like "2*a+3*b". The values for "a"
      and "b" will by default be taken from the calling function's frame
      (through use of sys._getframe()). Alternatively, they can be specifed
      using the 'local_dict' or 'global_dict' arguments.
  
      Parameters
      ----------
  
      local_dict : dictionary, optional
          A dictionary that replaces the local operands in current frame.
  
      global_dict : dictionary, optional
          A dictionary that replaces the global operands in current frame.
  
      out : NumPy array, optional
          An existing array where the outcome is going to be stored.  Care is
          required so that this array has the same shape and type than the
          actual outcome of the computation.  Useful for avoiding unnecessary
          new array allocations.
  
      order : {'C', 'F', 'A', or 'K'}, optional
          Controls the iteration order for operands. 'C' means C order, 'F'
          means Fortran order, 'A' means 'F' order if all the arrays are
          Fortran contiguous, 'C' order otherwise, and 'K' means as close to
          the order the array elements appear in memory as possible.  For
          efficient computations, typically 'K'eep order (the default) is
          desired.
  
      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
          Controls what kind of data casting may occur when making a copy or
          buffering.  Setting this to 'unsafe' is not recommended, as it can
          adversely affect accumulations.
  
            * 'no' means the data types should not be cast at all.
            * 'equiv' means only byte-order changes are allowed.
            * 'safe' means only casts which can preserve values are allowed.
            * 'same_kind' means only safe casts or casts within a kind,
              like float64 to float32, are allowed.
            * 'unsafe' means any data conversions may be done.
      """
      global _numexpr_last
      if not isinstance(ex, str):
          raise ValueError("must specify expression as a string")
      # Get the names for this expression
      context = getContext(kwargs, frame_depth=1)
      expr_key = (ex, tuple(sorted(context.items())))
      if expr_key not in _names_cache:
          _names_cache[expr_key] = getExprNames(ex, context)
      names, ex_uses_vml = _names_cache[expr_key]
      arguments = getArguments(names, local_dict, global_dict)
  
      # Create a signature
      signature = [(name, getType(arg)) for (name, arg) in
                   zip(names, arguments)]
  
      # Look up numexpr if possible.
      numexpr_key = expr_key + (tuple(signature),)
      try:
          compiled_ex = _numexpr_cache[numexpr_key]
      except KeyError:
          compiled_ex = _numexpr_cache[numexpr_key] = NumExpr(ex, signature, **context)
      kwargs = {'out': out, 'order': order, 'casting': casting,
                'ex_uses_vml': ex_uses_vml}
      _numexpr_last = dict(ex=compiled_ex, argnames=names, kwargs=kwargs)
      with evaluate_lock:
          return compiled_ex(*arguments, **kwargs)
  
  
  def re_evaluate(local_dict=None):
      """Re-evaluate the previous executed array expression without any check.
  
      This is meant for accelerating loops that are re-evaluating the same
      expression repeatedly without changing anything else than the operands.
      If unsure, use evaluate() which is safer.
  
      Parameters
      ----------
  
      local_dict : dictionary, optional
          A dictionary that replaces the local operands in current frame.
  
      """
      try:
          compiled_ex = _numexpr_last['ex']
      except KeyError:
          raise RuntimeError("not a previous evaluate() execution found")
      argnames = _numexpr_last['argnames']
      args = getArguments(argnames, local_dict)
      kwargs = _numexpr_last['kwargs']
      with evaluate_lock:
          return compiled_ex(*args, **kwargs)
  