###################################################################
# 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
double = numpy.double
int_ = numpy.int32
long_ = numpy.int64
typecode_to_kind = {'b': 'bool', 'i': 'int', 'l': 'long', 'f': 'float', 'd': 'double',
'c': 'complex', 'n': 'none', 's': 'str'}
kind_to_typecode = {'bool': 'b', 'int': 'i', 'long': 'l', 'float': 'f', 'double': 'd',
'complex': 'c', 'bytes': 's', 'str': 's', 'none': 'n'}
type_to_typecode = {bool: 'b', int_: 'i', long_: 'l', float: 'f',
double: 'd', complex: 'c', bytes: 's', str: 's'}
type_to_kind = expressions.type_to_kind
kind_to_type = expressions.kind_to_type
default_type = kind_to_type[expressions.default_kind]
scalar_constant_kinds = list(kind_to_typecode.keys())
# 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"
]
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 appropriate types to each node in the AST.
Will convert opcodes and functions to appropriate 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 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')
"""
constant_registers = set([node.reg for node in ast.allOf("constant")])
constants_order = sorted([r.node for r in constant_registers])
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:
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
[docs]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)
[docs]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 parseOp(op):
name, sig = [*op.rsplit(b'_', 1), ''][:2]
return name, sig
def getArg(pc, offset):
arg = nex.program[pc + (offset if offset < 4 else offset+1)]
_, sig = parseOp(rev_opcodes.get(nex.program[pc]))
try:
code = sig[offset - 1]
except IndexError:
return None
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):
op = rev_opcodes.get(nex.program[pc])
_, sig = parseOp(op)
parsed = [op]
for i in range(len(sig)):
parsed.append(getArg(pc, 1 + i))
while len(parsed) < 4:
parsed.append(None)
source.append(parsed)
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()
[docs]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)
[docs]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)