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# 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.
####################################################################
__all__ = ['E']
import operator
import sys
import threading
import numpy
from pkg_resources import parse_version
_np_version = parse_version(numpy.__version__)
# Declare a double type that does not exist in Python space
double = numpy.double
# The default kind for undeclared variables
default_kind = 'double'
if sys.version_info[0] < 3:
int_ = int
long_ = int
else:
int_ = numpy.int32
long_ = numpy.int64
type_to_kind = {bool: 'bool', int_: 'int', long_: 'long', float: 'float',
double: 'double', complex: 'complex', bytes: 'bytes'}
kind_to_type = {'bool': bool, 'int': int_, 'long': long_, 'float': float,
'double': double, 'complex': complex, 'bytes': bytes}
kind_rank = ('bool', 'int', 'long', 'float', 'double', 'complex', 'none')
scalar_constant_types = [bool, int_, int, float, double, complex, bytes]
# Final corrections for Python 3 (mainly for PyTables needs)
if sys.version_info[0] > 2:
type_to_kind[str] = 'str'
kind_to_type['str'] = str
scalar_constant_types.append(str)
scalar_constant_types = tuple(scalar_constant_types)
from numexpr import interpreter
class Expression(object):
def __init__(self):
object.__init__(self)
def __getattr__(self, name):
if name.startswith('_'):
try:
return self.__dict__[name]
except KeyError:
raise AttributeError
else:
return VariableNode(name, default_kind)
E = Expression()
class Context(threading.local):
def get(self, value, default):
return self.__dict__.get(value, default)
def get_current_context(self):
return self.__dict__
def set_new_context(self, dict_):
self.__dict__.update(dict_)
# This will be called each time the local object is used in a separate thread
_context = Context()
def get_optimization():
return _context.get('optimization', 'none')
# helper functions for creating __magic__ methods
def ophelper(f):
def func(*args):
args = list(args)
for i, x in enumerate(args):
if isConstant(x):
args[i] = x = ConstantNode(x)
if not isinstance(x, ExpressionNode):
raise TypeError("unsupported object type: %s" % type(x))
return f(*args)
func.__name__ = f.__name__
func.__doc__ = f.__doc__
func.__dict__.update(f.__dict__)
return func
def allConstantNodes(args):
"returns True if args are all ConstantNodes."
for x in args:
if not isinstance(x, ConstantNode):
return False
return True
def isConstant(ex):
"Returns True if ex is a constant scalar of an allowed type."
return isinstance(ex, scalar_constant_types)
def commonKind(nodes):
node_kinds = [node.astKind for node in nodes]
str_count = node_kinds.count('bytes') + node_kinds.count('str')
if 0 < str_count < len(node_kinds): # some args are strings, but not all
raise TypeError("strings can only be operated with strings")
if str_count > 0: # if there are some, all of them must be
return 'bytes'
n = -1
for x in nodes:
n = max(n, kind_rank.index(x.astKind))
return kind_rank[n]
max_int32 = 2147483647
min_int32 = -max_int32 - 1
def bestConstantType(x):
# ``numpy.string_`` is a subclass of ``bytes``
if isinstance(x, (bytes, str)):
return bytes
# Numeric conversion to boolean values is not tried because
# ``bool(1) == True`` (same for 0 and False), so 0 and 1 would be
# interpreted as booleans when ``False`` and ``True`` are already
# supported.
if isinstance(x, (bool, numpy.bool_)):
return bool
# ``long`` objects are kept as is to allow the user to force
# promotion of results by using long constants, e.g. by operating
# a 32-bit array with a long (64-bit) constant.
if isinstance(x, (long_, numpy.int64)):
return long_
# ``double`` objects are kept as is to allow the user to force
# promotion of results by using double constants, e.g. by operating
# a float (32-bit) array with a double (64-bit) constant.
if isinstance(x, double):
return double
if isinstance(x, (int, numpy.integer)):
# Constants needing more than 32 bits are always
# considered ``long``, *regardless of the platform*, so we
# can clearly tell 32- and 64-bit constants apart.
if not (min_int32 <= x <= max_int32):
return long_
return int_
# The duality of float and double in Python avoids that we have to list
# ``double`` too.
for converter in float, complex:
try:
y = converter(x)
except Exception as err:
continue
if y == x:
return converter
def getKind(x):
converter = bestConstantType(x)
return type_to_kind[converter]
def binop(opname, reversed=False, kind=None):
# Getting the named method from self (after reversal) does not
# always work (e.g. int constants do not have a __lt__ method).
opfunc = getattr(operator, "__%s__" % opname)
@ophelper
def operation(self, other):
if reversed:
self, other = other, self
if allConstantNodes([self, other]):
return ConstantNode(opfunc(self.value, other.value))
else:
return OpNode(opname, (self, other), kind=kind)
return operation
def func(func, minkind=None, maxkind=None):
@ophelper
def function(*args):
if allConstantNodes(args):
return ConstantNode(func(*[x.value for x in args]))
kind = commonKind(args)
if kind in ('int', 'long'):
# Exception for following NumPy casting rules
#FIXME: this is not always desirable. The following
# functions which return ints (for int inputs) on numpy
# but not on numexpr: copy, abs, fmod, ones_like
kind = 'double'
else:
# Apply regular casting rules
if minkind and kind_rank.index(minkind) > kind_rank.index(kind):
kind = minkind
if maxkind and kind_rank.index(maxkind) < kind_rank.index(kind):
kind = maxkind
return FuncNode(func.__name__, args, kind)
return function
@ophelper
def where_func(a, b, c):
if isinstance(a, ConstantNode):
#FIXME: This prevents where(True, a, b)
raise ValueError("too many dimensions")
if allConstantNodes([a, b, c]):
return ConstantNode(numpy.where(a, b, c))
return FuncNode('where', [a, b, c])
def encode_axis(axis):
if isinstance(axis, ConstantNode):
axis = axis.value
if axis is None:
axis = interpreter.allaxes
else:
if axis < 0:
raise ValueError("negative axis are not supported")
if axis > 254:
raise ValueError("cannot encode axis")
return RawNode(axis)
def gen_reduce_axis_func(name):
def _func(a, axis=None):
axis = encode_axis(axis)
if isinstance(a, ConstantNode):
return a
if isinstance(a, (bool, int_, long_, float, double, complex)):
a = ConstantNode(a)
return FuncNode(name, [a, axis], kind=a.astKind)
return _func
@ophelper
def contains_func(a, b):
return FuncNode('contains', [a, b], kind='bool')
@ophelper
def div_op(a, b):
if get_optimization() in ('moderate', 'aggressive'):
if (isinstance(b, ConstantNode) and
(a.astKind == b.astKind) and
a.astKind in ('float', 'double', 'complex')):
return OpNode('mul', [a, ConstantNode(1. / b.value)])
return OpNode('div', [a, b])
@ophelper
def truediv_op(a, b):
if get_optimization() in ('moderate', 'aggressive'):
if (isinstance(b, ConstantNode) and
(a.astKind == b.astKind) and
a.astKind in ('float', 'double', 'complex')):
return OpNode('mul', [a, ConstantNode(1. / b.value)])
kind = commonKind([a, b])
if kind in ('bool', 'int', 'long'):
kind = 'double'
return OpNode('div', [a, b], kind=kind)
@ophelper
def rtruediv_op(a, b):
return truediv_op(b, a)
@ophelper
def pow_op(a, b):
if (_np_version >= parse_version('1.12.0b1') and
b.astKind in ('int', 'long') and
a.astKind in ('int', 'long') and
numpy.any(b.value < 0)):
raise ValueError(
'Integers to negative integer powers are not allowed.')
if allConstantNodes([a, b]):
return ConstantNode(a ** b)
if isinstance(b, ConstantNode):
x = b.value
if get_optimization() == 'aggressive':
RANGE = 50 # Approximate break even point with pow(x,y)
# Optimize all integral and half integral powers in [-RANGE, RANGE]
# Note: for complex numbers RANGE could be larger.
if (int(2 * x) == 2 * x) and (-RANGE <= abs(x) <= RANGE):
n = int_(abs(x))
ishalfpower = int_(abs(2 * x)) % 2
def multiply(x, y):
if x is None: return y
return OpNode('mul', [x, y])
r = None
p = a
mask = 1
while True:
if (n & mask):
r = multiply(r, p)
mask <<= 1
if mask > n:
break
p = OpNode('mul', [p, p])
if ishalfpower:
kind = commonKind([a])
if kind in ('int', 'long'):
kind = 'double'
r = multiply(r, OpNode('sqrt', [a], kind))
if r is None:
r = OpNode('ones_like', [a])
if x < 0:
r = OpNode('div', [ConstantNode(1), r])
return r
if get_optimization() in ('moderate', 'aggressive'):
if x == -1:
return OpNode('div', [ConstantNode(1), a])
if x == 0:
return OpNode('ones_like', [a])
if x == 0.5:
kind = a.astKind
if kind in ('int', 'long'): kind = 'double'
return FuncNode('sqrt', [a], kind=kind)
if x == 1:
return a
if x == 2:
return OpNode('mul', [a, a])
return OpNode('pow', [a, b])
# The functions and the minimum and maximum types accepted
functions = {
'copy': func(numpy.copy),
'ones_like': func(numpy.ones_like),
'sqrt': func(numpy.sqrt, 'float'),
'sin': func(numpy.sin, 'float'),
'cos': func(numpy.cos, 'float'),
'tan': func(numpy.tan, 'float'),
'arcsin': func(numpy.arcsin, 'float'),
'arccos': func(numpy.arccos, 'float'),
'arctan': func(numpy.arctan, 'float'),
'sinh': func(numpy.sinh, 'float'),
'cosh': func(numpy.cosh, 'float'),
'tanh': func(numpy.tanh, 'float'),
'arcsinh': func(numpy.arcsinh, 'float'),
'arccosh': func(numpy.arccosh, 'float'),
'arctanh': func(numpy.arctanh, 'float'),
'fmod': func(numpy.fmod, 'float'),
'arctan2': func(numpy.arctan2, 'float'),
'log': func(numpy.log, 'float'),
'log1p': func(numpy.log1p, 'float'),
'log10': func(numpy.log10, 'float'),
'exp': func(numpy.exp, 'float'),
'expm1': func(numpy.expm1, 'float'),
'abs': func(numpy.absolute, 'float'),
'ceil': func(numpy.ceil, 'float', 'double'),
'floor': func(numpy.floor, 'float', 'double'),
'where': where_func,
'real': func(numpy.real, 'double', 'double'),
'imag': func(numpy.imag, 'double', 'double'),
'complex': func(complex, 'complex'),
'conj': func(numpy.conj, 'complex'),
'sum': gen_reduce_axis_func('sum'),
'prod': gen_reduce_axis_func('prod'),
'min': gen_reduce_axis_func('min'),
'max': gen_reduce_axis_func('max'),
'contains': contains_func,
}
class ExpressionNode(object):
"""An object that represents a generic number object.
This implements the number special methods so that we can keep
track of how this object has been used.
"""
astType = 'generic'
def __init__(self, value=None, kind=None, children=None):
object.__init__(self)
self.value = value
if kind is None:
kind = 'none'
self.astKind = kind
if children is None:
self.children = ()
else:
self.children = tuple(children)
def get_real(self):
if self.astType == 'constant':
return ConstantNode(complex(self.value).real)
return OpNode('real', (self,), 'double')
real = property(get_real)
def get_imag(self):
if self.astType == 'constant':
return ConstantNode(complex(self.value).imag)
return OpNode('imag', (self,), 'double')
imag = property(get_imag)
def __str__(self):
return '%s(%s, %s, %s)' % (self.__class__.__name__, self.value,
self.astKind, self.children)
def __repr__(self):
return self.__str__()
def __neg__(self):
return OpNode('neg', (self,))
def __invert__(self):
return OpNode('invert', (self,))
def __pos__(self):
return self
# The next check is commented out. See #24 for more info.
def __bool__(self):
raise TypeError("You can't use Python's standard boolean operators in "
"NumExpr expressions. You should use their bitwise "
"counterparts instead: '&' instead of 'and', "
"'|' instead of 'or', and '~' instead of 'not'.")
__add__ = __radd__ = binop('add')
__sub__ = binop('sub')
__rsub__ = binop('sub', reversed=True)
__mul__ = __rmul__ = binop('mul')
if sys.version_info[0] < 3:
__div__ = div_op
__rdiv__ = binop('div', reversed=True)
__truediv__ = truediv_op
__rtruediv__ = rtruediv_op
__pow__ = pow_op
__rpow__ = binop('pow', reversed=True)
__mod__ = binop('mod')
__rmod__ = binop('mod', reversed=True)
__lshift__ = binop('lshift')
__rlshift__ = binop('lshift', reversed=True)
__rshift__ = binop('rshift')
__rrshift__ = binop('rshift', reversed=True)
# boolean operations
__and__ = binop('and', kind='bool')
__or__ = binop('or', kind='bool')
__gt__ = binop('gt', kind='bool')
__ge__ = binop('ge', kind='bool')
__eq__ = binop('eq', kind='bool')
__ne__ = binop('ne', kind='bool')
__lt__ = binop('gt', reversed=True, kind='bool')
__le__ = binop('ge', reversed=True, kind='bool')
class LeafNode(ExpressionNode):
leafNode = True
class VariableNode(LeafNode):
astType = 'variable'
def __init__(self, value=None, kind=None, children=None):
LeafNode.__init__(self, value=value, kind=kind)
class RawNode(object):
"""Used to pass raw integers to interpreter.
For instance, for selecting what function to use in func1.
Purposely don't inherit from ExpressionNode, since we don't wan't
this to be used for anything but being walked.
"""
astType = 'raw'
astKind = 'none'
def __init__(self, value):
self.value = value
self.children = ()
def __str__(self):
return 'RawNode(%s)' % (self.value,)
__repr__ = __str__
class ConstantNode(LeafNode):
astType = 'constant'
def __init__(self, value=None, children=None):
kind = getKind(value)
# Python float constants are double precision by default
if kind == 'float':
kind = 'double'
LeafNode.__init__(self, value=value, kind=kind)
def __neg__(self):
return ConstantNode(-self.value)
def __invert__(self):
return ConstantNode(~self.value)
class OpNode(ExpressionNode):
astType = 'op'
def __init__(self, opcode=None, args=None, kind=None):
if (kind is None) and (args is not None):
kind = commonKind(args)
ExpressionNode.__init__(self, value=opcode, kind=kind, children=args)
class FuncNode(OpNode):
def __init__(self, opcode=None, args=None, kind=None):
if (kind is None) and (args is not None):
kind = commonKind(args)
OpNode.__init__(self, opcode, args, kind)
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