"""
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
WARNING
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

This directory is for the internal of Theano.

You are strongly advised not to use it, except if you know
what you are doing!

If you want to use a scalar variable in a Theano graph,
you probably want to use theano.tensor.[c,z,f,d,b,w,i,l,]scalar!
"""

import math
import warnings
from copy import copy
from itertools import imap

import numpy

import theano
from theano import gof
from theano.gof import Op, utils, Variable, Constant, Type, Apply, Env
from theano.gof.python25 import partial, all, any
from theano.configparser import config

builtin_complex = complex
builtin_int = int
builtin_float = float


class ComplexError(Exception):
    """Raised if complex numbers are used in an unsupported operation."""
    pass


class IntegerDivisionError(Exception):
    """Raised if someone tries to divide integers with '/' instead of '//'."""
    pass


def upcast(dtype, *dtypes):
    # Should we try to keep float32 instead of float64? This is used so that
    # for instance mixing int64 with float32 yields float32 instead of float64.
    # Note that we store this boolean as a one-element list so that it can be
    # modified within `make_array`.
    keep_float32 = [(config.cast_policy == 'numpy+floatX' and
                     config.floatX == 'float32')]

    def make_array(dt):
        if dt == 'float64':
            # There is an explicit float64 dtype: we cannot keep float32.
            keep_float32[0] = False
        return numpy.zeros((), dtype=dt)
    z = make_array(dtype)
    for dt in dtypes:
        z = z + make_array(dt=dt)
    rval = str(z.dtype)
    if rval == 'float64' and keep_float32[0]:
        return 'float32'
    else:
        return rval


def as_scalar(x, name=None):
    if isinstance(x, gof.Apply):
        if len(x.outputs) != 1:
            raise ValueError("It is ambiguous which output of a multi-output"
                             " Op has to be fetched.", x)
        else:
            x = x.outputs[0]
    if isinstance(x, Variable):
        if not isinstance(x.type, Scalar):
            raise TypeError("Variable type field must be a Scalar.", x, x.type)
        return x
    try:
        return constant(x)
    except TypeError:
        raise TypeError("Cannot convert %s to Scalar" % x, type(x))


def constant(x):
    # pass through numpy scalars, since they are already typed on
    # purpose typically.
    if hasattr(x, 'dtype'):
        assert x.ndim == 0
        return ScalarConstant(Scalar(str(x.dtype)), x)
    if isinstance(x, builtin_float):
        for dtype in ['float32', 'float64']:
            x_ = theano._asarray(x, dtype=dtype)
            if numpy.all(x == x_):
                break
            x_ = None
        assert x_ is not None
        return ScalarConstant(Scalar(str(x_.dtype)), x)
    if isinstance(x, builtin_int):
        for dtype in ['int8', 'int16', 'int32', 'int64']:
            x_ = theano._asarray(x, dtype=dtype)
            if numpy.all(x == x_):
                break
            x_ = None
        assert x_ is not None
        return ScalarConstant(Scalar(str(x_.dtype)), x)
    if isinstance(x, builtin_complex):
        #TODO: We have added the complex type, so this should be tested
        raise NotImplementedError()
    raise TypeError(x)
    #return ScalarConstant(float64, float(x))


class Scalar(Type):

    """
        Internal class, should not be used by clients
        Primarily used by tensor.elemwise and tensor.reduce
        Analogous to TensorType, but for zero-dimensional objects
        Maps directly to C primitives

        TODO: refactor to be named ScalarType for consistency with TensorType
    """

    def __init__(self, dtype):
        if dtype == 'floatX':
            dtype = config.floatX
        self.dtype = dtype
        self.dtype_specs()  # error checking

    def filter(self, data, strict=False, allow_downcast=None):
        py_type = self.dtype_specs()[0]
        if strict and not isinstance(data, py_type):
            raise TypeError("%s expected a %s, got %s of type %s" % (
                    self, py_type, data, type(data)), data)
        try:
            converted_data = py_type(data)
            if (allow_downcast or
                    (allow_downcast is None and
                        type(data) is float and
                        self.dtype == theano.config.floatX) or
                    data == converted_data):
                return py_type(data)
            else:
                raise TypeError('Value cannot accurately be converted to dtype'
                          ' (%s) and allow_downcast is not True' % self.dtype)
        except Exception, e:
            raise TypeError("Could not convert %s (value=%s) to %s" % (
                    type(data), data, self.dtype), e)

    def values_eq_approx(self, a, b, tolerance=1e-4):
        return abs(a - b) <= ((abs(a) + abs(b)) * tolerance)

    def c_headers(self):
        l = ['<math.h>']
        l.append('<numpy/arrayscalars.h>')
        if config.lib.amdlibm:
            l += ['<amdlibm.h>']
        return l

    def c_libraries(self):
        l = []
        if config.lib.amdlibm:
            l += ['amdlibm']
        return l

    def c_compile_args(self):
        if config.lib.amdlibm:
            return ['-DREPLACE_WITH_AMDLIBM']
        else:
            return []

    def __eq__(self, other):
        return type(self) == type(other) and other.dtype == self.dtype

    def __hash__(self):
        return hash('theano.scalar.Scalar') ^ hash(self.dtype)

    def dtype_specs(self):
        try:
            return {  # dtype: (py_type, c_type, cls_name)
                    'float32': (numpy.float32, 'npy_float32', 'Float32'),
                    'float64': (numpy.float64, 'npy_float64', 'Float64'),
                    'complex128': (numpy.complex128, 'theano_complex128',
                                   'Complex128'),
                    'complex64': (numpy.complex64, 'theano_complex64',
                                  'Complex64'),
                    'uint8':  (numpy.uint8, 'npy_uint8', 'UInt8'),
                    'int8':  (numpy.int8, 'npy_int8', 'Int8'),
                    'uint16':  (numpy.uint16, 'npy_uint16', 'UInt16'),
                    'int16': (numpy.int16, 'npy_int16', 'Int16'),
                    'uint32':  (numpy.uint32, 'npy_uint32', 'UInt32'),
                    'int32': (numpy.int32, 'npy_int32', 'Int32'),
                    'uint64':  (numpy.uint64, 'npy_uint64', 'UInt64'),
                    'int64': (numpy.int64, 'npy_int64', 'Int64')
                    }[self.dtype]
        except KeyError:
            raise TypeError("Unsupported dtype for %s: %s" % (
                    self.__class__.__name__, self.dtype))

    def upcast(self, *others):
        return upcast(*[x.dtype for x in [self] + list(others)])

    def make_variable(self, name=None):
        return ScalarVariable(self, name=name)

    def __str__(self):
        return str(self.dtype)

    def __repr__(self):
        return "Scalar(%s)" % self.dtype

    def c_literal(self, data):
        if 'complex' in self.dtype:
            raise NotImplementedError("No literal for complex values.")
        return str(data)

    def c_declare(self, name, sub):
        return """
        %(dtype)s %(name)s;
        typedef %(dtype)s %(name)s_dtype;
        """ % dict(name=name, dtype=self.dtype_specs()[1])

    def c_init(self, name, sub):
        return """
        %(name)s = 0;
        """ % locals()

    def c_extract(self, name, sub):
        specs = self.dtype_specs()
        return """
        if (!PyObject_TypeCheck(py_%(name)s, &%(pyarr_type)s))
        {
            PyErr_Format(PyExc_ValueError,
                "Scalar check failed (%(dtype)s)");
            %(fail)s
        }
        PyArray_ScalarAsCtype(py_%(name)s, &%(name)s);
        """ % dict(sub,
                   name=name,
                   dtype=specs[1],
                   pyarr_type='Py%sArrType_Type' % specs[2])

    def c_sync(self, name, sub):
        specs = self.dtype_specs()
        return """
        Py_XDECREF(py_%(name)s);
        py_%(name)s = PyArrayScalar_New(%(cls)s);
        if (!py_%(name)s)
        {
            Py_XINCREF(Py_None);
            py_%(name)s = Py_None;
            PyErr_Format(PyExc_MemoryError,
                "Instantiation of new Python scalar failed (%(dtype)s)");
            %(fail)s
        }
        PyArrayScalar_ASSIGN(py_%(name)s, %(cls)s, %(name)s);
        """ % dict(sub,
                   name=name,
                   dtype=specs[1],
                   cls=specs[2])

    def c_cleanup(self, name, sub):
        return ""

    def c_support_code(self):

        if self.dtype.startswith('complex'):
            cplx_types = ['theano_complex64', 'theano_complex128']
            real_types = ['npy_int8', 'npy_int16', 'npy_int32', 'npy_int64',
                          'npy_float32', 'npy_float64']
            # If the 'int' C type is not exactly the same as an existing
            # 'npy_intX', some C code may not compile, e.g. when assigning
            # the value 0 (cast to 'int' in C) to a theano_complex64.
            if (numpy.dtype('intc').num not in
                [numpy.dtype(d[4:]).num for d in real_types]):
                # In that case we add the 'int' type to the real types.
                real_types.append('int')

            template = """
            struct theano_complex%(nbits)s : public npy_complex%(nbits)s
            {
                typedef theano_complex%(nbits)s complex_type;
                typedef npy_float%(half_nbits)s scalar_type;

                complex_type operator +(const complex_type &y) const {
                    complex_type ret;
                    ret.real = this->real + y.real;
                    ret.imag = this->imag + y.imag;
                    return ret;
                }

                complex_type operator -() const {
                    complex_type ret;
                    ret.real = -this->real;
                    ret.imag = -this->imag;
                    return ret;
                }
                complex_type operator -(const complex_type &y) const {
                    complex_type ret;
                    ret.real = this->real - y.real;
                    ret.imag = this->imag - y.imag;
                    return ret;
                }
                complex_type operator *(const complex_type &y) const {
                    complex_type ret;
                    ret.real = this->real * y.real - this->imag * y.imag;
                    ret.imag = this->real * y.imag + this->imag * y.real;
                    return ret;
                }
                complex_type operator /(const complex_type &y) const {
                    complex_type ret;
                    scalar_type y_norm_square = y.real * y.real + y.imag * y.imag;
                    ret.real = (this->real * y.real + this->imag * y.imag) / y_norm_square;
                    ret.imag = (this->imag * y.real - this->real * y.imag) / y_norm_square;
                    return ret;
                }
                template <typename T>
                complex_type& operator =(const T& y);

                theano_complex%(nbits)s() {}

                template <typename T>
                theano_complex%(nbits)s(const T& y) { *this = y; }

                template <typename TR, typename TI>
                theano_complex%(nbits)s(const TR& r, const TI& i) { this->real=r; this->imag=i; }
            };
            """

            def operator_eq_real(mytype, othertype):
                return '''
                template <> %(mytype)s & %(mytype)s::operator=<%(othertype)s>(const %(othertype)s & y)
                { this->real=y; this->imag=0; return *this; }
                ''' % dict(mytype = mytype, othertype = othertype)

            def operator_eq_cplx(mytype, othertype):
                return '''
                template <> %(mytype)s & %(mytype)s::operator=<%(othertype)s>(const %(othertype)s & y)
                { this->real=y.real; this->imag=y.imag; return *this; }
                ''' % dict(mytype=mytype, othertype=othertype)

            operator_eq = ''.join(operator_eq_real(ctype, rtype)
                                for ctype in cplx_types
                                for rtype in real_types) \
                        + ''.join(operator_eq_cplx(ctype1, ctype2)
                                for ctype1 in cplx_types
                                for ctype2 in cplx_types)

            # We are not using C++ generic templating here, because this would
            # generate two different functions for adding a complex64 and a
            # complex128, one returning a complex64, the other a complex128,
            # and the compiler complains it is ambiguous.
            # Instead, we generate code for known and safe types only.

            def operator_plus_real(mytype, othertype):
                return '''
                const %(mytype)s operator+(const %(mytype)s &x, const %(othertype)s &y)
                { return %(mytype)s(x.real+y, x.imag); }

                const %(mytype)s operator+(const %(othertype)s &y, const %(mytype)s &x)
                { return %(mytype)s(x.real+y, x.imag); }
                ''' % dict(mytype=mytype, othertype=othertype)

            operator_plus = ''.join(operator_plus_real(ctype, rtype)
                                for ctype in cplx_types
                                for rtype in real_types)

            def operator_minus_real(mytype, othertype):
                return '''
                const %(mytype)s operator-(const %(mytype)s &x, const %(othertype)s &y)
                { return %(mytype)s(x.real-y, x.imag); }

                const %(mytype)s operator-(const %(othertype)s &y, const %(mytype)s &x)
                { return %(mytype)s(y-x.real, -x.imag); }
                ''' % dict(mytype=mytype, othertype=othertype)

            operator_minus = ''.join(operator_minus_real(ctype, rtype)
                                for ctype in cplx_types
                                for rtype in real_types)

            def operator_mul_real(mytype, othertype):
                return '''
                const %(mytype)s operator*(const %(mytype)s &x, const %(othertype)s &y)
                { return %(mytype)s(x.real*y, x.imag*y); }

                const %(mytype)s operator*(const %(othertype)s &y, const %(mytype)s &x)
                { return %(mytype)s(x.real*y, x.imag*y); }
                ''' % dict(mytype=mytype, othertype=othertype)

            operator_mul = ''.join(operator_mul_real(ctype, rtype)
                                for ctype in cplx_types
                                for rtype in real_types)

            return template % dict(nbits=64, half_nbits=32) \
                    + template % dict(nbits=128, half_nbits=64) \
                    + operator_eq \
                    + operator_plus \
                    + operator_minus \
                    + operator_mul

        else:
            return ""

    def c_code_cache_version(self):
        # Use the correct type checking and conversion functions
        return (10, numpy.__version__)
        # Make operators work with 64 and 128 arguments at the same time
        return (9, numpy.__version__)
        # put const around operators and added unary '-' operator
        return (8, numpy.__version__)
        # no need to put lib.amdlibm here as c_compile_args() are put
        # in the key.
        return (7,)  # make complex c code optional
        return (6,)  # added implemeentations of operators that work
                     # with scalar arguments
        return (5,)  # added constructors to theano_complex class
        return (4,)  # explicit T given in specialization of operator=
                     # lines.  This makes it compile with open64


int8 = Scalar('int8')
int16 = Scalar('int16')
int32 = Scalar('int32')
int64 = Scalar('int64')
uint8 = Scalar('uint8')
uint16 = Scalar('uint16')
uint32 = Scalar('uint32')
uint64 = Scalar('uint64')
float32 = Scalar('float32')
float64 = Scalar('float64')
complex64 = Scalar('complex64')
complex128 = Scalar('complex128')

int_types = int8, int16, int32, int64
uint_types = uint8, uint16, uint32, uint64
float_types = float32, float64
complex_types = complex64, complex128

discrete_types = int_types + uint_types
continuous_types = float_types + complex_types
all_types = discrete_types + continuous_types


class _scalar_py_operators:

    #UNARY
    def __abs__(self): return abs_(self)
    def __neg__(self): return neg(self)

    #CASTS
    #def __int__(self): return AsInt(self).out
    #def __float__(self): return AsDouble(self).out
    #def __complex__(self): return AsComplex(self).out

    #BITWISE
    def __invert__(self): return invert(self)
    def __and__(self,other): return and_(self, other)
    def __or__(self,other): return or_(self, other)
    def __xor__(self,other): return xor(self, other)
    def __rand__(self,other): return and_(other,self)
    def __ror__(self,other): return or_(other, self)
    def __rxor__(self,other): return xor(other, self)

    #COMPARISONS
    def __lt__(self,other): return lt(self, other)
    def __le__(self,other): return le(self, other)
    def __gt__(self,other): return gt(self, other)
    def __ge__(self,other): return ge(self, other)

    #ARITHMETIC - NORMAL
    def __add__(self,other): return add(self,other)
    def __sub__(self,other): return sub(self,other)
    def __mul__(self,other): return mul(self,other)
    def __div__(self,other): return div_proxy(self,other)
    def __floordiv__(self, other): return int_div(self, other)
    def __mod__(self, other): return mod_check(self, other)
    def __pow__(self,other): return pow(self,other)

    #ARITHMETIC - RIGHT-OPERAND
    def __radd__(self,other): return add(other,self)
    def __rsub__(self,other): return sub(other,self)
    def __rmul__(self,other): return mul(other,self)
    def __rdiv__(self,other): return div_proxy(other,self)
    def __rmod__(self,other): return mod(other,self)
    def __rpow__(self,other): return pow(other,self)


class ScalarVariable(_scalar_py_operators, Variable):
    pass


class ScalarConstant(_scalar_py_operators, Constant):
    pass


# Easy constructors

def _multi(*fns):
    def f2(f, names):
        if len(names) == 1:
            return f(names)
        else:
            return [f(name) for name in names]
    if len(fns) == 1:
        return partial(f2, fns[0])
    else:
        return [partial(f2, f) for f in fns]

ints = _multi(int64)
floats = _multi(float64)
complexs = _multi(complex128)
complexs64 = _multi(complex64)
complexs128 = _multi(complex128)


# Using a class instead of a function makes it possible to deep-copy it in
# Python 2.4.
# Note that currently only upcast_out uses this mechanism, because it is
# enough to make the test-suite pass with Python 2.4. However, it may prove
# necessary to use this same mechanism in other places as well in the future.
class upcast_out(object):
    def __new__(self, *types):
        return Scalar(dtype=Scalar.upcast(*types)),


def upcast_out_no_complex(*types):
    if any([type in complex_types for type in types]):
        raise TypeError('complex type are not supported')
    return Scalar(dtype=Scalar.upcast(*types)),


def same_out(type):
    return type,


def same_out_float_only(type):
    if type not in float_types:
        raise TypeError('only float type are supported')
    return type,


class transfer_type(gof.utils.object2):
    def __init__(self, *transfer):
        assert all(type(x) == int for x in transfer)
        self.transfer = transfer

    def __str__(self):
        return 'transfer_type{%s}' % self.transfer

    def __call__(self, *types):
        upcast = upcast_out(*types)
        retval = []
        for i in self.transfer:
            if i is None:
                retval += [upcast]
            else:
                retval += [types[i]]
        return retval
        #return [upcast if i is None else types[i] for i in self.transfer]

    def __eq__(self, other):
        return type(self) == type(other) and self.transfer == other.transfer

    def __hash__(self):
        return hash(self.transfer)


class specific_out(gof.utils.object2):
    def __init__(self, *spec):
        self.spec = spec

    def __call__(self, *types):
        return self.spec

    def __eq__(self, other):
        return type(self) == type(other) and self.spec == other.spec

    def __hash__(self):
        return hash(self.spec)


def int_out(*types):
    return int64,


def float_out(*types):
    return float64,


def upgrade_to_float(*types):
    """
    Upgrade any int types to float32 or float64 to avoid losing any precision.
    """
    conv = {int8: float32,
            int16: float32,
            int32: float64,
            int64: float64}
    return Scalar(Scalar.upcast(*[conv.get(type, type) for type in types])),


def upgrade_to_float_no_complex(*types):
    """
    don't accept complex, otherwise call upgrade_to_float().
    """
    for type in types:
        if type in complex_types:
            raise TypeError('complex argument not supported')
    return upgrade_to_float(*types)


def same_out_nocomplex(type):
    if type in complex_types:
        raise TypeError('complex argument not supported')
    return type,


def int_out_nocomplex(*types):
    for type in types:
        if type in complex_types:
            raise TypeError('complex argument not supported')
    return int64,


def float_out_nocomplex(*types):
    for type in types:
        if type in complex_types:
            raise TypeError('complex argument not supported')
    return float64,


class unary_out_lookup(gof.utils.object2):
    """
    get a output_types_preference object by passing a dictionary:

    unary_out_lookup({int8:int32, float32:complex128})

    The result is an op that maps in8 to int32 and float32 to
    complex128 and other input types lead to a TypeError.
    """
    def __init__(self, type_table):
        self.tbl = type_table

    def __call__(self, *types):
        if len(types) == 1:
            types = types[0]
        try:
            rval = self.tbl[types]
        except Exception:
            raise TypeError(types)
        if isinstance(types, (list, tuple)):
            return rval
        else:
            return [rval]

    def __eq__(self, other):
        return type(self) == type(other) and self.tbl == other.tbl

    def __hash__(self):
        return hash(type(self))  # ignore hash of table


def real_out(type):
    if type == complex64:
        return float32,
    if type == complex128:
        return float64,
    return type,


class ScalarOp(Op):

    nin = -1
    nout = 1

    def __init__(self, output_types_preference=None, name=None):
        self.name = name
        if output_types_preference is not None:
            if not callable(output_types_preference):
                raise TypeError("Expected a callable for the 'output_types_preference' argument to %s. (got: %s)" % (self.__class__, output_types_preference))
            self.output_types_preference = output_types_preference

    def make_node(self, *inputs):
        if self.nin >= 0:
            if len(inputs) != self.nin:
                raise TypeError("Wrong number of inputs for %s.make_node (got %i(%s), expected %i)" \
                                    % (self, len(inputs), str(inputs), self.nin))
        inputs = [as_scalar(input) for input in inputs]
        outputs = [t() for t in self.output_types([input.type for input in inputs])]
        if len(outputs) != self.nout:
            raise TypeError("Not the right number of outputs produced for %s(%s). Expected %s, got %s."
                            % (self, ", ".join(str(input) for input in inputs), self.nout, len(outputs)))
        return Apply(self, inputs, outputs)

    def output_types(self, types):
        if hasattr(self, 'output_types_preference'):
            variables = self.output_types_preference(*types)
            if not isinstance(variables, (list, tuple)) or any(not isinstance(x, Type) for x in variables):
                raise TypeError("output_types_preference should return a list or a tuple of types", self.output_types_preference, variables)
            if len(variables) != self.nout:
                raise TypeError("Not the right number of outputs types produced for %s(%s) by %s. Expected %s, got %s."
                                % (self, ", ".join(str(type) for type in variables),
                                   self.output_types_preference, self.nout, len(variables)))
            return variables
        else:
            raise NotImplementedError(
                "Cannot calculate the output types for %s" % self)

    def perform(self, node, inputs, output_storage):
        if self.nout == 1:
            output_storage[0][0] = self.impl(*inputs)
        else:
            variables = utils.from_return_values(self.impl(*inputs))
            assert len(variables) == len(output_storage)
            for storage, variable in zip(output_storage, variables):
                storage[0] = variable

    def impl(self, *inputs):
        raise utils.MethodNotDefined("impl", type(self),
                                     self.__class__.__name__)

    def grad(self, inputs, output_gradients):
        raise utils.MethodNotDefined("grad", type(self),
                                     self.__class__.__name__)

    def __eq__(self, other):
        test = type(self) == type(other) \
            and getattr(self, 'output_types_preference', None) \
            == getattr(other, 'output_types_preference', None)
        return test

    def __hash__(self):
        return hash(type(self).__name__) ^ hash(
            getattr(self, 'output_types_preference', 0))

    def __str__(self):
        if hasattr(self, 'name') and self.name:
            return self.name
        else:
            return "%s{%s}" % (self.__class__.__name__,
                               ", ".join("%s=%s" % (k, v) for k, v in
                                         self.__dict__.items() if k != "name"))

    def c_code_cache_version(self):
        return (3,)


class UnaryScalarOp(ScalarOp):
    nin = 1


class BinaryScalarOp(ScalarOp):
    # One may define in subclasses the following fields:
    #   - `identity`: for an associative operation, identity corresponds to
    #     the neutral element. For instance, it will be 0 for addition, 1 for
    #     multiplication, True for "and", False for "or".
    #   - `commutative`: whether op(a, b) == op(b, a)
    #   - `associative`: whether op(op(a, b), c) == op(a, op(b, c))
    nin = 2


###############
# Comparisons
###############

class LogicalComparison(BinaryScalarOp):
    def output_types(self, *input_dtypes):
        return [int8]

    def grad(self, inputs, output_gradients):
        return [None, None]


class FixedLogicalComparison(UnaryScalarOp):
    """
    Comparison to a fixed value.
    """
    def output_types(self, *input_dtypes):
        return [int8]

    def grad(self, inputs, output_gradients):
        return [None]


class LT(LogicalComparison):
    identity = False
    commutative = False
    associative = False

    def impl(self, x, y):
        # built-in < don't support complex
        return numpy.less(x, y)

    def c_code(self, node, name, (x, y), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = (%(x)s < %(y)s);" % locals()
lt = LT()


class GT(LogicalComparison):
    identity = False
    commutative = False
    associative = False

    def impl(self, x, y):
        # built-in > don't support complex
        return numpy.greater(x, y)

    def c_code(self, node, name, (x, y), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = (%(x)s > %(y)s);" % locals()
gt = GT()


class LE(LogicalComparison):
    identity = False
    commutative = False
    associative = False

    def impl(self, x, y):
        # built-in <= don't support complex
        return numpy.less_equal(x, y)

    def c_code(self, node, name, (x, y), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = (%(x)s <= %(y)s);" % locals()
le = LE()


class GE(LogicalComparison):
    identity = False
    commutative = False
    associative = False

    def impl(self, x, y):
        # built-in >= don't support complex
        return numpy.greater_equal(x, y)

    def c_code(self, node, name, (x, y), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = (%(x)s >= %(y)s);" % locals()
ge = GE()


class EQ(LogicalComparison):
    identity = False
    commutative = True
    associative = False

    def impl(self, x, y):
        return x == y

    def c_code(self, node, name, (x, y), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = (%(x)s == %(y)s);" % locals()
eq = EQ()


class NEQ(LogicalComparison):
    identity = False
    commutative = True
    associative = False

    def impl(self, x, y):
        return x != y

    def c_code(self, node, name, (x, y), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = (%(x)s != %(y)s);" % locals()
neq = NEQ()


class IsNan(FixedLogicalComparison):
    def impl(self, x):
        return numpy.isnan(x)

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        return "%(z)s = isnan(%(x)s);" % locals()
isnan = IsNan()


class IsInf(FixedLogicalComparison):
    def impl(self, x):
        return numpy.isinf(x)

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError()
        # Note that the C isinf returns -1 for -Inf and +1 for +Inf, while
        # numpy simply returns True: we mimic numpy's behavior here, thus
        # the absolute value.
        return "%(z)s = abs(isinf(%(x)s));" % locals()
isinf = IsInf()


class InRange(LogicalComparison):
    nin = 3

    def __init__(self, openlow, openhi):
        self.openlow = openlow
        self.openhi = openhi

    def impl(self, x, low, hi):
        if self.openlow and x <= low:
            return False
        elif not self.openlow and x < low:
            return False
        if self.openhi and x >= hi:
            return False
        elif not self.openhi and x > hi:
            return False
        return True

    def c_code(self, node, name, (x, low, hi), (z, ), sub):
        if self.openlow:
            cmp1 = '>'
        else:
            cmp1 = '>='

        #backport
        #cmp1 = '>' if self.openlow else '>='

        if self.openhi:
            cmp2 = '<'
        else:
            cmp2 = '<='

        #backport
        #cmp2 = '<' if self.openhi else '<='
        return ("%(z)s = %(x)s %(cmp1)s %(low)s &&"
                " %(x)s %(cmp2)s %(hi)s;" % locals())

    def grad(self, (x, low, hi), (gz, )):
        return None, None, None
inopenrange = InRange(True, True)
inclosedrange = InRange(False, False)


class Switch(ScalarOp):
    nin = 3

    def impl(self, cond, ift, iff):
        if cond:
            return ift
        else:
            return iff

            #backport
            #return ift if cond else iff
    def c_code(self, node, name, (cond, ift, iff), (z, ), sub):
        return "%(z)s = %(cond)s ? %(ift)s : %(iff)s;" % locals()

    def grad(self, (cond, ift, iff), (gz, )):
        if ift.type in continuous_types:
            first_part = switch(cond, gz, 0)
        else:
            first_part = None

        if iff.type in continuous_types:
            second_part = switch(cond, 0, gz)
        else:
            second_part = None

        return (None, first_part, second_part)

    def output_types(self, (cond_t, ift_t, iff_t)):
        return upcast_out(ift_t, iff_t)
switch = Switch()

####################
# BIT-WISE OPERATORS
####################


class UnaryBitOp(UnaryScalarOp):
    def output_types(self, *input_types):
        for i in input_types[0]:
            if i not in (int8, int16, int32, int64):
                raise TypeError('input to a BitOp must have type int8,'
                                ' int16, int32 or int64... not %s' % i)
        return upcast_out(*input_types[0])

    def grad(self, inputs, output_gradients):
        return [None]


class BinaryBitOp(BinaryScalarOp):
    def output_types(self, *input_types):
        t0, t1 = input_types[0]
        for i in input_types[0]:
            if i not in (int8, int16, int32, int64):
                raise TypeError('input to a BitOp must have type int8,'
                                ' int16, int32 or int64... not %s' % i)
        return upcast_out(*input_types[0])

    def grad(self, inputs, output_gradients):
        return [None, None]


class OR(BinaryBitOp):
    identity = 0
    commutative = True
    associative = True

    def impl(self, x, y):
        return x | y

    def c_code(self, node, name, (x, y), (z, ), sub):
        return "%(z)s = (%(x)s | %(y)s);" % locals()
or_ = OR()


class XOR(BinaryBitOp):
    identity = 0
    commutative = True
    associative = True

    def impl(self, x, y):
        return x ^ y

    def c_code(self, node, name, (x, y), (z, ), sub):
        return "%(z)s = (%(x)s ^ %(y)s);" % locals()
xor = XOR()


class AND(BinaryBitOp):
    identity = 1
    commutative = True
    associative = True

    def impl(self, x, y):
        return x & y

    def c_code(self, node, name, (x, y), (z, ), sub):
        return "%(z)s = (%(x)s & %(y)s);" % locals()
and_ = AND()


class Invert(UnaryBitOp):
    def impl(self, x):
        return ~x

    def c_code(self, node, name, (x,), (z, ), sub):
        return "%(z)s = (~%(x)s);" % locals()
invert = Invert()


##############
# Arithmetic
##############
class Maximum(BinaryScalarOp):
    commutative = True
    associative = True

    def impl(self, *inputs):
        # The built-in max function don't support complex type
        return numpy.maximum(*inputs)

    def c_code(self, node, name, (x, y), (z, ), sub):
        if any([i.type in complex_types for i in node.inputs]):
            raise NotImplementedError()
        return "%(z)s = ((%(y)s)>(%(x)s)? (%(y)s):(%(x)s));" % locals()

    def grad(self, (x, y), (gz, )):
        assert gz.type not in complex_types
        # max is not defined for complex_types
        gx, gy = None, None
        if x.type in float_types:
            gx = eq(maximum(x, y), x) * gz
        if y.type in float_types:
            gy = eq(maximum(x, y), y) * gz
        return (gx, gy)
maximum = Maximum(upcast_out, name='maximum')


class Minimum(BinaryScalarOp):
    commutative = True
    associative = True

    def impl(self, *inputs):
        # The built-in min function don't support complex type
        return numpy.minimum(*inputs)

    def c_code(self, node, name, (x, y), (z, ), sub):
        if any([i.type in complex_types for i in node.inputs]):
            raise NotImplementedError()
        return "%(z)s = ((%(y)s)<(%(x)s)? (%(y)s):(%(x)s));" % locals()

    def grad(self, (x, y), (gz, )):
        assert gz.type not in complex_types
        # max is not defined for complex_types
        gx, gy = None, None
        if x.type in float_types:
            gx = eq(minimum(x, y), x) * gz
        if y.type in float_types:
            gy = eq(minimum(x, y), y) * gz
        return (gx, gy)

minimum = Minimum(upcast_out, name='minimum')


class Add(ScalarOp):
    identity = 0
    commutative = True
    associative = True

    def impl(self, *inputs):
        return sum(inputs)

    def c_code(self, node, name, inputs, (z, ), sub):
        if not inputs:
            return z + " = 0;"
        else:
            return z + " = " + " + ".join(inputs) + ";"

    def grad(self, inputs, (gz, )):
        retval = []
        if gz.type in complex_types:
            for i in inputs:
                if i.type in complex_types:
                    retval += [cast(gz, i.type.dtype)]
                elif i.type in float_types:
                    retval += [cast(real(gz), i.type.dtype)]
                else:
                    retval += [None]
        elif gz.type in float_types:
            for i in inputs:
                if i.type in float_types:
                    retval += [cast(gz, i.type.dtype)]
                else:
                    retval += [None]
        else:
            retval += [None] * len(inputs)
        return retval
add = Add(upcast_out, name='add')


class Mul(ScalarOp):
    identity = 1
    commutative = True
    associative = True

    def impl(self, *inputs):
        return numpy.product(inputs)

    def c_code(self, node, name, inputs, (z, ), sub):
        if not inputs:
            return z + " = 1;"
        else:
            return z + " = " + " * ".join(inputs) + ";"

    def grad(self, inputs, (gz, )):
        retval = []
        for input in inputs:
            if input.type in continuous_types:
                if gz.type in complex_types:
                    # zr+zi = (xr + xi)(yr + yi)
                    # zr+zi = (xr*yr - xi*yi) + (xr yi + xi yr )
                    otherprod = mul(*(utils.difference(inputs, [input])))
                    yr = real(otherprod)
                    yi = imag(otherprod)
                    if input.type in complex_types:
                        retval += [complex(yr * real(gz) + yi * imag(gz),
                                           yr * imag(gz) - yi * real(gz))]
                    else:
                        retval += [cast(yr * real(gz) + yi * imag(gz),
                                        input.type.dtype)]
                else:
                    retval += [cast(mul(*([gz] + utils.difference(inputs,
                                                                  [input]))),
                                    input.type.dtype)]
            else:
                retval += [None]
        return retval
mul = Mul(upcast_out, name='mul')


class Sub(BinaryScalarOp):
    def impl(self, x, y):
        return x - y

    def c_code(self, node, name, (x, y), (z, ), sub):
        return "%(z)s = %(x)s - %(y)s;" % locals()

    def grad(self, (x, y), (gz, )):
        if gz.type in complex_types:
            raise NotImplementedError()

        if x.type in float_types:
            first_part = cast(gz, x.type.dtype)
        else:
            first_part = None

        if y.type in float_types:
            second_part = cast(-gz, y.type.dtype)
        else:
            second_part = None
        return first_part, second_part
sub = Sub(upcast_out, name='sub')


def int_or_true_div(x_discrete, y_discrete):
    """
    Return 'int' or 'true' depending on the type of division used for x / y.

    :param x_discrete: True if `x` is discrete ([unsigned] integer).

    :param y_discrete: True if `x` is discrete ([unsigned] integer).

    :returns: 'int' if `x / y` should be an integer division, or `true` if it
    should be a true division.

    Raises an IntegerDivisionError if both `x_discrete` and `y_discrete` are
    True and `config.int_division` is set to 'raise'.

    This function is used by both scalar/basic.py and tensor.basic/py.
    """
    if (x_discrete and y_discrete):
        if config.int_division == 'raise':
            raise IntegerDivisionError(
                "With `config.int_division` set to 'raise', dividing two "
                "integer types with '/' is forbidden to avoid confusion "
                "between integer and floating point divisions. Please "
                "use // for integer division, or if you want a float result "
                "either cast one of the arguments to a float or directly call "
                "`x.__truediv__(y)`.")
        elif config.int_division == 'int':
            warnings.warn(
                    "Division of two integer types with x / y is deprecated, "
                    "please use x // y for an integer division.",
                    DeprecationWarning,
                    stacklevel=4)
            return 'int'
        elif config.int_division == 'floatX':
            return 'true'
        else:
            raise NotImplementedError(config.int_division)
    else:
        return 'true'


def div_proxy(x, y):
    """Proxy for either true_div or int_div, depending on types of x, y."""
    f = eval('%s_div' % int_or_true_div(as_scalar(x).type in discrete_types,
                                        as_scalar(y).type in discrete_types))
    return f(x, y)


class TrueDiv(BinaryScalarOp):
    def output_types(self, types):
        if all(t in discrete_types for t in types):
            return [Scalar(config.floatX)]
        else:
            return super(TrueDiv, self).output_types(types)

    def impl(self, x, y):
        x = numpy.asarray(x)
        y = numpy.asarray(y)
        if all(a.dtype in discrete_types for a in (x, y)):
            return numpy.array(float(x) / y, dtype=config.floatX)
        else:
            return x / y

    def c_code(self, node, name, (x, y), (z, ), sub):
        # we generate good c code only when both are complex!
        if sum([node.inputs[0].type in complex_types,
                node.inputs[1].type in complex_types]) == 1:
            raise NotImplementedError('type not supported', type)
        if (node.inputs[0].type in discrete_types and
            node.inputs[1].type in discrete_types):
            return "%(z)s = ((double)%(x)s) / %(y)s;" % locals()
        return "%(z)s = %(x)s / %(y)s;" % locals()

    def grad(self, (x, y), (gz, )):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            first_part = cast(gz / y, x.type.dtype)
        else:
            assert x.type in discrete_types
            first_part = None

        if y.type in complex_types:
            raise NotImplementedError()
        if y.type in float_types:
            second_part = cast(-(gz * x) / (y * y), y.type.dtype)
        else:
            assert y.type in discrete_types
            second_part = None
        return first_part, second_part
true_div = TrueDiv(upcast_out, name='true_div')


class IntDiv(BinaryScalarOp):
    def impl(self, x, y):
        return x // y

    def c_code(self, node, name, (x, y), (z,), sub):
        raise NotImplementedError("For integer arguments the behavior of"
                                  " division in C and in Python [can] differ"
                                  " when the quotient is negative.  C actually"
                                  " does not even specify a correct behaviour"
                                  " in this case, it is up to the chip.")

    def grad(self, inputs, g_output):
        return [None] * len(inputs)
int_div = IntDiv(upcast_out, name='int_div')


floor_div = int_div


def mod_check(x, y):
    if (as_scalar(x).type in complex_types or
        as_scalar(y).type in complex_types):
        # Currently forbidden.
        raise Mod.complex_error
    else:
        return mod(x, y)


class Mod(BinaryScalarOp):
    complex_error = ComplexError(
                "Theano does not support the mod operator (%) on "
                "complex numbers, since numpy deprecated it.")

    def impl(self, x, y):
        if isinstance(x, numpy.complex) or isinstance(y, numpy.complex):
            raise self.complex_error
        return x % y

    def c_code_cache_version(self):
        return (5,)

    def c_support_code(self):
        #We use a macro as python use % as a special string caractere.
        return "#define THEANO_MACRO_MOD(x,y) (x % y)"

    def c_code(self, node, name, (x, y), (z, ), sub):
        """
        We want the result to have the same sign as python, not the other
        implementation of mod.
        """
        # raise NotImplementedError("Unlike Python, C's modulo returns negative
        # modulo on negative dividend (to implement)")
        t = node.inputs[0].type.upcast(*[i.type for i in node.inputs[1:]])
        if (str(t) in imap(str, discrete_types) or
                t in ['uint8', 'int8', 'uint16', 'int16'] or
                t in ['uint32', 'int32', 'uint64', 'int64'] or
                t in discrete_types):
            # The above or's should not be needed anymore. However, for now we
            # keep them out of safety, and verify they are useless with an
            # assert.
            assert str(t) in imap(str, discrete_types)
            x_mod_y = "THEANO_MACRO_MOD(%(x)s, %(y)s)" % locals()
            x_mod_ymm = "THEANO_MACRO_MOD(-%(x)s, -%(y)s)" % locals()
            x_mod_ypm = "THEANO_MACRO_MOD(%(x)s, -%(y)s)" % locals()
            x_mod_ymp = "THEANO_MACRO_MOD(-%(x)s, %(y)s)" % locals()
        elif (str(t) in imap(str, float_types) or
              t in ['float32', 'float64'] or
              t in float_types):
            # The above or's should not be needed anymore. However, for now we
            # keep them out of safety, and verify they are useless with an
            # assert.
            assert str(t) in imap(str, float_types)
            x_mod_y = "fmod(%(x)s,%(y)s)" % locals()
            x_mod_ymm = "fmod(-%(x)s,-%(y)s)" % locals()
            x_mod_ypm = "fmod(%(x)s,-%(y)s)" % locals()
            x_mod_ymp = "fmod(-%(x)s,%(y)s)" % locals()
        elif str(t) in imap(str, complex_types):
            raise self.complex_error
        else:
            raise NotImplementedError('type not supported', type)

        return """
if (%(x)s < 0){
   if (%(y)s < 0){
      %(z)s = -(%(x_mod_ymm)s);
   }else{
      %(z)s = - %(x_mod_ymp)s + (%(x_mod_ymp)s != 0 ? %(y)s : 0);
   }
}else if (%(y)s < 0){
   %(z)s = (%(x_mod_ypm)s) + (%(x_mod_ypm)s != 0 ? %(y)s : 0);
}else{
   %(z)s = %(x_mod_y)s;
}
        """ % locals()

    def grad(self, (x, y), (gz, )):
        return None, None
mod = Mod(upcast_out, name='mod')


class Pow(BinaryScalarOp):
    def impl(self, x, y):
        return x ** y

    def c_code(self, node, name, (x, y), (z, ), sub):
        if (node.inputs[0].type in complex_types or
            node.inputs[1].type in complex_types):
            raise NotImplementedError('type not supported', type)
        return "%(z)s = pow(%(x)s, %(y)s);" % locals()

    def grad(self, (x, y), (gz, )):
        if gz.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            first_part = gz * y * x ** (y - 1)
        else:
            first_part = None

        if y.type in float_types:
            second_part = gz * log(x) * x ** y
        else:
            second_part = None

        return (first_part, second_part)

pow = Pow(upcast_out, name='pow')


class Clip(ScalarOp):
    nin = 3

    def impl(self, x, min, max):
        if x < min:
            return min
        elif x > max:
            return max
        else:
            return x

    def c_code(self, node, name, (x, min, max), (z, ), sub):
        return "%(z)s = %(x)s < %(min)s ? %(min)s : %(x)s > %(max)s ? %(max)s : %(x)s;" % locals()

    def grad(self, (x, min, max), (gz, )):
        assert gz.type not in complex_types
        gx = ((x > min) & (x < max)) * gz
        if x.type in float_types:
            return gx, None, None
        else:
            return None, None, None
# Don't allow complex even if numpy do
# As there is no mathematical reason for this function on complex
clip = Clip(upcast_out_no_complex, name='clip')


class Second(BinaryScalarOp):
    def impl(self, x, y):
        return y

    def c_code(self, node, name, (x, y), (z, ), sub):
        return "%(z)s = %(y)s;" % locals()

    def grad(self, (x, y), (gz, )):
        if y.type in continuous_types:
            return None, gz
        else:
            return None, None
second = Second(transfer_type(1), name='second')


class Identity(UnaryScalarOp):
    def impl(self, input):
        return input

    def c_code(self, node, name, (x, ), (z, ), sub):
        return "%(z)s = %(x)s;" % locals()

    def grad(self, (x, ), (gz, )):
        if x.type in continuous_types:
            return gz,
        else:
            return None,
identity = Identity(same_out, name='identity')


#### CASTING OPERATIONS
class Cast(UnaryScalarOp):
    def __init__(self, o_type, name=None):
        if not isinstance(o_type, Scalar):
            raise TypeError(o_type)
        super(Cast, self).__init__(specific_out(o_type), name=name)
        self.o_type = o_type
        self.ctor = getattr(numpy, o_type.dtype)

    def __str__(self):
        return '%s{%s}' % (self.__class__.__name__, self.o_type.dtype)

    def impl(self, input):
        return self.ctor(input)

    def c_code(self, node, name, (x, ), (z, ), sub):
        return "%s = (%s)%s;" % (z, node.outputs[0].type.dtype_specs()[1], x)

    def grad(self, (x, ), (gz, )):
        if x.type in continuous_types and self.o_type in continuous_types:
            return [cast(gz, x.type.dtype)]
        else:
            return None,

    def c_code_cache_version(self):
        s = super(Cast, self).c_code_cache_version()
        if s:
            return (3,) + s
        else:
            return s

convert_to_int8 = Cast(int8, name='convert_to_int8')
convert_to_int16 = Cast(int16, name='convert_to_int16')
convert_to_int32 = Cast(int32, name='convert_to_int32')
convert_to_int64 = Cast(int64, name='convert_to_int64')
convert_to_uint8 = Cast(uint8, name='convert_to_uint8')
convert_to_uint16 = Cast(uint16, name='convert_to_uint16')
convert_to_uint32 = Cast(uint32, name='convert_to_uint32')
convert_to_uint64 = Cast(uint64, name='convert_to_uint64')
convert_to_float32 = Cast(float32, name='convert_to_float32')
convert_to_float64 = Cast(float64, name='convert_to_float64')
convert_to_complex64 = Cast(complex64, name='convert_to_complex64')
convert_to_complex128 = Cast(complex128, name='convert_to_complex128')

_cast_mapping = {
           'int8': convert_to_int8,
           'int16': convert_to_int16,
           'int32': convert_to_int32,
           'int64': convert_to_int64,
           'uint8': convert_to_uint8,
           'uint16': convert_to_uint16,
           'uint32': convert_to_uint32,
           'uint64': convert_to_uint64,
           'float32': convert_to_float32,
           'float64': convert_to_float64,
           'complex64': convert_to_complex64,
           'complex128': convert_to_complex128}


def cast(x, dtype):
    """Symbolically cast `x` to a Scalar of given `dtype`."""
    if dtype == 'floatX':
        dtype = config.floatX

    _x = as_scalar(x)
    if _x.type.dtype == dtype:
        return _x
    if _x.type.dtype.startswith('complex') and not dtype.startswith('complex'):
        raise TypeError('Casting from complex to real is ambiguous: consider'
                        ' real(), imag(), angle() or abs()')
    return _cast_mapping[dtype](_x)


class Abs(UnaryScalarOp):
    def make_node(self, x):
        inputs = [as_scalar(input) for input in [x]]
        if inputs[0].type == complex64:
            outputs = [float32()]
        elif inputs[0].type == complex128:
            outputs = [float64()]
        else:
            outputs = [t() for t in self.output_types(
                    [input.type for input in inputs])]
        return Apply(self, inputs, outputs)

    def impl(self, x):
        return numpy.abs(x)

    def grad(self, (x, ), (gz, )):
        if x.type in float_types + complex_types:
            return gz * x / abs(x),  # formula works for complex and real
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        type = node.inputs[0].type
        if type in int_types:
            return "%(z)s = abs(%(x)s);" % locals()
        if type in float_types:
            return "%(z)s = fabs(%(x)s);" % locals()
        if type in complex_types:
            return "%(z)s = sqrt(%(x)s.real*%(x)s.real + %(x)s.imag*%(x)s.imag);" % locals()
        raise NotImplementedError('type not supported', type)
abs_ = Abs(same_out)


class Sgn(UnaryScalarOp):
    def impl(self, x):
        #casting to output type is handled by filter
        return numpy.sign(x)

    def grad(self, (x, ), (gz, )):
        return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        #casting is done by compiler
        #TODO: use copysign
        type = node.inputs[0].type
        if type in float_types:
            return "%(z)s = (%(x)s >= 0) ? (%(x)s == 0) ? 0.0 : 1.0 : -1.0;" % locals()
        if type in int_types:
            return "%(z)s = (%(x)s >= 0) ? (%(x)s == 0) ? 0 : 1 : -1;" % locals()
        raise TypeError()  # complex has no sgn

    def c_code_cache_version(self):
        s = super(Sgn, self).c_code_cache_version()
        if s:
            return (3,) + s
        else:  # if parent is unversioned, we are too
            return s
sgn = Sgn(same_out_nocomplex, name='sgn')


class Ceil(UnaryScalarOp):
    def impl(self, x):
        return numpy.ceil(x)

    def grad(self, (x,), (gz,)):
        return None,

    def c_code(self, node, name, (x,), (z,), sub):
        return "%(z)s = ceil(%(x)s);" % locals()
ceil = Ceil(same_out_nocomplex, name='ceil')


class Floor(UnaryScalarOp):
    def impl(self, x):
        return numpy.floor(x)

    def grad(self, (x,), (gz,)):
        return None,

    def c_code(self, node, name, (x,), (z,), sub):
        return "%(z)s = floor(%(x)s);" % locals()
floor = Floor(same_out_nocomplex, name='floor')


class RoundHalfToEven(UnaryScalarOp):
    """
    This function implement the same rounding than numpy: Round half to even

    c/c++ round fct IS DIFFERENT!
    See http://en.wikipedia.org/wiki/Rounding for more detail
    """
    def impl(self, x):
        return numpy.round(x)

    def c_code___(self, node, name, (x, ), (z, ), sub):
        typ = node.outputs[0].type.dtype
        if not node.outputs[0].type.dtype in ['float32', 'float64']:
            Exception("The output should be float32 or float64")

        return """
#ifndef ROUNDING_EPSILON
#define ROUNDING_EPSILON 0.0000001
#endif

    if (%(x)s < 0.0){
      // We implement the else part like that: -else( -%(x)s);
      %(typ)s i;
      std::modf( -%(x)s, &i );

      // If %(x)s is exactly halfway between two integers
      if ((-%(x)s -(i +0.5)) < epsilon){
          // If 'i' is even then return 'i'
        if (std::fmod( i, 2.0 ) < epsilon){
          %(z)s = - i;
        }else{
          // Else return the nearest even integer
          %(z)s = - ceil( i +0.5 );
        }
      }else{
        // round to closest
        %(z)s = - round(%(x)s+5);
      }
    }else{
      %(typ)s i;
      std::modf( %(x)s, &i );

      // If %(x)s is exactly halfway between two integers
      if ((%(x)s -(i +0.5)) < epsilon){
          // If 'i' is even then return 'i'
        if (std::fmod( i, 2.0 ) < epsilon){
          %(z)s = i;
        }else{
          // Else return the nearest even integer
          %(z)s =  ceil( i +0.5 );
        }
      }else{
        // round to closest
        %(z)s = round(%(x)s+5);
      }
    }

#undef ROUNDING_EPSILON

        """
round_half_to_even = RoundHalfToEven(same_out_float_only)


def round_half_away_from_zero_(a):
    if a > 0:
        return numpy.floor(a + 0.5)
    else:
        return numpy.ceil(a - 0.5)

round_half_away_from_zero_vec64 = numpy.vectorize(
    round_half_away_from_zero_,
    doc='round_half_away_from_zero_vec64')
round_half_away_from_zero_vec32 = numpy.vectorize(
    round_half_away_from_zero_,
    doc='round_half_away_from_zero_vec32',
    otypes=['float32'])


def round_half_away_from_zero_vec(a):
    if getattr(a, 'dtype', None) == numpy.float32:
        return round_half_away_from_zero_vec32(a)
    return round_half_away_from_zero_vec64(a)


class RoundHalfAwayFromZero(UnaryScalarOp):
    """
    Implement the same rounding algo as c round() fct.
    numpy.round fct IS DIFFERENT!

    See http://en.wikipedia.org/wiki/Rounding for more detail
    """
    def impl(self, x):

        return round_half_away_from_zero_vec(x)

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.outputs[0].type.dtype in ['float32', 'float64']:
            return "%(z)s = round(%(x)s);" % locals()
        else:
            Exception("The output should be float32 or float64")
round_half_away_from_zero = RoundHalfAwayFromZero(same_out_float_only)


class Neg(UnaryScalarOp):
    def impl(self, x):
        return -x

    def grad(self, (x,), (gz,)):
        if x.type in continuous_types:
            return -gz,
        else:
            return None,

    def c_code(self, node, name, (x,), (z,), sub):
        return "%(z)s = -%(x)s;" % locals()
neg = Neg(same_out, name='neg')


class Inv(UnaryScalarOp):
    """ multiplicative inverse. Also called reciprocal"""
    def impl(self, x):
        return 1.0 / x

    def grad(self, (x,), (gz,)):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return -gz / (x * x),
        else:
            return None,

    def c_code(self, node, name, (x,), (z,), sub):
        return "%(z)s = 1.0 / %(x)s;" % locals()
inv = Inv(upgrade_to_float, name='inv')


class Log(UnaryScalarOp):
    """ log base e """
    def impl(self, x):
        return numpy.log(x)

    def grad(self, (x,), (gz,)):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz / x,
        else:
            return None,

    def c_code(self, node, name, (x,), (z,), sub):
        #todo: the version using log2 seems to be very slightly faster
        # on some machines for some reason, check if it's worth switching
        #return "%(z)s = log2(%(x)s) * 0.69314718055994529;" % locals()
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = log(%(x)s);" % locals()
log = Log(upgrade_to_float, name='log')


class Log2(UnaryScalarOp):
    """ log base 2 """
    def impl(self, x):
        return numpy.log2(x)

    def grad(self, (x,), (gz,)):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz / (x * math.log(2.0)),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = log2(%(x)s);" % locals()
log2 = Log2(upgrade_to_float, name='log2')


class Log10(UnaryScalarOp):
    """ log base 10 """
    def impl(self, x):
        return numpy.log10(x)

    def grad(self, (x,), (gz,)):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz / (x * numpy.log(10.0)),
        else:
            return None

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = log10(%(x)s);" % locals()
log10 = Log10(upgrade_to_float, name='log10')


class Log1p(UnaryScalarOp):
    """ log(1+x) """
    def impl(self, x):
        return numpy.log1p(x)

    def grad(self, (x,), (gz,)):
        if gz.type in complex_types:
            raise NotImplementedError()
        if gz.type in float_types:
            return [gz / (1 + x)]
        return [None]

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = log1p(%(x)s);" % locals()
log1p = Log1p(upgrade_to_float, name='log1p')


class Exp(UnaryScalarOp):
    def impl(self, x):
        return numpy.exp(x)

    def grad(self, (x, ), (gz, )):
        if x.type in complex_types:
            raise NotImplementedError()
        elif x.type in float_types:
            return gz * exp(x),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = exp(%(x)s);" % locals()
exp = Exp(upgrade_to_float, name='exp')


class Sqr(UnaryScalarOp):
    def impl(self, x):
        return x * x

    def grad(self, (x, ), (gz, )):
        if gz.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz * x * 2,
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        return "%(z)s = %(x)s * %(x)s;" % locals()
sqr = Sqr(same_out, name='sqr')


class Sqrt(UnaryScalarOp):
    def impl(self, x):
        return numpy.sqrt(x)

    def grad(self, (x,), (gz,)):
        if gz.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return (gz * 0.5) / sqrt(x),
        else:
            return None,

    def c_code(self, node, name, (x,), (z,), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = sqrt(%(x)s);" % locals()
sqrt = Sqrt(upgrade_to_float, name='sqrt')


class Cos(UnaryScalarOp):
    def impl(self, x):
        return numpy.cos(x)

    def grad(self, (x, ), (gz, )):
        if gz.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return -gz * sin(x),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = cos(%(x)s);" % locals()
cos = Cos(upgrade_to_float, name='cos')


class Arccos(UnaryScalarOp):
    def impl(self, x):
        return numpy.arccos(x)

    def grad(self, (x,), (gz,)):
        if gz.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return - gz / sqrt(numpy.cast[x.type](1) - sqr(x)),
        else:
            return None,

    def c_code(self, node, name, (x,), (z,), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = acos(%(x)s);" % locals()
arccos = Arccos(upgrade_to_float, name='arccos')


class Sin(UnaryScalarOp):
    def impl(self, x):
        return numpy.sin(x)

    def grad(self, (x, ), (gz, )):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz * cos(x),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = sin(%(x)s);" % locals()
sin = Sin(upgrade_to_float, name='sin')


class Tan(UnaryScalarOp):
    def impl(self, x):
        return numpy.tan(x)

    def grad(self, (x,), (gz,)):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz / sqr(cos(x)),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = tan(%(x)s);" % locals()
tan = Tan(upgrade_to_float, name='tan')


class Cosh(UnaryScalarOp):
    """
    cosh(x) = (exp(x) + exp(-x)) / 2
    """
    def impl(self, x):
        return numpy.cosh(x)

    def grad(self, (x, ), (gz, )):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz * sinh(x),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = cosh(%(x)s);" % locals()
cosh = Cosh(upgrade_to_float, name='cosh')


class Sinh(UnaryScalarOp):
    """
    sinh(x) = (exp(x) - exp(-x)) / 2
    """
    def impl(self, x):
        return numpy.sinh(x)

    def grad(self, (x, ), (gz, )):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz * cosh(x),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = sinh(%(x)s);" % locals()
sinh = Sinh(upgrade_to_float, name='sinh')


class Tanh(UnaryScalarOp):
    """
    tanh(x) = sinh(x) / cosh(x)
            = (exp(2*x) - 1) / (exp(2*x) + 1)
    """
    def impl(self, x):
        return numpy.tanh(x)

    def grad(self, (x, ), (gz, )):
        if x.type in complex_types:
            raise NotImplementedError()
        if x.type in float_types:
            return gz * (1 - sqr(tanh(x))),
        else:
            return None,

    def c_code(self, node, name, (x, ), (z, ), sub):
        if node.inputs[0].type in complex_types:
            raise NotImplementedError('type not supported', type)
        return "%(z)s = tanh(%(x)s);" % locals()
tanh = Tanh(upgrade_to_float, name='tanh')


class Real(UnaryScalarOp):
    """Extract the real coordinate of a complex number.  """
    def impl(self, x):
        return numpy.real(x)

    def grad(self, (x, ), (gz, )):
        return [complex(gz, 0)]

real = Real(real_out, name='real')


class Imag(UnaryScalarOp):
    def impl(self, x):
        return numpy.imag(x)

    def grad(self, (x, ), (gz, )):
        if x.type in complex_types:
            return [complex(0, gz)]
        elif x.type in float_types:
            return [second(x, 0)]
        else:
            return [None]
imag = Imag(real_out, name='imag')


class Angle(UnaryScalarOp):
    def impl(self, x):
        return numpy.angle(x)

    def grad(self, (c, ), (gtheta, )):
        # y = x.imag
        # r = sqrt(y**2 + x.real**2)
        # g = y/r
        # if x == 0 and y == 0:
        #     theta = 0
        # elif x >= 0:
        #     theta = numpy.arcsin(g)
        # else:
        #     theta = -numpy.arcsin(g)+numpy.pi

        x = real(c)
        y = imag(c)
        r = abs(c)

        gr = -gtheta * y / (r ** 2 * sqrt(1 - (y / r) ** 2))
        gx = gr * x / r
        gy = gr * y / r
        if c in complex_types:
            return [cast(complex(gx, gy), x.type.dtype)]
        elif c in float_types:
            return [cast(second(x, 0), x.type.dtype)]
        else:
            return [None]

angle = Angle(specific_out(float64), name='angle')


class Complex(BinaryScalarOp):
    @staticmethod
    def output_types_preference(x, y):
        if x in complex_types:
            raise TypeError(x)
        if y in complex_types:
            raise TypeError(y)

        up = Scalar.upcast(x, y)
        if up in ('float64', 'int64', 'uint64', 'int32', 'uint32'):
            return [complex128]
        else:
            return [complex64]

    def impl(self, x, y):
        return numpy.complex(x, y)

    def grad(self, (x, y), (gz,)):
        return [cast(real(gz), x.type.dtype),
                cast(imag(gz), y.type.dtype)]
complex = Complex(name='complex')


class Conj(UnaryScalarOp):
    def impl(self, x):
        return numpy.conj(x)

    def grad(self, (x, ), (gz, )):
        return [conj(gz)]
conj = Conj(same_out, name='conj')


class ComplexFromPolar(BinaryScalarOp):
    @staticmethod
    def output_types_preference(x, y):
        return Complex.output_types_preference(x, y)

    def impl(self, r, theta):
        if r < 0:
            raise ValueError('polar radius must be non-negative', r)
        x = r * numpy.cos(theta)
        y = r * numpy.sin(theta)
        if x.dtype == 'float32':
            return numpy.complex64(numpy.complex(x, y))
        else:
            return numpy.complex128(numpy.complex(x, y))

    def grad(self, (r, theta), (gz,)):
        gr = cos(theta) * real(gz) + sin(theta) * imag(gz)
        gtheta = -real(gz) * r * sin(theta) + imag(gz) * r * cos(theta)
        return [cast(gr, r.type.dtype),
                cast(gtheta, theta.type.dtype)]
complex_from_polar = ComplexFromPolar(name='complex_from_polar')


class Composite(ScalarOp):
    """
    Composite is an Op that takes a graph of scalar operations and
    produces c code for the whole graph. Its purpose is to implement loop
    fusion.

    Composite depends on all the Ops in its graph having C code.
    """
    def __str__(self):
        return self.name

    def make_new_inplace(self, output_types_preference=None, name=None):
        """
        This op.__init__ fct don't have the same parameter as other scalar op.
        This break the insert_inplace_optimizer optimization.
        This fct allow fix patch this.
        """
        out = self.__class__(self.inputs, self.outputs)
        if name:
            out.name = name
        else:
            name = out.name
        super(Composite, out).__init__(output_types_preference, name)
        return out

    def init_c_code(self):
        """Return the C code for this Composite Op.  """
        subd = dict(
                zip(self.env.inputs,
                    ["%%(i%i)s" % i for i in xrange(len(self.env.inputs))])
                + zip(self.env.outputs,
                    ["%%(o%i)s" % i for i in xrange(len(self.env.outputs))]))

        for orphan in self.env.variables:  # env.orphans:
            if orphan.owner is None and orphan not in self.env.inputs:
                if isinstance(orphan, Constant):
                    subd[orphan] = orphan.type.c_literal(orphan.data)
                else:
                    raise ValueError(
                            "All orphans in the env to Composite must"
                            " be Constant instances.")

        _c_code = "{\n"
        i = 0
        j = 0
        self.nodenames = ["%(nodename)s_" + ('subnode%i' % j)
                for j, n in enumerate(self.env.toposort())]

        for j, node in enumerate(self.env.toposort()):
            for output in node.outputs:
                if output not in subd:
                    i += 1
                    name = "V%%(id)s_tmp%i" % i
                    subd[output] = name
                    _c_code += "%s %s;\n" % (
                            output.type.dtype_specs()[1], name)
            s = node.op.c_code(node,
                      self.nodenames[j],
                      [subd[input] for input in node.inputs],
                      [subd[output] for output in node.outputs],
                      dict(fail="%(fail)s",
                          id="%%(id)s_%i" % j))
            _c_code += s
            _c_code += "\n"
        _c_code += "}\n"
        self._c_code = _c_code

    def init_py_impls(self):
        """Return a list of functions that compute each output of self
        """
        def compose_impl(r):
            # this is not optimal at all eg in add(*1 -> mul(x, y), *1)
            # it will calculate *1 twice
            # it also doesn't follow env.toposort but that's (presumably)
            # still correct since we only have scalar ops
            if r in self.env.inputs:
                idx = self.env.inputs.index(r)
                return lambda inputs: inputs[idx]
            elif r.owner is None:  # in env.orphans:
                return lambda inputs: r.data
            node = r.owner
            producers = [compose_impl(input) for input in node.inputs]
            return lambda inputs: node.op.impl(*[p(inputs) for p in producers])
        self._impls = [compose_impl(r) for r in self.env.outputs]

    def init_name(self):
        """Return a readable string representation of self.env
        """
        try:
            rval = self.name
        except AttributeError:
            if 0:
                l = []
                for n in env.toposort():
                    if hasattr(n.op, "name") and n.op.name is not None:
                        v = n.op.name
                        if v.startswith("Composite"):
                            v = v[len("Composite"):]
                    else:
                        v = n.op.__class__.__name__
                    l.append(v)
                rval = "Composite{" + ",".join(l) + "}"
            else:
                for i, r in enumerate(self.env.inputs):
                    r.name = 'i%i' % i
                for i, r in enumerate(self.env.outputs):
                    r.name = 'o%i' % i
                io = set(self.env.inputs + self.env.outputs)
                for i, r in enumerate(self.env.variables):
                    if r not in io and len(r.clients) > 1:
                        r.name = 't%i' % i
                rval = "Composite{%s}" % str(self.env)
        self.name = rval

    def init_env(self):
        env = Env(*gof.graph.clone(self.inputs, self.outputs))
        gof.MergeOptimizer().optimize(env)
        for node in env.nodes:
            if not isinstance(node.op, ScalarOp):
                raise ValueError("The env to Composite must be exclusively"
                                 " composed of ScalarOp instances.")
        self.env = env

    def __init__(self, inputs, outputs):
        self.inputs = copy(inputs)
        self.outputs = copy(outputs)
        self.inputs_type = tuple([input.type for input in inputs])
        self.outputs_type = tuple([output.type for output in outputs])
        self.nin = len(inputs)
        self.nout = len(outputs)
        self.init_env()       # self.env
        self.init_name()      # self.name
        self.init_c_code()    # self._c_code and self.nodenames
        self.init_py_impls()  # self._impls

    def output_types(self, input_types):
        if tuple(input_types) != self.inputs_type:
            raise TypeError("Wrong types for Composite. Expected %s, got %s."
                            % (self.inputs_type, tuple(input_types)))
        return self.outputs_type

    def perform(self, node, inputs, output_storage):
        for storage, impl in zip(output_storage, self._impls):
            storage[0] = impl(inputs)

    def impl(self, *inputs):
        output_storage = [[None] for i in xrange(self.nout)]
        self.perform(None, inputs, output_storage)
        return utils.to_return_values([storage[0] for storage in
                                       output_storage])

    def grad(self, inputs, output_grads):
        raise NotImplementedError("grad is not implemented for Composite")

    def c_code(self, node, nodename, inames, onames, sub):
        d = dict(zip(["i%i" % i for i in xrange(len(inames))],
                     inames) +
                 zip(["o%i" % i for i in xrange(len(onames))],
                     onames),
                 **sub)
        d['nodename'] = nodename
        if not sub.has_key('id'):
            #The use of a dummy id is safe as the code is in a separate block.
            #It won't generate conflicting variable name.
            d['id'] = '_DUMMY_ID_'

        return self._c_code % d

    def c_code_cache_version(self):
        rval = [3]
        for x in self.env.toposort():
            xv = x.op.c_code_cache_version()
            if xv:
                rval.append(xv)
            else:
                return ()
        return tuple(rval)

    def c_support_code(self):
        rval = []
        for subnode in self.env.toposort():
            try:
                rval.append(subnode.op.c_support_code())
            except gof.utils.MethodNotDefined:
                pass
        # remove duplicate code blocks
        return "\n".join(sorted(set(rval)))

    def c_support_code_apply(self, node, name):
        rval = []
        for subnode, subnodename in zip(self.env.toposort(), self.nodenames):
            try:
                rval.append(
                        subnode.op.c_support_code_apply(
                            subnode,
                            subnodename % dict(nodename=name)))
            except gof.utils.MethodNotDefined:
                pass
        # there should be no need to remove duplicate code blocks because
        # each block should have been specialized for the given nodename.
        # Any block that isn't specialized should be returned via
        # c_support_code instead of c_support_code_apply.
        return "\n".join(rval)

    def __eq__(self, other):
        if self is other:
            return True
        if (type(self) != type(other)
                or self.nin != other.nin
                or self.nout != other.nout):
            return False
        # see __hash__ for comment on why there is no mention of env
        # or module cache key here.
        return (self._c_code == other._c_code)

    def __hash__(self):
        rval = hash((type(self),
            self.nin,
            self.nout,
            self._c_code))
        # Note that in general, the configparser settings at the time
        # of code generation (__init__) affect the semantics of this Op.
        # This function assumes that all relevant info about the configparser
        # is embodied in _c_code.  So the _c_code, rather than self.env,
        # is the signature of the semantics of this Op.
        # _c_code is preserved through unpickling, so the Op will not change
        # semantics when it is reloaded with different configparser
        # settings.
        return rval

    def __getstate__(self):
        rval = dict(self.__dict__)
        del rval['_impls']
        del rval['env']
        return rval

    def __setstate__(self, d):
        self.__dict__.update(d)
        # We must call init to set env and _impls again, as otherwise
        # self.perform will not work.
        self.init_env()
        self.init_py_impls()
        assert self._c_code
