Vehicle-cpp/hkpc/software/sympy/printing/codeprinter.py

from __future__ import annotations
from typing import Any

from functools import wraps

from sympy.core import Add, Mul, Pow, S, sympify, Float
from sympy.core.basic import Basic
from sympy.core.expr import UnevaluatedExpr
from sympy.core.function import Lambda
from sympy.core.mul import _keep_coeff
from sympy.core.sorting import default_sort_key
from sympy.core.symbol import Symbol
from sympy.functions.elementary.complexes import re
from sympy.printing.str import StrPrinter
from sympy.printing.precedence import precedence, PRECEDENCE


class requires:
    """ Decorator for registering requirements on print methods. """
    def __init__(self, **kwargs):
        self._req = kwargs

    def __call__(self, method):
        def _method_wrapper(self_, *args, **kwargs):
            for k, v in self._req.items():
                getattr(self_, k).update(v)
            return method(self_, *args, **kwargs)
        return wraps(method)(_method_wrapper)


class AssignmentError(Exception):
    """
    Raised if an assignment variable for a loop is missing.
    """
    pass


def _convert_python_lists(arg):
    if isinstance(arg, list):
        from sympy.codegen.abstract_nodes import List
        return List(*(_convert_python_lists(e) for e in arg))
    elif isinstance(arg, tuple):
        return tuple(_convert_python_lists(e) for e in arg)
    else:
        return arg


class CodePrinter(StrPrinter):
    """
    The base class for code-printing subclasses.
    """

    _operators = {
        'and': '&&',
        'or': '||',
        'not': '!',
    }

    _default_settings: dict[str, Any] = {
        'order': None,
        'full_prec': 'auto',
        'error_on_reserved': False,
        'reserved_word_suffix': '_',
        'human': True,
        'inline': False,
        'allow_unknown_functions': False,
    }

    # Functions which are "simple" to rewrite to other functions that
    # may be supported
    # function_to_rewrite : (function_to_rewrite_to, iterable_with_other_functions_required)
    _rewriteable_functions = {
            'cot': ('tan', []),
            'csc': ('sin', []),
            'sec': ('cos', []),
            'acot': ('atan', []),
            'acsc': ('asin', []),
            'asec': ('acos', []),
            'coth': ('exp', []),
            'csch': ('exp', []),
            'sech': ('exp', []),
            'acoth': ('log', []),
            'acsch': ('log', []),
            'asech': ('log', []),
            'catalan': ('gamma', []),
            'fibonacci': ('sqrt', []),
            'lucas': ('sqrt', []),
            'beta': ('gamma', []),
            'sinc': ('sin', ['Piecewise']),
            'Mod': ('floor', []),
            'factorial': ('gamma', []),
            'factorial2': ('gamma', ['Piecewise']),
            'subfactorial': ('uppergamma', []),
            'RisingFactorial': ('gamma', ['Piecewise']),
            'FallingFactorial': ('gamma', ['Piecewise']),
            'binomial': ('gamma', []),
            'frac': ('floor', []),
            'Max': ('Piecewise', []),
            'Min': ('Piecewise', []),
            'Heaviside': ('Piecewise', []),
            'erf2': ('erf', []),
            'erfc': ('erf', []),
            'Li': ('li', []),
            'Ei': ('li', []),
            'dirichlet_eta': ('zeta', []),
            'riemann_xi': ('zeta', ['gamma']),
    }

    def __init__(self, settings=None):

        super().__init__(settings=settings)
        if not hasattr(self, 'reserved_words'):
            self.reserved_words = set()

    def _handle_UnevaluatedExpr(self, expr):
        return expr.replace(re, lambda arg: arg if isinstance(
            arg, UnevaluatedExpr) and arg.args[0].is_real else re(arg))

    def doprint(self, expr, assign_to=None):
        """
        Print the expression as code.

        Parameters
        ----------
        expr : Expression
            The expression to be printed.

        assign_to : Symbol, string, MatrixSymbol, list of strings or Symbols (optional)
            If provided, the printed code will set the expression to a variable or multiple variables
            with the name or names given in ``assign_to``.
        """
        from sympy.matrices.expressions.matexpr import MatrixSymbol
        from sympy.codegen.ast import CodeBlock, Assignment

        def _handle_assign_to(expr, assign_to):
            if assign_to is None:
                return sympify(expr)
            if isinstance(assign_to, (list, tuple)):
                if len(expr) != len(assign_to):
                    raise ValueError('Failed to assign an expression of length {} to {} variables'.format(len(expr), len(assign_to)))
                return CodeBlock(*[_handle_assign_to(lhs, rhs) for lhs, rhs in zip(expr, assign_to)])
            if isinstance(assign_to, str):
                if expr.is_Matrix:
                    assign_to = MatrixSymbol(assign_to, *expr.shape)
                else:
                    assign_to = Symbol(assign_to)
            elif not isinstance(assign_to, Basic):
                raise TypeError("{} cannot assign to object of type {}".format(
                        type(self).__name__, type(assign_to)))
            return Assignment(assign_to, expr)

        expr = _convert_python_lists(expr)
        expr = _handle_assign_to(expr, assign_to)

        # Remove re(...) nodes due to UnevaluatedExpr.is_real always is None:
        expr = self._handle_UnevaluatedExpr(expr)

        # keep a set of expressions that are not strictly translatable to Code
        # and number constants that must be declared and initialized
        self._not_supported = set()
        self._number_symbols = set()

        lines = self._print(expr).splitlines()

        # format the output
        if self._settings["human"]:
            frontlines = []
            if self._not_supported:
                frontlines.append(self._get_comment(
                        "Not supported in {}:".format(self.language)))
                for expr in sorted(self._not_supported, key=str):
                    frontlines.append(self._get_comment(type(expr).__name__))
            for name, value in sorted(self._number_symbols, key=str):
                frontlines.append(self._declare_number_const(name, value))
            lines = frontlines + lines
            lines = self._format_code(lines)
            result = "\n".join(lines)
        else:
            lines = self._format_code(lines)
            num_syms = {(k, self._print(v)) for k, v in self._number_symbols}
            result = (num_syms, self._not_supported, "\n".join(lines))
        self._not_supported = set()
        self._number_symbols = set()
        return result

    def _doprint_loops(self, expr, assign_to=None):
        # Here we print an expression that contains Indexed objects, they
        # correspond to arrays in the generated code.  The low-level implementation
        # involves looping over array elements and possibly storing results in temporary
        # variables or accumulate it in the assign_to object.

        if self._settings.get('contract', True):
            from sympy.tensor import get_contraction_structure
            # Setup loops over non-dummy indices  --  all terms need these
            indices = self._get_expression_indices(expr, assign_to)
            # Setup loops over dummy indices  --  each term needs separate treatment
            dummies = get_contraction_structure(expr)
        else:
            indices = []
            dummies = {None: (expr,)}
        openloop, closeloop = self._get_loop_opening_ending(indices)

        # terms with no summations first
        if None in dummies:
            text = StrPrinter.doprint(self, Add(*dummies[None]))
        else:
            # If all terms have summations we must initialize array to Zero
            text = StrPrinter.doprint(self, 0)

        # skip redundant assignments (where lhs == rhs)
        lhs_printed = self._print(assign_to)
        lines = []
        if text != lhs_printed:
            lines.extend(openloop)
            if assign_to is not None:
                text = self._get_statement("%s = %s" % (lhs_printed, text))
            lines.append(text)
            lines.extend(closeloop)

        # then terms with summations
        for d in dummies:
            if isinstance(d, tuple):
                indices = self._sort_optimized(d, expr)
                openloop_d, closeloop_d = self._get_loop_opening_ending(
                    indices)

                for term in dummies[d]:
                    if term in dummies and not ([list(f.keys()) for f in dummies[term]]
                            == [[None] for f in dummies[term]]):
                        # If one factor in the term has it's own internal
                        # contractions, those must be computed first.
                        # (temporary variables?)
                        raise NotImplementedError(
                            "FIXME: no support for contractions in factor yet")
                    else:

                        # We need the lhs expression as an accumulator for
                        # the loops, i.e
                        #
                        # for (int d=0; d < dim; d++){
                        #    lhs[] = lhs[] + term[][d]
                        # }           ^.................. the accumulator
                        #
                        # We check if the expression already contains the
                        # lhs, and raise an exception if it does, as that
                        # syntax is currently undefined.  FIXME: What would be
                        # a good interpretation?
                        if assign_to is None:
                            raise AssignmentError(
                                "need assignment variable for loops")
                        if term.has(assign_to):
                            raise ValueError("FIXME: lhs present in rhs,\
                                this is undefined in CodePrinter")

                        lines.extend(openloop)
                        lines.extend(openloop_d)
                        text = "%s = %s" % (lhs_printed, StrPrinter.doprint(
                            self, assign_to + term))
                        lines.append(self._get_statement(text))
                        lines.extend(closeloop_d)
                        lines.extend(closeloop)

        return "\n".join(lines)

    def _get_expression_indices(self, expr, assign_to):
        from sympy.tensor import get_indices
        rinds, junk = get_indices(expr)
        linds, junk = get_indices(assign_to)

        # support broadcast of scalar
        if linds and not rinds:
            rinds = linds
        if rinds != linds:
            raise ValueError("lhs indices must match non-dummy"
                    " rhs indices in %s" % expr)

        return self._sort_optimized(rinds, assign_to)

    def _sort_optimized(self, indices, expr):

        from sympy.tensor.indexed import Indexed

        if not indices:
            return []

        # determine optimized loop order by giving a score to each index
        # the index with the highest score are put in the innermost loop.
        score_table = {}
        for i in indices:
            score_table[i] = 0

        arrays = expr.atoms(Indexed)
        for arr in arrays:
            for p, ind in enumerate(arr.indices):
                try:
                    score_table[ind] += self._rate_index_position(p)
                except KeyError:
                    pass

        return sorted(indices, key=lambda x: score_table[x])

    def _rate_index_position(self, p):
        """function to calculate score based on position among indices

        This method is used to sort loops in an optimized order, see
        CodePrinter._sort_optimized()
        """
        raise NotImplementedError("This function must be implemented by "
                                  "subclass of CodePrinter.")

    def _get_statement(self, codestring):
        """Formats a codestring with the proper line ending."""
        raise NotImplementedError("This function must be implemented by "
                                  "subclass of CodePrinter.")

    def _get_comment(self, text):
        """Formats a text string as a comment."""
        raise NotImplementedError("This function must be implemented by "
                                  "subclass of CodePrinter.")

    def _declare_number_const(self, name, value):
        """Declare a numeric constant at the top of a function"""
        raise NotImplementedError("This function must be implemented by "
                                  "subclass of CodePrinter.")

    def _format_code(self, lines):
        """Take in a list of lines of code, and format them accordingly.

        This may include indenting, wrapping long lines, etc..."""
        raise NotImplementedError("This function must be implemented by "
                                  "subclass of CodePrinter.")

    def _get_loop_opening_ending(self, indices):
        """Returns a tuple (open_lines, close_lines) containing lists
        of codelines"""
        raise NotImplementedError("This function must be implemented by "
                                  "subclass of CodePrinter.")

    def _print_Dummy(self, expr):
        if expr.name.startswith('Dummy_'):
            return '_' + expr.name
        else:
            return '%s_%d' % (expr.name, expr.dummy_index)

    def _print_CodeBlock(self, expr):
        return '\n'.join([self._print(i) for i in expr.args])

    def _print_String(self, string):
        return str(string)

    def _print_QuotedString(self, arg):
        return '"%s"' % arg.text

    def _print_Comment(self, string):
        return self._get_comment(str(string))

    def _print_Assignment(self, expr):
        from sympy.codegen.ast import Assignment
        from sympy.functions.elementary.piecewise import Piecewise
        from sympy.matrices.expressions.matexpr import MatrixSymbol
        from sympy.tensor.indexed import IndexedBase
        lhs = expr.lhs
        rhs = expr.rhs
        # We special case assignments that take multiple lines
        if isinstance(expr.rhs, Piecewise):
            # Here we modify Piecewise so each expression is now
            # an Assignment, and then continue on the print.
            expressions = []
            conditions = []
            for (e, c) in rhs.args:
                expressions.append(Assignment(lhs, e))
                conditions.append(c)
            temp = Piecewise(*zip(expressions, conditions))
            return self._print(temp)
        elif isinstance(lhs, MatrixSymbol):
            # Here we form an Assignment for each element in the array,
            # printing each one.
            lines = []
            for (i, j) in self._traverse_matrix_indices(lhs):
                temp = Assignment(lhs[i, j], rhs[i, j])
                code0 = self._print(temp)
                lines.append(code0)
            return "\n".join(lines)
        elif self._settings.get("contract", False) and (lhs.has(IndexedBase) or
                rhs.has(IndexedBase)):
            # Here we check if there is looping to be done, and if so
            # print the required loops.
            return self._doprint_loops(rhs, lhs)
        else:
            lhs_code = self._print(lhs)
            rhs_code = self._print(rhs)
            return self._get_statement("%s = %s" % (lhs_code, rhs_code))

    def _print_AugmentedAssignment(self, expr):
        lhs_code = self._print(expr.lhs)
        rhs_code = self._print(expr.rhs)
        return self._get_statement("{} {} {}".format(
            *(self._print(arg) for arg in [lhs_code, expr.op, rhs_code])))

    def _print_FunctionCall(self, expr):
        return '%s(%s)' % (
            expr.name,
            ', '.join((self._print(arg) for arg in expr.function_args)))

    def _print_Variable(self, expr):
        return self._print(expr.symbol)

    def _print_Symbol(self, expr):

        name = super()._print_Symbol(expr)

        if name in self.reserved_words:
            if self._settings['error_on_reserved']:
                msg = ('This expression includes the symbol "{}" which is a '
                       'reserved keyword in this language.')
                raise ValueError(msg.format(name))
            return name + self._settings['reserved_word_suffix']
        else:
            return name

    def _can_print(self, name):
        """ Check if function ``name`` is either a known function or has its own
            printing method. Used to check if rewriting is possible."""
        return name in self.known_functions or getattr(self, '_print_{}'.format(name), False)

    def _print_Function(self, expr):
        if expr.func.__name__ in self.known_functions:
            cond_func = self.known_functions[expr.func.__name__]
            if isinstance(cond_func, str):
                return "%s(%s)" % (cond_func, self.stringify(expr.args, ", "))
            else:
                for cond, func in cond_func:
                    if cond(*expr.args):
                        break
                if func is not None:
                    try:
                        return func(*[self.parenthesize(item, 0) for item in expr.args])
                    except TypeError:
                        return "%s(%s)" % (func, self.stringify(expr.args, ", "))
        elif hasattr(expr, '_imp_') and isinstance(expr._imp_, Lambda):
            # inlined function
            return self._print(expr._imp_(*expr.args))
        elif expr.func.__name__ in self._rewriteable_functions:
            # Simple rewrite to supported function possible
            target_f, required_fs = self._rewriteable_functions[expr.func.__name__]
            if self._can_print(target_f) and all(self._can_print(f) for f in required_fs):
                return self._print(expr.rewrite(target_f))
        if expr.is_Function and self._settings.get('allow_unknown_functions', False):
            return '%s(%s)' % (self._print(expr.func), ', '.join(map(self._print, expr.args)))
        else:
            return self._print_not_supported(expr)

    _print_Expr = _print_Function

    # Don't inherit the str-printer method for Heaviside to the code printers
    _print_Heaviside = None

    def _print_NumberSymbol(self, expr):
        if self._settings.get("inline", False):
            return self._print(Float(expr.evalf(self._settings["precision"])))
        else:
            # A Number symbol that is not implemented here or with _printmethod
            # is registered and evaluated
            self._number_symbols.add((expr,
                Float(expr.evalf(self._settings["precision"]))))
            return str(expr)

    def _print_Catalan(self, expr):
        return self._print_NumberSymbol(expr)
    def _print_EulerGamma(self, expr):
        return self._print_NumberSymbol(expr)
    def _print_GoldenRatio(self, expr):
        return self._print_NumberSymbol(expr)
    def _print_TribonacciConstant(self, expr):
        return self._print_NumberSymbol(expr)
    def _print_Exp1(self, expr):
        return self._print_NumberSymbol(expr)
    def _print_Pi(self, expr):
        return self._print_NumberSymbol(expr)

    def _print_And(self, expr):
        PREC = precedence(expr)
        return (" %s " % self._operators['and']).join(self.parenthesize(a, PREC)
                for a in sorted(expr.args, key=default_sort_key))

    def _print_Or(self, expr):
        PREC = precedence(expr)
        return (" %s " % self._operators['or']).join(self.parenthesize(a, PREC)
                for a in sorted(expr.args, key=default_sort_key))

    def _print_Xor(self, expr):
        if self._operators.get('xor') is None:
            return self._print(expr.to_nnf())
        PREC = precedence(expr)
        return (" %s " % self._operators['xor']).join(self.parenthesize(a, PREC)
                for a in expr.args)

    def _print_Equivalent(self, expr):
        if self._operators.get('equivalent') is None:
            return self._print(expr.to_nnf())
        PREC = precedence(expr)
        return (" %s " % self._operators['equivalent']).join(self.parenthesize(a, PREC)
                for a in expr.args)

    def _print_Not(self, expr):
        PREC = precedence(expr)
        return self._operators['not'] + self.parenthesize(expr.args[0], PREC)

    def _print_BooleanFunction(self, expr):
        return self._print(expr.to_nnf())

    def _print_Mul(self, expr):

        prec = precedence(expr)

        c, e = expr.as_coeff_Mul()
        if c < 0:
            expr = _keep_coeff(-c, e)
            sign = "-"
        else:
            sign = ""

        a = []  # items in the numerator
        b = []  # items that are in the denominator (if any)

        pow_paren = []  # Will collect all pow with more than one base element and exp = -1

        if self.order not in ('old', 'none'):
            args = expr.as_ordered_factors()
        else:
            # use make_args in case expr was something like -x -> x
            args = Mul.make_args(expr)

        # Gather args for numerator/denominator
        for item in args:
            if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
                if item.exp != -1:
                    b.append(Pow(item.base, -item.exp, evaluate=False))
                else:
                    if len(item.args[0].args) != 1 and isinstance(item.base, Mul):   # To avoid situations like #14160
                        pow_paren.append(item)
                    b.append(Pow(item.base, -item.exp))
            else:
                a.append(item)

        a = a or [S.One]

        if len(a) == 1 and sign == "-":
            # Unary minus does not have a SymPy class, and hence there's no
            # precedence weight associated with it, Python's unary minus has
            # an operator precedence between multiplication and exponentiation,
            # so we use this to compute a weight.
            a_str = [self.parenthesize(a[0], 0.5*(PRECEDENCE["Pow"]+PRECEDENCE["Mul"]))]
        else:
            a_str = [self.parenthesize(x, prec) for x in a]
        b_str = [self.parenthesize(x, prec) for x in b]

        # To parenthesize Pow with exp = -1 and having more than one Symbol
        for item in pow_paren:
            if item.base in b:
                b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]

        if not b:
            return sign + '*'.join(a_str)
        elif len(b) == 1:
            return sign + '*'.join(a_str) + "/" + b_str[0]
        else:
            return sign + '*'.join(a_str) + "/(%s)" % '*'.join(b_str)

    def _print_not_supported(self, expr):
        try:
            self._not_supported.add(expr)
        except TypeError:
            # not hashable
            pass
        return self.emptyPrinter(expr)

    # The following can not be simply translated into C or Fortran
    _print_Basic = _print_not_supported
    _print_ComplexInfinity = _print_not_supported
    _print_Derivative = _print_not_supported
    _print_ExprCondPair = _print_not_supported
    _print_GeometryEntity = _print_not_supported
    _print_Infinity = _print_not_supported
    _print_Integral = _print_not_supported
    _print_Interval = _print_not_supported
    _print_AccumulationBounds = _print_not_supported
    _print_Limit = _print_not_supported
    _print_MatrixBase = _print_not_supported
    _print_DeferredVector = _print_not_supported
    _print_NaN = _print_not_supported
    _print_NegativeInfinity = _print_not_supported
    _print_Order = _print_not_supported
    _print_RootOf = _print_not_supported
    _print_RootsOf = _print_not_supported
    _print_RootSum = _print_not_supported
    _print_Uniform = _print_not_supported
    _print_Unit = _print_not_supported
    _print_Wild = _print_not_supported
    _print_WildFunction = _print_not_supported
    _print_Relational = _print_not_supported


# Code printer functions. These are included in this file so that they can be
# imported in the top-level __init__.py without importing the sympy.codegen
# module.

def ccode(expr, assign_to=None, standard='c99', **settings):
    """Converts an expr to a string of c code

    Parameters
    ==========

    expr : Expr
        A SymPy expression to be converted.
    assign_to : optional
        When given, the argument is used as the name of the variable to which
        the expression is assigned. Can be a string, ``Symbol``,
        ``MatrixSymbol``, or ``Indexed`` type. This is helpful in case of
        line-wrapping, or for expressions that generate multi-line statements.
    standard : str, optional
        String specifying the standard. If your compiler supports a more modern
        standard you may set this to 'c99' to allow the printer to use more math
        functions. [default='c89'].
    precision : integer, optional
        The precision for numbers such as pi [default=17].
    user_functions : dict, optional
        A dictionary where the keys are string representations of either
        ``FunctionClass`` or ``UndefinedFunction`` instances and the values
        are their desired C string representations. Alternatively, the
        dictionary value can be a list of tuples i.e. [(argument_test,
        cfunction_string)] or [(argument_test, cfunction_formater)]. See below
        for examples.
    dereference : iterable, optional
        An iterable of symbols that should be dereferenced in the printed code
        expression. These would be values passed by address to the function.
        For example, if ``dereference=[a]``, the resulting code would print
        ``(*a)`` instead of ``a``.
    human : bool, optional
        If True, the result is a single string that may contain some constant
        declarations for the number symbols. If False, the same information is
        returned in a tuple of (symbols_to_declare, not_supported_functions,
        code_text). [default=True].
    contract: bool, optional
        If True, ``Indexed`` instances are assumed to obey tensor contraction
        rules and the corresponding nested loops over indices are generated.
        Setting contract=False will not generate loops, instead the user is
        responsible to provide values for the indices in the code.
        [default=True].

    Examples
    ========

    >>> from sympy import ccode, symbols, Rational, sin, ceiling, Abs, Function
    >>> x, tau = symbols("x, tau")
    >>> expr = (2*tau)**Rational(7, 2)
    >>> ccode(expr)
    '8*M_SQRT2*pow(tau, 7.0/2.0)'
    >>> ccode(expr, math_macros={})
    '8*sqrt(2)*pow(tau, 7.0/2.0)'
    >>> ccode(sin(x), assign_to="s")
    's = sin(x);'
    >>> from sympy.codegen.ast import real, float80
    >>> ccode(expr, type_aliases={real: float80})
    '8*M_SQRT2l*powl(tau, 7.0L/2.0L)'

    Simple custom printing can be defined for certain types by passing a
    dictionary of {"type" : "function"} to the ``user_functions`` kwarg.
    Alternatively, the dictionary value can be a list of tuples i.e.
    [(argument_test, cfunction_string)].

    >>> custom_functions = {
    ...   "ceiling": "CEIL",
    ...   "Abs": [(lambda x: not x.is_integer, "fabs"),
    ...           (lambda x: x.is_integer, "ABS")],
    ...   "func": "f"
    ... }
    >>> func = Function('func')
    >>> ccode(func(Abs(x) + ceiling(x)), standard='C89', user_functions=custom_functions)
    'f(fabs(x) + CEIL(x))'

    or if the C-function takes a subset of the original arguments:

    >>> ccode(2**x + 3**x, standard='C99', user_functions={'Pow': [
    ...   (lambda b, e: b == 2, lambda b, e: 'exp2(%s)' % e),
    ...   (lambda b, e: b != 2, 'pow')]})
    'exp2(x) + pow(3, x)'

    ``Piecewise`` expressions are converted into conditionals. If an
    ``assign_to`` variable is provided an if statement is created, otherwise
    the ternary operator is used. Note that if the ``Piecewise`` lacks a
    default term, represented by ``(expr, True)`` then an error will be thrown.
    This is to prevent generating an expression that may not evaluate to
    anything.

    >>> from sympy import Piecewise
    >>> expr = Piecewise((x + 1, x > 0), (x, True))
    >>> print(ccode(expr, tau, standard='C89'))
    if (x > 0) {
    tau = x + 1;
    }
    else {
    tau = x;
    }

    Support for loops is provided through ``Indexed`` types. With
    ``contract=True`` these expressions will be turned into loops, whereas
    ``contract=False`` will just print the assignment expression that should be
    looped over:

    >>> from sympy import Eq, IndexedBase, Idx
    >>> len_y = 5
    >>> y = IndexedBase('y', shape=(len_y,))
    >>> t = IndexedBase('t', shape=(len_y,))
    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
    >>> i = Idx('i', len_y-1)
    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
    >>> ccode(e.rhs, assign_to=e.lhs, contract=False, standard='C89')
    'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'

    Matrices are also supported, but a ``MatrixSymbol`` of the same dimensions
    must be provided to ``assign_to``. Note that any expression that can be
    generated normally can also exist inside a Matrix:

    >>> from sympy import Matrix, MatrixSymbol
    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
    >>> A = MatrixSymbol('A', 3, 1)
    >>> print(ccode(mat, A, standard='C89'))
    A[0] = pow(x, 2);
    if (x > 0) {
       A[1] = x + 1;
    }
    else {
       A[1] = x;
    }
    A[2] = sin(x);
    """
    from sympy.printing.c import c_code_printers
    return c_code_printers[standard.lower()](settings).doprint(expr, assign_to)

def print_ccode(expr, **settings):
    """Prints C representation of the given expression."""
    print(ccode(expr, **settings))

def fcode(expr, assign_to=None, **settings):
    """Converts an expr to a string of fortran code

    Parameters
    ==========

    expr : Expr
        A SymPy expression to be converted.
    assign_to : optional
        When given, the argument is used as the name of the variable to which
        the expression is assigned. Can be a string, ``Symbol``,
        ``MatrixSymbol``, or ``Indexed`` type. This is helpful in case of
        line-wrapping, or for expressions that generate multi-line statements.
    precision : integer, optional
        DEPRECATED. Use type_mappings instead. The precision for numbers such
        as pi [default=17].
    user_functions : dict, optional
        A dictionary where keys are ``FunctionClass`` instances and values are
        their string representations. Alternatively, the dictionary value can
        be a list of tuples i.e. [(argument_test, cfunction_string)]. See below
        for examples.
    human : bool, optional
        If True, the result is a single string that may contain some constant
        declarations for the number symbols. If False, the same information is
        returned in a tuple of (symbols_to_declare, not_supported_functions,
        code_text). [default=True].
    contract: bool, optional
        If True, ``Indexed`` instances are assumed to obey tensor contraction
        rules and the corresponding nested loops over indices are generated.
        Setting contract=False will not generate loops, instead the user is
        responsible to provide values for the indices in the code.
        [default=True].
    source_format : optional
        The source format can be either 'fixed' or 'free'. [default='fixed']
    standard : integer, optional
        The Fortran standard to be followed. This is specified as an integer.
        Acceptable standards are 66, 77, 90, 95, 2003, and 2008. Default is 77.
        Note that currently the only distinction internally is between
        standards before 95, and those 95 and after. This may change later as
        more features are added.
    name_mangling : bool, optional
        If True, then the variables that would become identical in
        case-insensitive Fortran are mangled by appending different number
        of ``_`` at the end. If False, SymPy Will not interfere with naming of
        variables. [default=True]

    Examples
    ========

    >>> from sympy import fcode, symbols, Rational, sin, ceiling, floor
    >>> x, tau = symbols("x, tau")
    >>> fcode((2*tau)**Rational(7, 2))
    '      8*sqrt(2.0d0)*tau**(7.0d0/2.0d0)'
    >>> fcode(sin(x), assign_to="s")
    '      s = sin(x)'

    Custom printing can be defined for certain types by passing a dictionary of
    "type" : "function" to the ``user_functions`` kwarg. Alternatively, the
    dictionary value can be a list of tuples i.e. [(argument_test,
    cfunction_string)].

    >>> custom_functions = {
    ...   "ceiling": "CEIL",
    ...   "floor": [(lambda x: not x.is_integer, "FLOOR1"),
    ...             (lambda x: x.is_integer, "FLOOR2")]
    ... }
    >>> fcode(floor(x) + ceiling(x), user_functions=custom_functions)
    '      CEIL(x) + FLOOR1(x)'

    ``Piecewise`` expressions are converted into conditionals. If an
    ``assign_to`` variable is provided an if statement is created, otherwise
    the ternary operator is used. Note that if the ``Piecewise`` lacks a
    default term, represented by ``(expr, True)`` then an error will be thrown.
    This is to prevent generating an expression that may not evaluate to
    anything.

    >>> from sympy import Piecewise
    >>> expr = Piecewise((x + 1, x > 0), (x, True))
    >>> print(fcode(expr, tau))
          if (x > 0) then
             tau = x + 1
          else
             tau = x
          end if

    Support for loops is provided through ``Indexed`` types. With
    ``contract=True`` these expressions will be turned into loops, whereas
    ``contract=False`` will just print the assignment expression that should be
    looped over:

    >>> from sympy import Eq, IndexedBase, Idx
    >>> len_y = 5
    >>> y = IndexedBase('y', shape=(len_y,))
    >>> t = IndexedBase('t', shape=(len_y,))
    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
    >>> i = Idx('i', len_y-1)
    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
    >>> fcode(e.rhs, assign_to=e.lhs, contract=False)
    '      Dy(i) = (y(i + 1) - y(i))/(t(i + 1) - t(i))'

    Matrices are also supported, but a ``MatrixSymbol`` of the same dimensions
    must be provided to ``assign_to``. Note that any expression that can be
    generated normally can also exist inside a Matrix:

    >>> from sympy import Matrix, MatrixSymbol
    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
    >>> A = MatrixSymbol('A', 3, 1)
    >>> print(fcode(mat, A))
          A(1, 1) = x**2
             if (x > 0) then
          A(2, 1) = x + 1
             else
          A(2, 1) = x
             end if
          A(3, 1) = sin(x)
    """
    from sympy.printing.fortran import FCodePrinter
    return FCodePrinter(settings).doprint(expr, assign_to)


def print_fcode(expr, **settings):
    """Prints the Fortran representation of the given expression.

       See fcode for the meaning of the optional arguments.
    """
    print(fcode(expr, **settings))

def cxxcode(expr, assign_to=None, standard='c++11', **settings):
    """ C++ equivalent of :func:`~.ccode`. """
    from sympy.printing.cxx import cxx_code_printers
    return cxx_code_printers[standard.lower()](settings).doprint(expr, assign_to)