Source code for sympy.codegen.ast

"""
Types used to represent a full function/module as an Abstract Syntax Tree.

Most types are small, and are merely used as tokens in the AST. A tree diagram
has been included below to illustrate the relationships between the AST types.


AST Type Tree
-------------
::

  *Basic*
       |--->AssignmentBase
       |             |--->Assignment
       |             |--->AugmentedAssignment
       |                                    |--->AddAugmentedAssignment
       |                                    |--->SubAugmentedAssignment
       |                                    |--->MulAugmentedAssignment
       |                                    |--->DivAugmentedAssignment
       |                                    |--->ModAugmentedAssignment
       |
       |--->CodeBlock
       |
       |
       |--->Token
       |        |--->Attribute
       |        |--->For
       |        |--->String
       |        |       |--->QuotedString
       |        |       |--->Comment
       |        |--->Type
       |        |       |--->IntBaseType
       |        |       |              |--->_SizedIntType
       |        |       |                               |--->SignedIntType
       |        |       |                               |--->UnsignedIntType
       |        |       |--->FloatBaseType
       |        |                        |--->FloatType
       |        |                        |--->ComplexBaseType
       |        |                                           |--->ComplexType
       |        |--->Node
       |        |       |--->Variable
       |        |       |           |---> Pointer
       |        |       |--->FunctionPrototype
       |        |                            |--->FunctionDefinition
       |        |--->Element
       |        |--->Declaration
       |        |--->While
       |        |--->Scope
       |        |--->Stream
       |        |--->Print
       |        |--->FunctionCall
       |        |--->BreakToken
       |        |--->ContinueToken
       |        |--->NoneToken
       |
       |--->Statement
       |--->Return


Predefined types
----------------
A number of ``Type`` instances are provided in the ``sympy.codegen.ast`` module
for convenience. Perhaps the two most common ones for code-generation (of numeric
codes) are ``float32`` and ``float64`` (known as single and double precision respectively).
There are also precision generic versions of Types (for which the codeprinters selects the
underlying data type at time of printing): ``real``, ``integer``, ``complex_``, ``bool_``.

The other ``Type`` instances defined are:

- ``intc``: Integer type used by C's "int".
- ``intp``: Integer type used by C's "unsigned".
- ``int8``, ``int16``, ``int32``, ``int64``: n-bit integers.
- ``uint8``, ``uint16``, ``uint32``, ``uint64``: n-bit unsigned integers.
- ``float80``: known as "extended precision" on modern x86/amd64 hardware.
- ``complex64``: Complex number represented by two ``float32`` numbers
- ``complex128``: Complex number represented by two ``float64`` numbers

Using the nodes
---------------
It is possible to construct simple algorithms using the AST nodes. Let's construct a loop applying
Newton's method::

    >>> from sympy import symbols, cos
    >>> from sympy.codegen.ast import While, Assignment, aug_assign, Print
    >>> t, dx, x = symbols('tol delta val')
    >>> expr = cos(x) - x**3
    >>> whl = While(abs(dx) > t, [
    ...     Assignment(dx, -expr/expr.diff(x)),
    ...     aug_assign(x, '+', dx),
    ...     Print([x])
    ... ])
    >>> from sympy.printing import pycode
    >>> py_str = pycode(whl)
    >>> print(py_str)
    while (abs(delta) > tol):
        delta = (val**3 - math.cos(val))/(-3*val**2 - math.sin(val))
        val += delta
        print(val)
    >>> import math
    >>> tol, val, delta = 1e-5, 0.5, float('inf')
    >>> exec(py_str)
    1.1121416371
    0.909672693737
    0.867263818209
    0.865477135298
    0.865474033111
    >>> print('%3.1g' % (math.cos(val) - val**3))
    -3e-11

If we want to generate Fortran code for the same while loop we simple call ``fcode``::

    >>> from sympy.printing.fcode import fcode
    >>> print(fcode(whl, standard=2003, source_format='free'))
    do while (abs(delta) > tol)
       delta = (val**3 - cos(val))/(-3*val**2 - sin(val))
       val = val + delta
       print *, val
    end do

There is a function constructing a loop (or a complete function) like this in
:mod:`sympy.codegen.algorithms`.

"""

from __future__ import print_function, division

from functools import total_ordering
from itertools import chain
from collections import defaultdict
from sympy.core import Symbol, Tuple, Dummy
from sympy.core.basic import Basic
from sympy.core.expr import Expr
from sympy.core.compatibility import string_types
from sympy.core.numbers import Float, Integer, oo
from sympy.core.relational import Lt, Le, Ge, Gt
from sympy.core.sympify import _sympify, sympify, SympifyError
from sympy.logic import true, false
from sympy.utilities.iterables import iterable


def _mk_Tuple(args):
    """
    Create a Sympy Tuple object from an iterable, converting Python strings to
    AST strings.

    Parameters
    ==========
    args: iterable
        Arguments to :class:`sympy.Tuple`.

    Returns
    =======
    sympy.Tuple
    """
    args = [String(arg) if isinstance(arg, string_types) else arg for arg in args]
    return Tuple(*args)


[docs]class Token(Basic): """ Base class for the AST types. Defining fields are set in ``__slots__``. Attributes (defined in __slots__) are only allowed to contain instances of Basic (unless atomic, see ``String``). The arguments to ``__new__()`` correspond to the attributes in the order defined in ``__slots__`. The ``defaults`` class attribute is a dictionary mapping attribute names to their default values. Subclasses should not need to override the ``__new__()`` method. They may define a class or static method named ``_construct_<attr>`` for each attribute to process the value passed to ``__new__()``. Attributes listed in the class attribute ``not_in_args`` are not passed to :class:`sympy.Basic`. """ __slots__ = [] defaults = {} not_in_args = [] indented_args = ['body'] @property def is_Atom(self): return len(self.__slots__) == 0 @classmethod def _get_constructor(cls, attr): """ Get the constructor function for an attribute by name. """ return getattr(cls, '_construct_%s' % attr, lambda x: x) @classmethod def _construct(cls, attr, arg): """ Construct an attribute value from argument passed to ``__new__()``. """ if arg == None: return cls.defaults.get(attr, none) else: if isinstance(arg, Dummy): # sympy's replace uses Dummy instances return arg else: return cls._get_constructor(attr)(arg) def __new__(cls, *args, **kwargs): # Pass through existing instances when given as sole argument if len(args) == 1 and not kwargs and isinstance(args[0], cls): return args[0] if len(args) > len(cls.__slots__): raise ValueError("Too many arguments (%d), expected at most %d" % (len(args), len(cls.__slots__))) attrvals = [] # Process positional arguments for attrname, argval in zip(cls.__slots__, args): if attrname in kwargs: raise TypeError('Got multiple values for attribute %r' % attrname) attrvals.append(cls._construct(attrname, argval)) # Process keyword arguments for attrname in cls.__slots__[len(args):]: if attrname in kwargs: argval = kwargs.pop(attrname) elif attrname in cls.defaults: argval = cls.defaults[attrname] else: raise TypeError('No value for %r given and attribute has no default' % attrname) attrvals.append(cls._construct(attrname, argval)) if kwargs: raise ValueError("Unknown keyword arguments: %s" % ' '.join(kwargs)) # Parent constructor basic_args = [ val for attr, val in zip(cls.__slots__, attrvals) if attr not in cls.not_in_args ] obj = Basic.__new__(cls, *basic_args) # Set attributes for attr, arg in zip(cls.__slots__, attrvals): setattr(obj, attr, arg) return obj def __eq__(self, other): if not isinstance(other, self.__class__): return False for attr in self.__slots__: if getattr(self, attr) != getattr(other, attr): return False return True def _hashable_content(self): return tuple([getattr(self, attr) for attr in self.__slots__]) def __hash__(self): return super(Token, self).__hash__() def _joiner(self, k, indent_level): return (',\n' + ' '*indent_level) if k in self.indented_args else ', ' def _indented(self, printer, k, v, *args, **kwargs): il = printer._context['indent_level'] def _print(arg): if isinstance(arg, Token): return printer._print(arg, *args, joiner=self._joiner(k, il), **kwargs) else: return printer._print(v, *args, **kwargs) if isinstance(v, Tuple): joined = self._joiner(k, il).join([_print(arg) for arg in v.args]) if k in self.indented_args: return '(\n' + ' '*il + joined + ',\n' + ' '*(il - 4) + ')' else: return ('({0},)' if len(v.args) == 1 else '({0})').format(joined) else: return _print(v) def _sympyrepr(self, printer, *args, **kwargs): from sympy.printing.printer import printer_context exclude = kwargs.get('exclude', ()) values = [getattr(self, k) for k in self.__slots__] indent_level = printer._context.get('indent_level', 0) joiner = kwargs.pop('joiner', ', ') arg_reprs = [] for i, (attr, value) in enumerate(zip(self.__slots__, values)): if attr in exclude: continue # Skip attributes which have the default value if attr in self.defaults and value == self.defaults[attr]: continue ilvl = indent_level + 4 if attr in self.indented_args else 0 with printer_context(printer, indent_level=ilvl): indented = self._indented(printer, attr, value, *args, **kwargs) arg_reprs.append(('{1}' if i == 0 else '{0}={1}').format(attr, indented.lstrip())) return "{0}({1})".format(self.__class__.__name__, joiner.join(arg_reprs)) _sympystr = _sympyrepr def __repr__(self): # sympy.core.Basic.__repr__ uses sstr from sympy.printing import srepr return srepr(self)
[docs] def kwargs(self, exclude=(), apply=None): """ Get instance's attributes as dict of keyword arguments. Parameters ========== exclude : collection of str Collection of keywords to exclude. apply : callable, optional Function to apply to all values. """ kwargs = {k: getattr(self, k) for k in self.__slots__ if k not in exclude} if apply is not None: return {k: apply(v) for k, v in kwargs.items()} else: return kwargs
[docs]class BreakToken(Token): """ Represents 'break' in C/Python ('exit' in Fortran). Use the premade instance ``break_`` or instantiate manually. Examples ======== >>> from sympy.printing import ccode, fcode >>> from sympy.codegen.ast import break_ >>> ccode(break_) 'break' >>> fcode(break_, source_format='free') 'exit' """
break_ = BreakToken()
[docs]class ContinueToken(Token): """ Represents 'continue' in C/Python ('cycle' in Fortran) Use the premade instance ``continue_`` or instantiate manually. Examples ======== >>> from sympy.printing import ccode, fcode >>> from sympy.codegen.ast import continue_ >>> ccode(continue_) 'continue' >>> fcode(continue_, source_format='free') 'cycle' """
continue_ = ContinueToken()
[docs]class NoneToken(Token): """ The AST equivalence of Python's NoneType The corresponding instance of Python's ``None`` is ``none``. Examples ======== >>> from sympy.codegen.ast import none, Variable >>> from sympy.printing.pycode import pycode >>> print(pycode(Variable('x').as_Declaration(value=none))) x = None """ def __eq__(self, other): return other is None or isinstance(other, NoneToken) def _hashable_content(self): return () def __hash__(self): return super(Token, self).__hash__()
none = NoneToken()
[docs]class AssignmentBase(Basic): """ Abstract base class for Assignment and AugmentedAssignment. Attributes: =========== op : str Symbol for assignment operator, e.g. "=", "+=", etc. """ def __new__(cls, lhs, rhs): lhs = _sympify(lhs) rhs = _sympify(rhs) cls._check_args(lhs, rhs) return super(AssignmentBase, cls).__new__(cls, lhs, rhs) @property def lhs(self): return self.args[0] @property def rhs(self): return self.args[1] @classmethod def _check_args(cls, lhs, rhs): """ Check arguments to __new__ and raise exception if any problems found. Derived classes may wish to override this. """ from sympy.matrices.expressions.matexpr import ( MatrixElement, MatrixSymbol) from sympy.tensor.indexed import Indexed # Tuple of things that can be on the lhs of an assignment assignable = (Symbol, MatrixSymbol, MatrixElement, Indexed, Element, Variable) if not isinstance(lhs, assignable): raise TypeError("Cannot assign to lhs of type %s." % type(lhs)) # Indexed types implement shape, but don't define it until later. This # causes issues in assignment validation. For now, matrices are defined # as anything with a shape that is not an Indexed lhs_is_mat = hasattr(lhs, 'shape') and not isinstance(lhs, Indexed) rhs_is_mat = hasattr(rhs, 'shape') and not isinstance(rhs, Indexed) # If lhs and rhs have same structure, then this assignment is ok if lhs_is_mat: if not rhs_is_mat: raise ValueError("Cannot assign a scalar to a matrix.") elif lhs.shape != rhs.shape: raise ValueError("Dimensions of lhs and rhs don't align.") elif rhs_is_mat and not lhs_is_mat: raise ValueError("Cannot assign a matrix to a scalar.")
[docs]class Assignment(AssignmentBase): """ Represents variable assignment for code generation. Parameters ========== lhs : Expr Sympy object representing the lhs of the expression. These should be singular objects, such as one would use in writing code. Notable types include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that subclass these types are also supported. rhs : Expr Sympy object representing the rhs of the expression. This can be any type, provided its shape corresponds to that of the lhs. For example, a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as the dimensions will not align. Examples ======== >>> from sympy import symbols, MatrixSymbol, Matrix >>> from sympy.codegen.ast import Assignment >>> x, y, z = symbols('x, y, z') >>> Assignment(x, y) Assignment(x, y) >>> Assignment(x, 0) Assignment(x, 0) >>> A = MatrixSymbol('A', 1, 3) >>> mat = Matrix([x, y, z]).T >>> Assignment(A, mat) Assignment(A, Matrix([[x, y, z]])) >>> Assignment(A[0, 1], x) Assignment(A[0, 1], x) """ op = ':='
[docs]class AugmentedAssignment(AssignmentBase): """ Base class for augmented assignments. Attributes: =========== binop : str Symbol for binary operation being applied in the assignment, such as "+", "*", etc. """ @property def op(self): return self.binop + '='
class AddAugmentedAssignment(AugmentedAssignment): binop = '+' class SubAugmentedAssignment(AugmentedAssignment): binop = '-' class MulAugmentedAssignment(AugmentedAssignment): binop = '*' class DivAugmentedAssignment(AugmentedAssignment): binop = '/' class ModAugmentedAssignment(AugmentedAssignment): binop = '%' # Mapping from binary op strings to AugmentedAssignment subclasses augassign_classes = { cls.binop: cls for cls in [ AddAugmentedAssignment, SubAugmentedAssignment, MulAugmentedAssignment, DivAugmentedAssignment, ModAugmentedAssignment ] }
[docs]def aug_assign(lhs, op, rhs): """ Create 'lhs op= rhs'. Represents augmented variable assignment for code generation. This is a convenience function. You can also use the AugmentedAssignment classes directly, like AddAugmentedAssignment(x, y). Parameters ========== lhs : Expr Sympy object representing the lhs of the expression. These should be singular objects, such as one would use in writing code. Notable types include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that subclass these types are also supported. op : str Operator (+, -, /, \\*, %). rhs : Expr Sympy object representing the rhs of the expression. This can be any type, provided its shape corresponds to that of the lhs. For example, a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as the dimensions will not align. Examples ======== >>> from sympy import symbols >>> from sympy.codegen.ast import aug_assign >>> x, y = symbols('x, y') >>> aug_assign(x, '+', y) AddAugmentedAssignment(x, y) """ if op not in augassign_classes: raise ValueError("Unrecognized operator %s" % op) return augassign_classes[op](lhs, rhs)
[docs]class CodeBlock(Basic): """ Represents a block of code For now only assignments are supported. This restriction will be lifted in the future. Useful attributes on this object are: ``left_hand_sides``: Tuple of left-hand sides of assignments, in order. ``left_hand_sides``: Tuple of right-hand sides of assignments, in order. ``free_symbols``: Free symbols of the expressions in the right-hand sides which do not appear in the left-hand side of an assignment. Useful methods on this object are: ``topological_sort``: Class method. Return a CodeBlock with assignments sorted so that variables are assigned before they are used. ``cse``: Return a new CodeBlock with common subexpressions eliminated and pulled out as assignments. Example ======= >>> from sympy import symbols, ccode >>> from sympy.codegen.ast import CodeBlock, Assignment >>> x, y = symbols('x y') >>> c = CodeBlock(Assignment(x, 1), Assignment(y, x + 1)) >>> print(ccode(c)) x = 1; y = x + 1; """ def __new__(cls, *args): left_hand_sides = [] right_hand_sides = [] for i in args: if isinstance(i, Assignment): lhs, rhs = i.args left_hand_sides.append(lhs) right_hand_sides.append(rhs) obj = Basic.__new__(cls, *args) obj.left_hand_sides = Tuple(*left_hand_sides) obj.right_hand_sides = Tuple(*right_hand_sides) return obj def __iter__(self): return iter(self.args) def _sympyrepr(self, printer, *args, **kwargs): from sympy.printing.printer import printer_context il = printer._context.get('indent_level', 0) joiner = ',\n' + ' '*il joined = joiner.join(map(printer._print, self.args)) return ('{0}(\n'.format(' '*(il-4) + self.__class__.__name__,) + ' '*il + joined + '\n' + ' '*(il - 4) + ')') _sympystr = _sympyrepr @property def free_symbols(self): return super(CodeBlock, self).free_symbols - set(self.left_hand_sides)
[docs] @classmethod def topological_sort(cls, assignments): """ Return a CodeBlock with topologically sorted assignments so that variables are assigned before they are used. The existing order of assignments is preserved as much as possible. This function assumes that variables are assigned to only once. This is a class constructor so that the default constructor for CodeBlock can error when variables are used before they are assigned. Example ======= >>> from sympy import symbols >>> from sympy.codegen.ast import CodeBlock, Assignment >>> x, y, z = symbols('x y z') >>> assignments = [ ... Assignment(x, y + z), ... Assignment(y, z + 1), ... Assignment(z, 2), ... ] >>> CodeBlock.topological_sort(assignments) CodeBlock( Assignment(z, 2), Assignment(y, z + 1), Assignment(x, y + z) ) """ from sympy.utilities.iterables import topological_sort if not all(isinstance(i, Assignment) for i in assignments): # Will support more things later raise NotImplementedError("CodeBlock.topological_sort only supports Assignments") if any(isinstance(i, AugmentedAssignment) for i in assignments): raise NotImplementedError("CodeBlock.topological_sort doesn't yet work with AugmentedAssignments") # Create a graph where the nodes are assignments and there is a directed edge # between nodes that use a variable and nodes that assign that # variable, like # [(x := 1, y := x + 1), (x := 1, z := y + z), (y := x + 1, z := y + z)] # If we then topologically sort these nodes, they will be in # assignment order, like # x := 1 # y := x + 1 # z := y + z # A = The nodes # # enumerate keeps nodes in the same order they are already in if # possible. It will also allow us to handle duplicate assignments to # the same variable when those are implemented. A = list(enumerate(assignments)) # var_map = {variable: [nodes for which this variable is assigned to]} # like {x: [(1, x := y + z), (4, x := 2 * w)], ...} var_map = defaultdict(list) for node in A: i, a = node var_map[a.lhs].append(node) # E = Edges in the graph E = [] for dst_node in A: i, a = dst_node for s in a.rhs.free_symbols: for src_node in var_map[s]: E.append((src_node, dst_node)) ordered_assignments = topological_sort([A, E]) # De-enumerate the result return cls(*[a for i, a in ordered_assignments])
[docs] def cse(self, symbols=None, optimizations=None, postprocess=None, order='canonical'): """ Return a new code block with common subexpressions eliminated See the docstring of :func:`sympy.simplify.cse_main.cse` for more information. Examples ======== >>> from sympy import symbols, sin >>> from sympy.codegen.ast import CodeBlock, Assignment >>> x, y, z = symbols('x y z') >>> c = CodeBlock( ... Assignment(x, 1), ... Assignment(y, sin(x) + 1), ... Assignment(z, sin(x) - 1), ... ) ... >>> c.cse() CodeBlock( Assignment(x, 1), Assignment(x0, sin(x)), Assignment(y, x0 + 1), Assignment(z, x0 - 1) ) """ from sympy.simplify.cse_main import cse from sympy.utilities.iterables import numbered_symbols, filter_symbols # Check that the CodeBlock only contains assignments to unique variables if not all(isinstance(i, Assignment) for i in self.args): # Will support more things later raise NotImplementedError("CodeBlock.cse only supports Assignments") if any(isinstance(i, AugmentedAssignment) for i in self.args): raise NotImplementedError("CodeBlock.cse doesn't yet work with AugmentedAssignments") for i, lhs in enumerate(self.left_hand_sides): if lhs in self.left_hand_sides[:i]: raise NotImplementedError("Duplicate assignments to the same " "variable are not yet supported (%s)" % lhs) # Ensure new symbols for subexpressions do not conflict with existing existing_symbols = self.atoms(Symbol) if symbols is None: symbols = numbered_symbols() symbols = filter_symbols(symbols, existing_symbols) replacements, reduced_exprs = cse(list(self.right_hand_sides), symbols=symbols, optimizations=optimizations, postprocess=postprocess, order=order) new_block = [Assignment(var, expr) for var, expr in zip(self.left_hand_sides, reduced_exprs)] new_assignments = [Assignment(var, expr) for var, expr in replacements] return self.topological_sort(new_assignments + new_block)
[docs]class For(Token): """Represents a 'for-loop' in the code. Expressions are of the form: "for target in iter: body..." Parameters ========== target : symbol iter : iterable body : CodeBlock or iterable ! When passed an iterable it is used to instantiate a CodeBlock. Examples ======== >>> from sympy import symbols, Range >>> from sympy.codegen.ast import aug_assign, For >>> x, i, j, k = symbols('x i j k') >>> for_i = For(i, Range(10), [aug_assign(x, '+', i*j*k)]) >>> for_i # doctest: -NORMALIZE_WHITESPACE For(i, iterable=Range(0, 10, 1), body=CodeBlock( AddAugmentedAssignment(x, i*j*k) )) >>> for_ji = For(j, Range(7), [for_i]) >>> for_ji # doctest: -NORMALIZE_WHITESPACE For(j, iterable=Range(0, 7, 1), body=CodeBlock( For(i, iterable=Range(0, 10, 1), body=CodeBlock( AddAugmentedAssignment(x, i*j*k) )) )) >>> for_kji =For(k, Range(5), [for_ji]) >>> for_kji # doctest: -NORMALIZE_WHITESPACE For(k, iterable=Range(0, 5, 1), body=CodeBlock( For(j, iterable=Range(0, 7, 1), body=CodeBlock( For(i, iterable=Range(0, 10, 1), body=CodeBlock( AddAugmentedAssignment(x, i*j*k) )) )) )) """ __slots__ = ['target', 'iterable', 'body'] _construct_target = staticmethod(_sympify) @classmethod def _construct_body(cls, itr): if isinstance(itr, CodeBlock): return itr else: return CodeBlock(*itr) @classmethod def _construct_iterable(cls, itr): if not iterable(itr): raise TypeError("iterable must be an iterable") if isinstance(itr, list): # _sympify errors on lists because they are mutable itr = tuple(itr) return _sympify(itr)
[docs]class String(Token): """ SymPy object representing a string. Atomic object which is not an expression (as opposed to Symbol). Parameters ========== text : str Examples ======== >>> from sympy.codegen.ast import String >>> f = String('foo') >>> f foo >>> str(f) 'foo' >>> f.text 'foo' >>> print(repr(f)) String('foo') """ __slots__ = ['text'] not_in_args = ['text'] is_Atom = True @classmethod def _construct_text(cls, text): if not isinstance(text, string_types): raise TypeError("Argument text is not a string type.") return text def _sympystr(self, printer, *args, **kwargs): return self.text
[docs]class QuotedString(String): """ Represents a string which should be printed with quotes. """
[docs]class Comment(String): """ Represents a comment. """
[docs]class Node(Token): """ Subclass of Token, carrying the attribute 'attrs' (Tuple) Examples ======== >>> from sympy.codegen.ast import Node, value_const, pointer_const >>> n1 = Node([value_const]) >>> n1.attr_params('value_const') # get the parameters of attribute (by name) () >>> from sympy.codegen.fnodes import dimension >>> n2 = Node([value_const, dimension(5, 3)]) >>> n2.attr_params(value_const) # get the parameters of attribute (by Attribute instance) () >>> n2.attr_params('dimension') # get the parameters of attribute (by name) (5, 3) >>> n2.attr_params(pointer_const) is None True """ __slots__ = ['attrs'] defaults = {'attrs': Tuple()} _construct_attrs = staticmethod(_mk_Tuple)
[docs] def attr_params(self, looking_for): """ Returns the parameters of the Attribute with name ``looking_for`` in self.attrs """ for attr in self.attrs: if str(attr.name) == str(looking_for): return attr.parameters
[docs]class Type(Token): """ Represents a type. The naming is a super-set of NumPy naming. Type has a classmethod ``from_expr`` which offer type deduction. It also has a method ``cast_check`` which casts the argument to its type, possibly raising an exception if rounding error is not within tolerances, or if the value is not representable by the underlying data type (e.g. unsigned integers). Parameters ========== name : str Name of the type, e.g. ``object``, ``int16``, ``float16`` (where the latter two would use the ``Type`` sub-classes ``IntType`` and ``FloatType`` respectively). If a ``Type`` instance is given, the said instance is returned. Examples ======== >>> from sympy.codegen.ast import Type >>> t = Type.from_expr(42) >>> t integer >>> print(repr(t)) IntBaseType(String('integer')) >>> from sympy.codegen.ast import uint8 >>> uint8.cast_check(-1) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Minimum value for data type bigger than new value. >>> from sympy.codegen.ast import float32 >>> v6 = 0.123456 >>> float32.cast_check(v6) 0.123456 >>> v10 = 12345.67894 >>> float32.cast_check(v10) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Casting gives a significantly different value. >>> boost_mp50 = Type('boost::multiprecision::cpp_dec_float_50') >>> from sympy import Symbol >>> from sympy.printing.cxxcode import cxxcode >>> from sympy.codegen.ast import Declaration, Variable >>> cxxcode(Declaration(Variable('x', type=boost_mp50))) 'boost::multiprecision::cpp_dec_float_50 x' References ========== .. [1] https://docs.scipy.org/doc/numpy/user/basics.types.html """ __slots__ = ['name'] _construct_name = String def _sympystr(self, printer, *args, **kwargs): return str(self.name)
[docs] @classmethod def from_expr(cls, expr): """ Deduces type from an expression or a ``Symbol``. Parameters ========== expr : number or SymPy object The type will be deduced from type or properties. Examples ======== >>> from sympy.codegen.ast import Type, integer, complex_ >>> Type.from_expr(2) == integer True >>> from sympy import Symbol >>> Type.from_expr(Symbol('z', complex=True)) == complex_ True >>> Type.from_expr(sum) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Could not deduce type from expr. Raises ====== ValueError when type deduction fails. """ if isinstance(expr, (float, Float)): return real if isinstance(expr, (int, Integer)) or getattr(expr, 'is_integer', False): return integer if getattr(expr, 'is_real', False): return real if isinstance(expr, complex) or getattr(expr, 'is_complex', False): return complex_ if isinstance(expr, bool) or getattr(expr, 'is_Relational', False): return bool_ else: raise ValueError("Could not deduce type from expr.")
def _check(self, value): pass
[docs] def cast_check(self, value, rtol=None, atol=0, limits=None, precision_targets=None): """ Casts a value to the data type of the instance. Parameters ========== value : number rtol : floating point number Relative tolerance. (will be deduced if not given). atol : floating point number Absolute tolerance (in addition to ``rtol``). limits : dict Values given by ``limits.h``, x86/IEEE754 defaults if not given. Default: :attr:`default_limits`. type_aliases : dict Maps substitutions for Type, e.g. {integer: int64, real: float32} Examples ======== >>> from sympy.codegen.ast import Type, integer, float32, int8 >>> integer.cast_check(3.0) == 3 True >>> float32.cast_check(1e-40) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Minimum value for data type bigger than new value. >>> int8.cast_check(256) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Maximum value for data type smaller than new value. >>> v10 = 12345.67894 >>> float32.cast_check(v10) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Casting gives a significantly different value. >>> from sympy.codegen.ast import float64 >>> float64.cast_check(v10) 12345.67894 >>> from sympy import Float >>> v18 = Float('0.123456789012345646') >>> float64.cast_check(v18) Traceback (most recent call last): ... ValueError: Casting gives a significantly different value. >>> from sympy.codegen.ast import float80 >>> float80.cast_check(v18) 0.123456789012345649 """ from sympy.functions.elementary.complexes import im, re val = sympify(value) ten = Integer(10) exp10 = getattr(self, 'decimal_dig', None) if rtol is None: rtol = 1e-15 if exp10 is None else 2.0*ten**(-exp10) def tol(num): return atol + rtol*abs(num) new_val = self.cast_nocheck(value) self._check(new_val) delta = new_val - val if abs(delta) > tol(val): # rounding, e.g. int(3.5) != 3.5 raise ValueError("Casting gives a significantly different value.") return new_val
[docs]class IntBaseType(Type): """ Integer base type, contains no size information. """ __slots__ = ['name'] cast_nocheck = lambda self, i: Integer(int(i))
class _SizedIntType(IntBaseType): __slots__ = ['name', 'nbits'] _construct_nbits = Integer def _check(self, value): if value < self.min: raise ValueError("Value is too small: %d < %d" % (value, self.min)) if value > self.max: raise ValueError("Value is too big: %d > %d" % (value, self.max))
[docs]class SignedIntType(_SizedIntType): """ Represents a signed integer type. """ @property def min(self): return -2**(self.nbits-1) @property def max(self): return 2**(self.nbits-1) - 1
[docs]class UnsignedIntType(_SizedIntType): """ Represents an unsigned integer type. """ @property def min(self): return 0 @property def max(self): return 2**self.nbits - 1
two = Integer(2)
[docs]class FloatBaseType(Type): """ Represents a floating point number type. """ cast_nocheck = Float
[docs]class FloatType(FloatBaseType): """ Represents a floating point type with fixed bit width. Base 2 & one sign bit is assumed. Parameters ========== name : str Name of the type. nbits : integer Number of bits used (storage). nmant : integer Number of bits used to represent the mantissa. nexp : integer Number of bits used to represent the mantissa. Examples ======== >>> from sympy import S, Float >>> from sympy.codegen.ast import FloatType >>> half_precision = FloatType('f16', nbits=16, nmant=10, nexp=5) >>> half_precision.max 65504 >>> half_precision.tiny == S(2)**-14 True >>> half_precision.eps == S(2)**-10 True >>> half_precision.dig == 3 True >>> half_precision.decimal_dig == 5 True >>> half_precision.cast_check(1.0) 1.0 >>> half_precision.cast_check(1e5) # doctest: +ELLIPSIS Traceback (most recent call last): ... ValueError: Maximum value for data type smaller than new value. """ __slots__ = ['name', 'nbits', 'nmant', 'nexp'] _construct_nbits = _construct_nmant = _construct_nexp = Integer @property def max_exponent(self): """ The largest positive number n, such that 2**(n - 1) is a representable finite value. """ # cf. C++'s ``std::numeric_limits::max_exponent`` return two**(self.nexp - 1) @property def min_exponent(self): """ The lowest negative number n, such that 2**(n - 1) is a valid normalized number. """ # cf. C++'s ``std::numeric_limits::min_exponent`` return 3 - self.max_exponent @property def max(self): """ Maximum value representable. """ return (1 - two**-(self.nmant+1))*two**self.max_exponent @property def tiny(self): """ The minimum positive normalized value. """ # See C macros: FLT_MIN, DBL_MIN, LDBL_MIN # or C++'s ``std::numeric_limits::min`` # or numpy.finfo(dtype).tiny return two**(self.min_exponent - 1) @property def eps(self): """ Difference between 1.0 and the next representable value. """ return two**(-self.nmant) @property def dig(self): """ Number of decimal digits that are guaranteed to be preserved in text. When converting text -> float -> text, you are guaranteed that at least ``dig`` number of digits are preserved with respect to rounding or overflow. """ from sympy.functions import floor, log return floor(self.nmant * log(2)/log(10)) @property def decimal_dig(self): """ Number of digits needed to store & load without loss. Number of decimal digits needed to guarantee that two consecutive conversions (float -> text -> float) to be idempotent. This is useful when one do not want to loose precision due to rounding errors when storing a floating point value as text. """ from sympy.functions import ceiling, log return ceiling((self.nmant + 1) * log(2)/log(10) + 1)
[docs] def cast_nocheck(self, value): """ Casts without checking if out of bounds or subnormal. """ return Float(str(sympify(value).evalf(self.decimal_dig)), self.decimal_dig)
def _check(self, value): if value < -self.max: raise ValueError("Value is too small: %d < %d" % (value, -self.max)) if value > self.max: raise ValueError("Value is too big: %d > %d" % (value, self.max)) if abs(value) < self.tiny: raise ValueError("Smallest (absolute) value for data type bigger than new value.")
class ComplexBaseType(FloatBaseType): def cast_nocheck(self, value): """ Casts without checking if out of bounds or subnormal. """ from sympy.functions import re, im return ( super(ComplexBaseType, self).cast_nocheck(re(value)) + super(ComplexBaseType, self).cast_nocheck(im(value))*1j ) def _check(self, value): from sympy.functions import re, im super(ComplexBaseType, self)._check(re(value)) super(ComplexBaseType, self)._check(im(value))
[docs]class ComplexType(ComplexBaseType, FloatType): """ Represents a complex floating point number. """
# NumPy types: intc = IntBaseType('intc') intp = IntBaseType('intp') int8 = SignedIntType('int8', 8) int16 = SignedIntType('int16', 16) int32 = SignedIntType('int32', 32) int64 = SignedIntType('int64', 64) uint8 = UnsignedIntType('uint8', 8) uint16 = UnsignedIntType('uint16', 16) uint32 = UnsignedIntType('uint32', 32) uint64 = UnsignedIntType('uint64', 64) float16 = FloatType('float16', 16, nexp=5, nmant=10) # IEEE 754 binary16, Half precision float32 = FloatType('float32', 32, nexp=8, nmant=23) # IEEE 754 binary32, Single precision float64 = FloatType('float64', 64, nexp=11, nmant=52) # IEEE 754 binary64, Double precision float80 = FloatType('float80', 80, nexp=15, nmant=63) # x86 extended precision (1 integer part bit), "long double" float128 = FloatType('float128', 128, nexp=15, nmant=112) # IEEE 754 binary128, Quadruple precision float256 = FloatType('float256', 256, nexp=19, nmant=236) # IEEE 754 binary256, Octuple precision complex64 = ComplexType('complex64', nbits=64, **float32.kwargs(exclude=('name', 'nbits'))) complex128 = ComplexType('complex128', nbits=128, **float64.kwargs(exclude=('name', 'nbits'))) # Generic types (precision may be chosen by code printers): untyped = Type('untyped') real = FloatBaseType('real') integer = IntBaseType('integer') complex_ = ComplexBaseType('complex') bool_ = Type('bool')
[docs]class Attribute(Token): """ Attribute (possibly parametrized) For use with :class:`sympy.codegen.ast.Node` (which takes instances of ``Attribute`` as ``attrs``). Parameters ========== name : str parameters : Tuple Examples ======== >>> from sympy.codegen.ast import Attribute >>> volatile = Attribute('volatile') >>> volatile volatile >>> print(repr(volatile)) Attribute(String('volatile')) >>> a = Attribute('foo', [1, 2, 3]) >>> a foo(1, 2, 3) >>> a.parameters == (1, 2, 3) True """ __slots__ = ['name', 'parameters'] defaults = {'parameters': Tuple()} _construct_name = String _construct_parameters = staticmethod(_mk_Tuple) def _sympystr(self, printer, *args, **kwargs): result = str(self.name) if self.parameters: result += '(%s)' % ', '.join(map(lambda arg: printer._print( arg, *args, **kwargs), self.parameters)) return result
value_const = Attribute('value_const') pointer_const = Attribute('pointer_const')
[docs]class Variable(Node): """ Represents a variable Parameters ========== symbol : Symbol type : Type (optional) Type of the variable. attrs : iterable of Attribute instances Will be stored as a Tuple. Examples ======== >>> from sympy import Symbol >>> from sympy.codegen.ast import Variable, float32, integer >>> x = Symbol('x') >>> v = Variable(x, type=float32) >>> v.attrs () >>> v == Variable('x') False >>> v == Variable('x', type=float32) True >>> v Variable(x, type=float32) One may also construct a ``Variable`` instance with the type deduced from assumptions about the symbol using the ``deduced`` classmethod: >>> i = Symbol('i', integer=True) >>> v = Variable.deduced(i) >>> v.type == integer True >>> v == Variable('i') False >>> from sympy.codegen.ast import value_const >>> value_const in v.attrs False >>> w = Variable('w', attrs=[value_const]) >>> w Variable(w, attrs=(value_const,)) >>> value_const in w.attrs True >>> w.as_Declaration(value=42) Declaration(Variable(w, value=42, attrs=(value_const,))) """ __slots__ = ['symbol', 'type', 'value'] + Node.__slots__ defaults = dict(chain(Node.defaults.items(), { 'type': untyped, 'value': none }.items())) _construct_symbol = staticmethod(sympify) _construct_value = staticmethod(sympify)
[docs] @classmethod def deduced(cls, symbol, value=None, attrs=Tuple(), cast_check=True): """ Alt. constructor with type deduction from ``Type.from_expr``. Deduces type primarily from ``symbol``, secondarily from ``value``. Parameters ========== symbol : Symbol value : expr (optional) value of the variable. attrs : iterable of Attribute instances cast_check : bool Whether to apply ``Type.cast_check`` on ``value``. Examples ======== >>> from sympy import Symbol >>> from sympy.codegen.ast import Variable, complex_ >>> n = Symbol('n', integer=True) >>> str(Variable.deduced(n).type) 'integer' >>> x = Symbol('x', real=True) >>> v = Variable.deduced(x) >>> v.type real >>> z = Symbol('z', complex=True) >>> Variable.deduced(z).type == complex_ True """ if isinstance(symbol, Variable): return symbol try: type_ = Type.from_expr(symbol) except ValueError: type_ = Type.from_expr(value) if value is not None and cast_check: value = type_.cast_check(value) return cls(symbol, type=type_, value=value, attrs=attrs)
[docs] def as_Declaration(self, **kwargs): """ Convenience method for creating a Declaration instance. If the variable of the Declaration need to wrap a modified variable keyword arguments may be passed (overriding e.g. the ``value`` of the Variable instance). Examples ======== >>> from sympy.codegen.ast import Variable >>> x = Variable('x') >>> decl1 = x.as_Declaration() >>> decl1.variable.value == None True >>> decl2 = x.as_Declaration(value=42.0) >>> decl2.variable.value == 42 True """ kw = self.kwargs() kw.update(kwargs) return Declaration(self.func(**kw))
def _relation(self, rhs, op): try: rhs = _sympify(rhs) except SympifyError: raise TypeError("Invalid comparison %s < %s" % (self, rhs)) return op(self, rhs, evaluate=False) __lt__ = lambda self, other: self._relation(other, Lt) __le__ = lambda self, other: self._relation(other, Le) __ge__ = lambda self, other: self._relation(other, Ge) __gt__ = lambda self, other: self._relation(other, Gt)
[docs]class Pointer(Variable): """ Represents a pointer. See ``Variable``. Examples ======== Can create instances of ``Element``: >>> from sympy import Symbol >>> from sympy.codegen.ast import Pointer >>> i = Symbol('i', integer=True) >>> p = Pointer('x') >>> p[i+1] Element(x, indices=((i + 1,),)) """ def __getitem__(self, key): try: return Element(self.symbol, key) except TypeError: return Element(self.symbol, (key,))
[docs]class Element(Token): """ Element in (a possibly N-dimensional) array. Examples ======== >>> from sympy.codegen.ast import Element >>> elem = Element('x', 'ijk') >>> elem.symbol.name == 'x' True >>> elem.indices (i, j, k) >>> from sympy import ccode >>> ccode(elem) 'x[i][j][k]' >>> ccode(Element('x', 'ijk', strides='lmn', offset='o')) 'x[i*l + j*m + k*n + o]' """ __slots__ = ['symbol', 'indices', 'strides', 'offset'] defaults = {'strides': none, 'offset': none} _construct_symbol = staticmethod(sympify) _construct_indices = staticmethod(lambda arg: Tuple(*arg)) _construct_strides = staticmethod(lambda arg: Tuple(*arg)) _construct_offset = staticmethod(sympify)
[docs]class Declaration(Token): """ Represents a variable declaration Parameters ========== variable : Variable Examples ======== >>> from sympy import Symbol >>> from sympy.codegen.ast import Declaration, Type, Variable, integer, untyped >>> z = Declaration('z') >>> z.variable.type == untyped True >>> z.variable.value == None True """ __slots__ = ['variable'] _construct_variable = Variable
[docs]class While(Token): """ Represents a 'for-loop' in the code. Expressions are of the form: "while condition: body..." Parameters ========== condition : expression convertable to Boolean body : CodeBlock or iterable When passed an iterable it is used to instantiate a CodeBlock. Examples ======== >>> from sympy import symbols, Gt, Abs >>> from sympy.codegen import aug_assign, Assignment, While >>> x, dx = symbols('x dx') >>> expr = 1 - x**2 >>> whl = While(Gt(Abs(dx), 1e-9), [ ... Assignment(dx, -expr/expr.diff(x)), ... aug_assign(x, '+', dx) ... ]) """ __slots__ = ['condition', 'body'] _construct_condition = staticmethod(lambda cond: _sympify(cond)) @classmethod def _construct_body(cls, itr): if isinstance(itr, CodeBlock): return itr else: return CodeBlock(*itr)
[docs]class Scope(Token): """ Represents a scope in the code. Parameters ========== body : CodeBlock or iterable When passed an iterable it is used to instantiate a CodeBlock. """ __slots__ = ['body'] @classmethod def _construct_body(cls, itr): if isinstance(itr, CodeBlock): return itr else: return CodeBlock(*itr)
[docs]class Stream(Token): """ Represents a stream. There are two predefined Stream instances ``stdout`` & ``stderr``. Parameters ========== name : str Examples ======== >>> from sympy import Symbol >>> from sympy.printing.pycode import pycode >>> from sympy.codegen.ast import Print, stderr, QuotedString >>> print(pycode(Print(['x'], file=stderr))) print(x, file=sys.stderr) >>> x = Symbol('x') >>> print(pycode(Print([QuotedString('x')], file=stderr))) # print literally "x" print("x", file=sys.stderr) """ __slots__ = ['name'] _construct_name = String
stdout = Stream('stdout') stderr = Stream('stderr')
[docs]class Print(Token): """ Represents print command in the code. Parameters ========== formatstring : str *args : Basic instances (or convertible to such through sympify) Examples ======== >>> from sympy.codegen.ast import Print >>> from sympy.printing.pycode import pycode >>> print(pycode(Print('x y'.split(), "coordinate: %12.5g %12.5g"))) print("coordinate: %12.5g %12.5g" % (x, y)) """ __slots__ = ['print_args', 'format_string', 'file'] defaults = {'format_string': none, 'file': none} _construct_print_args = staticmethod(_mk_Tuple) _construct_format_string = QuotedString _construct_file = Stream
[docs]class FunctionPrototype(Node): """ Represents a function prototype Allows the user to generate forward declaration in e.g. C/C++. Parameters ========== return_type : Type name : str parameters: iterable of Variable instances attrs : iterable of Attribute instances Examples ======== >>> from sympy import symbols >>> from sympy.codegen.ast import real, FunctionPrototype >>> from sympy.printing.ccode import ccode >>> x, y = symbols('x y', real=True) >>> fp = FunctionPrototype(real, 'foo', [x, y]) >>> ccode(fp) 'double foo(double x, double y)' """ __slots__ = ['return_type', 'name', 'parameters', 'attrs'] _construct_return_type = Type _construct_name = String @staticmethod def _construct_parameters(args): def _var(arg): if isinstance(arg, Declaration): return arg.variable elif isinstance(arg, Variable): return arg else: return Variable.deduced(arg) return Tuple(*map(_var, args)) @classmethod def from_FunctionDefinition(cls, func_def): if not isinstance(func_def, FunctionDefinition): raise TypeError("func_def is not an instance of FunctionDefiniton") return cls(**func_def.kwargs(exclude=('body',)))
[docs]class FunctionDefinition(FunctionPrototype): """ Represents a function definition in the code. Parameters ========== return_type : Type name : str parameters: iterable of Variable instances body : CodeBlock or iterable attrs : iterable of Attribute instances Examples ======== >>> from sympy import symbols >>> from sympy.codegen.ast import real, FunctionPrototype >>> from sympy.printing.ccode import ccode >>> x, y = symbols('x y', real=True) >>> fp = FunctionPrototype(real, 'foo', [x, y]) >>> ccode(fp) 'double foo(double x, double y)' >>> from sympy.codegen.ast import FunctionDefinition, Return >>> body = [Return(x*y)] >>> fd = FunctionDefinition.from_FunctionPrototype(fp, body) >>> print(ccode(fd)) double foo(double x, double y){ return x*y; } """ __slots__ = FunctionPrototype.__slots__[:-1] + ['body', 'attrs'] @classmethod def _construct_body(cls, itr): if isinstance(itr, CodeBlock): return itr else: return CodeBlock(*itr) @classmethod def from_FunctionPrototype(cls, func_proto, body): if not isinstance(func_proto, FunctionPrototype): raise TypeError("func_proto is not an instance of FunctionPrototype") return cls(body=body, **func_proto.kwargs())
[docs]class Return(Basic): """ Represents a return command in the code. """
[docs]class FunctionCall(Token, Expr): """ Represents a call to a function in the code. Parameters ========== name : str function_args : Tuple Examples ======== >>> from sympy.codegen.ast import FunctionCall >>> from sympy.printing.pycode import pycode >>> fcall = FunctionCall('foo', 'bar baz'.split()) >>> print(pycode(fcall)) foo(bar, baz) """ __slots__ = ['name', 'function_args'] _construct_name = String _construct_function_args = staticmethod(lambda args: Tuple(*args))