o o h@sdZddlmZddlmZddlmZddlmZm Z m Z m Z ddl m Z mZmZddlmZddlmZmZdd lmZmZmZdd lmZmZmZdd lmZmZm Z m!Z!d d Z"GdddeZ#Gddde#Z$Gddde$Z%e%Z&Gddde$Z'e'Z(Gddde$Z)e)Z*Gddde#Z+Gddde+Z,Gddde+Z-Gddde-Z.Gd d!d!e-Z/Gd"d#d#e-Z0Gd$d%d%e-Z1Gd&d'd'e-Z2d(d)e.e/e0e1e2fDZ3d*d+Z4Gd,d-d-e#Z5Gd.d/d/e$Z6Gd0d1d1ee$Z7Gd2d3d3e7Z8Gd4d5d5e7Z9Gd6d7d7e$Z:Gd8d9d9e$Z;Gd:d;d;e;Zd?d?e=Z>Gd@dAdAe=Z?edBZ@GdCdDdDe;ZAGdEdFdFeAZBGdGdHdHeAZCGdIdJdJeCeBZDedMdNZGe>dOdPZHe>dQdRZIe>dSdTZJe?dUdNZKe?dVdPZLe?dWdRZMe?dXdTZNeBdYdPdZd[d\ZOeBd]dRdNd^d\ZPeBd_dTd`dad\ZQeBdbdcddded\ZReBdfdgdddhd\ZSeBdidjdkdld\ZTeDddndTiePjUdodpZVeDddndgieQjUdodpZWe;drZXeAdsZYeAssignmentBase | |--->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 |--->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, QuotedString >>> 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 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 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`. ) annotations)Any) defaultdict)GeGtLeLt)SymbolTupleDummy)Basic)ExprAtom)FloatIntegeroo)_sympifysympify SympifyError)iterabletopological_sortnumbered_symbolsfilter_symbolscCsdd|D}t|S)z 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 cSs"g|] }t|tr t|n|qS) isinstancestrString.0argrre/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/codegen/ast.py s"z_mk_Tuple..r argsrrr _mk_Tuplesr%c@eZdZdZdS) CodegenASTrN)__name__ __module__ __qualname__ __slots__rrrr r'r'cseZdZUdZdZded<eZiZded<gZded<d gZ e d d Z e d d Z e ddZddZddZddZfddZddZddZddddZeZd d!Zd%d#d$ZZS)&Tokena Base class for the AST types. Explanation =========== Defining fields are set in ``_fields``. Attributes (defined in _fields) 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 ``_fields`. 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_`` for each attribute to process the value passed to ``__new__()``. Attributes listed in the class attribute ``not_in_args`` are not passed to :class:`~.Basic`. rtuple[str, ...]r+dict[str, Any]defaultsz list[str] not_in_argsbodycCst|jdkSNr)len_fieldsselfrrr is_Atomz Token.is_AtomcCst|d|ddS)z8 Get the constructor function for an attribute by name. z _construct_%scSs|SNr)xrrr z(Token._get_constructor..getattr)clsattrrrr _get_constructorszToken._get_constructorcCs2|dkr |j|tSt|tr|S|||S)zE Construct an attribute value from argument passed to ``__new__()``. N)r0getnonerr rB)r@rArrrr _constructs  zToken._constructc sZt|dkr|st|dr|dSt|tjkr)tdt|tjfg}tj|D]\}}||vr?td||||q1jt|dD]&}||vr^||}n|j vrij |}ntd||||qR|rtdd |fdd tj|D}t j g|R}tj|D] \}} t ||| q|S) Nrz,Too many arguments (%d), expected at most %dz$Got multiple values for attribute %rz2No value for %r given and attribute has no defaultzUnknown keyword arguments: %s csg|] \}}|jvr|qSr)r1)rrAvalr@rr r!s  z!Token.__new__..)r4rr5 ValueErrorzip TypeErrorappendrEpopr0joinr'__new__setattr) r@r$kwargsattrvalsattrnameargval basic_argsobjrArrrIr rPs2       z Token.__new__cCs:t||jsdS|jD]}t||t||krdSq dS)NFT)r __class__r5r?)r7otherrArrr __eq__s  z Token.__eq__cstfddjDS)Ncg|]}t|qSrr>)rrAr6rr r! z+Token._hashable_content..)tupler5r6rr6r _hashable_content szToken._hashable_contentc tSr:super__hash__r6rXrr rb zToken.__hash__cCs||jvr dd|SdS)N, rG, ) indented_args)r7k indent_levelrrr _joinersz Token._joinercsjdfddt|trNfdd|jD}jvr=dd|ddd d St|jd krId |Sd |S|S)NricsFt|trj|gRdiSj|gRiS)Njoiner)rr-_printrjr)r$ilrhrRprinterr7rr rls $zToken._indented.._printcsg|]}|qSrrrrlrr r!z#Token._indented..z( rGre)rFz({0},)z({0})) _contextrr rjrOr$rgr4format)r7rorhvr$rRjoinedr)rlr$rnrhrRror7r _indenteds  " $"zToken._indentedrf)rkc sddlm}|dd}fddjD}|jdd}g} ttj|D]X\} \} } | |vr2q'| jvr?| j| kr?q'| jvrH|dnd} ||| d j || | g|Ri|}Wdn1siwY| | dkrvd nd | | q'd j j|| S) Nr)printer_contextexcludercr[rr>rrhr6rr r!(r\z$Token._sympyrepr..rirr)riz{1}z{0}={1}z{}({}))sympy.printing.printerryrCr5rt enumeraterKr0rgrxrMrulstriprXr(rO)r7rorkr$rRryrzvaluesri arg_reprsirAvalueilvlindentedrr6r _sympyrepr%s  $zToken._sympyreprcCsddlm}||S)Nr)srepr)sympy.printingr)r7rrrr __repr__>s zToken.__repr__Ncs8fddjD}durfdd|DS|S)a  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. cs i|] }|vr|t|qSrr>r{)rzr7rr Ns z Token.kwargs..Ncsi|] \}}||qSrr)rrhrv)applyrr rP)r5items)r7rzrrRr)rrzr7r rRBs z Token.kwargsrN)r(r)r*__doc__r+__annotations__r5r0r1rgpropertyr8 classmethodrBrErPrZr^rbrjrxr _sympystrrrR __classcell__rrrcr r-s.        . r-c@r&) BreakTokenaD Represents 'break' in C/Python ('exit' in Fortran). Use the premade instance ``break_`` or instantiate manually. Examples ======== >>> from sympy import ccode, fcode >>> from sympy.codegen.ast import break_ >>> ccode(break_) 'break' >>> fcode(break_, source_format='free') 'exit' Nr(r)r*rrrrr rTr,rc@r&) ContinueTokenaW Represents 'continue' in C/Python ('cycle' in Fortran) Use the premade instance ``continue_`` or instantiate manually. Examples ======== >>> from sympy import ccode, fcode >>> from sympy.codegen.ast import continue_ >>> ccode(continue_) 'continue' >>> fcode(continue_, source_format='free') 'cycle' Nrrrrr rgr,rcs0eZdZdZddZddZfddZZS) NoneTokena0 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 import pycode >>> print(pycode(Variable('x').as_Declaration(value=none))) x = None cCs|dupt|tSr:)rrr7rYrrr rZszNoneToken.__eq__cCdS)Nrrr6rrr r^zNoneToken._hashable_contentcr_r:r`r6rcrr rbrdzNoneToken.__hash__)r(r)r*rrZr^rbrrrrcr rys  rcsDeZdZdZfddZeddZeddZedd Z Z S) AssignmentBasez Abstract base class for Assignment and AugmentedAssignment. Attributes: =========== op : str Symbol for assignment operator, e.g. "=", "+=", etc. cs,t|}t|}|||t|||Sr:)r _check_argsrarP)r@lhsrhsrcrr rPs zAssignmentBase.__new__cC |jdSr3r#r6rrr r zAssignmentBase.lhscCr)NrFr#r6rrr rrzAssignmentBase.rhsc Csddlm}m}ddlm}ddlm}t|||tt |f}t ||s*t dt |t |do4t || }t |do?t || } |rT| sHtd|j|jkrRtdd S| r\|s^td d Sd S) z Check arguments to __new__ and raise exception if any problems found. Derived classes may wish to override this. r) MatrixElement MatrixSymbol)Indexed) ArrayElementz Cannot assign to lhs of type %s.shapez#Cannot assign a scalar to a matrix.z'Dimensions of lhs and rhs do not align.z#Cannot assign a matrix to a scalar.N)"sympy.matrices.expressions.matexprrrsympy.tensor.indexedrsympy.tensor.array.expressionsrr ElementVariablerrLtypehasattrrJr) r@rrrrrr assignable lhs_is_mat rhs_is_matrrr rs&     zAssignmentBase._check_args) r(r)r*rrPrrrrrrrrrcr rs   rc@eZdZdZdZdS) Assignmentam 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) z:=N)r(r)r*roprrrr rs$rc@s eZdZdZdZeddZdS)AugmentedAssignmentz Base class for augmented assignments. Attributes: =========== binop : str Symbol for binary operation being applied in the assignment, such as "+", "*", etc. NcCs |jdS)N=binopr6rrr rrzAugmentedAssignment.op)r(r)r*rrrrrrrr rs  rc@r&)AddAugmentedAssignment+Nr(r)r*rrrrr r r,rc@r&)SubAugmentedAssignment-Nrrrrr r r,rc@r&)MulAugmentedAssignment*Nrrrrr rr,rc@r&)DivAugmentedAssignment/Nrrrrr rr,rc@r&)ModAugmentedAssignment%Nrrrrr rr,rcCsi|]}|j|qSrr)rr@rrr rsrcCs"|tvr td|t|||S)ao Create 'lhs op= rhs'. Explanation =========== 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) zUnrecognized operator %s)augassign_classesrJ)rrrrrr aug_assign&s& rcsZeZdZdZddZddZddZeZefdd Z e d d Z dddZ Z S) CodeBlocka_ Represents a block of code. Explanation =========== 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. Examples ======== >>> 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; cGsdg}g}|D]}t|tr|j\}}||||qtj|g|R}t||_t||_|Sr:) rrr$rMr'rPr left_hand_sidesright_hand_sides)r@r$rrrrrrWrrr rPzs      zCodeBlock.__new__cC t|jSr:)iterr$r6rrr __iter__rdzCodeBlock.__iter__cOsh|jdd}dd|}|t|j|j}dd|d|jjd||dd|ddS) NrirrerGz{}( rr rs) rtrCrOmaprlr$rurXr()r7ror$rRrnrkrwrrr rs  zCodeBlock._sympyreprcstjt|jSr:)ra free_symbolssetrr6rcrr rzCodeBlock.free_symbolsc Cstdd|Ds tdtdd|Drtdtt|}tt}|D]}|\}}||j|q&g}|D]}|\}}|jj D]} || D] } || |fqIqCq9t ||g} |dd| DS)a Return a CodeBlock with topologically sorted assignments so that variables are assigned before they are used. Examples ======== 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. >>> 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) ) cs|]}t|tVqdSr:rrrrrrr z-CodeBlock.topological_sort..z4CodeBlock.topological_sort only supports Assignmentscsrr:rrrrrr rrzFCodeBlock.topological_sort does not yet work with AugmentedAssignmentscSsg|]\}}|qSrr)rrarrr r!rqz.CodeBlock.topological_sort..) allNotImplementedErroranylistr}rrrMrrr) r@ assignmentsAvar_mapnoderrEdst_nodessrc_nodeordered_assignmentsrrr rs&"    zCodeBlock.topological_sortN canonicalc Csddlm}tdd|jDstdtdd|jDr"tdt|jD]\}}||jd|vr:td |q'|t }|durGt }t ||}|t |j ||||d \} } d d t|j| D} d d | D} || | S)a Return a new code block with common subexpressions eliminated. Explanation =========== 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) ) r)csecsrr:rrrrr rrz CodeBlock.cse..z'CodeBlock.cse only supports Assignmentscsrr:rrrrr rrz9CodeBlock.cse does not yet work with AugmentedAssignmentsNzEDuplicate assignments to the same variable are not yet supported (%s))symbols optimizations postprocessordercSg|] \}}t||qSrrrvarexprrrr r!$rz!CodeBlock.cse..cSrrrrrrr r!&r)sympy.simplify.cse_mainrrr$rrr}ratomsr rrrrrKr) r7rrrrrrrexisting_symbols replacements reduced_exprs new_blocknew_assignmentsrrr rs0 !     z CodeBlock.cse)NNNr)r(r)r*rrPrrrrrrrrrrrrcr rQs( Prc@s8eZdZdZdZZeeZe ddZ e ddZ dS)ForaRepresents a 'for-loop' in the code. Expressions are of the form: "for target in iter: body..." Parameters ========== target : symbol iter : iterable body : CodeBlock or iterable ! When passed an iterable it is used to instantiate a CodeBlock. Examples ======== >>> from sympy import symbols, Range >>> from sympy.codegen.ast import aug_assign, For >>> x, i, j, k = symbols('x i j k') >>> for_i = For(i, Range(10), [aug_assign(x, '+', i*j*k)]) >>> for_i # doctest: -NORMALIZE_WHITESPACE For(i, iterable=Range(0, 10, 1), body=CodeBlock( AddAugmentedAssignment(x, i*j*k) )) >>> for_ji = For(j, Range(7), [for_i]) >>> for_ji # doctest: -NORMALIZE_WHITESPACE For(j, iterable=Range(0, 7, 1), body=CodeBlock( For(i, iterable=Range(0, 10, 1), body=CodeBlock( AddAugmentedAssignment(x, i*j*k) )) )) >>> for_kji =For(k, Range(5), [for_ji]) >>> for_kji # doctest: -NORMALIZE_WHITESPACE For(k, iterable=Range(0, 5, 1), body=CodeBlock( For(j, iterable=Range(0, 7, 1), body=CodeBlock( For(i, iterable=Range(0, 10, 1), body=CodeBlock( AddAugmentedAssignment(x, i*j*k) )) )) )) )targetrr2cCt|tr|St|Sr:rrr@itrrrr _construct_bodyX zFor._construct_bodycCs*t|stdt|trt|}t|S)Nziterable must be an iterable)rrLrrr]rrrrr _construct_iterable_s  zFor._construct_iterableN) r(r)r*rr+r5 staticmethodr_construct_targetrrrrrrr r*s* rc@sTeZdZdZdZZdgZdZeddZ ddZ dd d Z e d dZ ddZd S)rao SymPy object representing a string. Atomic object which is not an expression (as opposed to Symbol). Parameters ========== text : str Examples ======== >>> from sympy.codegen.ast import String >>> f = String('foo') >>> f foo >>> str(f) 'foo' >>> f.text 'foo' >>> print(repr(f)) String('foo') textrTcCst|ts td|S)Nz#Argument text is not a string type.)rrrL)r@rrrr _construct_texts zString._construct_textcOs|jSr:rr7ror$rRrrr rszString._sympystrrNcCsiSr:r)r7rzrrrr rRrz String.kwargscs fddS)NcsSr:rrr6rr r<r=zString.func..rr6rr6r funcs z String.funccCsddlm}d||jS)Nr latex_escapez\texttt{{"{}"}})sympy.printing.latexrrur)r7rorrrr _latexs z String._latexr)r(r)r*rr+r5r1r8rrrrRrrrrrrr rhs    rc@r&) QuotedStringz: Represents a string which should be printed with quotes. Nrrrrr r r,r c@r&)Commentz Represents a comment. Nrrrrr r r,r c@sDeZdZUdZdZded<eZdeiZded<e e Z dd Z d S) Nodea| 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 )attrsr.r+r r/r0cCs,|jD]}t|jt|kr|jSqdS)zQ Returns the parameters of the Attribute with name ``looking_for`` in self.attrs N)r rname parameters)r7 looking_forrArrr attr_paramss  zNode.attr_paramsN) r(r)r*rr+rr5r r0rr%_construct_attrsrrrrr r s   r c@sTeZdZUdZdZded<eZeZddZ e ddZ d d Z dd dZ ddZd S)Typea Represents a type. Explanation =========== 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 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://numpy.org/doc/stable/user/basics.types.html r r.r+cOrr:)rr rrrr rrdzType._sympystrcCs|t|ttfr tSt|ttfst|ddrtSt|ddr tSt|ts+t|ddr-t St|t s8t|ddr:t St d)a 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. is_integerFis_real is_complex is_Relationalz Could not deduce type from expr.) rfloatrrealintrr?integercomplexcomplex_boolbool_rJ)r@rrrr from_exprs zType.from_exprcCsdSr:rr7rrrr _check-rz Type._checkNrc st|}td}t|dd}dur|durdnd|| fdd}||} || | |} t| ||kr@td| S) a[ 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``). type_aliases : dict Maps substitutions for Type, e.g. {integer: int64, real: float32} Examples ======== >>> from sympy.codegen.ast import 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 decimal_digNgV瞯.tolz.Casting gives a significantly different value.)rrr? cast_nocheckr"r%rJ) r7rr)r(precision_targetsrHtenexp10r*new_valdeltarr'r cast_check0s/   zType.cast_checkcCs0ddlm}||jj}||jj}d||S)Nrrz%\text{{{}}}\left(\texttt{{{}}}\right))rrrXr(r rru)r7ror type_namer rrr rss    z Type._latex)NrN)r(r)r*rr+rr5r_construct_namerrr r"r1rrrrr rs  6 *  Crc@eZdZdZdZddZdS) IntBaseTypez2 Integer base type, contains no size information. rcCs tt|Sr:)rr)r7rrrr r<} zIntBaseType.N)r(r)r*rr+r+rrrr r5zs r5c@s&eZdZdZejeZeZddZdS) _SizedIntTypenbitscCs<||jkrtd||jf||jkrtd||jfdS)NValue is too small: %d < %dValue is too big: %d > %d)minrJmaxr!rrr r"s  z_SizedIntType._checkN) r(r)r*r+rr5r_construct_nbitsr"rrrr r7s   r7c@,eZdZdZdZeddZeddZdS) SignedIntTypez# Represents a signed integer type. rcCsd|jd SNrFr8r6rrr r<szSignedIntType.mincCsd|jddSrAr8r6rrr r=rzSignedIntType.maxNr(r)r*rr+rr<r=rrrr r@ r@c@r?)UnsignedIntTypez& Represents an unsigned integer type. rcCrr3rr6rrr r<szUnsignedIntType.mincCsd|jdSrAr8r6rrr r=r9zUnsignedIntType.maxNrCrrrr rErDrErBc@seZdZdZdZeZdS) FloatBaseTypez* Represents a floating point number type. rN)r(r)r*rr+rr+rrrr rFsrFc@seZdZdZdZejeZeZZ Z e ddZ e ddZ e ddZe d d Ze d d Ze d dZe ddZddZddZdS) FloatTypea 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 >>> 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. )r9nmantnexpcCt|jdS)zV The largest positive number n, such that 2**(n - 1) is a representable finite value. rF)tworIr6rrr max_exponentszFloatType.max_exponentcCs d|jS)zR The lowest negative number n, such that 2**(n - 1) is a valid normalized number. )rLr6rrr min_exponents zFloatType.min_exponentcCsdt|jd t|jS)z Maximum value representable. rF)rKrHrLr6rrr r=sz FloatType.maxcCrJ)z( The minimum positive normalized value. rF)rKrNr6rrr tinyszFloatType.tinycCs t|j S)z: Difference between 1.0 and the next representable value. )rKrHr6rrr epss z FloatType.epscCs*ddlm}m}||j|d|dS)z 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. r)floorlogrBr#)sympy.functionsrQrRrH)r7rQrRrrr digsz FloatType.digcCs2ddlm}m}||jd|d|ddS)a} Number of digits needed to store & load without loss. Explanation =========== 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. r)ceilingrRrFrBr#)rSrUrRrH)r7rUrRrrr r$s "zFloatType.decimal_digcCs@|tkrttS|t krtt Sttt||j|jS)7 Casts without checking if out of bounds or subnormal. )rrrrrevalfr$r!rrr r+s   zFloatType.cast_nocheckcCsV||j krtd||j f||jkrtd||jft||jkr)tddS)Nr:r;z>Smallest (absolute) value for data type bigger than new value.)r=rJr%rOr!rrr r"s  zFloatType._checkN)r(r)r*rr+rr5rr>_construct_nmant_construct_nexprrLrNr=rOrPrTr$r+r"rrrr rGs*(          rGcs,eZdZdZfddZfddZZS)ComplexBaseTypercs4ddlm}m}t||t||dS)rVrreimy?)rSr\r]rar+r7rr\r]rcrr r+&s zComplexBaseType.cast_nocheckcs4ddlm}m}t||t||dS)Nrr[)rSr\r]rar"r^rcrr r".szComplexBaseType._check)r(r)r*r+r+r"rrrrcr rZ"s rZc@r) ComplexTypez- Represents a complex floating point number. rN)r(r)r*rr+rrrr r_4sr_intcintpint8int16int32 int64@uint8uint16uint32uint64float16r#)rIrHfloat32float64 4float80P?float128pfloat256 complex64r9)r r9rz complex128untypedrrrrc@s6eZdZdZdZZdeiZeZ e e Z ddZ dS) Attributea Attribute (possibly parametrized) For use with :class:`sympy.codegen.ast.Node` (which takes instances of ``Attribute`` as ``attrs``). Parameters ========== name : str parameters : Tuple Examples ======== >>> from sympy.codegen.ast import Attribute >>> volatile = Attribute('volatile') >>> volatile volatile >>> print(repr(volatile)) Attribute(String('volatile')) >>> a = Attribute('foo', [1, 2, 3]) >>> a foo(1, 2, 3) >>> a.parameters == (1, 2, 3) True )r rrcs:t|j}|jr|ddfdd|jD7}|S)Nz(%s)rfc3s(|]}j|gRiVqdSr:rprr$rRrorr rzsz&Attribute._sympystr..)rr rrO)r7ror$rRresultrrr rws  zAttribute._sympystrN)r(r)r*rr+r5r r0rr3rr%_construct_parametersrrrrr rVs  r value_const pointer_constc@seZdZdZdZeejZejZe e e de e Ze e ZededfddZdd Zd d Zd d Zdd Zdd Zdd ZdS)ra 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,))) )symbolrr)rrNTcCs`t|tr|Szt|}Wntyt|}Ynw|dur(|r(||}|||||dS)a` 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 N)rrr )rrrr rJr1)r@rrr r1type_rrr deduceds !   zVariable.deducedcKs&|}||t|jdi|S)aV Convenience method for creating a Declaration instance. Explanation =========== 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, NoneToken >>> x = Variable('x') >>> decl1 = x.as_Declaration() >>> # value is special NoneToken() which must be tested with == operator >>> decl1.variable.value is None # won't work False >>> decl1.variable.value == None # not PEP-8 compliant True >>> decl1.variable.value == NoneToken() # OK True >>> decl2 = x.as_Declaration(value=42.0) >>> decl2.variable.value == 42.0 True Nr)rRupdate Declarationr)r7rRkwrrr as_Declarations zVariable.as_DeclarationcCs:zt|}Wntytd||fw|||ddS)NzInvalid comparison %s < %sF)evaluate)rrrL)r7rrrrr _relation s   zVariable._relationcC ||tSr:)rrrrrr r<r6zVariable.cCrr:)rrrrrr r<r6cCrr:)rrrrrr r<r6cCrr:)rrrrrr r<r6)r(r)r*rr+r r5r0copyrrrDrr_construct_symbol_construct_valuerr rrr__lt____le____ge____gt__rrrr rs 1  ,  rc@r4)Pointera2 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,)) rcCs0zt|j|WStyt|j|fYSwr:)rrrL)r7keyrrr __getitem__(s  zPointer.__getitem__N)r(r)r*rr+rrrrr rs rc@sJeZdZdZdZZeedZee Z eddZ eddZ ee Z dS)ra 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]' )rindicesstridesoffset)rrcCt|Sr:r"rmrrr r<EzElement.cCrr:r"rmrrr r<FrN)r(r)r*rr+r5rDr0rrr_construct_indices_construct_strides_construct_offsetrrrr r/s    rc@eZdZdZdZZeZdS)ra Represents a variable declaration Parameters ========== variable : Variable Examples ======== >>> from sympy.codegen.ast import Declaration, NoneToken, untyped >>> z = Declaration('z') >>> z.variable.type == untyped True >>> # value is special NoneToken() which must be tested with == operator >>> z.variable.value is None # won't work False >>> z.variable.value == None # not PEP-8 compliant True >>> z.variable.value == NoneToken() # OK True )variableN)r(r)r*rr+r5r_construct_variablerrrr rJsrc@s0eZdZdZdZZeddZeddZ dS)Whilea} Represents a 'for-loop' in the code. Expressions are of the form: "while condition: body..." Parameters ========== condition : expression convertible 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) ... ]) ) conditionr2cCst|Sr:)r)condrrr r<rzWhile.cCrr:rrrrr rrzWhile._construct_bodyN) r(r)r*rr+r5r_construct_conditionrrrrrr res  rc@s$eZdZdZdZZeddZdS)Scopez Represents a scope in the code. Parameters ========== body : CodeBlock or iterable When passed an iterable it is used to instantiate a CodeBlock. r2cCrr:rrrrr rrzScope._construct_bodyN)r(r)r*rr+r5rrrrrr rs  rc@r)Streama Represents a stream. There are two predefined Stream instances ``stdout`` & ``stderr``. Parameters ========== name : str Examples ======== >>> from sympy import pycode, Symbol >>> 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) rN)r(r)r*rr+r5rr3rrrr rsrstdoutstderrc@s2eZdZdZdZZeedZee Z e Z e ZdS)Printa 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 import pycode >>> print(pycode(Print('x y'.split(), "coordinate: %12.5g %12.5g\\n"))) print("coordinate: %12.5g %12.5g\n" % (x, y), end="") ) print_args format_stringfile)rrN)r(r)r*rr+r5rDr0rr%_construct_print_argsr _construct_format_stringr_construct_filerrrr rs rc@sHeZdZUdZdZeejZded<eZ e Z e ddZ eddZd S) FunctionPrototypea" 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 ccode, symbols >>> from sympy.codegen.ast import real, FunctionPrototype >>> x, y = symbols('x y', real=True) >>> fp = FunctionPrototype(real, 'foo', [x, y]) >>> ccode(fp) 'double foo(double x, double y)' ) return_typer rr.r5cCsdd}tt||S)NcSs(t|tr|jSt|tr|St|Sr:)rrrrrrmrrr _vars   z5FunctionPrototype._construct_parameters.._var)r r)r$rrrr rsz'FunctionPrototype._construct_parameterscCs(t|ts td|di|jddS)Nz1func_def is not an instance of FunctionDefinitionrrr)rFunctionDefinitionrLrR)r@func_defrrr from_FunctionDefinition z)FunctionPrototype.from_FunctionDefinitionN)r(r)r*rr+r r5rr_construct_return_typerr3rrrrrrrr rs   rc@sDeZdZdZdZejddeejZeddZ eddZ dS) ra 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 ccode, symbols >>> from sympy.codegen.ast import real, FunctionPrototype >>> 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; } rNcCrr:rrrrr r)rz"FunctionDefinition._construct_bodycCs(t|ts td|dd|i|S)Nz2func_proto is not an instance of FunctionPrototyper2r)rrrLrR)r@ func_protor2rrr from_FunctionPrototype0rz)FunctionDefinition.from_FunctionPrototype) r(r)r*rr+rr5r rrrrrrr rs rc@s eZdZdZdZZeeZdS)ReturnaC Represents a return command in the code. Parameters ========== return : Basic Examples ======== >>> from sympy.codegen.ast import Return >>> from sympy.printing.pycode import pycode >>> from sympy import Symbol >>> x = Symbol('x') >>> print(pycode(Return(x))) return x )returnN) r(r)r*rr+r5rr_construct_returnrrrr r7s rc@s(eZdZdZdZZeZeddZ dS) FunctionCallaR Represents a call to a function in the code. Parameters ========== name : str function_args : Tuple Examples ======== >>> from sympy.codegen.ast import FunctionCall >>> from sympy import pycode >>> fcall = FunctionCall('foo', 'bar baz'.split()) >>> print(pycode(fcall)) foo(bar, baz) )r  function_argscCrr:r"r#rrr r<drzFunctionCall.N) r(r)r*rr+r5rr3r_construct_function_argsrrrr rNs rc@seZdZdZdZZdS)Raisez4 Prints as 'raise ...' in Python, 'throw ...' in C++) exceptionN)r(r)r*rr+r5rrrr rgs rc@r) RuntimeError_z Represents 'std::runtime_error' in C++ and 'RuntimeError' in Python. Note that the latter is uncommon, and you might want to use e.g. ValueError. )messageN)r(r)r*rr+r5r_construct_messagerrrr rlsrN)r)r)pr __future__rtypingr collectionsrsympy.core.relationalrrrr sympy.corer r r sympy.core.basicr sympy.core.exprr rsympy.core.numbersrrrsympy.core.sympifyrrrsympy.utilities.iterablesrrrrr%r'r-rbreak_r continue_rrDrrrrrrrrrrrrrr r r rr5r7r@rErKrFrGrZr_r`rarbrdrfrhrjrkrlrmrnrprrruryr|rRrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr s    -;(+Z>2#8   w        (&1/