from typing import Set as tSet from sympy.core import Basic, S from sympy.core.function import Lambda from sympy.printing.codeprinter import CodePrinter from sympy.printing.precedence import precedence from functools import reduce known_functions = { 'Abs': 'abs', 'sin': 'sin', 'cos': 'cos', 'tan': 'tan', 'acos': 'acos', 'asin': 'asin', 'atan': 'atan', 'atan2': 'atan', 'ceiling': 'ceil', 'floor': 'floor', 'sign': 'sign', 'exp': 'exp', 'log': 'log', 'add': 'add', 'sub': 'sub', 'mul': 'mul', 'pow': 'pow' } class GLSLPrinter(CodePrinter): """ Rudimentary, generic GLSL printing tools. Additional settings: 'use_operators': Boolean (should the printer use operators for +,-,*, or functions?) """ _not_supported = set() # type: tSet[Basic] printmethod = "_glsl" language = "GLSL" _default_settings = { 'use_operators': True, 'zero': 0, 'mat_nested': False, 'mat_separator': ',\n', 'mat_transpose': False, 'array_type': 'float', 'glsl_types': True, 'order': None, 'full_prec': 'auto', 'precision': 9, 'user_functions': {}, 'human': True, 'allow_unknown_functions': False, 'contract': True, 'error_on_reserved': False, 'reserved_word_suffix': '_', } def __init__(self, settings={}): CodePrinter.__init__(self, settings) self.known_functions = dict(known_functions) userfuncs = settings.get('user_functions', {}) self.known_functions.update(userfuncs) def _rate_index_position(self, p): return p*5 def _get_statement(self, codestring): return "%s;" % codestring def _get_comment(self, text): return "// {}".format(text) def _declare_number_const(self, name, value): return "float {} = {};".format(name, value) def _format_code(self, lines): return self.indent_code(lines) def indent_code(self, code): """Accepts a string of code or a list of code lines""" if isinstance(code, str): code_lines = self.indent_code(code.splitlines(True)) return ''.join(code_lines) tab = " " inc_token = ('{', '(', '{\n', '(\n') dec_token = ('}', ')') code = [line.lstrip(' \t') for line in code] increase = [int(any(map(line.endswith, inc_token))) for line in code] decrease = [int(any(map(line.startswith, dec_token))) for line in code] pretty = [] level = 0 for n, line in enumerate(code): if line in ('', '\n'): pretty.append(line) continue level -= decrease[n] pretty.append("%s%s" % (tab*level, line)) level += increase[n] return pretty def _print_MatrixBase(self, mat): mat_separator = self._settings['mat_separator'] mat_transpose = self._settings['mat_transpose'] column_vector = (mat.rows == 1) if mat_transpose else (mat.cols == 1) A = mat.transpose() if mat_transpose != column_vector else mat glsl_types = self._settings['glsl_types'] array_type = self._settings['array_type'] array_size = A.cols*A.rows array_constructor = "{}[{}]".format(array_type, array_size) if A.cols == 1: return self._print(A[0]); if A.rows <= 4 and A.cols <= 4 and glsl_types: if A.rows == 1: return "vec{}{}".format( A.cols, A.table(self,rowstart='(',rowend=')') ) elif A.rows == A.cols: return "mat{}({})".format( A.rows, A.table(self,rowsep=', ', rowstart='',rowend='') ) else: return "mat{}x{}({})".format( A.cols, A.rows, A.table(self,rowsep=', ', rowstart='',rowend='') ) elif S.One in A.shape: return "{}({})".format( array_constructor, A.table(self,rowsep=mat_separator,rowstart='',rowend='') ) elif not self._settings['mat_nested']: return "{}(\n{}\n) /* a {}x{} matrix */".format( array_constructor, A.table(self,rowsep=mat_separator,rowstart='',rowend=''), A.rows, A.cols ) elif self._settings['mat_nested']: return "{}[{}][{}](\n{}\n)".format( array_type, A.rows, A.cols, A.table(self,rowsep=mat_separator,rowstart='float[](',rowend=')') ) def _print_SparseRepMatrix(self, mat): # do not allow sparse matrices to be made dense return self._print_not_supported(mat) def _traverse_matrix_indices(self, mat): mat_transpose = self._settings['mat_transpose'] if mat_transpose: rows,cols = mat.shape else: cols,rows = mat.shape return ((i, j) for i in range(cols) for j in range(rows)) def _print_MatrixElement(self, expr): # print('begin _print_MatrixElement') nest = self._settings['mat_nested']; glsl_types = self._settings['glsl_types']; mat_transpose = self._settings['mat_transpose']; if mat_transpose: cols,rows = expr.parent.shape i,j = expr.j,expr.i else: rows,cols = expr.parent.shape i,j = expr.i,expr.j pnt = self._print(expr.parent) if glsl_types and ((rows <= 4 and cols <=4) or nest): return "{}[{}][{}]".format(pnt, i, j) else: return "{}[{}]".format(pnt, i + j*rows) def _print_list(self, expr): l = ', '.join(self._print(item) for item in expr) glsl_types = self._settings['glsl_types'] array_type = self._settings['array_type'] array_size = len(expr) array_constructor = '{}[{}]'.format(array_type, array_size) if array_size <= 4 and glsl_types: return 'vec{}({})'.format(array_size, l) else: return '{}({})'.format(array_constructor, l) _print_tuple = _print_list _print_Tuple = _print_list def _get_loop_opening_ending(self, indices): open_lines = [] close_lines = [] loopstart = "for (int %(varble)s=%(start)s; %(varble)s<%(end)s; %(varble)s++){" for i in indices: # GLSL arrays start at 0 and end at dimension-1 open_lines.append(loopstart % { 'varble': self._print(i.label), 'start': self._print(i.lower), 'end': self._print(i.upper + 1)}) close_lines.append("}") return open_lines, close_lines def _print_Function_with_args(self, func, func_args): if func in self.known_functions: cond_func = self.known_functions[func] func = None if isinstance(cond_func, str): func = cond_func else: for cond, func in cond_func: if cond(func_args): break if func is not None: try: return func(*[self.parenthesize(item, 0) for item in func_args]) except TypeError: return '{}({})'.format(func, self.stringify(func_args, ", ")) elif isinstance(func, Lambda): # inlined function return self._print(func(*func_args)) else: return self._print_not_supported(func) def _print_Piecewise(self, expr): from sympy.codegen.ast import Assignment if expr.args[-1].cond != True: # We need the last conditional to be a True, otherwise the resulting # function may not return a result. raise ValueError("All Piecewise expressions must contain an " "(expr, True) statement to be used as a default " "condition. Without one, the generated " "expression may not evaluate to anything under " "some condition.") lines = [] if expr.has(Assignment): for i, (e, c) in enumerate(expr.args): if i == 0: lines.append("if (%s) {" % self._print(c)) elif i == len(expr.args) - 1 and c == True: lines.append("else {") else: lines.append("else if (%s) {" % self._print(c)) code0 = self._print(e) lines.append(code0) lines.append("}") return "\n".join(lines) else: # The piecewise was used in an expression, need to do inline # operators. This has the downside that inline operators will # not work for statements that span multiple lines (Matrix or # Indexed expressions). ecpairs = ["((%s) ? (\n%s\n)\n" % (self._print(c), self._print(e)) for e, c in expr.args[:-1]] last_line = ": (\n%s\n)" % self._print(expr.args[-1].expr) return ": ".join(ecpairs) + last_line + " ".join([")"*len(ecpairs)]) def _print_Idx(self, expr): return self._print(expr.label) def _print_Indexed(self, expr): # calculate index for 1d array dims = expr.shape elem = S.Zero offset = S.One for i in reversed(range(expr.rank)): elem += expr.indices[i]*offset offset *= dims[i] return "{}[{}]".format( self._print(expr.base.label), self._print(elem) ) def _print_Pow(self, expr): PREC = precedence(expr) if expr.exp == -1: return '1.0/%s' % (self.parenthesize(expr.base, PREC)) elif expr.exp == 0.5: return 'sqrt(%s)' % self._print(expr.base) else: try: e = self._print(float(expr.exp)) except TypeError: e = self._print(expr.exp) return self._print_Function_with_args('pow', ( self._print(expr.base), e )) def _print_int(self, expr): return str(float(expr)) def _print_Rational(self, expr): return "{}.0/{}.0".format(expr.p, expr.q) def _print_Relational(self, expr): lhs_code = self._print(expr.lhs) rhs_code = self._print(expr.rhs) op = expr.rel_op return "{} {} {}".format(lhs_code, op, rhs_code) def _print_Add(self, expr, order=None): if self._settings['use_operators']: return CodePrinter._print_Add(self, expr, order=order) terms = expr.as_ordered_terms() def partition(p,l): return reduce(lambda x, y: (x[0]+[y], x[1]) if p(y) else (x[0], x[1]+[y]), l, ([], [])) def add(a,b): return self._print_Function_with_args('add', (a, b)) # return self.known_functions['add']+'(%s, %s)' % (a,b) neg, pos = partition(lambda arg: arg.could_extract_minus_sign(), terms) if pos: s = pos = reduce(lambda a,b: add(a,b), map(lambda t: self._print(t),pos)) else: s = pos = self._print(self._settings['zero']) if neg: # sum the absolute values of the negative terms neg = reduce(lambda a,b: add(a,b), map(lambda n: self._print(-n),neg)) # then subtract them from the positive terms s = self._print_Function_with_args('sub', (pos,neg)) # s = self.known_functions['sub']+'(%s, %s)' % (pos,neg) return s def _print_Mul(self, expr, **kwargs): if self._settings['use_operators']: return CodePrinter._print_Mul(self, expr, **kwargs) terms = expr.as_ordered_factors() def mul(a,b): # return self.known_functions['mul']+'(%s, %s)' % (a,b) return self._print_Function_with_args('mul', (a,b)) s = reduce(lambda a,b: mul(a,b), map(lambda t: self._print(t), terms)) return s def glsl_code(expr,assign_to=None,**settings): """Converts an expr to a string of GLSL code Parameters ========== expr : Expr A SymPy expression to be converted. assign_to : optional When given, the argument is used for naming the variable or variables to which the expression is assigned. Can be a string, ``Symbol``, ``MatrixSymbol`` or ``Indexed`` type object. In cases where ``expr`` would be printed as an array, a list of string or ``Symbol`` objects can also be passed. This is helpful in case of line-wrapping, or for expressions that generate multi-line statements. It can also be used to spread an array-like expression into multiple assignments. use_operators: bool, optional If set to False, then *,/,+,- operators will be replaced with functions mul, add, and sub, which must be implemented by the user, e.g. for implementing non-standard rings or emulated quad/octal precision. [default=True] glsl_types: bool, optional Set this argument to ``False`` in order to avoid using the ``vec`` and ``mat`` types. The printer will instead use arrays (or nested arrays). [default=True] mat_nested: bool, optional GLSL version 4.3 and above support nested arrays (arrays of arrays). Set this to ``True`` to render matrices as nested arrays. [default=False] mat_separator: str, optional By default, matrices are rendered with newlines using this separator, making them easier to read, but less compact. By removing the newline this option can be used to make them more vertically compact. [default=',\n'] mat_transpose: bool, optional GLSL's matrix multiplication implementation assumes column-major indexing. By default, this printer ignores that convention. Setting this option to ``True`` transposes all matrix output. [default=False] array_type: str, optional The GLSL array constructor type. [default='float'] precision : integer, optional The precision for numbers such as pi [default=15]. 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, js_function_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]. Examples ======== >>> from sympy import glsl_code, symbols, Rational, sin, ceiling, Abs >>> x, tau = symbols("x, tau") >>> glsl_code((2*tau)**Rational(7, 2)) '8*sqrt(2)*pow(tau, 3.5)' >>> glsl_code(sin(x), assign_to="float y") 'float y = sin(x);' Various GLSL types are supported: >>> from sympy import Matrix, glsl_code >>> glsl_code(Matrix([1,2,3])) 'vec3(1, 2, 3)' >>> glsl_code(Matrix([[1, 2],[3, 4]])) 'mat2(1, 2, 3, 4)' Pass ``mat_transpose = True`` to switch to column-major indexing: >>> glsl_code(Matrix([[1, 2],[3, 4]]), mat_transpose = True) 'mat2(1, 3, 2, 4)' By default, larger matrices get collapsed into float arrays: >>> print(glsl_code( Matrix([[1,2,3,4,5],[6,7,8,9,10]]) )) float[10]( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ) /* a 2x5 matrix */ The type of array constructor used to print GLSL arrays can be controlled via the ``array_type`` parameter: >>> glsl_code(Matrix([1,2,3,4,5]), array_type='int') 'int[5](1, 2, 3, 4, 5)' Passing a list of strings or ``symbols`` to the ``assign_to`` parameter will yield a multi-line assignment for each item in an array-like expression: >>> x_struct_members = symbols('x.a x.b x.c x.d') >>> print(glsl_code(Matrix([1,2,3,4]), assign_to=x_struct_members)) x.a = 1; x.b = 2; x.c = 3; x.d = 4; This could be useful in cases where it's desirable to modify members of a GLSL ``Struct``. It could also be used to spread items from an array-like expression into various miscellaneous assignments: >>> misc_assignments = ('x[0]', 'x[1]', 'float y', 'float z') >>> print(glsl_code(Matrix([1,2,3,4]), assign_to=misc_assignments)) x[0] = 1; x[1] = 2; float y = 3; float z = 4; Passing ``mat_nested = True`` instead prints out nested float arrays, which are supported in GLSL 4.3 and above. >>> mat = Matrix([ ... [ 0, 1, 2], ... [ 3, 4, 5], ... [ 6, 7, 8], ... [ 9, 10, 11], ... [12, 13, 14]]) >>> print(glsl_code( mat, mat_nested = True )) float[5][3]( float[]( 0, 1, 2), float[]( 3, 4, 5), float[]( 6, 7, 8), float[]( 9, 10, 11), float[](12, 13, 14) ) 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, js_function_string)]. >>> custom_functions = { ... "ceiling": "CEIL", ... "Abs": [(lambda x: not x.is_integer, "fabs"), ... (lambda x: x.is_integer, "ABS")] ... } >>> glsl_code(Abs(x) + ceiling(x), user_functions=custom_functions) 'fabs(x) + CEIL(x)' If further control is needed, addition, subtraction, multiplication and division operators can be replaced with ``add``, ``sub``, and ``mul`` functions. This is done by passing ``use_operators = False``: >>> x,y,z = symbols('x,y,z') >>> glsl_code(x*(y+z), use_operators = False) 'mul(x, add(y, z))' >>> glsl_code(x*(y+z*(x-y)**z), use_operators = False) 'mul(x, add(y, mul(z, pow(sub(x, y), z))))' ``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(glsl_code(expr, tau)) 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])) >>> glsl_code(e.rhs, assign_to=e.lhs, contract=False) 'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);' >>> from sympy import Matrix, MatrixSymbol >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)]) >>> A = MatrixSymbol('A', 3, 1) >>> print(glsl_code(mat, A)) A[0][0] = pow(x, 2.0); if (x > 0) { A[1][0] = x + 1; } else { A[1][0] = x; } A[2][0] = sin(x); """ return GLSLPrinter(settings).doprint(expr,assign_to) def print_glsl(expr, **settings): """Prints the GLSL representation of the given expression. See GLSLPrinter init function for settings. """ print(glsl_code(expr, **settings))