558 lines
20 KiB
Python
558 lines
20 KiB
Python
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from __future__ import annotations
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from sympy.core import Basic, S
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from sympy.core.function import Lambda
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from sympy.core.numbers import equal_valued
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from sympy.printing.codeprinter import CodePrinter
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from sympy.printing.precedence import precedence
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from functools import reduce
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known_functions = {
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'Abs': 'abs',
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'sin': 'sin',
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'cos': 'cos',
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'tan': 'tan',
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'acos': 'acos',
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'asin': 'asin',
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'atan': 'atan',
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'atan2': 'atan',
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'ceiling': 'ceil',
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'floor': 'floor',
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'sign': 'sign',
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'exp': 'exp',
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'log': 'log',
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'add': 'add',
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'sub': 'sub',
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'mul': 'mul',
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'pow': 'pow'
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}
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class GLSLPrinter(CodePrinter):
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"""
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Rudimentary, generic GLSL printing tools.
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Additional settings:
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'use_operators': Boolean (should the printer use operators for +,-,*, or functions?)
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"""
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_not_supported: set[Basic] = set()
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printmethod = "_glsl"
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language = "GLSL"
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_default_settings = {
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'use_operators': True,
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'zero': 0,
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'mat_nested': False,
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'mat_separator': ',\n',
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'mat_transpose': False,
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'array_type': 'float',
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'glsl_types': True,
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'order': None,
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'full_prec': 'auto',
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'precision': 9,
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'user_functions': {},
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'human': True,
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'allow_unknown_functions': False,
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'contract': True,
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'error_on_reserved': False,
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'reserved_word_suffix': '_',
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}
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def __init__(self, settings={}):
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CodePrinter.__init__(self, settings)
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self.known_functions = dict(known_functions)
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userfuncs = settings.get('user_functions', {})
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self.known_functions.update(userfuncs)
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def _rate_index_position(self, p):
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return p*5
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def _get_statement(self, codestring):
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return "%s;" % codestring
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def _get_comment(self, text):
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return "// {}".format(text)
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def _declare_number_const(self, name, value):
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return "float {} = {};".format(name, value)
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def _format_code(self, lines):
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return self.indent_code(lines)
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def indent_code(self, code):
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"""Accepts a string of code or a list of code lines"""
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if isinstance(code, str):
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code_lines = self.indent_code(code.splitlines(True))
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return ''.join(code_lines)
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tab = " "
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inc_token = ('{', '(', '{\n', '(\n')
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dec_token = ('}', ')')
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code = [line.lstrip(' \t') for line in code]
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increase = [int(any(map(line.endswith, inc_token))) for line in code]
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decrease = [int(any(map(line.startswith, dec_token))) for line in code]
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pretty = []
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level = 0
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for n, line in enumerate(code):
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if line in ('', '\n'):
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pretty.append(line)
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continue
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level -= decrease[n]
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pretty.append("%s%s" % (tab*level, line))
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level += increase[n]
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return pretty
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def _print_MatrixBase(self, mat):
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mat_separator = self._settings['mat_separator']
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mat_transpose = self._settings['mat_transpose']
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column_vector = (mat.rows == 1) if mat_transpose else (mat.cols == 1)
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A = mat.transpose() if mat_transpose != column_vector else mat
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glsl_types = self._settings['glsl_types']
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array_type = self._settings['array_type']
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array_size = A.cols*A.rows
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array_constructor = "{}[{}]".format(array_type, array_size)
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if A.cols == 1:
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return self._print(A[0]);
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if A.rows <= 4 and A.cols <= 4 and glsl_types:
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if A.rows == 1:
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return "vec{}{}".format(
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A.cols, A.table(self,rowstart='(',rowend=')')
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)
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elif A.rows == A.cols:
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return "mat{}({})".format(
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A.rows, A.table(self,rowsep=', ',
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rowstart='',rowend='')
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)
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else:
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return "mat{}x{}({})".format(
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A.cols, A.rows,
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A.table(self,rowsep=', ',
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rowstart='',rowend='')
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)
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elif S.One in A.shape:
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return "{}({})".format(
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array_constructor,
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A.table(self,rowsep=mat_separator,rowstart='',rowend='')
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)
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elif not self._settings['mat_nested']:
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return "{}(\n{}\n) /* a {}x{} matrix */".format(
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array_constructor,
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A.table(self,rowsep=mat_separator,rowstart='',rowend=''),
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A.rows, A.cols
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)
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elif self._settings['mat_nested']:
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return "{}[{}][{}](\n{}\n)".format(
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array_type, A.rows, A.cols,
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A.table(self,rowsep=mat_separator,rowstart='float[](',rowend=')')
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)
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def _print_SparseRepMatrix(self, mat):
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# do not allow sparse matrices to be made dense
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return self._print_not_supported(mat)
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def _traverse_matrix_indices(self, mat):
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mat_transpose = self._settings['mat_transpose']
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if mat_transpose:
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rows,cols = mat.shape
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else:
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cols,rows = mat.shape
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return ((i, j) for i in range(cols) for j in range(rows))
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def _print_MatrixElement(self, expr):
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# print('begin _print_MatrixElement')
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nest = self._settings['mat_nested'];
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glsl_types = self._settings['glsl_types'];
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mat_transpose = self._settings['mat_transpose'];
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if mat_transpose:
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cols,rows = expr.parent.shape
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i,j = expr.j,expr.i
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else:
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rows,cols = expr.parent.shape
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i,j = expr.i,expr.j
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pnt = self._print(expr.parent)
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if glsl_types and ((rows <= 4 and cols <=4) or nest):
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return "{}[{}][{}]".format(pnt, i, j)
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else:
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return "{}[{}]".format(pnt, i + j*rows)
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def _print_list(self, expr):
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l = ', '.join(self._print(item) for item in expr)
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glsl_types = self._settings['glsl_types']
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array_type = self._settings['array_type']
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array_size = len(expr)
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array_constructor = '{}[{}]'.format(array_type, array_size)
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if array_size <= 4 and glsl_types:
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return 'vec{}({})'.format(array_size, l)
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else:
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return '{}({})'.format(array_constructor, l)
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_print_tuple = _print_list
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_print_Tuple = _print_list
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def _get_loop_opening_ending(self, indices):
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open_lines = []
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close_lines = []
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loopstart = "for (int %(varble)s=%(start)s; %(varble)s<%(end)s; %(varble)s++){"
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for i in indices:
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# GLSL arrays start at 0 and end at dimension-1
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open_lines.append(loopstart % {
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'varble': self._print(i.label),
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'start': self._print(i.lower),
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'end': self._print(i.upper + 1)})
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close_lines.append("}")
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return open_lines, close_lines
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def _print_Function_with_args(self, func, func_args):
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if func in self.known_functions:
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cond_func = self.known_functions[func]
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func = None
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if isinstance(cond_func, str):
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func = cond_func
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else:
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for cond, func in cond_func:
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if cond(func_args):
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break
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if func is not None:
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try:
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return func(*[self.parenthesize(item, 0) for item in func_args])
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except TypeError:
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return '{}({})'.format(func, self.stringify(func_args, ", "))
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elif isinstance(func, Lambda):
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# inlined function
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return self._print(func(*func_args))
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else:
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return self._print_not_supported(func)
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def _print_Piecewise(self, expr):
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from sympy.codegen.ast import Assignment
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if expr.args[-1].cond != True:
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# We need the last conditional to be a True, otherwise the resulting
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# function may not return a result.
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raise ValueError("All Piecewise expressions must contain an "
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"(expr, True) statement to be used as a default "
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"condition. Without one, the generated "
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"expression may not evaluate to anything under "
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"some condition.")
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lines = []
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if expr.has(Assignment):
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for i, (e, c) in enumerate(expr.args):
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if i == 0:
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lines.append("if (%s) {" % self._print(c))
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elif i == len(expr.args) - 1 and c == True:
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lines.append("else {")
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else:
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lines.append("else if (%s) {" % self._print(c))
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code0 = self._print(e)
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lines.append(code0)
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lines.append("}")
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return "\n".join(lines)
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else:
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# The piecewise was used in an expression, need to do inline
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# operators. This has the downside that inline operators will
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# not work for statements that span multiple lines (Matrix or
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# Indexed expressions).
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ecpairs = ["((%s) ? (\n%s\n)\n" % (self._print(c),
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self._print(e))
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for e, c in expr.args[:-1]]
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last_line = ": (\n%s\n)" % self._print(expr.args[-1].expr)
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return ": ".join(ecpairs) + last_line + " ".join([")"*len(ecpairs)])
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def _print_Idx(self, expr):
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return self._print(expr.label)
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def _print_Indexed(self, expr):
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# calculate index for 1d array
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dims = expr.shape
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elem = S.Zero
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offset = S.One
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for i in reversed(range(expr.rank)):
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elem += expr.indices[i]*offset
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offset *= dims[i]
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return "{}[{}]".format(
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self._print(expr.base.label),
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self._print(elem)
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)
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def _print_Pow(self, expr):
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PREC = precedence(expr)
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if equal_valued(expr.exp, -1):
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return '1.0/%s' % (self.parenthesize(expr.base, PREC))
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elif equal_valued(expr.exp, 0.5):
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return 'sqrt(%s)' % self._print(expr.base)
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else:
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try:
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e = self._print(float(expr.exp))
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except TypeError:
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e = self._print(expr.exp)
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return self._print_Function_with_args('pow', (
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self._print(expr.base),
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e
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))
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def _print_int(self, expr):
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return str(float(expr))
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def _print_Rational(self, expr):
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return "{}.0/{}.0".format(expr.p, expr.q)
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def _print_Relational(self, expr):
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lhs_code = self._print(expr.lhs)
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rhs_code = self._print(expr.rhs)
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op = expr.rel_op
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return "{} {} {}".format(lhs_code, op, rhs_code)
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def _print_Add(self, expr, order=None):
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if self._settings['use_operators']:
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return CodePrinter._print_Add(self, expr, order=order)
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terms = expr.as_ordered_terms()
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def partition(p,l):
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return reduce(lambda x, y: (x[0]+[y], x[1]) if p(y) else (x[0], x[1]+[y]), l, ([], []))
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def add(a,b):
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return self._print_Function_with_args('add', (a, b))
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# return self.known_functions['add']+'(%s, %s)' % (a,b)
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neg, pos = partition(lambda arg: arg.could_extract_minus_sign(), terms)
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if pos:
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s = pos = reduce(lambda a,b: add(a,b), (self._print(t) for t in pos))
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else:
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s = pos = self._print(self._settings['zero'])
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if neg:
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# sum the absolute values of the negative terms
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neg = reduce(lambda a,b: add(a,b), (self._print(-n) for n in neg))
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# then subtract them from the positive terms
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s = self._print_Function_with_args('sub', (pos,neg))
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# s = self.known_functions['sub']+'(%s, %s)' % (pos,neg)
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return s
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def _print_Mul(self, expr, **kwargs):
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if self._settings['use_operators']:
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return CodePrinter._print_Mul(self, expr, **kwargs)
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terms = expr.as_ordered_factors()
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def mul(a,b):
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# return self.known_functions['mul']+'(%s, %s)' % (a,b)
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return self._print_Function_with_args('mul', (a,b))
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s = reduce(lambda a,b: mul(a,b), (self._print(t) for t in terms))
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return s
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def glsl_code(expr,assign_to=None,**settings):
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"""Converts an expr to a string of GLSL code
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Parameters
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==========
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expr : Expr
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A SymPy expression to be converted.
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assign_to : optional
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When given, the argument is used for naming the variable or variables
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to which the expression is assigned. Can be a string, ``Symbol``,
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``MatrixSymbol`` or ``Indexed`` type object. In cases where ``expr``
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would be printed as an array, a list of string or ``Symbol`` objects
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can also be passed.
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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))
|