from __future__ import annotations
from sympy.core import Basic, S
from sympy.core.function import Lambda
from sympy.core.numbers import equal_valued
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[Basic] = set()
printmethod = "_glsl"
language = "GLSL"
_default_settings = dict(CodePrinter._default_settings, **{
'use_operators': True,
'zero': 0,
'mat_nested': False,
'mat_separator': ',\n',
'mat_transpose': False,
'array_type': 'float',
'glsl_types': True,
'precision': 9,
'user_functions': {},
'contract': True,
})
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 equal_valued(expr.exp, -1):
return '1.0/%s' % (self.parenthesize(expr.base, PREC))
elif equal_valued(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), (self._print(t) for t in 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), (self._print(-n) for n in 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), (self._print(t) for t in 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))