forked from sympy/sympy
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathast.py
More file actions
1815 lines (1412 loc) · 53.6 KB
/
ast.py
File metadata and controls
1815 lines (1412 loc) · 53.6 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
"""
Types used to represent a full function/module as an Abstract Syntax Tree.
Most types are small, and are merely used as tokens in the AST. A tree diagram
has been included below to illustrate the relationships between the AST types.
AST Type Tree
-------------
::
*Basic*
|--->AssignmentBase
| |--->Assignment
| |--->AugmentedAssignment
| |--->AddAugmentedAssignment
| |--->SubAugmentedAssignment
| |--->MulAugmentedAssignment
| |--->DivAugmentedAssignment
| |--->ModAugmentedAssignment
|
|--->CodeBlock
|
|
|--->Token
| |--->Attribute
| |--->For
| |--->String
| | |--->QuotedString
| | |--->Comment
| |--->Type
| | |--->IntBaseType
| | | |--->_SizedIntType
| | | |--->SignedIntType
| | | |--->UnsignedIntType
| | |--->FloatBaseType
| | |--->FloatType
| | |--->ComplexBaseType
| | |--->ComplexType
| |--->Node
| | |--->Variable
| | | |---> Pointer
| | |--->FunctionPrototype
| | |--->FunctionDefinition
| |--->Element
| |--->Declaration
| |--->While
| |--->Scope
| |--->Stream
| |--->Print
| |--->FunctionCall
| |--->BreakToken
| |--->ContinueToken
| |--->NoneToken
|
|--->Statement
|--->Return
Predefined types
----------------
A number of ``Type`` instances are provided in the ``sympy.codegen.ast`` module
for convenience. Perhaps the two most common ones for code-generation (of numeric
codes) are ``float32`` and ``float64`` (known as single and double precision respectively).
There are also precision generic versions of Types (for which the codeprinters selects the
underlying data type at time of printing): ``real``, ``integer``, ``complex_``, ``bool_``.
The other ``Type`` instances defined are:
- ``intc``: Integer type used by C's "int".
- ``intp``: Integer type used by C's "unsigned".
- ``int8``, ``int16``, ``int32``, ``int64``: n-bit integers.
- ``uint8``, ``uint16``, ``uint32``, ``uint64``: n-bit unsigned integers.
- ``float80``: known as "extended precision" on modern x86/amd64 hardware.
- ``complex64``: Complex number represented by two ``float32`` numbers
- ``complex128``: Complex number represented by two ``float64`` numbers
Using the nodes
---------------
It is possible to construct simple algorithms using the AST nodes. Let's construct a loop applying
Newton's method::
>>> from sympy import symbols, cos
>>> from sympy.codegen.ast import While, Assignment, aug_assign, Print
>>> t, dx, x = symbols('tol delta val')
>>> expr = cos(x) - x**3
>>> whl = While(abs(dx) > t, [
... Assignment(dx, -expr/expr.diff(x)),
... aug_assign(x, '+', dx),
... Print([x])
... ])
>>> from sympy.printing import pycode
>>> py_str = pycode(whl)
>>> print(py_str)
while (abs(delta) > tol):
delta = (val**3 - math.cos(val))/(-3*val**2 - math.sin(val))
val += delta
print(val)
>>> import math
>>> tol, val, delta = 1e-5, 0.5, float('inf')
>>> exec(py_str)
1.1121416371
0.909672693737
0.867263818209
0.865477135298
0.865474033111
>>> print('%3.1g' % (math.cos(val) - val**3))
-3e-11
If we want to generate Fortran code for the same while loop we simple call ``fcode``::
>>> from sympy.printing import fcode
>>> print(fcode(whl, standard=2003, source_format='free'))
do while (abs(delta) > tol)
delta = (val**3 - cos(val))/(-3*val**2 - sin(val))
val = val + delta
print *, val
end do
There is a function constructing a loop (or a complete function) like this in
:mod:`sympy.codegen.algorithms`.
"""
from typing import Any, Dict, List
from collections import defaultdict
from sympy import Lt, Le, Ge, Gt
from sympy.core import Symbol, Tuple, Dummy
from sympy.core.basic import Basic
from sympy.core.expr import Expr
from sympy.core.numbers import Float, Integer, oo
from sympy.core.sympify import _sympify, sympify, SympifyError
from sympy.utilities.iterables import iterable
def _mk_Tuple(args):
"""
Create a Sympy Tuple object from an iterable, converting Python strings to
AST strings.
Parameters
==========
args: iterable
Arguments to :class:`sympy.Tuple`.
Returns
=======
sympy.Tuple
"""
args = [String(arg) if isinstance(arg, str) else arg for arg in args]
return Tuple(*args)
class Token(Basic):
""" Base class for the AST types.
Defining fields are set in ``__slots__``. Attributes (defined in __slots__)
are only allowed to contain instances of Basic (unless atomic, see
``String``). The arguments to ``__new__()`` correspond to the attributes in
the order defined in ``__slots__`. The ``defaults`` class attribute is a
dictionary mapping attribute names to their default values.
Subclasses should not need to override the ``__new__()`` method. They may
define a class or static method named ``_construct_<attr>`` for each
attribute to process the value passed to ``__new__()``. Attributes listed
in the class attribute ``not_in_args`` are not passed to :class:`~.Basic`.
"""
__slots__ = ()
defaults = {} # type: Dict[str, Any]
not_in_args = [] # type: List[str]
indented_args = ['body']
@property
def is_Atom(self):
return len(self.__slots__) == 0
@classmethod
def _get_constructor(cls, attr):
""" Get the constructor function for an attribute by name. """
return getattr(cls, '_construct_%s' % attr, lambda x: x)
@classmethod
def _construct(cls, attr, arg):
""" Construct an attribute value from argument passed to ``__new__()``. """
# arg may be ``NoneToken()``, so comparation is done using == instead of ``is`` operator
if arg == None:
return cls.defaults.get(attr, none)
else:
if isinstance(arg, Dummy): # sympy's replace uses Dummy instances
return arg
else:
return cls._get_constructor(attr)(arg)
def __new__(cls, *args, **kwargs):
# Pass through existing instances when given as sole argument
if len(args) == 1 and not kwargs and isinstance(args[0], cls):
return args[0]
if len(args) > len(cls.__slots__):
raise ValueError("Too many arguments (%d), expected at most %d" % (len(args), len(cls.__slots__)))
attrvals = []
# Process positional arguments
for attrname, argval in zip(cls.__slots__, args):
if attrname in kwargs:
raise TypeError('Got multiple values for attribute %r' % attrname)
attrvals.append(cls._construct(attrname, argval))
# Process keyword arguments
for attrname in cls.__slots__[len(args):]:
if attrname in kwargs:
argval = kwargs.pop(attrname)
elif attrname in cls.defaults:
argval = cls.defaults[attrname]
else:
raise TypeError('No value for %r given and attribute has no default' % attrname)
attrvals.append(cls._construct(attrname, argval))
if kwargs:
raise ValueError("Unknown keyword arguments: %s" % ' '.join(kwargs))
# Parent constructor
basic_args = [
val for attr, val in zip(cls.__slots__, attrvals)
if attr not in cls.not_in_args
]
obj = Basic.__new__(cls, *basic_args)
# Set attributes
for attr, arg in zip(cls.__slots__, attrvals):
setattr(obj, attr, arg)
return obj
def __eq__(self, other):
if not isinstance(other, self.__class__):
return False
for attr in self.__slots__:
if getattr(self, attr) != getattr(other, attr):
return False
return True
def _hashable_content(self):
return tuple([getattr(self, attr) for attr in self.__slots__])
def __hash__(self):
return super().__hash__()
def _joiner(self, k, indent_level):
return (',\n' + ' '*indent_level) if k in self.indented_args else ', '
def _indented(self, printer, k, v, *args, **kwargs):
il = printer._context['indent_level']
def _print(arg):
if isinstance(arg, Token):
return printer._print(arg, *args, joiner=self._joiner(k, il), **kwargs)
else:
return printer._print(arg, *args, **kwargs)
if isinstance(v, Tuple):
joined = self._joiner(k, il).join([_print(arg) for arg in v.args])
if k in self.indented_args:
return '(\n' + ' '*il + joined + ',\n' + ' '*(il - 4) + ')'
else:
return ('({0},)' if len(v.args) == 1 else '({0})').format(joined)
else:
return _print(v)
def _sympyrepr(self, printer, *args, joiner=', ', **kwargs):
from sympy.printing.printer import printer_context
exclude = kwargs.get('exclude', ())
values = [getattr(self, k) for k in self.__slots__]
indent_level = printer._context.get('indent_level', 0)
arg_reprs = []
for i, (attr, value) in enumerate(zip(self.__slots__, values)):
if attr in exclude:
continue
# Skip attributes which have the default value
if attr in self.defaults and value == self.defaults[attr]:
continue
ilvl = indent_level + 4 if attr in self.indented_args else 0
with printer_context(printer, indent_level=ilvl):
indented = self._indented(printer, attr, value, *args, **kwargs)
arg_reprs.append(('{1}' if i == 0 else '{0}={1}').format(attr, indented.lstrip()))
return "{}({})".format(self.__class__.__name__, joiner.join(arg_reprs))
_sympystr = _sympyrepr
def __repr__(self): # sympy.core.Basic.__repr__ uses sstr
from sympy.printing import srepr
return srepr(self)
def kwargs(self, exclude=(), apply=None):
""" Get instance's attributes as dict of keyword arguments.
Parameters
==========
exclude : collection of str
Collection of keywords to exclude.
apply : callable, optional
Function to apply to all values.
"""
kwargs = {k: getattr(self, k) for k in self.__slots__ if k not in exclude}
if apply is not None:
return {k: apply(v) for k, v in kwargs.items()}
else:
return kwargs
class BreakToken(Token):
""" Represents 'break' in C/Python ('exit' in Fortran).
Use the premade instance ``break_`` or instantiate manually.
Examples
========
>>> from sympy.printing import ccode, fcode
>>> from sympy.codegen.ast import break_
>>> ccode(break_)
'break'
>>> fcode(break_, source_format='free')
'exit'
"""
break_ = BreakToken()
class ContinueToken(Token):
""" Represents 'continue' in C/Python ('cycle' in Fortran)
Use the premade instance ``continue_`` or instantiate manually.
Examples
========
>>> from sympy.printing import ccode, fcode
>>> from sympy.codegen.ast import continue_
>>> ccode(continue_)
'continue'
>>> fcode(continue_, source_format='free')
'cycle'
"""
continue_ = ContinueToken()
class NoneToken(Token):
""" The AST equivalence of Python's NoneType
The corresponding instance of Python's ``None`` is ``none``.
Examples
========
>>> from sympy.codegen.ast import none, Variable
>>> from sympy.printing.pycode import pycode
>>> print(pycode(Variable('x').as_Declaration(value=none)))
x = None
"""
def __eq__(self, other):
return other is None or isinstance(other, NoneToken)
def _hashable_content(self):
return ()
def __hash__(self):
return super().__hash__()
none = NoneToken()
class AssignmentBase(Basic):
""" Abstract base class for Assignment and AugmentedAssignment.
Attributes:
===========
op : str
Symbol for assignment operator, e.g. "=", "+=", etc.
"""
def __new__(cls, lhs, rhs):
lhs = _sympify(lhs)
rhs = _sympify(rhs)
cls._check_args(lhs, rhs)
return super().__new__(cls, lhs, rhs)
@property
def lhs(self):
return self.args[0]
@property
def rhs(self):
return self.args[1]
@classmethod
def _check_args(cls, lhs, rhs):
""" Check arguments to __new__ and raise exception if any problems found.
Derived classes may wish to override this.
"""
from sympy.matrices.expressions.matexpr import (
MatrixElement, MatrixSymbol)
from sympy.tensor.indexed import Indexed
# Tuple of things that can be on the lhs of an assignment
assignable = (Symbol, MatrixSymbol, MatrixElement, Indexed, Element, Variable)
if not isinstance(lhs, assignable):
raise TypeError("Cannot assign to lhs of type %s." % type(lhs))
# Indexed types implement shape, but don't define it until later. This
# causes issues in assignment validation. For now, matrices are defined
# as anything with a shape that is not an Indexed
lhs_is_mat = hasattr(lhs, 'shape') and not isinstance(lhs, Indexed)
rhs_is_mat = hasattr(rhs, 'shape') and not isinstance(rhs, Indexed)
# If lhs and rhs have same structure, then this assignment is ok
if lhs_is_mat:
if not rhs_is_mat:
raise ValueError("Cannot assign a scalar to a matrix.")
elif lhs.shape != rhs.shape:
raise ValueError("Dimensions of lhs and rhs don't align.")
elif rhs_is_mat and not lhs_is_mat:
raise ValueError("Cannot assign a matrix to a scalar.")
class Assignment(AssignmentBase):
"""
Represents variable assignment for code generation.
Parameters
==========
lhs : Expr
Sympy object representing the lhs of the expression. These should be
singular objects, such as one would use in writing code. Notable types
include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that
subclass these types are also supported.
rhs : Expr
Sympy object representing the rhs of the expression. This can be any
type, provided its shape corresponds to that of the lhs. For example,
a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as
the dimensions will not align.
Examples
========
>>> from sympy import symbols, MatrixSymbol, Matrix
>>> from sympy.codegen.ast import Assignment
>>> x, y, z = symbols('x, y, z')
>>> Assignment(x, y)
Assignment(x, y)
>>> Assignment(x, 0)
Assignment(x, 0)
>>> A = MatrixSymbol('A', 1, 3)
>>> mat = Matrix([x, y, z]).T
>>> Assignment(A, mat)
Assignment(A, Matrix([[x, y, z]]))
>>> Assignment(A[0, 1], x)
Assignment(A[0, 1], x)
"""
op = ':='
class AugmentedAssignment(AssignmentBase):
"""
Base class for augmented assignments.
Attributes:
===========
binop : str
Symbol for binary operation being applied in the assignment, such as "+",
"*", etc.
"""
binop = None # type: str
@property
def op(self):
return self.binop + '='
class AddAugmentedAssignment(AugmentedAssignment):
binop = '+'
class SubAugmentedAssignment(AugmentedAssignment):
binop = '-'
class MulAugmentedAssignment(AugmentedAssignment):
binop = '*'
class DivAugmentedAssignment(AugmentedAssignment):
binop = '/'
class ModAugmentedAssignment(AugmentedAssignment):
binop = '%'
# Mapping from binary op strings to AugmentedAssignment subclasses
augassign_classes = {
cls.binop: cls for cls in [
AddAugmentedAssignment, SubAugmentedAssignment, MulAugmentedAssignment,
DivAugmentedAssignment, ModAugmentedAssignment
]
}
def aug_assign(lhs, op, rhs):
"""
Create 'lhs op= rhs'.
Represents augmented variable assignment for code generation. This is a
convenience function. You can also use the AugmentedAssignment classes
directly, like AddAugmentedAssignment(x, y).
Parameters
==========
lhs : Expr
Sympy object representing the lhs of the expression. These should be
singular objects, such as one would use in writing code. Notable types
include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that
subclass these types are also supported.
op : str
Operator (+, -, /, \\*, %).
rhs : Expr
Sympy object representing the rhs of the expression. This can be any
type, provided its shape corresponds to that of the lhs. For example,
a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as
the dimensions will not align.
Examples
========
>>> from sympy import symbols
>>> from sympy.codegen.ast import aug_assign
>>> x, y = symbols('x, y')
>>> aug_assign(x, '+', y)
AddAugmentedAssignment(x, y)
"""
if op not in augassign_classes:
raise ValueError("Unrecognized operator %s" % op)
return augassign_classes[op](lhs, rhs)
class CodeBlock(Basic):
"""
Represents a block of code
For now only assignments are supported. This restriction will be lifted in
the future.
Useful attributes on this object are:
``left_hand_sides``:
Tuple of left-hand sides of assignments, in order.
``left_hand_sides``:
Tuple of right-hand sides of assignments, in order.
``free_symbols``: Free symbols of the expressions in the right-hand sides
which do not appear in the left-hand side of an assignment.
Useful methods on this object are:
``topological_sort``:
Class method. Return a CodeBlock with assignments
sorted so that variables are assigned before they
are used.
``cse``:
Return a new CodeBlock with common subexpressions eliminated and
pulled out as assignments.
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;
"""
def __new__(cls, *args):
left_hand_sides = []
right_hand_sides = []
for i in args:
if isinstance(i, Assignment):
lhs, rhs = i.args
left_hand_sides.append(lhs)
right_hand_sides.append(rhs)
obj = Basic.__new__(cls, *args)
obj.left_hand_sides = Tuple(*left_hand_sides)
obj.right_hand_sides = Tuple(*right_hand_sides)
return obj
def __iter__(self):
return iter(self.args)
def _sympyrepr(self, printer, *args, **kwargs):
il = printer._context.get('indent_level', 0)
joiner = ',\n' + ' '*il
joined = joiner.join(map(printer._print, self.args))
return ('{}(\n'.format(' '*(il-4) + self.__class__.__name__,) +
' '*il + joined + '\n' + ' '*(il - 4) + ')')
_sympystr = _sympyrepr
@property
def free_symbols(self):
return super().free_symbols - set(self.left_hand_sides)
@classmethod
def topological_sort(cls, assignments):
"""
Return a CodeBlock with topologically sorted assignments so that
variables are assigned before they are used.
The existing order of assignments is preserved as much as possible.
This function assumes that variables are assigned to only once.
This is a class constructor so that the default constructor for
CodeBlock can error when variables are used before they are assigned.
Examples
========
>>> from sympy import symbols
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y, z = symbols('x y z')
>>> assignments = [
... Assignment(x, y + z),
... Assignment(y, z + 1),
... Assignment(z, 2),
... ]
>>> CodeBlock.topological_sort(assignments)
CodeBlock(
Assignment(z, 2),
Assignment(y, z + 1),
Assignment(x, y + z)
)
"""
from sympy.utilities.iterables import topological_sort
if not all(isinstance(i, Assignment) for i in assignments):
# Will support more things later
raise NotImplementedError("CodeBlock.topological_sort only supports Assignments")
if any(isinstance(i, AugmentedAssignment) for i in assignments):
raise NotImplementedError("CodeBlock.topological_sort doesn't yet work with AugmentedAssignments")
# Create a graph where the nodes are assignments and there is a directed edge
# between nodes that use a variable and nodes that assign that
# variable, like
# [(x := 1, y := x + 1), (x := 1, z := y + z), (y := x + 1, z := y + z)]
# If we then topologically sort these nodes, they will be in
# assignment order, like
# x := 1
# y := x + 1
# z := y + z
# A = The nodes
#
# enumerate keeps nodes in the same order they are already in if
# possible. It will also allow us to handle duplicate assignments to
# the same variable when those are implemented.
A = list(enumerate(assignments))
# var_map = {variable: [nodes for which this variable is assigned to]}
# like {x: [(1, x := y + z), (4, x := 2 * w)], ...}
var_map = defaultdict(list)
for node in A:
i, a = node
var_map[a.lhs].append(node)
# E = Edges in the graph
E = []
for dst_node in A:
i, a = dst_node
for s in a.rhs.free_symbols:
for src_node in var_map[s]:
E.append((src_node, dst_node))
ordered_assignments = topological_sort([A, E])
# De-enumerate the result
return cls(*[a for i, a in ordered_assignments])
def cse(self, symbols=None, optimizations=None, postprocess=None,
order='canonical'):
"""
Return a new code block with common subexpressions eliminated
See the docstring of :func:`sympy.simplify.cse_main.cse` for more
information.
Examples
========
>>> from sympy import symbols, sin
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y, z = symbols('x y z')
>>> c = CodeBlock(
... Assignment(x, 1),
... Assignment(y, sin(x) + 1),
... Assignment(z, sin(x) - 1),
... )
...
>>> c.cse()
CodeBlock(
Assignment(x, 1),
Assignment(x0, sin(x)),
Assignment(y, x0 + 1),
Assignment(z, x0 - 1)
)
"""
from sympy.simplify.cse_main import cse
from sympy.utilities.iterables import numbered_symbols, filter_symbols
# Check that the CodeBlock only contains assignments to unique variables
if not all(isinstance(i, Assignment) for i in self.args):
# Will support more things later
raise NotImplementedError("CodeBlock.cse only supports Assignments")
if any(isinstance(i, AugmentedAssignment) for i in self.args):
raise NotImplementedError("CodeBlock.cse doesn't yet work with AugmentedAssignments")
for i, lhs in enumerate(self.left_hand_sides):
if lhs in self.left_hand_sides[:i]:
raise NotImplementedError("Duplicate assignments to the same "
"variable are not yet supported (%s)" % lhs)
# Ensure new symbols for subexpressions do not conflict with existing
existing_symbols = self.atoms(Symbol)
if symbols is None:
symbols = numbered_symbols()
symbols = filter_symbols(symbols, existing_symbols)
replacements, reduced_exprs = cse(list(self.right_hand_sides),
symbols=symbols, optimizations=optimizations, postprocess=postprocess,
order=order)
new_block = [Assignment(var, expr) for var, expr in
zip(self.left_hand_sides, reduced_exprs)]
new_assignments = [Assignment(var, expr) for var, expr in replacements]
return self.topological_sort(new_assignments + new_block)
class For(Token):
"""Represents a 'for-loop' in the code.
Expressions are of the form:
"for target in iter:
body..."
Parameters
==========
target : symbol
iter : iterable
body : CodeBlock or iterable
! When passed an iterable it is used to instantiate a CodeBlock.
Examples
========
>>> from sympy import symbols, Range
>>> from sympy.codegen.ast import aug_assign, For
>>> x, i, j, k = symbols('x i j k')
>>> for_i = For(i, Range(10), [aug_assign(x, '+', i*j*k)])
>>> for_i # doctest: -NORMALIZE_WHITESPACE
For(i, iterable=Range(0, 10, 1), body=CodeBlock(
AddAugmentedAssignment(x, i*j*k)
))
>>> for_ji = For(j, Range(7), [for_i])
>>> for_ji # doctest: -NORMALIZE_WHITESPACE
For(j, iterable=Range(0, 7, 1), body=CodeBlock(
For(i, iterable=Range(0, 10, 1), body=CodeBlock(
AddAugmentedAssignment(x, i*j*k)
))
))
>>> for_kji =For(k, Range(5), [for_ji])
>>> for_kji # doctest: -NORMALIZE_WHITESPACE
For(k, iterable=Range(0, 5, 1), body=CodeBlock(
For(j, iterable=Range(0, 7, 1), body=CodeBlock(
For(i, iterable=Range(0, 10, 1), body=CodeBlock(
AddAugmentedAssignment(x, i*j*k)
))
))
))
"""
__slots__ = ('target', 'iterable', 'body')
_construct_target = staticmethod(_sympify)
@classmethod
def _construct_body(cls, itr):
if isinstance(itr, CodeBlock):
return itr
else:
return CodeBlock(*itr)
@classmethod
def _construct_iterable(cls, itr):
if not iterable(itr):
raise TypeError("iterable must be an iterable")
if isinstance(itr, list): # _sympify errors on lists because they are mutable
itr = tuple(itr)
return _sympify(itr)
class String(Token):
""" SymPy object representing a string.
Atomic object which is not an expression (as opposed to Symbol).
Parameters
==========
text : str
Examples
========
>>> from sympy.codegen.ast import String
>>> f = String('foo')
>>> f
foo
>>> str(f)
'foo'
>>> f.text
'foo'
>>> print(repr(f))
String('foo')
"""
__slots__ = ('text',)
not_in_args = ['text']
is_Atom = True
@classmethod
def _construct_text(cls, text):
if not isinstance(text, str):
raise TypeError("Argument text is not a string type.")
return text
def _sympystr(self, printer, *args, **kwargs):
return self.text
class QuotedString(String):
""" Represents a string which should be printed with quotes. """
class Comment(String):
""" Represents a comment. """
class Node(Token):
""" Subclass of Token, carrying the attribute 'attrs' (Tuple)
Examples
========
>>> from sympy.codegen.ast import Node, value_const, pointer_const
>>> n1 = Node([value_const])
>>> n1.attr_params('value_const') # get the parameters of attribute (by name)
()
>>> from sympy.codegen.fnodes import dimension
>>> n2 = Node([value_const, dimension(5, 3)])
>>> n2.attr_params(value_const) # get the parameters of attribute (by Attribute instance)
()
>>> n2.attr_params('dimension') # get the parameters of attribute (by name)
(5, 3)
>>> n2.attr_params(pointer_const) is None
True
"""
__slots__ = ('attrs',)
defaults = {'attrs': Tuple()} # type: Dict[str, Any]
_construct_attrs = staticmethod(_mk_Tuple)
def attr_params(self, looking_for):
""" Returns the parameters of the Attribute with name ``looking_for`` in self.attrs """
for attr in self.attrs:
if str(attr.name) == str(looking_for):
return attr.parameters
class Type(Token):
""" Represents a type.
The naming is a super-set of NumPy naming. Type has a classmethod
``from_expr`` which offer type deduction. It also has a method
``cast_check`` which casts the argument to its type, possibly raising an
exception if rounding error is not within tolerances, or if the value is not
representable by the underlying data type (e.g. unsigned integers).
Parameters
==========
name : str
Name of the type, e.g. ``object``, ``int16``, ``float16`` (where the latter two
would use the ``Type`` sub-classes ``IntType`` and ``FloatType`` respectively).
If a ``Type`` instance is given, the said instance is returned.
Examples
========
>>> from sympy.codegen.ast import Type
>>> t = Type.from_expr(42)
>>> t
integer
>>> print(repr(t))
IntBaseType(String('integer'))
>>> from sympy.codegen.ast import uint8
>>> uint8.cast_check(-1) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
ValueError: Minimum value for data type bigger than new value.
>>> from sympy.codegen.ast import float32
>>> v6 = 0.123456
>>> float32.cast_check(v6)
0.123456
>>> v10 = 12345.67894
>>> float32.cast_check(v10) # doctest: +ELLIPSIS
Traceback (most recent call last):
...
ValueError: Casting gives a significantly different value.
>>> boost_mp50 = Type('boost::multiprecision::cpp_dec_float_50')
>>> from sympy.printing import cxxcode
>>> from sympy.codegen.ast import Declaration, Variable
>>> cxxcode(Declaration(Variable('x', type=boost_mp50)))
'boost::multiprecision::cpp_dec_float_50 x'
References
==========
.. [1] https://docs.scipy.org/doc/numpy/user/basics.types.html
"""
__slots__ = ('name',)
_construct_name = String
def _sympystr(self, printer, *args, **kwargs):
return str(self.name)
@classmethod
def from_expr(cls, expr):
""" Deduces type from an expression or a ``Symbol``.
Parameters
==========
expr : number or SymPy object
The type will be deduced from type or properties.
Examples
========