cbackend.py 24.6 KB
Newer Older
Martin Bauer's avatar
Martin Bauer committed
1
from collections import namedtuple
2
from typing import Set
3
4
5
6

import jinja2
import sympy as sp
from sympy.core import S
7
from sympy.printing.ccode import C89CodePrinter
8

9
10
11
from pystencils.astnodes import (DestructuringBindingsForFieldClass,
                                 KernelFunction, Node)
from pystencils.cpu.vectorization import vec_all, vec_any
12
from pystencils.data_types import (PointerType, VectorType, address_of,
13
                                   cast_func, create_type,
14
                                   get_type_of_expression,
15
16
17
18
19
20
21
                                   reinterpret_cast_func, vector_memory_access)
from pystencils.fast_approximation import (fast_division, fast_inv_sqrt,
                                           fast_sqrt)
from pystencils.integer_functions import (bit_shift_left, bit_shift_right,
                                          bitwise_and, bitwise_or, bitwise_xor,
                                          int_div, int_power_of_2, modulo_ceil)
from pystencils.kernelparameters import FieldPointerSymbol
22

Martin Bauer's avatar
Martin Bauer committed
23
24
try:
    from sympy.printing.ccode import C99CodePrinter as CCodePrinter
Martin Bauer's avatar
Martin Bauer committed
25
26
except ImportError:
    from sympy.printing.ccode import CCodePrinter  # for sympy versions < 1.1
Martin Bauer's avatar
Martin Bauer committed
27

28

29
__all__ = ['generate_c', 'CustomCodeNode', 'PrintNode', 'get_headers', 'CustomSympyPrinter']
30

Martin Bauer's avatar
Martin Bauer committed
31

32
33
KERNCRAFT_NO_TERNARY_MODE = False

Martin Bauer's avatar
Fixes    
Martin Bauer committed
34

35
def generate_c(ast_node: Node, signature_only: bool = False, dialect='c') -> str:
Martin Bauer's avatar
Martin Bauer committed
36
37
38
39
40
41
42
43
44
    """Prints an abstract syntax tree node as C or CUDA code.

    This function does not need to distinguish between C, C++ or CUDA code, it just prints 'C-like' code as encoded
    in the abstract syntax tree (AST). The AST is built differently for C or CUDA by calling different create_kernel
    functions.

    Args:
        ast_node:
        signature_only:
45
        dialect: 'c' or 'cuda'
Martin Bauer's avatar
Martin Bauer committed
46
47
    Returns:
        C-like code for the ast node and its descendants
Martin Bauer's avatar
Martin Bauer committed
48
    """
49
50
51
52
53
54
    global_declarations = get_global_declarations(ast_node)
    for d in global_declarations:
        if hasattr(ast_node, "global_variables"):
            ast_node.global_variables.update(d.symbols_defined)
        else:
            ast_node.global_variables = d.symbols_defined
55
    printer = CBackend(signature_only=signature_only,
56
57
                       vector_instruction_set=ast_node.instruction_set,
                       dialect=dialect)
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
    code = printer(ast_node)
    if not signature_only and isinstance(ast_node, KernelFunction):
        code = "\n" + code
        for declaration in global_declarations:
            code = printer(declaration) + "\n" + code

    return code


def get_global_declarations(ast):
    global_declarations = []

    def visit_node(sub_ast):
        if hasattr(sub_ast, "required_global_declarations"):
            nonlocal global_declarations
            global_declarations += sub_ast.required_global_declarations

        if hasattr(sub_ast, "args"):
            for node in sub_ast.args:
                visit_node(node)

    visit_node(ast)

    return set(global_declarations)
82
83


Martin Bauer's avatar
Martin Bauer committed
84
85
def get_headers(ast_node: Node) -> Set[str]:
    """Return a set of header files, necessary to compile the printed C-like code."""
86
87
    headers = set()

Martin Bauer's avatar
Martin Bauer committed
88
89
90
    if isinstance(ast_node, KernelFunction) and ast_node.instruction_set:
        headers.update(ast_node.instruction_set['headers'])

Martin Bauer's avatar
Martin Bauer committed
91
92
93
    if hasattr(ast_node, 'headers'):
        headers.update(ast_node.headers)
    for a in ast_node.args:
94
        if isinstance(a, Node):
Martin Bauer's avatar
Martin Bauer committed
95
            headers.update(get_headers(a))
96
97

    return headers
98
99


100
101
102
# --------------------------------------- Backend Specific Nodes -------------------------------------------------------


103
class CustomCodeNode(Node):
Martin Bauer's avatar
Martin Bauer committed
104
    def __init__(self, code, symbols_read, symbols_defined, parent=None):
105
        super(CustomCodeNode, self).__init__(parent=parent)
106
        self._code = "\n" + code
107
108
        self._symbols_read = set(symbols_read)
        self._symbols_defined = set(symbols_defined)
109
        self.headers = []
110

111
    def get_code(self, dialect, vector_instruction_set):
112
113
114
115
116
117
118
        return self._code

    @property
    def args(self):
        return []

    @property
Martin Bauer's avatar
Martin Bauer committed
119
    def symbols_defined(self):
120
        return self._symbols_defined
121
122

    @property
Martin Bauer's avatar
Martin Bauer committed
123
    def undefined_symbols(self):
124
        return self._symbols_read - self._symbols_defined
125
126


127
class PrintNode(CustomCodeNode):
Martin Bauer's avatar
Martin Bauer committed
128
129
130
131
    # noinspection SpellCheckingInspection
    def __init__(self, symbol_to_print):
        code = '\nstd::cout << "%s  =  " << %s << std::endl; \n' % (symbol_to_print.name, symbol_to_print.name)
        super(PrintNode, self).__init__(code, symbols_read=[symbol_to_print], symbols_defined=set())
132
        self.headers.append("<iostream>")
133
134
135
136


# ------------------------------------------- Printer ------------------------------------------------------------------

137

Martin Bauer's avatar
Martin Bauer committed
138
139
# noinspection PyPep8Naming
class CBackend:
140

Martin Bauer's avatar
Martin Bauer committed
141
    def __init__(self, sympy_printer=None, signature_only=False, vector_instruction_set=None, dialect='c'):
Martin Bauer's avatar
Martin Bauer committed
142
143
        if sympy_printer is None:
            if vector_instruction_set is not None:
144
                self.sympy_printer = VectorizedCustomSympyPrinter(vector_instruction_set, dialect)
145
            else:
146
                self.sympy_printer = CustomSympyPrinter(dialect)
147
        else:
Martin Bauer's avatar
Martin Bauer committed
148
            self.sympy_printer = sympy_printer
149

150
        self._vector_instruction_set = vector_instruction_set
151
        self._indent = "   "
152
        self._dialect = dialect
Martin Bauer's avatar
Martin Bauer committed
153
        self._signatureOnly = signature_only
154
155

    def __call__(self, node):
Martin Bauer's avatar
Martin Bauer committed
156
        prev_is = VectorType.instruction_set
157
        VectorType.instruction_set = self._vector_instruction_set
158
        result = str(self._print(node))
Martin Bauer's avatar
Martin Bauer committed
159
        VectorType.instruction_set = prev_is
160
        return result
161
162
163

    def _print(self, node):
        for cls in type(node).__mro__:
Martin Bauer's avatar
Martin Bauer committed
164
165
166
167
            method_name = "_print_" + cls.__name__
            if hasattr(self, method_name):
                return getattr(self, method_name)(node)
        raise NotImplementedError("CBackend does not support node of type " + str(type(node)))
168
169

    def _print_KernelFunction(self, node):
170
        function_arguments = ["%s %s" % (str(s.symbol.dtype), s.symbol.name) for s in node.get_parameters()]
171
172
173
174
175
176
177
        launch_bounds = ""
        if self._dialect == 'cuda':
            max_threads = node.indexing.max_threads_per_block()
            if max_threads:
                launch_bounds = "__launch_bounds__({}) ".format(max_threads)
        func_declaration = "FUNC_PREFIX %svoid %s(%s)" % (launch_bounds, node.function_name,
                                                          ", ".join(function_arguments))
178
        if self._signatureOnly:
Martin Bauer's avatar
Martin Bauer committed
179
            return func_declaration
180

181
        body = self._print(node.body)
Martin Bauer's avatar
Martin Bauer committed
182
        return func_declaration + "\n" + body
183
184

    def _print_Block(self, node):
Martin Bauer's avatar
Martin Bauer committed
185
186
        block_contents = "\n".join([self._print(child) for child in node.args])
        return "{\n%s\n}" % (self._indent + self._indent.join(block_contents.splitlines(True)))
187
188

    def _print_PragmaBlock(self, node):
Martin Bauer's avatar
Martin Bauer committed
189
        return "%s\n%s" % (node.pragma_line, self._print_Block(node))
190
191

    def _print_LoopOverCoordinate(self, node):
Martin Bauer's avatar
Martin Bauer committed
192
        counter_symbol = node.loop_counter_name
Martin Bauer's avatar
Martin Bauer committed
193
194
195
196
        start = "int %s = %s" % (counter_symbol, self.sympy_printer.doprint(node.start))
        condition = "%s < %s" % (counter_symbol, self.sympy_printer.doprint(node.stop))
        update = "%s += %s" % (counter_symbol, self.sympy_printer.doprint(node.step),)
        loop_str = "for (%s; %s; %s)" % (start, condition, update)
197

Martin Bauer's avatar
Martin Bauer committed
198
        prefix = "\n".join(node.prefix_lines)
199
200
        if prefix:
            prefix += "\n"
Martin Bauer's avatar
Martin Bauer committed
201
        return "%s%s\n%s" % (prefix, loop_str, self._print(node.body))
202
203

    def _print_SympyAssignment(self, node):
Martin Bauer's avatar
Martin Bauer committed
204
205
        if node.is_declaration:
            data_type = "const " + str(node.lhs.dtype) + " " if node.is_const else str(node.lhs.dtype) + " "
206
207
            return "%s%s = %s;" % (data_type, self.sympy_printer.doprint(node.lhs),
                                   self.sympy_printer.doprint(node.rhs))
208
        else:
Martin Bauer's avatar
Martin Bauer committed
209
            lhs_type = get_type_of_expression(node.lhs)
Martin Bauer's avatar
Martin Bauer committed
210
211
212
213
214
215
            if type(lhs_type) is VectorType and isinstance(node.lhs, cast_func):
                arg, data_type, aligned, nontemporal = node.lhs.args
                instr = 'storeU'
                if aligned:
                    instr = 'stream' if nontemporal else 'storeA'

216
217
218
219
220
221
                rhs_type = get_type_of_expression(node.rhs)
                if type(rhs_type) is not VectorType:
                    rhs = cast_func(node.rhs, VectorType(rhs_type))
                else:
                    rhs = node.rhs

222
223
                return self._vector_instruction_set[instr].format("&" + self.sympy_printer.doprint(node.lhs.args[0]),
                                                                  self.sympy_printer.doprint(rhs)) + ';'
224
            else:
Martin Bauer's avatar
Martin Bauer committed
225
                return "%s = %s;" % (self.sympy_printer.doprint(node.lhs), self.sympy_printer.doprint(node.rhs))
226
227

    def _print_TemporaryMemoryAllocation(self, node):
228
        align = 64
Martin Bauer's avatar
Martin Bauer committed
229
230
231
232
233
234
        np_dtype = node.symbol.dtype.base_type.numpy_dtype
        required_size = np_dtype.itemsize * node.size + align
        size = modulo_ceil(required_size, align)
        code = "{dtype} {name}=({dtype})aligned_alloc({align}, {size}) + {offset};"
        return code.format(dtype=node.symbol.dtype,
                           name=self.sympy_printer.doprint(node.symbol.name),
235
                           size=self.sympy_printer.doprint(size),
Martin Bauer's avatar
Martin Bauer committed
236
237
                           offset=int(node.offset(align)),
                           align=align)
238
239

    def _print_TemporaryMemoryFree(self, node):
240
        align = 64
Martin Bauer's avatar
Martin Bauer committed
241
        return "free(%s - %d);" % (self.sympy_printer.doprint(node.symbol.name), node.offset(align))
242

Martin Bauer's avatar
Martin Bauer committed
243
244
245
246
247
248
    def _print_SkipIteration(self, _):
        if self._dialect == 'cuda':
            return "return;"
        else:
            return "continue;"

249
250
    def _print_CustomCodeNode(self, node):
        return node.get_code(self._dialect, self._vector_instruction_set)
251

252
    def _print_Conditional(self, node):
253
254
255
        cond_type = get_type_of_expression(node.condition_expr)
        if isinstance(cond_type, VectorType):
            raise ValueError("Problem with Conditional inside vectorized loop - use vec_any or vec_all")
Martin Bauer's avatar
Martin Bauer committed
256
257
        condition_expr = self.sympy_printer.doprint(node.condition_expr)
        true_block = self._print_Block(node.true_block)
Martin Bauer's avatar
Martin Bauer committed
258
        result = "if (%s)\n%s " % (condition_expr, true_block)
Martin Bauer's avatar
Martin Bauer committed
259
260
        if node.false_block:
            false_block = self._print_Block(node.false_block)
Martin Bauer's avatar
Martin Bauer committed
261
            result += "else " + false_block
262
263
        return result

264
265
266
267
268
269
270
271
272
273
    def _print_DestructuringBindingsForFieldClass(self, node: Node):
        # Define all undefined symbols
        undefined_field_symbols = node.symbols_defined
        destructuring_bindings = ["%s = %s.%s%s;" %
                                  (u.name,
                                   u.field_name if hasattr(u, 'field_name') else u.field_names[0],
                                   DestructuringBindingsForFieldClass.CLASS_TO_MEMBER_DICT[u.__class__],
                                   "" if type(u) == FieldPointerSymbol else ("[%i]" % u.coordinate))
                                  for u in undefined_field_symbols
                                  ]
274
        destructuring_bindings.sort()  # only for code aesthetics
275
276
277
278
279
280
281
282
283
284
285
286
287
        template = jinja2.Template(
            """{
   {% for binding in bindings -%}
   {{ binding | indent(3) }}
   {% endfor -%}
   {{ block | indent(3) }}
}

""")
        code = template.render(bindings=destructuring_bindings,
                               block=self._print(node.body))
        return code

288
289
290
291

# ------------------------------------------ Helper function & classes -------------------------------------------------


Martin Bauer's avatar
Martin Bauer committed
292
# noinspection PyPep8Naming
293
class CustomSympyPrinter(CCodePrinter):
Martin Bauer's avatar
Martin Bauer committed
294

295
    def __init__(self, dialect):
Martin Bauer's avatar
Martin Bauer committed
296
        super(CustomSympyPrinter, self).__init__()
297
        self._float_type = create_type("float32")
298
        self._dialect = dialect
299
300
301
302
        if 'Min' in self.known_functions:
            del self.known_functions['Min']
        if 'Max' in self.known_functions:
            del self.known_functions['Max']
Martin Bauer's avatar
Martin Bauer committed
303

304
305
306
    def _print_Pow(self, expr):
        """Don't use std::pow function, for small integer exponents, write as multiplication"""
        if expr.exp.is_integer and expr.exp.is_number and 0 < expr.exp < 8:
307
            return "(" + self._print(sp.Mul(*[expr.base] * expr.exp, evaluate=False)) + ")"
308
309
        elif expr.exp.is_integer and expr.exp.is_number and - 8 < expr.exp < 0:
            return "1 / ({})".format(self._print(sp.Mul(*[expr.base] * (-expr.exp), evaluate=False)))
310
311
312
313
314
        else:
            return super(CustomSympyPrinter, self)._print_Pow(expr)

    def _print_Rational(self, expr):
        """Evaluate all rationals i.e. print 0.25 instead of 1.0/4.0"""
Martin Bauer's avatar
Martin Bauer committed
315
316
        res = str(expr.evalf().num)
        return res
317
318
319
320
321
322
323
324

    def _print_Equality(self, expr):
        """Equality operator is not printable in default printer"""
        return '((' + self._print(expr.lhs) + ") == (" + self._print(expr.rhs) + '))'

    def _print_Piecewise(self, expr):
        """Print piecewise in one line (remove newlines)"""
        result = super(CustomSympyPrinter, self)._print_Piecewise(expr)
Martin Bauer's avatar
Martin Bauer committed
325
326
        return result.replace("\n", "")

327
    def _print_Function(self, expr):
328
        infix_functions = {
Martin Bauer's avatar
Martin Bauer committed
329
330
331
332
333
            bitwise_xor: '^',
            bit_shift_right: '>>',
            bit_shift_left: '<<',
            bitwise_or: '|',
            bitwise_and: '&',
Martin Bauer's avatar
Martin Bauer committed
334
        }
Martin Bauer's avatar
Martin Bauer committed
335
336
        if hasattr(expr, 'to_c'):
            return expr.to_c(self._print)
337
338
339
        if isinstance(expr, reinterpret_cast_func):
            arg, data_type = expr.args
            return "*((%s)(& %s))" % (PointerType(data_type, restrict=False), self._print(arg))
340
341
342
        elif isinstance(expr, address_of):
            assert len(expr.args) == 1, "address_of must only have one argument"
            return "&(%s)" % self._print(expr.args[0])
343
        elif isinstance(expr, cast_func):
Martin Bauer's avatar
Martin Bauer committed
344
            arg, data_type = expr.args
345
346
347
            if isinstance(arg, sp.Number):
                return self._typed_number(arg, data_type)
            else:
348
349
350
351
352
353
354
355
356
357
358
                return "((%s)(%s))" % (data_type, self._print(arg))
        elif isinstance(expr, fast_division):
            if self._dialect == "cuda":
                return "__fdividef(%s, %s)" % tuple(self._print(a) for a in expr.args)
            else:
                return "({})".format(self._print(expr.args[0] / expr.args[1]))
        elif isinstance(expr, fast_sqrt):
            if self._dialect == "cuda":
                return "__fsqrt_rn(%s)" % tuple(self._print(a) for a in expr.args)
            else:
                return "({})".format(self._print(sp.sqrt(expr.args[0])))
359
360
        elif isinstance(expr, vec_any) or isinstance(expr, vec_all):
            return self._print(expr.args[0])
361
362
363
364
365
        elif isinstance(expr, fast_inv_sqrt):
            if self._dialect == "cuda":
                return "__frsqrt_rn(%s)" % tuple(self._print(a) for a in expr.args)
            else:
                return "({})".format(self._print(1 / sp.sqrt(expr.args[0])))
366
367
        elif expr.func in infix_functions:
            return "(%s %s %s)" % (self._print(expr.args[0]), infix_functions[expr.func], self._print(expr.args[1]))
368
369
370
371
        elif expr.func == int_power_of_2:
            return "(1 << (%s))" % (self._print(expr.args[0]))
        elif expr.func == int_div:
            return "((%s) / (%s))" % (self._print(expr.args[0]), self._print(expr.args[1]))
372
        else:
373
            return super(CustomSympyPrinter, self)._print_Function(expr)
Martin Bauer's avatar
Martin Bauer committed
374

375
376
    def _typed_number(self, number, dtype):
        res = self._print(number)
377
        if dtype.is_float():
378
379
380
381
382
383
384
385
            if dtype == self._float_type:
                if '.' not in res:
                    res += ".0f"
                else:
                    res += "f"
            return res
        else:
            return res
386

387
388
389
    _print_Max = C89CodePrinter._print_Max
    _print_Min = C89CodePrinter._print_Min

390

Martin Bauer's avatar
Martin Bauer committed
391
# noinspection PyPep8Naming
392
393
394
class VectorizedCustomSympyPrinter(CustomSympyPrinter):
    SummandInfo = namedtuple("SummandInfo", ['sign', 'term'])

395
396
    def __init__(self, instruction_set, dialect):
        super(VectorizedCustomSympyPrinter, self).__init__(dialect=dialect)
Martin Bauer's avatar
Martin Bauer committed
397
        self.instruction_set = instruction_set
398

Martin Bauer's avatar
Martin Bauer committed
399
400
401
402
    def _scalarFallback(self, func_name, expr, *args, **kwargs):
        expr_type = get_type_of_expression(expr)
        if type(expr_type) is not VectorType:
            return getattr(super(VectorizedCustomSympyPrinter, self), func_name)(expr, *args, **kwargs)
403
        else:
Martin Bauer's avatar
Martin Bauer committed
404
            assert self.instruction_set['width'] == expr_type.width
405
406
            return None

407
    def _print_Function(self, expr):
408
        if isinstance(expr, vector_memory_access):
Martin Bauer's avatar
Martin Bauer committed
409
410
411
            arg, data_type, aligned, _ = expr.args
            instruction = self.instruction_set['loadA'] if aligned else self.instruction_set['loadU']
            return instruction.format("& " + self._print(arg))
412
        elif isinstance(expr, cast_func):
Martin Bauer's avatar
Martin Bauer committed
413
414
            arg, data_type = expr.args
            if type(data_type) is VectorType:
Martin Bauer's avatar
Martin Bauer committed
415
                return self.instruction_set['makeVec'].format(self._print(arg))
416
        elif expr.func == fast_division:
417
418
            result = self._scalarFallback('_print_Function', expr)
            if not result:
419
420
                result = self.instruction_set['/'].format(self._print(expr.args[0]), self._print(expr.args[1]))
            return result
421
422
423
        elif expr.func == fast_sqrt:
            return "({})".format(self._print(sp.sqrt(expr.args[0])))
        elif expr.func == fast_inv_sqrt:
424
425
426
427
428
429
            result = self._scalarFallback('_print_Function', expr)
            if not result:
                if self.instruction_set['rsqrt']:
                    return self.instruction_set['rsqrt'].format(self._print(expr.args[0]))
                else:
                    return "({})".format(self._print(1 / sp.sqrt(expr.args[0])))
430
431
432
433
434
435
436
437
438
439
440
441
442
        elif isinstance(expr, vec_any):
            expr_type = get_type_of_expression(expr.args[0])
            if type(expr_type) is not VectorType:
                return self._print(expr.args[0])
            else:
                return self.instruction_set['any'].format(self._print(expr.args[0]))
        elif isinstance(expr, vec_all):
            expr_type = get_type_of_expression(expr.args[0])
            if type(expr_type) is not VectorType:
                return self._print(expr.args[0])
            else:
                return self.instruction_set['all'].format(self._print(expr.args[0]))

443
444
        return super(VectorizedCustomSympyPrinter, self)._print_Function(expr)

445
446
447
448
449
    def _print_And(self, expr):
        result = self._scalarFallback('_print_And', expr)
        if result:
            return result

Martin Bauer's avatar
Martin Bauer committed
450
451
452
453
        arg_strings = [self._print(a) for a in expr.args]
        assert len(arg_strings) > 0
        result = arg_strings[0]
        for item in arg_strings[1:]:
Martin Bauer's avatar
Martin Bauer committed
454
            result = self.instruction_set['&'].format(result, item)
455
456
457
458
459
460
461
        return result

    def _print_Or(self, expr):
        result = self._scalarFallback('_print_Or', expr)
        if result:
            return result

Martin Bauer's avatar
Martin Bauer committed
462
463
464
465
        arg_strings = [self._print(a) for a in expr.args]
        assert len(arg_strings) > 0
        result = arg_strings[0]
        for item in arg_strings[1:]:
Martin Bauer's avatar
Martin Bauer committed
466
            result = self.instruction_set['|'].format(result, item)
467
468
        return result

469
    def _print_Add(self, expr, order=None):
470
471
472
        result = self._scalarFallback('_print_Add', expr)
        if result:
            return result
473
474
475
476

        summands = []
        for term in expr.args:
            if term.func == sp.Mul:
Martin Bauer's avatar
Martin Bauer committed
477
                sign, t = self._print_Mul(term, inside_add=True)
478
479
480
481
482
483
484
485
486
487
488
489
490
            else:
                t = self._print(term)
                sign = 1
            summands.append(self.SummandInfo(sign, t))
        # Use positive terms first
        summands.sort(key=lambda e: e.sign, reverse=True)
        # if no positive term exists, prepend a zero
        if summands[0].sign == -1:
            summands.insert(0, self.SummandInfo(1, "0"))

        assert len(summands) >= 2
        processed = summands[0].term
        for summand in summands[1:]:
Martin Bauer's avatar
Martin Bauer committed
491
            func = self.instruction_set['-'] if summand.sign == -1 else self.instruction_set['+']
492
493
494
            processed = func.format(processed, summand.term)
        return processed

495
    def _print_Pow(self, expr):
496
497
498
        result = self._scalarFallback('_print_Pow', expr)
        if result:
            return result
499

500
501
        one = self.instruction_set['makeVec'].format(1.0)

502
503
        if expr.exp.is_integer and expr.exp.is_number and 0 < expr.exp < 8:
            return "(" + self._print(sp.Mul(*[expr.base] * expr.exp, evaluate=False)) + ")"
504
505
506
507
508
        elif expr.exp == -1:
            one = self.instruction_set['makeVec'].format(1.0)
            return self.instruction_set['/'].format(one, self._print(expr.base))
        elif expr.exp == 0.5:
            return self.instruction_set['sqrt'].format(self._print(expr.base))
509
510
511
        elif expr.exp == -0.5:
            root = self.instruction_set['sqrt'].format(self._print(expr.base))
            return self.instruction_set['/'].format(one, root)
512
513
514
        elif expr.exp.is_integer and expr.exp.is_number and - 8 < expr.exp < 0:
            return self.instruction_set['/'].format(one,
                                                    self._print(sp.Mul(*[expr.base] * (-expr.exp), evaluate=False)))
515
        else:
516
            raise ValueError("Generic exponential not supported: " + str(expr))
517

Martin Bauer's avatar
Martin Bauer committed
518
519
520
521
    def _print_Mul(self, expr, inside_add=False):
        # noinspection PyProtectedMember
        from sympy.core.mul import _keep_coeff

522
523
524
        result = self._scalarFallback('_print_Mul', expr)
        if result:
            return result
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

        c, e = expr.as_coeff_Mul()
        if c < 0:
            expr = _keep_coeff(-c, e)
            sign = -1
        else:
            sign = 1

        a = []  # items in the numerator
        b = []  # items that are in the denominator (if any)

        # Gather args for numerator/denominator
        for item in expr.as_ordered_factors():
            if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
                if item.exp != -1:
                    b.append(sp.Pow(item.base, -item.exp, evaluate=False))
                else:
                    b.append(sp.Pow(item.base, -item.exp))
            else:
                a.append(item)

        a = a or [S.One]

        a_str = [self._print(x) for x in a]
        b_str = [self._print(x) for x in b]

        result = a_str[0]
        for item in a_str[1:]:
Martin Bauer's avatar
Martin Bauer committed
553
            result = self.instruction_set['*'].format(result, item)
554
555
556
557

        if len(b) > 0:
            denominator_str = b_str[0]
            for item in b_str[1:]:
Martin Bauer's avatar
Martin Bauer committed
558
559
                denominator_str = self.instruction_set['*'].format(denominator_str, item)
            result = self.instruction_set['/'].format(result, denominator_str)
560

Martin Bauer's avatar
Martin Bauer committed
561
        if inside_add:
562
563
564
            return sign, result
        else:
            if sign < 0:
Martin Bauer's avatar
Martin Bauer committed
565
                return self.instruction_set['*'].format(self._print(S.NegativeOne), result)
566
567
568
            else:
                return result

569
    def _print_Relational(self, expr):
570
571
572
        result = self._scalarFallback('_print_Relational', expr)
        if result:
            return result
Martin Bauer's avatar
Martin Bauer committed
573
        return self.instruction_set[expr.rel_op].format(self._print(expr.lhs), self._print(expr.rhs))
574
575

    def _print_Equality(self, expr):
576
577
578
        result = self._scalarFallback('_print_Equality', expr)
        if result:
            return result
Martin Bauer's avatar
Martin Bauer committed
579
        return self.instruction_set['=='].format(self._print(expr.lhs), self._print(expr.rhs))
580
581

    def _print_Piecewise(self, expr):
582
583
584
        result = self._scalarFallback('_print_Piecewise', expr)
        if result:
            return result
585

Martin Bauer's avatar
Martin Bauer committed
586
        if expr.args[-1].cond.args[0] is not sp.sympify(True):
587
588
589
590
591
592
593
594
595
            # 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.")

        result = self._print(expr.args[-1][0])
Martin Bauer's avatar
Martin Bauer committed
596
        for true_expr, condition in reversed(expr.args[:-1]):
597
            if isinstance(condition, cast_func) and get_type_of_expression(condition.args[0]) == create_type("bool"):
598
599
600
601
602
                if not KERNCRAFT_NO_TERNARY_MODE:
                    result = "(({}) ? ({}) : ({}))".format(self._print(condition.args[0]), self._print(true_expr),
                                                           result)
                else:
                    print("Warning - skipping ternary op")
603
604
605
            else:
                # noinspection SpellCheckingInspection
                result = self.instruction_set['blendv'].format(result, self._print(true_expr), self._print(condition))
606
        return result