cbackend.py 24.2 KB
Newer Older
Martin Bauer's avatar
Martin Bauer committed
1
from collections import namedtuple
2
from typing import Set
3

4
import numpy as np
5
6
import sympy as sp
from sympy.core import S
7
from sympy.printing.ccode import C89CodePrinter
8

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

Martin Bauer's avatar
Martin Bauer committed
20
21
try:
    from sympy.printing.ccode import C99CodePrinter as CCodePrinter
Martin Bauer's avatar
Martin Bauer committed
22
23
except ImportError:
    from sympy.printing.ccode import CCodePrinter  # for sympy versions < 1.1
Martin Bauer's avatar
Martin Bauer committed
24

25
__all__ = ['generate_c', 'CustomCodeNode', 'PrintNode', 'get_headers', 'CustomSympyPrinter']
26

27
28
KERNCRAFT_NO_TERNARY_MODE = False

Martin Bauer's avatar
Fixes    
Martin Bauer committed
29

30
def generate_c(ast_node: Node, signature_only: bool = False, dialect='c', custom_backend=None) -> str:
Martin Bauer's avatar
Martin Bauer committed
31
32
33
34
35
36
37
38
39
    """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:
40
        dialect: 'c' or 'cuda'
Martin Bauer's avatar
Martin Bauer committed
41
42
    Returns:
        C-like code for the ast node and its descendants
Martin Bauer's avatar
Martin Bauer committed
43
    """
44
45
46
47
48
49
    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
50
51
52
    if custom_backend:
        printer = custom_backend
    elif dialect == 'c':
53
54
55
56
        try:
            instruction_set = ast_node.instruction_set
        except Exception:
            instruction_set = None
57
        printer = CBackend(signature_only=signature_only,
58
                           vector_instruction_set=instruction_set)
59
60
61
62
    elif dialect == 'cuda':
        from pystencils.backends.cuda_backend import CudaBackend
        printer = CudaBackend(signature_only=signature_only)
    else:
Martin Bauer's avatar
Martin Bauer committed
63
        raise ValueError("Unknown dialect: " + str(dialect))
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
    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)
88
89


Martin Bauer's avatar
Martin Bauer committed
90
91
def get_headers(ast_node: Node) -> Set[str]:
    """Return a set of header files, necessary to compile the printed C-like code."""
92
93
    headers = set()

Martin Bauer's avatar
Martin Bauer committed
94
95
96
    if isinstance(ast_node, KernelFunction) and ast_node.instruction_set:
        headers.update(ast_node.instruction_set['headers'])

Martin Bauer's avatar
Martin Bauer committed
97
98
99
    if hasattr(ast_node, 'headers'):
        headers.update(ast_node.headers)
    for a in ast_node.args:
100
        if isinstance(a, Node):
Martin Bauer's avatar
Martin Bauer committed
101
            headers.update(get_headers(a))
102
103

    return headers
104
105


106
107
108
# --------------------------------------- Backend Specific Nodes -------------------------------------------------------


109
class CustomCodeNode(Node):
Martin Bauer's avatar
Martin Bauer committed
110
    def __init__(self, code, symbols_read, symbols_defined, parent=None):
111
        super(CustomCodeNode, self).__init__(parent=parent)
112
        self._code = "\n" + code
113
114
        self._symbols_read = set(symbols_read)
        self._symbols_defined = set(symbols_defined)
115
        self.headers = []
116

117
    def get_code(self, dialect, vector_instruction_set):
118
119
120
121
122
123
124
        return self._code

    @property
    def args(self):
        return []

    @property
Martin Bauer's avatar
Martin Bauer committed
125
    def symbols_defined(self):
126
        return self._symbols_defined
127
128

    @property
Martin Bauer's avatar
Martin Bauer committed
129
    def undefined_symbols(self):
130
        return self._symbols_read - self._symbols_defined
131
132


133
class PrintNode(CustomCodeNode):
Martin Bauer's avatar
Martin Bauer committed
134
135
136
137
    # 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())
138
        self.headers.append("<iostream>")
139
140
141
142


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

143

Martin Bauer's avatar
Martin Bauer committed
144
145
# noinspection PyPep8Naming
class CBackend:
146

Martin Bauer's avatar
Martin Bauer committed
147
    def __init__(self, sympy_printer=None, signature_only=False, vector_instruction_set=None, dialect='c'):
Martin Bauer's avatar
Martin Bauer committed
148
149
        if sympy_printer is None:
            if vector_instruction_set is not None:
150
                self.sympy_printer = VectorizedCustomSympyPrinter(vector_instruction_set)
151
            else:
152
                self.sympy_printer = CustomSympyPrinter()
153
        else:
Martin Bauer's avatar
Martin Bauer committed
154
            self.sympy_printer = sympy_printer
155

156
        self._vector_instruction_set = vector_instruction_set
157
        self._indent = "   "
158
        self._dialect = dialect
Martin Bauer's avatar
Martin Bauer committed
159
        self._signatureOnly = signature_only
160
161

    def __call__(self, node):
Martin Bauer's avatar
Martin Bauer committed
162
        prev_is = VectorType.instruction_set
163
        VectorType.instruction_set = self._vector_instruction_set
164
        result = str(self._print(node))
Martin Bauer's avatar
Martin Bauer committed
165
        VectorType.instruction_set = prev_is
166
        return result
167
168
169

    def _print(self, node):
        for cls in type(node).__mro__:
Martin Bauer's avatar
Martin Bauer committed
170
171
172
            method_name = "_print_" + cls.__name__
            if hasattr(self, method_name):
                return getattr(self, method_name)(node)
173
        raise NotImplementedError(self.__class__.__name__ + " does not support node of type " + node.__class__.__name__)
174
175

    def _print_KernelFunction(self, node):
176
        function_arguments = ["%s %s" % (str(s.symbol.dtype), s.symbol.name) for s in node.get_parameters()]
177
        launch_bounds = ""
178
        if self._dialect == 'cuda':
179
180
181
182
183
            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))
184
        if self._signatureOnly:
Martin Bauer's avatar
Martin Bauer committed
185
            return func_declaration
186

187
        body = self._print(node.body)
Martin Bauer's avatar
Martin Bauer committed
188
        return func_declaration + "\n" + body
189
190

    def _print_Block(self, node):
Martin Bauer's avatar
Martin Bauer committed
191
192
        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)))
193
194

    def _print_PragmaBlock(self, node):
Martin Bauer's avatar
Martin Bauer committed
195
        return "%s\n%s" % (node.pragma_line, self._print_Block(node))
196
197

    def _print_LoopOverCoordinate(self, node):
Martin Bauer's avatar
Martin Bauer committed
198
        counter_symbol = node.loop_counter_name
Martin Bauer's avatar
Martin Bauer committed
199
200
201
202
        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)
203

Martin Bauer's avatar
Martin Bauer committed
204
        prefix = "\n".join(node.prefix_lines)
205
206
        if prefix:
            prefix += "\n"
Martin Bauer's avatar
Martin Bauer committed
207
        return "%s%s\n%s" % (prefix, loop_str, self._print(node.body))
208
209

    def _print_SympyAssignment(self, node):
Martin Bauer's avatar
Martin Bauer committed
210
211
        if node.is_declaration:
            data_type = "const " + str(node.lhs.dtype) + " " if node.is_const else str(node.lhs.dtype) + " "
212
213
            return "%s%s = %s;" % (data_type, self.sympy_printer.doprint(node.lhs),
                                   self.sympy_printer.doprint(node.rhs))
214
        else:
Martin Bauer's avatar
Martin Bauer committed
215
            lhs_type = get_type_of_expression(node.lhs)
Martin Bauer's avatar
Martin Bauer committed
216
217
218
219
220
221
            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'

222
223
224
225
226
227
                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

228
229
                return self._vector_instruction_set[instr].format("&" + self.sympy_printer.doprint(node.lhs.args[0]),
                                                                  self.sympy_printer.doprint(rhs)) + ';'
230
            else:
Martin Bauer's avatar
Martin Bauer committed
231
                return "%s = %s;" % (self.sympy_printer.doprint(node.lhs), self.sympy_printer.doprint(node.rhs))
232
233

    def _print_TemporaryMemoryAllocation(self, node):
234
        align = 64
Martin Bauer's avatar
Martin Bauer committed
235
236
237
238
239
240
        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),
241
                           size=self.sympy_printer.doprint(size),
Martin Bauer's avatar
Martin Bauer committed
242
243
                           offset=int(node.offset(align)),
                           align=align)
244
245

    def _print_TemporaryMemoryFree(self, node):
246
        align = 64
Martin Bauer's avatar
Martin Bauer committed
247
        return "free(%s - %d);" % (self.sympy_printer.doprint(node.symbol.name), node.offset(align))
248

Martin Bauer's avatar
Martin Bauer committed
249
    def _print_SkipIteration(self, _):
250
        return "continue;"
Martin Bauer's avatar
Martin Bauer committed
251

252
253
    def _print_CustomCodeNode(self, node):
        return node.get_code(self._dialect, self._vector_instruction_set)
254

255
    def _print_Conditional(self, node):
256
257
258
        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
259
260
        condition_expr = self.sympy_printer.doprint(node.condition_expr)
        true_block = self._print_Block(node.true_block)
Martin Bauer's avatar
Martin Bauer committed
261
        result = "if (%s)\n%s " % (condition_expr, true_block)
Martin Bauer's avatar
Martin Bauer committed
262
263
        if node.false_block:
            false_block = self._print_Block(node.false_block)
Martin Bauer's avatar
Martin Bauer committed
264
            result += "else " + false_block
265
266
        return result

267
    def _print_DestructuringBindingsForFieldClass(self, node):
268
269
        # Define all undefined symbols
        undefined_field_symbols = node.symbols_defined
270
271
272
        destructuring_bindings = ["%s %s = %s.%s;" %
                                  (u.dtype,
                                   u.name,
273
                                   u.field_name if hasattr(u, 'field_name') else u.field_names[0],
274
275
                                   node.CLASS_TO_MEMBER_DICT[u.__class__] %
                                   (() if type(u) == FieldPointerSymbol else (u.coordinate,)))
276
277
                                  for u in undefined_field_symbols
                                  ]
278
        destructuring_bindings.sort()  # only for code aesthetics
279
280
281
282
283
        return "{\n" + self._indent + \
            ("\n" + self._indent).join(destructuring_bindings) + \
            "\n" + self._indent + \
            ("\n" + self._indent).join(self._print(node.body).splitlines()) + \
            "\n}"
284

285
286
287
288

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


Martin Bauer's avatar
Martin Bauer committed
289
# noinspection PyPep8Naming
290
class CustomSympyPrinter(CCodePrinter):
Martin Bauer's avatar
Martin Bauer committed
291

292
    def __init__(self):
Martin Bauer's avatar
Martin Bauer committed
293
        super(CustomSympyPrinter, self).__init__()
294
        self._float_type = create_type("float32")
295
296
297
298
        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
299

300
301
    def _print_Pow(self, expr):
        """Don't use std::pow function, for small integer exponents, write as multiplication"""
Martin Bauer's avatar
Martin Bauer committed
302
303
304
        if not expr.free_symbols:
            return self._typed_number(expr.evalf(), get_type_of_expression(expr))

305
        if expr.exp.is_integer and expr.exp.is_number and 0 < expr.exp < 8:
306
            return "(" + self._print(sp.Mul(*[expr.base] * expr.exp, evaluate=False)) + ")"
307
308
        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)))
309
310
311
312
313
        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
314
315
        res = str(expr.evalf().num)
        return res
316
317
318
319
320
321
322
323

    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
324
325
        return result.replace("\n", "")

326
    def _print_Function(self, expr):
327
        infix_functions = {
Martin Bauer's avatar
Martin Bauer committed
328
329
330
331
332
            bitwise_xor: '^',
            bit_shift_right: '>>',
            bit_shift_left: '<<',
            bitwise_or: '|',
            bitwise_and: '&',
Martin Bauer's avatar
Martin Bauer committed
333
        }
Martin Bauer's avatar
Martin Bauer committed
334
335
        if hasattr(expr, 'to_c'):
            return expr.to_c(self._print)
336
337
338
        if isinstance(expr, reinterpret_cast_func):
            arg, data_type = expr.args
            return "*((%s)(& %s))" % (PointerType(data_type, restrict=False), self._print(arg))
339
340
341
        elif isinstance(expr, address_of):
            assert len(expr.args) == 1, "address_of must only have one argument"
            return "&(%s)" % self._print(expr.args[0])
342
        elif isinstance(expr, cast_func):
Martin Bauer's avatar
Martin Bauer committed
343
            arg, data_type = expr.args
344
345
346
            if isinstance(arg, sp.Number):
                return self._typed_number(arg, data_type)
            else:
347
348
                return "((%s)(%s))" % (data_type, self._print(arg))
        elif isinstance(expr, fast_division):
349
            return "({})".format(self._print(expr.args[0] / expr.args[1]))
350
        elif isinstance(expr, fast_sqrt):
351
            return "({})".format(self._print(sp.sqrt(expr.args[0])))
352
353
        elif isinstance(expr, vec_any) or isinstance(expr, vec_all):
            return self._print(expr.args[0])
354
        elif isinstance(expr, fast_inv_sqrt):
355
            return "({})".format(self._print(1 / sp.sqrt(expr.args[0])))
356
357
        elif expr.func in infix_functions:
            return "(%s %s %s)" % (self._print(expr.args[0]), infix_functions[expr.func], self._print(expr.args[1]))
358
359
360
361
        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]))
362
        else:
363
            return super(CustomSympyPrinter, self)._print_Function(expr)
Martin Bauer's avatar
Martin Bauer committed
364

365
366
    def _typed_number(self, number, dtype):
        res = self._print(number)
367
368
369
370
        if dtype.numpy_dtype == np.float32:
            return res + '.0f' if '.' not in res else res + 'f'
        elif dtype.numpy_dtype == np.float64:
            return res + '.0' if '.' not in res else res
371
372
        else:
            return res
373

374
375
376
    _print_Max = C89CodePrinter._print_Max
    _print_Min = C89CodePrinter._print_Min

377

Martin Bauer's avatar
Martin Bauer committed
378
# noinspection PyPep8Naming
379
380
381
class VectorizedCustomSympyPrinter(CustomSympyPrinter):
    SummandInfo = namedtuple("SummandInfo", ['sign', 'term'])

382
383
    def __init__(self, instruction_set):
        super(VectorizedCustomSympyPrinter, self).__init__()
Martin Bauer's avatar
Martin Bauer committed
384
        self.instruction_set = instruction_set
385

Martin Bauer's avatar
Martin Bauer committed
386
387
388
389
    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)
390
        else:
Martin Bauer's avatar
Martin Bauer committed
391
            assert self.instruction_set['width'] == expr_type.width
392
393
            return None

394
    def _print_Function(self, expr):
395
        if isinstance(expr, vector_memory_access):
Martin Bauer's avatar
Martin Bauer committed
396
397
398
            arg, data_type, aligned, _ = expr.args
            instruction = self.instruction_set['loadA'] if aligned else self.instruction_set['loadU']
            return instruction.format("& " + self._print(arg))
399
        elif isinstance(expr, cast_func):
Martin Bauer's avatar
Martin Bauer committed
400
401
            arg, data_type = expr.args
            if type(data_type) is VectorType:
Martin Bauer's avatar
Martin Bauer committed
402
                return self.instruction_set['makeVec'].format(self._print(arg))
403
        elif expr.func == fast_division:
404
405
            result = self._scalarFallback('_print_Function', expr)
            if not result:
406
407
                result = self.instruction_set['/'].format(self._print(expr.args[0]), self._print(expr.args[1]))
            return result
408
409
410
        elif expr.func == fast_sqrt:
            return "({})".format(self._print(sp.sqrt(expr.args[0])))
        elif expr.func == fast_inv_sqrt:
411
412
413
414
415
416
            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])))
417
418
419
420
421
422
423
424
425
426
427
428
429
        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]))

430
431
        return super(VectorizedCustomSympyPrinter, self)._print_Function(expr)

432
433
434
435
436
    def _print_And(self, expr):
        result = self._scalarFallback('_print_And', expr)
        if result:
            return result

Martin Bauer's avatar
Martin Bauer committed
437
438
439
440
        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
441
            result = self.instruction_set['&'].format(result, item)
442
443
444
445
446
447
448
        return result

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

Martin Bauer's avatar
Martin Bauer committed
449
450
451
452
        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
453
            result = self.instruction_set['|'].format(result, item)
454
455
        return result

456
    def _print_Add(self, expr, order=None):
457
458
459
        result = self._scalarFallback('_print_Add', expr)
        if result:
            return result
460
461
462
463

        summands = []
        for term in expr.args:
            if term.func == sp.Mul:
Martin Bauer's avatar
Martin Bauer committed
464
                sign, t = self._print_Mul(term, inside_add=True)
465
466
467
468
469
470
471
472
473
474
475
476
477
            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
478
            func = self.instruction_set['-'] if summand.sign == -1 else self.instruction_set['+']
479
480
481
            processed = func.format(processed, summand.term)
        return processed

482
    def _print_Pow(self, expr):
483
484
485
        result = self._scalarFallback('_print_Pow', expr)
        if result:
            return result
486

487
488
        one = self.instruction_set['makeVec'].format(1.0)

489
490
        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)) + ")"
491
492
493
494
495
        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))
496
497
498
        elif expr.exp == -0.5:
            root = self.instruction_set['sqrt'].format(self._print(expr.base))
            return self.instruction_set['/'].format(one, root)
499
500
501
        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)))
502
        else:
503
            raise ValueError("Generic exponential not supported: " + str(expr))
504

Martin Bauer's avatar
Martin Bauer committed
505
506
507
508
    def _print_Mul(self, expr, inside_add=False):
        # noinspection PyProtectedMember
        from sympy.core.mul import _keep_coeff

509
510
511
        result = self._scalarFallback('_print_Mul', expr)
        if result:
            return result
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

        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
540
            result = self.instruction_set['*'].format(result, item)
541
542
543
544

        if len(b) > 0:
            denominator_str = b_str[0]
            for item in b_str[1:]:
Martin Bauer's avatar
Martin Bauer committed
545
546
                denominator_str = self.instruction_set['*'].format(denominator_str, item)
            result = self.instruction_set['/'].format(result, denominator_str)
547

Martin Bauer's avatar
Martin Bauer committed
548
        if inside_add:
549
550
551
            return sign, result
        else:
            if sign < 0:
Martin Bauer's avatar
Martin Bauer committed
552
                return self.instruction_set['*'].format(self._print(S.NegativeOne), result)
553
554
555
            else:
                return result

556
    def _print_Relational(self, expr):
557
558
559
        result = self._scalarFallback('_print_Relational', expr)
        if result:
            return result
Martin Bauer's avatar
Martin Bauer committed
560
        return self.instruction_set[expr.rel_op].format(self._print(expr.lhs), self._print(expr.rhs))
561
562

    def _print_Equality(self, expr):
563
564
565
        result = self._scalarFallback('_print_Equality', expr)
        if result:
            return result
Martin Bauer's avatar
Martin Bauer committed
566
        return self.instruction_set['=='].format(self._print(expr.lhs), self._print(expr.rhs))
567
568

    def _print_Piecewise(self, expr):
569
570
571
        result = self._scalarFallback('_print_Piecewise', expr)
        if result:
            return result
572

Martin Bauer's avatar
Martin Bauer committed
573
        if expr.args[-1].cond.args[0] is not sp.sympify(True):
574
575
576
577
578
579
580
581
582
            # 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
583
        for true_expr, condition in reversed(expr.args[:-1]):
584
            if isinstance(condition, cast_func) and get_type_of_expression(condition.args[0]) == create_type("bool"):
585
586
587
588
589
                if not KERNCRAFT_NO_TERNARY_MODE:
                    result = "(({}) ? ({}) : ({}))".format(self._print(condition.args[0]), self._print(true_expr),
                                                           result)
                else:
                    print("Warning - skipping ternary op")
590
591
592
            else:
                # noinspection SpellCheckingInspection
                result = self.instruction_set['blendv'].format(result, self._print(true_expr), self._print(condition))
593
        return result