07-internal-representations
December 6, 2015
1
Working with Internal Representations
In [1]: from pymbolic import parse
x = parse("x")
h = parse("h")
1.1
Visualizing an Expression Tree
In [2]: u = (x+4)**3
h = parse("h")
expr = u + 2*u*h + 4*u*h**2
In [3]: # Load an IPython extension for graph drawing
%load_ext gvmagic
In [4]: from pymbolic.mapper.graphviz import GraphvizMapper
gvm = GraphvizMapper()
gvm(expr)
In [5]: %dotstr gvm.get_dot_code()
1
+
*
h
*
2
+
x
1.2
Power
Power
3
h
4
2
4
Serialization
The need may arise to store expressions on disk, likely as part of larger problem descriptions. One particular
application of this might be caching. To do so, one can simply use Python’s built-in ‘pickle’ mechanism:
In [6]: import pickle
expr_data = pickle.dumps(expr)
print(type(expr_data), len(expr_data))
expr2 = pickle.loads(expr_data)
print(expr2 == expr)
print(expr2 is expr)
<class ’bytes’> 238
True
False
1.3
Caching
Some operations on expression data (such as an entire compilation down to an OpenCL binary) may be
somewhat expensive, which often makes caching a worthwhile investment. In principle, a Python dictionary
2
is all that is needed, because the expression types that have been demonstrated are immutable and support
hashing, and therefore work seamlessly with Python’s set and dictionary types.
In connection with caches, one important question that needs to be answered is cache lifetime. In the
example below, this is answered by attaching the lifetime of the cash to the lifetime of a containing object:
In [16]: from pytools import memoize_method
class ExpressionCompiler:
@memoize_method
def compile(self, expr):
print("compiling...")
from time import sleep
sleep(1.5)
from pymbolic.mapper.c_code import CCodeMapper
ccm = CCodeMapper()
return ccm(expr)
(pytools is a supporting package that pymbolic depends on.)
In [21]: ec = ExpressionCompiler()
ec.compile(expr)
compiling...
Out[21]: ’pow(x + 4, 3) + 4 * pow(x + 4, 3) * h * h + 2 * pow(x + 4, 3) * h’
In [22]: ec.compile(expr)
Out[22]: ’pow(x + 4, 3) + 4 * pow(x + 4, 3) * h * h + 2 * pow(x + 4, 3) * h’
In [ ]:
3