From 804e15d65e32479a476ef212238c25ada4865e3f Mon Sep 17 00:00:00 2001
From: Adrian Kummerlaender
Date: Tue, 18 Jun 2019 14:47:13 +0200
Subject: Expand square expressions

Yields another ~5-10 MLUPS in the simple D2Q9 example.
Now averaging at ~840 MLUPS for D2Q9 and ~ 400 MLUPS for D3Q19 on a K2200.
---
 symbolic/generator.py     |  6 ++++--
 symbolic/optimizations.py | 10 ++++++++++
 2 files changed, 14 insertions(+), 2 deletions(-)
 create mode 100644 symbolic/optimizations.py

diff --git a/symbolic/generator.py b/symbolic/generator.py
index 161e2f4..7315ae0 100644
--- a/symbolic/generator.py
+++ b/symbolic/generator.py
@@ -1,6 +1,8 @@
 from sympy import *
 from sympy.codegen.ast import Assignment
 
+import symbolic.optimizations as optimizations
+
 class LBM:
     def __init__(self, descriptor):
         self.descriptor = descriptor
@@ -18,7 +20,7 @@ class LBM:
                 Assignment(u_i, sum([ (c_j*self.f_curr[j])[i] for j, c_j in enumerate(self.descriptor.c) ]) / sum(self.f_curr)))
 
         if optimize:
-            return cse(exprs, optimizations='basic', symbols=numbered_symbols(prefix='m'))
+            return cse(exprs, optimizations=optimizations.custom, symbols=numbered_symbols(prefix='m'))
         else:
             return ([], exprs)
 
@@ -41,6 +43,6 @@ class LBM:
         exprs = [ Assignment(self.f_next[i], self.f_curr[i] + 1/tau * (f_eq_i - self.f_curr[i])) for i, f_eq_i in enumerate(f_eq) ]
 
         if optimize:
-            return cse(exprs, optimizations='basic')
+            return cse(exprs, optimizations=optimizations.custom)
         else:
             return ([], exprs)
diff --git a/symbolic/optimizations.py b/symbolic/optimizations.py
new file mode 100644
index 0000000..93dad09
--- /dev/null
+++ b/symbolic/optimizations.py
@@ -0,0 +1,10 @@
+from sympy import *
+
+from sympy.codegen.rewriting import ReplaceOptim
+
+expand_square = ReplaceOptim(
+    lambda e: e.is_Pow and e.exp.is_integer and e.exp == 2,
+    lambda p: UnevaluatedExpr(Mul(p.base, p.base, evaluate = False))
+)
+
+custom = [ (expand_square, expand_square) ] + cse_main.basic_optimizations
-- 
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