From 743d6ec03250772020279779677a51ca67d0f324 Mon Sep 17 00:00:00 2001
From: Dominic Kempf <dominic.kempf@iwr.uni-heidelberg.de>
Date: Thu, 21 Sep 2017 17:37:21 +0200
Subject: [PATCH] Add a first draft for a cost model
---
python/dune/perftool/sumfact/costmodel.py | 25 ++++++++++++
python/dune/perftool/sumfact/permutation.py | 3 +-
python/dune/perftool/sumfact/symbolic.py | 45 +++++++++++++++++++++
python/dune/perftool/sumfact/tabulation.py | 26 ++++++++++++
4 files changed, 98 insertions(+), 1 deletion(-)
create mode 100644 python/dune/perftool/sumfact/costmodel.py
diff --git a/python/dune/perftool/sumfact/costmodel.py b/python/dune/perftool/sumfact/costmodel.py
new file mode 100644
index 00000000..c0362767
--- /dev/null
+++ b/python/dune/perftool/sumfact/costmodel.py
@@ -0,0 +1,25 @@
+""" Implementation of the cost model used for vectorization
+"""
+
+
+def ilp_heuristic(sf):
+ """ A heuristic measure for the ILP capabilities of the kernel
+
+ Return is the throttle of insufficient ILP, generally in (0., 1.0].
+ 1.0 indicates perfect instruction level parallelism.
+ """
+ return 1.0
+
+
+def vectorization_costfunction(sf):
+ # kernel characteristics necessary
+ traffic = sf.memory_traffic
+ intensity = sf.operations / sf.memory_traffic
+
+ # hardware characteristics necessary
+ bandwidth = 100000000000000000.0
+ peakperformance = 100.0
+
+ roofline = min(bandwidth * intensity, ilp_heuristics(sf) * peakperformance)
+
+ return (traffic * intensity) / roofline
diff --git a/python/dune/perftool/sumfact/permutation.py b/python/dune/perftool/sumfact/permutation.py
index 7ebc0be7..b00be306 100644
--- a/python/dune/perftool/sumfact/permutation.py
+++ b/python/dune/perftool/sumfact/permutation.py
@@ -38,7 +38,8 @@ def flop_cost(matrix_sequence):
for i in range(l, len(matrix_sequence)):
cost_n *= matrix_sequence[i].cols
cost += cost_m * cost_n
- return cost
+ # The factor of 2 indicates FMA
+ return 2 * cost
def sumfact_permutation_strategy(sf):
diff --git a/python/dune/perftool/sumfact/symbolic.py b/python/dune/perftool/sumfact/symbolic.py
index 296d6f6d..44ae9f79 100644
--- a/python/dune/perftool/sumfact/symbolic.py
+++ b/python/dune/perftool/sumfact/symbolic.py
@@ -308,6 +308,29 @@ class SumfactKernel(SumfactKernelBase, ImmutableRecord, prim.Variable):
def vector_width(self):
return 1
+ #
+ # Implement properties needed by cost models
+ #
+
+ @property
+ def memory_traffic(self):
+ """ The total number of bytes needed from RAM for the kernel
+ to be executed - neglecting the existence of caches of course
+ """
+ input = product(mat.basis_size for mat in self.matrix_sequence)
+ matrices = sum(mat.memory_traffic for mat in set(matrix_sequence))
+
+ # TODO: this is a hard coded sizeof(double)
+ return (input + matrices) * 8
+
+ @property
+ def operations(self):
+ """ The total number of floating point operations for the kernel
+ to be carried out """
+ from dune.perftool.sumfact.tabulation import flop_cost
+ return flop_cost(self.matrix_sequence)
+
+
# Extract the argument list and store it on the class. This needs to be done
# outside of the class because the SumfactKernel class object needs to be fully
# initialized in order to extract the information from __init__.
@@ -587,3 +610,25 @@ class VectorizedSumfactKernel(SumfactKernelBase, ImmutableRecord, prim.Variable)
@property
def tag(self):
return "vecsumfac_h{}_v{}".format(self.horizontal_width, self.vertical_width)
+
+ #
+ # Implement properties needed by cost models
+ #
+
+ @property
+ def memory_traffic(self):
+ """ The total number of bytes needed from RAM for the kernel
+ to be executed - neglecting the existence of caches of course
+ """
+ dofs = product(mat.basis_size for mat in self.matrix_sequence)
+ matrices = sum(mat.memory_traffic for mat in set(matrix_sequence))
+
+ # TODO: this is a hard coded sizeof(double)
+ return (dofs + matrices) * 8
+
+ @property
+ def operations(self):
+ """ The total number of floating point operations for the kernel
+ to be carried out """
+ from dune.perftool.sumfact.tabulation import flop_cost
+ return flop_cost(self.matrix_sequence)
diff --git a/python/dune/perftool/sumfact/tabulation.py b/python/dune/perftool/sumfact/tabulation.py
index e8518668..3e7c6375 100644
--- a/python/dune/perftool/sumfact/tabulation.py
+++ b/python/dune/perftool/sumfact/tabulation.py
@@ -98,6 +98,17 @@ class BasisTabulationMatrix(BasisTabulationMatrixBase, ImmutableRecord):
def vectorized(self):
return False
+ #
+ # Implement properties needed by cost models
+ #
+
+ @property
+ def memory_traffic(self):
+ """ The total number of bytes needed from RAM for the kernel
+ to be executed - neglecting the existence of caches of course
+ """
+ return mat.rows * mat.cols
+
class BasisTabulationMatrixArray(BasisTabulationMatrixBase):
def __init__(self, tabs, width=None):
@@ -200,6 +211,21 @@ class BasisTabulationMatrixArray(BasisTabulationMatrixBase):
def vectorized(self):
return True
+ #
+ # Implement properties needed by cost models
+ #
+
+ @property
+ def memory_traffic(self):
+ """ The total number of bytes needed from RAM for the kernel
+ to be executed - neglecting the existence of caches of course
+ """
+ if len(set(self.tabs)) == 1:
+ factor = 1
+ else:
+ factor = self.width
+ return factor * mat.rows * mat.cols
+
def quadrature_points_per_direction():
# Quadrature order per direction
--
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