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stencil-numba.py
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#!/usr/bin/env python3
#
# Copyright (c) 2015, Intel Corporation
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials provided
# with the distribution.
# * Neither the name of Intel Corporation nor the names of its
# contributors may be used to endorse or promote products
# derived from this software without specific prior written
# permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
# COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
#
#
# *******************************************************************
#
# NAME: Stencil
#
# PURPOSE: This program tests the efficiency with which a space-invariant,
# linear, symmetric filter (stencil) can be applied to a square
# grid or image.
#
# USAGE: The program takes as input the linear
# dimension of the grid, and the number of iterations on the grid
#
# <progname> <iterations> <grid size>
#
# The output consists of diagnostics to make sure the
# algorithm worked, and of timing statistics.
#
# HISTORY: - Written by Rob Van der Wijngaart, February 2009.
# - RvdW: Removed unrolling pragmas for clarity;
# added constant to array "in" at end of each iteration to force
# refreshing of neighbor data in parallel versions; August 2013
# - Converted to Python by Jeff Hammond, February 2016.
#
# *******************************************************************
import sys
print('Python version = ', str(sys.version_info.major)+'.'+str(sys.version_info.minor))
if sys.version_info >= (3, 3):
from time import process_time as timer
else:
from timeit import default_timer as timer
from numba import jit
import numpy
print('Numpy version = ', numpy.version.version)
@jit
def grid(n,r,W,A,B):
if r>0:
b = n-r
for s in range(-r, r+1):
for t in range(-r, r+1):
B[r:b,r:b] += W[r+t,r+s] * A[r+t:b+t,r+s:b+s]
@jit
def star2(n,W,A,B):
B[2:n-2,2:n-2] += W[2,2] * A[2:n-2,2:n-2] \
+ W[2,0] * A[2:n-2,0:n-4] \
+ W[2,1] * A[2:n-2,1:n-3] \
+ W[2,3] * A[2:n-2,3:n-1] \
+ W[2,4] * A[2:n-2,4:n-0] \
+ W[0,2] * A[0:n-4,2:n-2] \
+ W[1,2] * A[1:n-3,2:n-2] \
+ W[3,2] * A[3:n-1,2:n-2] \
+ W[4,2] * A[4:n-0,2:n-2]
@jit
def star(n,r,W,A,B):
b = n-r
B[r:b,r:b] += W[r,r] * A[r:b,r:b]
for s in range(1,r+1):
B[r:b,r:b] += W[r,r-s] * A[r:b,r-s:b-s] \
+ W[r,r+s] * A[r:b,r+s:b+s] \
+ W[r-s,r] * A[r-s:b-s,r:b] \
+ W[r+s,r] * A[r+s:b+s,r:b]
def main():
# ********************************************************************
# read and test input parameters
# ********************************************************************
print('Parallel Research Kernels version ') #, PRKVERSION
print('Python stencil execution on 2D grid')
if len(sys.argv) < 3:
print('argument count = ', len(sys.argv))
sys.exit("Usage: ./stencil <# iterations> <array dimension> [<star/grid> <radius>]")
iterations = int(sys.argv[1])
if iterations < 1:
sys.exit("ERROR: iterations must be >= 1")
n = int(sys.argv[2])
if n < 1:
sys.exit("ERROR: array dimension must be >= 1")
if len(sys.argv) > 3:
pattern = sys.argv[3]
else:
pattern = 'star'
if len(sys.argv) > 4:
r = int(sys.argv[4])
if r < 1:
sys.exit("ERROR: Stencil radius should be positive")
if (2*r+1) > n:
sys.exit("ERROR: Stencil radius exceeds grid size")
else:
r = 2 # radius=2 is what other impls use right now
print('Grid size = ', n)
print('Radius of stencil = ', r)
if pattern == 'star':
print('Type of stencil = ','star')
else:
print('Type of stencil = ','grid')
print('Data type = double precision')
print('Compact representation of stencil loop body')
print('Number of iterations = ', iterations)
# there is certainly a more Pythonic way to initialize W,
# but it will have no impact on performance.
W = numpy.zeros(((2*r+1),(2*r+1)))
if pattern == 'star':
stencil_size = 4*r+1
for i in range(1,r+1):
W[r,r+i] = +1./(2*i*r)
W[r+i,r] = +1./(2*i*r)
W[r,r-i] = -1./(2*i*r)
W[r-i,r] = -1./(2*i*r)
else:
stencil_size = (2*r+1)**2
for j in range(1,r+1):
for i in range(-j+1,j):
W[r+i,r+j] = +1./(4*j*(2*j-1)*r)
W[r+i,r-j] = -1./(4*j*(2*j-1)*r)
W[r+j,r+i] = +1./(4*j*(2*j-1)*r)
W[r-j,r+i] = -1./(4*j*(2*j-1)*r)
W[r+j,r+j] = +1./(4*j*r)
W[r-j,r-j] = -1./(4*j*r)
A = numpy.fromfunction(lambda i,j: i+j, (n,n), dtype=float)
B = numpy.zeros((n,n))
for k in range(iterations+1):
# start timer after a warmup iteration
if k<1: t0 = timer()
if pattern == 'star':
if r == 2:
star2(n,W,A,B)
else:
star(n,r,W,A,B)
else: # grid
grid(n,r,W,A,B)
A += 1.0
t1 = timer()
stencil_time = t1 - t0
#******************************************************************************
#* Analyze and output results.
#******************************************************************************
norm = numpy.linalg.norm(numpy.reshape(B,n*n),ord=1)
active_points = (n-2*r)**2
norm /= active_points
epsilon=1.e-8
# verify correctness
reference_norm = 2*(iterations+1)
if abs(norm-reference_norm) < epsilon:
print('Solution validates')
flops = (2*stencil_size+1) * active_points
avgtime = stencil_time/iterations
print('Rate (MFlops/s): ',1.e-6*flops/avgtime, ' Avg time (s): ',avgtime)
else:
print('ERROR: L1 norm = ', norm,' Reference L1 norm = ', reference_norm)
sys.exit()
if __name__ == '__main__':
main()