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-#!/usr/bin/env python
-##
-## Name: findthreshold.py
-## Purpose: Find a good threshold for recursive multiplication.
-## Author: M. J. Fromberger <http://spinning-yarns.org/michael/>
-## Info: $Id: findthreshold.py 456 2006-08-16 14:24:06Z sting $
-##
-## This tool computes some timing statistics to help you select a suitable
-## recursive multiplication breakpoint. It uses the imtimer tool to run a
-## series of tests varying precision and breakpoint, and prints out a summary
-## of the "best" values for each category. Each summary line contains the
-## following fields, tab-separated:
-##
-## prec -- the precision of the operands (in digits).
-## thresh -- the threshold for recursive multiplication (digits).
-## trec -- total time using recursive algorithm (sec).
-## tnorm -- total time without recursive algorithm (sec).
-## ratio -- speedup (ratio of tnorm/trec).
-##
-## You are responsible for reading and interpreting the resulting table to
-## obtain a useful value for your workload. Change the value of MP_MULT_THRESH
-## in imath.h once you have a satisfactory result.
-##
-import math, os, random, sys, time
-
-def get_timing_stats(num_tests, precision, threshold, seed = None):
- """Obtain timing statistics for multiplication.
-
- num_tests -- number of tests to run.
- precision -- number of digits per operand.
- threshold -- threshold in digits for recursive multiply.
- seed -- random seed; if None, the clock is used.
-
- Returns a tuple of (seed, bits, time) where seed is the random seed used,
- bits is the number of bits per operand, and time is a float giving the
- total time taken for the test run.
- """
- if seed is None:
- seed = int(time.time())
-
- line = os.popen('./imtimer -mn -p %d -t %d -s %d %d' %
- (precision, threshold, seed, num_tests), 'r').readline()
-
- count, prec, bits, thresh, status = line.strip().split('\t')
- kind, total, unit = status.split()
-
- return seed, int(bits), float(total)
-
-def check_binary(name):
- if not os.path.exists(name):
- os.system('make %s' % name)
- if not os.path.exists(name):
- raise ValueError("Unable to build %s" % name)
- elif not os.path.isfile(name):
- raise ValueError("Path exists with wrong type")
-
-def compute_stats():
- check_binary('imtimer')
- seed = int(time.time())
-
- print >> sys.stderr, "Computing timer statistics (this may take a while)"
- stats = {}
- for prec in (32, 40, 64, 80, 128, 150, 256, 384, 512, 600, 768, 1024):
- sys.stderr.write('%-4d ' % prec)
- stats[prec] = (None, 1000000., 0.)
-
- for thresh in xrange(16, 65, 2):
- s, b, t = get_timing_stats(1000, prec, thresh, seed)
- sp, bp, tp = get_timing_stats(1000, prec, prec + 1, seed)
-
- if t < stats[prec][1]:
- stats[prec] = (thresh, t, tp)
- sys.stderr.write('+')
- else:
- sys.stderr.write('.')
- sys.stderr.write('\n')
-
- return list((p, h, t, tp) for p, (h, t, tp) in stats.iteritems())
-
-if __name__ == "__main__":
- stats = compute_stats()
- stats.sort(key = lambda s: s[3]/s[2])
- for prec, thresh, trec, tnorm in stats:
- print "%d\t%d\t%.3f\t%.3f\t%.4f" % (prec, thresh, trec, tnorm,
- tnorm / trec)
-
- print
-
-# Here there be dragons
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