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+# THIS PURPOSELY DOES NOT HAVE A !# LINE !!!!
+#
+# Date: Mon, 9 Sep 2013 14:49:43 -0700
+# From: Bob Jewett <jewett@bill.scs.agilent.com>
+# Message-Id: <201309092149.r89Lnh94010909@bill.scs.agilent.com>
+# To: arnold@skeeve.com
+# Subject: Re: [bug-gawk] Bug in random() in builtin.c
+# 
+# Hi Arnold,
+# 
+# Attached below is a script that tests gawk for this particular
+# rand() problem.  The pair-wise combinations show a strong
+# autocorrelation for a delay of 31 pairs of rand() samples. 
+# 
+# The script prints out the measured autocorrelation for a record
+# of NSAMPLES pairs.  It also prints a fail message at the end if
+# it fails. 
+# 
+# If you want to see the autocorrelation values, there is a print
+# statement that if uncommented will save them to a file.
+# 
+# Please let me know if the mailer screws up the transfer or
+# if you have any questions about the test.
+# 
+# Best regards,
+# Bob
+# 
+# -------------- test_pair_power_autocorrelation -----------------------
+# 
+#!/bin/ksh
+
+#GAWK=/bin/gawk
+
+# ADR: Get GAWK from the environment.
+# Additional note: This wants ksh/bash for the use of $RANDOM below to
+# seed the generator. However, shells that don't provide it won't be
+# a problem since gawk will then seed the generator with the time of day,
+# as srand() will be called without an argument.
+
+# large NSAMPLES and NRUNS will bring any correlation out of the noise better
+NSAMPLES=1024; MAX_ALLOWED_SIGMA=5; NRUNS=50;
+
+$GAWK 'BEGIN{ 
+    srand('$RANDOM');
+    nsamples=('$NSAMPLES');
+    max_allowed_sigma=('$MAX_ALLOWED_SIGMA');
+    nruns=('$NRUNS');
+    for(tau=0;tau<nsamples/2;tau++) corr[tau]=0;
+
+    for(run=0;run<nruns;run++) {
+	sum=0;
+
+	# Fill an array with a sequence of samples that are a
+	# function of pairs of rand() values.
+
+	for(i=0;i<nsamples;i++) {
+	   samp[i]=((rand()-0.5)*(rand()-0.5))^2;
+	   sum=sum+samp[i];
+	   }
+
+	# Subtract off the mean of the sequence:
+
+	mean=sum/nsamples;
+	for(i=0;i<nsamples;i++) samp[i]=samp[i]-mean;
+
+	# Calculate an autocorrelation function on the sequence.
+	# Because the values of rand() should be independent, there
+	# should be no peaks in the autocorrelation.
+
+	for(tau=0;tau<nsamples/2;tau++) {
+	    sum=0;
+	    for(i=0;i<nsamples/2;i++) sum=sum+samp[i]*samp[i+tau];
+	    corr[tau]=corr[tau]+sum;
+	    }
+
+	}
+    # Normalize the autocorrelation to the tau=0 value.
+
+    max_corr=corr[0];
+    for(tau=0;tau<nsamples/2;tau++) corr[tau]=corr[tau]/max_corr;
+
+    # OPTIONALLY Print out the autocorrelation values:
+
+    # for(tau=0;tau<nsamples/2;tau++) print tau, corr[tau] > "pairpower_corr.data";
+
+    # Calculate the sigma for the non-zero tau values: 
+
+    power_sum=0;
+
+    for(tau=1;tau<nsamples/2;tau++) power_sum=power_sum+(corr[tau])^2;
+
+    sigma=sqrt(power_sum/(nsamples/2-1));
+
+    # See if any of the correlations exceed a reasonable number of sigma:
+
+    passed=1;
+    for(tau=1;tau<nsamples/2;tau++) {
+	if ( abs(corr[tau])/sigma > max_allowed_sigma ) {
+	    print "Tau=", tau ", Autocorr=", corr[tau]/sigma, "sigma";
+	    passed=0;
+	    }
+        }
+    if(!passed) {
+	print "Test failed."
+	exit(1);
+        }
+    else exit (0);
+    }
+
+function abs(abs_input) { return(sqrt(abs_input^2)) ; }
+'
+
+exit 0