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Initial set of tests
A set of tests and a bash script which I use to make performance comparisons between two form/tform binaries. The tests run in /dev/shm (which should be a tmpfs) to keep disk access performance out of the comparison. There are no promises that this works properly on other systems at this point. `hyperfine' is used for the timings.
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‎run.sh‎

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#!/bin/bash
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ORIGDIR=$(pwd)
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TIMESTAMP=$(date +%Y-%m-%d-%H-%M-%S)
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RESULTSDIR=$ORIGDIR/output/$TIMESTAMP/results/
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LOGDIR=$ORIGDIR/output/$TIMESTAMP/logs/
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mkdir -p $RESULTSDIR
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mkdir -p $LOGDIR
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TESTDIR="/dev/shm/form-bench-$TIMESTAMP/"
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mkdir $TESTDIR
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TMPDIR=$TESTDIR/formtmp
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mkdir $TMPDIR
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export FORMTMP=$TMPDIR
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cp -r $ORIGDIR/tests/* $TESTDIR
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cd $TESTDIR
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N=2
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declare -A runs
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runs["trace"]=$(($N * 30 ))
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runs["mincer"]=$(($N * 4 ))
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runs["minceex"]=$(($N * 6 ))
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runs["mass-fact"]=$(($N * 4 ))
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runs["forcer"]=$(($N * 3 ))
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runs["forcer-exp"]=$(($N * 4 ))
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runs["mbox1l"]=$(($N * 15 ))
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runs["color"]=$(($N * 15 ))
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runs["chromatic"]=$(($N * 4 ))
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declare -A warmup
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warmup["trace"]=3
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warmup["mincer"]=0
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warmup["minceex"]=0
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warmup["mass-fact"]=0
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warmup["forcer"]=0
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warmup["forcer-exp"]=0
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warmup["mbox1l"]=1
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warmup["color"]=1
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warmup["chromatic"]=0
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FORM1=tform-test
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FORM2=tform-test-ps
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CPU=24
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#TESTS="trace mincer minceex mass-fact forcer forcer-exp mbox1l color chromatic"
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TESTS="trace minceex forcer forcer-exp mbox1l color chromatic"
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for test in $TESTS; do
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cd $test
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echo ""
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echo ""
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echo Running $test
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hyperfine --warmup ${warmup[$test]} --runs ${runs[$test]} \
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--export-json $RESULTSDIR/results-$test.json \
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--command-name "$FORM1" \
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--command-name "$FORM2" \
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"nice -n -10 $FORM1 -w$CPU $test.frm > $LOGDIR/$test.log1" \
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"nice -n -10 $FORM2 -w$CPU $test.frm > $LOGDIR/$test.log2"
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cd ..
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done
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cd $ORIGDIR
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rm -rf $TESTDIR
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‎tests/chromatic/chromatic.frm‎

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‎tests/color/color.frm‎

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#-
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#: ScratchSize 1G
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Off Statistics;
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#define SIZE "8"
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* Extend the runtime without increasing SIZE:
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#define LONGER "2"
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*#define ALTERNATEMETHOD "1"
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*
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* Test program for the color traces in the paper and a few more.
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* The paper: "Color traces for arbitrary groups"
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* by T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren.
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*
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* The object is to express color traces in terms of group invariants
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* in such a way that the group has not been specified yet. The few
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* remaining invariants can be substituted afterwards. The expressions
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* in terms of invariants are better for publications. One sees more
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* about the structure of the problem this way.
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*
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* All declarations are made in the file cfactors.h
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* One needs version 3 or later of FORM to run these programs.
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* The programs will handle all color structures with up to 14 vertices.
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* One vertex is one generator in any representation.
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* Currently the program handles only one type of non-adjoint representaion.
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* If there are two different representations of such type one has to
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* try to run the problem in stages.
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*
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* Examples are:
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* One quark-loop with SIZE gluons in a maximally non-planar configuration
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* (TYPE = qloop)
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* Same but qluon loop (everything in the adjoint representation)
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* (TYPE = gloop)
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* Two quark loops with SIZE connecting gluons like a circular ladder.
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* (TYPE = qqloop)
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* Same with one quark loop and one gluon loop.
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* (TYPE = qgloop)
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* Same with two gluon loops.
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* (TYPE = ggloop)
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* The Coxeter graph (diagram with 14 vertices in the adjoint representation
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* in which there are no loops with fewer than 6 lines) (TYPE = g14)
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*
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* One should not choose SIZE larger than 7 or most likely the simplification
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* routine cannot simplify the final result completely (in some rare cases
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* it can though for SIZE = 8).
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* For execution times, see the paper.
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* It does get very slow for quarks and SIZE > 7.
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*
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* Program by J.Vermaseren, 24-may-1997
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*
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#include color.h
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AutoDeclare Index i,j,k;
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CFunction acc;
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Symbol x,y;
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.global
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G Q{2*`SIZE'} = <T(i1,i2,j1)>*...*<T(i`SIZE',i{`SIZE'+1},j`SIZE')>
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*<T(i{`SIZE'+1},i{`SIZE'+2},j1)>*...*<T(i{`SIZE'*2},i{2*`SIZE'+1},j`SIZE')>
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*replace_(i{`SIZE'*2+1},i1);
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G G{2*`SIZE'} = <f(i1,i2,j1)>*...*<f(i`SIZE',i{`SIZE'+1},j`SIZE')>
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*<f(i{`SIZE'+1},i{`SIZE'+2},j1)>*...*<f(i{`SIZE'*2},i{2*`SIZE'+1},j`SIZE')>
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*replace_(i{`SIZE'*2+1},i1);
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G QQ`SIZE' = <T(i1,i2,j1)>*...*<T(i`SIZE',i{`SIZE'+1},j`SIZE')>
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*<T(k1,k2,j1)>*...*<T(k`SIZE',k{`SIZE'+1},j`SIZE')>
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*replace_(i{`SIZE'+1},i1,k{`SIZE'+1},k1);
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G QG`SIZE' = <T(i1,i2,j1)>*...*<T(i`SIZE',i{`SIZE'+1},j`SIZE')>
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*<f(k1,k2,j1)>*...*<f(k`SIZE',k{`SIZE'+1},j`SIZE')>
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*replace_(i{`SIZE'+1},i1,k{`SIZE'+1},k1);
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G GG`SIZE' = <f(i1,i2,j1)>*...*<f(i`SIZE',i{`SIZE'+1},j`SIZE')>
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*<f(k1,k2,j1)>*...*<f(k`SIZE',k{`SIZE'+1},j`SIZE')>
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*replace_(i{`SIZE'+1},i1,k{`SIZE'+1},k1);
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G girth14 =
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f(i1,i2,i3)*f(i1,i4,i5)*f(i2,i6,i7)*f(i3,i8,i9)
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*f(i4,i10,i11)*f(i5,i12,i13)*f(i6,i14,i15)*f(i7,i16,i17)
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*f(i8,i18,i19)*f(i9,i20,i21)
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*f(i10,i21,i15)*f(i13,i19,i14)*f(i17,i11,i18)*f(i12,i16,i20);
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* Takes too long
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*G girth24 =
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* f(i36,i1,i2)*f(i36,i3,i4)*f(i1,i5,i6)*f(i2,i7,i8)
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* *f(i3,i9,i10)*f(i4,i11,i12)*f(i5,i13,i14)*f(i6,i15,i16)
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* *f(i7,i17,i18)*f(i8,i19,i20)*f(i9,i21,i22)*f(i10,i23,i24)
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* *f(i11,i25,i26)*f(i12,i27,i28)*f(i13,i23,i29)*f(i14,i27,i30)
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* *f(i15,i25,i31)*f(i16,i21,i32)*f(i17,i26,i29)*f(i18,i32,i33)
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* *f(i19,i31,i34)*f(i20,i22,i30)*f(i24,i34,i35)*f(i28,i33,i35);
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G fiveq = T(i1,i2,j1)*T(i2,i3,j2)*T(i3,i1,j3)*
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T(i4,i5,j2)*T(i5,i6,j4)*T(i6,i4,j5)*
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T(i7,i8,j4)*T(i8,i9,j6)*T(i9,i7,j7)*
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T(i10,i11,j6)*T(i11,i12,j1)*T(i12,i10,j8)*
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T(i13,i14,j3)*T(i14,i15,j5)*T(i15,i16,j7)*T(i16,i13,j8);
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Sum i1,...,i{`SIZE'*2},j1,...,j`SIZE',k1,...,k`SIZE';
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Sum i{`SIZE'*2+1},...,i36,j{`SIZE'+1},...,j8;
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Multiply <y^1>+...+<y^`LONGER'>;
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.sort
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#message call color
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#call color
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#call SORT(tloop-1)
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#message call adjoint
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#call adjoint
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#call SORT(tloop-2)
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#call simpli
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id acc(x?) = x;
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id y^x? = 1/`LONGER';
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.sort
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*--#[ Check results
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Local Q16 = -Q16
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+ NA*I2R*cR^7
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- 14*NA*I2R*cA*cR^6
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+ 161/2*NA*I2R*cA^2*cR^5
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- 2975/12*NA*I2R*cA^3*cR^4
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+ 64085/144*NA*I2R*cA^4*cR^3
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- 67655/144*NA*I2R*cA^5*cR^2
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+ 1413487/5184*NA*I2R*cA^6*cR
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- 14740249/217728*NA*I2R*cA^7
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+ 70*d44(cOlpR1,cOlpA1)*cR^4
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- 546*d44(cOlpR1,cOlpA1)*cA*cR^3
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+ 9191/6*d44(cOlpR1,cOlpA1)*cA^2*cR^2
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- 66199/36*d44(cOlpR1,cOlpA1)*cA^3*cR
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+ 4463815489/5598720*d44(cOlpR1,cOlpA1)*cA^4
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+ 18763481/3110400*d44(cOlpR1,cOlpA1)*d44(cOlpA2,cOlpA3)*NA^-1
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+ 56/3*d44(cOlpA1,cOlpA2)*I2R*cR^3
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- 1813/15*d44(cOlpA1,cOlpA2)*I2R*cA*cR^2
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+ 7637/30*d44(cOlpA1,cOlpA2)*I2R*cA^2*cR
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- 21073/120*d44(cOlpA1,cOlpA2)*I2R*cA^3
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- 224*d66(cOlpR1,cOlpA1)*cR^2
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+ 2704/3*d66(cOlpR1,cOlpA1)*cA*cR
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- 7912/9*d66(cOlpR1,cOlpA1)*cA^2
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+ 168*d444(cOlpR1,cOlpA1,cOlpA2)*cR^2
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- 3416/5*d444(cOlpR1,cOlpA1,cOlpA2)*cA*cR
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+ 4380543991/6220800*d444(cOlpR1,cOlpA1,cOlpA2)*cA^2
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+ 536/15*d444(cOlpA1,cOlpA2,cOlpA3)*I2R*cR
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- 125711/1575*d444(cOlpA1,cOlpA2,cOlpA3)*I2R*cA
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+ 896/3*d644(cOlpR1,cOlpA1,cOlpA2)*cR
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- 9296/15*d644(cOlpR1,cOlpA1,cOlpA2)*cA
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- 2624/9*d644(cOlpA1,cOlpR1,cOlpA2)*cR
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+ 3902758067/6531840*d644(cOlpA1,cOlpR1,cOlpA2)*cA
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- 4544/135*d644(cOlpA1,cOlpA2,cOlpA3)*I2R
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+ 136*d88(cOlpR1,cOlpA1)
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+ 35*d844(cOlpR1,cOlpA1,cOlpA2)
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- 31931/1440*d844(cOlpA1,cOlpR1,cOlpA2)
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- 1312/3*d664(cOlpR1,cOlpA1,cOlpA2)
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+ 659/12*d664(cOlpA1,cOlpA2,cOlpR1)
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- 14215999/1036800*d4444a(cOlpR1,cOlpA1,cOlpA2,cOlpA3)
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+ 213768787/1036800*d4444b(cOlpA1,cOlpA2,cOlpR1,cOlpA3)
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;
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Local G16 = -G16
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- 121/31104*NA*cA^8
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- 13/432*d44(cOlpA1,cOlpA2)*cA^4
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+ 91/90*d444(cOlpA1,cOlpA2,cOlpA3)*cA^2
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- 16/27*d644(cOlpA1,cOlpA2,cOlpA3)*cA
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+ d4444a(cOlpA1,cOlpA2,cOlpA3,cOlpA4)
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;
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Local QQ8 = -QQ8
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+ 367/54432*NA*I2R^2*cA^6
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+ 64899031/16588800*cOldddff(cOlpR1,cOlpR2,cOlpA1)*cA
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- 17/12*cOldff554(cOlpR1,cOlpR2,cOlpA1)
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- 159094348241/5016453120000*d33(cOlpR1,cOlpR2)*cA^5
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+ 35065709/17915904000*d33(cOlpR1,cOlpR2)*d44(cOlpA1,cOlpA2)*NA^-1*cA
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+ 9012683/18662400*d44(cOlpR1,cOlpR2)*cA^4
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+ 318287/3110400*d44(cOlpR1,cOlpR2)*d44(cOlpA1,cOlpA2)*NA^-1
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- 7/27*d44(cOlpR1,cOlpA1)*I2R*cA^3
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- 431647/12441600*d44(cOlpR1,cOlpA1)*d44(cOlpR2,cOlpA2)*NA^-1
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+ 11/360*d44(cOlpA1,cOlpA2)*I2R^2*cA^2
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- 359/432*d55(cOlpR1,cOlpR2)*cA^3
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+ 49/24*d66(cOlpR1,cOlpR2)*cA^2
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+ 4/9*d66(cOlpR1,cOlpA1)*I2R*cA
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+ 20096267/41472000*d543(cOlpR1,cOlpA1,cOlpR2)*cA^2
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+ 256036391/580608000*d543(cOlpR2,cOlpA1,cOlpR1)*cA^2
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- 1099101299/248832000*d444(cOlpR1,cOlpR2,cOlpA1)*cA^2
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- 7/30*d444(cOlpR1,cOlpA1,cOlpA2)*I2R*cA
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+ 17/1575*d444(cOlpA1,cOlpA2,cOlpA3)*I2R^2
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- 7/3*d77(cOlpR1,cOlpR2)*cA
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+ 4794133/4147200*d653(cOlpA1,cOlpR1,cOlpR2)*cA
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+ 70310809/58060800*d653(cOlpA1,cOlpR2,cOlpR1)*cA
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- 49/36*d644(cOlpR1,cOlpR2,cOlpA1)*cA
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+ 7/45*d644(cOlpR1,cOlpA1,cOlpA2)*I2R
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- 49/36*d644(cOlpR2,cOlpR1,cOlpA1)*cA
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+ 7804501/1814400*d644(cOlpA1,cOlpR1,cOlpR2)*cA
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- 5/27*d644(cOlpA1,cOlpR1,cOlpA2)*I2R
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- 359/180*d554(cOlpR1,cOlpR2,cOlpA1)*cA
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- 19720033979/104509440000*d4433b(cOlpA1,cOlpA2,cOlpR1,cOlpR2)*cA
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+ d88(cOlpR1,cOlpR2)
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+ 35/96*d853(cOlpA1,cOlpR1,cOlpR2)
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+ 13/1440*d853(cOlpA1,cOlpR2,cOlpR1)
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+ 199/540*d844(cOlpA1,cOlpR1,cOlpR2)
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- 1/3*d763(cOlpR1,cOlpA1,cOlpR2)
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- 1/3*d763(cOlpR2,cOlpA1,cOlpR1)
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+ 7/6*d754(cOlpR2,cOlpR1,cOlpA1)
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+ 7/4*d664(cOlpR1,cOlpR2,cOlpA1)
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- 5/6*d664(cOlpR1,cOlpA1,cOlpR2)
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- 5/6*d664(cOlpR2,cOlpA1,cOlpR1)
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- 1/6*d655(cOlpA1,cOlpR1,cOlpR2)
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- 7437791/41472000*d6433b(cOlpA1,cOlpA2,cOlpR1,cOlpR2)
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- 12199/1382400*d6433c(cOlpA1,cOlpA2,cOlpR1,cOlpR2)
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- 119473/6220800*d6433c(cOlpA1,cOlpA2,cOlpR2,cOlpR1)
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+ 1403/115200*d5443a(cOlpR1,cOlpA1,cOlpA2,cOlpR2)
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- 226219/4147200*d5443a(cOlpR2,cOlpA1,cOlpA2,cOlpR1)
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+ 18757/57600*d5443c(cOlpR1,cOlpA1,cOlpA2,cOlpR2)
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+ 951979/2073600*d5443c(cOlpR2,cOlpA1,cOlpA2,cOlpR1)
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- 253697/1658880*d4444a(cOlpR1,cOlpR2,cOlpA1,cOlpA2)
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+ 1167989/2764800*d4444a(cOlpR1,cOlpA1,cOlpR2,cOlpA2)
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+ 1498639/4147200*d4444b(cOlpR2,cOlpA1,cOlpR1,cOlpA2)
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- 76367/1036800*d4444b(cOlpA1,cOlpA2,cOlpR1,cOlpR2)
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;
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Local QG8 = -QG8
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+ 353/54432*NA*I2R*cA^7
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+ 4641769/44789760*d44(cOlpR1,cOlpA1)*cA^4
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+ 2638717/12441600*d44(cOlpR1,cOlpA1)*d44(cOlpA2,cOlpA3)*NA^-1
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- 19/180*d44(cOlpA1,cOlpA2)*I2R*cA^3
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+ 163/72*d66(cOlpR1,cOlpA1)*cA^2
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- 2085523/24883200*d444(cOlpR1,cOlpA1,cOlpA2)*cA^2
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+ 52/1575*d444(cOlpA1,cOlpA2,cOlpA3)*I2R*cA
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- 77/60*d644(cOlpR1,cOlpA1,cOlpA2)*cA
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- 3874757/26127360*d644(cOlpA1,cOlpR1,cOlpA2)*cA
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- 2/135*d644(cOlpA1,cOlpA2,cOlpA3)*I2R
227+
+ d88(cOlpR1,cOlpA1)
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+ 199/540*d844(cOlpA1,cOlpR1,cOlpA2)
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+ 11/12*d664(cOlpR1,cOlpA1,cOlpA2)
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- 5/6*d664(cOlpA1,cOlpA2,cOlpR1)
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+ 2914957/4147200*d4444a(cOlpR1,cOlpA1,cOlpA2,cOlpA3)
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- 120809/829440*d4444b(cOlpA1,cOlpA2,cOlpR1,cOlpA3)
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;
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Local GG8 = -GG8
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+ 61/15552*NA*cA^8
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- 13/432*d44(cOlpA1,cOlpA2)*cA^4
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+ 91/90*d444(cOlpA1,cOlpA2,cOlpA3)*cA^2
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- 16/27*d644(cOlpA1,cOlpA2,cOlpA3)*cA
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+ d4444a(cOlpA1,cOlpA2,cOlpA3,cOlpA4)
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;
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Local girth14 = -girth14
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+ 1/648*NA*cA^7
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- 8/15*d444(cOlpA1,cOlpA2,cOlpA3)*cA
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+ 16/9*d644(cOlpA1,cOlpA2,cOlpA3)
247+
;
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Local fiveq = -fiveq
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+ 1/192*NA*I2R^5*cA^3
251+
+ 1/4*d33(cOlpR1,cOlpR2)*I2R^3*cA^2
252+
+ 5/48*d33(cOlpR1,cOlpR2)*d33(cOlpR3,cOlpR4)*NA^-1*I2R*cA
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+ 5/48*d33(cOlpR1,cOlpR3)*d33(cOlpR2,cOlpR4)*NA^-1*I2R*cA
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+ 1/8*d33(cOlpR1,cOlpR4)*d33(cOlpR2,cOlpR3)*NA^-1*I2R*cA
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+ 1/16*d44(cOlpR1,cOlpA1)*I2R^4
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+ 3/8*d433(cOlpR3,cOlpR1,cOlpR2)*I2R^2*cA
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+ 1/2*d3333(cOlpR1,cOlpR2,cOlpR3,cOlpR4)*I2R*cA
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+ d43333a(cOlpR5,cOlpR2,cOlpR1,cOlpR4,cOlpR3)
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;
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.sort
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#do ex = {`activeexprnames_'}
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#if `ZERO_`ex'' == 0
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#message Error in `ex'
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#terminate
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#endif
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#enddo
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*--#]
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.end

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