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|
/* -------------------------------------------------------------------------- *
* Simbody(tm): SimTKcommon *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2008-12 Stanford University and the Authors. *
* Authors: Michael Sherman *
* Contributors: *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
#include "SimTKcommon.h"
#include "SimTKcommon/Testing.h"
#include <iostream>
using std::cout;
using std::endl;
using namespace SimTK;
void testIsNaN() {
const float fltRegular = -12.34f;
const double dblRegular = -12.34;
const float fltNaN = NTraits<float>::getNaN();
const double dblNaN = NTraits<double>::getNaN();
const float nfltNaN = -fltNaN;
const double ndblNaN = -dblNaN;
SimTK_TEST(isNaN(fltNaN) && isNaN(dblNaN));
SimTK_TEST(isNaN(nfltNaN) && isNaN(ndblNaN));
SimTK_TEST(!isNaN(fltRegular) && !isNaN(dblRegular));
std::complex<float> cflt(fltRegular, -2*fltRegular);
std::complex<double> cdbl(dblRegular, -2*dblRegular);
conjugate<float> cjflt(fltRegular, -2*fltRegular);
conjugate<double> cjdbl(dblRegular, -2*dblRegular);
SimTK_TEST(!isNaN(cflt) && !isNaN(cdbl));
SimTK_TEST(!isNaN(cjflt) && !isNaN(cjdbl));
// Reference the same memory as a negator of its contents.
const negator<float>& nflt = reinterpret_cast<const negator<float>&>(fltRegular);
const negator<double>& ndbl = reinterpret_cast<const negator<double>&>(dblRegular);
negator<std::complex<float> >& ncflt = reinterpret_cast<negator<std::complex<float> >&> (cflt);
negator<std::complex<double> >& ncdbl = reinterpret_cast<negator<std::complex<double> >&>(cdbl);
negator<conjugate<float> >& ncjflt = reinterpret_cast<negator<conjugate<float> >&> (cjflt);
negator<conjugate<double> >& ncjdbl = reinterpret_cast<negator<conjugate<double> >&> (cjdbl);
// Test that negators are working properly.
SimTK_TEST_EQ(nflt, -fltRegular);
SimTK_TEST_EQ(ndbl, -dblRegular);
SimTK_TEST_EQ(ncflt, -cflt);
SimTK_TEST_EQ(-ncflt, cflt);
SimTK_TEST_EQ(ncjflt, -cjflt);
SimTK_TEST_EQ(-ncjflt, cjflt);
SimTK_TEST(!isNaN(nflt) && !isNaN(ndbl));
SimTK_TEST(!isNaN(ncflt) && !isNaN(ncdbl));
SimTK_TEST(!isNaN(ncjflt) && !isNaN(ncjdbl));
// Should be NaN if either or both parts are NaN.
cflt = std::complex<float>(cflt.real(), fltNaN);
cdbl = std::complex<double>(cdbl.real(), dblNaN);
cjflt = conjugate<float>(cjflt.real(), fltNaN);
cjdbl = conjugate<double>(cjdbl.real(), dblNaN);
// Imaginary only is NaN.
SimTK_TEST(isNaN(cflt) && isNaN(cdbl));
SimTK_TEST(isNaN(cjflt) && isNaN(cjdbl));
SimTK_TEST(isNaN(ncflt) && isNaN(ncdbl));
SimTK_TEST(isNaN(ncjflt) && isNaN(ncjdbl));
cflt = std::complex<float>(fltNaN, cflt.imag());
cdbl = std::complex<double>(dblNaN, cdbl.imag());
cjflt = conjugate<float>(fltNaN, cjflt.imag());
cjdbl = conjugate<double>(dblNaN, cjdbl.imag());
// Both parts are NaN.
SimTK_TEST(isNaN(cflt) && isNaN(cdbl));
SimTK_TEST(isNaN(cjflt) && isNaN(cjdbl));
SimTK_TEST(isNaN(ncflt) && isNaN(ncdbl));
SimTK_TEST(isNaN(ncjflt) && isNaN(ncjdbl));
// Restore imaginary part to normal.
cflt = std::complex<float>(cflt.real(), fltRegular);
cdbl = std::complex<double>(cdbl.real(), dblRegular);
cjflt = conjugate<float>(cjflt.real(), fltRegular);
cjdbl = conjugate<double>(cjdbl.real(), dblRegular);
// Real part only is NaN;
SimTK_TEST(isNaN(cflt) && isNaN(cdbl));
SimTK_TEST(isNaN(cjflt) && isNaN(cjdbl));
SimTK_TEST(isNaN(ncflt) && isNaN(ncdbl));
SimTK_TEST(isNaN(ncjflt) && isNaN(ncjdbl));
}
void testIsInf() {
const float fltRegular = -12.34f;
const double dblRegular = -12.34;
const float fltInf = NTraits<float>::getInfinity();
const double dblInf = NTraits<double>::getInfinity();
const float mfltInf = -fltInf;
const double mdblInf = -dblInf;
const negator<float>& nfltInf = reinterpret_cast<const negator<float>&>(fltInf);
const negator<double>& ndblInf = reinterpret_cast<const negator<double>&>(dblInf);
SimTK_TEST(nfltInf == -fltInf);
SimTK_TEST(ndblInf == -dblInf);
SimTK_TEST(isInf(fltInf) && isInf(dblInf));
SimTK_TEST(isInf(mfltInf) && isInf(mdblInf));
SimTK_TEST(isInf(nfltInf) && isInf(ndblInf));
SimTK_TEST(!isInf(fltRegular) && !isInf(dblRegular));
std::complex<float> cflt(fltRegular, -2*fltRegular);
std::complex<double> cdbl(dblRegular, -2*dblRegular);
conjugate<float> cjflt(fltRegular, -2*fltRegular);
conjugate<double> cjdbl(dblRegular, -2*dblRegular);
SimTK_TEST(!isInf(cflt) && !isInf(cdbl));
SimTK_TEST(!isInf(cjflt) && !isInf(cjdbl));
// Reference the same memory as a negator of its contents.
const negator<float>& nflt = reinterpret_cast<const negator<float>&>(fltRegular);
const negator<double>& ndbl = reinterpret_cast<const negator<double>&>(dblRegular);
negator<std::complex<float> >& ncflt = reinterpret_cast<negator<std::complex<float> >&> (cflt);
negator<std::complex<double> >& ncdbl = reinterpret_cast<negator<std::complex<double> >&>(cdbl);
negator<conjugate<float> >& ncjflt = reinterpret_cast<negator<conjugate<float> >&> (cjflt);
negator<conjugate<double> >& ncjdbl = reinterpret_cast<negator<conjugate<double> >&> (cjdbl);
// Test that negators are working properly.
SimTK_TEST_EQ(nflt, -fltRegular);
SimTK_TEST_EQ(ndbl, -dblRegular);
SimTK_TEST_EQ(ncflt, -cflt);
SimTK_TEST_EQ(-ncflt, cflt);
SimTK_TEST_EQ(ncjflt, -cjflt);
SimTK_TEST_EQ(-ncjflt, cjflt);
SimTK_TEST(!isInf(nflt) && !isInf(ndbl));
SimTK_TEST(!isInf(ncflt) && !isInf(ncdbl));
SimTK_TEST(!isInf(ncjflt) && !isInf(ncjdbl));
// Should be Inf if either or both parts are Inf, as long as neither
// part is NaN.
cflt = std::complex<float>(cflt.real(), fltInf);
cdbl = std::complex<double>(cdbl.real(), dblInf);
cjflt = conjugate<float>(cjflt.real(), fltInf);
cjdbl = conjugate<double>(cjdbl.real(), dblInf);
// Imaginary only is Inf.
SimTK_TEST(isInf(cflt) && isInf(cdbl));
SimTK_TEST(isInf(cjflt) && isInf(cjdbl));
SimTK_TEST(isInf(ncflt) && isInf(ncdbl));
SimTK_TEST(isInf(ncjflt) && isInf(ncjdbl));
cflt = std::complex<float>(fltInf, cflt.imag());
cdbl = std::complex<double>(dblInf, cdbl.imag());
cjflt = conjugate<float>(fltInf, cjflt.imag());
cjdbl = conjugate<double>(dblInf, cjdbl.imag());
// Both parts are Inf.
SimTK_TEST(isInf(cflt) && isInf(cdbl));
SimTK_TEST(isInf(cjflt) && isInf(cjdbl));
SimTK_TEST(isInf(ncflt) && isInf(ncdbl));
SimTK_TEST(isInf(ncjflt) && isInf(ncjdbl));
// Restore imaginary part to normal.
cflt = std::complex<float>(cflt.real(), fltRegular);
cdbl = std::complex<double>(cdbl.real(), dblRegular);
cjflt = conjugate<float>(cjflt.real(), fltRegular);
cjdbl = conjugate<double>(cjdbl.real(), dblRegular);
// Real part only is Inf;
SimTK_TEST(isInf(cflt) && isInf(cdbl));
SimTK_TEST(isInf(cjflt) && isInf(cjdbl));
SimTK_TEST(isInf(ncflt) && isInf(ncdbl));
SimTK_TEST(isInf(ncjflt) && isInf(ncjdbl));
// Set real part to minus infinity.
cflt = std::complex<float>(mfltInf, cflt.imag());
cdbl = std::complex<double>(mdblInf, cdbl.imag());
cjflt = conjugate<float>(mfltInf, cjflt.imag());
cjdbl = conjugate<double>(mdblInf, cjdbl.imag());
SimTK_TEST(isInf(cflt) && isInf(cdbl));
SimTK_TEST(isInf(cjflt) && isInf(cjdbl));
SimTK_TEST(isInf(ncflt) && isInf(ncdbl));
SimTK_TEST(isInf(ncjflt) && isInf(ncjdbl));
// Set real part to NaN.
const float fltNaN = NTraits<float>::getNaN();
const double dblNaN = NTraits<double>::getNaN();
cflt = std::complex<float>(fltNaN, cflt.imag());
cdbl = std::complex<double>(dblNaN, cdbl.imag());
cjflt = conjugate<float>(fltNaN, cjflt.imag());
cjdbl = conjugate<double>(dblNaN, cjdbl.imag());
SimTK_TEST(!isInf(cflt) && !isInf(cdbl));
SimTK_TEST(!isInf(cjflt) && !isInf(cjdbl));
SimTK_TEST(!isInf(ncflt) && !isInf(ncdbl));
SimTK_TEST(!isInf(ncjflt) && !isInf(ncjdbl));
}
void testIsFinite() {
const float fltRegular = -12.34f;
const double dblRegular = -12.34;
const float fltNaN = NTraits<float>::getNaN();
const double dblNaN = NTraits<double>::getNaN();
const float nfltNaN = -fltNaN;
const double ndblNaN = -dblNaN;
const float fltInf = NTraits<float>::getInfinity();
const double dblInf = NTraits<double>::getInfinity();
const float mfltInf = -fltInf;
const double mdblInf = -dblInf;
SimTK_TEST(isFinite(fltRegular) && isFinite(dblRegular));
SimTK_TEST(!isFinite(fltNaN) && !isFinite(dblNaN));
SimTK_TEST(!isFinite(fltInf) && !isFinite(dblInf));
SimTK_TEST(!isFinite(mfltInf) && !isFinite(mdblInf));
std::complex<float> cflt(fltRegular, -2*fltRegular);
std::complex<double> cdbl(dblRegular, -2*dblRegular);
conjugate<float> cjflt(fltRegular, -2*fltRegular);
conjugate<double> cjdbl(dblRegular, -2*dblRegular);
SimTK_TEST(isFinite(cflt) && isFinite(cdbl));
SimTK_TEST(isFinite(cjflt) && isFinite(cjdbl));
// Reference the same memory as a negator of its contents.
const negator<float>& nflt = reinterpret_cast<const negator<float>&>(fltRegular);
const negator<double>& ndbl = reinterpret_cast<const negator<double>&>(dblRegular);
negator<std::complex<float> >& ncflt = reinterpret_cast<negator<std::complex<float> >&> (cflt);
negator<std::complex<double> >& ncdbl = reinterpret_cast<negator<std::complex<double> >&>(cdbl);
negator<conjugate<float> >& ncjflt = reinterpret_cast<negator<conjugate<float> >&> (cjflt);
negator<conjugate<double> >& ncjdbl = reinterpret_cast<negator<conjugate<double> >&> (cjdbl);
// Test that negators are working properly.
SimTK_TEST_EQ(nflt, -fltRegular);
SimTK_TEST_EQ(ndbl, -dblRegular);
SimTK_TEST_EQ(ncflt, -cflt);
SimTK_TEST_EQ(-ncflt, cflt);
SimTK_TEST_EQ(ncjflt, -cjflt);
SimTK_TEST_EQ(-ncjflt, cjflt);
SimTK_TEST(isFinite(nflt) && isFinite(ndbl));
SimTK_TEST(isFinite(ncflt) && isFinite(ncdbl));
SimTK_TEST(isFinite(ncjflt) && isFinite(ncjdbl));
// Should be finite only if both parts are finite.
cflt = std::complex<float>(cflt.real(), fltInf);
cdbl = std::complex<double>(cdbl.real(), mdblInf);
cjflt = conjugate<float>(cjflt.real(), fltNaN);
cjdbl = conjugate<double>(cjdbl.real(), dblInf);
// Imaginary only is NaN.
SimTK_TEST(!isFinite(cflt) && !isFinite(cdbl));
SimTK_TEST(!isFinite(cjflt) && !isFinite(cjdbl));
SimTK_TEST(!isFinite(ncflt) && !isFinite(ncdbl));
SimTK_TEST(!isFinite(ncjflt) && !isFinite(ncjdbl));
cflt = std::complex<float> (fltInf, cflt.imag());
cdbl = std::complex<double>(mdblInf, cdbl.imag());
cjflt = conjugate<float> (fltNaN, cjflt.imag());
cjdbl = conjugate<double> (dblInf, cjdbl.imag());
// Both parts are non-finite.
SimTK_TEST(!isFinite(cflt) && !isFinite(cdbl));
SimTK_TEST(!isFinite(cjflt) && !isFinite(cjdbl));
SimTK_TEST(!isFinite(ncflt) && !isFinite(ncdbl));
SimTK_TEST(!isFinite(ncjflt) && !isFinite(ncjdbl));
// Restore imaginary part to normal.
cflt = std::complex<float>(cflt.real(), fltRegular);
cdbl = std::complex<double>(cdbl.real(), dblRegular);
cjflt = conjugate<float>(cjflt.real(), fltRegular);
cjdbl = conjugate<double>(cjdbl.real(), dblRegular);
// Real part only is non-finite;
SimTK_TEST(!isFinite(cflt) && !isFinite(cdbl));
SimTK_TEST(!isFinite(cjflt) && !isFinite(cjdbl));
SimTK_TEST(!isFinite(ncflt) && !isFinite(ncdbl));
SimTK_TEST(!isFinite(ncjflt) && !isFinite(ncjdbl));
}
void testSignBit() {
const unsigned char ucm=0xff, ucz=0, ucp=27;
const unsigned short usm=0xffff, usz=0, usp=2342;
const unsigned int uim=0xffffffff, uiz=0, uip=2342344;
const unsigned long ulm=(unsigned long)-23423L, ulz=0, ulp=234234UL;
const unsigned long long ullm=(unsigned long long)-234234234LL, ullz=0, ullp=234234234ULL;
SimTK_TEST(!(signBit(ucm)||signBit(ucz)||signBit(ucp)));
SimTK_TEST(!(signBit(usm)||signBit(usz)||signBit(usp)));
SimTK_TEST(!(signBit(uim)||signBit(uiz)||signBit(uip)));
SimTK_TEST(!(signBit(ulm)||signBit(ulz)||signBit(ulp)));
SimTK_TEST(!(signBit(ullm)||signBit(ullz)||signBit(ullp)));
// Note that signBit(char) doesn't exist.
const signed char cm=-23, cz=0, cp=99;
const short sm=-1234, sz=0, sp=23423;
const int im=-2342343, iz=0, ip=29472383;
const long lm=-43488, lz=0, lp=3454545;
const long long llm=-2342342343433LL, llz=0, llp=874578478478574LL;
SimTK_TEST(signBit(cm) && !(signBit(cz)||signBit(cp)));
SimTK_TEST(signBit(sm) && !(signBit(sz)||signBit(sp)));
SimTK_TEST(signBit(im) && !(signBit(iz)||signBit(ip)));
SimTK_TEST(signBit(lm) && !(signBit(lz)||signBit(lp)));
SimTK_TEST(signBit(llm) && !(signBit(llz)||signBit(llp)));
const float fm=-12398.34f, fz=0, fp=4354.331f;
const double dm=-234234.454, dz=0, dp=345345.2342;
float mfz=-fz; double mdz=-dz;// -0 for some compilers
SimTK_TEST(signBit(fm) && !(signBit(fz)||signBit(fp)));
SimTK_TEST(signBit(dm) && !(signBit(dz)||signBit(dp)));
// Can't be sure whether the compiler will actually have produced
// a minus zero here.
// SimTK_TEST(signBit(mfz) && signBit(mdz));
// Note: signBit of negated float or double should be the
// *same* as the underlying float or double; it is the
// interpretation of that bit that is supposed to be
// different.
const negator<float>& nfm=reinterpret_cast<const negator<float>&>(fm);
const negator<float>& nfz=reinterpret_cast<const negator<float>&>(fz);
const negator<float>& nfp=reinterpret_cast<const negator<float>&>(fp);
const negator<float>& nmfz=reinterpret_cast<const negator<float>&>(mfz);
const negator<double>& ndm=reinterpret_cast<const negator<double>&>(dm);
const negator<double>& ndz=reinterpret_cast<const negator<double>&>(dz);
const negator<double>& ndp=reinterpret_cast<const negator<double>&>(dp);
const negator<double>& nmdz=reinterpret_cast<const negator<double>&>(mdz);
SimTK_TEST(signBit(nfm) && !(signBit(nfz)||signBit(nfp)));
SimTK_TEST(signBit(ndm) && !(signBit(ndz)||signBit(ndp)));
SimTK_TEST(signBit(nmfz)==signBit(mfz) && signBit(nmdz)==signBit(mdz));
const float fltInf = NTraits<float>::getInfinity();
const double dblInf = NTraits<double>::getInfinity();
const float mfltInf = -fltInf;
const double mdblInf = -dblInf;
SimTK_TEST(!signBit(fltInf) && !signBit(dblInf));
SimTK_TEST(signBit(mfltInf) && signBit(mdblInf));
}
void testSign() {
const unsigned char ucm=0xff, ucz=0, ucp=27;
const unsigned short usm=0xffff, usz=0, usp=2342;
const unsigned int uim=0xffffffff, uiz=0, uip=2342344;
const unsigned long ulm=(unsigned long)-23423L, ulz=0, ulp=234234UL;
const unsigned long long ullm=(unsigned long long)-234234234LL, ullz=0, ullp=234234234ULL;
SimTK_TEST(sign(ucm)==1 && sign(ucz)==0 && sign(ucp)==1);
SimTK_TEST(sign(usm)==1 && sign(usz)==0 && sign(usp)==1);
SimTK_TEST(sign(uim)==1 && sign(uiz)==0 && sign(uip)==1);
SimTK_TEST(sign(ulm)==1 && sign(ulz)==0 && sign(ulp)==1);
SimTK_TEST(sign(ullm)==1 && sign(ullz)==0 && sign(ullp)==1);
// Note that sign(char) doesn't exist.
const signed char cm=-23, cz=0, cp=99;
const short sm=-1234, sz=0, sp=23423;
const int im=-2342343, iz=0, ip=29472383;
const long lm=-43488, lz=0, lp=3454545;
const long long llm=-2342342343433LL, llz=0, llp=874578478478574LL;
SimTK_TEST(sign(cm)==-1 && sign(cz)==0 && sign(cp)==1);
SimTK_TEST(sign(sm)==-1 && sign(sz)==0 && sign(sp)==1);
SimTK_TEST(sign(im)==-1 && sign(iz)==0 && sign(ip)==1);
SimTK_TEST(sign(lm)==-1 && sign(lz)==0 && sign(lp)==1);
SimTK_TEST(sign(llm)==-1 && sign(llz)==0 && sign(llp)==1);
const float fm=-12398.34f, fz=0, fp=4354.331f;
const double dm=-234234.454, dz=0, dp=345345.2342;
float mfz=-fz; double mdz=-dz;// -0
SimTK_TEST(sign(fm)==-1 && sign(fz)==0 && sign(fp)==1);
SimTK_TEST(sign(dm)==-1 && sign(dz)==0 && sign(dp)==1);
SimTK_TEST(sign(mfz)==0 && sign(mdz)==0); // doesn't matter if it's -0
// Note: sign of negated float or double should be the
// *opposite* as the underlying float or double.
const negator<float>& nfm=reinterpret_cast<const negator<float>&>(fm);
const negator<float>& nfz=reinterpret_cast<const negator<float>&>(fz);
const negator<float>& nfp=reinterpret_cast<const negator<float>&>(fp);
const negator<float>& nmfz=reinterpret_cast<const negator<float>&>(mfz);
const negator<double>& ndm=reinterpret_cast<const negator<double>&>(dm);
const negator<double>& ndz=reinterpret_cast<const negator<double>&>(dz);
const negator<double>& ndp=reinterpret_cast<const negator<double>&>(dp);
const negator<double>& nmdz=reinterpret_cast<const negator<double>&>(mdz);
SimTK_TEST(sign(nfm)==1 && sign(nfz)==0 && sign(nfp)==-1);
SimTK_TEST(sign(ndm)==1 && sign(ndz)==0 && sign(ndp)==-1);
SimTK_TEST(sign(nmfz)==0 && sign(nmdz)==0); // doesn't matter if it's -0
const float fltInf = NTraits<float>::getInfinity();
const double dblInf = NTraits<double>::getInfinity();
const float mfltInf = -fltInf;
const double mdblInf = -dblInf;
const negator<float>& nfltInf = reinterpret_cast<const negator<float>&>(fltInf);
const negator<double>& ndblInf = reinterpret_cast<const negator<double>&>(dblInf);
SimTK_TEST(sign(fltInf)==1 && sign(dblInf)==1);
SimTK_TEST(sign(mfltInf)==-1 && sign(mdblInf)==-1);
SimTK_TEST(sign(nfltInf)==-1 && sign(ndblInf)==-1);
}
void testSquareAndCube() {
const float fval = -23.33f;
const double dval = -234443.441;
const negator<float>& nfval = reinterpret_cast<const negator<float>&>(fval);
const negator<double>& ndval = reinterpret_cast<const negator<double>&>(dval);
// Basic test.
SimTK_TEST_EQ(square(fval), fval*fval);
SimTK_TEST_EQ(square(dval), dval*dval);
SimTK_TEST_EQ(cube(fval), fval*fval*fval);
SimTK_TEST_EQ(cube(dval), dval*dval*dval);
// Test scalar negators.
SimTK_TEST_EQ(square(nfval), nfval*nfval);
SimTK_TEST_EQ(square(nfval), fval*fval);
SimTK_TEST_EQ(square(ndval), ndval*ndval);
SimTK_TEST_EQ(square(ndval), dval*dval);
SimTK_TEST_EQ(cube(nfval), nfval*nfval*nfval);
SimTK_TEST_EQ(cube(nfval), -fval*fval*fval);
SimTK_TEST_EQ(cube(ndval), ndval*ndval*ndval);
SimTK_TEST_EQ(cube(ndval), -dval*dval*dval);
// Create complex and conjugate values.
std::complex<float> fc(-234.343f, 45345e7f);
std::complex<double> dc(-234.343, 45345e7);
conjugate<float> fcj(-19.1e3f, -454.234f);
conjugate<double> dcj(-19.1e3, -454.234);
// Manual conjugates
std::complex<float> fcmj(fcj.real(), fcj.imag());
std::complex<double> dcmj(dcj.real(), dcj.imag());
SimTK_TEST(fcj == fcmj); // sign change only; should be exact
SimTK_TEST(dcj == dcmj);
SimTK_TEST_EQ(fcj*fcj, fcmj*fcmj);
SimTK_TEST_EQ(dcj*dcj, dcmj*dcmj);
SimTK_TEST_EQ(fcj*fcj*fcj, fcmj*fcmj*fcmj);
SimTK_TEST_EQ(dcj*dcj*dcj, dcmj*dcmj*dcmj);
// Negators of complex an conjugate.
negator<std::complex<float> >& nfc = reinterpret_cast<negator<std::complex<float> >&> (fc);
negator<std::complex<double> >& ndc = reinterpret_cast<negator<std::complex<double> >&>(dc);
negator<conjugate<float> >& nfcj = reinterpret_cast<negator<conjugate<float> >&> (fcj);
negator<conjugate<double> >& ndcj = reinterpret_cast<negator<conjugate<double> >&> (dcj);
// Change of sign should be exact.
SimTK_TEST(nfc == -fc);
SimTK_TEST(ndc == -dc);
SimTK_TEST(nfcj == -fcj);
SimTK_TEST(ndcj == -dcj);
// Basic complex and conjugate tests.
SimTK_TEST_EQ(square(fc), fc*fc);
SimTK_TEST_EQ(cube(fc), fc*fc*fc);
SimTK_TEST_EQ(square(dc), dc*dc);
SimTK_TEST_EQ(cube(dc), dc*dc*dc);
SimTK_TEST_EQ(square(fcj), fcj*fcj);
SimTK_TEST_EQ(cube(fcj), fcj*fcj*fcj);
SimTK_TEST_EQ(square(dcj), dcj*dcj);
SimTK_TEST_EQ(cube(dcj), dcj*dcj*dcj);
// Tests involving negators of complex and conjugate.
SimTK_TEST_EQ(square(nfc), nfc*nfc);
SimTK_TEST_EQ(square(nfc), fc*fc);
SimTK_TEST_EQ(square(ndc), ndc*ndc);
SimTK_TEST_EQ(square(ndc), dc*dc);
SimTK_TEST_EQ(cube(nfc), nfc*nfc*nfc);
SimTK_TEST_EQ(cube(nfc), -fc*fc*fc);
SimTK_TEST_EQ(cube(ndc), ndc*ndc*ndc);
SimTK_TEST_EQ(cube(ndc), -dc*dc*dc);
SimTK_TEST_EQ(square(nfcj), nfcj*nfcj);
SimTK_TEST_EQ(square(nfcj), fcj*fcj);
SimTK_TEST_EQ(square(ndcj), ndcj*ndcj);
SimTK_TEST_EQ(square(ndcj), dcj*dcj);
SimTK_TEST_EQ(cube(nfcj), nfcj*nfcj*nfcj);
SimTK_TEST_EQ(cube(nfcj), -fcj*fcj*fcj);
SimTK_TEST_EQ(cube(ndcj), ndcj*ndcj*ndcj);
SimTK_TEST_EQ(cube(ndcj), -dcj*dcj*dcj);
}
void testIsNumericallyEqual() {
const float f=1.234f, fn=1.234f+1e-5f, fe=1.234f+1e-9f;
const double d=1.234, dn=1.234 +1e-12, de=1.234 +1e-15;
const negator<float>& nf=negator<float>::recast(f);
const negator<float>& nfn=negator<float>::recast(fn);
const negator<float>& nfe=negator<float>::recast(fe);
SimTK_TEST(isNumericallyEqual(f,f))
SimTK_TEST(isNumericallyEqual(f,fe));
SimTK_TEST(!isNumericallyEqual(f,fn));
SimTK_TEST(isNumericallyEqual(f,fn,1e-4f));
SimTK_TEST(!isNumericallyEqual(f,fn,1e-6f));
SimTK_TEST(CNT<float>::isNumericallyEqual(f,f));
SimTK_TEST(CNT<float>::isNumericallyEqual(f,fe));
SimTK_TEST(!CNT<float>::isNumericallyEqual(f,fn));
SimTK_TEST(CNT<float>::isNumericallyEqual(f,fn,1e-4f));
SimTK_TEST(!CNT<float>::isNumericallyEqual(f,fn,1e-6f));
SimTK_TEST(nf.isNumericallyEqual(nf));
SimTK_TEST(nf.isNumericallyEqual(-f));
SimTK_TEST(!nf.isNumericallyEqual(f));
SimTK_TEST(isNumericallyEqual(1000*f,1234));
SimTK_TEST(isNumericallyEqual(1234,1000*f));
SimTK_TEST(isNumericallyEqual(1000*fe,1234));
SimTK_TEST(isNumericallyEqual(1234,1000*fe));
SimTK_TEST(!isNumericallyEqual(1000*fn,1234));
SimTK_TEST(!isNumericallyEqual(1234,1000*fn));
SimTK_TEST(isNumericallyEqual(d,d));
SimTK_TEST(isNumericallyEqual(d,de));
SimTK_TEST(!isNumericallyEqual(d,dn));
SimTK_TEST(isNumericallyEqual(1000*d,1234));
SimTK_TEST(isNumericallyEqual(1234,1000*d));
SimTK_TEST(isNumericallyEqual(1000*de,1234));
SimTK_TEST(isNumericallyEqual(1234,1000*de));
SimTK_TEST(!isNumericallyEqual(1000*dn,1234));
SimTK_TEST(!isNumericallyEqual(1234,1000*dn));
// Mixed should use float tolerance
SimTK_TEST(isNumericallyEqual(fe,de));
SimTK_TEST(!isNumericallyEqual((double)fe,de));
}
void testClamp() {
const int i4=4;
const double d325=3.25;
const float fn325=-3.25;
// int
SimTK_TEST(clamp(4,i4,4)==4);
SimTK_TEST(clamp(0,i4,9)==4);
SimTK_TEST(clamp(5,i4,9)==5);
SimTK_TEST(clamp(-7,i4,-5)==-5);
// double
SimTK_TEST(clamp(3.25,d325,3.25)==3.25);
SimTK_TEST(clamp(0.,d325,9.)==3.25);
SimTK_TEST(clamp(5.,d325,9.)==5);
SimTK_TEST(clamp(-7.,d325,-5.)==-5);
// float
SimTK_TEST(clamp(-3.25f,fn325,-3.25f)==-3.25);
SimTK_TEST(clamp(-9.f,fn325,0.f)==-3.25f);
SimTK_TEST(clamp(-9.f,fn325,-5.f)==-5);
SimTK_TEST(clamp(5.f,fn325,7.f)==5);
// Test methods that take integer bounds.
SimTK_TEST(clamp(0,d325,9)==3.25);
SimTK_TEST(clamp(5,d325,9)==5);
SimTK_TEST(clamp(-7,d325,-5)==-5);
SimTK_TEST(clamp(-9,fn325,0)==-3.25);
SimTK_TEST(clamp(-9,fn325,-5)==-5);
SimTK_TEST(clamp(5,fn325,7)==5);
SimTK_TEST(clamp(0.,d325,9)==3.25);
SimTK_TEST(clamp(5.,d325,9)==5);
SimTK_TEST(clamp(-7.,d325,-5)==-5);
SimTK_TEST(clamp(-9.f,fn325,0)==-3.25);
SimTK_TEST(clamp(-9.f,fn325,-5)==-5);
SimTK_TEST(clamp(5.f,fn325,7)==5);
SimTK_TEST(clamp(0,d325,9.)==3.25);
SimTK_TEST(clamp(5,d325,9.)==5);
SimTK_TEST(clamp(-7,d325,-5.)==-5);
SimTK_TEST(clamp(-9,fn325,0.f)==-3.25);
SimTK_TEST(clamp(-9,fn325,-5.f)==-5);
SimTK_TEST(clamp(5,fn325,7.f)==5);
int i; double d; float f;
i=i4;
SimTK_TEST(clampInPlace(-2,i,3)==3 && i==3);
d=d325;
SimTK_TEST(clampInPlace(-2.,d,3.)==3 && d==3);
f=fn325;
SimTK_TEST(clampInPlace(-2,f,3)==-2 && f==-2);
// Do a test for each of the less-common supported types.
char c='j'; unsigned char uc=3; signed char sc=-2;
SimTK_TEST(clamp('a',c,'e')=='e');
SimTK_TEST(clamp('a',c,'z')=='j');
SimTK_TEST(clamp((unsigned char)4,uc,(unsigned char)5)==4);
SimTK_TEST(clamp((signed char)-7,sc,(signed char)-1)==-2);
short s=-32000; unsigned short us=17; unsigned ui=4023456789U;
SimTK_TEST(clamp((short)-29000,s,(short)400)==-29000);
SimTK_TEST(clamp((unsigned short)4,us,(unsigned short)15)==15);
SimTK_TEST(clamp(100000000U,ui,4010000000U)==4010000000U);
long l=-234234L; unsigned long ul=293493849UL;
long long ll=-123456789123LL; unsigned long long ull=123456789123ULL;
SimTK_TEST(clamp(-1000000L,l,-200000L)==-234234);
SimTK_TEST(clamp(1000000UL,ul,4000000000UL)==293493849);
SimTK_TEST(clamp(-100000000000LL,ll,27LL)==-100000000000LL);
SimTK_TEST(clamp(-1000000000000LL,ll,27LL)==-123456789123LL);
}
void testStep() {
// double
SimTK_TEST(stepUp(0.)==0 && stepUp(.5)==.5 && stepUp(1.)==1);
SimTK_TEST(0 < stepUp(.3) && stepUp(.3) < .5);
SimTK_TEST(.5 < stepUp(.7) && stepUp(.7) < 1);
SimTK_TEST(stepDown(0.)==1 && stepDown(.5)==.5 && stepDown(1.)==0);
SimTK_TEST(.5 < stepDown(.3) && stepDown(.3) < 1);
SimTK_TEST(0 < stepDown(.7) && stepDown(.7) < .5);
SimTK_TEST(dstepUp(0.)==0 && dstepUp(.5)>0 && dstepUp(1.)==0);
SimTK_TEST(dstepDown(0.)==0 && dstepDown(.5)<0 && dstepDown(1.)==0);
SimTK_TEST(d2stepUp(0.)==0 && d2stepUp(1.)==0);
SimTK_TEST(d2stepDown(0.)==0 && d2stepDown(1.)==0);
// float
SimTK_TEST(stepUp(0.f)==0 && stepUp(.5f)==.5f && stepUp(1.f)==1);
SimTK_TEST(0 < stepUp(.3f) && stepUp(.3f) < .5f);
SimTK_TEST(.5f < stepUp(.7f) && stepUp(.7f) < 1);
SimTK_TEST(stepDown(0.f)==1 && stepDown(.5f)==.5f && stepDown(1.f)==0);
SimTK_TEST(.5f < stepDown(.3f) && stepDown(.3f) < 1);
SimTK_TEST(0 < stepDown(.7f) && stepDown(.7f) < .5f);
SimTK_TEST(dstepUp(0.f)==0 && dstepUp(.5f)>0 && dstepUp(1.f)==0);
SimTK_TEST(dstepDown(0.f)==0 && dstepDown(.5f)<0 && dstepDown(1.f)==0);
SimTK_TEST(d2stepUp(0.f)==0 && d2stepUp(1.f)==0);
SimTK_TEST(d2stepDown(0.f)==0 && d2stepDown(1.f)==0);
// int is treated as a double, but only for stepUp()/stepDown()
SimTK_TEST(stepUp(0)==0 && stepUp(1)==1);
SimTK_TEST(stepDown(0)==1 && stepDown(1)==0);
// Don't know anything analytic about d3 but can test with finite
// differencing below.
// Central difference estimates should give around 10
// decimal places in double, 4 in float.
const double dupEst = (stepUp(.799+1e-6)-stepUp(.799-1e-6))/2e-6;
const double ddnEst = (stepDown(.799+1e-6)-stepDown(.799-1e-6))/2e-6;
const double d2upEst = (dstepUp(.723+1e-6)-dstepUp(.723-1e-6))/2e-6;
const double d2dnEst = (dstepDown(.723+1e-6)-dstepDown(.723-1e-6))/2e-6;
const double d3upEst = (d2stepUp(.123+1e-6)-d2stepUp(.123-1e-6))/2e-6;
const double d3dnEst = (d2stepDown(.123+1e-6)-d2stepDown(.123-1e-6))/2e-6;
SimTK_TEST_EQ_TOL(dstepUp(.799), dupEst, 1e-8);
SimTK_TEST_EQ_TOL(dstepDown(.799), ddnEst, 1e-8);
SimTK_TEST_EQ_TOL(d2stepUp(.723), d2upEst, 1e-8);
SimTK_TEST_EQ_TOL(d2stepDown(.723), d2dnEst, 1e-8);
SimTK_TEST_EQ_TOL(d3stepUp(.123), d3upEst, 1e-8);
SimTK_TEST_EQ_TOL(d3stepDown(.123), d3dnEst, 1e-8);
const float fdupEst = (stepUp(.699f+1e-3f)-stepUp(.699f-1e-3f))/2e-3f;
const float fddnEst = (stepDown(.699f+1e-3f)-stepDown(.699f-1e-3f))/2e-3f;
const float fd2upEst = (dstepUp(.623f+1e-3f)-dstepUp(.623f-1e-3f))/2e-3f;
const float fd2dnEst = (dstepDown(.623f+1e-3f)-dstepDown(.623f-1e-3f))/2e-3f;
const float fd3upEst = (d2stepUp(.211f+1e-3f)-d2stepUp(.211f-1e-3f))/2e-3f;
const float fd3dnEst = (d2stepDown(.211f+1e-3f)-d2stepDown(.211f-1e-3f))/2e-3f;
SimTK_TEST_EQ_TOL(dstepUp(.699f), fdupEst, 1e-3);
SimTK_TEST_EQ_TOL(dstepDown(.699f), fddnEst, 1e-3);
SimTK_TEST_EQ_TOL(d2stepUp(.623f), fd2upEst, 1e-3);
SimTK_TEST_EQ_TOL(d2stepDown(.623f), fd2dnEst, 1e-3);
SimTK_TEST_EQ_TOL(d3stepUp(.211f), fd3upEst, 1e-3);
SimTK_TEST_EQ_TOL(d3stepDown(.211f), fd3dnEst, 1e-3);
// y = stepAny(y0,yrange,x0,1/xrange, x)
// y goes from -1 to 1 as x goes from 0 to 1, exact arithmetic.
SimTK_TEST(stepAny(-1,2,0,1,0.) == -1);
SimTK_TEST(stepAny(-1,2,0,1,.5) == 0);
SimTK_TEST(stepAny(-1,2,0,1,1.) == 1);
SimTK_TEST(stepAny(-1,2,0,1,0.f) == -1);
SimTK_TEST(stepAny(-1,2,0,1,.5f) == 0);
SimTK_TEST(stepAny(-1,2,0,1,1.f) == 1);
// y goes from -7 down to -14 as x goes from -3.1 up to +429.3.
const double x0=-3.1, x1=429.3, y0=-7., y1=-14.;
const double xr=(x1-x0), ooxr=1/xr, yr=(y1-y0);
SimTK_TEST_EQ(stepAny(y0,yr,x0,ooxr,-3.1), y0);
SimTK_TEST_EQ(stepAny(y0,yr,x0,ooxr,429.3), y1);
SimTK_TEST_EQ(stepAny(y0,yr,x0,ooxr,x0+xr/2), y0+yr/2);
const float fx0=-3.1f, fx1=429.3f, fy0=-7.f, fy1=-14.f;
const float fxr=(fx1-fx0), fooxr=1/fxr, fyr=(fy1-fy0);
SimTK_TEST_EQ(stepAny(fy0,fyr,fx0,fooxr,-3.1f),fy0);
SimTK_TEST_EQ(stepAny(fy0,fyr,fx0,fooxr,429.3f),fy1);
SimTK_TEST_EQ(stepAny(fy0,fyr,fx0,fooxr,fx0+fxr/2),fy0+fyr/2);
// Check derivatives
const double danyEst =
(stepAny(y0,yr,x0,ooxr,.799+1e-6)-stepAny(y0,yr,x0,ooxr,.799-1e-6))/2e-6;
const double d2anyEst =
(dstepAny(yr,x0,ooxr,.723+1e-6)-dstepAny(yr,x0,ooxr,.723-1e-6))/2e-6;
const double d3anyEst =
(d2stepAny(yr,x0,ooxr,.123+1e-6)-d2stepAny(yr,x0,ooxr,.123-1e-6))/2e-6;
SimTK_TEST_EQ_TOL(dstepAny(yr,x0,ooxr,.799), danyEst, 1e-8);
SimTK_TEST_EQ_TOL(d2stepAny(yr,x0,ooxr,.723), d2anyEst, 1e-8);
SimTK_TEST_EQ_TOL(d3stepAny(yr,x0,ooxr,.123), d3anyEst, 1e-8);
const float fdanyEst =
(stepAny(fy0,fyr,fx0,fooxr,.799f+1e-3f)
-stepAny(fy0,fyr,fx0,fooxr,.799f-1e-3f))/2e-3f;
const float fd2anyEst =
(dstepAny(fyr,fx0,fooxr,.723f+1e-3f)
-dstepAny(fyr,fx0,fooxr,.723f-1e-3f))/2e-3f;
const float fd3anyEst =
(d2stepAny(fyr,fx0,fooxr,.123f+1e-3f)
-d2stepAny(fyr,fx0,fooxr,.123f-1e-3f))/2e-3f;
SimTK_TEST_EQ_TOL(dstepAny(fyr,fx0,fooxr,.799f), fdanyEst, 1e-3);
SimTK_TEST_EQ_TOL(d2stepAny(fyr,fx0,fooxr,.723f), fd2anyEst, 1e-3);
SimTK_TEST_EQ_TOL(d3stepAny(fyr,fx0,fooxr,.123f), fd3anyEst, 1e-3);
}
int main() {
SimTK_START_TEST("TestScalar");
SimTK_SUBTEST(testIsNaN);
SimTK_SUBTEST(testIsInf);
SimTK_SUBTEST(testIsFinite);
SimTK_SUBTEST(testSignBit);
SimTK_SUBTEST(testSign);
SimTK_SUBTEST(testSquareAndCube);
SimTK_SUBTEST(testIsNumericallyEqual);
SimTK_SUBTEST(testClamp);
SimTK_SUBTEST(testStep);
SimTK_END_TEST();
}
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