vtk-m/vtkm/testing/TestingMath.h

//=============================================================================
//
//  Copyright (c) Kitware, Inc.
//  All rights reserved.
//  See LICENSE.txt for details.
//
//  This software is distributed WITHOUT ANY WARRANTY; without even
//  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
//  PURPOSE.  See the above copyright notice for more information.
//
//  Copyright 2015 Sandia Corporation.
//  Copyright 2015 UT-Battelle, LLC.
//  Copyright 2015 Los Alamos National Security.
//
//  Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
//  the U.S. Government retains certain rights in this software.
//  Under the terms of Contract DE-AC52-06NA25396 with Los Alamos National
//  Laboratory (LANL), the U.S. Government retains certain rights in
//  this software.
//
//=============================================================================
#ifndef vtk_m_testing_TestingMath_h
#define vtk_m_testing_TestingMath_h

#include <vtkm/Math.h>

#include <vtkm/TypeListTag.h>
#include <vtkm/VecTraits.h>

#include <vtkm/exec/FunctorBase.h>

#include <vtkm/cont/DeviceAdapterAlgorithm.h>

#include <vtkm/cont/testing/Testing.h>

#define VTKM_MATH_ASSERT(condition, message) \
  if (!(condition)) \
  { \
    this->RaiseError(message); \
  }

//-----------------------------------------------------------------------------
namespace UnitTestMathNamespace {

const vtkm::IdComponent NUM_NUMBERS = 5;
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 NumberList[NUM_NUMBERS] = { 0.25, 0.5, 1.0, 2.0, 3.75 };

VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 AngleList[NUM_NUMBERS] =
  { 0.643501108793284,  // angle for 3, 4, 5 triangle.
    0.78539816339745,   // pi/4
    0.5235987755983,    // pi/6
    1.0471975511966,    // pi/3
    0.0 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 OppositeList[NUM_NUMBERS] =   { 3.0, 1.0, 1.0, 1.732050807568877 /*sqrt(3)*/, 0.0 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 AdjacentList[NUM_NUMBERS] =   { 4.0, 1.0, 1.732050807568877 /*sqrt(3)*/, 1.0, 1.0 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 HypotenuseList[NUM_NUMBERS] = { 5.0, 1.414213562373095 /*sqrt(2)*/, 2.0, 2.0, 1.0 };

VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 NumeratorList[NUM_NUMBERS] =   { 6.5, 5.8, 9.3, 77.0, 0.1 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 DenominatorList[NUM_NUMBERS] = { 2.3, 1.6, 3.1, 19.0, 0.4 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 FModRemainderList[NUM_NUMBERS]={ 1.9, 1.0, 0.0,  1.0, 0.1 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 RemainderList[NUM_NUMBERS] =   {-0.4,-0.6, 0.0,  1.0, 0.1 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Int64   QuotientList[NUM_NUMBERS] =    { 3  , 4  , 3  ,  4  , 0   };

VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 XList[NUM_NUMBERS] =           {4.6, 0.1, 73.4, 55.0, 3.75 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 FractionalList[NUM_NUMBERS] =  {0.6, 0.1,  0.4,  0.0, 0.75 };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 FloorList[NUM_NUMBERS] =       {4.0, 0.0, 73.0, 55.0, 3.0  };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 CeilList[NUM_NUMBERS] =        {5.0, 1.0, 74.0, 55.0, 4.0  };
VTKM_EXEC_CONSTANT_EXPORT
const vtkm::Float64 RoundList[NUM_NUMBERS] =       {5.0, 0.0, 73.0, 55.0, 4.0  };

//-----------------------------------------------------------------------------
template<typename T>
struct ScalarFieldTests : public vtkm::exec::FunctorBase
{
  VTKM_EXEC_EXPORT
  void TestPi() const
  {
//    std::cout << "Testing Pi" << std::endl;
    VTKM_MATH_ASSERT(test_equal(vtkm::Pi(), 3.14159265), "Pi not correct.");
  }

  VTKM_EXEC_EXPORT
  void TestArcTan2() const
  {
//    std::cout << "Testing arc tan 2" << std::endl;

    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(0.0), T(1.0)),
                                T(0.0)),
                     "ATan2 x+ axis.");
    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(1.0), T(0.0)),
                                T(0.5*vtkm::Pi())),
                     "ATan2 y+ axis.");
    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(-1.0), T(0.0)),
                                T(-0.5*vtkm::Pi())),
                     "ATan2 y- axis.");

    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(1.0), T(1.0)),
                                T(0.25*vtkm::Pi())),
                     "ATan2 Quadrant 1");
    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(1.0), T(-1.0)),
                                T(0.75*vtkm::Pi())),
                     "ATan2 Quadrant 2");
    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(-1.0), T(-1.0)),
                                T(-0.75*vtkm::Pi())),
                     "ATan2 Quadrant 3");
    VTKM_MATH_ASSERT(test_equal(vtkm::ATan2(T(-1.0), T(1.0)),
                                T(-0.25*vtkm::Pi())),
                     "ATan2 Quadrant 4");
  }

  VTKM_EXEC_EXPORT
  void TestPow() const
  {
//    std::cout << "Running power tests." << std::endl;
    for (vtkm::IdComponent index = 0; index < NUM_NUMBERS; index++)
      {
      T x = static_cast<T>(NumberList[index]);
      T powx = vtkm::Pow(x, static_cast<T>(2.0));
      T sqrx = x*x;
      VTKM_MATH_ASSERT(test_equal(powx, sqrx), "Power gave wrong result.");
      }
  }

  VTKM_EXEC_EXPORT
  void TestLog2() const
  {
//    std::cout << "Testing Log2" << std::endl;
    VTKM_MATH_ASSERT(test_equal(vtkm::Log2(T(0.25)), T(-2.0)),
                     "Bad value from Log2");
    VTKM_MATH_ASSERT(
          test_equal(vtkm::Log2(vtkm::Vec<T,4>(0.5, 1.0, 2.0, 4.0)),
                     vtkm::Vec<T,4>(-1.0, 0.0, 1.0, 2.0)),
          "Bad value from Log2");
  }

  VTKM_EXEC_EXPORT
  void TestNonFinites() const
  {
//    std::cout << "Testing non-finites." << std::endl;

    T zero = 0.0;
    T finite = 1.0;
    T nan = vtkm::Nan<T>();
    T inf = vtkm::Infinity<T>();
    T neginf = vtkm::NegativeInfinity<T>();
    T epsilon = vtkm::Epsilon<T>();

    // General behavior.
    VTKM_MATH_ASSERT(nan != vtkm::Nan<T>(), "Nan not equal itself.");
    VTKM_MATH_ASSERT(!(nan >= zero), "Nan not greater or less.");
    VTKM_MATH_ASSERT(!(nan <= zero), "Nan not greater or less.");
    VTKM_MATH_ASSERT(!(nan >= finite), "Nan not greater or less.");
    VTKM_MATH_ASSERT(!(nan <= finite), "Nan not greater or less.");

    VTKM_MATH_ASSERT(neginf < inf, "Infinity big");
    VTKM_MATH_ASSERT(zero < inf, "Infinity big");
    VTKM_MATH_ASSERT(finite < inf, "Infinity big");
    VTKM_MATH_ASSERT(zero > -inf, "-Infinity small");
    VTKM_MATH_ASSERT(finite > -inf, "-Infinity small");
    VTKM_MATH_ASSERT(zero > neginf, "-Infinity small");
    VTKM_MATH_ASSERT(finite > neginf, "-Infinity small");

    VTKM_MATH_ASSERT(zero < epsilon, "Negative epsilon");
    VTKM_MATH_ASSERT(finite > epsilon, "Large epsilon");

    // Math check functions.
    VTKM_MATH_ASSERT(!vtkm::IsNan(zero), "Bad IsNan check.");
    VTKM_MATH_ASSERT(!vtkm::IsNan(finite), "Bad IsNan check.");
    VTKM_MATH_ASSERT(vtkm::IsNan(nan), "Bad IsNan check.");
    VTKM_MATH_ASSERT(!vtkm::IsNan(inf), "Bad IsNan check.");
    VTKM_MATH_ASSERT(!vtkm::IsNan(neginf), "Bad IsNan check.");
    VTKM_MATH_ASSERT(!vtkm::IsNan(epsilon), "Bad IsNan check.");

    VTKM_MATH_ASSERT(!vtkm::IsInf(zero), "Bad infinity check.");
    VTKM_MATH_ASSERT(!vtkm::IsInf(finite), "Bad infinity check.");
    VTKM_MATH_ASSERT(!vtkm::IsInf(nan), "Bad infinity check.");
    VTKM_MATH_ASSERT(vtkm::IsInf(inf), "Bad infinity check.");
    VTKM_MATH_ASSERT(vtkm::IsInf(neginf), "Bad infinity check.");
    VTKM_MATH_ASSERT(!vtkm::IsInf(epsilon), "Bad infinity check.");

    VTKM_MATH_ASSERT(vtkm::IsFinite(zero), "Bad finite check.");
    VTKM_MATH_ASSERT(vtkm::IsFinite(finite), "Bad finite check.");
    VTKM_MATH_ASSERT(!vtkm::IsFinite(nan), "Bad finite check.");
    VTKM_MATH_ASSERT(!vtkm::IsFinite(inf), "Bad finite check.");
    VTKM_MATH_ASSERT(!vtkm::IsFinite(neginf), "Bad finite check.");
    VTKM_MATH_ASSERT(vtkm::IsFinite(epsilon), "Bad finite check.");
  }

  VTKM_EXEC_EXPORT
  void TestRemainders() const
  {
//    std::cout << "Testing remainders." << std::endl;
    for (vtkm::IdComponent index = 0; index < NUM_NUMBERS; index++)
    {
      T numerator = static_cast<T>(NumeratorList[index]);
      T denominator = static_cast<T>(DenominatorList[index]);
      T fmodremainder = static_cast<T>(FModRemainderList[index]);
      T remainder = static_cast<T>(RemainderList[index]);
      vtkm::Int64 quotient = QuotientList[index];

      VTKM_MATH_ASSERT(test_equal(vtkm::FMod(numerator, denominator), fmodremainder),
                       "Bad FMod remainder.");
      VTKM_MATH_ASSERT(test_equal(vtkm::Remainder(numerator, denominator), remainder),
                       "Bad remainder.");
      vtkm::Int64 q;
      VTKM_MATH_ASSERT(test_equal(vtkm::RemainderQuotient(numerator, denominator, q), remainder),
                       "Bad remainder-quotient remainder.");
      VTKM_MATH_ASSERT(test_equal(q, quotient),
                       "Bad reminder-quotient quotient.");
    }
  }

  VTKM_EXEC_EXPORT
  void TestRound() const
  {
//    std::cout << "Testing round." << std::endl;
    for (vtkm::IdComponent index = 0; index < NUM_NUMBERS; index++)
    {
      T x = static_cast<T>(XList[index]);
      T fractional = static_cast<T>(FractionalList[index]);
      T floor = static_cast<T>(FloorList[index]);
      T ceil = static_cast<T>(CeilList[index]);
      T round = static_cast<T>(RoundList[index]);

      T intPart;
      VTKM_MATH_ASSERT(test_equal(vtkm::ModF(x,intPart), fractional),
                       "ModF returned wrong fractional part.");
      VTKM_MATH_ASSERT(test_equal(intPart, floor),
                       "ModF returned wrong integral part.");
      VTKM_MATH_ASSERT(test_equal(vtkm::Floor(x), floor),
                       "Bad floor.");
      VTKM_MATH_ASSERT(test_equal(vtkm::Ceil(x), ceil),
                       "Bad ceil.");
      VTKM_MATH_ASSERT(test_equal(vtkm::Round(x), round),
                       "Bad round.");
    }
  }

  VTKM_EXEC_EXPORT
  void TestIsNegative() const
  {
//    std::cout << "Testing SignBit and IsNegative." << std::endl;
    T x = 0;
    VTKM_MATH_ASSERT(vtkm::SignBit(x) == 0, "SignBit wrong for 0.");
    VTKM_MATH_ASSERT(!vtkm::IsNegative(x), "IsNegative wrong for 0.");

    x = 20;
    VTKM_MATH_ASSERT(vtkm::SignBit(x) == 0, "SignBit wrong for 20.");
    VTKM_MATH_ASSERT(!vtkm::IsNegative(x), "IsNegative wrong for 20.");

    x = -20;
    VTKM_MATH_ASSERT(vtkm::SignBit(x) != 0, "SignBit wrong for -20.");
    VTKM_MATH_ASSERT(vtkm::IsNegative(x), "IsNegative wrong for -20.");

    x = 0.02f;
    VTKM_MATH_ASSERT(vtkm::SignBit(x) == 0, "SignBit wrong for 0.02.");
    VTKM_MATH_ASSERT(!vtkm::IsNegative(x), "IsNegative wrong for 0.02.");

    x = -0.02f;
    VTKM_MATH_ASSERT(vtkm::SignBit(x) != 0, "SignBit wrong for -0.02.");
    VTKM_MATH_ASSERT(vtkm::IsNegative(x), "IsNegative wrong for -0.02.");
  }

  VTKM_EXEC_EXPORT
  void operator()(vtkm::Id) const
  {
    this->TestPi();
    this->TestArcTan2();
    this->TestPow();
    this->TestLog2();
    this->TestNonFinites();
    this->TestRemainders();
    this->TestRound();
    this->TestIsNegative();
  }
};

template<typename Device>
struct TryScalarFieldTests
{
  template<typename T>
  void operator()(const T&) const
  {
    vtkm::cont::DeviceAdapterAlgorithm<Device>::Schedule(
          ScalarFieldTests<T>(), 1);
  }
};

//-----------------------------------------------------------------------------
template<typename VectorType>
struct ScalarVectorFieldTests : public vtkm::exec::FunctorBase
{
  typedef vtkm::VecTraits<VectorType> Traits;
  typedef typename Traits::ComponentType ComponentType;
  enum {
    NUM_COMPONENTS = Traits::NUM_COMPONENTS
  };

  VTKM_EXEC_EXPORT
  void TestTriangleTrig() const
  {
//    std::cout << "Testing normal trig functions." << std::endl;

    for (vtkm::IdComponent index = 0;
         index < NUM_NUMBERS - NUM_COMPONENTS + 1;
         index++)
    {
      VectorType angle;
      VectorType opposite;
      VectorType adjacent;
      VectorType hypotenuse;
      for (vtkm::IdComponent componentIndex = 0;
           componentIndex < NUM_COMPONENTS;
           componentIndex++)
      {
        Traits::SetComponent(
              angle,
              componentIndex,
              static_cast<ComponentType>(AngleList[componentIndex+index]));
        Traits::SetComponent(
              opposite,
              componentIndex,
              static_cast<ComponentType>(OppositeList[componentIndex+index]));
        Traits::SetComponent(
              adjacent,
              componentIndex,
              static_cast<ComponentType>(AdjacentList[componentIndex+index]));
        Traits::SetComponent(
              hypotenuse,
              componentIndex,
              static_cast<ComponentType>(HypotenuseList[componentIndex+index]));
      }

      VTKM_MATH_ASSERT(test_equal(vtkm::Sin(angle), opposite/hypotenuse),
                      "Sin failed test.");
      VTKM_MATH_ASSERT(test_equal(vtkm::Cos(angle), adjacent/hypotenuse),
                      "Cos failed test.");
      VTKM_MATH_ASSERT(test_equal(vtkm::Tan(angle), opposite/adjacent),
                      "Tan failed test.");

      VTKM_MATH_ASSERT(test_equal(vtkm::ASin(opposite/hypotenuse), angle),
                      "Arc Sin failed test.");
      VTKM_MATH_ASSERT(test_equal(vtkm::ACos(adjacent/hypotenuse), angle),
                      "Arc Cos failed test.");
      VTKM_MATH_ASSERT(test_equal(vtkm::ATan(opposite/adjacent), angle),
                      "Arc Tan failed test.");
    }
  }

  VTKM_EXEC_EXPORT
  void TestHyperbolicTrig() const
  {
//    std::cout << "Testing hyperbolic trig functions." << std::endl;

    const VectorType zero(0);
    const VectorType half(0.5);

    for (vtkm::IdComponent index = 0;
         index < NUM_NUMBERS - NUM_COMPONENTS + 1;
         index++)
    {
      VectorType x;
      for (vtkm::IdComponent componentIndex = 0;
           componentIndex < NUM_COMPONENTS;
           componentIndex++)
      {
        Traits::SetComponent(
              x,
              componentIndex,
              static_cast<ComponentType>(AngleList[componentIndex+index]));
      }

      const VectorType minusX = zero - x;

      VTKM_MATH_ASSERT(test_equal(vtkm::SinH(x),
                                  half*(vtkm::Exp(x) - vtkm::Exp(minusX))),
                      "SinH does not match definition.");
      VTKM_MATH_ASSERT(test_equal(vtkm::CosH(x),
                                  half*(vtkm::Exp(x) + vtkm::Exp(minusX))),
                      "SinH does not match definition.");
      VTKM_MATH_ASSERT(test_equal(vtkm::TanH(x), vtkm::SinH(x)/vtkm::CosH(x)),
                      "TanH does not match definition");

      VTKM_MATH_ASSERT(test_equal(vtkm::ASinH(vtkm::SinH(x)), x),
                      "SinH not inverting.");
      VTKM_MATH_ASSERT(test_equal(vtkm::ACosH(vtkm::CosH(x)), x),
                      "CosH not inverting.");
      VTKM_MATH_ASSERT(test_equal(vtkm::ATanH(vtkm::TanH(x)), x),
                      "TanH not inverting.");
    }
  }

  template<typename FunctionType>
  VTKM_EXEC_EXPORT
  void RaiseToTest(FunctionType function,
                   ComponentType exponent) const
  {
    for (vtkm::IdComponent index = 0;
         index < NUM_NUMBERS - NUM_COMPONENTS + 1;
         index++)
    {
      VectorType original;
      VectorType raiseresult;
      for (vtkm::IdComponent componentIndex = 0;
           componentIndex < NUM_COMPONENTS;
           componentIndex++)
      {
        ComponentType x =
            static_cast<ComponentType>(NumberList[componentIndex + index]);
        Traits::SetComponent(original, componentIndex, x);
        Traits::SetComponent(raiseresult, componentIndex, vtkm::Pow(x, exponent));
      }

      VectorType mathresult = function(original);

      VTKM_MATH_ASSERT(test_equal(mathresult, raiseresult),
                      "Exponent functions do not agree.");
    }
  }

  struct SqrtFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const { return vtkm::Sqrt(x); }
  };
  VTKM_EXEC_EXPORT
  void TestSqrt() const
  {
//    std::cout << "  Testing Sqrt" << std::endl;
    RaiseToTest(SqrtFunctor(), 0.5);
  }

  struct RSqrtFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::RSqrt(x);}
  };
  VTKM_EXEC_EXPORT
  void TestRSqrt() const
  {
//    std::cout << "  Testing RSqrt"<< std::endl;
    RaiseToTest(RSqrtFunctor(), -0.5);
  }

  struct CbrtFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const { return vtkm::Cbrt(x); }
  };
  VTKM_EXEC_EXPORT
  void TestCbrt() const
  {
//    std::cout << "  Testing Cbrt" << std::endl;
    RaiseToTest(CbrtFunctor(), vtkm::Float32(1.0/3.0));
  }

  struct RCbrtFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::RCbrt(x);}
  };
  VTKM_EXEC_EXPORT
  void TestRCbrt() const
  {
//    std::cout << "  Testing RCbrt" << std::endl;
    RaiseToTest(RCbrtFunctor(), vtkm::Float32(-1.0/3.0));
  }

  template<typename FunctionType>
  VTKM_EXEC_EXPORT
  void RaiseByTest(FunctionType function,
                   ComponentType base,
                   ComponentType exponentbias = 0.0,
                   ComponentType resultbias = 0.0) const
  {
    for (vtkm::IdComponent index = 0;
         index < NUM_NUMBERS - NUM_COMPONENTS + 1;
         index++)
    {
      VectorType original;
      VectorType raiseresult;
      for (vtkm::IdComponent componentIndex = 0;
           componentIndex < NUM_COMPONENTS;
           componentIndex++)
      {
        ComponentType x =
            static_cast<ComponentType>(NumberList[componentIndex + index]);
        Traits::SetComponent(original, componentIndex, x);
        Traits::SetComponent(raiseresult,
                             componentIndex,
                             vtkm::Pow(base, x + exponentbias) + resultbias);
      }

      VectorType mathresult = function(original);

      VTKM_MATH_ASSERT(test_equal(mathresult, raiseresult),
                      "Exponent functions do not agree.");
    }
  }

  struct ExpFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::Exp(x);}
  };
  VTKM_EXEC_EXPORT
  void TestExp() const
  {
//    std::cout << "  Testing Exp" << std::endl;
    RaiseByTest(ExpFunctor(), vtkm::Float32(2.71828183));
  }

  struct Exp2Functor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::Exp2(x);}
  };
  VTKM_EXEC_EXPORT
  void TestExp2() const
  {
//    std::cout << "  Testing Exp2" << std::endl;
    RaiseByTest(Exp2Functor(), 2.0);
  }

  struct ExpM1Functor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::ExpM1(x);}
  };
  VTKM_EXEC_EXPORT
  void TestExpM1() const
  {
//    std::cout << "  Testing ExpM1" << std::endl;
    RaiseByTest(ExpM1Functor(),
                ComponentType(2.71828183),
                0.0,
                -1.0);
  }

  struct Exp10Functor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::Exp10(x);}
  };
  VTKM_EXEC_EXPORT
  void TestExp10() const
  {
//    std::cout << "  Testing Exp10" << std::endl;
    RaiseByTest(Exp10Functor(), 10.0);
  }

  template<typename FunctionType>
  VTKM_EXEC_EXPORT
  void LogBaseTest(FunctionType function,
                   ComponentType base,
                   ComponentType bias=0.0) const
  {
    for (vtkm::IdComponent index = 0;
         index < NUM_NUMBERS - NUM_COMPONENTS + 1;
         index++)
    {
      VectorType basevector(base);
      VectorType original;
      VectorType biased;
      for (vtkm::IdComponent componentIndex = 0;
           componentIndex < NUM_COMPONENTS;
           componentIndex++)
      {
        ComponentType x =
            static_cast<ComponentType>(NumberList[componentIndex + index]);
        Traits::SetComponent(original, componentIndex, x);
        Traits::SetComponent(biased, componentIndex, x + bias);
      }

      VectorType logresult = vtkm::Log2(biased)/vtkm::Log2(basevector);

      VectorType mathresult = function(original);

      VTKM_MATH_ASSERT(test_equal(mathresult, logresult),
                      "Exponent functions do not agree.");
    }
  }

  struct LogFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::Log(x);}
  };
  VTKM_EXEC_EXPORT
  void TestLog() const
  {
//    std::cout << "  Testing Log" << std::endl;
    LogBaseTest(LogFunctor(), vtkm::Float32(2.71828183));
  }

  struct Log10Functor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::Log10(x);}
  };
  VTKM_EXEC_EXPORT
  void TestLog10() const
  {
//    std::cout << "  Testing Log10" << std::endl;
    LogBaseTest(Log10Functor(), 10.0);
  }

  struct Log1PFunctor {
    VTKM_EXEC_EXPORT
    VectorType operator()(VectorType x) const {return vtkm::Log1P(x);}
  };
  VTKM_EXEC_EXPORT
  void TestLog1P() const
  {
//    std::cout << "  Testing Log1P" << std::endl;
    LogBaseTest(Log1PFunctor(),
                ComponentType(2.71828183),
                1.0);
  }

  VTKM_EXEC_EXPORT
  void TestCopySign() const
  {
//    std::cout << "Testing CopySign." << std::endl;
    // Assuming all TestValues positive.
    VectorType positive1 = TestValue(1, VectorType());
    VectorType positive2 = TestValue(2, VectorType());
    VectorType negative1 = -positive1;
    VectorType negative2 = -positive2;

    VTKM_MATH_ASSERT(test_equal(vtkm::CopySign(positive1, positive2), positive1),
                     "CopySign failed.");
    VTKM_MATH_ASSERT(test_equal(vtkm::CopySign(negative1, positive2), positive1),
                     "CopySign failed.");
    VTKM_MATH_ASSERT(test_equal(vtkm::CopySign(positive1, negative2), negative1),
                     "CopySign failed.");
    VTKM_MATH_ASSERT(test_equal(vtkm::CopySign(negative1, negative2), negative1),
                     "CopySign failed.");
  }

  VTKM_EXEC_EXPORT
  void operator()(vtkm::Id) const
  {
    this->TestTriangleTrig();
    this->TestHyperbolicTrig();
    this->TestSqrt();
    this->TestRSqrt();
    this->TestCbrt();
    this->TestRCbrt();
    this->TestExp();
    this->TestExp2();
    this->TestExpM1();
    this->TestExp10();
    this->TestLog();
    this->TestLog10();
    this->TestLog1P();
    this->TestCopySign();
  }
};

template<typename Device>
struct TryScalarVectorFieldTests
{
  template<typename VectorType>
  void operator()(const VectorType&) const
  {
    vtkm::cont::DeviceAdapterAlgorithm<Device>::Schedule(
          ScalarVectorFieldTests<VectorType>(), 1);
  }
};

//-----------------------------------------------------------------------------
template<typename T>
struct AllTypesTests : public vtkm::exec::FunctorBase
{
  VTKM_EXEC_EXPORT
  void TestMinMax() const
  {
    T low = TestValue(2, T());
    T high = TestValue(10, T());
//    std::cout << "Testing min/max " << low << " " << high << std::endl;
    VTKM_MATH_ASSERT(test_equal(vtkm::Min(low, high), low), "Wrong min.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Min(high, low), low), "Wrong min.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Max(low, high), high), "Wrong max.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Max(high, low), high), "Wrong max.");

    typedef vtkm::VecTraits<T> Traits;
    T mixed1 = low;
    T mixed2 = high;
    Traits::SetComponent(mixed1, 0, Traits::GetComponent(high, 0));
    Traits::SetComponent(mixed2, 0, Traits::GetComponent(low, 0));
    VTKM_MATH_ASSERT(test_equal(vtkm::Min(mixed1, mixed2), low), "Wrong min.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Min(mixed2, mixed1), low), "Wrong min.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Max(mixed1, mixed2), high), "Wrong max.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Max(mixed2, mixed1), high), "Wrong max.");
  }

  VTKM_EXEC_EXPORT
  void operator()(vtkm::Id) const
  {
    this->TestMinMax();
  }
};

template<typename Device>
struct TryAllTypesTests
{
  template<typename T>
  void operator()(const T&) const
  {
    vtkm::cont::DeviceAdapterAlgorithm<Device>::Schedule(
          AllTypesTests<T>(), 1);
  }
};

//-----------------------------------------------------------------------------
template<typename T>
struct AbsTests : public vtkm::exec::FunctorBase
{
  VTKM_EXEC_EXPORT
  void operator()(vtkm::Id index) const {
//    std::cout << "Testing Abs." << std::endl;
    T positive = TestValue(index, T());  // Assuming all TestValues positive.
    T negative = -positive;

    VTKM_MATH_ASSERT(test_equal(vtkm::Abs(positive), positive),
                     "Abs returned wrong value.");
    VTKM_MATH_ASSERT(test_equal(vtkm::Abs(negative), positive),
                     "Abs returned wrong value.");
  }
};

template<typename Device>
struct TryAbsTests
{
  template<typename T>
  void operator()(const T&) const
  {
    vtkm::cont::DeviceAdapterAlgorithm<Device>::Schedule(
          AbsTests<T>(), 10);
  }
};

struct TypeListTagAbs
    : vtkm::ListTagJoin<
        vtkm::ListTagJoin<
          vtkm::ListTagBase<vtkm::Int32, vtkm::Int64>,
          vtkm::TypeListTagIndex>,
        vtkm::TypeListTagField> {  };

//-----------------------------------------------------------------------------
template<typename Device>
void RunMathTests()
{
  std::cout << "Tests for scalar types." << std::endl;
  vtkm::testing::Testing::TryTypes(TryScalarFieldTests<Device>(),
                                   vtkm::TypeListTagFieldScalar());
  std::cout << "Test for scalar and vector types." << std::endl;
  vtkm::testing::Testing::TryTypes(TryScalarVectorFieldTests<Device>(),
                                   vtkm::TypeListTagField());
  std::cout << "Test for all types." << std::endl;
  vtkm::testing::Testing::TryAllTypes(TryAllTypesTests<Device>());
  std::cout << "Test all Abs types" << std::endl;
  vtkm::testing::Testing::TryTypes(TryAbsTests<Device>(),
                                   TypeListTagAbs());
}

} // namespace UnitTestMathNamespace

#endif //vtk_m_testing_TestingMath_h