Introduce SimulatorBuilder

[gromacs.git] / src / gromacs / tables / quadraticsplinetable.h

/*
 * This file is part of the GROMACS molecular simulation package.
 *
 * Copyright (c) 2016, by the GROMACS development team, led by
 * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
 * and including many others, as listed in the AUTHORS file in the
 * top-level source directory and at http://www.gromacs.org.
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/*! \libinternal
 * \defgroup module_tables  Classes for table interpolation
 * \ingroup group_utilitymodules
 *
 * \brief Table interpolation from analytical or numerical input
 *
 * This module provides quadratic spline interpolation tables used
 * both for the nonbonded kernels and listed interactions.
 *
 * \author Erik Lindahl <erik.lindahl@scilifelab.se>
 */


/*! \libinternal \file
 * \brief
 * Declares classes for quadratic spline table
 *
 * \inlibraryapi
 * \author Erik Lindahl <erik.lindahl@gmail.com>
 * \ingroup module_tables
 */
#ifndef GMX_TABLES_QUADRATICSPLINETABLE_H
#define GMX_TABLES_QUADRATICSPLINETABLE_H

#include <functional>
#include <initializer_list>
#include <vector>

#include "gromacs/simd/simd.h"
#include "gromacs/tables/tableinput.h"
#include "gromacs/utility/alignedallocator.h"
#include "gromacs/utility/classhelpers.h"
#include "gromacs/utility/exceptions.h"
#include "gromacs/utility/gmxassert.h"
#include "gromacs/utility/real.h"

namespace gmx
{

/*! \libinternal \brief Quadratic spline interpolation table.
 *
 * This class interpolates a function specified either as an analytical
 * expression or from user-provided table data.
 *
 * At initialization, you provide the reference function of vectors
 * as a list of tuples that contain a brief name, the function, and
 * derivative for each function to tabulate. To create a table with
 * two functions this initializer list can for instance look like
 *
 *     { {"LJ6", lj6Func, lj6Der}, {"LJ12", lj12Func, lj12Der} }
 *
 * The names are only used so exceptions during initialization can
 * be traced to a specific table.
 *
 * When interpolating, there are methods to interpolate either 1, 2, or 3
 * functions in one go. By default these interpolation routines will
 * operate on tables with the same number of functions as specified in
 * the interpolation method (debug builds check that this is consistent with
 * the table). However, it is also possible to use optional template
 * parameters that specify the total number of functions in a table, and
 * what function index to interpolate. For instance, to interpolate the
 * derivative of the second function (i.e., index 1) in a
 * multi-function-table with three functions in total, you can write
 *
 *     table.evaluateDerivative<3,1>(x,&der);
 *
 * Here too, debug builds will check that the template parameters are
 * consistent with the table.
 *
 * The table data is internally adjusted to guarantee that the interpolated
 * derivative is the true derivative of the interpolated potential, which is
 * important to avoid systematic errors for the common case when the derivative
 * is concave/convex in the entire interval.
 * We do this by expressing the difference in the function value
 * at a small offset h relative to a reference value in position 0 with a forward
 * Taylor series expanded around 0, and then doing the opposite of expressing
 * difference in the function at position 0 relative to a reference value in
 * position h when using a backward Taylor expansion:
 *
 * \f{eqnarray*}{
 *  \Delta V & = & hV'(0) + \frac{1}{2} h^2 V''(0) + \frac{1}{6} h^3 V'''(0) + O(h^4) \\
 *  \Delta V & = & hV'(h) - \frac{1}{2} h^2 V''(h) + \frac{1}{6} h^3 V'''(h) + O(h^4)
 * \f}
 *
 * Summing the equations leads to
 *
 * \f[
 *  2 \Delta V = h(V'(0) + V'(h)) + \frac{1}{2} h^2 (V''(0)-V''(h)) + \frac{1}{6}h^3(V'''(0)+V'''(h)) + O(h^4)
 * \f]
 *
 * To make the second term symmetric too, we can replace it with the average of
 * the Taylor expansion at 0 and h (i.e., using the third derivative). This gives
 *
 * \f[
 *  2 \Delta V = h(V'(0) + V'(h)) - \frac{1}{12} h^3 (V'''(0)+V'''(h)) + O(h^4)
 * \f]
 *
 * Thus, if we replace the derivative in the internal quadratic table data with
 *
 * \f[
 *  V' - \frac{1}{12}h^2 V'''
 * \f]
 *
 * we will cancel the h^3 term in the error. This will make the integral of the
 * forces match the potential much better (The h^4 term actually disappears, so
 * when summing over 1/h points the remaining error will be O(h^4).
 *
 * While it is possible to create tables only from function values
 * (i.e., no derivatives), it is recommended to provide derivatives for higher
 * accuracy and to avoid issues with numerical differentiation. Note that the
 * table input should be smooth, i.e. it should not contain noise e.g. from an
 * (iterative) Boltzmann inversion procedure - you have been warned.
 *
 * \note This class is responsible for fundamental interpolation of any function,
 *       which might or might not correspond to a potential. For this reason
 *       both input and output derivatives are proper function derivatives, and
 *       we do not swap any signs to get forces directly from the table.
 *
 * \note There will be a small additional accuracy loss from the internal
 *       operation where we calculate the epsilon offset from the nearest table
 *       point, since the integer part we subtract can get large in those cases.
 *       The absolute such error both in the function and derivative value will
 *       be roughly f''*x*GMX_REAL_EPS, where x is the argument and f'' the
 *       second derivative.
 *       While this is technically possible to solve with extended precision
 *       arithmetics, that would introduce extra instructions in some highly
 *       performance-sensitive code parts. For typical GROMACS interaction
 *       functions the derivatives will decay faster than the potential, which
 *       means it will never play any role. For other functions it will only
 *       cause a small increase in the relative error for arguments where the
 *       magnitude of the function or derivative is very small.
 *       Since we typically sum several results in GROMACS, this should never
 *       show up in any real cases, and for this reason we choose not to do
 *       the extended precision arithmetics.
 *
 * \note These routines are not suitable for table ranges starting far away
 *       from zero, since we allocate memory and calculate indices starting from
 *       range zero for efficiency reasons.
 */
class QuadraticSplineTable
{
    private:
        /*! \brief Change that function value falls inside range when debugging
         *
         *  \tparam T   Lookup argument floating-point type, typically SimdReal or real.
         *  \param  r   Lookup argument to test
         *
         *  \throws Debug builds will throw gmx::RangeError for values that are
         *          larger than the upper limit of the range, or smaller than 0.
         *          We allow the table to be called with arguments between 0 and
         *          the lower limit of the range, since this might in theory occur
         *          once-in-a-blue-moon with some algorithms.
         */
        template <typename T>
        void
        rangeCheck(T gmx_unused r) const
        {
#ifndef NDEBUG
            // Check that all values fall in range when debugging
            if (anyTrue( r < T(0.0) || T(range_.second) <= r ) )
            {
                GMX_THROW(RangeError("Interpolation input value falls outside table definition range"));
            }
#endif
        }

    public:

        /*! \brief Default tolerance for tables is 10*GMX_FLOAT_EPS
         *
         *  \note Even for double precision builds we set the tolerance to
         *        one order of magnitude above the single precision epsilon.
         */
        static const real defaultTolerance;

        /*! \brief Initialize table data from function
         *
         * \param analyticalInputList Initializer list with one or more functions to tabulate,
         *                            specified as pairs containing analytical
         *                            functions and their derivatives. The function will also
         *                            be called for values smaller than the lower limit of the
         *                            range, but we avoid calling it for 0.0 if that value
         *                            is not included in the range.
         * \param range               Range over which the function will be tabulated.
         *                            Constructor will throw gmx::APIError for negative values.
         *                            Due to the way the numerical derivative evaluation depends
         *                            on machine precision internally, this range must be
         *                            at least 0.001, or the constructor throws gmx::APIError.
         * \param tolerance           Requested accuracy of the table. This will be used to
         *                            calculate the required internal spacing. If this cannot
         *                            be achieved (for instance because the table would require
         *                            too much memory) the constructor will throw gmx::ToleranceError.
         *
         * \note The functions are always defined in double precision to avoid
         *       losing accuracy when constructing tables.
         *
         * \note Since we fill the table for values below range.first, you can achieve
         *       a smaller table by using a smaller range where the tolerance has to be
         *       met, and accept that a few function calls below range.first do not
         *       quite reach the tolerance.
         *
         * \warning For efficiency reasons (since this code is used in some inner
         *       (kernels), we always allocate memory and calculate table indices
         *       for the complete interval [0,range.second], although the data will
         *       not be valid outside the definition range to avoid calling the
         *       function there. This means you should \a not use this class
         *       to tabulate functions for small ranges very far away from zero,
         *       since you would both waste a huge amount of memory and incur
         *       truncation errors when calculating the index.
         *
         * \throws gmx::ToleranceError if the requested tolerance cannot be achieved,
         *         and gmx::APIError for other incorrect input.
         */
        QuadraticSplineTable(std::initializer_list<AnalyticalSplineTableInput>   analyticalInputList,
                             const std::pair<real, real>                        &range,
                             real                                                tolerance = defaultTolerance);

        /*! \brief Initialize table data from tabulated values and derivatives
         *
         * \param numericalInputList  Initializer list with one or more functions to tabulate,
         *                            specified as pairs containing containing vectors for the
         *                            function values and their derivatives. Data points are
         *                            separated by the spacing parameter, starting from 0.
         *                            Values below the lower limit of the range will be used to
         *                            attempt defining the table, but we avoid using index 0
         *                            unless 0.0 is included in the range. Some extra points beyond
         *                            range.second are required to re-interpolate values, so add
         *                            some margin. The constructor will throw gmx::APIError if the
         *                            input vectors are too short to cover the requested range
         *                            (and they must always be at least five points).
         * \param range               Range over which the function will be tabulated.
         *                            Constructor will throw gmx::APIError for negative values,
         *                            or if the value/derivative vector does not cover the
         *                            range.
         * \param tolerance           Requested accuracy of the table in the range. This will be
         *                            used to calculate the required internal spacing and possibly
         *                            re-interpolate. The constructor will throw
         *                            gmx::ToleranceError if the input spacing is too coarse
         *                            to achieve this accuracy.
         *
         * \note The input data vectors are always double precision to avoid
         *       losing accuracy when constructing tables.
         *
         * \note Since we fill the table for values below range.first, you can achieve
         *       a smaller table by using a smaller range where the tolerance has to be
         *       met, and accept that a few function calls below range.first do not
         *       quite reach the tolerance.
         *
         * \warning For efficiency reasons (since this code is used in some inner
         *       (kernels), we always allocate memory and calculate table indices
         *       for the complete interval [0,range.second], although the data will
         *       not be valid outside the definition range to avoid calling the
         *       function there. This means you should \a not use this class
         *       to tabulate functions for small ranges very far away from zero,
         *       since you would both waste a huge amount of memory and incur
         *       truncation errors when calculating the index.
         */
        QuadraticSplineTable(std::initializer_list<NumericalSplineTableInput>    numericalInputList,
                             const std::pair<real, real>                        &range,
                             real                                                tolerance = defaultTolerance);


        /************************************************************
         *           Evaluation methods for single functions        *
         ************************************************************/

        /*! \brief Evaluate both function and derivative, single table function
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable  Number of separate functions in table, default is 1
         *  \tparam     funcIndex       Index of function to evaluate in table, default is 0
         *  \tparam     T               Type (SimdReal or real) of lookup and result
         *  \param      r               Points for which to evaluate function and derivative
         *  \param[out] functionValue   Function value
         *  \param[out] derivativeValue Function derivative
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 1, int funcIndex = 0, typename T>
        void
        evaluateFunctionAndDerivative(T     r,
                                      T *   functionValue,
                                      T *   derivativeValue) const
        {
            rangeCheck(r);
            GMX_ASSERT(numFuncInTable == numFuncInTable_, "Evaluation method not matching number of functions in table");
            GMX_ASSERT(funcIndex < numFuncInTable, "Function index not in range of the number of tables");

            T     rTable   = r * T(tableScale_);
            auto  tabIndex = cvttR2I(rTable); // type is either std::int32_t or SimdInt32
            T     eps      = rTable - trunc(rTable);
            T     t0;
            T     t1;
            T     t2;
            T     t3 gmx_unused;

            // Load Derivative, Delta, Function, and Zero values for each table point.
            // The 4 refers to these four values - not any SIMD width.
            gatherLoadBySimdIntTranspose<4*numFuncInTable>(ddfzMultiTableData_.data() + 4 * funcIndex, tabIndex, &t0, &t1, &t2, &t3);

            t1               = t0 + eps * t1;
            *functionValue   = fma( eps * T(halfSpacing_),  t0 + t1, t2);
            *derivativeValue = t1;
        }

        /*! \brief Evaluate function value only, single table function
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable  Number of separate functions in table, default is 1
         *  \tparam     funcIndex       Index of function to evaluate in table, default is 0
         *  \tparam     T               Type (SimdReal or real) of lookup and result
         *  \param      r               Points for which to evaluate function value
         *  \param[out] functionValue   Function value
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 1, int funcIndex = 0, typename T>
        void
        evaluateFunction(T     r,
                         T *   functionValue) const
        {
            T     der gmx_unused;

            evaluateFunctionAndDerivative<numFuncInTable, funcIndex>(r, functionValue, &der);
        }

        /*! \brief Evaluate function derivative only, single table function
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable  Number of separate functions in table, default is 1
         *  \tparam     funcIndex       Index of function to evaluate in table, default is 0
         *  \tparam     T               Type (SimdReal or real) of lookup and result
         *  \param      r               Points for which to evaluate function derivative
         *  \param[out] derivativeValue Function derivative
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 1, int funcIndex = 0, typename T>
        void
        evaluateDerivative(T     r,
                           T *   derivativeValue) const
        {
            rangeCheck(r);
            GMX_ASSERT(numFuncInTable == numFuncInTable_, "Evaluation method not matching number of functions in table");
            GMX_ASSERT(funcIndex < numFuncInTable, "Function index not in range of the number of tables");

            T     rTable   = r * T(tableScale_);
            auto  tabIndex = cvttR2I(rTable); // type is either std::int32_t or SimdInt32
            T     eps      = rTable - trunc(rTable);
            T     t0;
            T     t1;
            T     t2 gmx_unused;

            if (numFuncInTable == 1)
            {
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex, tabIndex, &t0, &t1); // works for scalar T too
            }
            else
            {
                // This is not ideal, but we need a version of gatherLoadUBySimdIntTranspose that
                // only loads a single value from memory to implement it better (will be written)
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex, tabIndex, &t0, &t2);        // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex, tabIndex + T(1), &t1, &t2); // works for scalar T too
            }

            // (1-eps)*t0 + eps*t1
            *derivativeValue = fma(t1-t0, eps, t0);
        }

        /************************************************************
         *             Evaluation methods for two functions         *
         ************************************************************/

        /*! \brief Evaluate both function and derivative, two table functions
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable  Number of separate functions in table, default is 2
         *  \tparam     funcIndex0       Index of 1st function to evaluate in table, default is 0
         *  \tparam     funcIndex1       Index of 2nd function to evaluate in table, default is 1
         *  \tparam     T                Type (SimdReal or real) of lookup and result
         *  \param      r                Points for which to evaluate function and derivative
         *  \param[out] functionValue1   Interpolated value for first function
         *  \param[out] derivativeValue1 Interpolated derivative for first function
         *  \param[out] functionValue2   Interpolated value for second function
         *  \param[out] derivativeValue2 Interpolated derivative for second function
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 2, int funcIndex0 = 0, int funcIndex1 = 1, typename T>
        void
        evaluateFunctionAndDerivative(T     r,
                                      T *   functionValue1,
                                      T *   derivativeValue1,
                                      T *   functionValue2,
                                      T *   derivativeValue2) const
        {
            rangeCheck(r);
            GMX_ASSERT(numFuncInTable == numFuncInTable_, "Evaluation method not matching number of functions in table");
            GMX_ASSERT(funcIndex0 < numFuncInTable && funcIndex1 < numFuncInTable, "Function index not in range of the number of tables");

            T     rTable   = r * T(tableScale_);
            auto  tabIndex = cvttR2I(rTable); // type is either std::int32_t or SimdInt32
            T     eps      = rTable - trunc(rTable);
            T     t0;
            T     t1;
            T     t2;
            T     t3 gmx_unused;

            // Load Derivative, Delta, Function, and Zero values for each table point.
            // The 4 refers to these four values - not any SIMD width.
            gatherLoadBySimdIntTranspose<4*numFuncInTable>(ddfzMultiTableData_.data() + 4*funcIndex0, tabIndex, &t0, &t1, &t2, &t3);
            t1                = t0 + eps * t1;
            *functionValue1   = fma( eps * T(halfSpacing_),  t0 + t1, t2);
            *derivativeValue1 = t1;

            gatherLoadBySimdIntTranspose<4*numFuncInTable>(ddfzMultiTableData_.data() + 4*funcIndex1, tabIndex, &t0, &t1, &t2, &t3);
            t1                = t0 + eps * t1;
            *functionValue2   = fma( eps * T(halfSpacing_),  t0 + t1, t2);
            *derivativeValue2 = t1;
        }

        /*! \brief Evaluate function value only, two table functions
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable   Number of separate functions in table, default is 2
         *  \tparam     funcIndex0       Index of 1st function to evaluate in table, default is 0
         *  \tparam     funcIndex1       Index of 2nd function to evaluate in table, default is 1
         *  \tparam     T                Type (SimdReal or real) of lookup and result
         *  \param      r                Points for which to evaluate function value
         *  \param[out] functionValue1   Interpolated value for first function
         *  \param[out] functionValue2   Interpolated value for second function
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 2, int funcIndex0 = 0, int funcIndex1 = 1, typename T>
        void
        evaluateFunction(T     r,
                         T *   functionValue1,
                         T *   functionValue2) const
        {
            T     der1 gmx_unused;
            T     der2 gmx_unused;

            evaluateFunctionAndDerivative<numFuncInTable, funcIndex0, funcIndex1>(r, functionValue1, &der1, functionValue2, &der2);
        }

        /*! \brief Evaluate function derivative only, two table functions
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable   Number of separate functions in table, default is 2
         *  \tparam     funcIndex0       Index of 1st function to evaluate in table, default is 0
         *  \tparam     funcIndex1       Index of 2nd function to evaluate in table, default is 1
         *  \tparam     T                Type (SimdReal or real) of lookup and result
         *  \param      r                Points for which to evaluate function derivative
         *  \param[out] derivativeValue1 Interpolated derivative for first function
         *  \param[out] derivativeValue2 Interpolated derivative for second function
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 2, int funcIndex0 = 0, int funcIndex1 = 1, typename T>
        void
        evaluateDerivative(T     r,
                           T *   derivativeValue1,
                           T *   derivativeValue2) const
        {
            rangeCheck(r);
            GMX_ASSERT(numFuncInTable == numFuncInTable_, "Evaluation method not matching number of functions in table");
            GMX_ASSERT(funcIndex0 < numFuncInTable && funcIndex1 < numFuncInTable, "Function index not in range of the number of tables");

            T     rTable   = r * T(tableScale_);
            auto  tabIndex = cvttR2I(rTable); // type is either std::int32_t or SimdInt32
            T     eps      = rTable - trunc(rTable);

            if (numFuncInTable == 2 && funcIndex0 == 0 && funcIndex1 == 1)
            {
                T t0A, t0B, t1A, t1B;
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data(), tabIndex, &t0A, &t0B);     // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + 2, tabIndex, &t1A, &t1B); // works for scalar T too
                *derivativeValue1 = fma(t1A-t0A, eps, t0A);
                *derivativeValue2 = fma(t1B-t0B, eps, t0B);
            }
            else
            {
                T t0, t1, t2;
                // This is not ideal, but we need a version of gatherLoadUBySimdIntTranspose that
                // only loads a single value from memory to implement it better (will be written)
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex0, tabIndex, &t0, &t2);        // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex0, tabIndex + T(1), &t1, &t2); // works for scalar T too
                *derivativeValue1 = fma(t1-t0, eps, t0);

                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex1, tabIndex, &t0, &t2);        // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex1, tabIndex + T(1), &t1, &t2); // works for scalar T too
                *derivativeValue2 = fma(t1-t0, eps, t0);
            }
        }

        /************************************************************
         *            Evaluation methods for three functions        *
         ************************************************************/


        /*! \brief Evaluate both function and derivative, three table functions
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable   Number of separate functions in table, default is 3
         *  \tparam     funcIndex0       Index of 1st function to evaluate in table, default is 0
         *  \tparam     funcIndex1       Index of 2nd function to evaluate in table, default is 1
         *  \tparam     funcIndex2       Index of 3rd function to evaluate in table, default is 2
         *  \tparam     T                Type (SimdReal or real) of lookup and result
         *  \param      r                Points for which to evaluate function and derivative
         *  \param[out] functionValue1   Interpolated value for first function
         *  \param[out] derivativeValue1 Interpolated derivative for first function
         *  \param[out] functionValue2   Interpolated value for second function
         *  \param[out] derivativeValue2 Interpolated derivative for second function
         *  \param[out] functionValue3   Interpolated value for third function
         *  \param[out] derivativeValue3 Interpolated derivative for third function
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 3, int funcIndex0 = 0, int funcIndex1 = 1, int funcIndex2 = 2, typename T>
        void
        evaluateFunctionAndDerivative(T     r,
                                      T *   functionValue1,
                                      T *   derivativeValue1,
                                      T *   functionValue2,
                                      T *   derivativeValue2,
                                      T *   functionValue3,
                                      T *   derivativeValue3) const
        {
            rangeCheck(r);
            GMX_ASSERT(numFuncInTable == numFuncInTable, "Evaluation method not matching number of functions in table");
            GMX_ASSERT(funcIndex0 < numFuncInTable  && funcIndex1 < numFuncInTable  && funcIndex2 < numFuncInTable,
                       "Function index not in range of the number of tables");

            T     rTable   = r * T(tableScale_);
            auto  tabIndex = cvttR2I(rTable); // type is either std::int32_t or SimdInt32
            T     eps      = rTable - trunc(rTable);
            T     t0;
            T     t1;
            T     t2;
            T     t3 gmx_unused;

            gatherLoadBySimdIntTranspose<4*numFuncInTable>(ddfzMultiTableData_.data() + 4*funcIndex0, tabIndex, &t0, &t1, &t2, &t3);
            t1                = t0 + eps * t1;
            *functionValue1   = fma( eps * T(halfSpacing_),  t0 + t1, t2);
            *derivativeValue1 = t1;

            gatherLoadBySimdIntTranspose<4*numFuncInTable>(ddfzMultiTableData_.data() + 4*funcIndex1, tabIndex, &t0, &t1, &t2, &t3);
            t1                = t0 + eps * t1;
            *functionValue2   = fma( eps * T(halfSpacing_),  t0 + t1, t2);
            *derivativeValue2 = t1;

            gatherLoadBySimdIntTranspose<4*numFuncInTable>(ddfzMultiTableData_.data() + 4*funcIndex2, tabIndex, &t0, &t1, &t2, &t3);
            t1                = t0 + eps * t1;
            *functionValue3   = fma( eps * T(halfSpacing_),  t0 + t1, t2);
            *derivativeValue3 = t1;
        }

        /*! \brief Evaluate function value only, three table functions
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable   Number of separate functions in table, default is 3
         *  \tparam     funcIndex0       Index of 1st function to evaluate in table, default is 0
         *  \tparam     funcIndex1       Index of 2nd function to evaluate in table, default is 1
         *  \tparam     funcIndex2       Index of 3rd function to evaluate in table, default is 2
         *  \tparam     T                Type (SimdReal or real) of lookup and result
         *  \param      r                Points for which to evaluate function value
         *  \param[out] functionValue1   Interpolated value for first function
         *  \param[out] functionValue2   Interpolated value for second function
         *  \param[out] functionValue3   Interpolated value for third function
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 3, int funcIndex0 = 0, int funcIndex1 = 1, int funcIndex2 = 2, typename T>
        void
        evaluateFunction(T     r,
                         T *   functionValue1,
                         T *   functionValue2,
                         T *   functionValue3) const
        {
            T     der1 gmx_unused;
            T     der2 gmx_unused;
            T     der3 gmx_unused;

            evaluateFunctionAndDerivative<numFuncInTable, funcIndex0, funcIndex1, funcIndex2>(r, functionValue1, &der1, functionValue2, &der2, functionValue3, &der3);
        }

        /*! \brief Evaluate function derivative only, three table functions
         *
         *  This is a templated method where the template can be either real or SimdReal.
         *
         *  \tparam     numFuncInTable   Number of separate functions in table, default is 3
         *  \tparam     funcIndex0       Index of 1st function to evaluate in table, default is 0
         *  \tparam     funcIndex1       Index of 2nd function to evaluate in table, default is 1
         *  \tparam     funcIndex2       Index of 3rd function to evaluate in table, default is 2
         *  \tparam     T                Type (SimdReal or real) of lookup and result
         *  \param      r                Points for which to evaluate function derivative
         *  \param[out] derivativeValue1 Interpolated derivative for first function
         *  \param[out] derivativeValue2 Interpolated derivative for second function
         *  \param[out] derivativeValue3 Interpolated derivative for third function
         *
         *  For debug builds we assert that the input values fall in the range
         *  specified when constructing the table.
         */
        template <int numFuncInTable = 3, int funcIndex0 = 0, int funcIndex1 = 1, int funcIndex2 = 2, typename T>
        void
        evaluateDerivative(T     r,
                           T *   derivativeValue1,
                           T *   derivativeValue2,
                           T *   derivativeValue3) const
        {
            rangeCheck(r);
            GMX_ASSERT(numFuncInTable == numFuncInTable_, "Evaluation method not matching number of functions in table");
            GMX_ASSERT(funcIndex0 < numFuncInTable  && funcIndex1 < numFuncInTable  && funcIndex2 < numFuncInTable,
                       "Function index not in range of the number of tables");

            T     rTable   = r * T(tableScale_);
            auto  tabIndex = cvttR2I(rTable); // type is either std::int32_t or SimdInt32
            T     eps      = rTable - trunc(rTable);

            if (numFuncInTable == 3 && funcIndex0 == 0 && funcIndex1 == 1 && funcIndex2 == 2)
            {
                T t0A, t0B, t0C, t1A, t1B, t1C;
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data(), tabIndex, &t0A, &t0B);
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + 2, tabIndex, &t0C, &t1A);
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + 4, tabIndex, &t1B, &t1C);
                *derivativeValue1 = fma(t1A-t0A, eps, t0A);
                *derivativeValue2 = fma(t1B-t0B, eps, t0B);
                *derivativeValue3 = fma(t1C-t0C, eps, t0C);
            }
            else
            {
                T t0, t1, t2;
                // This is not ideal, but we need a version of gatherLoadUBySimdIntTranspose that
                // only loads a single value from memory to implement it better (will be written)
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex0, tabIndex, &t0, &t2);        // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex0, tabIndex + T(1), &t1, &t2); // works for scalar T too
                *derivativeValue1 = fma(t1-t0, eps, t0);

                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex1, tabIndex, &t0, &t2);        // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex1, tabIndex + T(1), &t1, &t2); // works for scalar T too
                *derivativeValue2 = fma(t1-t0, eps, t0);

                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex2, tabIndex, &t0, &t2);        // works for scalar T too
                gatherLoadUBySimdIntTranspose<numFuncInTable>(derivativeMultiTableData_.data() + funcIndex2, tabIndex + T(1), &t1, &t2); // works for scalar T too
                *derivativeValue3 = fma(t1-t0, eps, t0);
            }
        }

        /*! \brief Return the table spacing (distance between points)
         *
         *  You should never have to use this for normal code, but due to the
         *  way tables are constructed internally we need this in the unit tests
         *  to check relative tolerances over each interval.
         *
         *  \return table spacing.
         */
        real
        tableSpacing() const { return 1.0 / tableScale_; }

    private:

        std::size_t             numFuncInTable_; //!< Number of separate tabluated functions
        std::pair<real, real>   range_;          //!< Range for which table evaluation is allowed
        real                    tableScale_;     //!< Table scale (inverse of spacing between points)
        real                    halfSpacing_;    //!< 0.5*spacing (used for DDFZ table data)

        //!< Derivative values only, with the third-derivative subtraction described in the class documentation.
        std::vector<real>      derivativeMultiTableData_;

        /*! \brief Combined derivative, difference to next derivative, value, and zero.
         *
         *  For table point i, this vector contains the four values:
         *  - derivative[i]
         *  - (derivative[i+1]-derivative[i])
         *  - value[i]
         *  - 0.0
         *
         *  For the derivative terms we have subtracted the third-derivative term described
         *  in the main class documentation.
         *
         *  This is typically more efficient than the individual tables, in particular
         *  when using SIMD. The result should be identical outside the class, so this
         *  is merely an internal implementation optimization. However, to allow
         *  aligned SIMD loads we need to use an aligned allocator for this container.
         *  We occasionally abbreviate this data as DDFZ.
         */
        std::vector<real, AlignedAllocator<real> >  ddfzMultiTableData_;

        // There should never be any reason to copy the table since it is read-only
        GMX_DISALLOW_COPY_AND_ASSIGN(QuadraticSplineTable);
};


}      // namespace gmx

#endif // GMX_TABLES_QUADRATICSPLINETABLE_H