libgromacs-dev 5.1.2-1ubuntu1 / usr / include / gromacs / math / vec.h

/*
 * This file is part of the GROMACS molecular simulation package.
 *
 * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
 * Copyright (c) 2001-2004, The GROMACS development team.
 * Copyright (c) 2013,2014, 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.
 *
 * GROMACS is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1
 * of the License, or (at your option) any later version.
 *
 * GROMACS is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with GROMACS; if not, see
 * http://www.gnu.org/licenses, or write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA.
 *
 * If you want to redistribute modifications to GROMACS, please
 * consider that scientific software is very special. Version
 * control is crucial - bugs must be traceable. We will be happy to
 * consider code for inclusion in the official distribution, but
 * derived work must not be called official GROMACS. Details are found
 * in the README & COPYING files - if they are missing, get the
 * official version at http://www.gromacs.org.
 *
 * To help us fund GROMACS development, we humbly ask that you cite
 * the research papers on the package. Check out http://www.gromacs.org.
 */
#ifndef GMX_MATH_VEC_H
#define GMX_MATH_VEC_H

/*
   collection of in-line ready operations:

   lookup-table optimized scalar operations:
   real gmx_invsqrt(real x)
   real sqr(real x)
   double dsqr(double x)

   vector operations:
   void rvec_add(const rvec a,const rvec b,rvec c)  c = a + b
   void dvec_add(const dvec a,const dvec b,dvec c)  c = a + b
   void ivec_add(const ivec a,const ivec b,ivec c)  c = a + b
   void rvec_inc(rvec a,const rvec b)               a += b
   void dvec_inc(dvec a,const dvec b)               a += b
   void ivec_inc(ivec a,const ivec b)               a += b
   void rvec_sub(const rvec a,const rvec b,rvec c)  c = a - b
   void dvec_sub(const dvec a,const dvec b,dvec c)  c = a - b
   void rvec_dec(rvec a,rvec b)                     a -= b
   void copy_rvec(const rvec a,rvec b)              b = a (reals)
   void copy_dvec(const dvec a,dvec b)              b = a (reals)
   void copy_ivec(const ivec a,ivec b)              b = a (integers)
   void ivec_sub(const ivec a,const ivec b,ivec c)  c = a - b
   void svmul(real a,rvec v1,rvec v2)               v2 = a * v1
   void dsvmul(double a,dvec v1,dvec v2)            v2 = a * v1
   void clear_rvec(rvec a)                          a = 0
   void clear_dvec(dvec a)                          a = 0
   void clear_ivec(rvec a)                          a = 0
   void clear_rvecs(int n,rvec v[])
   real iprod(rvec a,rvec b)                        = a . b (inner product)
   double diprod(dvec a,dvec b)                     = a . b (inner product)
   real iiprod(ivec a,ivec b)                       = a . b (integers)
   real norm2(rvec a)                               = | a |^2 ( = x*y*z )
   double dnorm2(dvec a)                            = | a |^2 ( = x*y*z )
   real norm(rvec a)                                = | a |
   double dnorm(dvec a)                             = | a |
   void cprod(rvec a,rvec b,rvec c)                 c = a x b (cross product)
   void dprod(rvec a,rvec b,rvec c)                 c = a x b (cross product)
   void dprod(rvec a,rvec b,rvec c)                 c = a * b (direct product)
   real cos_angle(rvec a,rvec b)
   real cos_angle_no_table(rvec a,rvec b)
   real distance2(rvec v1, rvec v2)                 = | v2 - v1 |^2
   void unitv(rvec src,rvec dest)                   dest = src / |src|
   void unitv_no_table(rvec src,rvec dest)          dest = src / |src|

   matrix (3x3) operations:
    ! indicates that dest should not be the same as a, b or src
    the _ur0 varieties work on matrices that have only zeros
    in the upper right part, such as box matrices, these varieties
    could produce less rounding errors, not due to the operations themselves,
    but because the compiler can easier recombine the operations
   void copy_mat(matrix a,matrix b)                 b = a
   void clear_mat(matrix a)                         a = 0
   void mmul(matrix a,matrix b,matrix dest)      !  dest = a . b
   void mmul_ur0(matrix a,matrix b,matrix dest)     dest = a . b
   void transpose(matrix src,matrix dest)        !  dest = src*
   void tmmul(matrix a,matrix b,matrix dest)     !  dest = a* . b
   void mtmul(matrix a,matrix b,matrix dest)     !  dest = a . b*
   real det(matrix a)                               = det(a)
   void m_add(matrix a,matrix b,matrix dest)        dest = a + b
   void m_sub(matrix a,matrix b,matrix dest)        dest = a - b
   void msmul(matrix m1,real r1,matrix dest)        dest = r1 * m1
   void m_inv_ur0(matrix src,matrix dest)           dest = src^-1
   void m_inv(matrix src,matrix dest)            !  dest = src^-1
   void mvmul(matrix a,rvec src,rvec dest)       !  dest = a . src
   void mvmul_ur0(matrix a,rvec src,rvec dest)      dest = a . src
   void tmvmul_ur0(matrix a,rvec src,rvec dest)     dest = a* . src
   real trace(matrix m)                             = trace(m)
 */

/* The file only depends on config.h for GMX_SOFTWARE_INVSQRT and
   HAVE_*SQRT*. This is no problem with public headers because
   it is OK if user code uses a different rsqrt implementation */
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include <math.h>

#include "gromacs/math/units.h"
#include "gromacs/math/utilities.h"
#include "gromacs/math/vectypes.h"
#include "gromacs/utility/basedefinitions.h"
#include "gromacs/utility/fatalerror.h"
#include "gromacs/utility/real.h"

#ifdef __cplusplus
extern "C" {
#elif 0
} /* avoid screwing up indentation */
#endif

#ifdef GMX_SOFTWARE_INVSQRT
#define EXP_LSB         0x00800000
#define EXP_MASK        0x7f800000
#define EXP_SHIFT       23
#define FRACT_MASK      0x007fffff
#define FRACT_SIZE      11              /* significant part of fraction */
#define FRACT_SHIFT     (EXP_SHIFT-FRACT_SIZE)
#define EXP_ADDR(val)   (((val)&EXP_MASK)>>EXP_SHIFT)
#define FRACT_ADDR(val) (((val)&(FRACT_MASK|EXP_LSB))>>FRACT_SHIFT)

extern const unsigned int gmx_invsqrt_exptab[];
extern const unsigned int gmx_invsqrt_fracttab[];

typedef union
{
    unsigned int bval;
    float        fval;
} t_convert;

static gmx_inline real gmx_software_invsqrt(real x)
{
    const real   half  = 0.5;
    const real   three = 3.0;
    t_convert    result, bit_pattern;
    unsigned int exp, fract;
    real         lu;
    real         y;
#ifdef GMX_DOUBLE
    real         y2;
#endif

    bit_pattern.fval = x;
    exp              = EXP_ADDR(bit_pattern.bval);
    fract            = FRACT_ADDR(bit_pattern.bval);
    result.bval      = gmx_invsqrt_exptab[exp] | gmx_invsqrt_fracttab[fract];
    lu               = result.fval;

    y = (half*lu*(three-((x*lu)*lu)));
#ifdef GMX_DOUBLE
    y2 = (half*y*(three-((x*y)*y)));

    return y2;                  /* 10 Flops */
#else
    return y;                   /* 5  Flops */
#endif
}
#define gmx_invsqrt(x) gmx_software_invsqrt(x)
#define INVSQRT_DONE
#endif /* gmx_invsqrt */

#ifndef INVSQRT_DONE
#    ifdef GMX_DOUBLE
#        ifdef HAVE_RSQRT
#            define gmx_invsqrt(x)     rsqrt(x)
#        else
#            define gmx_invsqrt(x)     (1.0/sqrt(x))
#        endif
#    else /* single */
#        ifdef HAVE_RSQRTF
#            define gmx_invsqrt(x)     rsqrtf(x)
#        elif defined HAVE_RSQRT
#            define gmx_invsqrt(x)     rsqrt(x)
#        elif defined HAVE_SQRTF
#            define gmx_invsqrt(x)     (1.0/sqrtf(x))
#        else
#            define gmx_invsqrt(x)     (1.0/sqrt(x))
#        endif
#    endif
#endif


static gmx_inline real sqr(real x)
{
    return (x*x);
}

static gmx_inline double dsqr(double x)
{
    return (x*x);
}

/* Maclaurin series for sinh(x)/x, useful for NH chains and MTTK pressure control
   Here, we compute it to 10th order, which might be overkill, 8th is probably enough,
   but it's not very much more expensive. */

static gmx_inline real series_sinhx(real x)
{
    real x2 = x*x;
    return (1 + (x2/6.0)*(1 + (x2/20.0)*(1 + (x2/42.0)*(1 + (x2/72.0)*(1 + (x2/110.0))))));
}

static gmx_inline void rvec_add(const rvec a, const rvec b, rvec c)
{
    real x, y, z;

    x = a[XX]+b[XX];
    y = a[YY]+b[YY];
    z = a[ZZ]+b[ZZ];

    c[XX] = x;
    c[YY] = y;
    c[ZZ] = z;
}

static gmx_inline void dvec_add(const dvec a, const dvec b, dvec c)
{
    double x, y, z;

    x = a[XX]+b[XX];
    y = a[YY]+b[YY];
    z = a[ZZ]+b[ZZ];

    c[XX] = x;
    c[YY] = y;
    c[ZZ] = z;
}

static gmx_inline void ivec_add(const ivec a, const ivec b, ivec c)
{
    int x, y, z;

    x = a[XX]+b[XX];
    y = a[YY]+b[YY];
    z = a[ZZ]+b[ZZ];

    c[XX] = x;
    c[YY] = y;
    c[ZZ] = z;
}

static gmx_inline void rvec_inc(rvec a, const rvec b)
{
    real x, y, z;

    x = a[XX]+b[XX];
    y = a[YY]+b[YY];
    z = a[ZZ]+b[ZZ];

    a[XX] = x;
    a[YY] = y;
    a[ZZ] = z;
}

static gmx_inline void dvec_inc(dvec a, const dvec b)
{
    double x, y, z;

    x = a[XX]+b[XX];
    y = a[YY]+b[YY];
    z = a[ZZ]+b[ZZ];

    a[XX] = x;
    a[YY] = y;
    a[ZZ] = z;
}

static gmx_inline void rvec_sub(const rvec a, const rvec b, rvec c)
{
    real x, y, z;

    x = a[XX]-b[XX];
    y = a[YY]-b[YY];
    z = a[ZZ]-b[ZZ];

    c[XX] = x;
    c[YY] = y;
    c[ZZ] = z;
}

static gmx_inline void dvec_sub(const dvec a, const dvec b, dvec c)
{
    double x, y, z;

    x = a[XX]-b[XX];
    y = a[YY]-b[YY];
    z = a[ZZ]-b[ZZ];

    c[XX] = x;
    c[YY] = y;
    c[ZZ] = z;
}

static gmx_inline void rvec_dec(rvec a, const rvec b)
{
    real x, y, z;

    x = a[XX]-b[XX];
    y = a[YY]-b[YY];
    z = a[ZZ]-b[ZZ];

    a[XX] = x;
    a[YY] = y;
    a[ZZ] = z;
}

static gmx_inline void copy_rvec(const rvec a, rvec b)
{
    b[XX] = a[XX];
    b[YY] = a[YY];
    b[ZZ] = a[ZZ];
}

static gmx_inline void copy_rvecn(gmx_cxx_const rvec *a, rvec *b, int startn, int endn)
{
    int i;
    for (i = startn; i < endn; i++)
    {
        b[i][XX] = a[i][XX];
        b[i][YY] = a[i][YY];
        b[i][ZZ] = a[i][ZZ];
    }
}

static gmx_inline void copy_dvec(const dvec a, dvec b)
{
    b[XX] = a[XX];
    b[YY] = a[YY];
    b[ZZ] = a[ZZ];
}

static gmx_inline void copy_ivec(const ivec a, ivec b)
{
    b[XX] = a[XX];
    b[YY] = a[YY];
    b[ZZ] = a[ZZ];
}

static gmx_inline void ivec_sub(const ivec a, const ivec b, ivec c)
{
    int x, y, z;

    x = a[XX]-b[XX];
    y = a[YY]-b[YY];
    z = a[ZZ]-b[ZZ];

    c[XX] = x;
    c[YY] = y;
    c[ZZ] = z;
}

static gmx_inline void copy_mat(gmx_cxx_const matrix a, matrix b)
{
    copy_rvec(a[XX], b[XX]);
    copy_rvec(a[YY], b[YY]);
    copy_rvec(a[ZZ], b[ZZ]);
}

static gmx_inline void svmul(real a, const rvec v1, rvec v2)
{
    v2[XX] = a*v1[XX];
    v2[YY] = a*v1[YY];
    v2[ZZ] = a*v1[ZZ];
}

static gmx_inline void dsvmul(double a, const dvec v1, dvec v2)
{
    v2[XX] = a*v1[XX];
    v2[YY] = a*v1[YY];
    v2[ZZ] = a*v1[ZZ];
}

static gmx_inline real distance2(const rvec v1, const rvec v2)
{
    return sqr(v2[XX]-v1[XX]) + sqr(v2[YY]-v1[YY]) + sqr(v2[ZZ]-v1[ZZ]);
}

static gmx_inline void clear_rvec(rvec a)
{
    /* The ibm compiler has problems with inlining this
     * when we use a const real variable
     */
    a[XX] = 0.0;
    a[YY] = 0.0;
    a[ZZ] = 0.0;
}

static gmx_inline void clear_dvec(dvec a)
{
    /* The ibm compiler has problems with inlining this
     * when we use a const real variable
     */
    a[XX] = 0.0;
    a[YY] = 0.0;
    a[ZZ] = 0.0;
}

static gmx_inline void clear_ivec(ivec a)
{
    a[XX] = 0;
    a[YY] = 0;
    a[ZZ] = 0;
}

static gmx_inline void clear_rvecs(int n, rvec v[])
{
    int i;

    for (i = 0; (i < n); i++)
    {
        clear_rvec(v[i]);
    }
}

static gmx_inline void clear_mat(matrix a)
{
    const real nul = 0.0;

    a[XX][XX] = a[XX][YY] = a[XX][ZZ] = nul;
    a[YY][XX] = a[YY][YY] = a[YY][ZZ] = nul;
    a[ZZ][XX] = a[ZZ][YY] = a[ZZ][ZZ] = nul;
}

static gmx_inline real iprod(const rvec a, const rvec b)
{
    return (a[XX]*b[XX]+a[YY]*b[YY]+a[ZZ]*b[ZZ]);
}

static gmx_inline double diprod(const dvec a, const dvec b)
{
    return (a[XX]*b[XX]+a[YY]*b[YY]+a[ZZ]*b[ZZ]);
}

static gmx_inline int iiprod(const ivec a, const ivec b)
{
    return (a[XX]*b[XX]+a[YY]*b[YY]+a[ZZ]*b[ZZ]);
}

static gmx_inline real norm2(const rvec a)
{
    return a[XX]*a[XX]+a[YY]*a[YY]+a[ZZ]*a[ZZ];
}

static gmx_inline double dnorm2(const dvec a)
{
    return a[XX]*a[XX]+a[YY]*a[YY]+a[ZZ]*a[ZZ];
}

/* WARNING:
 * As dnorm() uses sqrt() (which is slow) _only_ use it if you are sure you
 * don't need 1/dnorm(), otherwise use dnorm2()*dinvnorm(). */
static gmx_inline double dnorm(const dvec a)
{
    return sqrt(diprod(a, a));
}

/* WARNING:
 * As norm() uses sqrtf() (which is slow) _only_ use it if you are sure you
 * don't need 1/norm(), otherwise use norm2()*invnorm(). */
static gmx_inline real norm(const rvec a)
{
    /* This is ugly, but we deliberately do not define gmx_sqrt() and handle the
     * float/double case here instead to avoid gmx_sqrt() being accidentally used. */
#ifdef GMX_DOUBLE
    return dnorm(a);
#elif defined HAVE_SQRTF
    return sqrtf(iprod(a, a));
#else
    return sqrt(iprod(a, a));
#endif
}

static gmx_inline real invnorm(const rvec a)
{
    return gmx_invsqrt(norm2(a));
}

static gmx_inline real dinvnorm(const dvec a)
{
    return gmx_invsqrt(dnorm2(a));
}

/* WARNING:
 * Do _not_ use these routines to calculate the angle between two vectors
 * as acos(cos_angle(u,v)). While it might seem obvious, the acos function
 * is very flat close to -1 and 1, which will lead to accuracy-loss.
 * Instead, use the new gmx_angle() function directly.
 */
static gmx_inline real
cos_angle(const rvec a, const rvec b)
{
    /*
     *                  ax*bx + ay*by + az*bz
     * cos-vec (a,b) =  ---------------------
     *                      ||a|| * ||b||
     */
    real   cosval;
    int    m;
    double aa, bb, ip, ipa, ipb, ipab; /* For accuracy these must be double! */

    ip = ipa = ipb = 0.0;
    for (m = 0; (m < DIM); m++) /* 18 */
    {
        aa   = a[m];
        bb   = b[m];
        ip  += aa*bb;
        ipa += aa*aa;
        ipb += bb*bb;
    }
    ipab = ipa*ipb;
    if (ipab > 0)
    {
        cosval = ip*gmx_invsqrt(ipab);  /*  7 */
    }
    else
    {
        cosval = 1;
    }
    /* 25 TOTAL */
    if (cosval > 1.0)
    {
        return 1.0;
    }
    if (cosval < -1.0)
    {
        return -1.0;
    }

    return cosval;
}

/* WARNING:
 * Do _not_ use these routines to calculate the angle between two vectors
 * as acos(cos_angle(u,v)). While it might seem obvious, the acos function
 * is very flat close to -1 and 1, which will lead to accuracy-loss.
 * Instead, use the new gmx_angle() function directly.
 */
static gmx_inline real
cos_angle_no_table(const rvec a, const rvec b)
{
    /* This version does not need the invsqrt lookup table */
    real   cosval;
    int    m;
    double aa, bb, ip, ipa, ipb; /* For accuracy these must be double! */

    ip = ipa = ipb = 0.0;
    for (m = 0; (m < DIM); m++) /* 18 */
    {
        aa   = a[m];
        bb   = b[m];
        ip  += aa*bb;
        ipa += aa*aa;
        ipb += bb*bb;
    }
    cosval = ip/sqrt(ipa*ipb);  /* 12 */
    /* 30 TOTAL */
    if (cosval > 1.0)
    {
        return 1.0;
    }
    if (cosval < -1.0)
    {
        return -1.0;
    }

    return cosval;
}


static gmx_inline void cprod(const rvec a, const rvec b, rvec c)
{
    c[XX] = a[YY]*b[ZZ]-a[ZZ]*b[YY];
    c[YY] = a[ZZ]*b[XX]-a[XX]*b[ZZ];
    c[ZZ] = a[XX]*b[YY]-a[YY]*b[XX];
}

static gmx_inline void dcprod(const dvec a, const dvec b, dvec c)
{
    c[XX] = a[YY]*b[ZZ]-a[ZZ]*b[YY];
    c[YY] = a[ZZ]*b[XX]-a[XX]*b[ZZ];
    c[ZZ] = a[XX]*b[YY]-a[YY]*b[XX];
}

/* This routine calculates the angle between a & b without any loss of accuracy close to 0/PI.
 * If you only need cos(theta), use the cos_angle() routines to save a few cycles.
 * This routine is faster than it might appear, since atan2 is accelerated on many CPUs (e.g. x86).
 */
static gmx_inline real
gmx_angle(const rvec a, const rvec b)
{
    rvec w;
    real wlen, s;

    cprod(a, b, w);

    wlen  = norm(w);
    s     = iprod(a, b);

    return atan2(wlen, s);
}

static gmx_inline void mmul_ur0(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
{
    dest[XX][XX] = a[XX][XX]*b[XX][XX];
    dest[XX][YY] = 0.0;
    dest[XX][ZZ] = 0.0;
    dest[YY][XX] = a[YY][XX]*b[XX][XX]+a[YY][YY]*b[YY][XX];
    dest[YY][YY] =                    a[YY][YY]*b[YY][YY];
    dest[YY][ZZ] = 0.0;
    dest[ZZ][XX] = a[ZZ][XX]*b[XX][XX]+a[ZZ][YY]*b[YY][XX]+a[ZZ][ZZ]*b[ZZ][XX];
    dest[ZZ][YY] =                    a[ZZ][YY]*b[YY][YY]+a[ZZ][ZZ]*b[ZZ][YY];
    dest[ZZ][ZZ] =                                        a[ZZ][ZZ]*b[ZZ][ZZ];
}

static gmx_inline void mmul(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
{
    dest[XX][XX] = a[XX][XX]*b[XX][XX]+a[XX][YY]*b[YY][XX]+a[XX][ZZ]*b[ZZ][XX];
    dest[YY][XX] = a[YY][XX]*b[XX][XX]+a[YY][YY]*b[YY][XX]+a[YY][ZZ]*b[ZZ][XX];
    dest[ZZ][XX] = a[ZZ][XX]*b[XX][XX]+a[ZZ][YY]*b[YY][XX]+a[ZZ][ZZ]*b[ZZ][XX];
    dest[XX][YY] = a[XX][XX]*b[XX][YY]+a[XX][YY]*b[YY][YY]+a[XX][ZZ]*b[ZZ][YY];
    dest[YY][YY] = a[YY][XX]*b[XX][YY]+a[YY][YY]*b[YY][YY]+a[YY][ZZ]*b[ZZ][YY];
    dest[ZZ][YY] = a[ZZ][XX]*b[XX][YY]+a[ZZ][YY]*b[YY][YY]+a[ZZ][ZZ]*b[ZZ][YY];
    dest[XX][ZZ] = a[XX][XX]*b[XX][ZZ]+a[XX][YY]*b[YY][ZZ]+a[XX][ZZ]*b[ZZ][ZZ];
    dest[YY][ZZ] = a[YY][XX]*b[XX][ZZ]+a[YY][YY]*b[YY][ZZ]+a[YY][ZZ]*b[ZZ][ZZ];
    dest[ZZ][ZZ] = a[ZZ][XX]*b[XX][ZZ]+a[ZZ][YY]*b[YY][ZZ]+a[ZZ][ZZ]*b[ZZ][ZZ];
}

static gmx_inline void transpose(gmx_cxx_const matrix src, matrix dest)
{
    dest[XX][XX] = src[XX][XX];
    dest[YY][XX] = src[XX][YY];
    dest[ZZ][XX] = src[XX][ZZ];
    dest[XX][YY] = src[YY][XX];
    dest[YY][YY] = src[YY][YY];
    dest[ZZ][YY] = src[YY][ZZ];
    dest[XX][ZZ] = src[ZZ][XX];
    dest[YY][ZZ] = src[ZZ][YY];
    dest[ZZ][ZZ] = src[ZZ][ZZ];
}

static gmx_inline void tmmul(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
{
    /* Computes dest=mmul(transpose(a),b,dest) - used in do_pr_pcoupl */
    dest[XX][XX] = a[XX][XX]*b[XX][XX]+a[YY][XX]*b[YY][XX]+a[ZZ][XX]*b[ZZ][XX];
    dest[XX][YY] = a[XX][XX]*b[XX][YY]+a[YY][XX]*b[YY][YY]+a[ZZ][XX]*b[ZZ][YY];
    dest[XX][ZZ] = a[XX][XX]*b[XX][ZZ]+a[YY][XX]*b[YY][ZZ]+a[ZZ][XX]*b[ZZ][ZZ];
    dest[YY][XX] = a[XX][YY]*b[XX][XX]+a[YY][YY]*b[YY][XX]+a[ZZ][YY]*b[ZZ][XX];
    dest[YY][YY] = a[XX][YY]*b[XX][YY]+a[YY][YY]*b[YY][YY]+a[ZZ][YY]*b[ZZ][YY];
    dest[YY][ZZ] = a[XX][YY]*b[XX][ZZ]+a[YY][YY]*b[YY][ZZ]+a[ZZ][YY]*b[ZZ][ZZ];
    dest[ZZ][XX] = a[XX][ZZ]*b[XX][XX]+a[YY][ZZ]*b[YY][XX]+a[ZZ][ZZ]*b[ZZ][XX];
    dest[ZZ][YY] = a[XX][ZZ]*b[XX][YY]+a[YY][ZZ]*b[YY][YY]+a[ZZ][ZZ]*b[ZZ][YY];
    dest[ZZ][ZZ] = a[XX][ZZ]*b[XX][ZZ]+a[YY][ZZ]*b[YY][ZZ]+a[ZZ][ZZ]*b[ZZ][ZZ];
}

static gmx_inline void mtmul(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
{
    /* Computes dest=mmul(a,transpose(b),dest) - used in do_pr_pcoupl */
    dest[XX][XX] = a[XX][XX]*b[XX][XX]+a[XX][YY]*b[XX][YY]+a[XX][ZZ]*b[XX][ZZ];
    dest[XX][YY] = a[XX][XX]*b[YY][XX]+a[XX][YY]*b[YY][YY]+a[XX][ZZ]*b[YY][ZZ];
    dest[XX][ZZ] = a[XX][XX]*b[ZZ][XX]+a[XX][YY]*b[ZZ][YY]+a[XX][ZZ]*b[ZZ][ZZ];
    dest[YY][XX] = a[YY][XX]*b[XX][XX]+a[YY][YY]*b[XX][YY]+a[YY][ZZ]*b[XX][ZZ];
    dest[YY][YY] = a[YY][XX]*b[YY][XX]+a[YY][YY]*b[YY][YY]+a[YY][ZZ]*b[YY][ZZ];
    dest[YY][ZZ] = a[YY][XX]*b[ZZ][XX]+a[YY][YY]*b[ZZ][YY]+a[YY][ZZ]*b[ZZ][ZZ];
    dest[ZZ][XX] = a[ZZ][XX]*b[XX][XX]+a[ZZ][YY]*b[XX][YY]+a[ZZ][ZZ]*b[XX][ZZ];
    dest[ZZ][YY] = a[ZZ][XX]*b[YY][XX]+a[ZZ][YY]*b[YY][YY]+a[ZZ][ZZ]*b[YY][ZZ];
    dest[ZZ][ZZ] = a[ZZ][XX]*b[ZZ][XX]+a[ZZ][YY]*b[ZZ][YY]+a[ZZ][ZZ]*b[ZZ][ZZ];
}

static gmx_inline real det(gmx_cxx_const matrix a)
{
    return ( a[XX][XX]*(a[YY][YY]*a[ZZ][ZZ]-a[ZZ][YY]*a[YY][ZZ])
             -a[YY][XX]*(a[XX][YY]*a[ZZ][ZZ]-a[ZZ][YY]*a[XX][ZZ])
             +a[ZZ][XX]*(a[XX][YY]*a[YY][ZZ]-a[YY][YY]*a[XX][ZZ]));
}


static gmx_inline void m_add(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
{
    dest[XX][XX] = a[XX][XX]+b[XX][XX];
    dest[XX][YY] = a[XX][YY]+b[XX][YY];
    dest[XX][ZZ] = a[XX][ZZ]+b[XX][ZZ];
    dest[YY][XX] = a[YY][XX]+b[YY][XX];
    dest[YY][YY] = a[YY][YY]+b[YY][YY];
    dest[YY][ZZ] = a[YY][ZZ]+b[YY][ZZ];
    dest[ZZ][XX] = a[ZZ][XX]+b[ZZ][XX];
    dest[ZZ][YY] = a[ZZ][YY]+b[ZZ][YY];
    dest[ZZ][ZZ] = a[ZZ][ZZ]+b[ZZ][ZZ];
}

static gmx_inline void m_sub(gmx_cxx_const matrix a, gmx_cxx_const matrix b, matrix dest)
{
    dest[XX][XX] = a[XX][XX]-b[XX][XX];
    dest[XX][YY] = a[XX][YY]-b[XX][YY];
    dest[XX][ZZ] = a[XX][ZZ]-b[XX][ZZ];
    dest[YY][XX] = a[YY][XX]-b[YY][XX];
    dest[YY][YY] = a[YY][YY]-b[YY][YY];
    dest[YY][ZZ] = a[YY][ZZ]-b[YY][ZZ];
    dest[ZZ][XX] = a[ZZ][XX]-b[ZZ][XX];
    dest[ZZ][YY] = a[ZZ][YY]-b[ZZ][YY];
    dest[ZZ][ZZ] = a[ZZ][ZZ]-b[ZZ][ZZ];
}

static gmx_inline void msmul(gmx_cxx_const matrix m1, real r1, matrix dest)
{
    dest[XX][XX] = r1*m1[XX][XX];
    dest[XX][YY] = r1*m1[XX][YY];
    dest[XX][ZZ] = r1*m1[XX][ZZ];
    dest[YY][XX] = r1*m1[YY][XX];
    dest[YY][YY] = r1*m1[YY][YY];
    dest[YY][ZZ] = r1*m1[YY][ZZ];
    dest[ZZ][XX] = r1*m1[ZZ][XX];
    dest[ZZ][YY] = r1*m1[ZZ][YY];
    dest[ZZ][ZZ] = r1*m1[ZZ][ZZ];
}

static gmx_inline void m_inv_ur0(gmx_cxx_const matrix src, matrix dest)
{
    double tmp = src[XX][XX]*src[YY][YY]*src[ZZ][ZZ];
    if (fabs(tmp) <= 100*GMX_REAL_MIN)
    {
        gmx_fatal(FARGS, "Can not invert matrix, determinant is zero");
    }

    dest[XX][XX] = 1/src[XX][XX];
    dest[YY][YY] = 1/src[YY][YY];
    dest[ZZ][ZZ] = 1/src[ZZ][ZZ];
    dest[ZZ][XX] = (src[YY][XX]*src[ZZ][YY]*dest[YY][YY]
                    - src[ZZ][XX])*dest[XX][XX]*dest[ZZ][ZZ];
    dest[YY][XX] = -src[YY][XX]*dest[XX][XX]*dest[YY][YY];
    dest[ZZ][YY] = -src[ZZ][YY]*dest[YY][YY]*dest[ZZ][ZZ];
    dest[XX][YY] = 0.0;
    dest[XX][ZZ] = 0.0;
    dest[YY][ZZ] = 0.0;
}

static gmx_inline void m_inv(gmx_cxx_const matrix src, matrix dest)
{
    const real smallreal = (real)1.0e-24;
    const real largereal = (real)1.0e24;
    real       deter, c, fc;

    deter = det(src);
    c     = (real)1.0/deter;
    fc    = (real)fabs(c);

    if ((fc <= smallreal) || (fc >= largereal))
    {
        gmx_fatal(FARGS, "Can not invert matrix, determinant = %e", deter);
    }

    dest[XX][XX] = c*(src[YY][YY]*src[ZZ][ZZ]-src[ZZ][YY]*src[YY][ZZ]);
    dest[XX][YY] = -c*(src[XX][YY]*src[ZZ][ZZ]-src[ZZ][YY]*src[XX][ZZ]);
    dest[XX][ZZ] = c*(src[XX][YY]*src[YY][ZZ]-src[YY][YY]*src[XX][ZZ]);
    dest[YY][XX] = -c*(src[YY][XX]*src[ZZ][ZZ]-src[ZZ][XX]*src[YY][ZZ]);
    dest[YY][YY] = c*(src[XX][XX]*src[ZZ][ZZ]-src[ZZ][XX]*src[XX][ZZ]);
    dest[YY][ZZ] = -c*(src[XX][XX]*src[YY][ZZ]-src[YY][XX]*src[XX][ZZ]);
    dest[ZZ][XX] = c*(src[YY][XX]*src[ZZ][YY]-src[ZZ][XX]*src[YY][YY]);
    dest[ZZ][YY] = -c*(src[XX][XX]*src[ZZ][YY]-src[ZZ][XX]*src[XX][YY]);
    dest[ZZ][ZZ] = c*(src[XX][XX]*src[YY][YY]-src[YY][XX]*src[XX][YY]);
}

static gmx_inline void mvmul(gmx_cxx_const matrix a, const rvec src, rvec dest)
{
    dest[XX] = a[XX][XX]*src[XX]+a[XX][YY]*src[YY]+a[XX][ZZ]*src[ZZ];
    dest[YY] = a[YY][XX]*src[XX]+a[YY][YY]*src[YY]+a[YY][ZZ]*src[ZZ];
    dest[ZZ] = a[ZZ][XX]*src[XX]+a[ZZ][YY]*src[YY]+a[ZZ][ZZ]*src[ZZ];
}


static gmx_inline void mvmul_ur0(gmx_cxx_const matrix a, const rvec src, rvec dest)
{
    dest[ZZ] = a[ZZ][XX]*src[XX]+a[ZZ][YY]*src[YY]+a[ZZ][ZZ]*src[ZZ];
    dest[YY] = a[YY][XX]*src[XX]+a[YY][YY]*src[YY];
    dest[XX] = a[XX][XX]*src[XX];
}

static gmx_inline void tmvmul_ur0(gmx_cxx_const matrix a, const rvec src, rvec dest)
{
    dest[XX] = a[XX][XX]*src[XX]+a[YY][XX]*src[YY]+a[ZZ][XX]*src[ZZ];
    dest[YY] =                   a[YY][YY]*src[YY]+a[ZZ][YY]*src[ZZ];
    dest[ZZ] =                                     a[ZZ][ZZ]*src[ZZ];
}

static gmx_inline void unitv(const rvec src, rvec dest)
{
    real linv;

    linv     = gmx_invsqrt(norm2(src));
    dest[XX] = linv*src[XX];
    dest[YY] = linv*src[YY];
    dest[ZZ] = linv*src[ZZ];
}

static gmx_inline void unitv_no_table(const rvec src, rvec dest)
{
    real linv;

    linv     = 1.0/sqrt(norm2(src));
    dest[XX] = linv*src[XX];
    dest[YY] = linv*src[YY];
    dest[ZZ] = linv*src[ZZ];
}

static void calc_lll(const rvec box, rvec lll)
{
    lll[XX] = 2.0*M_PI/box[XX];
    lll[YY] = 2.0*M_PI/box[YY];
    lll[ZZ] = 2.0*M_PI/box[ZZ];
}

static gmx_inline real trace(gmx_cxx_const matrix m)
{
    return (m[XX][XX]+m[YY][YY]+m[ZZ][ZZ]);
}

static gmx_inline real _divide_err(real a, real b, const char *file, int line)
{
    if (fabs(b) <= GMX_REAL_MIN)
    {
        gmx_fatal(FARGS, "Dividing by zero, file %s, line %d", file, line);
    }
    return a/b;
}

static gmx_inline int _mod(int a, int b, char *file, int line)
{
    if (b == 0)
    {
        gmx_fatal(FARGS, "Modulo zero, file %s, line %d", file, line);
    }
    return a % b;
}

/* Operations on multidimensional rvecs, used e.g. in edsam.c */
static gmx_inline void m_rveccopy(int dim, gmx_cxx_const rvec *a, rvec *b)
{
    /* b = a */
    int i;

    for (i = 0; i < dim; i++)
    {
        copy_rvec(a[i], b[i]);
    }
}

/*computer matrix vectors from base vectors and angles */
static gmx_inline void matrix_convert(matrix box, const rvec vec, rvec angle)
{
    svmul(DEG2RAD, angle, angle);
    box[XX][XX] = vec[XX];
    box[YY][XX] = vec[YY]*cos(angle[ZZ]);
    box[YY][YY] = vec[YY]*sin(angle[ZZ]);
    box[ZZ][XX] = vec[ZZ]*cos(angle[YY]);
    box[ZZ][YY] = vec[ZZ]
        *(cos(angle[XX])-cos(angle[YY])*cos(angle[ZZ]))/sin(angle[ZZ]);
    box[ZZ][ZZ] = sqrt(sqr(vec[ZZ])
                       -box[ZZ][XX]*box[ZZ][XX]-box[ZZ][YY]*box[ZZ][YY]);
}

#define divide_err(a, b) _divide_err((a), (b), __FILE__, __LINE__)
#define mod(a, b)    _mod((a), (b), __FILE__, __LINE__)

#ifdef __cplusplus
}
#endif

#endif