include/maths.h

   1 /* -*- mode: c; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4; c-file-style: "stroustrup"; -*-
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  36
  37 #ifndef _maths_h
  38 #define _maths_h
  39
  40 #include <math.h>
  41 #include "types/simple.h"
  42 #include "typedefs.h"
  43
  44 #ifdef __cplusplus
  45 extern "C" {
  46 #endif
  47
  48 #ifndef M_PI
  49 #define M_PI            3.14159265358979323846
  50 #endif
  51
  52 #ifndef M_PI_2
  53 #define M_PI_2          1.57079632679489661923
  54 #endif
  55
  56 #ifndef M_2PI
  57 #define M_2PI           6.28318530717958647692
  58 #endif
  59
  60 #ifndef M_SQRT2
  61 #define M_SQRT2 sqrt(2.0)
  62 #endif
  63
  64 /* Suzuki-Yoshida Constants, for n=3 and n=5, for symplectic integration  */
  65 /* for n=1, w0 = 1 */
  66 /* for n=3, w0 = w2 = 1/(2-2^-(1/3)), w1 = 1-2*w0 */
  67 /* for n=5, w0 = w1 = w3 = w4 = 1/(4-4^-(1/3)), w1 = 1-4*w0 */
  68
  69 #define MAX_SUZUKI_YOSHIDA_NUM 5
  70 #define SUZUKI_YOSHIDA_NUM  5
  71
  72 static const double sy_const_1[] = { 1. };
  73 static const double sy_const_3[] = { 0.828981543588751,-0.657963087177502,0.828981543588751 };
  74 static const double sy_const_5[] = { 0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065 };
  75
  76 static const double* sy_const[] = {
  77     NULL,
  78     sy_const_1,
  79     NULL,
  80     sy_const_3,
  81     NULL,
  82     sy_const_5
  83 };
  84
  85 /*
  86 static const double sy_const[MAX_SUZUKI_YOSHIDA_NUM+1][MAX_SUZUKI_YOSHIDA_NUM+1] = {
  87     {},
  88     {1},
  89     {},
  90     {0.828981543588751,-0.657963087177502,0.828981543588751},
  91     {},
  92     {0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065}
  93 };*/
  94
  95 int             gmx_nint(real a);
  96 real    sign(real x,real y);
  97
  98 int             gmx_nint(real a);
  99 real    sign(real x,real y);
 100 real    cuberoot (real a);
 101 real    gmx_erf(real x);
 102 real    gmx_erfc(real x);
 103
 104 /*! \brief Check if two numbers are within a tolerance
 105  *
 106  *  This routine checks if the relative difference between two numbers is
 107  *  approximately within the given tolerance, defined as
 108  *  fabs(f1-f2)<=tolerance*fabs(f1+f2).
 109  *
 110  *  To check if two floating-point numbers are almost identical, use this routine
 111  *  with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
 112  *  done in double regardless of Gromacs precision.
 113  *
 114  *  To check if two algorithms produce similar results you will normally need
 115  *  to relax the tolerance significantly since many operations (e.g. summation)
 116  *  accumulate floating point errors.
 117  *
 118  *  \param f1  First number to compare
 119  *  \param f2  Second number to compare
 120  *  \param tol Tolerance to use
 121  *
 122  *  \return 1 if the relative difference is within tolerance, 0 if not.
 123  */
 124 static int
 125 gmx_within_tol(double   f1,
 126                double   f2,
 127                double   tol)
 128 {
 129     /* The or-equal is important - otherwise we return false if f1==f2==0 */
 130     if( fabs(f1-f2) <= tol*0.5*(fabs(f1)+fabs(f2)) )
 131     {
 132         return 1;
 133     }
 134     else
 135     {
 136         return 0;
 137     }
 138 }
 139
 140
 141
 142 /**
 143  * Check if a number is smaller than some preset safe minimum
 144  * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
 145  *
 146  * If a number is smaller than this value we risk numerical overflow
 147  * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
 148  *
 149  * \return 1  if 'almost' numerically zero, 0 otherwise.
 150  */
 151 static int
 152 gmx_numzero(double a)
 153 {
 154   return gmx_within_tol(a,0.0,GMX_REAL_MIN/GMX_REAL_EPS);
 155 }
 156
 157
 158 static real
 159 gmx_log2(real x)
 160 {
 161   const real iclog2 = 1.0/log( 2.0 );
 162
 163     return log( x ) * iclog2;
 164 }
 165
 166
 167 #ifdef __cplusplus
 168 }
 169 #endif
 170
 171 #endif  /* _maths_h */