include/maths.h

   1 /*
   2  * This file is part of the GROMACS molecular simulation package.
   3  *
   4  * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
   5  * Copyright (c) 2001-2004, The GROMACS development team,
   6  * check out http://www.gromacs.org for more information.
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   8  * David van der Spoel, Berk Hess, Erik Lindahl, and including many
   9  * others, as listed in the AUTHORS file in the top-level source
  10  * directory and at http://www.gromacs.org.
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  38
  39 #ifndef _maths_h
  40 #define _maths_h
  41
  42 #include <math.h>
  43 #include "visibility.h"
  44 #include "types/simple.h"
  45 #include "typedefs.h"
  46
  47 #ifdef __cplusplus
  48 extern "C" {
  49 #endif
  50
  51 #ifndef M_PI
  52 #define M_PI            3.14159265358979323846
  53 #endif
  54
  55 #ifndef M_PI_2
  56 #define M_PI_2          1.57079632679489661923
  57 #endif
  58
  59 #ifndef M_2PI
  60 #define M_2PI           6.28318530717958647692
  61 #endif
  62
  63 #ifndef M_SQRT2
  64 #define M_SQRT2 sqrt(2.0)
  65 #endif
  66
  67 #ifndef M_1_PI
  68 #define M_1_PI      0.31830988618379067154
  69 #endif
  70
  71 #ifndef M_FLOAT_1_SQRTPI /* used in CUDA kernels */
  72 /* 1.0 / sqrt(M_PI) */
  73 #define M_FLOAT_1_SQRTPI 0.564189583547756f
  74 #endif
  75
  76 #ifndef M_1_SQRTPI
  77 /* 1.0 / sqrt(M_PI) */
  78 #define M_1_SQRTPI 0.564189583547756
  79 #endif
  80
  81 #ifndef M_2_SQRTPI
  82 /* 2.0 / sqrt(M_PI) */
  83 #define M_2_SQRTPI  1.128379167095513
  84 #endif
  85
  86 /* Suzuki-Yoshida Constants, for n=3 and n=5, for symplectic integration  */
  87 /* for n=1, w0 = 1 */
  88 /* for n=3, w0 = w2 = 1/(2-2^-(1/3)), w1 = 1-2*w0 */
  89 /* for n=5, w0 = w1 = w3 = w4 = 1/(4-4^-(1/3)), w1 = 1-4*w0 */
  90
  91 #define MAX_SUZUKI_YOSHIDA_NUM 5
  92 #define SUZUKI_YOSHIDA_NUM  5
  93
  94 static const double sy_const_1[] = { 1. };
  95 static const double sy_const_3[] = { 0.828981543588751,-0.657963087177502,0.828981543588751 };
  96 static const double sy_const_5[] = { 0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065 };
  97
  98 static const double* sy_const[] = {
  99     NULL,
 100     sy_const_1,
 101     NULL,
 102     sy_const_3,
 103     NULL,
 104     sy_const_5
 105 };
 106
 107 /*
 108 static const double sy_const[MAX_SUZUKI_YOSHIDA_NUM+1][MAX_SUZUKI_YOSHIDA_NUM+1] = {
 109     {},
 110     {1},
 111     {},
 112     {0.828981543588751,-0.657963087177502,0.828981543588751},
 113     {},
 114     {0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065}
 115 };*/
 116
 117 GMX_LIBGMX_EXPORT
 118 int             gmx_nint(real a);
 119 real    sign(real x,real y);
 120
 121 real    cuberoot (real a);
 122 GMX_LIBGMX_EXPORT
 123 double  gmx_erfd(double x);
 124 GMX_LIBGMX_EXPORT
 125 double  gmx_erfcd(double x);
 126 GMX_LIBGMX_EXPORT
 127 float   gmx_erff(float x);
 128 GMX_LIBGMX_EXPORT
 129 float   gmx_erfcf(float x);
 130 #ifdef GMX_DOUBLE
 131 #define gmx_erf(x)   gmx_erfd(x)
 132 #define gmx_erfc(x)  gmx_erfcd(x)
 133 #else
 134 #define gmx_erf(x)   gmx_erff(x)
 135 #define gmx_erfc(x)  gmx_erfcf(x)
 136 #endif
 137
 138 GMX_LIBGMX_EXPORT
 139 gmx_bool gmx_isfinite(real x);
 140
 141 /*! \brief Check if two numbers are within a tolerance
 142  *
 143  *  This routine checks if the relative difference between two numbers is
 144  *  approximately within the given tolerance, defined as
 145  *  fabs(f1-f2)<=tolerance*fabs(f1+f2).
 146  *
 147  *  To check if two floating-point numbers are almost identical, use this routine
 148  *  with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
 149  *  done in double regardless of Gromacs precision.
 150  *
 151  *  To check if two algorithms produce similar results you will normally need
 152  *  to relax the tolerance significantly since many operations (e.g. summation)
 153  *  accumulate floating point errors.
 154  *
 155  *  \param f1  First number to compare
 156  *  \param f2  Second number to compare
 157  *  \param tol Tolerance to use
 158  *
 159  *  \return 1 if the relative difference is within tolerance, 0 if not.
 160  */
 161 static int
 162 gmx_within_tol(double   f1,
 163                double   f2,
 164                double   tol)
 165 {
 166     /* The or-equal is important - otherwise we return false if f1==f2==0 */
 167     if( fabs(f1-f2) <= tol*0.5*(fabs(f1)+fabs(f2)) )
 168     {
 169         return 1;
 170     }
 171     else
 172     {
 173         return 0;
 174     }
 175 }
 176
 177
 178
 179 /**
 180  * Check if a number is smaller than some preset safe minimum
 181  * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
 182  *
 183  * If a number is smaller than this value we risk numerical overflow
 184  * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
 185  *
 186  * \return 1  if 'almost' numerically zero, 0 otherwise.
 187  */
 188 static int
 189 gmx_numzero(double a)
 190 {
 191   return gmx_within_tol(a,0.0,GMX_REAL_MIN/GMX_REAL_EPS);
 192 }
 193
 194
 195 static real
 196 gmx_log2(real x)
 197 {
 198   const real iclog2 = 1.0/log( 2.0 );
 199
 200     return log( x ) * iclog2;
 201 }
 202
 203 /*! /brief Multiply two large ints
 204  *
 205  *  Returns true when overflow did not occur.
 206  */
 207 GMX_LIBGMX_EXPORT
 208 gmx_bool
 209 check_int_multiply_for_overflow(gmx_large_int_t a,
 210                                 gmx_large_int_t b,
 211                                 gmx_large_int_t *result);
 212
 213 #ifdef __cplusplus
 214 }
 215 #endif
 216
 217 #endif  /* _maths_h */