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 #ifndef M_1_PI
  65 #define M_1_PI      0.31830988618379067154
  66 #endif
  67
  68 /* Suzuki-Yoshida Constants, for n=3 and n=5, for symplectic integration  */
  69 /* for n=1, w0 = 1 */
  70 /* for n=3, w0 = w2 = 1/(2-2^-(1/3)), w1 = 1-2*w0 */
  71 /* for n=5, w0 = w1 = w3 = w4 = 1/(4-4^-(1/3)), w1 = 1-4*w0 */
  72
  73 #define MAX_SUZUKI_YOSHIDA_NUM 5
  74 #define SUZUKI_YOSHIDA_NUM  5
  75
  76 static const double sy_const_1[] = { 1. };
  77 static const double sy_const_3[] = { 0.828981543588751,-0.657963087177502,0.828981543588751 };
  78 static const double sy_const_5[] = { 0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065 };
  79
  80 static const double* sy_const[] = {
  81     NULL,
  82     sy_const_1,
  83     NULL,
  84     sy_const_3,
  85     NULL,
  86     sy_const_5
  87 };
  88
  89 /*
  90 static const double sy_const[MAX_SUZUKI_YOSHIDA_NUM+1][MAX_SUZUKI_YOSHIDA_NUM+1] = {
  91     {},
  92     {1},
  93     {},
  94     {0.828981543588751,-0.657963087177502,0.828981543588751},
  95     {},
  96     {0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065}
  97 };*/
  98
  99 int             gmx_nint(real a);
 100 real    sign(real x,real y);
 101
 102 int             gmx_nint(real a);
 103 real    sign(real x,real y);
 104 real    cuberoot (real a);
 105 double  gmx_erfd(double x);
 106 double  gmx_erfcd(double x);
 107 float   gmx_erff(float x);
 108 float   gmx_erfcf(float x);
 109 #ifdef GMX_DOUBLE
 110 #define gmx_erf(x)   gmx_erfd(x)
 111 #define gmx_erfc(x)  gmx_erfcd(x)
 112 #else
 113 #define gmx_erf(x)   gmx_erff(x)
 114 #define gmx_erfc(x)  gmx_erfcf(x)
 115 #endif
 116
 117 gmx_bool gmx_isfinite(real x);
 118
 119 /*! \brief Check if two numbers are within a tolerance
 120  *
 121  *  This routine checks if the relative difference between two numbers is
 122  *  approximately within the given tolerance, defined as
 123  *  fabs(f1-f2)<=tolerance*fabs(f1+f2).
 124  *
 125  *  To check if two floating-point numbers are almost identical, use this routine
 126  *  with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
 127  *  done in double regardless of Gromacs precision.
 128  *
 129  *  To check if two algorithms produce similar results you will normally need
 130  *  to relax the tolerance significantly since many operations (e.g. summation)
 131  *  accumulate floating point errors.
 132  *
 133  *  \param f1  First number to compare
 134  *  \param f2  Second number to compare
 135  *  \param tol Tolerance to use
 136  *
 137  *  \return 1 if the relative difference is within tolerance, 0 if not.
 138  */
 139 static int
 140 gmx_within_tol(double   f1,
 141                double   f2,
 142                double   tol)
 143 {
 144     /* The or-equal is important - otherwise we return false if f1==f2==0 */
 145     if( fabs(f1-f2) <= tol*0.5*(fabs(f1)+fabs(f2)) )
 146     {
 147         return 1;
 148     }
 149     else
 150     {
 151         return 0;
 152     }
 153 }
 154
 155
 156
 157 /**
 158  * Check if a number is smaller than some preset safe minimum
 159  * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
 160  *
 161  * If a number is smaller than this value we risk numerical overflow
 162  * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
 163  *
 164  * \return 1  if 'almost' numerically zero, 0 otherwise.
 165  */
 166 static int
 167 gmx_numzero(double a)
 168 {
 169   return gmx_within_tol(a,0.0,GMX_REAL_MIN/GMX_REAL_EPS);
 170 }
 171
 172
 173 static real
 174 gmx_log2(real x)
 175 {
 176   const real iclog2 = 1.0/log( 2.0 );
 177
 178     return log( x ) * iclog2;
 179 }
 180
 181 /*! /brief Multiply two large ints
 182  *
 183  *  Returns true when overflow did not occur.
 184  */
 185 gmx_bool
 186 check_int_multiply_for_overflow(gmx_large_int_t a,
 187                                 gmx_large_int_t b,
 188                                 gmx_large_int_t *result);
 189
 190 #ifdef __cplusplus
 191 }
 192 #endif
 193
 194 #endif  /* _maths_h */