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