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Check out http://www.gromacs.org. 37 */ 38 #ifndef GMX_MATH_UTILITIES_H 39 #define GMX_MATH_UTILITIES_H 40 41 #include <limits.h> 42 43 #include <cmath> 44 45 #include "gromacs/utility/basedefinitions.h" 46 #include "gromacs/utility/real.h" 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 #ifndef M_FLOAT_1_SQRTPI /* used in GPU kernels */ 69 /* 1.0 / sqrt(M_PI) */ 70 # define M_FLOAT_1_SQRTPI 0.564189583547756f 71 #endif 72 73 #ifndef M_1_SQRTPI 74 /* 1.0 / sqrt(M_PI) */ 75 # define M_1_SQRTPI 0.564189583547756 76 #endif 77 78 #ifndef M_2_SQRTPI 79 /* 2.0 / sqrt(M_PI) */ 80 # define M_2_SQRTPI 1.128379167095513 81 #endif 82 83 /*! \brief Enum to select safe or highly unsafe (faster) math functions. 84 * 85 * Normally all the Gromacs math functions should apply reasonable care with 86 * input arguments. While we do not necessarily adhere strictly to IEEE 87 * (in particular not for arguments that might result in NaN, inf, etc.), the 88 * functions should return reasonable values or e.g. clamp results to zero. 89 * 90 * However, in a few cases where we are extremely performance-sensitive it 91 * makes sense to forego these checks too in cases where we know the exact 92 * properties if the input data, and we really need to save every cycle we can. 93 * 94 * This class is typically used as a template parameter to such calls to enable 95 * the caller to select the level of aggressiveness. We should always use the 96 * safe alternative as the default value, and document carefully what might 97 * happen with the unsafe alternative. 98 */ 99 enum class MathOptimization 100 { 101 Safe, //!< Don't do unsafe optimizations. This should always be default. 102 Unsafe //!< Allow optimizations that can be VERY dangerous for general code. 103 }; 104 105 /*! \brief Check if two numbers are within a tolerance 106 * 107 * This routine checks if the relative difference between two numbers is 108 * approximately within the given tolerance, defined as 109 * fabs(f1-f2)<=tolerance*fabs(f1+f2). 110 * 111 * To check if two floating-point numbers are almost identical, use this routine 112 * with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be 113 * done in double regardless of Gromacs precision. 114 * 115 * To check if two algorithms produce similar results you will normally need 116 * to relax the tolerance significantly since many operations (e.g. summation) 117 * accumulate floating point errors. 118 * 119 * \param f1 First number to compare 120 * \param f2 Second number to compare 121 * \param tol Tolerance to use 122 * 123 * \return 1 if the relative difference is within tolerance, 0 if not. 124 */ 125 bool gmx_within_tol(double f1, double f2, double tol); 126 127 /*! 128 * \brief Check if a number is smaller than some preset safe minimum 129 * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS. 130 * 131 * If a number is smaller than this value we risk numerical overflow 132 * if any number larger than 1.0/GMX_REAL_EPS is divided by it. 133 * 134 * \return True if 'almost' numerically zero, false otherwise. 135 */ 136 bool gmx_numzero(double a); 137 138 /*! \brief Multiply two large ints 139 * 140 * \return False iff overflow occurred 141 */ 142 gmx_bool check_int_multiply_for_overflow(int64_t a, int64_t b, int64_t* result); 143 144 /*! \brief Enable floating-point exceptions if supported on OS 145 * 146 * Enables division-by-zero, invalid value, and overflow. 147 * 148 * \returns 0 if successful in enabling exceptions, anything else in case of failure/unsupported OS. 149 */ 150 int gmx_feenableexcept(); 151 152 /*! \brief Disable floating-point exceptions if supported on OS 153 * 154 * Disables division-by-zero, invalid value, and overflow. 155 * 156 * \returns 0 if successful in disabling exceptions, anything else in case of failure/unsupported OS. 157 */ 158 int gmx_fedisableexcept(); 159 160 #endif 161