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37 #ifndef GMX_MATH_UTILITIES_H
38 #define GMX_MATH_UTILITIES_H
43 #include "gromacs/utility/basedefinitions.h"
44 #include "gromacs/utility/real.h"
51 #define M_PI 3.14159265358979323846
55 #define M_PI_2 1.57079632679489661923
59 #define M_2PI 6.28318530717958647692
63 #define M_SQRT2 sqrt(2.0)
67 #define M_1_PI 0.31830988618379067154
70 #ifndef M_FLOAT_1_SQRTPI /* used in CUDA kernels */
71 /* 1.0 / sqrt(M_PI) */
72 #define M_FLOAT_1_SQRTPI 0.564189583547756f
76 /* 1.0 / sqrt(M_PI) */
77 #define M_1_SQRTPI 0.564189583547756
81 /* 2.0 / sqrt(M_PI) */
82 #define M_2_SQRTPI 1.128379167095513
86 real sign(real x, real y);
88 real cuberoot (real a);
89 double gmx_erfd(double x);
90 double gmx_erfcd(double x);
91 float gmx_erff(float x);
92 float gmx_erfcf(float x);
94 #define gmx_erf(x) gmx_erfd(x)
95 #define gmx_erfc(x) gmx_erfcd(x)
97 #define gmx_erf(x) gmx_erff(x)
98 #define gmx_erfc(x) gmx_erfcf(x)
101 gmx_bool gmx_isfinite(real x);
102 gmx_bool gmx_isnan(real x);
104 /*! \brief Check if two numbers are within a tolerance
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).
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.
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.
118 * \param f1 First number to compare
119 * \param f2 Second number to compare
120 * \param tol Tolerance to use
122 * \return 1 if the relative difference is within tolerance, 0 if not.
125 gmx_within_tol(double f1,
130 * \brief Check if a number is smaller than some preset safe minimum
131 * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
133 * If a number is smaller than this value we risk numerical overflow
134 * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
136 * \return 1 if 'almost' numerically zero, 0 otherwise.
139 gmx_numzero(double a);
141 /*! \brief Compute floor of logarithm to base 2
146 gmx_log2i(unsigned int x);
148 /*! \brief Multiply two large ints
150 * \return False iff overflow occured
153 check_int_multiply_for_overflow(gmx_int64_t a,
155 gmx_int64_t *result);
157 /*! \brief Find greatest common divisor of two numbers
159 * \return GCD of the two inputs
162 gmx_greatest_common_divisor(int p, int q);