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37 #ifndef GMX_MATH_UTILITIES_H
38 #define GMX_MATH_UTILITIES_H
43 #include "../legacyheaders/types/simple.h"
50 #define M_PI 3.14159265358979323846
54 #define M_PI_2 1.57079632679489661923
58 #define M_2PI 6.28318530717958647692
62 #define M_SQRT2 sqrt(2.0)
66 #define M_1_PI 0.31830988618379067154
69 #ifndef M_FLOAT_1_SQRTPI /* used in CUDA kernels */
70 /* 1.0 / sqrt(M_PI) */
71 #define M_FLOAT_1_SQRTPI 0.564189583547756f
75 /* 1.0 / sqrt(M_PI) */
76 #define M_1_SQRTPI 0.564189583547756
80 /* 2.0 / sqrt(M_PI) */
81 #define M_2_SQRTPI 1.128379167095513
85 real sign(real x, real y);
87 real cuberoot (real a);
88 double gmx_erfd(double x);
89 double gmx_erfcd(double x);
90 float gmx_erff(float x);
91 float gmx_erfcf(float x);
93 #define gmx_erf(x) gmx_erfd(x)
94 #define gmx_erfc(x) gmx_erfcd(x)
96 #define gmx_erf(x) gmx_erff(x)
97 #define gmx_erfc(x) gmx_erfcf(x)
100 gmx_bool gmx_isfinite(real x);
101 gmx_bool gmx_isnan(real x);
103 /*! \brief Check if two numbers are within a tolerance
105 * This routine checks if the relative difference between two numbers is
106 * approximately within the given tolerance, defined as
107 * fabs(f1-f2)<=tolerance*fabs(f1+f2).
109 * To check if two floating-point numbers are almost identical, use this routine
110 * with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
111 * done in double regardless of Gromacs precision.
113 * To check if two algorithms produce similar results you will normally need
114 * to relax the tolerance significantly since many operations (e.g. summation)
115 * accumulate floating point errors.
117 * \param f1 First number to compare
118 * \param f2 Second number to compare
119 * \param tol Tolerance to use
121 * \return 1 if the relative difference is within tolerance, 0 if not.
124 gmx_within_tol(double f1,
129 * \brief Check if a number is smaller than some preset safe minimum
130 * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
132 * If a number is smaller than this value we risk numerical overflow
133 * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
135 * \return 1 if 'almost' numerically zero, 0 otherwise.
138 gmx_numzero(double a);
140 /*! \brief Compute floor of logarithm to base 2
145 gmx_log2i(unsigned int x);
147 /*! /brief Multiply two large ints
149 * \return False iff overflow occured
152 check_int_multiply_for_overflow(gmx_int64_t a,
154 gmx_int64_t *result);
156 /*! \brief Find greatest common divisor of two numbers
158 * \return GCD of the two inputs
161 gmx_greatest_common_divisor(int p, int q);