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41 #include "types/simple.h"
49 #define M_PI 3.14159265358979323846
53 #define M_PI_2 1.57079632679489661923
57 #define M_2PI 6.28318530717958647692
61 #define M_SQRT2 sqrt(2.0)
65 #define M_1_PI 0.31830988618379067154
68 #ifndef M_FLOAT_1_SQRTPI /* used in CUDA kernels */
69 /* 1.0 / sqrt(M_PI) */
70 #define M_FLOAT_1_SQRTPI 0.564189583547756f
74 /* 1.0 / sqrt(M_PI) */
75 #define M_1_SQRTPI 0.564189583547756
79 /* 2.0 / sqrt(M_PI) */
80 #define M_2_SQRTPI 1.128379167095513
84 real sign(real x, real y);
86 real cuberoot (real a);
87 double gmx_erfd(double x);
88 double gmx_erfcd(double x);
89 float gmx_erff(float x);
90 float gmx_erfcf(float x);
92 #define gmx_erf(x) gmx_erfd(x)
93 #define gmx_erfc(x) gmx_erfcd(x)
95 #define gmx_erf(x) gmx_erff(x)
96 #define gmx_erfc(x) gmx_erfcf(x)
99 gmx_bool gmx_isfinite(real x);
101 /*! \brief Check if two numbers are within a tolerance
103 * This routine checks if the relative difference between two numbers is
104 * approximately within the given tolerance, defined as
105 * fabs(f1-f2)<=tolerance*fabs(f1+f2).
107 * To check if two floating-point numbers are almost identical, use this routine
108 * with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
109 * done in double regardless of Gromacs precision.
111 * To check if two algorithms produce similar results you will normally need
112 * to relax the tolerance significantly since many operations (e.g. summation)
113 * accumulate floating point errors.
115 * \param f1 First number to compare
116 * \param f2 Second number to compare
117 * \param tol Tolerance to use
119 * \return 1 if the relative difference is within tolerance, 0 if not.
122 gmx_within_tol(double f1,
126 /* The or-equal is important - otherwise we return false if f1==f2==0 */
127 if (fabs(f1-f2) <= tol*0.5*(fabs(f1)+fabs(f2)) )
140 * Check if a number is smaller than some preset safe minimum
141 * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
143 * If a number is smaller than this value we risk numerical overflow
144 * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
146 * \return 1 if 'almost' numerically zero, 0 otherwise.
149 gmx_numzero(double a)
151 return gmx_within_tol(a, 0.0, GMX_REAL_MIN/GMX_REAL_EPS);
158 const real iclog2 = 1.0/log( 2.0 );
160 return log( x ) * iclog2;
163 /*! /brief Multiply two large ints
165 * Returns true when overflow did not occur.
168 check_int_multiply_for_overflow(gmx_large_int_t a,
170 gmx_large_int_t *result);
176 #endif /* _maths_h */