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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 /* Suzuki-Yoshida Constants, for n=3 and n=5, for symplectic integration */
70 /* for n=3, w0 = w2 = 1/(2-2^-(1/3)), w1 = 1-2*w0 */
71 /* for n=5, w0 = w1 = w3 = w4 = 1/(4-4^-(1/3)), w1 = 1-4*w0 */
73 #define MAX_SUZUKI_YOSHIDA_NUM 5
74 #define SUZUKI_YOSHIDA_NUM 5
76 static const double sy_const_1
[] = { 1. };
77 static const double sy_const_3
[] = { 0.828981543588751,-0.657963087177502,0.828981543588751 };
78 static const double sy_const_5
[] = { 0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065 };
80 static const double* sy_const
[] = {
90 static const double sy_const[MAX_SUZUKI_YOSHIDA_NUM+1][MAX_SUZUKI_YOSHIDA_NUM+1] = {
94 {0.828981543588751,-0.657963087177502,0.828981543588751},
96 {0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065}
100 real
sign(real x
,real y
);
102 real
cuberoot (real a
);
103 double gmx_erfd(double x
);
104 double gmx_erfcd(double x
);
105 float gmx_erff(float x
);
106 float gmx_erfcf(float x
);
108 #define gmx_erf(x) gmx_erfd(x)
109 #define gmx_erfc(x) gmx_erfcd(x)
111 #define gmx_erf(x) gmx_erff(x)
112 #define gmx_erfc(x) gmx_erfcf(x)
115 gmx_bool
gmx_isfinite(real x
);
117 /*! \brief Check if two numbers are within a tolerance
119 * This routine checks if the relative difference between two numbers is
120 * approximately within the given tolerance, defined as
121 * fabs(f1-f2)<=tolerance*fabs(f1+f2).
123 * To check if two floating-point numbers are almost identical, use this routine
124 * with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
125 * done in double regardless of Gromacs precision.
127 * To check if two algorithms produce similar results you will normally need
128 * to relax the tolerance significantly since many operations (e.g. summation)
129 * accumulate floating point errors.
131 * \param f1 First number to compare
132 * \param f2 Second number to compare
133 * \param tol Tolerance to use
135 * \return 1 if the relative difference is within tolerance, 0 if not.
138 gmx_within_tol(double f1
,
142 /* The or-equal is important - otherwise we return false if f1==f2==0 */
143 if( fabs(f1
-f2
) <= tol
*0.5*(fabs(f1
)+fabs(f2
)) )
156 * Check if a number is smaller than some preset safe minimum
157 * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
159 * If a number is smaller than this value we risk numerical overflow
160 * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
162 * \return 1 if 'almost' numerically zero, 0 otherwise.
165 gmx_numzero(double a
)
167 return gmx_within_tol(a
,0.0,GMX_REAL_MIN
/GMX_REAL_EPS
);
174 const real iclog2
= 1.0/log( 2.0 );
176 return log( x
) * iclog2
;
179 /*! /brief Multiply two large ints
181 * Returns true when overflow did not occur.
184 check_int_multiply_for_overflow(gmx_large_int_t a
,
186 gmx_large_int_t
*result
);
192 #endif /* _maths_h */