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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
69 real sign(real x,real y);
72 real sign(real x,real y);
73 real cuberoot (real a);
74 double gmx_erfd(double x);
75 double gmx_erfcd(double x);
76 float gmx_erff(float x);
77 float gmx_erfcf(float x);
79 #define gmx_erf(x) gmx_erfd(x)
80 #define gmx_erfc(x) gmx_erfcd(x)
82 #define gmx_erf(x) gmx_erff(x)
83 #define gmx_erfc(x) gmx_erfcf(x)
86 gmx_bool gmx_isfinite(real x);
88 /*! \brief Check if two numbers are within a tolerance
90 * This routine checks if the relative difference between two numbers is
91 * approximately within the given tolerance, defined as
92 * fabs(f1-f2)<=tolerance*fabs(f1+f2).
94 * To check if two floating-point numbers are almost identical, use this routine
95 * with the tolerance GMX_REAL_EPS, or GMX_DOUBLE_EPS if the check should be
96 * done in double regardless of Gromacs precision.
98 * To check if two algorithms produce similar results you will normally need
99 * to relax the tolerance significantly since many operations (e.g. summation)
100 * accumulate floating point errors.
102 * \param f1 First number to compare
103 * \param f2 Second number to compare
104 * \param tol Tolerance to use
106 * \return 1 if the relative difference is within tolerance, 0 if not.
109 gmx_within_tol(double f1,
113 /* The or-equal is important - otherwise we return false if f1==f2==0 */
114 if( fabs(f1-f2) <= tol*0.5*(fabs(f1)+fabs(f2)) )
127 * Check if a number is smaller than some preset safe minimum
128 * value, currently defined as GMX_REAL_MIN/GMX_REAL_EPS.
130 * If a number is smaller than this value we risk numerical overflow
131 * if any number larger than 1.0/GMX_REAL_EPS is divided by it.
133 * \return 1 if 'almost' numerically zero, 0 otherwise.
136 gmx_numzero(double a)
138 return gmx_within_tol(a,0.0,GMX_REAL_MIN/GMX_REAL_EPS);
145 const real iclog2 = 1.0/log( 2.0 );
147 return log( x ) * iclog2;
150 /*! /brief Multiply two large ints
152 * Returns true when overflow did not occur.
155 check_int_multiply_for_overflow(gmx_large_int_t a,
157 gmx_large_int_t *result);
163 #endif /* _maths_h */