constants.h

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#ifndef THEORETICA_CONSTANTS_H
#define THEORETICA_CONSTANTS_H
 
 
#include <limits>
#include <cstdint>
 
#ifndef THEORETICA_DISABLE_X86
 
#ifndef THEORETICA_X86
#if defined(__amd64__) || defined(__amd64) || defined(__x86_64__) \
    || defined(_M_AMD64) || defined(_M_X64) || defined(i386) \
    || defined(__i386) || defined(__i386__) || defined(_M_IX86) \
    || defined(_X86_) || defined(_M_I86) || defined(__X86__)
 
#define THEORETICA_X86
#endif
#endif
#endif
 
 
#ifndef THEORETICA_DISABLE_CPP20
#ifndef THEORETICA_USE_CPP20
#if (__cplusplus >= 202002L)
#define THEORETICA_USE_CPP20
#endif
#endif
#endif
 
#ifndef THEORETICA_ALGEBRA_ELEMENT_TOL
#define THEORETICA_ALGEBRA_ELEMENT_TOL (10*MACH_EPSILON)
#endif
 
 
#ifndef THEORETICA_ALGEBRA_EIGEN_TOL
#define THEORETICA_ALGEBRA_EIGEN_TOL 1E-08
#endif
 
 
#ifndef THEORETICA_ALGEBRA_EIGEN_ITER
#define THEORETICA_ALGEBRA_EIGEN_ITER 100
#endif
 
 
#ifndef THEORETICA_CORE_TAYLOR_ORDER
#define THEORETICA_CORE_TAYLOR_ORDER 12
#endif
 
#ifndef THEORETICA_CALCULUS_INTEGRAL_STEPS
#define THEORETICA_CALCULUS_INTEGRAL_STEPS 100
#endif
 
// Default tolerance for integral approximation
#ifndef THEORETICA_CALCULUS_INTEGRAL_TOL
#define THEORETICA_CALCULUS_INTEGRAL_TOL 1E-08
#endif
    
#ifndef THEORETICA_OPTIMIZATION_TOL
#define THEORETICA_OPTIMIZATION_TOL 1E-08
#endif
 
#ifndef THEORETICA_OPTIMIZATION_BISECTION_ITER
#define THEORETICA_OPTIMIZATION_BISECTION_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_GOLDENSECTION_ITER
#define THEORETICA_OPTIMIZATION_GOLDENSECTION_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_HALLEY_ITER
#define THEORETICA_OPTIMIZATION_HALLEY_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_NEWTON_ITER
#define THEORETICA_OPTIMIZATION_NEWTON_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_STEFFENSEN_ITER
#define THEORETICA_OPTIMIZATION_STEFFENSEN_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_CHEBYSHEV_ITER
#define THEORETICA_OPTIMIZATION_CHEBYSHEV_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_OSTROWSKI_ITER
#define THEORETICA_OPTIMIZATION_OSTROWSKI_ITER 100
#endif
 
#ifndef THEORETICA_OPTIMIZATION_JARRAT_ITER
#define THEORETICA_OPTIMIZATION_JARRAT_ITER 100
#endif
 
#ifndef THEORETICA_STATISTICS_TRYANDCATCH_ITER
#define THEORETICA_STATISTICS_TRYANDCATCH_ITER 100
#endif
 
#ifndef THEORETICA_CALCULUS_DERIV_STEP
#define THEORETICA_CALCULUS_DERIV_STEP 1E-3
#endif
 
#ifndef THEORETICA_OPTIMIZATION_MINGRAD_GAMMA
#define THEORETICA_OPTIMIZATION_MINGRAD_GAMMA -0.005
#endif
 
#ifndef THEORETICA_OPTIMIZATION_MINGRAD_TOLERANCE
#define THEORETICA_OPTIMIZATION_MINGRAD_TOLERANCE 1E-3
#endif
 
#ifndef THEORETICA_OPTIMIZATION_MINGRAD_ITER
#define THEORETICA_OPTIMIZATION_MINGRAD_ITER 50000
#endif
 
 
#ifndef THEORETICA_STATISTICS_RAND_PREC
 
#ifdef THEORETICA_FLOAT_PREC
#define THEORETICA_STATISTICS_RAND_PREC (uint64_t(1) << 23)
#else
#define THEORETICA_STATISTICS_RAND_PREC (uint64_t(1) << 31)
#endif
 
#endif
 
 
#ifndef THEORETICA_STATISTICS_METROPOLIS_DEPTH
#define THEORETICA_STATISTICS_METROPOLIS_DEPTH 16
#endif
 
 
#if (__cplusplus >= 201402L)
#define TH_CONSTEXPR constexpr
#else
#define TH_CONSTEXPR
#endif
 
 
#if (__cplusplus >= 201703L)
#define TH_CONSTIF constexpr
#else
#define TH_CONSTIF
#endif
 
 
namespace theoretica {
 
 
#ifdef THEORETICA_LONG_DOUBLE_PREC
 
    using real = long double;
 
#elif defined(THEORETICA_FLOAT_PREC)
 
    using real = float;
 
#elif defined(THEORETICA_ARBITRARY_PREC)
 
// TO-DO bigfloat arbitrary precision
 
#else
 
    using real = double;
 
#endif
 
 
    // Mathematical constants and default algorithm parameters.
 
 
    constexpr real MACH_EPSILON = std::numeric_limits<real>::epsilon();
 
    constexpr real PHI = 1.6180339887498948482045868;
 
    constexpr real INVPHI = 0.6180339887498948482045868;
 
    constexpr real PI = 3.141592653589793238462643;
 
    constexpr real PI2 = 1.57079632679489655799898;
 
    constexpr real PI4 = PI / 4.0;
 
    constexpr real PIDOUBLE = PI * 2;
 
    constexpr real TAU = PI * 2;
 
    constexpr real INVPI = 1.0 / PI;
 
    constexpr real SQRTPI = 1.7724538509055159927;
 
    constexpr real E = 2.718281828459045235360287;
 
    constexpr real LOG2E = 1.44269504088896338700465094;
 
    constexpr real LOG210 = 3.32192809488736218170856773213;
 
    constexpr real LOG10E = 0.434294481903;
 
    constexpr real LN2 = 0.69314718056;
 
    constexpr real LN10 = 2.30258509299;
 
    constexpr real DEG2RAD = 0.017453292519943295474371680598;
 
    constexpr real RAD2DEG = 57.2957795130823228646477218717;
 
    constexpr real SQRT2 = 1.4142135623730950488;
 
    constexpr real INVSQR2 = 0.7071067811865475;
 
    constexpr real SQRT3 = 1.732050807568877;
 
    constexpr real ALGEBRA_ELEMENT_TOL = THEORETICA_ALGEBRA_ELEMENT_TOL;
 
    constexpr real ALGEBRA_EIGEN_TOL = THEORETICA_ALGEBRA_EIGEN_TOL;
 
    constexpr real ALGEBRA_EIGEN_ITER = THEORETICA_ALGEBRA_EIGEN_ITER;
 
    constexpr int CORE_TAYLOR_ORDER = THEORETICA_CORE_TAYLOR_ORDER;
 
    constexpr int CALCULUS_INTEGRAL_STEPS = THEORETICA_CALCULUS_INTEGRAL_STEPS;
 
    // Default tolerance for integral approximation
    constexpr real CALCULUS_INTEGRAL_TOL = THEORETICA_CALCULUS_INTEGRAL_TOL;
 
    constexpr real OPTIMIZATION_TOL = THEORETICA_OPTIMIZATION_TOL;
 
    constexpr unsigned int OPTIMIZATION_BISECTION_ITER = THEORETICA_OPTIMIZATION_BISECTION_ITER;
 
    constexpr unsigned int OPTIMIZATION_GOLDENSECTION_ITER = THEORETICA_OPTIMIZATION_GOLDENSECTION_ITER;
 
    constexpr unsigned int OPTIMIZATION_HALLEY_ITER = THEORETICA_OPTIMIZATION_HALLEY_ITER;
 
    constexpr unsigned int OPTIMIZATION_NEWTON_ITER = THEORETICA_OPTIMIZATION_NEWTON_ITER;
 
    constexpr unsigned int OPTIMIZATION_STEFFENSEN_ITER = THEORETICA_OPTIMIZATION_STEFFENSEN_ITER;
 
    constexpr unsigned int OPTIMIZATION_CHEBYSHEV_ITER = THEORETICA_OPTIMIZATION_CHEBYSHEV_ITER;
 
    constexpr unsigned int OPTIMIZATION_OSTROWSKI_ITER = THEORETICA_OPTIMIZATION_OSTROWSKI_ITER;
 
    constexpr unsigned int OPTIMIZATION_JARRAT_ITER = THEORETICA_OPTIMIZATION_JARRAT_ITER;
 
    constexpr unsigned int STATISTICS_TRYANDCATCH_ITER = THEORETICA_STATISTICS_TRYANDCATCH_ITER;
 
    constexpr real CALCULUS_DERIV_STEP = THEORETICA_CALCULUS_DERIV_STEP;
 
    constexpr real OPTIMIZATION_MINGRAD_GAMMA = THEORETICA_OPTIMIZATION_MINGRAD_GAMMA;
 
    constexpr real OPTIMIZATION_MINGRAD_TOLERANCE = THEORETICA_OPTIMIZATION_MINGRAD_TOLERANCE;
 
    constexpr unsigned int OPTIMIZATION_MINGRAD_ITER = THEORETICA_OPTIMIZATION_MINGRAD_ITER;
 
    constexpr uint64_t STATISTICS_RAND_PREC = THEORETICA_STATISTICS_RAND_PREC;
 
    constexpr unsigned int STATISTICS_METROPOLIS_DEPTH = THEORETICA_STATISTICS_METROPOLIS_DEPTH;
 
}
 
// Define THEORETICA_NO_NAMESPACE_ALIAS to prevent
// defining the alias "th" for "theoretica"
#ifndef THEORETICA_NO_NAMESPACE_ALIAS
namespace th = theoretica;
#endif
 
#endif