xi.h

Go to the documentation of this file.

 
#ifndef OAKFIELD_MATH_XI_H
#define OAKFIELD_MATH_XI_H
 
#include <stddef.h>
 
#include "zeta.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
#define SIM_XI_FLAG_USED_LOG_ASSEMBLY 0x1u
#define SIM_XI_FLAG_USED_REFLECTION 0x2u
#define SIM_XI_FLAG_EXACT_LIMIT 0x4u
#define SIM_XI_FLAG_USED_NEAR_ONE_EXPANSION 0x8u
#define SIM_XI_FLAG_USED_LOCAL_EXPANSION 0x10u
#define SIM_XI_FLAG_USED_ZERO_REFINEMENT 0x20u
#define SIM_XI_FLAG_ZERO_BRACKET_VALIDATED 0x40u
#define SIM_XI_FLAG_ZERO_BRACKET_FORMAL 0x80u
 
typedef struct SimXiContext {
    SimZetaContext zeta;        
    double abs_tol;             
    double rel_tol;             
    double exact_limit_radius;  
    double zero_tolerance;      
    size_t zero_max_iterations; 
} SimXiContext;
 
typedef struct SimXiResult {
    SimComplexDouble value;              
    double abs_error;                    
    double rel_error;                    
    size_t terms_used;                   
    size_t refinement_rounds;            
    unsigned int working_precision_bits; 
    SimZetaBranch zeta_branch;           
    SimZetaStatus status;                
    unsigned int flags;                  
} SimXiResult;
 
typedef struct SimXiDerivativeResult {
    SimComplexDouble value;              
    SimComplexDouble derivative;         
    double abs_error;                    
    double rel_error;                    
    double derivative_abs_error;         
    double derivative_rel_error;         
    size_t refinement_rounds;            
    unsigned int working_precision_bits; 
    SimZetaBranch zeta_branch;           
    SimZetaStatus status;                
    unsigned int flags;                  
} SimXiDerivativeResult;
 
typedef struct SimXiZeroResult {
    double t;                    
    SimComplexBall xi_ball;      
    SimBallRigor bracket_rigor;  
    double derivative;           
    double derivative_abs_error; 
    size_t iterations;           
    SimZetaBranch zeta_branch;   
    SimZetaStatus status;        
    unsigned int flags;          
} SimXiZeroResult;
 
SimXiContext sim_xi_context_default(void);
 
SimXiContext sim_xi_context_interactive(void);
 
const char *sim_xi_status_string(SimZetaStatus status);
 
SimXiResult sim_xi_eval(SimComplexDouble s, const SimXiContext *context);
 
SimXiResult sim_xi_eval_critical_line(double t, const SimXiContext *context);
 
SimXiDerivativeResult sim_xi_eval_with_derivative(SimComplexDouble s, const SimXiContext *context);
 
SimComplexBall sim_xi_eval_ball(SimComplexDouble s, const SimXiContext *context);
 
SimXiZeroResult sim_xi_find_critical_zero(double t_lo, double t_hi, const SimXiContext *context);
 
#ifdef __cplusplus
}
#endif
 
#endif /* OAKFIELD_MATH_XI_H */