zeta.h

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#ifndef OAKFIELD_MATH_ZETA_H
#define OAKFIELD_MATH_ZETA_H
 
#include <stddef.h>
 
#include "oakfield/field.h"
 
#ifdef __cplusplus
extern "C" {
#endif
 
typedef enum SimZetaStatus {
    SIM_ZETA_STATUS_OK = 0,           
    SIM_ZETA_STATUS_SINGULAR,         
    SIM_ZETA_STATUS_INVALID_ARGUMENT, 
    SIM_ZETA_STATUS_NO_CONVERGENCE,   
    SIM_ZETA_STATUS_NUMERIC_FAILURE   
} SimZetaStatus;
 
typedef enum SimBallRigor {
    SIM_BALL_RIGOR_HEURISTIC = 0, 
    SIM_BALL_RIGOR_VALIDATED,     
    SIM_BALL_RIGOR_FORMAL         
} SimBallRigor;
 
typedef enum SimZetaBranch {
    SIM_ZETA_BRANCH_DIRECT_EULER_MACLAURIN = 0, 
    SIM_ZETA_BRANCH_ETA_ACCELERATED,            
    SIM_ZETA_BRANCH_APPROXIMATE_FUNCTIONAL_EQUATION, 
    SIM_ZETA_BRANCH_RIEMANN_SIEGEL,                  
    SIM_ZETA_BRANCH_NEAR_ONE_LAURENT,                
    SIM_ZETA_BRANCH_LOCAL_EXPANSION,                 
    SIM_ZETA_BRANCH_REFLECTION                       
} SimZetaBranch;
 
#define SIM_ZETA_FLAG_USED_REFLECTION 0x1u
#define SIM_ZETA_FLAG_NEAR_POLE 0x2u
#define SIM_ZETA_FLAG_TRIVIAL_ZERO 0x4u
#define SIM_ZETA_FLAG_USED_ETA 0x8u
#define SIM_ZETA_FLAG_USED_NEAR_ONE_LAURENT 0x10u
#define SIM_ZETA_FLAG_USED_AFE 0x20u
#define SIM_ZETA_FLAG_USED_ADAPTIVE_REFINEMENT 0x40u
#define SIM_ZETA_FLAG_USED_RIEMANN_SIEGEL 0x80u
#define SIM_ZETA_FLAG_USED_LOCAL_EXPANSION 0x100u
#define SIM_ZETA_FLAG_ZERO_PROXIMITY 0x200u
 
typedef struct SimComplexBall {
    SimComplexDouble center;             
    double radius;                       
    SimZetaStatus status;                
    unsigned int flags;                  
    size_t refinement_rounds;            
    unsigned int working_precision_bits; 
    SimBallRigor rigor;                  
    size_t validation_passes;            
} SimComplexBall;
 
typedef struct SimZetaContext {
    double abs_tol;                  
    double rel_tol;                  
    size_t initial_terms;            
    size_t max_terms;                
    size_t euler_maclaurin_terms;    
    size_t eta_initial_terms;        
    size_t eta_max_terms;            
    double eta_sigma_limit;          
    double eta_imag_limit;           
    size_t afe_initial_cutoff;       
    size_t afe_max_cutoff;           
    double afe_sigma_limit;          
    double afe_imag_min;             
    double riemann_siegel_imag_min;  
    double critical_line_tolerance;  
    size_t riemann_siegel_max_terms; 
    double pole_radius;              
    double near_one_radius;          
    double local_expansion_radius;   
    size_t ball_validation_rounds;   
    double ball_validation_scale;    
    size_t adaptive_max_rounds;      
    double adaptive_tightening_factor; 
} SimZetaContext;
 
typedef struct SimZetaResult {
    SimComplexDouble value;              
    double abs_error;                    
    double rel_error;                    
    size_t terms_used;                   
    size_t correction_terms;             
    size_t refinement_rounds;            
    unsigned int working_precision_bits; 
    SimZetaBranch branch;                
    SimZetaStatus status;                
    unsigned int flags;                  
} SimZetaResult;
 
typedef struct SimZetaDerivativeResult {
    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 branch;                
    SimZetaStatus status;                
    unsigned int flags;                  
} SimZetaDerivativeResult;
 
const char *sim_zeta_status_string(SimZetaStatus status);
 
const char *sim_zeta_branch_string(SimZetaBranch branch);
 
SimZetaContext sim_zeta_context_default(void);
 
SimZetaContext sim_zeta_context_interactive(void);
 
SimZetaResult sim_zeta_eval_direct_euler_maclaurin(SimComplexDouble s,
                                                   const SimZetaContext *context);
 
SimZetaResult sim_zeta_eval_eta_accelerated(SimComplexDouble s, const SimZetaContext *context);
 
SimZetaResult sim_zeta_eval_approximate_fe(SimComplexDouble s, const SimZetaContext *context);
 
SimZetaResult sim_zeta_eval_riemann_siegel(double t, const SimZetaContext *context);
 
SimZetaDerivativeResult sim_zeta_eval_with_derivative(SimComplexDouble s,
                                                      const SimZetaContext *context);
 
SimComplexBall sim_zeta_eval_ball(SimComplexDouble s, const SimZetaContext *context);
 
SimZetaResult sim_zeta_eval(SimComplexDouble s, const SimZetaContext *context);
 
#ifdef __cplusplus
}
#endif
 
#endif /* OAKFIELD_MATH_ZETA_H */