#ifndef PROBOL_STDLIB_H #define PROBOL_STDLIB_H #include #include #include /*============================================================================ Configuration – adjust for target RAM / precision ============================================================================*/ #ifndef PROBOL_MAX_STATES #define PROBOL_MAX_STATES 256 /* max distinct values in a probability tensor */ #endif #ifndef PROBOL_FIXED_POINT_SHIFT #define PROBOL_FIXED_POINT_SHIFT 12 /* 12 bits fractional = 1/4096 precision */ #endif #ifndef PROBOL_CCT_WINDOW #define PROBOL_CCT_WINDOW 30 /* look‑ahead days for entropy gradient */ #endif /*============================================================================ Basic type definitions ============================================================================*/ typedef int64_t prob_fixed_t; /* fixed‑point decimal: value * 2^SHIFT */ /* Probability tensor – explicit list of (value, probability) pairs. Probabilities are also fixed‑point, sum = 1.0 exactly (scale = 2^SHIFT). */ typedef struct { prob_fixed_t values[PROBOL_MAX_STATES]; prob_fixed_t probs[PROBOL_MAX_STATES]; int count; } ProbTensor; /* Parametric distribution (Normal / Gaussian) */ typedef struct { prob_fixed_t mu; /* mean */ prob_fixed_t sigma; /* standard deviation (>0) */ } ProbNormal; /* GARCH(1,1) parameters */ typedef struct { prob_fixed_t omega; prob_fixed_t alpha; prob_fixed_t beta; prob_fixed_t init_var; } GARCH11; /* Copula types */ typedef enum { COPULA_GAUSSIAN, COPULA_T, COPULA_CLAYTON, COPULA_GUMBEL, COPULA_DCC_GARCH, COPULA_REGIME_SWITCH } CopulaType; /* Gaussian copula with correlation matrix (dense, max 32 assets) */ #define PROBOL_MAX_ASSETS 32 typedef struct { int dim; prob_fixed_t corr[PROBOL_MAX_ASSETS][PROBOL_MAX_ASSETS]; prob_fixed_t cholesky[PROBOL_MAX_ASSETS][PROBOL_MAX_ASSETS]; } CopulaGaussian; /* t‑copula with ν degrees of freedom */ typedef struct { CopulaGaussian base; int df; } CopulaT; /* Clayton / Gumbel copulas (single parameter θ) */ typedef struct { prob_fixed_t theta; } CopulaArchimedean; /* DCC‑GARCH parameters */ typedef struct { prob_fixed_t a, b; prob_fixed_t initial_rho; prob_fixed_t *var_series; /* GARCH variances per asset, size = dim */ } CopulaDCC; /* Regime‑switching copula with two regimes */ typedef struct { prob_fixed_t trans_matrix[2][2]; /* P(regime_j | regime_i) */ CopulaGaussian regime_copula[2]; } CopulaRegimeSwitch; /* Union of all copula types */ typedef struct { CopulaType type; union { CopulaGaussian gaussian; CopulaT t; CopulaArchimedean arch; CopulaDCC dcc; CopulaRegimeSwitch regime; }; } Copula; /* Time series state – used by SIMULATEP */ typedef struct { prob_fixed_t value; /* current simulated value (collapsed) */ prob_fixed_t variance; /* GARCH variance (if applicable) */ int regime; /* current regime (0 or 1) */ } TimeSeriesState; /* CCT collapse schedule – array of time steps where MEAS should be called */ typedef struct { int collapse_points[256]; int num_collapses; } CCTSchedule; /*============================================================================ Probability Tensor Primitives ============================================================================*/ void probol_init_tensor(ProbTensor *t); void probol_add_state(ProbTensor *t, prob_fixed_t val, prob_fixed_t prob); void probol_normalize(ProbTensor *t); /* ensure probs sum to 1.0 */ /* Convolution (ADDP) – returns new tensor = A + B (combined distribution) */ void probol_add_tensors(const ProbTensor *A, const ProbTensor *B, ProbTensor *C); /* Product (MULTIPLYP) – returns distribution of A * B */ void probol_multiply_tensors(const ProbTensor *A, const ProbTensor *B, ProbTensor *C); /* Analytic quantile (QUANTILEP) – smallest value v such that P(X ≤ v) ≥ quantile */ prob_fixed_t probol_quantile(const ProbTensor *t, prob_fixed_t quantile); /* Measure (collapse) – sample one value according to probabilities */ prob_fixed_t probol_measure(const ProbTensor *t); /* Probability of condition (PROBP) – sum of probabilities where f(value) is true */ prob_fixed_t probol_prob_condition(const ProbTensor *t, bool (*condition)(prob_fixed_t)); /* Entropy of a tensor (used by CCT) */ prob_fixed_t probol_entropy(const ProbTensor *t); /*============================================================================ Parametric Distributions – create tensors from Normal, etc. ============================================================================*/ void probol_normal_to_tensor(const ProbNormal *n, ProbTensor *out, int num_bins); void probol_gaussian(prob_fixed_t mu, prob_fixed_t sigma, ProbTensor *out); /*============================================================================ Copula Functions ============================================================================*/ void probol_copula_init_gaussian(CopulaGaussian *c, int dim); void probol_copula_set_correlation(CopulaGaussian *c, int i, int j, prob_fixed_t rho); void probol_copula_compute_cholesky(CopulaGaussian *c); /* Cholesky decomposition */ /* Sample from a copula given uniform marginals U[0,1] (inverse CDF method) */ void probol_copula_sample(const Copula *c, const prob_fixed_t *uniforms, prob_fixed_t *correlated, int n); /*============================================================================ GARCH Volatility ============================================================================*/ void probol_garch_update(const GARCH11 *params, prob_fixed_t innovation, prob_fixed_t *variance); prob_fixed_t probol_garch_simulate(const GARCH11 *params, int steps, prob_fixed_t *var_out); /*============================================================================ CCT Scheduler – detects when to insert MEAS operations ============================================================================*/ CCTSchedule probol_cct_schedule(const ProbTensor *initial_distribution, int time_horizon, prob_fixed_t (*dynamics)(int t, const ProbTensor *state)); /*============================================================================ Time Series Simulation (SIMULATEP) ============================================================================*/ typedef struct { int horizon; /* days to simulate */ int num_assets; ProbTensor *marginals; /* per‑asset probability tensors */ Copula *copula; GARCH11 *garch_params; /* optional, may be NULL */ CCTSchedule collapse_schedule; } SimulationConfig; void probol_simulate(const SimulationConfig *cfg, TimeSeriesState *history, /* output array of length horizon */ ProbTensor *final_tensor); /* final distribution after horizon */ /*============================================================================ I/O Extensions (compatible with probol_compiler's PRINT, COLOR, etc.) ============================================================================*/ void probol_print(const char *str); void probol_print_tensor(const ProbTensor *t); void probol_clear_screen(void); void probol_set_color(int ansi_code); void probol_gotoxy(int x, int y); void probol_get_terminal_size(int *width, int *height); char probol_getch(void); void probol_raw_mode_enable(void); void probol_raw_mode_disable(void); /*============================================================================ Fixed‑Point Arithmetic Helpers ============================================================================*/ #define FP_ONE ((prob_fixed_t)(1 << PROBOL_FIXED_POINT_SHIFT)) #define FP_FROM(x) ((prob_fixed_t)((x) * FP_ONE)) #define FP_TO_DOUBLE(x) ((double)(x) / FP_ONE) static inline prob_fixed_t fp_add(prob_fixed_t a, prob_fixed_t b) { return a + b; } static inline prob_fixed_t fp_sub(prob_fixed_t a, prob_fixed_t b) { return a - b; } static inline prob_fixed_t fp_mul(prob_fixed_t a, prob_fixed_t b) { return (prob_fixed_t)(((int64_t)a * b) >> PROBOL_FIXED_POINT_SHIFT); } static inline prob_fixed_t fp_div(prob_fixed_t a, prob_fixed_t b) { return (prob_fixed_t)((((int64_t)a) << PROBOL_FIXED_POINT_SHIFT) / b); } #endif /* PROBOL_STDLIB_H */