diff options
Diffstat (limited to 'source/luametatex/source/mp/mpc/mpmathposit.c')
| -rw-r--r-- | source/luametatex/source/mp/mpc/mpmathposit.c | 1308 |
1 files changed, 1308 insertions, 0 deletions
diff --git a/source/luametatex/source/mp/mpc/mpmathposit.c b/source/luametatex/source/mp/mpc/mpmathposit.c new file mode 100644 index 000000000..138f2a02a --- /dev/null +++ b/source/luametatex/source/mp/mpc/mpmathposit.c @@ -0,0 +1,1308 @@ +/* This file is generated by "mtxrun --script "mtx-wtoc.lua" from the metapost cweb files. */ + + +# include "mpconfig.h" +# include "mpmathposit.h" + + +# define mp_fraction_multiplier 4096 +# define mp_angle_multiplier 16 +# define mp_warning_limit pow(2.0,52) +# define odd(A) (abs(A)%2==1) +# define two_to_the(A) (1<<(unsigned)(A)) +# define set_cur_cmd(A) mp->cur_mod_->command = (A) +# define set_cur_mod(A) mp->cur_mod_->data.n.data.pval = (A) + +static void mp_allocate_abs (MP mp, mp_number *n, mp_number_type t, mp_number *v); +static void mp_allocate_clone (MP mp, mp_number *n, mp_number_type t, mp_number *v); +static void mp_allocate_double (MP mp, mp_number *n, double v); +static void mp_allocate_number (MP mp, mp_number *n, mp_number_type t); +static int mp_posit_ab_vs_cd (mp_number *a, mp_number *b, mp_number *c, mp_number *d); +static void mp_posit_abs (mp_number *A); +static void mp_posit_crossing_point (MP mp, mp_number *ret, mp_number *a, mp_number *b, mp_number *c); +static void mp_posit_fraction_to_round_scaled (mp_number *x); +static void mp_posit_m_exp (MP mp, mp_number *ret, mp_number *x_orig); +static void mp_posit_m_log (MP mp, mp_number *ret, mp_number *x_orig); +static void mp_posit_m_norm_rand (MP mp, mp_number *ret); +static void mp_posit_m_unif_rand (MP mp, mp_number *ret, mp_number *x_orig); +static void mp_posit_n_arg (MP mp, mp_number *ret, mp_number *x, mp_number *y); +static void mp_posit_number_make_fraction (MP mp, mp_number *r, mp_number *p, mp_number *q); +static void mp_posit_number_make_scaled (MP mp, mp_number *r, mp_number *p, mp_number *q); +static void mp_posit_number_take_fraction (MP mp, mp_number *r, mp_number *p, mp_number *q); +static void mp_posit_number_take_scaled (MP mp, mp_number *r, mp_number *p, mp_number *q); +static void mp_posit_power_of (MP mp, mp_number *r, mp_number *a, mp_number *b); +static void mp_posit_print_number (MP mp, mp_number *n); +static void mp_posit_pyth_add (MP mp, mp_number *r, mp_number *a, mp_number *b); +static void mp_posit_pyth_sub (MP mp, mp_number *r, mp_number *a, mp_number *b); +static void mp_posit_scan_fractional_token (MP mp, int n); +static void mp_posit_scan_numeric_token (MP mp, int n); +static void mp_posit_set_precision (MP mp); +static void mp_posit_sin_cos (MP mp, mp_number *z_orig, mp_number *n_cos, mp_number *n_sin); +static void mp_posit_slow_add (MP mp, mp_number *ret, mp_number *x_orig, mp_number *y_orig); +static void mp_posit_square_rt (MP mp, mp_number *ret, mp_number *x_orig); +static void mp_posit_velocity (MP mp, mp_number *ret, mp_number *st, mp_number *ct, mp_number *sf, mp_number *cf, mp_number *t); +static void mp_free_posit_math (MP mp); +static void mp_free_number (MP mp, mp_number *n); +static void mp_init_randoms (MP mp, int seed); +static void mp_number_abs_clone (mp_number *A, mp_number *B); +static void mp_number_add (mp_number *A, mp_number *B); +static void mp_number_add_scaled (mp_number *A, int B); +static void mp_number_angle_to_scaled (mp_number *A); +static void mp_number_clone (mp_number *A, mp_number *B); +static void mp_number_divide_int (mp_number *A, int B); +static void mp_number_double (mp_number *A); +static int mp_number_equal (mp_number *A, mp_number *B); +static void mp_number_floor (mp_number *i); +static void mp_number_fraction_to_scaled (mp_number *A); +static int mp_number_greater (mp_number *A, mp_number *B); +static void mp_number_half (mp_number *A); +static int mp_number_less (mp_number *A, mp_number *B); +static void mp_number_modulo (mp_number *a, mp_number *b); +static void mp_number_multiply_int (mp_number *A, int B); +static void mp_number_negate (mp_number *A); +static void mp_number_negated_clone (mp_number *A, mp_number *B); +static int mp_number_nonequalabs (mp_number *A, mp_number *B); +static int mp_number_odd (mp_number *A); +static void mp_number_scaled_to_angle (mp_number *A); +static void mp_number_scaled_to_fraction (mp_number *A); +static void mp_number_subtract (mp_number *A, mp_number *B); +static void mp_number_swap (mp_number *A, mp_number *B); +static int mp_number_to_boolean (mp_number *A); +static double mp_number_to_double (mp_number *A); +static int mp_number_to_int (mp_number *A); +static int mp_number_to_scaled (mp_number *A); +static int mp_round_unscaled (mp_number *x_orig); +static void mp_set_posit_from_addition (mp_number *A, mp_number *B, mp_number *C); +static void mp_set_posit_from_boolean (mp_number *A, int B); +static void mp_set_posit_from_div (mp_number *A, mp_number *B, mp_number *C); +static void mp_set_posit_from_double (mp_number *A, double B); +static void mp_set_posit_from_int (mp_number *A, int B); +static void mp_set_posit_from_int_div (mp_number *A, mp_number *B, int C); +static void mp_set_posit_from_int_mul (mp_number *A, mp_number *B, int C); +static void mp_set_posit_from_mul (mp_number *A, mp_number *B, mp_number *C); +static void mp_set_posit_from_of_the_way (MP mp, mp_number *A, mp_number *t, mp_number *B, mp_number *C); +static void mp_set_posit_from_scaled (mp_number *A, int B); +static void mp_set_posit_from_subtraction (mp_number *A, mp_number *B, mp_number *C); +static void mp_set_posit_half_from_addition (mp_number *A, mp_number *B, mp_number *C); +static void mp_set_posit_half_from_subtraction (mp_number *A, mp_number *B, mp_number *C); +static void mp_wrapup_numeric_token (MP mp, unsigned char *start, unsigned char *stop); +static char *mp_posit_number_tostring (MP mp, mp_number *n); +typedef struct mp_posit_info { + posit_t unity; + posit_t zero; + posit_t one; + posit_t two; + posit_t three; + posit_t four; + posit_t five; + posit_t eight; + posit_t seven; + posit_t sixteen; + posit_t half_unit; + posit_t minusone; + posit_t three_quarter_unit; + posit_t d16; + posit_t d64; + posit_t d256; + posit_t d4096; + posit_t d65536; + posit_t dp90; + posit_t dp180; + posit_t dp270; + posit_t dp360; + posit_t dm90; + posit_t dm180; + posit_t dm270; + posit_t dm360; + posit_t fraction_multiplier; + posit_t negative_fraction_multiplier; + posit_t angle_multiplier; + posit_t fraction_one; + posit_t fraction_two; + posit_t fraction_three; + posit_t fraction_four; + posit_t fraction_half; + posit_t fraction_one_and_half; + posit_t one_eighty_degrees; + posit_t negative_one_eighty_degrees; + posit_t three_sixty_degrees; + posit_t no_crossing; + posit_t one_crossing; + posit_t zero_crossing; + posit_t error_correction; + posit_t pi; + posit_t pi_divided_by_180; + posit_t epsilon; + posit_t EL_GORDO; + posit_t negative_EL_GORDO; + posit_t one_third_EL_GORDO; + posit_t coef; + posit_t coef_bound; + posit_t scaled_threshold; + posit_t fraction_threshold; + posit_t equation_threshold; + posit_t near_zero_angle; + posit_t p_over_v_threshold; + posit_t warning_limit; + posit_t sqrt_two_mul_fraction_one; + posit_t sqrt_five_minus_one_mul_fraction_one_and_half; + posit_t three_minus_sqrt_five_mul_fraction_one_and_half; + posit_t d180_divided_by_pi_mul_angle; + int initialized; +} mp_posit_info; +mp_posit_info mp_posit_data = { + .initialized = 0, +}; +inline static posit_t mp_posit_make_fraction (posit_t p, posit_t q) { return posit_mul(posit_div(p,q), mp_posit_data.fraction_multiplier); } +inline static posit_t mp_posit_take_fraction (posit_t p, posit_t q) { return posit_div(posit_mul(p,q), mp_posit_data.fraction_multiplier); } +inline static posit_t mp_posit_make_scaled (posit_t p, posit_t q) { return posit_div(p,q); } +math_data *mp_initialize_posit_math(MP mp) +{ + math_data *math = (math_data *) mp_memory_allocate(sizeof(math_data)); + if (! mp_posit_data.initialized) { + mp_posit_data.initialized = 1; + mp_posit_data.unity = integer_to_posit(1); + mp_posit_data.zero = integer_to_posit(0); + mp_posit_data.one = integer_to_posit(1); + mp_posit_data.two = integer_to_posit(2); + mp_posit_data.three = integer_to_posit(3); + mp_posit_data.four = integer_to_posit(4); + mp_posit_data.five = integer_to_posit(5); + mp_posit_data.seven = integer_to_posit(7); + mp_posit_data.eight = integer_to_posit(8); + mp_posit_data.sixteen = integer_to_posit(16); + mp_posit_data.dp90 = integer_to_posit(90); + mp_posit_data.dp180 = integer_to_posit(180); + mp_posit_data.dp270 = integer_to_posit(270); + mp_posit_data.dp360 = integer_to_posit(360); + mp_posit_data.dm90 = integer_to_posit(-90); + mp_posit_data.dm180 = integer_to_posit(-180); + mp_posit_data.dm270 = integer_to_posit(-270); + mp_posit_data.dm360 = integer_to_posit(-360); + mp_posit_data.d16 = integer_to_posit(16); + mp_posit_data.d64 = integer_to_posit(64); + mp_posit_data.d256 = integer_to_posit(256); + mp_posit_data.d4096 = integer_to_posit(4096); + mp_posit_data.d65536 = integer_to_posit(65536); + mp_posit_data.minusone = posit_neg(mp_posit_data.one); + mp_posit_data.half_unit = posit_div(mp_posit_data.unity, mp_posit_data.two); + mp_posit_data.three_quarter_unit = posit_mul(mp_posit_data.three, posit_div(mp_posit_data.unity,mp_posit_data.four)); + mp_posit_data.fraction_multiplier = integer_to_posit(mp_fraction_multiplier); + mp_posit_data.negative_fraction_multiplier = posit_neg(mp_posit_data.fraction_multiplier); + mp_posit_data.angle_multiplier = integer_to_posit(mp_angle_multiplier); + mp_posit_data.fraction_one = mp_posit_data.fraction_multiplier; + mp_posit_data.fraction_two = posit_mul(mp_posit_data.fraction_multiplier, mp_posit_data.two); + mp_posit_data.fraction_three = posit_mul(mp_posit_data.fraction_multiplier, mp_posit_data.three); + mp_posit_data.fraction_four = posit_mul(mp_posit_data.fraction_multiplier, mp_posit_data.four); + mp_posit_data.fraction_half = posit_div(mp_posit_data.fraction_multiplier, mp_posit_data.two); + mp_posit_data.fraction_one_and_half = posit_add(mp_posit_data.fraction_multiplier, mp_posit_data.fraction_half); + mp_posit_data.one_eighty_degrees = posit_mul(mp_posit_data.angle_multiplier, mp_posit_data.dp180); + mp_posit_data.negative_one_eighty_degrees = posit_mul(mp_posit_data.angle_multiplier, mp_posit_data.dm180); + mp_posit_data.three_sixty_degrees = posit_mul(mp_posit_data.angle_multiplier, mp_posit_data.dp360); + mp_posit_data.no_crossing = posit_add(mp_posit_data.fraction_multiplier, mp_posit_data.one); + mp_posit_data.one_crossing = mp_posit_data.fraction_multiplier; + mp_posit_data.zero_crossing = mp_posit_data.zero; + mp_posit_data.error_correction = double_to_posit(1E-12); + mp_posit_data.warning_limit = posit_pow(mp_posit_data.two, integer_to_posit(52)); + mp_posit_data.pi = double_to_posit(3.1415926535897932384626433832795028841971); + mp_posit_data.pi_divided_by_180 = posit_div(mp_posit_data.pi, mp_posit_data.dp180); + mp_posit_data.epsilon = posit_pow(mp_posit_data.two, integer_to_posit(-52.0)); + mp_posit_data.EL_GORDO = posit_sub(posit_div(double_to_posit(DBL_MAX),mp_posit_data.two), mp_posit_data.one); + mp_posit_data.negative_EL_GORDO = posit_neg(mp_posit_data.EL_GORDO); + mp_posit_data.one_third_EL_GORDO = posit_div(mp_posit_data.EL_GORDO, mp_posit_data.three); + mp_posit_data.coef = posit_div(mp_posit_data.seven, mp_posit_data.three); + mp_posit_data.coef_bound = posit_mul(mp_posit_data.coef, mp_posit_data.fraction_multiplier); + mp_posit_data.scaled_threshold = double_to_posit(0.000122); + mp_posit_data.near_zero_angle = posit_mul(double_to_posit(0.0256), mp_posit_data.angle_multiplier); + mp_posit_data.p_over_v_threshold = integer_to_posit(0x80000); + mp_posit_data.equation_threshold = double_to_posit(0.001); + mp_posit_data.sqrt_two_mul_fraction_one = + posit_mul( + posit_sqrt(mp_posit_data.two), + mp_posit_data.fraction_one + ); + mp_posit_data.sqrt_five_minus_one_mul_fraction_one_and_half = + posit_mul( + posit_mul( + mp_posit_data.three, + mp_posit_data.fraction_half + ), + posit_sub( + posit_sqrt(mp_posit_data.five), + mp_posit_data.one + ) + ); + mp_posit_data.three_minus_sqrt_five_mul_fraction_one_and_half = + posit_mul( + posit_mul( + mp_posit_data.three, + mp_posit_data.fraction_half + ), + posit_sub( + mp_posit_data.three, + posit_sqrt(mp_posit_data.five) + ) + ); + mp_posit_data.d180_divided_by_pi_mul_angle = + posit_mul( + posit_div( + mp_posit_data.dp180, + mp_posit_data.pi + ), + mp_posit_data.angle_multiplier + ); + } + math->md_allocate = mp_allocate_number; + math->md_free = mp_free_number; + math->md_allocate_clone = mp_allocate_clone; + math->md_allocate_abs = mp_allocate_abs; + math->md_allocate_double = mp_allocate_double; + mp_allocate_number(mp, &math->md_precision_default, mp_scaled_type); + mp_allocate_number(mp, &math->md_precision_max, mp_scaled_type); + mp_allocate_number(mp, &math->md_precision_min, mp_scaled_type); + mp_allocate_number(mp, &math->md_epsilon_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_inf_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_negative_inf_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_warning_limit_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_one_third_inf_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_unity_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_two_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_three_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_half_unit_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_three_quarter_unit_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_zero_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_arc_tol_k, mp_fraction_type); + mp_allocate_number(mp, &math->md_fraction_one_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_fraction_half_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_fraction_three_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_fraction_four_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_three_sixty_deg_t, mp_angle_type); + mp_allocate_number(mp, &math->md_one_eighty_deg_t, mp_angle_type); + mp_allocate_number(mp, &math->md_negative_one_eighty_deg_t, mp_angle_type); + mp_allocate_number(mp, &math->md_one_k, mp_scaled_type); + mp_allocate_number(mp, &math->md_sqrt_8_e_k, mp_scaled_type); + mp_allocate_number(mp, &math->md_twelve_ln_2_k, mp_fraction_type); + mp_allocate_number(mp, &math->md_coef_bound_k, mp_fraction_type); + mp_allocate_number(mp, &math->md_coef_bound_minus_1, mp_fraction_type); + mp_allocate_number(mp, &math->md_twelvebits_3, mp_scaled_type); + mp_allocate_number(mp, &math->md_twentysixbits_sqrt2_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_twentyeightbits_d_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_twentysevenbits_sqrt2_d_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_fraction_threshold_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_half_fraction_threshold_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_scaled_threshold_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_half_scaled_threshold_t, mp_scaled_type); + mp_allocate_number(mp, &math->md_near_zero_angle_t, mp_angle_type); + mp_allocate_number(mp, &math->md_p_over_v_threshold_t, mp_fraction_type); + mp_allocate_number(mp, &math->md_equation_threshold_t, mp_scaled_type); + math->md_precision_default.data.pval = posit_mul(mp_posit_data.d16, mp_posit_data.unity); + math->md_precision_max.data.pval = posit_mul(mp_posit_data.d16, mp_posit_data.unity); + math->md_precision_min.data.pval = posit_mul(mp_posit_data.d16, mp_posit_data.unity); + math->md_epsilon_t.data.pval = mp_posit_data.epsilon; + math->md_inf_t.data.pval = mp_posit_data.EL_GORDO; + math->md_negative_inf_t.data.pval = mp_posit_data.negative_EL_GORDO; + math->md_one_third_inf_t.data.pval = mp_posit_data.one_third_EL_GORDO; + math->md_warning_limit_t.data.pval = mp_posit_data.warning_limit; + math->md_unity_t.data.pval = mp_posit_data.unity; + math->md_two_t.data.pval = mp_posit_data.two; + math->md_three_t.data.pval = mp_posit_data.three; + math->md_half_unit_t.data.pval = mp_posit_data.half_unit; + math->md_three_quarter_unit_t.data.pval = mp_posit_data.three_quarter_unit; + math->md_arc_tol_k.data.pval = posit_div(mp_posit_data.unity, mp_posit_data.d4096); + math->md_fraction_one_t.data.pval = mp_posit_data.fraction_one; + math->md_fraction_half_t.data.pval = mp_posit_data.fraction_half; + math->md_fraction_three_t.data.pval = mp_posit_data.fraction_three; + math->md_fraction_four_t.data.pval = mp_posit_data.fraction_four; + math->md_three_sixty_deg_t.data.pval = mp_posit_data.three_sixty_degrees; + math->md_one_eighty_deg_t.data.pval = mp_posit_data.one_eighty_degrees; + math->md_negative_one_eighty_deg_t.data.pval = mp_posit_data.negative_one_eighty_degrees; + math->md_one_k.data.pval = posit_div(mp_posit_data.one, mp_posit_data.d64); + math->md_sqrt_8_e_k.data.pval = double_to_posit(1.71552776992141359295); + math->md_twelve_ln_2_k.data.pval = posit_mul(double_to_posit(8.31776616671934371292), mp_posit_data.d256); + math->md_twelvebits_3.data.pval = posit_div(integer_to_posit(1365), mp_posit_data.unity); + math->md_twentysixbits_sqrt2_t.data.pval = posit_div(integer_to_posit(94906266), mp_posit_data.d65536); + math->md_twentyeightbits_d_t.data.pval = posit_div(integer_to_posit(35596755), mp_posit_data.d65536); + math->md_twentysevenbits_sqrt2_d_t.data.pval = posit_div(integer_to_posit(25170707), mp_posit_data.d65536); + math->md_coef_bound_k.data.pval = mp_posit_data.coef_bound; + math->md_coef_bound_minus_1.data.pval = posit_sub(mp_posit_data.coef_bound, posit_div(mp_posit_data.one, mp_posit_data.d65536)); + math->md_fraction_threshold_t.data.pval = double_to_posit(0.04096); + math->md_half_fraction_threshold_t.data.pval = posit_div(mp_posit_data.fraction_threshold, mp_posit_data.two); + math->md_scaled_threshold_t.data.pval = mp_posit_data.scaled_threshold; + math->md_half_scaled_threshold_t.data.pval = posit_div(mp_posit_data.scaled_threshold,mp_posit_data.two); + math->md_near_zero_angle_t.data.pval = mp_posit_data.near_zero_angle; + math->md_p_over_v_threshold_t.data.pval = mp_posit_data.p_over_v_threshold; + math->md_equation_threshold_t.data.pval = mp_posit_data.equation_threshold; + math->md_from_int = mp_set_posit_from_int; + math->md_from_boolean = mp_set_posit_from_boolean; + math->md_from_scaled = mp_set_posit_from_scaled; + math->md_from_double = mp_set_posit_from_double; + math->md_from_addition = mp_set_posit_from_addition; + math->md_half_from_addition = mp_set_posit_half_from_addition; + math->md_from_subtraction = mp_set_posit_from_subtraction; + math->md_half_from_subtraction = mp_set_posit_half_from_subtraction; + math->md_from_oftheway = mp_set_posit_from_of_the_way; + math->md_from_div = mp_set_posit_from_div; + math->md_from_mul = mp_set_posit_from_mul; + math->md_from_int_div = mp_set_posit_from_int_div; + math->md_from_int_mul = mp_set_posit_from_int_mul; + math->md_negate = mp_number_negate; + math->md_add = mp_number_add; + math->md_subtract = mp_number_subtract; + math->md_half = mp_number_half; + math->md_do_double = mp_number_double; + math->md_abs = mp_posit_abs; + math->md_clone = mp_number_clone; + math->md_negated_clone = mp_number_negated_clone; + math->md_abs_clone = mp_number_abs_clone; + math->md_swap = mp_number_swap; + math->md_add_scaled = mp_number_add_scaled; + math->md_multiply_int = mp_number_multiply_int; + math->md_divide_int = mp_number_divide_int; + math->md_to_boolean = mp_number_to_boolean; + math->md_to_scaled = mp_number_to_scaled; + math->md_to_double = mp_number_to_double; + math->md_to_int = mp_number_to_int; + math->md_odd = mp_number_odd; + math->md_equal = mp_number_equal; + math->md_less = mp_number_less; + math->md_greater = mp_number_greater; + math->md_nonequalabs = mp_number_nonequalabs; + math->md_round_unscaled = mp_round_unscaled; + math->md_floor_scaled = mp_number_floor; + math->md_fraction_to_round_scaled = mp_posit_fraction_to_round_scaled; + math->md_make_scaled = mp_posit_number_make_scaled; + math->md_make_fraction = mp_posit_number_make_fraction; + math->md_take_fraction = mp_posit_number_take_fraction; + math->md_take_scaled = mp_posit_number_take_scaled; + math->md_velocity = mp_posit_velocity; + math->md_n_arg = mp_posit_n_arg; + math->md_m_log = mp_posit_m_log; + math->md_m_exp = mp_posit_m_exp; + math->md_m_unif_rand = mp_posit_m_unif_rand; + math->md_m_norm_rand = mp_posit_m_norm_rand; + math->md_pyth_add = mp_posit_pyth_add; + math->md_pyth_sub = mp_posit_pyth_sub; + math->md_power_of = mp_posit_power_of; + math->md_fraction_to_scaled = mp_number_fraction_to_scaled; + math->md_scaled_to_fraction = mp_number_scaled_to_fraction; + math->md_scaled_to_angle = mp_number_scaled_to_angle; + math->md_angle_to_scaled = mp_number_angle_to_scaled; + math->md_init_randoms = mp_init_randoms; + math->md_sin_cos = mp_posit_sin_cos; + math->md_slow_add = mp_posit_slow_add; + math->md_sqrt = mp_posit_square_rt; + math->md_print = mp_posit_print_number; + math->md_tostring = mp_posit_number_tostring; + math->md_modulo = mp_number_modulo; + math->md_ab_vs_cd = mp_posit_ab_vs_cd; + math->md_crossing_point = mp_posit_crossing_point; + math->md_scan_numeric = mp_posit_scan_numeric_token; + math->md_scan_fractional = mp_posit_scan_fractional_token; + math->md_free_math = mp_free_posit_math; + math->md_set_precision = mp_posit_set_precision; + return math; +} +void mp_posit_set_precision (MP mp) +{ + (void) mp; +} +void mp_free_posit_math (MP mp) +{ + mp_free_number(mp, &(mp->math->md_three_sixty_deg_t)); + mp_free_number(mp, &(mp->math->md_one_eighty_deg_t)); + mp_free_number(mp, &(mp->math->md_negative_one_eighty_deg_t)); + mp_free_number(mp, &(mp->math->md_fraction_one_t)); + mp_free_number(mp, &(mp->math->md_zero_t)); + mp_free_number(mp, &(mp->math->md_half_unit_t)); + mp_free_number(mp, &(mp->math->md_three_quarter_unit_t)); + mp_free_number(mp, &(mp->math->md_unity_t)); + mp_free_number(mp, &(mp->math->md_two_t)); + mp_free_number(mp, &(mp->math->md_three_t)); + mp_free_number(mp, &(mp->math->md_one_third_inf_t)); + mp_free_number(mp, &(mp->math->md_inf_t)); + mp_free_number(mp, &(mp->math->md_negative_inf_t)); + mp_free_number(mp, &(mp->math->md_warning_limit_t)); + mp_free_number(mp, &(mp->math->md_one_k)); + mp_free_number(mp, &(mp->math->md_sqrt_8_e_k)); + mp_free_number(mp, &(mp->math->md_twelve_ln_2_k)); + mp_free_number(mp, &(mp->math->md_coef_bound_k)); + mp_free_number(mp, &(mp->math->md_coef_bound_minus_1)); + mp_free_number(mp, &(mp->math->md_fraction_threshold_t)); + mp_free_number(mp, &(mp->math->md_half_fraction_threshold_t)); + mp_free_number(mp, &(mp->math->md_scaled_threshold_t)); + mp_free_number(mp, &(mp->math->md_half_scaled_threshold_t)); + mp_free_number(mp, &(mp->math->md_near_zero_angle_t)); + mp_free_number(mp, &(mp->math->md_p_over_v_threshold_t)); + mp_free_number(mp, &(mp->math->md_equation_threshold_t)); + mp_memory_free(mp->math); +} + +void mp_allocate_number (MP mp, mp_number *n, mp_number_type t) +{ + (void) mp; + n->data.pval = mp_posit_data.zero; + n->type = t; +} + +void mp_allocate_clone (MP mp, mp_number *n, mp_number_type t, mp_number *v) +{ + (void) mp; + n->type = t; + n->data.pval = v->data.pval; +} + +void mp_allocate_abs (MP mp, mp_number *n, mp_number_type t, mp_number *v) +{ + (void) mp; + n->type = t; + n->data.pval = posit_fabs(v->data.pval); +} + +void mp_allocate_double (MP mp, mp_number *n, double v) +{ + (void) mp; + n->type = mp_scaled_type; + n->data.pval = double_to_posit(v); +} + +void mp_free_number (MP mp, mp_number *n) +{ + (void) mp; + n->type = mp_nan_type; +} + +void mp_set_posit_from_int(mp_number *A, int B) +{ + A->data.pval = integer_to_posit(B); +} + +void mp_set_posit_from_boolean(mp_number *A, int B) +{ + A->data.pval = integer_to_posit(B); +} + +void mp_set_posit_from_scaled(mp_number *A, int B) +{ + A->data.pval = posit_div(integer_to_posit(B), mp_posit_data.d65536); +} + +void mp_set_posit_from_double(mp_number *A, double B) +{ + A->data.pval = double_to_posit(B); +} + +void mp_set_posit_from_addition(mp_number *A, mp_number *B, mp_number *C) +{ + A->data.pval = posit_add(B->data.pval, C->data.pval); +} + +void mp_set_posit_half_from_addition(mp_number *A, mp_number *B, mp_number *C) +{ + A->data.pval = posit_div(posit_add(B->data.pval,C->data.pval), mp_posit_data.two); +} + +void mp_set_posit_from_subtraction(mp_number *A, mp_number *B, mp_number *C) +{ + A->data.pval = posit_sub(B->data.pval, C->data.pval); +} + +void mp_set_posit_half_from_subtraction(mp_number *A, mp_number *B, mp_number *C) +{ + A->data.pval = posit_div(posit_sub(B->data.pval, C->data.pval), mp_posit_data.two); +} + +void mp_set_posit_from_div(mp_number *A, mp_number *B, mp_number *C) +{ + A->data.pval = posit_div(B->data.pval, C->data.pval); +} + +void mp_set_posit_from_mul(mp_number *A, mp_number *B, mp_number *C) +{ + A->data.pval = posit_mul(B->data.pval, C->data.pval); +} + +void mp_set_posit_from_int_div(mp_number *A, mp_number *B, int C) +{ + A->data.pval = posit_div(B->data.pval, integer_to_posit(C)); +} + +void mp_set_posit_from_int_mul(mp_number *A, mp_number *B, int C) +{ + A->data.pval = posit_mul(A->data.pval, integer_to_posit(C)); +} + +void mp_set_posit_from_of_the_way (MP mp, mp_number *A, mp_number *t, mp_number *B, mp_number *C) +{ + (void) mp; + A->data.pval = posit_sub(B->data.pval, mp_posit_take_fraction(posit_sub(B->data.pval, C->data.pval), t->data.pval)); +} + +void mp_number_negate(mp_number *A) +{ + A->data.pval = posit_neg(A->data.pval); +} + +void mp_number_add(mp_number *A, mp_number *B) +{ + A->data.pval = posit_add(A->data.pval, B->data.pval); +} + +void mp_number_subtract(mp_number *A, mp_number *B) +{ + A->data.pval = posit_sub(A->data.pval, B->data.pval); +} + +void mp_number_half(mp_number *A) +{ + A->data.pval = posit_div(A->data.pval, mp_posit_data.two); +} + +void mp_number_double(mp_number *A) +{ + A->data.pval = posit_mul(A->data.pval, mp_posit_data.two); +} + +void mp_number_add_scaled(mp_number *A, int B) +{ + A->data.pval = posit_add(A->data.pval, posit_div(integer_to_posit(B), mp_posit_data.d65536)); +} + +void mp_number_multiply_int(mp_number *A, int B) +{ + A->data.pval = posit_mul(A->data.pval, integer_to_posit(B)); +} + +void mp_number_divide_int(mp_number *A, int B) +{ + A->data.pval = posit_div(A->data.pval, integer_to_posit(B)); +} + +void mp_posit_abs(mp_number *A) +{ + A->data.pval = posit_fabs(A->data.pval); +} + +void mp_number_clone(mp_number *A, mp_number *B) +{ + A->data.pval = B->data.pval; +} + +void mp_number_negated_clone(mp_number *A, mp_number *B) +{ + A->data.pval = posit_neg(B->data.pval); +} + +void mp_number_abs_clone(mp_number *A, mp_number *B) +{ + A->data.pval = posit_fabs(B->data.pval); +} + +void mp_number_swap(mp_number *A, mp_number *B) +{ + posit_t swap_tmp = A->data.pval; + A->data.pval = B->data.pval; + B->data.pval = swap_tmp; +} + +void mp_number_fraction_to_scaled(mp_number *A) +{ + A->type = mp_scaled_type; + A->data.pval = posit_div(A->data.pval, mp_posit_data.fraction_multiplier); +} + +void mp_number_angle_to_scaled(mp_number *A) +{ + A->type = mp_scaled_type; + A->data.pval = posit_div(A->data.pval, mp_posit_data.angle_multiplier); +} + +void mp_number_scaled_to_fraction(mp_number *A) +{ + A->type = mp_fraction_type; + A->data.pval = posit_mul(A->data.pval, mp_posit_data.fraction_multiplier); +} + +void mp_number_scaled_to_angle(mp_number *A) +{ + A->type = mp_angle_type; + A->data.pval = posit_mul(A->data.pval, mp_posit_data.angle_multiplier); +} + +int mp_number_to_scaled(mp_number *A) +{ + return posit_to_integer(posit_mul(A->data.pval, mp_posit_data.d65536)); +} + +int mp_number_to_int(mp_number *A) +{ + return posit_to_integer(A->data.pval); +} + +int mp_number_to_boolean(mp_number *A) +{ + return posit_eq_zero(A->data.pval) ? 0 : 1; +} + +double mp_number_to_double(mp_number *A) +{ + return posit_to_double(A->data.pval); +} + +int mp_number_odd(mp_number *A) +{ + return odd(posit_to_integer(A->data.pval)); +} + +int mp_number_equal(mp_number *A, mp_number *B) +{ + return posit_eq(A->data.pval, B->data.pval); +} + +int mp_number_greater(mp_number *A, mp_number *B) +{ + return posit_gt(A->data.pval, B->data.pval); +} + +int mp_number_less(mp_number *A, mp_number *B) +{ + return posit_lt(A->data.pval, B->data.pval); +} + +int mp_number_nonequalabs(mp_number *A, mp_number *B) +{ + return ! posit_eq(posit_fabs(A->data.pval), posit_fabs(B->data.pval)); +} + +char *mp_posit_number_tostring (MP mp, mp_number *n) +{ + static char set[64]; + int l = 0; + char *ret = mp_memory_allocate(64); + (void) mp; + snprintf(set, 64, "%.20g", posit_to_double(n->data.pval)); + while (set[l] == ' ') { + l++; + } + strcpy(ret, set+l); + return ret; +} + +void mp_posit_print_number (MP mp, mp_number *n) +{ + char *str = mp_posit_number_tostring(mp, n); + mp_print_e_str(mp, str); + mp_memory_free(str); +} + + +void mp_posit_slow_add (MP mp, mp_number *ret, mp_number *x_orig, mp_number *y_orig) +{ + if (posit_gt(x_orig->data.pval, mp_posit_data.zero)) { + if (posit_le(y_orig->data.pval, posit_sub(mp_posit_data.EL_GORDO, x_orig->data.pval))) { + ret->data.pval = posit_add(x_orig->data.pval, y_orig->data.pval); + } else { + mp->arith_error = 1; + ret->data.pval = mp_posit_data.EL_GORDO; + } + } else if (posit_le(posit_neg(y_orig->data.pval), posit_add(mp_posit_data.EL_GORDO, x_orig->data.pval))) { + ret->data.pval = posit_add(x_orig->data.pval, y_orig->data.pval); + } else { + mp->arith_error = 1; + ret->data.pval = mp_posit_data.negative_EL_GORDO; + } +} + +void mp_posit_number_make_fraction (MP mp, mp_number *ret, mp_number *p, mp_number *q) { + (void) mp; + ret->data.pval = mp_posit_make_fraction(p->data.pval, q->data.pval); +} + +void mp_posit_number_take_fraction (MP mp, mp_number *ret, mp_number *p, mp_number *q) { + (void) mp; + ret->data.pval = mp_posit_take_fraction(p->data.pval, q->data.pval); +} + +void mp_posit_number_take_scaled (MP mp, mp_number *ret, mp_number *p_orig, mp_number *q_orig) +{ + (void) mp; + ret->data.pval = posit_mul(p_orig->data.pval, q_orig->data.pval); +} + +void mp_posit_number_make_scaled (MP mp, mp_number *ret, mp_number *p_orig, mp_number *q_orig) +{ + (void) mp; + ret->data.pval = posit_div(p_orig->data.pval, q_orig->data.pval); +} + +void mp_wrapup_numeric_token (MP mp, unsigned char *start, unsigned char *stop) +{ + double result; + char *end = (char *) stop; + errno = 0; + result = strtod((char *) start, &end); + if (errno == 0) { + set_cur_mod(double_to_posit(result)); + if (result >= mp_warning_limit) { + if (posit_gt(internal_value(mp_warning_check_internal).data.pval, mp_posit_data.zero) && (mp->scanner_status != mp_tex_flushing_state)) { + char msg[256]; + mp_snprintf(msg, 256, "Number is too large (%g)", result); + mp_error( + mp, + msg, + "Continue and I'll try to cope with that big value; but it might be dangerous." + "(Set warningcheck := 0 to suppress this message.)" + ); + } + } + } else if (mp->scanner_status != mp_tex_flushing_state) { + mp_error( + mp, + "Enormous number has been reduced.", + "I could not handle this number specification probably because it is out of" + "range." + ); + set_cur_mod(mp_posit_data.EL_GORDO); + } + set_cur_cmd(mp_numeric_command); +} + +static void mp_posit_aux_find_exponent (MP mp) +{ + if (mp->buffer[mp->cur_input.loc_field] == 'e' || mp->buffer[mp->cur_input.loc_field] == 'E') { + mp->cur_input.loc_field++; + if (!(mp->buffer[mp->cur_input.loc_field] == '+' + || mp->buffer[mp->cur_input.loc_field] == '-' + || mp->char_class[mp->buffer[mp->cur_input.loc_field]] == mp_digit_class)) { + mp->cur_input.loc_field--; + return; + } + if (mp->buffer[mp->cur_input.loc_field] == '+' + || mp->buffer[mp->cur_input.loc_field] == '-') { + mp->cur_input.loc_field++; + } + while (mp->char_class[mp->buffer[mp->cur_input.loc_field]] == mp_digit_class) { + mp->cur_input.loc_field++; + } + } +} + +void mp_posit_scan_fractional_token (MP mp, int n) +{ + unsigned char *start = &mp->buffer[mp->cur_input.loc_field -1]; + unsigned char *stop; + (void) n; + while (mp->char_class[mp->buffer[mp->cur_input.loc_field]] == mp_digit_class) { + mp->cur_input.loc_field++; + } + mp_posit_aux_find_exponent(mp); + stop = &mp->buffer[mp->cur_input.loc_field-1]; + mp_wrapup_numeric_token(mp, start, stop); +} + +void mp_posit_scan_numeric_token (MP mp, int n) +{ + unsigned char *start = &mp->buffer[mp->cur_input.loc_field -1]; + unsigned char *stop; + (void) n; + while (mp->char_class[mp->buffer[mp->cur_input.loc_field]] == mp_digit_class) { + mp->cur_input.loc_field++; + } + if (mp->buffer[mp->cur_input.loc_field] == '.' && mp->buffer[mp->cur_input.loc_field+1] != '.') { + mp->cur_input.loc_field++; + while (mp->char_class[mp->buffer[mp->cur_input.loc_field]] == mp_digit_class) { + mp->cur_input.loc_field++; + } + } + mp_posit_aux_find_exponent(mp); + stop = &mp->buffer[mp->cur_input.loc_field-1]; + mp_wrapup_numeric_token(mp, start, stop); +} + +void mp_posit_velocity (MP mp, mp_number *ret, mp_number *st, mp_number *ct, mp_number *sf, mp_number *cf, mp_number *t) +{ + posit_t acc, num, denom; + (void) mp; + acc = mp_posit_take_fraction( + mp_posit_take_fraction( + posit_sub(st->data.pval, posit_div(sf->data.pval, mp_posit_data.sixteen)), + posit_sub(sf->data.pval, posit_div(st->data.pval, mp_posit_data.sixteen)) + ), + posit_sub(ct->data.pval,cf->data.pval) + ); + num = posit_add( + mp_posit_data.fraction_two, + mp_posit_take_fraction( + acc, + mp_posit_data.sqrt_two_mul_fraction_one + ) + ); + denom = posit_add( + mp_posit_data.fraction_three, + posit_add( + mp_posit_take_fraction( + ct->data.pval, + mp_posit_data.sqrt_five_minus_one_mul_fraction_one_and_half + ), + mp_posit_take_fraction( + cf->data.pval, + mp_posit_data.three_minus_sqrt_five_mul_fraction_one_and_half + ) + ) + ); + if (posit_ne(t->data.pval, mp_posit_data.unity)) { + num = mp_posit_make_scaled(num, t->data.pval); + } + if (posit_ge(posit_div(num, mp_posit_data.four), denom)) { + ret->data.pval = mp_posit_data.fraction_four; + } else { + ret->data.pval = mp_posit_make_fraction(num, denom); + } +} + +int mp_posit_ab_vs_cd (mp_number *a_orig, mp_number *b_orig, mp_number *c_orig, mp_number *d_orig) +{ + posit_t ab = posit_mul(a_orig->data.pval, b_orig->data.pval); + posit_t cd = posit_mul(c_orig->data.pval, d_orig->data.pval); + if (posit_eq(ab,cd)) { + return 0; + } else if (posit_lt(ab,cd)) { + return -1; + } else { + return 1; + } +} + +static void mp_posit_crossing_point (MP mp, mp_number *ret, mp_number *aa, mp_number *bb, mp_number *cc) +{ + posit_t d; + posit_t xx, x0, x1, x2; + posit_t a = aa->data.pval; + posit_t b = bb->data.pval; + posit_t c = cc->data.pval; + (void) mp; + if (posit_lt(a, mp_posit_data.zero)) { + ret->data.pval = mp_posit_data.zero_crossing; + return; + } + if (posit_ge(c, mp_posit_data.zero)) { + if (posit_ge(b, mp_posit_data.zero)) { + if (posit_gt(c, mp_posit_data.zero)) { + ret->data.pval = mp_posit_data.no_crossing; + } else if (posit_eq_zero(a) && posit_eq_zero(b)) { + ret->data.pval = mp_posit_data.no_crossing; + } else { + ret->data.pval = mp_posit_data.one_crossing; + } + return; + } + if (posit_eq_zero(a)) { + ret->data.pval = mp_posit_data.zero_crossing; + return; + } + } else if (posit_eq_zero(a) && posit_le(b, mp_posit_data.zero)) { + ret->data.pval = mp_posit_data.zero_crossing; + return; + } + d = mp_posit_data.epsilon; + x0 = a; + x1 = posit_sub(a, b); + x2 = posit_sub(b, c); + do { + posit_t x = posit_add(posit_div(posit_add(x1, x2), mp_posit_data.two), mp_posit_data.error_correction); + if (posit_gt(posit_sub(x1, x0), x0)) { + x2 = x; + x0 = posit_add(x0, x0); + d = posit_add(d, d); + } else { + xx = posit_sub(posit_add(x1, x), x0); + if (posit_gt(xx, x0)) { + x2 = x; + x0 = posit_add(x0, x0); + d = posit_add(d, d); + } else { + x0 = posit_sub(x0, xx); + if (posit_le(x, x0) && posit_le(posit_add(x, x2), x0)) { + ret->data.pval = mp_posit_data.no_crossing; + return; + } + x1 = x; + d = posit_add(posit_add(d, d), mp_posit_data.epsilon); + } + } + } while (posit_lt(d, mp_posit_data.fraction_one)); + ret->data.pval = posit_sub(d, mp_posit_data.fraction_one); +} + +int mp_round_unscaled(mp_number *x_orig) +{ + return posit_i_round(x_orig->data.pval); +} + +void mp_number_floor(mp_number *i) +{ + i->data.pval = posit_floor(i->data.pval); +} + +void mp_posit_fraction_to_round_scaled(mp_number *x_orig) +{ + x_orig->type = mp_scaled_type; + x_orig->data.pval = posit_div(x_orig->data.pval, mp_posit_data.fraction_multiplier); +} + +void mp_posit_square_rt (MP mp, mp_number *ret, mp_number *x_orig) +{ + if (posit_gt(x_orig->data.pval, mp_posit_data.zero)) { + ret->data.pval = posit_sqrt(x_orig->data.pval); + } else { + if (posit_lt(x_orig->data.pval, mp_posit_data.zero)) { + char msg[256]; + char *xstr = mp_posit_number_tostring(mp, x_orig); + mp_snprintf(msg, 256, "Square root of %s has been replaced by 0", xstr); + mp_memory_free(xstr); + mp_error( + mp, + msg, + "Since I don't take square roots of negative numbers, I'm zeroing this one.\n" + "Proceed, with fingers crossed." + ); + } + ret->data.pval = mp_posit_data.zero; + } +} + +void mp_posit_pyth_add (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig) +{ + ret->data.pval = posit_sqrt( + posit_add( + posit_mul( + a_orig->data.pval, + a_orig->data.pval + ), + posit_mul( + b_orig->data.pval, + b_orig->data.pval + ) + ) + ); +} + +void mp_posit_pyth_sub (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig) +{ + if (posit_gt(a_orig->data.pval,b_orig->data.pval)) { + a_orig->data.pval = posit_sqrt( + posit_sub( + posit_mul( + a_orig->data.pval, + a_orig->data.pval + ), + posit_mul( + b_orig->data.pval, + b_orig->data.pval + ) + ) + ); + } else { + if (posit_lt(a_orig->data.pval,b_orig->data.pval)) { + char msg[256]; + char *astr = mp_posit_number_tostring(mp, a_orig); + char *bstr = mp_posit_number_tostring(mp, b_orig); + mp_snprintf(msg, 256, "Pythagorean subtraction %s+-+%s has been replaced by 0", astr, bstr); + mp_memory_free(astr); + mp_memory_free(bstr); + mp_error( + mp, + msg, + "Since I don't take square roots of negative numbers, Im zeroing this one.\n" + "Proceed, with fingers crossed." + ); + } + a_orig->data.pval = mp_posit_data.zero; + } + ret->data.pval = a_orig->data.pval; +} + +void mp_posit_power_of (MP mp, mp_number *ret, mp_number *a_orig, mp_number *b_orig) +{ + errno = 0; + ret->data.pval = posit_pow(a_orig->data.pval, b_orig->data.pval); + if (errno) { + mp->arith_error = 1; + ret->data.pval = mp_posit_data.EL_GORDO; + } +} + +void mp_posit_m_log (MP mp, mp_number *ret, mp_number *x_orig) +{ + if (posit_gt(x_orig->data.pval,mp_posit_data.zero)) { + ret->data.pval = posit_mul(posit_log(x_orig->data.pval),mp_posit_data.d256); + } else { + char msg[256]; + char *xstr = mp_posit_number_tostring(mp, x_orig); + mp_snprintf(msg, 256, "Logarithm of %s has been replaced by 0", xstr); + mp_memory_free(xstr); + mp_error( + mp, + msg, + "Since I don't take logs of non-positive numbers, I'm zeroing this one.\n" + "Proceed, with fingers crossed." + ); + ret->data.pval = mp_posit_data.zero; + } +} + +void mp_posit_m_exp (MP mp, mp_number *ret, mp_number *x_orig) +{ + errno = 0; + ret->data.pval = posit_exp(posit_div(x_orig->data.pval,mp_posit_data.d256)); + if (errno) { + if (posit_gt(x_orig->data.pval,mp_posit_data.zero)) { + mp->arith_error = 1; + ret->data.pval = mp_posit_data.EL_GORDO; + } else { + ret->data.pval = mp_posit_data.zero; + } + } +} + +void mp_posit_n_arg (MP mp, mp_number *ret, mp_number *x_orig, mp_number *y_orig) +{ + if (posit_eq_zero(x_orig->data.pval) && posit_eq_zero(y_orig->data.pval)) { + mp_error( + mp, + "angle(0,0) is taken as zero", + "The 'angle' between two identical points is undefined. I'm zeroing this one.\n" + "Proceed, with fingers crossed." + ); + ret->data.pval = mp_posit_data.zero; + } else { + ret->type = mp_angle_type; + ret->data.pval = posit_mul( + posit_atan2( + y_orig->data.pval, + x_orig->data.pval + ), + mp_posit_data.d180_divided_by_pi_mul_angle + ); + } +} + +void mp_posit_sin_cos (MP mp, mp_number *z_orig, mp_number *n_cos, mp_number *n_sin) +{ + posit_t rad = posit_div(z_orig->data.pval, mp_posit_data.angle_multiplier); + (void) mp; + if (posit_eq(rad, mp_posit_data.dp90) || posit_eq(rad, mp_posit_data.dm270)) { + n_cos->data.pval = mp_posit_data.zero; + n_sin->data.pval = mp_posit_data.fraction_multiplier; + } else if (posit_eq(rad, mp_posit_data.dm90) || posit_eq(rad, mp_posit_data.dp270)) { + n_cos->data.pval = mp_posit_data.zero; + n_sin->data.pval = mp_posit_data.negative_fraction_multiplier; + } else if (posit_eq(rad, mp_posit_data.dp180) || posit_eq(rad, mp_posit_data.dm180)) { + n_cos->data.pval = mp_posit_data.negative_fraction_multiplier; + n_sin->data.pval = mp_posit_data.zero; + } else { + rad = posit_mul(rad,mp_posit_data.pi_divided_by_180); + n_cos->data.pval = posit_mul(posit_cos(rad),mp_posit_data.fraction_multiplier); + n_sin->data.pval = posit_mul(posit_sin(rad),mp_posit_data.fraction_multiplier); + } +} + +# define KK 100 +# define LL 37 +# define MM (1L<<30) +# define mod_diff(x,y) (((x)-(y))&(MM-1)) +# define TT 70 +# define is_odd(x) ((x)&1) +# define QUALITY 1009 + + +typedef struct mp_posit_random_info { + long x[KK]; + long buf[QUALITY]; + long dummy; + long started; + long *ptr; +} mp_posit_random_info; + +static mp_posit_random_info mp_posit_random_data = { + .dummy = -1, + .started = -1, + .ptr = &mp_posit_random_data.dummy +}; + +static void mp_posit_aux_ran_array(long aa[], int n) +{ + int i, j; + for (j = 0; j < KK; j++) { + aa[j] = mp_posit_random_data.x[j]; + } + for (; j < n; j++) { + aa[j] = mod_diff(aa[j - KK], aa[j - LL]); + } + for (i = 0; i < LL; i++, j++) { + mp_posit_random_data.x[i] = mod_diff(aa[j - KK], aa[j - LL]); + } + for (; i < KK; i++, j++) { + mp_posit_random_data.x[i] = mod_diff(aa[j - KK], mp_posit_random_data.x[i - LL]); + } +} + + +static void mp_posit_aux_ran_start(long seed) +{ + int t, j; + long x[KK + KK - 1]; + long ss = (seed+2) & (MM - 2); + for (j = 0; j < KK; j++) { + x[j] = ss; + ss <<= 1; + if (ss >= MM) { + ss -= MM - 2; + } + } + x[1]++; + for (ss = seed & (MM - 1), t = TT - 1; t;) { + for (j = KK - 1; j > 0; j--) { + x[j + j] = x[j]; + x[j + j - 1] = 0; + } + for (j = KK + KK - 2; j >= KK; j--) { + x[j - (KK -LL)] = mod_diff(x[j - (KK - LL)], x[j]); + x[j - KK] = mod_diff(x[j - KK], x[j]); + } + if (is_odd(ss)) { + for (j = KK; j>0; j--) { + x[j] = x[j-1]; + } + x[0] = x[KK]; + x[LL] = mod_diff(x[LL], x[KK]); + } + if (ss) { + ss >>= 1; + } else { + t--; + } + } + for (j = 0; j < LL; j++) { + mp_posit_random_data.x[j + KK - LL] = x[j]; + } + for (;j < KK; j++) { + mp_posit_random_data.x[j - LL] = x[j]; + } + for (j = 0; j < 10; j++) { + mp_posit_aux_ran_array(x, KK + KK - 1); + } + mp_posit_random_data.ptr = &mp_posit_random_data.started; +} + +static long mp_posit_aux_ran_arr_cycle(void) +{ + if (mp_posit_random_data.ptr == &mp_posit_random_data.dummy) { + mp_posit_aux_ran_start(314159L); + } + mp_posit_aux_ran_array(mp_posit_random_data.buf, QUALITY); + mp_posit_random_data.buf[KK] = -1; + mp_posit_random_data.ptr = mp_posit_random_data.buf + 1; + return mp_posit_random_data.buf[0]; +} + +void mp_init_randoms (MP mp, int seed) +{ + int k = 1; + int j = abs(seed); + int f = (int) mp_fraction_multiplier; + while (j >= f) { + j = j/2; + } + for (int i = 0; i <= 54; i++) { + int jj = k; + k = j - k; + j = jj; + if (k < 0) { + k += f; + } + mp->randoms[(i * 21) % 55].data.pval = integer_to_posit(j); + } + mp_new_randoms(mp); + mp_new_randoms(mp); + mp_new_randoms(mp); + mp_posit_aux_ran_start((unsigned long) seed); +} + +void mp_number_modulo(mp_number *a, mp_number *b) +{ + a->data.pval = posit_mul(posit_modf(posit_div(a->data.pval, b->data.pval)), b->data.pval); +} + +static void mp_next_unif_random (MP mp, mp_number *ret) +{ + unsigned long int op = (unsigned) (*mp_posit_random_data.ptr >=0 ? *mp_posit_random_data.ptr++: mp_posit_aux_ran_arr_cycle()); + double a = op / (MM * 1.0); + (void) mp; + ret->data.pval = double_to_posit(a); +} + +static void mp_next_random (MP mp, mp_number *ret) +{ + if ( mp->j_random==0) { + mp_new_randoms(mp); + } else { + mp->j_random = mp->j_random-1; + } + mp_number_clone(ret, &(mp->randoms[mp->j_random])); +} + +static void mp_posit_m_unif_rand (MP mp, mp_number *ret, mp_number *x_orig) +{ + mp_number x, abs_x, u, y; + mp_allocate_number(mp, &y, mp_fraction_type); + mp_allocate_clone(mp, &x, mp_scaled_type, x_orig); + mp_allocate_abs(mp, &abs_x, mp_scaled_type, &x); + mp_allocate_number(mp, &u, mp_scaled_type); + mp_next_unif_random(mp, &u); + y.data.pval = posit_mul(abs_x.data.pval, u.data.pval); + mp_free_number(mp, &u); + if (mp_number_equal(&y, &abs_x)) { + mp_number_clone(ret, &((math_data *)mp->math)->md_zero_t); + } else if (mp_number_greater(&x, &((math_data *)mp->math)->md_zero_t)) { + mp_number_clone(ret, &y); + } else { + mp_number_negated_clone(ret, &y); + } + mp_free_number(mp, &abs_x); + mp_free_number(mp, &x); + mp_free_number(mp, &y); +} + +static void mp_posit_m_norm_rand (MP mp, mp_number *ret) +{ + mp_number abs_x, u, r, la, xa; + mp_allocate_number(mp, &la, mp_scaled_type); + mp_allocate_number(mp, &xa, mp_scaled_type); + mp_allocate_number(mp, &abs_x, mp_scaled_type); + mp_allocate_number(mp, &u, mp_scaled_type); + mp_allocate_number(mp, &r, mp_scaled_type); + do { + do { + mp_number v; + mp_allocate_number(mp, &v, mp_scaled_type); + mp_next_random(mp, &v); + mp_number_subtract(&v, &((math_data *)mp->math)->md_fraction_half_t); + mp_posit_number_take_fraction(mp, &xa, &((math_data *)mp->math)->md_sqrt_8_e_k, &v); + mp_free_number(mp, &v); + mp_next_random(mp, &u); + mp_number_clone(&abs_x, &xa); + mp_posit_abs(&abs_x); + } while (! mp_number_less(&abs_x, &u)); + mp_posit_number_make_fraction(mp, &r, &xa, &u); + mp_number_clone(&xa, &r); + mp_posit_m_log(mp, &la, &u); + mp_set_posit_from_subtraction(&la, &((math_data *)mp->math)->md_twelve_ln_2_k, &la); + } while (mp_posit_ab_vs_cd(&((math_data *)mp->math)->md_one_k, &la, &xa, &xa) < 0); + mp_number_clone(ret, &xa); + mp_free_number(mp, &r); + mp_free_number(mp, &abs_x); + mp_free_number(mp, &la); + mp_free_number(mp, &xa); + mp_free_number(mp, &u); +} + |