#include <tgmath.h>
#include <gmp.h>
#include <mpfr.h>
#include <stdio.h>
#include <stdbool.h>

char *name = "Migdal et al, Equation (51)";

double f_if(float k, float n) {
        float r22435 = 1;
        float r22436 = k;
        float r22437 = sqrt(r22436);
        float r22438 = r22435 / r22437;
        float r22439 = 2;
        float r22440 = atan2(1.0, 0.0);
        float r22441 = r22439 * r22440;
        float r22442 = n;
        float r22443 = r22441 * r22442;
        float r22444 = r22435 - r22436;
        float r22445 = r22444 / r22439;
        float r22446 = pow(r22443, r22445);
        float r22447 = r22438 * r22446;
        return r22447;
}

double f_id(double k, double n) {
        double r22448 = 1;
        double r22449 = k;
        double r22450 = sqrt(r22449);
        double r22451 = r22448 / r22450;
        double r22452 = 2;
        double r22453 = atan2(1.0, 0.0);
        double r22454 = r22452 * r22453;
        double r22455 = n;
        double r22456 = r22454 * r22455;
        double r22457 = r22448 - r22449;
        double r22458 = r22457 / r22452;
        double r22459 = pow(r22456, r22458);
        double r22460 = r22451 * r22459;
        return r22460;
}


double f_of(float k, float n) {
        float r22461 = n;
        float r22462 = r22461 + r22461;
        float r22463 = atan2(1.0, 0.0);
        float r22464 = r22462 * r22463;
        float r22465 = 1;
        float r22466 = 2;
        float r22467 = r22465 / r22466;
        float r22468 = pow(r22464, r22467);
        float r22469 = k;
        float r22470 = r22469 / r22466;
        float r22471 = pow(r22464, r22470);
        float r22472 = r22468 / r22471;
        float r22473 = sqrt(r22469);
        float r22474 = r22472 / r22473;
        return r22474;
}

double f_od(double k, double n) {
        double r22475 = n;
        double r22476 = r22475 + r22475;
        double r22477 = atan2(1.0, 0.0);
        double r22478 = r22476 * r22477;
        double r22479 = 1;
        double r22480 = 2;
        double r22481 = r22479 / r22480;
        double r22482 = pow(r22478, r22481);
        double r22483 = k;
        double r22484 = r22483 / r22480;
        double r22485 = pow(r22478, r22484);
        double r22486 = r22482 / r22485;
        double r22487 = sqrt(r22483);
        double r22488 = r22486 / r22487;
        return r22488;
}

void mpfr_fmod2(mpfr_t r, mpfr_t n, mpfr_t d, mpfr_rnd_t rmd) {
        mpfr_fmod(r, n, d, rmd);
        if (mpfr_cmp_ui(r, 0) < 0) mpfr_add(r, r, d, rmd);
}


static mpfr_t r22489, r22490, r22491, r22492, r22493, r22494, r22495, r22496, r22497, r22498, r22499, r22500, r22501;

void setup_mpfr_f_im() {
        mpfr_set_default_prec(1424);
        mpfr_init_set_str(r22489, "1", 10, MPFR_RNDN);
        mpfr_init(r22490);
        mpfr_init(r22491);
        mpfr_init(r22492);
        mpfr_init_set_str(r22493, "2", 10, MPFR_RNDN);
        mpfr_init(r22494);
        mpfr_init(r22495);
        mpfr_init(r22496);
        mpfr_init(r22497);
        mpfr_init(r22498);
        mpfr_init(r22499);
        mpfr_init(r22500);
        mpfr_init(r22501);
}

double f_im(double k, double n) {
        ;
        mpfr_set_d(r22490, k, MPFR_RNDN);
        mpfr_sqrt(r22491, r22490, MPFR_RNDN);
        mpfr_div(r22492, r22489, r22491, MPFR_RNDN);
        ;
        mpfr_const_pi(r22494, MPFR_RNDN);
        mpfr_mul(r22495, r22493, r22494, MPFR_RNDN);
        mpfr_set_d(r22496, n, MPFR_RNDN);
        mpfr_mul(r22497, r22495, r22496, MPFR_RNDN);
        mpfr_sub(r22498, r22489, r22490, MPFR_RNDN);
        mpfr_div(r22499, r22498, r22493, MPFR_RNDN);
        mpfr_pow(r22500, r22497, r22499, MPFR_RNDN);
        mpfr_mul(r22501, r22492, r22500, MPFR_RNDN);
        return mpfr_get_d(r22501, MPFR_RNDN);
}

static mpfr_t r22502, r22503, r22504, r22505, r22506, r22507, r22508, r22509, r22510, r22511, r22512, r22513, r22514, r22515;

void setup_mpfr_f_fm() {
        mpfr_set_default_prec(1424);
        mpfr_init(r22502);
        mpfr_init(r22503);
        mpfr_init(r22504);
        mpfr_init(r22505);
        mpfr_init_set_str(r22506, "1", 10, MPFR_RNDN);
        mpfr_init_set_str(r22507, "2", 10, MPFR_RNDN);
        mpfr_init(r22508);
        mpfr_init(r22509);
        mpfr_init(r22510);
        mpfr_init(r22511);
        mpfr_init(r22512);
        mpfr_init(r22513);
        mpfr_init(r22514);
        mpfr_init(r22515);
}

double f_fm(double k, double n) {
        mpfr_set_d(r22502, n, MPFR_RNDN);
        mpfr_add(r22503, r22502, r22502, MPFR_RNDN);
        mpfr_const_pi(r22504, MPFR_RNDN);
        mpfr_mul(r22505, r22503, r22504, MPFR_RNDN);
        ;
        ;
        mpfr_div(r22508, r22506, r22507, MPFR_RNDN);
        mpfr_pow(r22509, r22505, r22508, MPFR_RNDN);
        mpfr_set_d(r22510, k, MPFR_RNDN);
        mpfr_div(r22511, r22510, r22507, MPFR_RNDN);
        mpfr_pow(r22512, r22505, r22511, MPFR_RNDN);
        mpfr_div(r22513, r22509, r22512, MPFR_RNDN);
        mpfr_sqrt(r22514, r22510, MPFR_RNDN);
        mpfr_div(r22515, r22513, r22514, MPFR_RNDN);
        return mpfr_get_d(r22515, MPFR_RNDN);
}

static mpfr_t r22516, r22517, r22518, r22519, r22520, r22521, r22522, r22523, r22524, r22525, r22526, r22527, r22528, r22529;

void setup_mpfr_f_dm() {
        mpfr_set_default_prec(1424);
        mpfr_init(r22516);
        mpfr_init(r22517);
        mpfr_init(r22518);
        mpfr_init(r22519);
        mpfr_init_set_str(r22520, "1", 10, MPFR_RNDN);
        mpfr_init_set_str(r22521, "2", 10, MPFR_RNDN);
        mpfr_init(r22522);
        mpfr_init(r22523);
        mpfr_init(r22524);
        mpfr_init(r22525);
        mpfr_init(r22526);
        mpfr_init(r22527);
        mpfr_init(r22528);
        mpfr_init(r22529);
}

double f_dm(double k, double n) {
        mpfr_set_d(r22516, n, MPFR_RNDN);
        mpfr_add(r22517, r22516, r22516, MPFR_RNDN);
        mpfr_const_pi(r22518, MPFR_RNDN);
        mpfr_mul(r22519, r22517, r22518, MPFR_RNDN);
        ;
        ;
        mpfr_div(r22522, r22520, r22521, MPFR_RNDN);
        mpfr_pow(r22523, r22519, r22522, MPFR_RNDN);
        mpfr_set_d(r22524, k, MPFR_RNDN);
        mpfr_div(r22525, r22524, r22521, MPFR_RNDN);
        mpfr_pow(r22526, r22519, r22525, MPFR_RNDN);
        mpfr_div(r22527, r22523, r22526, MPFR_RNDN);
        mpfr_sqrt(r22528, r22524, MPFR_RNDN);
        mpfr_div(r22529, r22527, r22528, MPFR_RNDN);
        return mpfr_get_d(r22529, MPFR_RNDN);
}