#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 r22368 = 1;
        float r22369 = k;
        float r22370 = sqrt(r22369);
        float r22371 = r22368 / r22370;
        float r22372 = 2;
        float r22373 = atan2(1.0, 0.0);
        float r22374 = r22372 * r22373;
        float r22375 = n;
        float r22376 = r22374 * r22375;
        float r22377 = r22368 - r22369;
        float r22378 = r22377 / r22372;
        float r22379 = pow(r22376, r22378);
        float r22380 = r22371 * r22379;
        return r22380;
}

double f_id(double k, double n) {
        double r22381 = 1;
        double r22382 = k;
        double r22383 = sqrt(r22382);
        double r22384 = r22381 / r22383;
        double r22385 = 2;
        double r22386 = atan2(1.0, 0.0);
        double r22387 = r22385 * r22386;
        double r22388 = n;
        double r22389 = r22387 * r22388;
        double r22390 = r22381 - r22382;
        double r22391 = r22390 / r22385;
        double r22392 = pow(r22389, r22391);
        double r22393 = r22384 * r22392;
        return r22393;
}


double f_of(float k, float n) {
        float r22394 = n;
        float r22395 = r22394 + r22394;
        float r22396 = atan2(1.0, 0.0);
        float r22397 = r22395 * r22396;
        float r22398 = 1;
        float r22399 = 2;
        float r22400 = r22398 / r22399;
        float r22401 = pow(r22397, r22400);
        float r22402 = k;
        float r22403 = r22402 / r22399;
        float r22404 = pow(r22397, r22403);
        float r22405 = r22401 / r22404;
        float r22406 = sqrt(r22402);
        float r22407 = r22405 / r22406;
        return r22407;
}

double f_od(double k, double n) {
        double r22408 = n;
        double r22409 = r22408 + r22408;
        double r22410 = atan2(1.0, 0.0);
        double r22411 = r22409 * r22410;
        double r22412 = 1;
        double r22413 = 2;
        double r22414 = r22412 / r22413;
        double r22415 = pow(r22411, r22414);
        double r22416 = k;
        double r22417 = r22416 / r22413;
        double r22418 = pow(r22411, r22417);
        double r22419 = r22415 / r22418;
        double r22420 = sqrt(r22416);
        double r22421 = r22419 / r22420;
        return r22421;
}

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 r22422, r22423, r22424, r22425, r22426, r22427, r22428, r22429, r22430, r22431, r22432, r22433, r22434;

void setup_mpfr_f_im() {
        mpfr_set_default_prec(1424);
        mpfr_init_set_str(r22422, "1", 10, MPFR_RNDN);
        mpfr_init(r22423);
        mpfr_init(r22424);
        mpfr_init(r22425);
        mpfr_init_set_str(r22426, "2", 10, MPFR_RNDN);
        mpfr_init(r22427);
        mpfr_init(r22428);
        mpfr_init(r22429);
        mpfr_init(r22430);
        mpfr_init(r22431);
        mpfr_init(r22432);
        mpfr_init(r22433);
        mpfr_init(r22434);
}

double f_im(double k, double n) {
        ;
        mpfr_set_d(r22423, k, MPFR_RNDN);
        mpfr_sqrt(r22424, r22423, MPFR_RNDN);
        mpfr_div(r22425, r22422, r22424, MPFR_RNDN);
        ;
        mpfr_const_pi(r22427, MPFR_RNDN);
        mpfr_mul(r22428, r22426, r22427, MPFR_RNDN);
        mpfr_set_d(r22429, n, MPFR_RNDN);
        mpfr_mul(r22430, r22428, r22429, MPFR_RNDN);
        mpfr_sub(r22431, r22422, r22423, MPFR_RNDN);
        mpfr_div(r22432, r22431, r22426, MPFR_RNDN);
        mpfr_pow(r22433, r22430, r22432, MPFR_RNDN);
        mpfr_mul(r22434, r22425, r22433, MPFR_RNDN);
        return mpfr_get_d(r22434, MPFR_RNDN);
}

static mpfr_t r22435, r22436, r22437, r22438, r22439, r22440, r22441, r22442, r22443, r22444, r22445, r22446, r22447, r22448;

void setup_mpfr_f_fm() {
        mpfr_set_default_prec(1424);
        mpfr_init(r22435);
        mpfr_init(r22436);
        mpfr_init(r22437);
        mpfr_init(r22438);
        mpfr_init_set_str(r22439, "1", 10, MPFR_RNDN);
        mpfr_init_set_str(r22440, "2", 10, MPFR_RNDN);
        mpfr_init(r22441);
        mpfr_init(r22442);
        mpfr_init(r22443);
        mpfr_init(r22444);
        mpfr_init(r22445);
        mpfr_init(r22446);
        mpfr_init(r22447);
        mpfr_init(r22448);
}

double f_fm(double k, double n) {
        mpfr_set_d(r22435, n, MPFR_RNDN);
        mpfr_add(r22436, r22435, r22435, MPFR_RNDN);
        mpfr_const_pi(r22437, MPFR_RNDN);
        mpfr_mul(r22438, r22436, r22437, MPFR_RNDN);
        ;
        ;
        mpfr_div(r22441, r22439, r22440, MPFR_RNDN);
        mpfr_pow(r22442, r22438, r22441, MPFR_RNDN);
        mpfr_set_d(r22443, k, MPFR_RNDN);
        mpfr_div(r22444, r22443, r22440, MPFR_RNDN);
        mpfr_pow(r22445, r22438, r22444, MPFR_RNDN);
        mpfr_div(r22446, r22442, r22445, MPFR_RNDN);
        mpfr_sqrt(r22447, r22443, MPFR_RNDN);
        mpfr_div(r22448, r22446, r22447, MPFR_RNDN);
        return mpfr_get_d(r22448, MPFR_RNDN);
}

static mpfr_t r22449, r22450, r22451, r22452, r22453, r22454, r22455, r22456, r22457, r22458, r22459, r22460, r22461, r22462;

void setup_mpfr_f_dm() {
        mpfr_set_default_prec(1424);
        mpfr_init(r22449);
        mpfr_init(r22450);
        mpfr_init(r22451);
        mpfr_init(r22452);
        mpfr_init_set_str(r22453, "1", 10, MPFR_RNDN);
        mpfr_init_set_str(r22454, "2", 10, MPFR_RNDN);
        mpfr_init(r22455);
        mpfr_init(r22456);
        mpfr_init(r22457);
        mpfr_init(r22458);
        mpfr_init(r22459);
        mpfr_init(r22460);
        mpfr_init(r22461);
        mpfr_init(r22462);
}

double f_dm(double k, double n) {
        mpfr_set_d(r22449, n, MPFR_RNDN);
        mpfr_add(r22450, r22449, r22449, MPFR_RNDN);
        mpfr_const_pi(r22451, MPFR_RNDN);
        mpfr_mul(r22452, r22450, r22451, MPFR_RNDN);
        ;
        ;
        mpfr_div(r22455, r22453, r22454, MPFR_RNDN);
        mpfr_pow(r22456, r22452, r22455, MPFR_RNDN);
        mpfr_set_d(r22457, k, MPFR_RNDN);
        mpfr_div(r22458, r22457, r22454, MPFR_RNDN);
        mpfr_pow(r22459, r22452, r22458, MPFR_RNDN);
        mpfr_div(r22460, r22456, r22459, MPFR_RNDN);
        mpfr_sqrt(r22461, r22457, MPFR_RNDN);
        mpfr_div(r22462, r22460, r22461, MPFR_RNDN);
        return mpfr_get_d(r22462, MPFR_RNDN);
}