Determines f^i(y) with f(x) = (x^2 + a) mod n fast, using gmplib

fn.c

/*  gcc -O3 -Wall -Wextra -pedantic -fomit-frame-pointer -m64 -mtune=skylake -march=broadwell -o fn fn.c -lgmp

./fn n a y i
  Determines f^i(y) with f(x) = (x^2 + a) mod n
*/
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <inttypes.h>
#include <time.h>
#include <sys/time.h>
#include <assert.h>

#include <gmp.h>

void fn(mpz_t n, mpz_t y, unsigned long i)
{
  mpz_t t, t2;

  mpz_inits (t, t2, NULL);
  for (; i > 0; --i)
  {
    mpz_mul (t, y, y);
    mpz_add_ui (y, t, 1);
    mpz_mod (y, y, n);
  }
  gmp_printf ("%Zd\n", y);
}

int main (int argc, char *argv[])
{
  mpz_t n, y;
  unsigned long i;

  assert(argc==4);

  mpz_inits(n, y, i, NULL);

  struct timespec t0, t1;

  mpz_set_str (n, argv[1], 0);
  mpz_set_str (y, argv[2], 0);
  assert(atol(argv[3]) >= 0);
  i = (unsigned long) atol(argv[3]);

  clock_gettime(CLOCK_REALTIME, &t0);
  fn(n, y, i);
  clock_gettime(CLOCK_REALTIME, &t1);

  printf(" %ldns\n", (t1.tv_sec-t0.tv_sec) * 1000000000 + t1.tv_nsec - t0.tv_nsec);

  exit (0);
}

https://www.raspberrypi.org/forums/viewtopic.php?f=33&t=312344&p=1898988#p1898988

Used to compute values for different i (in square brackets) in this ρ digraph (i=216698+4782220904 took 5.5 minutes):

Revision 2 fixes lint complaint:
https://www.raspberrypi.org/forums/viewtopic.php?f=33&t=317340&p=1899285#p1899285