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Negative values of n are
supported by mpz_bin_ui , using the identity bin(-n,k) = (-1)^k * bin(n+k-1,k) , see Knuth volume 1 section 1.2.6
part G. Function: void mpz_fib_ui (mpz_t fn , unsigned long int n ) ¶ Function: void mpz_fib2_ui (mpz_t fn , mpz_t fnsub1 , unsigned long int n ) ¶ mpz_fib_ui sets fn to F[n] , the n th Fibonacci
number. mpz_fib2_ui sets fn to F[n] , and fnsub1 to F[n-1] .