inverse seems to give incorrect results [solved]

[niekbouman]

Update:

problem solved. Inverse was "GF11::inv" was computed as the modular inverse, but should be the negated modular inverse. (This key fact is missing in the comments in Fp_model.hpp)

Changing the following line (in Fp_model.hpp)

static mp_limb_t inv; // modulus^(-1) mod W, where W = 2^(word size)

into

static mp_limb_t inv; // -modulus^(-1) mod W, where W = 2^(word size)

would make this more clear.

original post

Hello developers,
First of all, thank you for releasing your work under the mit license.

As a sanity check, I tried to use libff for the field GF(11).
However, if I compute an inverse, I get an incorrect result.
Either I set up the field in a wrong way, or there is something wrong with the inverse function.

header file modulus.hpp:

#include <libff/algebra/fields/bigint.hpp>
auto mymodulus = libff::bigint<1>("11");

and main cpp file

#include "modulus.hpp"

//...

using namespace libff;
extern bigint<1L> mymodulus;
using GF11 = Fp_model<1L,mymodulus>;

GF11::euler = bigint<1>("5");
GF11::t = bigint<1>("5");
GF11::t_minus_1_over_2 = bigint<1>("2");
GF11::Rsquared = bigint<1>("3");
GF11::Rcubed = bigint<1>("4");
GF11::s = 1;
GF11::num_bits = 4;
GF11::inv = 3353953467947191203UL;

auto field_elem = GF11(5UL);

field_elem.inverse().print();

The program then prints 2, (clang 3.9 on mac os 10.9 mavericks)
while the multiplicative inverse of 5 in GF(11) should be 9...

best,
Niek