// Computes q = exp(2 pi i tau).
static void compute_q(mpc_t q, mpc_t tau) {
mpc_t z0;
mpf_t f0, f1;
mpf_ptr fp0;
pbc_mpui pwr;
mpc_init(z0);
mpf_init(f0);
mpf_init(f1);
//compute z0 = 2 pi i tau
mpc_set(z0, tau);
//first remove integral part of Re(tau)
//since exp(2 pi i) = 1
//it seems |Re(tau)| < 1 anyway?
fp0 = mpc_re(z0);
mpf_trunc(f1, fp0);
mpf_sub(fp0, fp0, f1);
mpc_mul_mpf(z0, z0, pi);
mpc_mul_ui(z0, z0, 2);
mpc_muli(z0, z0);
//compute q = exp(z0);
//first write z0 = A + a + b i
//where A is a (negative) integer
//and a, b are in [-1, 1]
//compute e^A separately
fp0 = mpc_re(z0);
pwr = mpf_get_ui(fp0);
mpf_pow_ui(f0, recipeulere, pwr);
mpf_add_ui(fp0, fp0, pwr);
mpf_exp(f1, mpc_re(z0));
mpf_mul(f0, f1, f0);
mpc_cis(q, mpc_im(z0));
/*
old_mpc_exp(q, z0);
*/
mpc_mul_mpf(q, q, f0);
mpc_clear(z0);
mpf_clear(f0);
mpf_clear(f1);
}
void fft_init(size_t N, mpfr_prec_t prec)
{
if (prec) precision = prec;
if (N) LEN = N;
twid_fact = (Sequence) calloc(LEN, sizeof(mpc_t));
mpfr_init_set_d(ZERO, 0.0, MPFR_RNDA);
mpfr_init2(tmp, precision);
mpfr_const_pi(tmp, MPFR_RNDA);
mpfr_mul_si(tmp, tmp, -2, MPFR_RNDA);
mpfr_div_ui(tmp, tmp, N, MPFR_RNDA);
mpc_init2(min2pii, precision);
mpc_set_fr_fr(min2pii, ZERO, tmp, RND);
mpc_init2(temp, precision);
new_seq = (Sequence) calloc(N, sizeof(mpc_t));
size_t n = N / 2;
while (n--)
{
mpc_init2(twid_fact + n, precision);
mpc_mul_ui(twid_fact + n, min2pii, n, RND);
mpc_exp(twid_fact + n, twid_fact + n, RND);
}
}
mpcomplex operator*(const long int& a, const mpcomplex& b) {
mpc_t value;
mpc_init3( value , b.mpc_prec, b.mpc_prec );
mpc_mul_ui(value, b.mpc_val, a, b.default_rnd);
return mpcomplex(value);
}
void Lib_Mpcr_Mul_Ui(MpcrPtr f, MpcrPtr g, unsigned int x, long rnd)
{
mpc_mul_ui( (mpc_ptr) f, (mpc_ptr) g, x, (mpc_rnd_t) rnd);
}
