void mpn_mul_fft_main(mp_limb_t * r1, mp_limb_t * i1, mp_size_t n1,
mp_limb_t * i2, mp_size_t n2)
{
mp_size_t off, depth = 6;
mp_size_t w = 1;
mp_size_t n = ((mp_size_t) 1 << depth);
mp_bitcnt_t bits = (n*w - (depth+1))/2;
mp_bitcnt_t bits1 = n1*FLINT_BITS;
mp_bitcnt_t bits2 = n2*FLINT_BITS;
mp_size_t j1 = (bits1 - 1)/bits + 1;
mp_size_t j2 = (bits2 - 1)/bits + 1;
FLINT_ASSERT(n1 > 0);
FLINT_ASSERT(n2 > 0);
FLINT_ASSERT(j1 + j2 - 1 > 2*n);
while (j1 + j2 - 1 > 4*n) /* find initial n, w */
{
if (w == 1) w = 2;
else
{
depth++;
w = 1;
n *= 2;
}
bits = (n*w - (depth+1))/2;
j1 = (bits1 - 1)/bits + 1;
j2 = (bits2 - 1)/bits + 1;
}
if (depth < 11)
{
mp_size_t wadj = 1;
off = fft_tuning_table[depth - 6][w - 1]; /* adjust n and w */
depth -= off;
n = ((mp_size_t) 1 << depth);
w *= ((mp_size_t) 1 << (2*off));
if (depth < 6) wadj = ((mp_size_t) 1 << (6 - depth));
if (w > wadj)
{
do { /* see if a smaller w will work */
w -= wadj;
bits = (n*w - (depth+1))/2;
j1 = (bits1 - 1)/bits + 1;
j2 = (bits2 - 1)/bits + 1;
} while (j1 + j2 - 1 <= 4*n && w > wadj);
w += wadj;
}
mul_truncate_sqrt2(r1, i1, n1, i2, n2, depth, w);
} else
mul_mfa_truncate_sqrt2(r1, i1, n1, i2, n2, depth, w);
}
int bernoulli_mod_p_mpz(unsigned long *res, unsigned long p)
{
FLINT_ASSERT(p > 2);
FLINT_ASSERT(z_isprime(p) == 1);
unsigned long g, g_inv, g_sqr, g_sqr_inv;
double p_inv = z_precompute_inverse(p);
g = z_primitive_root(p);
if(!g)
{
return FALSE;
}
g_inv = z_invert(g, p);
g_sqr = z_mulmod_precomp(g, g, p, p_inv);
g_sqr_inv = z_mulmod_precomp(g_inv, g_inv, p, p_inv);
unsigned long poly_size = (p-1)/2;
int is_odd = poly_size % 2;
unsigned long g_power, g_power_inv;
g_power = g_inv;
g_power_inv = 1;
// constant is (g-1)/2 mod p
unsigned long constant;
if(g % 2)
{
constant = (g-1)/2;
}
else
{
constant = (g+p-1)/2;
}
// fudge holds g^{i^2}, fudge_inv holds g^{-i^2}
unsigned long fudge, fudge_inv;
fudge = fudge_inv = 1;
// compute the polynomials F(X) and G(X)
mpz_poly_t F, G;
mpz_poly_init2(F, poly_size);
mpz_poly_init2(G, poly_size);
unsigned long i, temp, h;
for(i = 0; i < poly_size; i++)
{
// compute h(g^i)/g^i (h(x) is as in latex notes)
temp = g * g_power;
h = z_mulmod_precomp(p + constant - (temp / p), g_power_inv, p, p_inv);
g_power = z_mod_precomp(temp, p, p_inv);
g_power_inv = z_mulmod_precomp(g_power_inv, g_inv, p, p_inv);
// store coefficient g^{i^2} h(g^i)/g^i
mpz_poly_set_coeff_ui(G, i, z_mulmod_precomp(h, fudge, p, p_inv));
mpz_poly_set_coeff_ui(F, i, fudge_inv);
// update fudge and fudge_inv
fudge = z_mulmod_precomp(z_mulmod_precomp(fudge, g_power, p, p_inv), z_mulmod_precomp(g_power, g, p, p_inv), p, p_inv);
fudge_inv = z_mulmod_precomp(z_mulmod_precomp(fudge_inv, g_power_inv, p, p_inv), z_mulmod_precomp(g_power_inv, g, p, p_inv), p, p_inv);
}
mpz_poly_set_coeff_ui(F, 0, 0);
// step 2: multiply the polynomials...
mpz_poly_t product;
mpz_poly_init(product);
mpz_poly_mul(product, G, F);
// step 3: assemble the result...
unsigned long g_sqr_power, value;
g_sqr_power = g_sqr;
fudge = g;
res[0] = 1;
mpz_t value_coeff;
mpz_init(value_coeff);
unsigned long value_coeff_ui;
for(i = 1; i < poly_size; i++)
{
mpz_poly_get_coeff(value_coeff, product, i + poly_size);
value = mpz_fdiv_ui(value_coeff, p);
value = z_mod_precomp(mpz_poly_get_coeff_ui(product, i + poly_size), p, p_inv);
mpz_poly_get_coeff(value_coeff, product, i);
if(is_odd)
{
value = z_mod_precomp(mpz_poly_get_coeff_ui(G, i) + mpz_fdiv_ui(value_coeff, p) + p - value, p, p_inv);
}
else
{
value = z_mod_precomp(mpz_poly_get_coeff_ui(G, i) + mpz_fdiv_ui(value_coeff, p) + value, p, p_inv);
}
value = z_mulmod_precomp(z_mulmod_precomp(z_mulmod_precomp(4, i, p, p_inv), fudge, p, p_inv), value, p, p_inv);
value = z_mulmod_precomp(value, z_invert(p+1-g_sqr_power, p), p, p_inv);
res[i] = value;
g_sqr_power = z_mulmod_precomp(g_sqr_power, g, p, p_inv);
fudge = z_mulmod_precomp(fudge, g_sqr_power, p, p_inv);
g_sqr_power = z_mulmod_precomp(g_sqr_power, g, p, p_inv);
}
mpz_clear(value_coeff);
mpz_poly_clear(F);
mpz_poly_clear(G);
mpz_poly_clear(product);
return TRUE;
}
