void mpn_normmod_2expp1(mp_limb_t * t, mp_size_t limbs)
{
mp_limb_signed_t hi = t[limbs];
if (hi)
{
t[limbs] = 0;
mpn_addmod_2expp1_1(t, limbs, -hi);
/* hi will now be in [-1,1] */
if ((hi = t[limbs]))
{
t[limbs] = 0;
mpn_addmod_2expp1_1(t, limbs, -hi);
if (t[limbs] == ~(mp_limb_signed_t) 0) /* if we now have -1 (very unlikely) */
{
t[limbs] = 0;
mpn_addmod_2expp1_1(t, limbs, 1);
}
}
}
}
void fft_adjust_sqrt2(mp_limb_t * r, mp_limb_t * i1,
mp_size_t i, mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp)
{
mp_bitcnt_t wn = limbs*FLINT_BITS;
mp_limb_t cy;
mp_size_t j = i/2, k = w/2;
mp_size_t y;
mp_bitcnt_t b1;
int negate = 0;
b1 = j + wn/4 + i*k;
if (b1 >= wn)
{
negate = 1;
b1 -= wn;
}
y = b1/FLINT_BITS;
b1 = b1%FLINT_BITS;
/* multiply by 2^{j + wn/4 + i*k} */
if (y)
{
mpn_copyi(temp + y, i1, limbs - y);
cy = mpn_neg_n(temp, i1 + limbs - y, y);
temp[limbs] = 0;
mpn_addmod_2expp1_1(temp + y, limbs - y, -i1[limbs]);
mpn_sub_1(temp + y, temp + y, limbs - y + 1, cy);
mpn_mul_2expmod_2expp1(r, temp, limbs, b1);
} else
mpn_mul_2expmod_2expp1(r, i1, limbs, b1);
/* multiply by 2^{wn/2} */
y = limbs/2;
cy = 0;
mpn_copyi(temp + y, r, limbs - y);
temp[limbs] = 0;
if (y) cy = mpn_neg_n(temp, r + limbs - y, y);
mpn_addmod_2expp1_1(temp + y, limbs - y, -r[limbs]);
mpn_sub_1(temp + y, temp + y, limbs - y + 1, cy);
/* shift by an additional half limb (rare) */
if (limbs & 1)
mpn_mul_2expmod_2expp1(temp, temp, limbs, FLINT_BITS/2);
/* subtract */
if (negate)
mpn_sub_n(r, r, temp, limbs + 1);
else
mpn_sub_n(r, temp, r, limbs + 1);
}
void mpir_butterfly_lshB(mp_ptr t, mp_ptr u, mp_ptr i1,
mp_ptr i2, mp_size_t limbs, mp_size_t x, mp_size_t y)
{
mp_limb_t cy, cy1, cy2;
if (x == 0)
{
if (y == 0)
cy = mpn_sumdiff_n(t + x, u + y, i1, i2, limbs + 1);
else
{
cy = mpn_sumdiff_n(t, u + y, i1, i2, limbs - y);
u[limbs] = -(cy&1);
cy1 = cy>>1;
cy = mpn_sumdiff_n(t + limbs - y, u, i2 + limbs - y, i1 + limbs - y, y);
t[limbs] = cy>>1;
mpn_add_1(t + limbs - y, t + limbs - y, y + 1, cy1);
cy1 = -(cy&1) + (i2[limbs] - i1[limbs]);
mpn_addmod_2expp1_1(u + y, limbs - y, cy1);
cy1 = -(i1[limbs] + i2[limbs]);
mpn_addmod_2expp1_1(t, limbs, cy1);
}
} else if (y == 0)
void mpir_fft_adjust(mp_ptr r, mp_ptr i1, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w)
{
mp_bitcnt_t b1;
mp_limb_t cy;
mp_size_t x;
b1 = i*w;
x = b1/GMP_LIMB_BITS;
b1 = b1%GMP_LIMB_BITS;
if (x)
{
mpn_copyi(r + x, i1, limbs - x);
r[limbs] = 0;
cy = mpn_neg_n(r, i1 + limbs - x, x);
mpn_addmod_2expp1_1(r + x, limbs - x, -i1[limbs]);
mpn_sub_1(r + x, r + x, limbs - x + 1, cy);
mpn_mul_2expmod_2expp1(r, r, limbs, b1);
} else
mpn_mul_2expmod_2expp1(r, i1, limbs, b1);
}
void mpir_fft_mulmod_2expp1(mp_ptr r1, mp_srcptr i1, mp_srcptr i2,
mp_size_t r_limbs, mp_bitcnt_t depth, mp_bitcnt_t w)
{
mp_size_t n = (((mp_size_t)1)<<depth);
mp_bitcnt_t bits1 = (r_limbs*GMP_LIMB_BITS)/(2*n);
mp_size_t limb_add, limbs = (n*w)/GMP_LIMB_BITS;
mp_size_t size = limbs + 1;
mp_size_t i, j, ll;
mp_limb_t * ptr;
mp_limb_t ** ii, ** jj, *tt, *t1, *t2, *s1, *r, *ii0, *jj0;
mp_limb_t c;
TMP_DECL;
TMP_MARK;
ii = TMP_BALLOC_MP_PTRS(2*(n + n*size) + 4*n + 5*size);
for (i = 0, ptr = (mp_ptr) ii + 2*n; i < 2*n; i++, ptr += size)
{
ii[i] = ptr;
}
ii0 = ptr;
t1 = ii0 + 2*n;
t2 = t1 + size;
s1 = t2 + size;
r = s1 + size;
tt = r + 2*n;
if (i1 != i2)
{
jj = TMP_BALLOC_MP_PTRS(2*(n + n*size) + 2*n);
for (i = 0, ptr = (mp_ptr) jj + 2*n; i < 2*n; i++, ptr += size)
{
jj[i] = ptr;
}
jj0 = ptr;
} else
{
jj = ii;
jj0 = ii0;
}
j = mpir_fft_split_bits(ii, i1, r_limbs, bits1, limbs);
for ( ; j < 2*n; j++)
mpn_zero(ii[j], limbs + 1);
for (i = 0; i < 2*n; i++)
ii0[i] = ii[i][0];
mpir_fft_negacyclic(ii, n, w, &t1, &t2, &s1);
for (j = 0; j < 2*n; j++)
mpn_normmod_2expp1(ii[j], limbs);
if (i1 != i2)
{
j = mpir_fft_split_bits(jj, i2, r_limbs, bits1, limbs);
for ( ; j < 2*n; j++)
mpn_zero(jj[j], limbs + 1);
for (i = 0; i < 2*n; i++)
jj0[i] = jj[i][0];
mpir_fft_negacyclic(jj, n, w, &t1, &t2, &s1);
}
for (j = 0; j < 2*n; j++)
{
if (i1 != i2) mpn_normmod_2expp1(jj[j], limbs);
c = 2*ii[j][limbs] + jj[j][limbs];
ii[j][limbs] = mpn_mulmod_2expp1_basecase(ii[j], ii[j], jj[j], c, n*w, tt);
}
mpir_ifft_negacyclic(ii, n, w, &t1, &t2, &s1);
mpir_fft_naive_convolution_1(r, ii0, jj0, 2*n);
for (j = 0; j < 2*n; j++)
{
mp_limb_t t, cy2;
mpn_div_2expmod_2expp1(ii[j], ii[j], limbs, depth + 1);
mpn_normmod_2expp1(ii[j], limbs);
t = ii[j][limbs];
ii[j][limbs] = r[j] - ii[j][0];
cy2 = mpn_add_1(ii[j], ii[j], limbs + 1, ii[j][limbs]);
add_ssaaaa(r[j], ii[j][limbs], 0, ii[j][limbs], 0, t);
if (cy2) r[j]++;
}
mpn_zero(r1, r_limbs + 1);
mpir_fft_combine_bits(r1, ii, 2*n - 1, bits1, limbs + 1, r_limbs + 1);
/*
as the negacyclic convolution has effectively done subtractions
some of the coefficients will be negative, so need to subtract p
*/
ll = 0;
limb_add = bits1/GMP_LIMB_BITS;
for (j = 0; j < 2*n - 2; j++)
{
if (r[j])
mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
else if ((mp_limb_signed_t) ii[j][limbs] < 0) /* coefficient was -ve */
{
mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
mpn_sub_1(r1 + ll + limbs + 1, r1 + ll + limbs + 1, r_limbs - limbs - ll, 1);
}
ll += limb_add;
}
/* penultimate coefficient, top bit was already ignored */
if (r[j] || (mp_limb_signed_t) ii[j][limbs] < 0) /* coefficient was -ve */
mpn_sub_1(r1 + ll + 1, r1 + ll + 1, r_limbs - ll, 1);
/* final coefficient wraps around */
if (limb_add)
r1[r_limbs] += mpn_add_n(r1 + r_limbs - limb_add, r1 + r_limbs - limb_add, ii[2*n - 1], limb_add);
c = mpn_sub_n(r1, r1, ii[2*n - 1] + limb_add, limbs + 1 - limb_add);
mpn_addmod_2expp1_1(r1 + limbs + 1 - limb_add, r_limbs - limbs - 1 + limb_add, -c);
mpn_normmod_2expp1(r1, r_limbs);
TMP_FREE;
}
