void
fmpr_divappr_abs_ubound(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec)
{
if (fmpr_is_special(x) || fmpr_is_special(y) || fmpz_is_pm1(fmpr_manref(y)))
{
fmpr_div(z, x, y, prec, FMPR_RND_UP);
fmpr_abs(z, z);
}
else
{
fmpz_t t, u;
slong xbits, ybits, tbits, ubits, shift;
xbits = fmpz_bits(fmpr_manref(x));
ybits = fmpz_bits(fmpr_manref(y));
fmpz_init(t);
fmpz_init(u);
ubits = FLINT_MIN(ybits, prec);
tbits = prec + ubits + 1;
/* upper bound for |x|, shifted */
if (xbits <= tbits)
{
fmpz_mul_2exp(t, fmpr_manref(x), tbits - xbits);
fmpz_abs(t, t);
}
else if (fmpz_sgn(fmpr_manref(x)) > 0)
{
fmpz_cdiv_q_2exp(t, fmpr_manref(x), xbits - tbits);
}
else
{
fmpz_fdiv_q_2exp(t, fmpr_manref(x), xbits - tbits);
fmpz_neg(t, t);
}
/* lower bound for |y|, shifted */
if (ybits <= ubits)
fmpz_mul_2exp(u, fmpr_manref(y), ubits - ybits);
else
fmpz_tdiv_q_2exp(u, fmpr_manref(y), ybits - ubits);
fmpz_abs(u, u);
fmpz_cdiv_q(fmpr_manref(z), t, u);
shift = (ubits - ybits) - (tbits - xbits);
fmpz_sub(fmpr_expref(z), fmpr_expref(x), fmpr_expref(y));
if (shift >= 0)
fmpz_add_ui(fmpr_expref(z), fmpr_expref(z), shift);
else
fmpz_sub_ui(fmpr_expref(z), fmpr_expref(z), -shift);
_fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, FMPR_RND_UP);
fmpz_clear(t);
fmpz_clear(u);
}
}
static void
fmpz_mul_or_div_2exp(fmpz_t x, fmpz_t y, slong s)
{
if (s >= 0)
fmpz_mul_2exp(x, y, s);
else
fmpz_fdiv_q_2exp(x, y, -s);
}
void fmpq_mul_2exp(fmpq_t res, const fmpq_t x, mp_bitcnt_t exp)
{
if (fmpq_is_zero(x) || exp == 0)
{
fmpq_set(res, x);
}
else
{
mp_bitcnt_t v = fmpz_val2(fmpq_denref(x));
if (exp <= v)
{
fmpz_set(fmpq_numref(res), fmpq_numref(x));
fmpz_fdiv_q_2exp(fmpq_denref(res), fmpq_denref(x), exp);
}
else
{
fmpz_mul_2exp(fmpq_numref(res), fmpq_numref(x), exp - v);
fmpz_fdiv_q_2exp(fmpq_denref(res), fmpq_denref(x), v);
}
}
}
/* Balanced product of linear factors (x+alpha_i) using
fixed-point arithmetic with prec bits */
static void
balanced_product(fmpz * c, fmpz * alpha, slong len, slong prec)
{
if (len == 1)
{
fmpz_one(c + 1);
fmpz_mul_2exp(c + 1, c + 1, prec);
fmpz_set(c, alpha);
}
else if (len == 2)
{
fmpz_mul(c, alpha, alpha + 1);
fmpz_fdiv_q_2exp(c, c, prec);
fmpz_add(c + 1, alpha, alpha + 1);
fmpz_one(c + 2);
fmpz_mul_2exp(c + 2, c + 2, prec);
}
else
{
fmpz *L, *R;
slong i, m;
m = len / 2;
L = _fmpz_vec_init(len + 2);
R = L + m + 1;
balanced_product(L, alpha, m, prec);
balanced_product(R, alpha + m, len - m, prec);
_fmpz_poly_mul(c, R, len - m + 1, L, m + 1);
for (i = 0; i < len + 1; i++)
fmpz_fdiv_q_2exp(c + i, c + i, prec);
_fmpz_vec_clear(L, len + 2);
}
}
void _fmpz_vec_scalar_smod_fmpz(fmpz *res, const fmpz *vec, slong len, const fmpz_t p)
{
slong i;
fmpz_t pdiv2;
fmpz_init(pdiv2);
fmpz_fdiv_q_2exp(pdiv2, p, 1);
for (i = 0; i < len; i++)
{
fmpz_mod(res + i, vec + i, p);
if (fmpz_cmp(res + i, pdiv2) > 0)
{
fmpz_sub(res + i, res + i, p);
}
}
fmpz_clear(pdiv2);
}
void
fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha)
{
long r, c, i, j, d;
fmpz_t tmp;
r = mat->r;
c = mat->c;
d = r;
if (c != r)
{
printf("Exception: fmpz_mat_ajtai called on an ill-formed matrix\n");
abort();
}
fmpz_init(tmp);
for (i = 0; i < d; i++)
{
mp_bitcnt_t bits = (mp_bitcnt_t) pow((double) (2 * d - i), alpha);
fmpz_one(tmp);
fmpz_mul_2exp(tmp, tmp, bits);
fmpz_sub_ui(tmp, tmp, 1);
fmpz_randm(mat->rows[i] + i, state, tmp);
fmpz_add_ui(mat->rows[i] + i, mat->rows[i] + i, 2);
fmpz_fdiv_q_2exp(mat->rows[i] + i, mat->rows[i] + i, 1);
for (j = i + 1; j <= d; j++)
{
fmpz_randm(mat->rows[j] + i, state, tmp);
if (n_randint(state, 2))
fmpz_neg(mat->rows[j] + i, mat->rows[j] + i);
fmpz_zero(mat->rows[i] + j);
}
}
fmpz_clear(tmp);
}
void
fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha)
{
const slong c = mat->c, r = mat->r, d = r;
slong i, j;
fmpz_t tmp;
if (c != r)
{
flint_printf("Exception (fmpz_mat_ajtai): Non-square matrix.\n");
abort();
}
fmpz_init(tmp);
for (i = 0; i < d; i++)
{
mp_bitcnt_t bits = (mp_bitcnt_t) pow((double) (2 * d - i), alpha);
fmpz_one(tmp);
fmpz_mul_2exp(tmp, tmp, bits);
fmpz_sub_ui(tmp, tmp, 1);
fmpz_randm(mat->rows[i] + i, state, tmp);
fmpz_add_ui(mat->rows[i] + i, mat->rows[i] + i, 2);
fmpz_fdiv_q_2exp(mat->rows[i] + i, mat->rows[i] + i, 1);
for (j = i + 1; j <= d; j++)
{
fmpz_randm(mat->rows[j] + i, state, tmp);
if (n_randint(state, 2))
fmpz_neg(mat->rows[j] + i, mat->rows[j] + i);
fmpz_zero(mat->rows[i] + j);
}
}
fmpz_clear(tmp);
}
void
test0(slong b)
{
fmpz_t M; fmpz_init_set_ui(M,1);
fmpz_mul_2exp(M,M,(ulong)b);
test1_ui(b,M,0);
test1_ui(b,M,1);
test1_ui(b,M,(mp_limb_t)-1);
test1(b,M,M); // M
fmpz_t n; fmpz_init_set(n,M);
fmpz_add_ui(n,M,1);
test1(b,M,n); // M+1
fmpz_sub_ui(n,M,1);
test1(b,M,n); // M-1
slong i;
fmpz_t m; fmpz_init(m);
fmpz_t Mhalf; fmpz_init(Mhalf);
fmpz_fdiv_q_2exp(Mhalf,M,1);
for(i=100;i--;)
{
fmpz_randm(m,rst,n); // m = random(M-1)
test1(b,M,m);
fmpz_add(m,m,Mhalf); // m+M/2
test1(b,M,m);
}
fmpz_mul_2exp(m,M,1);
test1(b,M,m); // M<<1
fmpz_mul_2exp(m,m,1);
test1(b,M,m); // M<<2
fmpz_mul_2exp(m,m,1);
test1(b,M,m); // M<<3
fmpz_mul(m,m,M);
test1(b,M,m); // M*(M<<3)
fmpz_clear(Mhalf);
fmpz_clear(m);
fmpz_clear(n);
fmpz_clear(M);
}
void
_arith_cos_minpoly(fmpz * coeffs, slong d, ulong n)
{
slong i, j;
fmpz * alpha;
fmpz_t half;
mpfr_t t, u;
mp_bitcnt_t prec;
slong exp;
if (n <= MAX_32BIT)
{
for (i = 0; i <= d; i++)
fmpz_set_si(coeffs + i, lookup_table[n - 1][i]);
return;
}
/* Direct formula for odd primes > 3 */
if (n_is_prime(n))
{
slong s = (n - 1) / 2;
switch (s % 4)
{
case 0:
fmpz_set_si(coeffs, WORD(1));
fmpz_set_si(coeffs + 1, -s);
break;
case 1:
fmpz_set_si(coeffs, WORD(1));
fmpz_set_si(coeffs + 1, s + 1);
break;
case 2:
fmpz_set_si(coeffs, WORD(-1));
fmpz_set_si(coeffs + 1, s);
break;
case 3:
fmpz_set_si(coeffs, WORD(-1));
fmpz_set_si(coeffs + 1, -s - 1);
break;
}
for (i = 2; i <= s; i++)
{
slong b = (s - i) % 2;
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, s+i-b, s+2-b-i);
fmpz_divexact2_uiui(coeffs + i, coeffs + i, i, i-1);
fmpz_neg(coeffs + i, coeffs + i);
}
return;
}
prec = magnitude_bound(d) + 5 + FLINT_BIT_COUNT(d);
alpha = _fmpz_vec_init(d);
fmpz_init(half);
mpfr_init2(t, prec);
mpfr_init2(u, prec);
fmpz_one(half);
fmpz_mul_2exp(half, half, prec - 1);
mpfr_const_pi(t, prec);
mpfr_div_ui(t, t, n, MPFR_RNDN);
for (i = j = 0; j < d; i++)
{
if (n_gcd(n, i) == 1)
{
mpfr_mul_ui(u, t, 2 * i, MPFR_RNDN);
mpfr_cos(u, u, MPFR_RNDN);
mpfr_neg(u, u, MPFR_RNDN);
exp = mpfr_get_z_2exp(_fmpz_promote(alpha + j), u);
_fmpz_demote_val(alpha + j);
fmpz_mul_or_div_2exp(alpha + j, alpha + j, exp + prec);
j++;
}
}
balanced_product(coeffs, alpha, d, prec);
/* Scale and round */
for (i = 0; i < d + 1; i++)
{
slong r = d;
if ((n & (n - 1)) == 0)
r--;
fmpz_mul_2exp(coeffs + i, coeffs + i, r);
fmpz_add(coeffs + i, coeffs + i, half);
fmpz_fdiv_q_2exp(coeffs + i, coeffs + i, prec);
}
fmpz_clear(half);
mpfr_clear(t);
mpfr_clear(u);
_fmpz_vec_clear(alpha, d);
}
int
arb_get_unique_fmpz(fmpz_t z, const arb_t x)
{
if (!arb_is_finite(x))
{
return 0;
}
else if (arb_is_exact(x))
{
/* x = b*2^e, e >= 0 */
if (arf_is_int(arb_midref(x)))
{
/* arf_get_fmpz aborts on overflow */
arf_get_fmpz(z, arb_midref(x), ARF_RND_DOWN);
return 1;
}
else
{
return 0;
}
}
/* if the radius is >= 1, there are at least two integers */
else if (mag_cmp_2exp_si(arb_radref(x), 0) >= 0)
{
return 0;
}
/* there are 0 or 1 integers if the radius is < 1 */
else
{
fmpz_t a, b, exp;
int res;
/* if the midpoint is exactly an integer, it is what we want */
if (arf_is_int(arb_midref(x)))
{
/* arf_get_fmpz aborts on overflow */
arf_get_fmpz(z, arb_midref(x), ARF_RND_DOWN);
return 1;
}
fmpz_init(a);
fmpz_init(b);
fmpz_init(exp);
/* if the radius is tiny, it can't be an integer */
arf_bot(a, arb_midref(x));
if (fmpz_cmp(a, MAG_EXPREF(arb_radref(x))) > 0)
{
res = 0;
}
else
{
arb_get_interval_fmpz_2exp(a, b, exp, x);
if (COEFF_IS_MPZ(*exp))
{
flint_printf("arb_get_unique_fmpz: input too large\n");
abort();
}
if (*exp >= 0)
{
res = fmpz_equal(a, b);
if (res)
{
fmpz_mul_2exp(a, a, *exp);
fmpz_mul_2exp(b, b, *exp);
}
}
else
{
fmpz_cdiv_q_2exp(a, a, -(*exp));
fmpz_fdiv_q_2exp(b, b, -(*exp));
res = fmpz_equal(a, b);
}
if (res)
fmpz_set(z, a);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(exp);
return res;
}
}
