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);
}
}
void fmpz_multi_mod_ui(unsigned long * out, fmpz_t in, fmpz_comb_t comb, fmpz_t ** temp)
{
ulong i, j, k;
ulong n = comb->n;
long log_comb;
ulong size;
mp_limb_t * ptr;
ulong num;
unsigned long num_primes = comb->num_primes;
if (num_primes == 1) // we are reducing modulo a single prime which is assumed to be big enough
{
if ((long)in[0] > 0L) out[0] = in[1];
else if ((long)in[0] < 0L) out[0] = comb->primes[0] - in[1];
else out[0] = 0L;
return;
}
log_comb = n - 1;
// find level in comb with entries bigger than the input integer
log_comb = 0;
if ((long) in[0] < 0L)
while ((fmpz_bits(in) >= fmpz_bits(comb->comb[log_comb][0]) - 1) && (log_comb < comb->n - 1)) log_comb++;
else
while (fmpz_cmpabs(in, comb->comb[log_comb][0]) >= 0) log_comb++;
num = (1L<<(n - log_comb - 1));
// set each entry of this level of temp to the input integer
for (i = 0; i < num; i++)
{
fmpz_set(temp[log_comb][i], in);
}
log_comb--;
num *= 2;
// fill in other entries of temp by taking entries of temp at higher level mod pairs from comb
while (log_comb > FLINT_LOG_MULTI_MOD_CUTOFF) // keep going until we reach the basecase
{
for (i = 0, j = 0; i < num; i += 2, j++)
{
fmpz_mod(temp[log_comb][i], temp[log_comb + 1][j], comb->comb[log_comb][i]);
fmpz_mod(temp[log_comb][i+1], temp[log_comb + 1][j], comb->comb[log_comb][i+1]);
}
num *= 2;
log_comb--;
}
// do basecase
num /= 2;
log_comb++;
ulong stride = (1L << (log_comb + 1));
for (i = 0, j = 0; j < num_primes; i++, j += stride)
{
fmpz_multi_mod_ui_basecase(out + j, temp[log_comb][i], comb->primes + j, FLINT_MIN(stride, num_primes - j));
}
}
slong
fmpr_add_naive(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
slong shift, xsize, ysize;
if (fmpr_is_special(x) || fmpr_is_special(y))
{
return _fmpr_add_special(z, x, y, prec, rnd);
}
shift = _fmpz_sub_small(fmpr_expref(x), fmpr_expref(y));
if (shift == 0)
{
fmpz_add(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y));
fmpz_set(fmpr_expref(z), fmpr_expref(x));
}
else if (shift > 0)
{
ysize = _fmpz_size(fmpr_manref(y)) * FLINT_BITS;
/* x and y do not overlap */
if (shift > ysize && prec != FMPR_PREC_EXACT)
{
/* y does not overlap with result */
if (ysize + prec - (slong) fmpz_bits(fmpr_manref(x)) < shift)
{
return _fmpr_add_eps(z, x, fmpz_sgn(fmpr_manref(y)), prec, rnd);
}
}
fmpz_add_mul2exp(fmpr_manref(z), fmpr_manref(y), fmpr_manref(x), shift);
fmpz_set(fmpr_expref(z), fmpr_expref(y));
}
else
{
shift = -shift;
xsize = _fmpz_size(fmpr_manref(x)) * FLINT_BITS;
/* x and y do not overlap */
if (shift > xsize && prec != FMPR_PREC_EXACT)
{
/* y does not overlap with result */
if (xsize + prec - (slong) fmpz_bits(fmpr_manref(y)) < shift)
{
return _fmpr_add_eps(z, y, fmpz_sgn(fmpr_manref(x)), prec, rnd);
}
}
fmpz_add_mul2exp(fmpr_manref(z), fmpr_manref(x), fmpr_manref(y), shift);
fmpz_set(fmpr_expref(z), fmpr_expref(x));
}
return _fmpr_normalise(fmpr_manref(z), fmpr_expref(z), prec, rnd);
}
mp_bitcnt_t _fmpz_poly_2norm_normalised_bits(const fmpz * poly, long len)
{
fmpz_t norm;
mp_bitcnt_t bits;
fmpz_init(norm);
_fmpz_poly_2norm(norm, poly, len);
bits = fmpz_bits(norm);
fmpz_clear(norm);
return bits - fmpz_bits(poly + len - 1) + 1;
}
void
fmpz_poly_bit_unpack_unsigned(fmpz_poly_t poly, const fmpz_t f,
mp_bitcnt_t bit_size)
{
slong len;
mpz_t tmp;
if (fmpz_sgn(f) < 0)
{
flint_printf("Exception (fmpz_poly_bit_unpack_unsigned). Expected an unsigned value.\n");
abort();
}
if (bit_size == 0 || fmpz_is_zero(f))
{
fmpz_poly_zero(poly);
return;
}
len = (fmpz_bits(f) + bit_size - 1) / bit_size;
mpz_init2(tmp, bit_size*len);
flint_mpn_zero(tmp->_mp_d, tmp->_mp_alloc);
fmpz_get_mpz(tmp, f);
fmpz_poly_fit_length(poly, len);
_fmpz_poly_bit_unpack_unsigned(poly->coeffs, len, tmp->_mp_d, bit_size);
_fmpz_poly_set_length(poly, len);
_fmpz_poly_normalise(poly);
mpz_clear(tmp);
}
void
arb_log_arf_huge(arb_t z, const arf_t x, slong prec)
{
arf_t t;
arb_t c;
fmpz_t exp;
slong wp;
arf_init(t);
arb_init(c);
fmpz_init(exp);
fmpz_neg(exp, ARF_EXPREF(x));
arf_mul_2exp_fmpz(t, x, exp);
wp = prec + 4 - fmpz_bits(exp);
wp = FLINT_MAX(wp, 4);
arb_log_arf(z, t, wp);
arb_const_log2(c, prec + 4);
arb_submul_fmpz(z, c, exp, prec);
arf_clear(t);
arb_clear(c);
fmpz_clear(exp);
}
slong
fmpq_cfrac_bound(const fmpq_t x)
{
if (fmpz_is_one(fmpq_denref(x)))
return 1;
return fmpz_bits(fmpq_denref(x)) * ONE_OVER_LOG2_PHI + 2;
}
void
fmpr_randtest_not_zero(fmpr_t x, flint_rand_t state, slong bits, slong mag_bits)
{
fmpz_randtest_not_zero(fmpr_manref(x), state, bits);
fmpz_randtest(fmpr_expref(x), state, mag_bits);
fmpz_sub_ui(fmpr_expref(x), fmpr_expref(x), fmpz_bits(fmpr_manref(x)));
_fmpr_normalise(fmpr_manref(x), fmpr_expref(x), bits, FMPR_RND_DOWN);
}
void
arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec)
{
if (arb_is_zero(y))
{
arb_one(z);
return;
}
if (arb_is_zero(x))
{
if (arb_is_positive(y))
arb_zero(z);
else
arb_indeterminate(z);
return;
}
if (arb_is_exact(y) && !arf_is_special(arb_midref(x)))
{
const arf_struct * ymid = arb_midref(y);
/* small half-integer or integer */
if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 &&
arf_is_int_2exp_si(ymid, -1))
{
fmpz_t e;
fmpz_init(e);
if (arf_is_int(ymid))
{
arf_get_fmpz_fixed_si(e, ymid, 0);
arb_pow_fmpz_binexp(z, x, e, prec);
}
else
{
arf_get_fmpz_fixed_si(e, ymid, -1);
arb_sqrt(z, x, prec + fmpz_bits(e));
arb_pow_fmpz_binexp(z, z, e, prec);
}
fmpz_clear(e);
return;
}
else if (arf_is_int(ymid) && arf_sgn(arb_midref(x)) < 0)
{
/* use (-x)^n = (-1)^n * x^n to avoid NaNs
at least at high enough precision */
int odd = !arf_is_int_2exp_si(ymid, 1);
_arb_pow_exp(z, x, 1, y, prec);
if (odd)
arb_neg(z, z);
return;
}
}
_arb_pow_exp(z, x, 0, y, prec);
}
void renf_randtest(renf_t nf, flint_rand_t state, slong len, slong prec, mp_bitcnt_t bits)
{
fmpz_poly_t p;
fmpq_poly_t p2;
fmpz * c_array;
slong * k_array;
slong n_interval, n_exact;
ulong i;
arb_t emb;
/* compute a random irreducible polynomial */
if (len <= 1)
{
fprintf(stderr, "ERROR (renf_randtest): got length < 2\n");
abort();
}
fmpz_poly_init(p);
do{
fmpz_poly_randtest_irreducible(p, state, len, bits);
}while(!fmpz_poly_has_real_root(p));
/* pick a random real root */
c_array = _fmpz_vec_init(p->length);
k_array = malloc((p->length) * sizeof(slong));
n_interval = 0;
fmpz_poly_isolate_real_roots(NULL, &n_exact,
c_array, k_array, &n_interval, p);
if (n_interval == 0)
{
fprintf(stderr, "Runtime error\n");
abort();
}
i = n_randint(state, n_interval);
/* construct the associated number field */
arb_init(emb);
arb_from_interval(emb, c_array+i, k_array[i], fmpz_bits(c_array + i) + FLINT_MAX(k_array[i], 0) + 2);
fmpq_poly_init(p2);
fmpq_poly_set_fmpz_poly(p2, p);
/* NOTE: renf init might not be happy with the ball emb */
renf_init(nf, p2, emb, prec);
_fmpz_vec_clear(c_array, p->length);
free(k_array);
fmpz_poly_clear(p);
fmpq_poly_clear(p2);
arb_clear(emb);
}
/* The coefficients in 2^d * \prod_{i=1}^d (x - cos(a_i)) are
easily bounded using the binomial theorem. */
static slong
magnitude_bound(slong d)
{
slong res;
fmpz_t t;
fmpz_init(t);
fmpz_bin_uiui(t, d, d / 2);
res = fmpz_bits(t);
fmpz_clear(t);
return FLINT_ABS(res) + d;
}
int
main(void)
{
int i, result;
double output;
slong exp;
FLINT_TEST_INIT(state);
flint_printf("get_d_2exp....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a;
fmpz_init(a);
fmpz_randtest(a, state, 200);
output = fmpz_get_d_2exp(&exp, a);
result = (fmpz_bits(a) == exp);
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a = "), fmpz_print(a), flint_printf("\n");
flint_printf("output = %f\n", output);
flint_printf("exp = %wd, bits = %wu\n", exp, fmpz_bits(a));
abort();
}
fmpz_clear(a);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
acb_quadratic_roots_fmpz(acb_t r1, acb_t r2,
const fmpz_t a, const fmpz_t b, const fmpz_t c, slong prec)
{
fmpz_t d;
fmpz_init(d);
/* d = b^2 - 4ac */
fmpz_mul(d, a, c);
fmpz_mul_2exp(d, d, 2);
fmpz_submul(d, b, b);
fmpz_neg(d, d);
/* +/- sqrt(d) */
acb_zero(r1);
if (fmpz_sgn(d) >= 0)
{
arb_sqrt_fmpz(acb_realref(r1), d, prec + fmpz_bits(d) + 4);
}
else
{
fmpz_neg(d, d);
arb_sqrt_fmpz(acb_imagref(r1), d, prec + fmpz_bits(d) + 4);
}
acb_neg(r2, r1);
/* -b */
acb_sub_fmpz(r1, r1, b, prec + 4);
acb_sub_fmpz(r2, r2, b, prec + 4);
/* divide by 2a */
fmpz_mul_2exp(d, a, 1);
acb_div_fmpz(r1, r1, d, prec);
acb_div_fmpz(r2, r2, d, prec);
fmpz_clear(d);
return;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("height....");
fflush(stdout);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
fmpz *a;
fmpz_t h;
long len, bits, bits2;
fmpz_init(h);
len = n_randint(state, 100);
a = _fmpz_vec_init(len);
bits = n_randint(state, 200);
_fmpz_vec_randtest(a, state, len, bits);
bits2 = _fmpz_vec_max_bits(a, len);
_fmpz_vec_height(h, a, len);
result = (fmpz_bits(h) == FLINT_ABS(bits2)) && (fmpz_sgn(h) >= 0);
if (!result)
{
printf("FAIL:\n");
printf("bits = %ld, bits2 = %ld\n", bits, bits2);
printf("Computed height:\n");
fmpz_print(h);
printf("\n");
abort();
}
fmpz_clear(h);
_fmpz_vec_clear(a, len);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void
acb_pow_arb(acb_t z, const acb_t x, const arb_t y, long prec)
{
const arf_struct * ymid = arb_midref(y);
const mag_struct * yrad = arb_radref(y);
if (arb_is_zero(y))
{
acb_one(z);
return;
}
if (mag_is_zero(yrad))
{
/* small half-integer or integer */
if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 &&
arf_is_int_2exp_si(ymid, -1))
{
fmpz_t e;
fmpz_init(e);
if (arf_is_int(ymid))
{
arf_get_fmpz_fixed_si(e, ymid, 0);
acb_pow_fmpz_binexp(z, x, e, prec);
}
else
{
/* hack: give something finite here (should fix sqrt/rsqrt etc) */
if (arb_contains_zero(acb_imagref(x)) && arb_contains_nonpositive(acb_realref(x)))
{
_acb_pow_arb_exp(z, x, y, prec);
fmpz_clear(e);
return;
}
arf_get_fmpz_fixed_si(e, ymid, -1);
acb_sqrt(z, x, prec + fmpz_bits(e));
acb_pow_fmpz_binexp(z, z, e, prec);
}
fmpz_clear(e);
return;
}
}
_acb_pow_arb_exp(z, x, y, prec);
}
void _qadic_exp(fmpz *rop, const fmpz *op, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N, const fmpz_t pN)
{
if (N < (WORD(1) << 13) / (slong) fmpz_bits(p))
{
_qadic_exp_rectangular(rop, op, v, len, a, j, lena, p, N, pN);
}
else
{
const slong d = j[lena - 1];
_qadic_exp_balanced(rop, op, v, len, a, j, lena, p, N, pN);
_fmpz_vec_zero(rop + d, d - 1);
}
}
long
_fmpz_vec_max_bits(const fmpz * vec, long len)
{
long i, bits, max_bits = 0, sign = 1;
for (i = 0; i < len; i++)
{
bits = fmpz_bits(vec + i);
if (bits > max_bits)
max_bits = bits;
if (fmpz_sgn(vec + i) < 0)
sign = -1L;
}
return max_bits * sign;
}
void arb_from_interval(arb_t x, const fmpz_t c, const slong k, const slong prec)
{
/* we build the ball that gives exactly (c 2^k, (c+1) 2^k) */
/* center: (2c+1) 2^(k-1) */
/* radius: 2^(k-1) */
if (prec <= 0 || prec < fmpz_bits(c) + 2)
{
fprintf(stderr, "not enough precision");
abort();
}
arb_set_fmpz(x, c);
arb_mul_2exp_si(x, x, 1);
arb_add_si(x, x, 1, prec);
arb_mul_2exp_si(x, x, k-1);
arb_add_error_2exp_si(x, k-1);
}
void
fmpr_pow_sloppy_fmpz(fmpr_t y, const fmpr_t b, const fmpz_t e,
long prec, fmpr_rnd_t rnd)
{
long i, wp, bits;
if (fmpz_is_zero(e))
{
fmpr_set_ui(y, 1UL);
return;
}
if (fmpz_sgn(e) < 0)
{
fmpz_t f;
fmpz_init(f);
fmpz_neg(f, e);
fmpr_pow_sloppy_fmpz(y, b, f, prec + 2,
(rnd == FMPR_RND_FLOOR || rnd == FMPR_RND_DOWN)
? FMPR_RND_UP : FMPR_RND_DOWN);
fmpr_ui_div(y, 1UL, y, prec, rnd);
fmpz_clear(f);
}
if (y == b)
{
fmpr_t t;
fmpr_init(t);
fmpr_set(t, b);
fmpr_pow_sloppy_fmpz(y, t, e, prec, rnd);
fmpr_clear(t);
return;
}
fmpr_set(y, b);
bits = fmpz_bits(e);
wp = FMPR_PREC_ADD(prec, bits);
for (i = bits - 2; i >= 0; i--)
{
fmpr_mul(y, y, y, wp, rnd);
if (fmpz_tstbit(e, i))
fmpr_mul(y, y, b, wp, rnd);
}
}
void
arb_bernoulli_fmpz(arb_t res, const fmpz_t n, slong prec)
{
if (fmpz_cmp_ui(n, UWORD_MAX) <= 0)
{
if (fmpz_sgn(n) >= 0)
arb_bernoulli_ui(res, fmpz_get_ui(n), prec);
else
arb_zero(res);
}
else if (fmpz_is_odd(n))
{
arb_zero(res);
}
else
{
arb_t t;
slong wp;
arb_init(t);
wp = prec + 2 * fmpz_bits(n);
/* zeta(n) ~= 1 */
arf_one(arb_midref(res));
mag_one(arb_radref(res));
mag_mul_2exp_si(arb_radref(res), arb_radref(res), WORD_MIN);
/* |B_n| = 2 * n! / (2*pi)^n * zeta(n) */
arb_gamma_fmpz(t, n, wp);
arb_mul_fmpz(t, t, n, wp);
arb_mul(res, res, t, wp);
arb_const_pi(t, wp);
arb_mul_2exp_si(t, t, 1);
arb_pow_fmpz(t, t, n, wp);
arb_div(res, res, t, prec);
arb_mul_2exp_si(res, res, 1);
if (fmpz_fdiv_ui(n, 4) == 0)
arb_neg(res, res);
arb_clear(t);
}
}
void
fmpz_randtest_mod(fmpz_t f, flint_rand_t state, const fmpz_t m)
{
fmpz_t t;
fmpz_init(t);
fmpz_randtest_unsigned(t, state, fmpz_bits(m) + 2);
fmpz_mod(t, t, m);
if (n_randlimb(state) & UWORD(1))
{
fmpz_sub(t, m, t);
fmpz_sub_ui(t, t, UWORD(1));
}
fmpz_set(f, t);
fmpz_clear(t);
}
void
fmpz_poly_bit_unpack(fmpz_poly_t poly, const fmpz_t f, mp_bitcnt_t bit_size)
{
slong len;
mpz_t tmp;
int negate, borrow;
if (bit_size == 0 || fmpz_is_zero(f))
{
fmpz_poly_zero(poly);
return;
}
/* Round up */
len = (fmpz_bits(f) + bit_size - 1) / bit_size;
negate = (fmpz_sgn(f) < 0) ? -1 : 0;
mpz_init2(tmp, bit_size*len);
/* TODO: avoid all this wastefulness */
flint_mpn_zero(tmp->_mp_d, tmp->_mp_alloc);
fmpz_get_mpz(tmp, f);
fmpz_poly_fit_length(poly, len + 1);
borrow = _fmpz_poly_bit_unpack(poly->coeffs, len,
tmp->_mp_d, bit_size, negate);
if (borrow)
{
fmpz_set_si(poly->coeffs + len, negate ? WORD(-1) : WORD(1));
_fmpz_poly_set_length(poly, len + 1);
}
else
{
_fmpz_poly_set_length(poly, len);
_fmpz_poly_normalise(poly);
}
mpz_clear(tmp);
}
int main(void)
{
int i, j, result;
ulong count = UWORD(0);
gmp_randstate_t st;
FLINT_TEST_INIT(state);
gmp_randinit_default(st);
flint_printf("factor_pp1....");
fflush(stdout);
for (i = 0; i < 50 * flint_test_multiplier(); i++) /* Test random numbers */
{
mp_bitcnt_t bits;
mpz_t m, n;
fmpz_t n1, n2, r;
mpz_init(n);
mpz_init(m);
fmpz_init(n1);
fmpz_init(n2);
fmpz_init(r);
do {
mpz_urandomb(n, st, n_randint(state, 128) + 2);
} while (flint_mpz_cmp_ui(n, 2) < 0);
do {
mpz_urandomb(m, st, n_randint(state, 50) + 2);
} while (!mpz_probab_prime_p(m, 20));
mpz_mul(n, n, m);
fmpz_set_mpz(n1, n);
bits = FLINT_MIN(fmpz_bits(n1), FLINT_BITS);
for (j = 0; j < 20; j++)
{
fmpz_factor_pp1(n2, n1, 10000, 10000, n_randbits(state, bits - 2) + 3);
if (fmpz_cmp_ui(n2, 1) > 0) break;
}
if (fmpz_cmp_ui(n2, 1) > 0)
{
count++;
fmpz_mod(r, n1, n2);
result = (fmpz_is_zero(r));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n1 = ");
fmpz_print(n1);
flint_printf(", n2 = ");
fmpz_print(n2);
flint_printf("\n");
fmpz_print(r); flint_printf("\n");
abort();
}
}
fmpz_clear(n1);
fmpz_clear(n2);
fmpz_clear(r);
mpz_clear(m);
mpz_clear(n);
}
if (count < 49 * flint_test_multiplier())
{
flint_printf("FAIL:\n");
flint_printf("Only %wu numbers factored\n", count);
abort();
}
gmp_randclear(st);
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("multi_CRT_ui....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
slong bits, prime_bits, rows, cols, num_primes, j;
fmpz_t mod;
fmpz_mat_t A, B, C;
nmod_mat_t Amod[1000];
mp_limb_t primes[1000];
bits = n_randint(state, 500) + 1;
rows = n_randint(state, 10);
cols = n_randint(state, 10);
prime_bits = 1 + n_randint(state, FLINT_BITS - 1);
fmpz_mat_init(A, rows, cols);
fmpz_mat_init(B, rows, cols);
fmpz_mat_init(C, rows, cols);
fmpz_mat_randtest(A, state, bits);
fmpz_init(mod);
num_primes = 0;
primes[0] = n_nextprime(UWORD(1) << prime_bits, 0);
fmpz_set_ui(mod, primes[0]);
/* + 1 for sign */
while (fmpz_bits(mod) <= bits + 1)
{
primes[num_primes + 1] = n_nextprime(primes[num_primes], 0);
fmpz_mul_ui(mod, mod, primes[num_primes + 1]);
num_primes++;
}
num_primes++;
for (j = 0; j < num_primes; j++)
nmod_mat_init(Amod[j], rows, cols, primes[j]);
fmpz_mat_multi_mod_ui(Amod, num_primes, A);
fmpz_mat_multi_CRT_ui(B, Amod, num_primes, 1);
if (!fmpz_mat_equal(B, A))
{
flint_printf("FAIL!\n");
flint_printf("primes: ");
for (j = 0; j < num_primes; j++)
flint_printf("%wu ", primes[j]);
flint_printf("\nA: \n");
fmpz_mat_print_pretty(A);
flint_printf("\nB: \n");
fmpz_mat_print_pretty(B);
flint_printf("\n");
abort();
}
for (j = 0; j < num_primes; j++)
nmod_mat_clear(Amod[j]);
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(C);
fmpz_clear(mod);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main()
{
slong iter, iter2;
flint_rand_t state;
flint_printf("addmul_si....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
arf_t x, z, v;
slong y;
slong prec, r1, r2;
arf_rnd_t rnd;
arf_init(x);
arf_init(z);
arf_init(v);
for (iter2 = 0; iter2 < 100; iter2++)
{
arf_randtest_special(x, state, 2000, 100);
y = z_randtest(state);
arf_randtest_special(z, state, 2000, 100);
arf_set(v, z);
prec = 2 + n_randint(state, 2000);
if (n_randint(state, 10) == 0 &&
fmpz_bits(ARF_EXPREF(x)) < 10 &&
fmpz_bits(ARF_EXPREF(z)) < 10)
{
prec = ARF_PREC_EXACT;
}
switch (n_randint(state, 5))
{
case 0: rnd = ARF_RND_DOWN; break;
case 1: rnd = ARF_RND_UP; break;
case 2: rnd = ARF_RND_FLOOR; break;
case 3: rnd = ARF_RND_CEIL; break;
default: rnd = ARF_RND_NEAR; break;
}
switch (n_randint(state, 2))
{
case 0:
r1 = arf_addmul_si(z, x, y, prec, rnd);
r2 = arf_addmul_si_naive(v, x, y, prec, rnd);
if (!arf_equal(z, v) || r1 != r2)
{
flint_printf("FAIL!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = %wd", y); flint_printf("\n\n");
flint_printf("z = "); arf_debug(z); flint_printf("\n\n");
flint_printf("v = "); arf_debug(v); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
default:
r2 = arf_addmul_si_naive(v, v, y, prec, rnd);
r1 = arf_addmul_si(z, z, y, prec, rnd);
if (!arf_equal(v, z) || r1 != r2)
{
flint_printf("FAIL (aliasing)!\n");
flint_printf("prec = %wd, rnd = %d\n\n", prec, rnd);
flint_printf("y = %wd", y); flint_printf("\n\n");
flint_printf("v = "); arf_print(v); flint_printf("\n\n");
flint_printf("z = "); arf_print(z); flint_printf("\n\n");
flint_printf("r1 = %wd, r2 = %wd\n", r1, r2);
abort();
}
break;
}
}
arf_clear(x);
arf_clear(z);
arf_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("add....");
fflush(stdout);
flint_randinit(state);
/* test exact addition: (x + y) + z == x + (y + z) */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
slong bits, res1, res2, res3, res4;
fmpr_t x, y, z, t, u;
bits = 2 + n_randint(state, 200);
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(t);
fmpr_init(u);
fmpr_randtest_special(x, state, bits, 10);
fmpr_randtest_special(y, state, bits, 10);
fmpr_randtest_special(z, state, bits, 10);
fmpr_randtest_special(t, state, bits, 10);
fmpr_randtest_special(u, state, bits, 10);
res1 = fmpr_add(t, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res2 = fmpr_add(t, t, z, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res3 = fmpr_add(u, y, z, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res4 = fmpr_add(u, x, u, FMPR_PREC_EXACT, FMPR_RND_DOWN);
if (!fmpr_equal(t, u) ||
res1 != FMPR_RESULT_EXACT || res2 != FMPR_RESULT_EXACT ||
res3 != FMPR_RESULT_EXACT || res4 != FMPR_RESULT_EXACT)
{
flint_printf("FAIL\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("t = "); fmpr_print(t); flint_printf("\n\n");
flint_printf("u = "); fmpr_print(u); flint_printf("\n\n");
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(t);
fmpr_clear(u);
}
/* compare with add_naive */
for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++)
{
slong prec, ret1, ret2;
fmpr_t x, y, z, w;
fmpr_rnd_t rnd;
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(w);
fmpr_randtest_special(x, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
fmpr_randtest_special(y, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
fmpr_randtest_special(z, state, 1 + n_randint(state, 1000), 1 + n_randint(state, 200));
prec = 2 + n_randint(state, 1000);
if (n_randint(state, 10) == 0 &&
fmpz_bits(fmpr_expref(x)) < 10 &&
fmpz_bits(fmpr_expref(y)) < 10)
prec = FMPR_PREC_EXACT;
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
ret1 = fmpr_add(z, x, y, prec, rnd);
ret2 = fmpr_add_naive(w, x, y, prec, rnd);
if (!fmpr_equal(z, w) || ret1 != ret2 ||
!fmpr_check_ulp(z, ret1, prec) || !fmpr_check_ulp(w, ret2, prec))
{
flint_printf("FAIL\n\n");
flint_printf("iter %wd\n", iter);
flint_printf("prec = %wd\n", prec);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("w = "); fmpr_print(w); flint_printf("\n\n");
flint_printf("ret1 = %wd, ret2 = %wd\n", ret1, ret2);
abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(w);
}
/* compare rounding with mpfr */
for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++)
{
slong bits, res;
int mpfr_res;
fmpr_t x, y, z, w;
mpfr_t X, Y, Z;
bits = 2 + n_randint(state, 500);
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(w);
mpfr_init2(X, bits + 500);
mpfr_init2(Y, bits + 500);
mpfr_init2(Z, bits);
fmpr_randtest_special(x, state, bits + n_randint(state, 500), 10);
fmpr_randtest_special(y, state, bits + n_randint(state, 500), 10);
fmpr_randtest_special(z, state, bits, 10);
fmpr_get_mpfr(X, x, MPFR_RNDN);
fmpr_get_mpfr(Y, y, MPFR_RNDN);
switch (n_randint(state, 4))
{
case 0:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDZ);
res = fmpr_add(z, x, y, bits, FMPR_RND_DOWN);
break;
case 1:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDA);
res = fmpr_add(z, x, y, bits, FMPR_RND_UP);
break;
case 2:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDD);
res = fmpr_add(z, x, y, bits, FMPR_RND_FLOOR);
break;
default:
mpfr_res = mpfr_add(Z, X, Y, MPFR_RNDU);
res = fmpr_add(z, x, y, bits, FMPR_RND_CEIL);
break;
}
fmpr_set_mpfr(w, Z);
if (!fmpr_equal(z, w) || (res == FMPR_RESULT_EXACT) != (mpfr_res == 0)
|| !fmpr_check_ulp(z, res, bits))
{
flint_printf("FAIL\n\n");
flint_printf("iter %wd\n", iter);
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("w = "); fmpr_print(w); flint_printf("\n\n");
flint_printf("returned: %wd, %d\n", res, mpfr_res);
abort();
}
/* check error bound */
if (!fmpr_is_nan(z) && !fmpr_is_inf(z))
{
fmpr_t z_exact, error_bound, true_error;
fmpr_init(z_exact);
fmpr_init(error_bound);
fmpr_init(true_error);
fmpr_set_error_result(error_bound, z, res);
fmpr_add(z_exact, x, y, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_sub(true_error, z, z_exact, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_abs(true_error, true_error);
if (fmpr_is_zero(error_bound) != fmpr_is_zero(true_error) ||
fmpr_cmp(true_error, error_bound) > 0)
{
flint_printf("FAIL: error bound\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("z_exact = "); fmpr_print(z_exact); flint_printf("\n\n");
flint_printf("true_error = "); fmpr_print(true_error); flint_printf("\n\n");
flint_printf("error_bound = "); fmpr_print(error_bound); flint_printf("\n\n");
abort();
}
fmpr_clear(z_exact);
fmpr_clear(error_bound);
fmpr_clear(true_error);
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(w);
mpfr_clear(X);
mpfr_clear(Y);
mpfr_clear(Z);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
static void
_fmprb_gamma(fmprb_t y, const fmprb_t x, long prec, int inverse)
{
int reflect;
long r, n, wp;
fmprb_t t, u, v;
if (fmprb_is_exact(x))
{
const fmpr_struct * mid = fmprb_midref(x);
if (fmpr_is_special(mid))
{
if (!inverse && fmpr_is_pos_inf(mid))
{
fmprb_set(y, x);
}
else if (fmpr_is_nan(mid) || fmpr_is_neg_inf(mid) || !inverse)
{
fmpr_nan(fmprb_midref(y));
fmpr_pos_inf(fmprb_radref(y));
}
else
{
fmprb_zero(y);
}
return;
}
else
{
const fmpz exp = *fmpr_expref(mid);
const fmpz man = *fmpr_manref(mid);
/* fast gamma(n), gamma(n/2) or gamma(n/4) */
if (!COEFF_IS_MPZ(exp) && (exp >= -2) &&
((double) fmpz_bits(&man) + exp < prec))
{
fmpq_t a;
fmpq_init(a);
fmpr_get_fmpq(a, mid);
fmprb_gamma_fmpq(y, a, prec + 2 * inverse);
if (inverse)
fmprb_ui_div(y, 1, y, prec);
fmpq_clear(a);
return;
}
}
}
wp = prec + FLINT_BIT_COUNT(prec);
gamma_stirling_choose_param_fmprb(&reflect, &r, &n, x, 1, 0, wp);
fmprb_init(t);
fmprb_init(u);
fmprb_init(v);
if (reflect)
{
/* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */
fmprb_sub_ui(t, x, 1, wp);
fmprb_neg(t, t);
gamma_rising_fmprb_ui_bsplit(u, t, r, wp);
fmprb_const_pi(v, wp);
fmprb_mul(u, u, v, wp);
fmprb_add_ui(t, t, r, wp);
gamma_stirling_eval_fmprb(v, t, n, 0, wp);
fmprb_exp(v, v, wp);
fmprb_sin_pi(t, x, wp);
fmprb_mul(v, v, t, wp);
}
else
{
/* gamma(x) = gamma(x+r) / rf(x,r) */
fmprb_add_ui(t, x, r, wp);
gamma_stirling_eval_fmprb(u, t, n, 0, wp);
fmprb_exp(u, u, prec);
gamma_rising_fmprb_ui_bsplit(v, x, r, wp);
}
if (inverse)
fmprb_div(y, v, u, prec);
else
fmprb_div(y, u, v, prec);
fmprb_clear(t);
fmprb_clear(u);
fmprb_clear(v);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("resultant_div....");
fflush(stdout);
for (i = 0; i < 50; i++)
{
fmpq_poly_t f, g, h, p;
fmpq_t x, y, z, zz;
fmpz_t den;
slong nbits;
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(p);
fmpq_poly_init(h);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
fmpq_init(zz);
fmpz_init(den);
fmpq_poly_randtest(f, state, n_randint(state, 50), 100);
fmpq_poly_randtest(g, state, n_randint(state, 50), 100);
fmpq_poly_randtest(h, state, n_randint(state, 50), 100);
fmpz_set(den, fmpq_poly_denref(f));
fmpq_poly_scalar_mul_fmpz(f, f, den);
fmpz_set(den, fmpq_poly_denref(g));
fmpq_poly_scalar_mul_fmpz(g, g, den);
fmpz_set(den, fmpq_poly_denref(h));
fmpq_poly_scalar_mul_fmpz(h, h, den);
fmpq_poly_mul(p, f, g);
fmpq_poly_resultant(x, f, h);
if (!fmpz_is_one(fmpq_denref(x)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("f = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(y, g, h);
if (!fmpz_is_one(fmpq_denref(y)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("h = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_resultant(z, p, h);
if (!fmpz_is_one(fmpq_denref(z)))
{
flint_printf("FAIL resultant not integral\n");
flint_printf("p = "), fmpq_poly_print(f), flint_printf("\n\n");
flint_printf("g = "), fmpq_poly_print(g), flint_printf("\n\n");
flint_printf("y = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
if (fmpq_is_zero(z))
{
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
continue;
}
nbits = (slong)fmpz_bits(fmpq_numref(y)) + 1;
fmpq_poly_resultant_div(z, p, h, fmpq_numref(x), nbits);
fmpq_poly_resultant(zz, p, h);
result = fmpq_equal(z, y);
if (!result)
{
flint_printf("FAIL (res(p, g)/div == res(p, g)/div:\n");
flint_printf("p = "), fmpq_poly_print_pretty(p, "x"), flint_printf("\n\n");
flint_printf("h = "), fmpq_poly_print_pretty(h, "x"), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(zz), flint_printf("\n\n");
flint_printf("res(p, h) = "), fmpq_print(x), flint_printf(" * "), fmpq_print(y), flint_printf("\n\n");
flint_printf("supplied divisor = "), fmpq_print(x), flint_printf("\n\n");
flint_printf("nbits = %wu\n\n", nbits);
flint_printf("divisor found = "), fmpq_print(z), flint_printf("\n\n");
flint_printf("correct result = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
fmpq_clear(zz);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
acb_pow_fmpz_binexp(acb_t y, const acb_t b, const fmpz_t e, long prec)
{
long i, wp, bits;
if (-2L <= *e && *e <= 4L)
{
if (*e == 0L)
{
acb_one(y);
}
else if (*e == 1L)
{
acb_set_round(y, b, prec);
}
else if (*e == -1L)
{
acb_inv(y, b, prec);
}
else if (*e == 2L)
{
acb_mul(y, b, b, prec);
}
else if (*e == 3L)
{
acb_cube(y, b, prec);
}
else if (*e == 4L)
{
acb_mul(y, b, b, prec);
acb_mul(y, y, y, prec);
}
else
{
acb_inv(y, b, prec);
acb_mul(y, y, y, prec);
}
return;
}
if (fmpz_sgn(e) < 0)
{
fmpz_t f;
fmpz_init(f);
fmpz_neg(f, e);
acb_pow_fmpz_binexp(y, b, f, prec + 2);
acb_inv(y, y, prec);
fmpz_clear(f);
return;
}
if (!COEFF_IS_MPZ(*e) && ((*e) % 3 == 0))
{
fmpz e3 = (*e) / 3;
acb_pow_fmpz_binexp(y, b, &e3, prec);
acb_cube(y, y, prec);
return;
}
if (y == b)
{
acb_t t;
acb_init(t);
acb_set(t, b);
acb_pow_fmpz_binexp(y, t, e, prec);
acb_clear(t);
return;
}
acb_set(y, b);
bits = fmpz_bits(e);
wp = ARF_PREC_ADD(prec, bits);
for (i = bits - 2; i >= 0; i--)
{
acb_mul(y, y, y, wp);
if (fmpz_tstbit(e, i))
acb_mul(y, y, b, wp);
}
}
void _fq_nmod_pow(mp_limb_t *rop, const mp_limb_t *op, slong len, const fmpz_t e,
const fq_nmod_ctx_t ctx)
{
const slong d = fq_nmod_ctx_degree(ctx);
if (fmpz_is_zero(e))
{
rop[0] = WORD(1);
_nmod_vec_zero(rop + 1, 2 * d - 1 - 1);
}
else if (fmpz_is_one(e))
{
_nmod_vec_set(rop, op, len);
_nmod_vec_zero(rop + len, 2 * d - 1 - len);
}
else
{
ulong bit;
mp_limb_t *v = _nmod_vec_init(2 * d - 1);
mp_limb_t *R, *S, *T;
_nmod_vec_zero(v, 2 * d - 1);
_nmod_vec_zero(rop, 2 * d - 1);
/*
Set bits to the bitmask with a 1 one place lower than the msb of e
*/
bit = fmpz_bits(e) - 2;
/*
Trial run without any polynomial arithmetic to determine the parity
of the number of swaps; then set R and S accordingly
*/
{
unsigned int swaps = 0U;
ulong bit2 = bit;
if (fmpz_tstbit(e, bit2))
swaps = ~swaps;
while (bit2--)
if (!fmpz_tstbit(e, bit2))
swaps = ~swaps;
if (swaps == 0U)
{
R = rop;
S = v;
}
else
{
R = v;
S = rop;
}
}
/*
We unroll the first step of the loop, referring to {op, len}
*/
_nmod_poly_mul(R, op, len, op, len, ctx->mod);
_fq_nmod_reduce(R, 2 * len - 1, ctx);
if (fmpz_tstbit(e, bit))
{
_nmod_poly_mul(S, R, d, op, len, ctx->mod);
_fq_nmod_reduce(S, d + len - 1, ctx);
T = R;
R = S;
S = T;
}
while (bit--)
{
if (fmpz_tstbit(e, bit))
{
_nmod_poly_mul(S, R, d, R, d, ctx->mod);
_fq_nmod_reduce(S, 2 * d - 1, ctx);
_nmod_poly_mul(R, S, d, op, len, ctx->mod);
_fq_nmod_reduce(R, d + len - 1, ctx);
}
else
{
_nmod_poly_mul(S, R, d, R, d, ctx->mod);
_fq_nmod_reduce(S, 2 * d - 1, ctx);
T = R;
R = S;
S = T;
}
}
_nmod_vec_clear(v);
}
}