/* TODO: move it to ANTIC? */
int _nf_equal_fmpq(const nf_elem_t a, const fmpq_t b, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
return (fmpz_equal(LNF_ELEM_NUMREF(a), fmpq_numref(b)) &&
fmpz_equal(LNF_ELEM_DENREF(a), fmpq_denref(b)));
}
else if (nf->flag & NF_QUADRATIC)
{
const fmpz * const num = QNF_ELEM_NUMREF(a);
const fmpz * const den = QNF_ELEM_DENREF(a);
return (fmpz_is_zero(num + 1) &&
fmpz_equal(num, fmpq_numref(b)) &&
fmpz_equal(den, fmpq_denref(b)));
}
else
{
if (NF_ELEM(a)->length > 1) return 0;
else if (NF_ELEM(a)->length == 0) return fmpq_is_zero(b);
return (fmpz_equal(NF_ELEM_NUMREF(a), fmpq_numref(b)) &&
fmpz_equal(NF_ELEM_DENREF(a), fmpq_denref(b)));
}
return -1;
}
void
fmpr_get_fmpq(fmpq_t y, const fmpr_t x)
{
if (fmpr_is_zero(x))
{
fmpq_zero(y);
}
else if (fmpr_is_special(x) || COEFF_IS_MPZ(*fmpr_expref(x)))
{
printf("exception: fmpr_get_fmpq: cannot convert to rational\n");
abort();
}
else
{
long exp = *fmpr_expref(x);
fmpz_set_ui(fmpq_denref(y), 1UL);
if (exp >= 0)
{
fmpz_mul_2exp(fmpq_numref(y), fmpr_manref(x), exp);
}
else
{
fmpz_set(fmpq_numref(y), fmpr_manref(x));
fmpz_mul_2exp(fmpq_denref(y), fmpq_denref(y), -exp);
}
}
}
void
arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, long prec)
{
if (n == 0)
{
arb_one(y);
}
else if (n == 1)
{
arb_set_fmpq(y, x, prec);
}
else
{
long wp;
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
bsplit(y, fmpq_numref(x), fmpq_denref(x), 0, n, wp);
if (fmpz_is_one(fmpq_denref(x)))
{
arb_set_round(y, y, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set_fmpz(t, fmpq_denref(x));
arb_pow_ui(t, t, n, wp);
arb_div(y, y, t, prec);
arb_clear(t);
}
}
}
void nf_elem_scalar_div_fmpq(nf_elem_t a, const nf_elem_t b,
const fmpq_t c, const nf_t nf)
{
if (nf->flag & NF_LINEAR)
{
fmpz * den = LNF_ELEM_DENREF(a);
fmpz * num = LNF_ELEM_NUMREF(a);
const fmpz * const den2 = LNF_ELEM_DENREF(b);
const fmpz * const num2 = LNF_ELEM_NUMREF(b);
_fmpq_mul(num, den, num2, den2, fmpq_denref(c), fmpq_numref(c));
}
else if (nf->flag & NF_QUADRATIC)
{
fmpz * den = QNF_ELEM_DENREF(a);
fmpz * num = QNF_ELEM_NUMREF(a);
const fmpz * const den2 = QNF_ELEM_DENREF(b);
const fmpz * const num2 = QNF_ELEM_NUMREF(b);
_fmpq_poly_scalar_div_fmpq(num, den,
num2, den2, 2, fmpq_numref(c), fmpq_denref(c));
} else
{
fmpq_poly_scalar_div_fmpq(NF_ELEM(a),
NF_ELEM(b), c);
}
}
void fmpq_poly_resultant(fmpq_t r, const fmpq_poly_t f, const fmpq_poly_t g)
{
const long len1 = f->length;
const long len2 = g->length;
if (len1 == 0 || len2 == 0)
{
fmpq_zero(r);
}
else
{
if (len1 >= len2)
{
_fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r),
f->coeffs, f->den, len1,
g->coeffs, g->den, len2);
}
else
{
_fmpq_poly_resultant(fmpq_numref(r), fmpq_denref(r),
g->coeffs, g->den, len2,
f->coeffs, f->den, len1);
if (((len1 | len2) & 1L) == 0L)
fmpq_neg(r, r);
}
}
}
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 fmpq_div(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
{
if (fmpq_is_zero(op2))
{
printf("Exception: fmpq_div: division by zero");
abort();
}
_fmpq_div(fmpq_numref(res), fmpq_denref(res),
fmpq_numref(op1), fmpq_denref(op1),
fmpq_numref(op2), fmpq_denref(op2));
}
void
_fmpq_bsplit_sum_abpq(fmpz_t P, fmpz_t Q, fmpz_t B, fmpz_t T,
const fmpq * ab, const fmpq * pq, long n1, long n2)
{
if (n2 - n1 <= 0)
{
fmpz_zero(P);
fmpz_one(Q);
}
else if (n2 - n1 == 1)
{
fmpz_set(P, fmpq_numref(pq + n1));
fmpz_set(Q, fmpq_denref(pq + n1));
fmpz_set(B, fmpq_denref(ab + n1));
fmpz_mul(T, P, fmpq_numref(ab + n1));
}
else
{
long m = (n1 + n2) / 2;
fmpz_t P2, Q2, B2, T2;
fmpz_init(P2);
fmpz_init(Q2);
fmpz_init(B2);
fmpz_init(T2);
_fmpq_bsplit_sum_abpq(P, Q, B, T, ab, pq, n1, m);
_fmpq_bsplit_sum_abpq(P2, Q2, B2, T2, ab, pq, m, n2);
if (!fmpz_is_one(B2))
fmpz_mul(T, T, B2);
fmpz_mul(T, T, Q2);
if (!fmpz_is_one(B))
fmpz_mul(T2, T2, B);
fmpz_mul(T2, T2, P);
fmpz_add(T, T, T2);
fmpz_mul(P, P, P2);
fmpz_mul(Q, Q, Q2);
fmpz_mul(B, B, B2);
fmpz_clear(P2);
fmpz_clear(Q2);
fmpz_clear(B2);
fmpz_clear(T2);
}
}
int main()
{
printf("seq_set_fmpq_pow....");
fflush(stdout);
{
long i;
fmpq_t t, u;
fmpz_holonomic_t op;
fmpq_t c, initial;
fmpz_holonomic_init(op);
fmpq_init(t);
fmpq_init(u);
fmpq_init(c);
fmpq_init(initial);
fmpq_set_si(c, -7, 3);
fmpz_holonomic_seq_set_fmpq_pow(op, c);
fmpq_set_si(initial, -2, 1);
for (i = 0; i < 20; i++)
{
fmpz_holonomic_get_nth_fmpq(t, op, initial, 0, i);
fmpz_pow_ui(fmpq_numref(u), fmpq_numref(c), i);
fmpz_pow_ui(fmpq_denref(u), fmpq_denref(c), i);
fmpz_mul_si(fmpq_numref(u), fmpq_numref(u), -2);
if (!fmpq_equal(t, u))
{
printf("FAIL\n");
printf("i = %ld, t = ", i); fmpq_print(t);
printf(" u = "); fmpq_print(u);
printf("\n");
abort();
}
}
fmpq_clear(c);
fmpq_clear(t);
fmpq_clear(u);
fmpq_clear(initial);
fmpz_holonomic_clear(op);
}
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
bernoulli_cache_compute(long n)
{
if (bernoulli_cache_num < n)
{
long i, new_num;
bernoulli_rev_t iter;
if (bernoulli_cache_num == 0)
{
flint_register_cleanup_function(bernoulli_cleanup);
}
new_num = FLINT_MAX(bernoulli_cache_num + 128, n);
bernoulli_cache = flint_realloc(bernoulli_cache, new_num * sizeof(fmpq));
for (i = bernoulli_cache_num; i < new_num; i++)
fmpq_init(bernoulli_cache + i);
i = new_num - 1;
i -= (i % 2);
bernoulli_rev_init(iter, i);
for ( ; i >= bernoulli_cache_num; i -= 2)
{
bernoulli_rev_next(fmpq_numref(bernoulli_cache + i),
fmpq_denref(bernoulli_cache + i), iter);
}
bernoulli_rev_clear(iter);
if (new_num > 1)
fmpq_set_si(bernoulli_cache + 1, -1, 2);
bernoulli_cache_num = new_num;
}
}
bool renf_elem_class::is_integer() const noexcept
{
if (nf == nullptr)
return fmpz_is_one(fmpq_denref(b));
else
return renf_elem_is_integer(a, nf->renf_t());
}
int
fmpq_get_mpfr(mpfr_t r, const fmpq_t x, mpfr_rnd_t rnd)
{
__mpq_struct mpq;
fmpz p, q;
mp_limb_t pp, qq;
p = *fmpq_numref(x);
q = *fmpq_denref(x);
if (p == 0)
return mpfr_set_ui(r, 0, rnd);
if (COEFF_IS_MPZ(p))
mpq._mp_num = *COEFF_TO_PTR(p);
else
{
pp = FLINT_ABS(p);
mpq._mp_num._mp_alloc = 1;
mpq._mp_num._mp_size = (p < 0) ? -1 : 1;
mpq._mp_num._mp_d = &pp;
}
if (COEFF_IS_MPZ(q))
mpq._mp_den = *COEFF_TO_PTR(q);
else
{
qq = q;
mpq._mp_den._mp_alloc = 1;
mpq._mp_den._mp_size = 1;
mpq._mp_den._mp_d = &qq;
}
return mpfr_set_q(r, &mpq, rnd);
}
void fmpq_div_fmpz(fmpq_t res, const fmpq_t op, const fmpz_t x)
{
fmpz_t y;
fmpz_init(y);
fmpz_one(y);
_fmpq_mul(fmpq_numref(res), fmpq_denref(res),
fmpq_numref(op), fmpq_denref(op), y, x);
fmpz_clear(y);
if (fmpz_sgn(fmpq_denref(res)) < 0)
{
fmpz_neg(fmpq_numref(res), fmpq_numref(res));
fmpz_neg(fmpq_denref(res), fmpq_denref(res));
}
}
void renf_elem_class::assign(ulong value) noexcept
{
if (nf == nullptr)
{
fmpz_one(fmpq_denref(b));
fmpz_set_ui(fmpq_numref(b), value);
}
else
renf_elem_set_ui(a, value, nf->renf_t());
}
mpz_class renf_elem_class::ceil() const noexcept
{
fmpz_t tmp;
fmpz_init(tmp);
if (nf == nullptr)
{
fmpz_add(tmp, fmpq_numref(b), fmpq_denref(b));
fmpz_sub_ui(tmp, tmp, 1);
fmpz_fdiv_q(tmp, tmp, fmpq_denref(b));
}
else
renf_elem_ceil(tmp, a, nf->renf_t());
mpz_class z;
fmpz_get_mpz(z.get_mpz_t(), tmp);
fmpz_clear(tmp);
return z;
}
void renf_elem_class::assign(const mpz_class & value) noexcept
{
if (nf == nullptr)
{
fmpz_one(fmpq_denref(b));
fmpz_set_mpz(fmpq_numref(b), value.__get_mp());
}
else
renf_elem_set_mpz(a, value.get_mpz_t(), nf->renf_t());
}
void
arf_get_fmpq(fmpq_t y, const arf_t x)
{
if (arf_is_zero(x))
{
fmpq_zero(y);
}
else if (arf_is_special(x) || !ARF_IS_LAGOM(x))
{
flint_printf("exception: arf_get_fmpq: cannot convert to rational\n");
abort();
}
else
{
fmpz_t man, exp;
slong e;
fmpz_init(man);
fmpz_init(exp);
arf_get_fmpz_2exp(man, exp, x);
e = *exp;
fmpz_set_ui(fmpq_denref(y), UWORD(1));
if (e >= 0)
{
fmpz_mul_2exp(fmpq_numref(y), man, e);
}
else
{
fmpz_set(fmpq_numref(y), man);
fmpz_mul_2exp(fmpq_denref(y), fmpq_denref(y), -e);
}
fmpz_clear(man);
fmpz_clear(exp);
}
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("cfrac_bound....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
fmpq_t x, r;
fmpz * c;
slong n, bound;
fmpq_init(x);
fmpq_init(r);
/* Test worst case (quotient of Fibonacci numbers) */
if (n_randint(state, 50) == 1)
{
slong v = 1 + n_randint(state, 1000);
fmpz_fib_ui(fmpq_numref(x), v + 1);
fmpz_fib_ui(fmpq_denref(x), v);
}
else
{
fmpq_randtest(x, state, 1 + n_randint(state, 1000));
}
bound = fmpq_cfrac_bound(x);
c = _fmpz_vec_init(bound + 10);
n = fmpq_get_cfrac(c, r, x, bound);
if (n > bound)
{
flint_printf("FAIL: length=%wd > bound=%wd\n", n, bound);
abort();
}
_fmpz_vec_clear(c, bound + 10);
fmpq_clear(x);
fmpq_clear(r);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
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);
}
}
}
int main()
{
slong i, bound;
double a, b;
fmpq_t q;
fmpr_t t;
flint_printf("bound_2exp_si....");
fflush(stdout);
fmpq_init(q);
fmpr_init(t);
for (i = 0; i < 1000; i++)
{
arith_bernoulli_number(q, i);
bound = bernoulli_bound_2exp_si(i);
fmpr_set_round_fmpz(t, fmpq_numref(q), 32, FMPR_RND_UP);
fmpr_div_fmpz(t, t, fmpq_denref(q), 32, FMPR_RND_UP);
if (fmpr_cmpabs_2exp_si(t, bound) > 0)
{
flint_printf("FAIL: %wd\n", i);
fmpr_print(t); flint_printf("\n\n");
flint_printf("%wd\n", bound); flint_printf("\n\n");
abort();
}
}
fmpq_clear(q);
fmpr_clear(t);
for (i = 100; i < 4000000; i += 1)
{
i += (i & 1);
a = bernoulli_bound_2exp_si(i);
b = log2bern_approx(i);
if (a < b || a > 1.01 * b)
{
flint_printf("FAIL: %wd\n", i);
flint_printf("%wd: %f %f %f\n", i, a, b, (float) a / b);
abort();
}
}
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sin_pi_fmpq....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t s1, s2;
fmpq_t x;
slong prec;
prec = 2 + n_randint(state, 5000);
arb_init(s1);
arb_init(s2);
fmpq_init(x);
fmpq_randtest(x, state, 1 + n_randint(state, 200));
arb_sin_pi_fmpq(s1, x, prec);
arb_const_pi(s2, prec);
arb_mul_fmpz(s2, s2, fmpq_numref(x), prec);
arb_div_fmpz(s2, s2, fmpq_denref(x), prec);
arb_sin(s2, s2, prec);
if (!arb_overlaps(s1, s2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("s1 = "); arb_printd(s1, 15); flint_printf("\n\n");
flint_printf("s2 = "); arb_printd(s2, 15); flint_printf("\n\n");
abort();
}
arb_clear(s1);
arb_clear(s2);
fmpq_clear(x);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("cos_pi_fmpq....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmprb_t c1, c2;
fmpq_t x;
long prec;
prec = 2 + n_randint(state, 5000);
fmprb_init(c1);
fmprb_init(c2);
fmpq_init(x);
fmpq_randtest(x, state, 1 + n_randint(state, 200));
fmprb_cos_pi_fmpq(c1, x, prec);
fmprb_const_pi(c2, prec);
fmprb_mul_fmpz(c2, c2, fmpq_numref(x), prec);
fmprb_div_fmpz(c2, c2, fmpq_denref(x), prec);
fmprb_cos(c2, c2, prec);
if (!fmprb_overlaps(c1, c2))
{
printf("FAIL: overlap\n\n");
printf("x = "); fmpq_print(x); printf("\n\n");
printf("c1 = "); fmprb_printd(c1, 15); printf("\n\n");
printf("c2 = "); fmprb_printd(c2, 15); printf("\n\n");
abort();
}
fmprb_clear(c1);
fmprb_clear(c2);
fmpq_clear(x);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
arb_pow_fmpq(arb_t y, const arb_t x, const fmpq_t a, long prec)
{
if (fmpz_is_one(fmpq_denref(a)))
{
arb_pow_fmpz(y, x, fmpq_numref(a), prec);
}
else if (fmpz_cmp_ui(fmpq_denref(a), 36) <= 0)
{
arb_root(y, x, *fmpq_denref(a), prec);
arb_pow_fmpz(y, y, fmpq_numref(a), prec);
}
else
{
long wp;
wp = prec + 10;
arb_log(y, x, wp);
arb_mul_fmpz(y, y, fmpq_numref(a), wp);
arb_div_fmpz(y, y, fmpq_denref(a), wp);
arb_exp(y, y, prec);
}
}
mpz_class renf_elem_class::floor() const noexcept
{
fmpz_t tmp;
fmpz_init(tmp);
if (nf == nullptr)
fmpz_fdiv_q(tmp, fmpq_numref(b), fmpq_denref(b));
else
renf_elem_floor(tmp, a, nf->renf_t());
mpz_class z;
fmpz_get_mpz(z.get_mpz_t(), tmp);
fmpz_clear(tmp);
return z;
}
mpz_class renf_elem_class::den() const noexcept {
mpz_class res;
if (nf == nullptr)
fmpz_get_mpz(res.__get_mp(), fmpq_denref(b));
else
{
fmpz_t z;
fmpz_init(z);
nf_elem_get_den(z, a->elem, nf->renf_t()->nf);
fmpz_get_mpz(res.__get_mp(), z);
fmpz_clear(z);
}
return res;
}
void test_field1(flint_rand_t state)
{
/* tests in QQ[sqrt(5)] */
int iter;
fmpq_t k;
fmpq_poly_t p;
arb_t emb;
renf_t nf;
renf_elem_t a;
fmpq_poly_init(p);
fmpq_poly_set_coeff_si(p, 2, 1);
fmpq_poly_set_coeff_si(p, 1, -1);
fmpq_poly_set_coeff_si(p, 0, -1);
arb_init(emb);
arb_set_d(emb, 1.61803398874989);
arb_add_error_2exp_si(emb, -20);
renf_init(nf, p, emb, 20 + n_randint(state, 20));
arb_clear(emb);
renf_elem_init(a, nf);
fmpq_init(k);
/* (1+sqrt(5))/2 vs Fibonacci */
fmpq_poly_zero(p);
fmpq_poly_set_coeff_si(p, 1, -1);
for (iter = 1; iter < 50; iter++)
{
fprintf(stderr, "start iter = %d\n", iter);
fflush(stderr);
fmpz_fib_ui(fmpq_numref(k), iter+1);
fmpz_fib_ui(fmpq_denref(k), iter);
fmpq_poly_set_coeff_fmpq(p, 0, k);
renf_elem_set_fmpq_poly(a, p, nf);
check_ceil(a, nf, 1 - iter % 2, "sqrt(5)");
fprintf(stderr, "end\n");
fflush(stderr);
}
renf_elem_clear(a, nf);
renf_clear(nf);
fmpq_clear(k);
fmpq_poly_clear(p);
}
static unsigned int
reduce_octant(fmpz_t v, fmpz_t w, const fmpq_t x)
{
const fmpz * p = fmpq_numref(x);
const fmpz * q = fmpq_denref(x);
unsigned int octant;
mp_bitcnt_t vval, wval;
if (*p > COEFF_MIN / 8 &&
*p < COEFF_MAX / 8 &&
*q > 0 &&
*q < COEFF_MAX / 4)
{
slong pp, qq, ww, vv, tt;
pp = *p;
qq = *q;
tt = pp * 4;
ww = tt / qq;
vv = tt - qq * ww;
/* compute correct (floor) quotient and remainder */
if (vv < 0)
{
ww--;
vv += qq;
}
octant = ((ulong) ww) % 8;
ww = qq * 4;
if (octant % 2 != 0)
vv = qq - vv;
if (vv != 0)
{
count_trailing_zeros(vval, vv);
count_trailing_zeros(wval, ww);
vval = FLINT_MIN(vval, wval);
vv >>= vval;
ww >>= vval;
}
void
_fmpq_bsplit_sum_pq(fmpz_t P, fmpz_t Q, fmpz_t T,
const fmpq * pq, long n1, long n2)
{
if (n2 - n1 <= 0)
{
fmpz_zero(P);
fmpz_one(Q);
}
else if (n2 - n1 == 1)
{
fmpz_set(P, fmpq_numref(pq + n1));
fmpz_set(Q, fmpq_denref(pq + n1));
fmpz_set(T, P);
}
else
{
long m = (n1 + n2) / 2;
fmpz_t P2, Q2, T2;
fmpz_init(P2);
fmpz_init(Q2);
fmpz_init(T2);
_fmpq_bsplit_sum_pq(P, Q, T, pq, n1, m);
_fmpq_bsplit_sum_pq(P2, Q2, T2, pq, m, n2);
fmpz_mul(T, T, Q2);
fmpz_mul(T2, T2, P);
fmpz_add(T, T, T2);
fmpz_mul(P, P, P2);
fmpz_mul(Q, Q, Q2);
fmpz_clear(P2);
fmpz_clear(Q2);
fmpz_clear(T2);
}
}
void
fmprb_get_rand_fmpq(fmpq_t q, flint_rand_t state, const fmprb_t x, long bits)
{
/* there is only one rational */
if (fmprb_is_exact(x))
{
fmpr_get_fmpq(q, fmprb_midref(x));
return;
}
/* pick a denominator */
fmpz_randbits(fmpq_denref(q), state, n_randint(state, bits + 1));
fmpz_abs(fmpq_denref(q), fmpq_denref(q));
if (fmpz_is_zero(fmpq_denref(q)))
fmpz_one(fmpq_denref(q));
_fmprb_get_rand_fmpq(fmpq_numref(q), fmpq_denref(q), state, fmpq_denref(q), x);
fmpq_canonicalise(q);
}
void fmpq_poly_scalar_div_fmpq(fmpq_poly_t rop, const fmpq_poly_t op, const fmpq_t c)
{
if (fmpq_is_zero(c))
{
flint_printf("Exception (fmpq_poly_scalar_div_fmpq). Division by zero.\n");
abort();
}
if (fmpq_poly_is_zero(op))
{
fmpq_poly_zero(rop);
}
else
{
fmpq_poly_fit_length(rop, op->length);
_fmpq_poly_set_length(rop, op->length);
_fmpq_poly_scalar_div_fmpq(rop->coeffs, rop->den,
op->coeffs, op->den, op->length,
fmpq_numref(c), fmpq_denref(c));
}
}
