void
test_1(fmpz_t n)
{
mpfr_t q0; mpfr_init(q0);
mpfr_t q1; mpfr_init(q1);
fmpz_t m; fmpz_init(m);
int c;
fmpz_get_mpfr( q0, n , MPFR_RNDA );
fmpz_get_mpfr_3arg(q1, n[0], MPFR_RNDA );
assert( mpfr_equal_p( q0, q1 ) );
fmpz_set_mpfr(m, q0, MPFR_RNDA);
if( fmpz_cmp_ui( n, WORD(0) ) >= 0 )
{
if( fmpz_cmp(n,m) > 0 )
{
flint_printf("RNDA test failed, n="); fmpz_print(n);
flint_printf(", m="); fmpz_print(m); flint_printf("\n");
assert(0);
}
fmpz_sub(m, m, n);
IF_MORE_THAN_2;
}
else
{
if( fmpz_cmp(n,m) < 0 )
{
flint_printf("RNDA test failed, n="); fmpz_print(n);
flint_printf(", m="); fmpz_print(m); flint_printf("\n");
assert(0);
}
fmpz_sub(m, n, m);
IF_MORE_THAN_2;
}
fmpz_get_mpfr( q0, n, MPFR_RNDZ );
fmpz_set_mpfr( m, q0, MPFR_RNDZ );
c=fmpz_cmp_si( n, WORD(0) );
if(c==0)
assert(0 == fmpz_cmp_si(m,WORD(0)));
else
{
if(c<0)
{
fmpz_neg(n, n);
fmpz_neg(m, m);
}
assert( fmpz_cmp(n,m) >= 0 );
if(c)
assert( fmpz_cmp_si(m,WORD(0)) >= 0 );
fmpz_sub(m, n, m);
IF_MORE_THAN_2_AGAIN;
}
fmpz_clear(m);
mpfr_clear(q1);
mpfr_clear(q0);
}
slong
fmpr_rsqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd)
{
slong r;
if (fmpr_is_special(x))
{
if (fmpr_is_zero(x))
fmpr_pos_inf(y);
else if (fmpr_is_pos_inf(x))
fmpr_zero(y);
else
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
if (fmpr_sgn(x) < 0)
{
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
/* special case: 4^n */
if (fmpz_is_one(fmpr_manref(x)) && fmpz_is_even(fmpr_expref(x)))
{
r = fmpr_set_round(y, x, prec, rnd);
fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1);
fmpz_neg(fmpr_expref(y), fmpr_expref(y));
return r;
}
{
fmpr_t t;
fmpz_t e;
fmpr_init(t);
fmpz_init(e);
fmpz_neg(e, fmpr_expref(x));
if (fmpz_is_odd(e))
fmpz_add_ui(e, e, 1);
fmpr_mul_2exp_fmpz(t, x, e);
CALL_MPFR_FUNC(r, mpfr_rec_sqrt, y, t, prec, rnd);
fmpz_tdiv_q_2exp(e, e, 1);
fmpr_mul_2exp_fmpz(y, y, e);
fmpr_clear(t);
fmpz_clear(e);
return r;
}
}
void
acb_lambertw_left(acb_t res, const acb_t z, const fmpz_t k, slong prec)
{
if (acb_contains_zero(z) && !(fmpz_equal_si(k, -1) && acb_is_real(z)))
{
acb_indeterminate(res);
return;
}
if (arb_is_positive(acb_imagref(z)))
{
acb_lambertw(res, z, k, 0, prec);
}
else if (arb_is_nonpositive(acb_imagref(z)))
{
fmpz_t kk;
fmpz_init(kk);
fmpz_add_ui(kk, k, 1);
fmpz_neg(kk, kk);
acb_conj(res, z);
acb_lambertw(res, res, kk, 0, prec);
acb_conj(res, res);
fmpz_clear(kk);
}
else
{
acb_t za, zb;
fmpz_t kk;
acb_init(za);
acb_init(zb);
fmpz_init(kk);
acb_set(za, z);
acb_conj(zb, z);
arb_nonnegative_part(acb_imagref(za), acb_imagref(za));
arb_nonnegative_part(acb_imagref(zb), acb_imagref(zb));
fmpz_add_ui(kk, k, 1);
fmpz_neg(kk, kk);
acb_lambertw(za, za, k, 0, prec);
acb_lambertw(zb, zb, kk, 0, prec);
acb_conj(zb, zb);
acb_union(res, za, zb, prec);
acb_clear(za);
acb_clear(zb);
fmpz_clear(kk);
}
}
int
main(void)
{
long i;
fmpz_t x;
printf("fits_si....");
fflush(stdout);
fmpz_init(x);
fmpz_set_si(x, COEFF_MIN);
check(x, 1);
fmpz_set_si(x, COEFF_MAX);
check(x, 1);
fmpz_set_si(x, LONG_MAX);
check(x, 1);
fmpz_set_si(x, LONG_MIN);
check(x, 1);
fmpz_set_ui(x, ULONG_MAX);
check(x, 0);
fmpz_set_ui(x, ULONG_MAX);
fmpz_neg(x, x);
check(x, 0);
fmpz_set_si(x, LONG_MAX);
fmpz_add_ui(x, x, 1);
check(x, 0);
fmpz_set_si(x, LONG_MIN);
fmpz_sub_ui(x, x, 1);
check(x, 0);
for (i = 0; i < 1000; i++)
{
fmpz_set_ui(x, 1);
fmpz_mul_2exp(x, x, i);
check(x, i < FLINT_BITS - 1);
fmpz_neg(x, x);
check(x, i < FLINT_BITS); /* LONG_MIN fits */
}
fmpz_clear(x);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void _arith_euler_number_zeta(fmpz_t res, ulong n)
{
mpz_t r;
mpfr_t t, z, pi;
mp_bitcnt_t prec, pi_prec;
if (n % 2)
{
fmpz_zero(res);
return;
}
if (n < SMALL_EULER_LIMIT)
{
fmpz_set_ui(res, euler_number_small[n / 2]);
if (n % 4 == 2)
fmpz_neg(res, res);
return;
}
prec = arith_euler_number_size(n) + 10;
pi_prec = prec + FLINT_BIT_COUNT(n);
mpz_init(r);
mpfr_init2(t, prec);
mpfr_init2(z, prec);
mpfr_init2(pi, pi_prec);
flint_mpz_fac_ui(r, n);
mpfr_set_z(t, r, GMP_RNDN);
mpfr_mul_2exp(t, t, n + 2, GMP_RNDN);
/* pi^(n + 1) * L(n+1) */
mpfr_zeta_inv_euler_product(z, n + 1, 1);
mpfr_const_pi(pi, GMP_RNDN);
mpfr_pow_ui(pi, pi, n + 1, GMP_RNDN);
mpfr_mul(z, z, pi, GMP_RNDN);
mpfr_div(t, t, z, GMP_RNDN);
/* round */
mpfr_round(t, t);
mpfr_get_z(r, t, GMP_RNDN);
fmpz_set_mpz(res, r);
if (n % 4 == 2)
fmpz_neg(res, res);
mpz_clear(r);
mpfr_clear(t);
mpfr_clear(z);
mpfr_clear(pi);
}
void
_fmpz_mat_inv_2x2(fmpz ** b, fmpz_t den, fmpz ** const a)
{
fmpz_t tmp;
_fmpz_mat_det_cofactor_2x2(den, a);
fmpz_neg(&b[0][1], &a[0][1]);
fmpz_neg(&b[1][0], &a[1][0]);
fmpz_init(tmp);
fmpz_set(tmp, &a[0][0]);
fmpz_set(&b[0][0], &a[1][1]);
fmpz_set(&b[1][1], tmp);
fmpz_clear(tmp);
}
void
_fmpz_vec_neg(fmpz * vec1, const fmpz * vec2, long len2)
{
long i;
for (i = 0; i < len2; i++)
fmpz_neg(vec1 + i, vec2 + i);
}
void
_fmpz_holonomic_bsplit_hypgeom_fmpz(fmpz_t P, fmpz_t Q,
const fmpz_poly_t R0, const fmpz_poly_t R1, long start, long a, long b)
{
if (b - a == 1)
{
fmpz c = start + a;
fmpz_poly_evaluate_fmpz(P, R0, &c);
fmpz_poly_evaluate_fmpz(Q, R1, &c);
fmpz_neg(P, P);
}
else
{
fmpz_t P2, Q2;
long m = a + (b - a) / 2;
fmpz_init(P2);
fmpz_init(Q2);
_fmpz_holonomic_bsplit_hypgeom_fmpz(P, Q, R0, R1, start, a, m);
_fmpz_holonomic_bsplit_hypgeom_fmpz(P2, Q2, R0, R1, start, m, b);
fmpz_mul(P, P, P2);
fmpz_mul(Q, Q, Q2);
fmpz_clear(P2);
fmpz_clear(Q2);
}
}
void
_fmpz_holonomic_eval_companion_matrix_fmpz(fmpz_mat_t M, fmpz_t Q,
const fmpz_holonomic_t op, long n)
{
fmpz_t c;
long r = fmpz_holonomic_order(op);
long i, j;
fmpz_init(c);
fmpz_set_si(c, n);
fmpz_poly_evaluate_fmpz(Q, op->coeffs + r, c);
for (i = 0; i < r - 1; i++)
{
for (j = 0; j < r; j++)
{
if (i + 1 == j)
fmpz_set(M->rows[i] + j, Q);
else
fmpz_zero(M->rows[i] + j);
}
}
for (j = 0; j < r; j++)
{
fmpz_poly_evaluate_fmpz(M->rows[r - 1] + j, op->coeffs + j, c);
fmpz_neg(M->rows[r - 1] + j, M->rows[r - 1] + j);
}
fmpz_clear(c);
}
void _fmpq_poly_canonicalise(fmpz * poly, fmpz_t den, slong len)
{
if (*den == WORD(1))
return;
if (*den == WORD(-1))
{
_fmpz_vec_neg(poly, poly, len);
fmpz_one(den);
}
else if (len == 0)
{
fmpz_one(den);
}
else
{
fmpz_t gcd;
fmpz_init(gcd);
_fmpz_vec_content(gcd, poly, len);
if (*gcd != WORD(1))
fmpz_gcd(gcd, gcd, den);
if (fmpz_sgn(den) < 0)
fmpz_neg(gcd, gcd);
if (*gcd != WORD(1))
{
_fmpz_vec_scalar_divexact_fmpz(poly, poly, len, gcd);
fmpz_divexact(den, den, gcd);
}
fmpz_clear(gcd);
}
}
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
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);
}
void
fmpz_sub_ui(fmpz_t f, const fmpz_t g, ulong x)
{
fmpz c = *g;
if (!COEFF_IS_MPZ(c)) /* coeff is small */
{
mp_limb_t sum[2];
if (c < 0L) /* g negative, x positive, so difference is negative */
{
add_ssaaaa(sum[1], sum[0], 0, -c, 0, x);
if (sum[1] == 0)
{
fmpz_set_ui(f, sum[0]); /* result fits in 1 limb */
fmpz_neg(f, f);
}
else /* result takes two limbs */
{
__mpz_struct * mpz_ptr;
mpz_t temp;
temp->_mp_d = sum;
temp->_mp_size = -2; /* result is negative number minus negative number, hence negative */
mpz_ptr = _fmpz_promote(f); /* g has already been read */
mpz_set(mpz_ptr, temp);
}
}
else /* coeff is non-negative, x non-negative */
{
if (x < c)
fmpz_set_ui(f, c - x); /* won't be negative and is smaller than c */
else
{
fmpz_set_ui(f, x - c); /* positive or zero */
fmpz_neg(f, f);
}
}
}
else
{
__mpz_struct *mpz_ptr, *mpz_ptr2;
mpz_ptr = COEFF_TO_PTR(c);
mpz_ptr2 = _fmpz_promote(f); /* g is already large */
mpz_sub_ui(mpz_ptr2, mpz_ptr, x);
_fmpz_demote_val(f); /* cancellation may have occurred */
}
}
int
main(void)
{
long i;
fmpz_t x;
printf("abs_fits_ui....");
fflush(stdout);
fmpz_init(x);
fmpz_set_si(x, COEFF_MIN);
check(x, 1);
fmpz_set_si(x, COEFF_MAX);
check(x, 1);
fmpz_set_ui(x, ULONG_MAX);
check(x, 1);
fmpz_set_ui(x, ULONG_MAX);
fmpz_neg(x, x);
check(x, 1);
fmpz_set_ui(x, ULONG_MAX);
fmpz_add_ui(x, x, 1UL);
check(x, 0);
fmpz_neg(x, x);
check(x, 0);
for (i = 0; i < 1000; i++)
{
fmpz_set_ui(x, 1UL);
fmpz_mul_2exp(x, x, i);
check(x, i < FLINT_BITS);
fmpz_neg(x, x);
check(x, i < FLINT_BITS);
}
fmpz_clear(x);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
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));
}
}
static void entry(fmpz_t rop_u, long *rop_v,
const long *u, const long *v, const fmpz *a, const fmpz *dinv,
const fmpz **mu, long M, const long **C, const long *lenC,
long n, long d, long p, long N, long N2)
{
const long ku = diagfrob_k(u, n, d);
const long kv = diagfrob_k(v, n, d);
fmpz_t f, g, P;
fmpz_init(f);
fmpz_init(g);
fmpz_init_set_ui(P, p);
/*
Compute $g := (u'-1)! \alpha_{u+1,v+1}$ to precision $N2$.
*/
fmpz_fac_ui(f, ku - 1);
alpha(g, u, v, a, dinv, mu, M, C, lenC, n, d, p, N2);
fmpz_mul(g, f, g);
/*
Compute $f := (-1)^{u'+v'} (v'-1)!$ exactly.
*/
fmpz_fac_ui(f, kv - 1);
if ((ku + kv) % 2 != 0)
{
fmpz_neg(f, f);
}
/*
Set rop to the product of $f$ and $g^{-1} mod $p^N$.
*/
*rop_v = fmpz_remove(f, f, P) + n - fmpz_remove(g, g, P);
if (*rop_v >= N)
{
fmpz_zero(rop_u);
*rop_v = 0;
}
else
{
_padic_inv(g, g, P, N - *rop_v);
fmpz_mul(rop_u, f, g);
fmpz_pow_ui(f, P, N - *rop_v);
fmpz_mod(rop_u, rop_u, f);
}
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(P);
}
void
_padic_log_balanced(fmpz_t z, const fmpz_t y, long v, const fmpz_t p, long N)
{
fmpz_t pv, pN, r, t, u;
long val;
padic_inv_t S;
fmpz_init(pv);
fmpz_init(pN);
fmpz_init(r);
fmpz_init(t);
fmpz_init(u);
_padic_inv_precompute(S, p, N);
fmpz_set(t, y);
fmpz_set(pv, p);
fmpz_pow_ui(pN, p, N);
fmpz_zero(z);
val = 1;
/*
TODO: Abort earlier if larger than $p^N$, possible
with variable precision?
*/
while (!fmpz_is_zero(t))
{
fmpz_mul(pv, pv, pv);
fmpz_fdiv_qr(t, r, t, pv);
if (!fmpz_is_zero(t))
{
fmpz_mul(t, t, pv);
fmpz_add_ui(u, r, 1);
_padic_inv_precomp(u, u, S);
fmpz_mul(t, t, u);
fmpz_mod(t, t, pN);
}
if (!fmpz_is_zero(r))
{
fmpz_neg(r, r);
_padic_log_bsplit(r, r, val, p, N);
fmpz_sub(z, z, r);
}
val *= 2;
}
fmpz_clear(pv);
fmpz_clear(pN);
fmpz_clear(r);
fmpz_clear(t);
fmpz_clear(u);
_padic_inv_clear(S);
}
void
fmpz_randtest(fmpz_t f, flint_rand_t state, mp_bitcnt_t bits)
{
ulong m;
fmpz_randtest_unsigned(f, state, bits);
m = n_randlimb(state);
if (m & UWORD(1))
fmpz_neg(f, f);
}
/* quotient of absolute value, rounded up */
static __inline__ void
fmpz_cdiv_abs_q(fmpz_t q, const fmpz_t x, const fmpz_t y)
{
if (fmpz_sgn(x) == fmpz_sgn(y))
{
fmpz_cdiv_q(q, x, y);
}
else
{
fmpz_fdiv_q(q, x, y);
fmpz_neg(q, q);
}
}
void
_fmpq_div(fmpz_t rnum, fmpz_t rden, const fmpz_t op1num, const fmpz_t op1den,
const fmpz_t op2num, const fmpz_t op2den)
{
fmpz_t t, u;
fmpz_init(t);
fmpz_init(u);
fmpz_set(t, op2den);
fmpz_set(u, op2num);
_fmpq_mul(rnum, rden, op1num, op1den, t, u);
fmpz_clear(t);
fmpz_clear(u);
if (fmpz_sgn(rden) < 0)
{
fmpz_neg(rnum, rnum);
fmpz_neg(rden, rden);
}
}
void
_fmpz_mat_det_bareiss(fmpz_t det, fmpz_mat_t tmp)
{
long *perm, n = fmpz_mat_nrows(tmp);
perm = _perm_init(n);
fmpz_mat_fflu(tmp, det, perm, tmp, 1);
if (_perm_parity(perm, n) == 1)
fmpz_neg(det, det);
_perm_clear(perm);
}
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;
}
explicit
FlintZZ(const ZZ& a)
{
long n = NumBits(a);
fmpz_init(value);
for (long i = 0; i < n; i++)
if (bit(a, i)) fmpz_setbit(value, i);
if (a < 0)
fmpz_neg(value, value);
}
void
acb_lambertw_cleared_cut_fix_small(acb_t res, const acb_t z,
const acb_t ez1, const fmpz_t k, int flags, slong prec)
{
acb_t zz, zmid, zmide1;
arf_t eps;
acb_init(zz);
acb_init(zmid);
acb_init(zmide1);
arf_init(eps);
arf_mul_2exp_si(eps, arb_midref(acb_realref(z)), -prec);
acb_set(zz, z);
if (arf_sgn(arb_midref(acb_realref(zz))) < 0 &&
(!fmpz_is_zero(k) || arf_sgn(arb_midref(acb_realref(ez1))) < 0) &&
arf_cmpabs(arb_midref(acb_imagref(zz)), eps) < 0)
{
/* now the value must be in [0,2eps] */
arf_get_mag(arb_radref(acb_imagref(zz)), eps);
arf_set_mag(arb_midref(acb_imagref(zz)), arb_radref(acb_imagref(zz)));
if (arf_sgn(arb_midref(acb_imagref(z))) >= 0)
{
acb_lambertw_cleared_cut(res, zz, k, flags, prec);
}
else
{
fmpz_t kk;
fmpz_init(kk);
fmpz_neg(kk, k);
acb_lambertw_cleared_cut(res, zz, kk, flags, prec);
acb_conj(res, res);
fmpz_clear(kk);
}
}
else
{
acb_lambertw_cleared_cut(res, zz, k, flags, prec);
}
acb_clear(zz);
acb_clear(zmid);
acb_clear(zmide1);
arf_clear(eps);
}
void
_fmpz_poly_sub(fmpz * res, const fmpz * poly1, slong len1, const fmpz * poly2,
slong len2)
{
slong i, min = FLINT_MIN(len1, len2);
for (i = 0; i < min; i++) /* subtract up to the length of the shorter poly */
fmpz_sub(res + i, poly1 + i, poly2 + i);
if (poly1 != res) /* copy any remaining coefficients from poly1 */
for (i = min; i < len1; i++)
fmpz_set(res + i, poly1 + i);
/* careful, it is *always* necessary to negate coeffs from poly2, even if this is already res */
for (i = min; i < len2; i++)
fmpz_neg(res + i, poly2 + i);
}
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 _fmpq_poly_scalar_div_si(fmpz * rpoly, fmpz_t rden, const fmpz * poly,
const fmpz_t den, long len, long c)
{
if (c == 1)
{
if (rpoly != poly)
{
_fmpz_vec_set(rpoly, poly, len);
fmpz_set(rden, den);
}
}
else if (c == -1)
{
_fmpz_vec_neg(rpoly, poly, len);
fmpz_set(rden, den);
}
else
{
fmpz_t d, f;
fmpz_init(d);
fmpz_init(f);
fmpz_set_si(f, c);
_fmpz_vec_content(d, poly, len);
fmpz_gcd(d, d, f);
if (c > 0)
{
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, d);
fmpz_mul_si(rden, den, c / fmpz_get_si(d));
}
else
{
ulong q = (- (ulong) c) / fmpz_get_ui(d);
fmpz_neg(d, d);
_fmpz_vec_scalar_divexact_fmpz(rpoly, poly, len, d);
fmpz_mul_ui(rden, den, q);
}
fmpz_clear(d);
fmpz_clear(f);
}
}
void
mag_root(mag_t y, const mag_t x, ulong n)
{
if (n == 0)
{
mag_inf(y);
}
else if (n == 1 || mag_is_special(x))
{
mag_set(y, x);
}
else if (n == 2)
{
mag_sqrt(y, x);
}
else if (n == 4)
{
mag_sqrt(y, x);
mag_sqrt(y, y);
}
else
{
fmpz_t e, f;
fmpz_init_set_ui(e, MAG_BITS);
fmpz_init(f);
/* We evaluate exp(log(1+2^(kn)x)/n) 2^-k where k is chosen
so that 2^(kn) x ~= 2^30. TODO: this rewriting is probably
unnecessary with the new exp/log functions. */
fmpz_sub(e, e, MAG_EXPREF(x));
fmpz_cdiv_q_ui(e, e, n);
fmpz_mul_ui(f, e, n);
mag_mul_2exp_fmpz(y, x, f);
mag_log1p(y, y);
mag_div_ui(y, y, n);
mag_exp(y, y);
fmpz_neg(e, e);
mag_mul_2exp_fmpz(y, y, e);
fmpz_clear(e);
fmpz_clear(f);
}
}
void
fmpz_poly_bit_pack(fmpz_t f, const fmpz_poly_t poly,
mp_bitcnt_t bit_size)
{
long len;
__mpz_struct * mpz;
long i, d;
int negate;
len = fmpz_poly_length(poly);
if (len == 0 || bit_size == 0)
{
fmpz_zero(f);
return;
}
mpz = _fmpz_promote(f);
mpz_realloc2(mpz, len * bit_size);
d = mpz->_mp_alloc;
mpn_zero(mpz->_mp_d, d);
if (fmpz_sgn(fmpz_poly_lead(poly)) < 0)
negate = -1;
else
negate = 0;
_fmpz_poly_bit_pack(mpz->_mp_d, poly->coeffs, len, bit_size, negate);
for (i = d - 1; i >= 0; i--)
{
if (mpz->_mp_d[i] != 0)
break;
}
d = i + 1;
mpz->_mp_size = d;
_fmpz_demote_val(f);
if (negate)
fmpz_neg(f, f);
}
void
fmpz_divexact(fmpz_t f, const fmpz_t g, const fmpz_t h)
{
fmpz c1 = *g;
fmpz c2 = *h;
if (fmpz_is_zero(h))
{
flint_printf("Exception (fmpz_divexact). Division by zero.\n");
abort();
}
if (!COEFF_IS_MPZ(c1)) /* g is small, h must be also or division isn't exact */
{
fmpz_set_si(f, c1 / c2);
}
else /* g is large */
{
__mpz_struct * mpz_ptr = _fmpz_promote(f);
if (!COEFF_IS_MPZ(c2)) /* h is small */
{
if (c2 > 0) /* h > 0 */
{
flint_mpz_divexact_ui(mpz_ptr, COEFF_TO_PTR(c1), c2);
_fmpz_demote_val(f); /* division by h may result in small value */
}
else
{
flint_mpz_divexact_ui(mpz_ptr, COEFF_TO_PTR(c1), -c2);
_fmpz_demote_val(f); /* division by h may result in small value */
fmpz_neg(f, f);
}
}
else /* both are large */
{
mpz_divexact(mpz_ptr, COEFF_TO_PTR(c1), COEFF_TO_PTR(c2));
_fmpz_demote_val(f); /* division by h may result in small value */
}
}
}
