int
fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd)
{
int r;
if (fmpr_is_special(y))
{
if (fmpr_is_zero(y)) mpfr_set_zero(x, 0);
else if (fmpr_is_pos_inf(y)) mpfr_set_inf(x, 1);
else if (fmpr_is_neg_inf(y)) mpfr_set_inf(x, -1);
else mpfr_set_nan(x);
r = 0;
}
else if (COEFF_IS_MPZ(*fmpr_expref(y)))
{
flint_printf("exception: exponent too large to convert to mpfr");
abort();
}
else
{
if (!COEFF_IS_MPZ(*fmpr_manref(y)))
#if defined(__MINGW64__)
r = mpfr_set_sj_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd);
#else
r = mpfr_set_si_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd);
#endif
else
r = mpfr_set_z_2exp(x, COEFF_TO_PTR(*fmpr_manref(y)), *fmpr_expref(y), rnd);
if (!mpfr_regular_p(x))
{
flint_printf("exception: exponent too large to convert to mpfr");
abort();
}
}
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
fmpz_tdiv_qr(fmpz_t f, fmpz_t s, const fmpz_t g, const fmpz_t h)
{
fmpz c1 = *g;
fmpz c2 = *h;
if (fmpz_is_zero(h))
{
flint_printf("Exception: division by zero in fmpz_tdiv_qr\n");
abort();
}
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (!COEFF_IS_MPZ(c2)) /* h is also small */
{
fmpz q = c1 / c2; /* compute C quotient */
fmpz r = c1 - c2 * q; /* compute remainder */
fmpz_set_si(f, q);
fmpz_set_si(s, r);
}
else /* h is large and g is small */
{
fmpz_set_ui(f, WORD(0)); /* g is zero */
fmpz_set_si(s, c1);
}
}
else /* g is large */
{
__mpz_struct *mpz_ptr, *mpz_ptr2;
_fmpz_promote(f); /* must not hang on to ptr whilst promoting s */
mpz_ptr2 = _fmpz_promote(s);
mpz_ptr = COEFF_TO_PTR(*f);
if (!COEFF_IS_MPZ(c2)) /* h is small */
{
if (c2 > 0) /* h > 0 */
{
flint_mpz_tdiv_qr_ui(mpz_ptr, mpz_ptr2, COEFF_TO_PTR(c1), c2);
}
else
{
flint_mpz_tdiv_qr_ui(mpz_ptr, mpz_ptr2, COEFF_TO_PTR(c1), -c2);
mpz_neg(mpz_ptr, mpz_ptr);
}
}
else /* both are large */
{
mpz_tdiv_qr(mpz_ptr, mpz_ptr2, COEFF_TO_PTR(c1), COEFF_TO_PTR(c2));
}
_fmpz_demote_val(f); /* division by h may result in small value */
_fmpz_demote_val(s); /* division by h may result in small value */
}
}
void fmpz_powm(fmpz_t f, const fmpz_t g, const fmpz_t e, const fmpz_t m)
{
if (fmpz_sgn(m) <= 0)
{
flint_printf("Exception (fmpz_powm). Modulus is less than 1.\n");
abort();
}
else if (!COEFF_IS_MPZ(*e)) /* e is small */
{
fmpz_powm_ui(f, g, *e, m);
}
else /* e is large */
{
if (!COEFF_IS_MPZ(*m)) /* m is small */
{
ulong g1 = fmpz_fdiv_ui(g, *m);
mpz_t g2, m2;
__mpz_struct *mpz_ptr;
flint_mpz_init_set_ui(g2, g1);
flint_mpz_init_set_ui(m2, *m);
mpz_ptr = _fmpz_promote(f);
mpz_powm(mpz_ptr, g2, COEFF_TO_PTR(*e), m2);
mpz_clear(g2);
mpz_clear(m2);
_fmpz_demote_val(f);
}
else /* m is large */
{
if (!COEFF_IS_MPZ(*g)) /* g is small */
{
mpz_t g2;
__mpz_struct *mpz_ptr;
flint_mpz_init_set_si(g2, *g);
mpz_ptr = _fmpz_promote(f);
mpz_powm(mpz_ptr, g2, COEFF_TO_PTR(*e), COEFF_TO_PTR(*m));
mpz_clear(g2);
_fmpz_demote_val(f);
}
else /* g is large */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f);
mpz_powm(mpz_ptr,
COEFF_TO_PTR(*g), COEFF_TO_PTR(*e), COEFF_TO_PTR(*m));
_fmpz_demote_val(f);
}
}
}
}
void
fmpz_fdiv_q(fmpz_t f, const fmpz_t g, const fmpz_t h)
{
fmpz c1 = *g;
fmpz c2 = *h;
if (fmpz_is_zero(h))
{
printf("Exception: division by zero in fmpz_fdiv_q\n");
abort();
}
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (!COEFF_IS_MPZ(c2)) /* h is also small */
{
fmpz q = c1 / c2; /* compute C quotient */
fmpz r = c1 - c2 * q; /* compute remainder */
if (r && (c2 ^ r) < 0L)
--q;
fmpz_set_si(f, q);
}
else /* h is large and g is small */
{
if ((c1 > 0L && fmpz_sgn(h) < 0) || (c1 < 0L && fmpz_sgn(h) > 0)) /* signs are the same */
fmpz_set_si(f, -1L); /* quotient is negative, round down to minus one */
else
fmpz_zero(f);
}
}
else /* g is large */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f);
if (!COEFF_IS_MPZ(c2)) /* h is small */
{
if (c2 > 0) /* h > 0 */
{
mpz_fdiv_q_ui(mpz_ptr, COEFF_TO_PTR(c1), c2);
}
else
{
mpz_cdiv_q_ui(mpz_ptr, COEFF_TO_PTR(c1), -c2);
mpz_neg(mpz_ptr, mpz_ptr);
}
}
else /* both are large */
{
mpz_fdiv_q(mpz_ptr, COEFF_TO_PTR(c1), COEFF_TO_PTR(c2));
}
_fmpz_demote_val(f); /* division by h may result in small value */
}
}
void
mag_sqrt(mag_t y, const mag_t x)
{
if (mag_is_special(x))
{
mag_set(y, x);
}
else
{
double t;
fmpz e;
t = MAG_MAN(x) * ldexp(1.0, -MAG_BITS);
e = MAG_EXP(x);
if (!COEFF_IS_MPZ(e))
{
if (e % 2 != 0)
{
e = (e - 1) >> 1;
t *= 2.0;
}
else
{
e >>= 1;
}
t = sqrt(t) * (1 + 1e-13);
mag_set_d_2exp_fmpz(y, t, &e);
}
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);
}
}
}
int fmpz_fprint(FILE * file, const fmpz_t x)
{
if (!COEFF_IS_MPZ(*x))
return fprintf(file, "%ld", *x);
else
return (int) mpz_out_str(file, 10, COEFF_TO_PTR(*x));
}
void
arf_ceil(arf_t z, const arf_t x)
{
if (arf_is_special(x) || arf_is_int(x))
{
arf_set(z, x);
}
else
{
slong exp = ARF_EXP(x);
/* now exp cannot be too large, as we would have
caught this in arf_is_int() */
if (COEFF_IS_MPZ(exp) || exp <= 0)
{
if (ARF_SGNBIT(x))
arf_zero(z);
else
arf_one(z);
}
else if (exp == 1)
{
arf_set_si(z, ARF_SGNBIT(x) ? -1 : 2);
}
else
{
arf_set_round(z, x, exp, ARF_RND_CEIL);
}
}
}
static int
use_algebraic(const fmpz_t v, const fmpz_t w, slong prec)
{
fmpz q = *w;
int r;
if (COEFF_IS_MPZ(q))
return 0;
if (q <= 6)
return 1;
count_trailing_zeros(r, q);
q >>= r;
if (r >= 4 && prec < (r - 3) * 300)
return 0;
if (q > 1000)
return 0;
if (prec < 1500 + 150 * q)
return 0;
return 1;
}
ulong
fmpz_fdiv_ui(const fmpz_t g, ulong h)
{
fmpz c1 = *g;
ulong r;
if (h == 0UL)
{
printf("Exception: division by 0 in fmpz_fdiv_ui\n");
abort();
}
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (c1 < 0L)
{
r = h - (-c1 % h); /* C doesn't correctly handle negative mods */
if (r == h)
r = 0;
}
else
r = c1 % h;
return r;
}
else /* g is large */
{
return mpz_fdiv_ui(COEFF_TO_PTR(c1), h);
}
}
void
fmpz_tdiv_q_ui(fmpz_t f, const fmpz_t g, ulong h)
{
fmpz c1 = *g;
ulong c2 = h;
if (h == 0)
{
printf("Exception: division by zero in fmpz_tdiv_q_ui\n");
abort();
}
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (c1 > 0)
{
fmpz_set_ui(f, c1 / c2);
}
else
{
ulong q = ((ulong) -c1) / c2;
fmpz_set_si(f, - (long) q);
}
}
else /* g is large */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f);
mpz_tdiv_q_ui(mpz_ptr, COEFF_TO_PTR(c1), c2);
_fmpz_demote_val(f); /* division by h may result in small value */
}
}
void padic_ctx_init(padic_ctx_t ctx, const fmpz_t p, long N,
enum padic_print_mode mode)
{
fmpz_init(ctx->p);
fmpz_set(ctx->p, p);
ctx->N = N;
ctx->pinv = (!COEFF_IS_MPZ(*p)) ? n_precompute_inverse(fmpz_get_ui(p)) : 0;
if (N > 0)
{
long i, len;
ctx->min = FLINT_MAX(1, N - 10);
ctx->max = N + 10;
len = ctx->max - ctx->min;
ctx->pow = _fmpz_vec_init(len);
fmpz_pow_ui(ctx->pow, p, ctx->min);
for (i = 1; i < len; i++)
fmpz_mul(ctx->pow + i, ctx->pow + (i - 1), p);
}
else
{
ctx->min = 0;
ctx->max = 0;
ctx->pow = NULL;
}
ctx->mode = mode;
}
void
fmpz_gcd(fmpz_t f, const fmpz_t g, const fmpz_t h)
{
fmpz c1 = *g;
fmpz c2 = *h;
if (fmpz_is_zero(g))
{
fmpz_abs(f, h);
return;
}
if (fmpz_is_zero(h))
{
fmpz_abs(f, g);
return;
}
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (!COEFF_IS_MPZ(c2)) /* h is also small */
{
fmpz_set_si(f, z_gcd(c1, c2));
}
else /* h is large, but g is small */
{
fmpz c2d = fmpz_fdiv_ui(h, FLINT_ABS(c1));
fmpz_set_si(f, z_gcd(c1, c2d));
}
}
else
{
if (!COEFF_IS_MPZ(c2)) /* h is small, but g is large */
{
fmpz c1d = fmpz_fdiv_ui(g, FLINT_ABS(c2));
fmpz_set_si(f, z_gcd(c2, c1d));
}
else /* g and h are both large */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f); /* aliasing fine as g, h already large */
mpz_gcd(mpz_ptr, COEFF_TO_PTR(c1), COEFF_TO_PTR(c2));
_fmpz_demote_val(f); /* gcd may be small */
}
}
}
slong
fmpr_mul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd)
{
fmpz xv, yv;
fmpz yexp;
if (fmpr_is_special(x) || fmpz_is_zero(y))
{
if (fmpr_is_zero(x))
{
fmpr_zero(z);
}
else if (fmpz_is_zero(y) && fmpr_is_finite(x))
{
fmpr_zero(z);
}
else if (fmpr_is_inf(x) && !fmpz_is_zero(y))
{
if (fmpr_sgn(x) == fmpz_sgn(y))
fmpr_pos_inf(z);
else
fmpr_neg_inf(z);
}
else
{
fmpr_nan(z);
}
return FMPR_RESULT_EXACT;
}
xv = *fmpr_manref(x);
yv = *y;
if (!COEFF_IS_MPZ(xv) && !COEFF_IS_MPZ(yv))
{
mp_limb_t ytmp;
unsigned int bc;
ytmp = FLINT_ABS(yv);
count_trailing_zeros(bc, ytmp);
ytmp >>= bc;
yexp = bc;
return _fmpr_mul_1x1(z, FLINT_ABS(xv), fmpr_expref(x),
ytmp, &yexp, (xv ^ yv) < 0, prec, rnd);
}
static __inline__ void
fmpz_clear_and_zero(fmpz_t f)
// works like fmpz_zero(), but does not assign zero twice --- one time
// is quite enough
{
if (COEFF_IS_MPZ(*f))
_fmpz_clear_mpz(*f);
(*f) = WORD(0);
}
void
_fmprb_get_rand_fmpq(fmpz_t num, fmpz_t den, flint_rand_t state,
const fmpz_t den_mult, const fmprb_t x)
{
fmpz_t a, b, exp;
fmpz_init(a);
fmpz_init(b);
fmpz_init(exp);
fmprb_get_interval_fmpz_2exp(a, b, exp, x);
if (COEFF_IS_MPZ(*exp))
{
printf("exception: fmprb_get_rand_fmpq: too large exponent\n");
abort();
}
if (*exp >= 0)
{
fmpz_mul_2exp(a, a, *exp);
fmpz_mul_2exp(b, b, *exp);
}
/* generate random integer in [a*den, b*den] */
fmpz_mul(a, a, den_mult);
fmpz_mul(b, b, den_mult);
fmpz_add_ui(b, b, 1UL);
fmpz_sub(b, b, a);
/* return one endpoint with high probability (used for stress
testing rounding) */
if (n_randint(state, 6) == 0)
{
if (n_randint(state, 2))
fmpz_zero(num);
else
fmpz_sub_ui(num, b, 1UL);
}
else
{
fmpz_randtest_mod(num, state, b);
}
fmpz_add(num, num, a);
fmpz_set(den, den_mult);
if (*exp < 0)
fmpz_mul_2exp(den, den, -(*exp));
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(exp);
}
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 */
}
}
}
int fmpz_fits_si(const fmpz_t f)
{
if (!COEFF_IS_MPZ(*f))
{
return 1;
}
else
{
return mpz_fits_slong_p(COEFF_TO_PTR(*f));
}
}
void flint_mpz_init_set_readonly(mpz_t z, const fmpz_t f)
{
if (COEFF_IS_MPZ(*f))
{
*z = *COEFF_TO_PTR(*f);
}
else
{
mpz_init_set_si(z, *f);
}
}
__mpz_struct * _fmpz_promote(fmpz_t f)
{
if (!COEFF_IS_MPZ(*f)) /* f is small so promote it first */
{
__mpz_struct * mpz_ptr = _fmpz_new_mpz();
(*f) = PTR_TO_COEFF(mpz_ptr);
return mpz_ptr;
}
else /* f is large already, just return the pointer */
return COEFF_TO_PTR(*f);
}
int fmpz_cmpabs(const fmpz_t f, const fmpz_t g)
{
if (f == g) return 0; /* aliased inputs */
if (!COEFF_IS_MPZ(*f))
{
if (!COEFF_IS_MPZ(*g))
{
mp_limb_t uf = FLINT_ABS(*f);
mp_limb_t ug = FLINT_ABS(*g);
return (uf < ug ? -1 : (uf > ug));
}
else return -1;
}
else
{
if (!COEFF_IS_MPZ(*g)) return 1; /* f is large, so if g isn't... */
else return mpz_cmpabs(COEFF_TO_PTR(*f), COEFF_TO_PTR(*g));
}
}
mp_size_t
fmpz_size(const fmpz_t f)
{
fmpz d = *f;
if (d == 0)
return 0;
if (!COEFF_IS_MPZ(d))
return 1;
else
return mpz_size(COEFF_TO_PTR(d));
}
void
fmpz_neg_1arg( fmpz_t v )
// inspired by FLINT fmpz_neg
{
if (!COEFF_IS_MPZ(*v))
*v = -*v;
else
{
__mpz_struct* mpz_ptr = _fmpz_promote(v);
// TODO: write effective subroutine to invert GMP mpz in-place
mpz_neg(mpz_ptr, mpz_ptr);
}
}
static __inline__ int
low_bits_are_zero(const fmpz_t u, int bits)
{
fmpz f = *u;
mp_limb_t low;
if (!COEFF_IS_MPZ(f))
low = FLINT_ABS(f);
else
low = COEFF_TO_PTR(f)->_mp_d[0];
return (low & ((UWORD(1) << bits) - 1)) == 0;
}
void fmpz_add(fmpz_t f, const fmpz_t g, const fmpz_t h)
{
fmpz c1 = *g;
fmpz c2 = *h;
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (!COEFF_IS_MPZ(c2)) /* both inputs are small */
{
fmpz_set_si(f, c1 + c2);
} else /* g is small, h is large */
{
__mpz_struct * mpz3 = _fmpz_promote(f); /* g is saved and h is large */
__mpz_struct * mpz2 = COEFF_TO_PTR(c2);
if (c1 < 0L) mpz_sub_ui(mpz3, mpz2, -c1);
else mpz_add_ui(mpz3, mpz2, c1);
_fmpz_demote_val(f); /* may have cancelled */
}
}
else
{
if (!COEFF_IS_MPZ(c2)) /* g is large, h is small */
{
__mpz_struct * mpz3 = _fmpz_promote(f); /* h is saved and g is large */
__mpz_struct * mpz1 = COEFF_TO_PTR(c1);
if (c2 < 0L) mpz_sub_ui(mpz3, mpz1, -c2);
else mpz_add_ui(mpz3, mpz1, c2);
_fmpz_demote_val(f); /* may have cancelled */
}
else /* g and h are large */
{
__mpz_struct * mpz3 = _fmpz_promote(f); /* aliasing means f is already large */
__mpz_struct * mpz1 = COEFF_TO_PTR(c1);
__mpz_struct * mpz2 = COEFF_TO_PTR(c2);
mpz_add(mpz3, mpz1, mpz2);
_fmpz_demote_val(f); /* may have cancelled */
}
}
}
__mpz_struct * _fmpz_promote_val(fmpz_t f)
{
fmpz c = (*f);
if (!COEFF_IS_MPZ(c)) /* f is small so promote it */
{
__mpz_struct * mpz_ptr = _fmpz_new_mpz();
(*f) = PTR_TO_COEFF(mpz_ptr);
mpz_set_si(mpz_ptr, c);
return mpz_ptr;
}
else /* f is large already, just return the pointer */
return COEFF_TO_PTR(c);
}
int
fmpz_cmp_ui(const fmpz_t f, ulong g)
{
fmpz c = *f;
if (!COEFF_IS_MPZ(c)) /* f is small */
{
if (c < 0L || g > COEFF_MAX)
return -1;
else
return c < (long) g ? -1 : c > (long) g;
}
else /* f is large */
return mpz_cmp_ui(COEFF_TO_PTR(c), g);
}
int fmpz_fits_si(const fmpz_t f)
{
if (!COEFF_IS_MPZ(*f))
{
return 1;
}
else
{
#if defined(_WIN64)
return flint_mpz_fits_si_p(COEFF_TO_PTR(*f));
#else
return mpz_fits_slong_p(COEFF_TO_PTR(*f));
#endif
}
}
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 */
}
}
