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_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 fmpz_primorial(fmpz_t res, long n)
{
mp_size_t len, pi;
ulong bits;
__mpz_struct * mpz_ptr;
if (n <= LARGEST_ULONG_PRIMORIAL)
{
if (n <= 2)
fmpz_set_ui(res, 1 + (n==2));
else
fmpz_set_ui(res, ULONG_PRIMORIALS[(n-1)/2-1]);
return;
}
pi = n_prime_pi(n);
n_compute_primes(pi);
bits = FLINT_BIT_COUNT(flint_primes[pi - 1]);
mpz_ptr = _fmpz_promote(res);
mpz_realloc2(mpz_ptr, pi*bits);
len = mpn_prod_limbs(mpz_ptr->_mp_d, flint_primes, pi, bits);
mpz_ptr->_mp_size = len;
}
void fmpz_fib_ui(fmpz_t f, ulong n)
{
if (n < NUM_SMALL_FIB)
fmpz_set_ui(f, small_fib[n]);
else
mpz_fib_ui(_fmpz_promote(f), n);
}
void fmpz_fac_ui(fmpz_t f, ulong n)
{
if (n < FLINT_NUM_TINY_FACTORIALS)
fmpz_set_ui(f, flint_tiny_factorials[n]);
else
mpz_fac_ui(_fmpz_promote(f), n);
}
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 */
}
}
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
fmpz_mul_si(fmpz_t f, const fmpz_t g, long x)
{
fmpz c2 = *g;
if (x == 0)
{
fmpz_zero(f);
return;
}
else if (!COEFF_IS_MPZ(c2)) /* c2 is small */
{
mp_limb_t prod[2];
mp_limb_t uc2 = FLINT_ABS(c2);
mp_limb_t ux = FLINT_ABS(x);
/* unsigned limb by limb multiply (assembly for most CPU's) */
umul_ppmm(prod[1], prod[0], uc2, ux);
if (!prod[1]) /* result fits in one limb */
{
fmpz_set_ui(f, prod[0]);
if ((c2 ^ x) < 0L)
fmpz_neg(f, f);
}
else /* result takes two limbs */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f);
/* two limbs, least significant first, native endian, no nails, stored in prod */
mpz_import(mpz_ptr, 2, -1, sizeof(mp_limb_t), 0, 0, prod);
if ((c2 ^ x) < 0L)
mpz_neg(mpz_ptr, mpz_ptr);
}
}
else /* c2 is large */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f); /* ok without val as if aliased both are large */
mpz_mul_si(mpz_ptr, COEFF_TO_PTR(c2), x);
}
}
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);
}
}
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 */
}
}
}
void
number_of_partitions(fmpz_t x, ulong n)
{
if (n < NUMBER_OF_SMALL_PARTITIONS)
{
fmpz_set_ui(x, partitions_lookup[n]);
}
else
{
mpfr_t t;
mpfr_init(t);
number_of_partitions_mpfr(t, n);
mpfr_get_z(_fmpz_promote(x), t, MPFR_RNDN);
_fmpz_demote_val(x);
mpfr_clear(t);
}
}
void
fmpz_set(fmpz_t f, const fmpz_t g)
{
if (f == g)
return; /* aliased inputs */
if (!COEFF_IS_MPZ(*g)) /* g is small */
{
_fmpz_demote(f);
*f = *g;
}
else /* g is large */
{
__mpz_struct *mpz_ptr = _fmpz_promote(f);
mpz_set(mpz_ptr, COEFF_TO_PTR(*g));
}
}
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 */
}
}
}
void
fmpz_set_mpf(fmpz_t f, const mpf_t x)
{
#if defined(__MPIR_VERSION)
if (mpf_fits_si_p(x))
#else
if (flint_mpf_fits_slong_p(x))
#endif
{
slong cx = flint_mpf_get_si(x);
fmpz_set_si(f, cx);
}
else
{
__mpz_struct *z = _fmpz_promote(f);
mpz_set_f(z, x);
}
}
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 */
}
}
}
void
arf_get_fmpz(fmpz_t z, const arf_t x, arf_rnd_t rnd)
{
if (arf_is_special(x))
{
if (arf_is_zero(x))
{
fmpz_zero(z);
}
else
{
flint_printf("arf_get_fmpz: cannot convert infinity or nan to integer\n");
abort();
}
}
else if (COEFF_IS_MPZ(*ARF_EXPREF(x)))
{
/* tiny */
if (fmpz_sgn(ARF_EXPREF(x)) < 0)
{
int negative = ARF_SGNBIT(x);
if (rnd == ARF_RND_NEAR
|| rnd == ARF_RND_DOWN
|| (rnd == ARF_RND_FLOOR && !negative)
|| (rnd == ARF_RND_CEIL && negative))
{
fmpz_zero(z);
}
else
{
fmpz_set_si(z, negative ? -1 : 1);
}
}
else
{
flint_printf("arf_get_fmpz: number too large to convert to integer\n");
abort();
}
}
else
{
slong exp;
int negative, inexact;
mp_size_t xn, zn;
mp_srcptr xp;
__mpz_struct * zz;
/* TBD: implement efficiently */
if (rnd == ARF_RND_NEAR)
{
fmpr_t t;
fmpr_init(t);
arf_get_fmpr(t, x);
fmpr_get_fmpz(z, t, rnd);
fmpr_clear(t);
return;
}
exp = ARF_EXP(x);
negative = ARF_SGNBIT(x);
/* |x| < 1 */
if (exp <= 0)
{
if (rnd == ARF_RND_DOWN ||
(rnd == ARF_RND_FLOOR && !negative) ||
(rnd == ARF_RND_CEIL && negative))
{
fmpz_zero(z);
}
else
{
fmpz_set_si(z, negative ? -1 : 1);
}
return;
}
ARF_GET_MPN_READONLY(xp, xn, x);
/* |x| < 2^31 or 2^63 (must save 1 bit for rounding up!) */
if (exp < FLINT_BITS)
{
mp_limb_t v, v2;
v = xp[xn - 1];
v2 = v >> (FLINT_BITS - exp);
inexact = (xn > 1) || ((v2 << (FLINT_BITS - exp)) != v);
if (inexact && rnd != ARF_RND_DOWN)
{
if (negative && (rnd == ARF_RND_UP || rnd == ARF_RND_FLOOR))
v2++;
if (!negative && (rnd == ARF_RND_UP || rnd == ARF_RND_CEIL))
v2++;
}
if (negative)
fmpz_neg_ui(z, v2);
else
fmpz_set_ui(z, v2);
return;
}
/* |x| >= 1 */
zn = (exp + FLINT_BITS - 1) / FLINT_BITS;
zz = _fmpz_promote(z);
if (zz->_mp_alloc < zn)
mpz_realloc2(zz, zn * FLINT_BITS);
inexact = _arf_get_integer_mpn(zz->_mp_d, xp, xn, exp);
zz->_mp_size = negative ? -zn : zn;
_fmpz_demote_val(z);
if (inexact && rnd != ARF_RND_DOWN)
{
if (negative && (rnd == ARF_RND_UP || rnd == ARF_RND_FLOOR))
fmpz_sub_ui(z, z, 1);
if (!negative && (rnd == ARF_RND_UP || rnd == ARF_RND_CEIL))
fmpz_add_ui(z, z, 1);
}
}
void fmpz_powm_ui(fmpz_t f, const fmpz_t g, ulong e, const fmpz_t m)
{
if (fmpz_sgn(m) <= 0)
{
printf("Exception (fmpz_powm_ui). Modulus is less than 1.\n");
abort();
}
if (fmpz_is_one(m))
{
fmpz_zero(f);
}
else if (e == 0)
{
fmpz_one(f);
}
else /* e != 0, m > 0 */
{
fmpz g2 = *g;
fmpz m2 = *m;
if (!COEFF_IS_MPZ(m2)) /* m is small */
{
if (!COEFF_IS_MPZ(g2)) /* g is small */
{
mp_limb_t minv = n_preinvert_limb(m2);
_fmpz_demote(f);
if (g2 >= 0)
{
g2 = n_mod2_preinv(g2, m2, minv);
*f = n_powmod2_preinv(g2, e, m2, minv);
}
else
{
g2 = n_mod2_preinv(-g2, m2, minv);
*f = n_powmod2_preinv(g2, e, m2, minv);
if ((e & 1UL))
*f = n_negmod(*f, m2);
}
}
else /* g is large */
{
__mpz_struct *ptr = _fmpz_promote(f);
mpz_t m3;
mpz_init_set_ui(m3, m2);
mpz_powm_ui(ptr, COEFF_TO_PTR(g2), e, m3);
mpz_clear(m3);
_fmpz_demote_val(f);
}
}
else /* m is large */
{
if (!COEFF_IS_MPZ(g2)) /* g is small */
{
__mpz_struct *ptr = _fmpz_promote(f);
mpz_t g3;
mpz_init_set_si(g3, g2);
mpz_powm_ui(ptr, g3, e, COEFF_TO_PTR(m2));
mpz_clear(g3);
_fmpz_demote_val(f);
}
else /* g is large */
{
__mpz_struct *ptr = _fmpz_promote(f);
mpz_powm_ui(ptr, COEFF_TO_PTR(g2), e, COEFF_TO_PTR(m2));
_fmpz_demote_val(f);
}
}
}
}
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);
}
void
fmpz_fdiv_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))
{
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 ((c2 > 0L && r < 0L) || (c2 < 0L && r > 0L))
{
q--; /* q cannot overflow as remainder implies |c2| != 1 */
r += c2;
}
fmpz_set_si(f, q);
fmpz_set_si(s, r);
}
else /* h is large and g is small */
{
if (c1 == 0L)
{
fmpz_set_ui(f, 0L); /* g is zero */
fmpz_set_si(s, c1);
}
else if ((c1 < 0L && fmpz_sgn(h) < 0) || (c1 > 0L && fmpz_sgn(h) > 0)) /* signs are the same */
{
fmpz_zero(f); /* quotient is positive, round down to zero */
fmpz_set_si(s, c1);
}
else
{
fmpz_add(s, g, h);
fmpz_set_si(f, -1L); /* quotient is negative, round down to minus one */
}
}
}
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 */
{
mpz_fdiv_qr_ui(mpz_ptr, mpz_ptr2, COEFF_TO_PTR(c1), c2);
}
else
{
mpz_cdiv_qr_ui(mpz_ptr, mpz_ptr2, COEFF_TO_PTR(c1), -c2);
mpz_neg(mpz_ptr, mpz_ptr);
}
}
else /* both are large */
{
mpz_fdiv_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 */
}
}
