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_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 */
}
}
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
}
}
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 _fmpz_demote_val(fmpz_t f)
{
__mpz_struct * mpz_ptr = COEFF_TO_PTR(*f);
long size = mpz_ptr->_mp_size;
if (size == 0L) /* value is zero */
{
_fmpz_clear_mpz(*f);
(*f) = 0;
} else if (size == 1L) /* value is positive and 1 limb */
{
ulong uval = mpz_get_ui(mpz_ptr);
if (uval <= (ulong) COEFF_MAX)
{
_fmpz_clear_mpz(*f);
(*f) = (fmpz) uval;
}
}
else if (size == -1L) /* value is negative and 1 limb */
{
ulong uval = mpz_get_ui(mpz_ptr);
if (uval <= (ulong) COEFF_MAX)
{
_fmpz_clear_mpz(*f);
(*f) = (fmpz) -uval;
}
}
/* don't do anything if value has to be multi precision */
}
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 */
}
}
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);
}
}
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();
}
}
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_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));
}
}
double
fmpz_dlog(const fmpz_t x)
{
if (!COEFF_IS_MPZ(*x))
{
return log(*x);
}
else
{
double s;
slong e;
#if defined(__MPIR_VERSION)
s = mpz_get_d_2exp(&e, COEFF_TO_PTR(*x));
#else
s = mpz_get_d_2exp((long *) &e, COEFF_TO_PTR(*x));
#endif
return log(s) + e * 0.69314718055994530942;
}
}
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));
}
__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);
}
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 */
}
}
}
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;
}
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);
}
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_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_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_clrbit(fmpz_t f, ulong i)
{
if (!COEFF_IS_MPZ(*f))
{
if (i < FLINT_BITS - 2)
{
*f &= ~(WORD(1) << i);
}
/* i >= FLINT_BITS --> nop */
}
else
{
__mpz_struct *ptr = COEFF_TO_PTR(*f);
mpz_clrbit(ptr, i);
_fmpz_demote_val(f);
}
}
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_demote_val(fmpz_t f)
{
__mpz_struct * mpz_ptr = COEFF_TO_PTR(*f);
int size = mpz_ptr->_mp_size;
if (!(((unsigned int) size + 1U) & ~2U)) /* size +-1 */
{
ulong uval = mpz_ptr->_mp_d[0];
if (uval <= (ulong) COEFF_MAX)
{
_fmpz_clear_mpz(*f);
*f = size * (fmpz) uval;
}
}
else if (size == 0) /* value is 0 */
{
_fmpz_clear_mpz(*f);
*f = 0;
}
/* don't do anything if value has to be multi precision */
}
/*
Divide (arrayg, limbsg) by the positive value gc inplace and
return the number of limbs written
*/
mp_size_t mpn_tdiv_q_fmpz_inplace(mp_ptr arrayg, mp_size_t limbsg, fmpz_t gc)
{
if (fmpz_size(gc) == 1)
{
mpn_divmod_1(arrayg, arrayg, limbsg, fmpz_get_ui(gc));
return limbsg - (arrayg[limbsg - 1] == 0);
}
else
{
mp_size_t tlimbs;
__mpz_struct * mpz_ptr = COEFF_TO_PTR(*gc);
mp_ptr temp = flint_malloc(limbsg*sizeof(mp_limb_t));
mpn_copyi(temp, arrayg, limbsg);
mpn_tdiv_q(arrayg, temp, limbsg, mpz_ptr->_mp_d, mpz_ptr->_mp_size);
tlimbs = limbsg - mpz_ptr->_mp_size + 1;
tlimbs -= (arrayg[tlimbs - 1] == 0);
flint_free(temp);
return tlimbs;
}
}
char *
_fmpz_poly_get_str_pretty(const fmpz * poly, long len, const char *x)
{
char *str;
size_t off;
long i, bound, nz;
if (len == 0)
{
str = flint_malloc(2);
str[0] = '0';
str[1] = '\0';
return str;
}
if (len == 1)
{
str = fmpz_get_str(NULL, 10, poly);
return str;
}
nz = 0;
bound = 1;
for (i = 0; i < len; i++)
if (!fmpz_is_zero(poly + i))
{
bound += fmpz_sizeinbase(poly + i, 10) + 1;
nz++;
}
bound += nz * (3 + strlen(x) + (long) (ceil(log10(len))));
str = flint_malloc(bound);
off = 0;
i = len - 1;
if (poly[i] == 1L)
{
}
else if (poly[i] == -1L)
str[off++] = '-';
else if (!COEFF_IS_MPZ(poly[i]))
off += sprintf(str + off, "%ld*", poly[i]);
else
off += gmp_sprintf(str + off, "%Zd*", COEFF_TO_PTR(poly[i]));
if (i > 1)
off += sprintf(str + off, "%s^%ld", x, i);
else
off += sprintf(str + off, "%s", x);
for (--i; i > 0; --i)
{
if (poly[i] == 0L)
continue;
if (fmpz_sgn(poly + i) > 0)
str[off++] = '+';
if (poly[i] == -1L)
str[off++] = '-';
if (poly[i] != 1L && poly[i] != -1L)
{
if (!COEFF_IS_MPZ(poly[i]))
off += sprintf(str + off, "%ld*", poly[i]);
else
off += gmp_sprintf(str + off, "%Zd*", COEFF_TO_PTR(poly[i]));
}
if (i > 1)
off += sprintf(str + off, "%s^%ld", x, i);
else
off += sprintf(str + off, "%s", x);
}
if (poly[i] != 0L)
{
if (fmpz_sgn(poly + i) > 0)
str[off++] = '+';
if (!COEFF_IS_MPZ(poly[i]))
off += sprintf(str + off, "%ld", poly[i]);
else
off += gmp_sprintf(str + off, "%Zd", COEFF_TO_PTR(poly[i]));
}
return str;
}
void
fmpz_addmul_ui(fmpz_t f, const fmpz_t g, ulong x)
{
fmpz c1, r;
c1 = *g;
if ((x == 0) || (c1 == 0)) /* product is zero */
return;
r = *f;
if (r == 0)
{
fmpz_mul_ui(f, g, x); /* we are adding product to 0 */
return;
}
if (x == UWORD(1)) /* special case, adding g*1 to f */
{
fmpz_add(f, f, g);
return;
}
if (c1 == UWORD(1)) /* special case, adding 1*x to f */
{
fmpz_add_ui(f, f, x);
return;
}
if (!COEFF_IS_MPZ(c1)) /* c1 is small */
{
mp_limb_t prod[2];
ulong uc1 = FLINT_ABS(c1);
umul_ppmm(prod[1], prod[0], uc1, x); /* compute product */
if (prod[1] == 0) /* product fits in one limb */
{
if (c1 < WORD(0))
fmpz_sub_ui(f, f, prod[0]);
else
fmpz_add_ui(f, f, prod[0]);
return;
}
else if ((prod[1] == 1) && (!COEFF_IS_MPZ(r)) && ((r ^ c1) < WORD(0)))
{
/*
only chance at cancellation is if product is one bit past
a limb and res is small and opposite sign to this product
*/
ulong ur = FLINT_ABS(r);
if (ur > prod[0]) /* cancellation will occur */
{
fmpz_set_ui(f, prod[0] - ur);
if (r > WORD(0))
fmpz_neg(f, f);
return;
}
}
/*
in all remaining cases res is either big already,
or will be big in the end
*/
{
__mpz_struct * mpz_ptr = _fmpz_promote_val(f);
mpz_t temp; /* set up a temporary, cheap mpz_t to contain prod */
temp->_mp_d = prod;
temp->_mp_size = (c1 < WORD(0) ? -2 : 2);
mpz_add(mpz_ptr, mpz_ptr, temp);
_fmpz_demote_val(f); /* cancellation may have occurred */
}
}
else /* c1 is large */
{
__mpz_struct * mpz_ptr = _fmpz_promote_val(f);
flint_mpz_addmul_ui(mpz_ptr, COEFF_TO_PTR(c1), x);
_fmpz_demote_val(f); /* cancellation may have occurred */
}
}
