int
mpfr_add_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mp_rnd_t rnd_mode)
{
if (u) /* if u=0, do nothing */
{
mpfr_t uu;
mp_limb_t up[1];
unsigned long cnt;
int inex;
MPFR_INIT1(up, uu, BITS_PER_MP_LIMB, 1);
count_leading_zeros(cnt, (mp_limb_t) u);
*up = (mp_limb_t) u << cnt;
MPFR_EXP(uu) = BITS_PER_MP_LIMB - cnt;
/* Optimization note: Exponent operations may be removed
if mpfr_add works even when uu is out-of-range. */
mpfr_save_emin_emax();
inex = mpfr_add(y, x, uu, rnd_mode);
MPFR_RESTORE_RET(inex, y, rnd_mode);
}
else
return mpfr_set (y, x, rnd_mode);
}
/* set f to the rational q */
int
mpfr_set_q (mpfr_ptr f, mpq_srcptr q, mp_rnd_t rnd)
{
mpz_srcptr num, den;
mpfr_t n, d;
int inexact;
mp_prec_t prec;
MPFR_CLEAR_FLAGS (f);
num = mpq_numref (q);
if (mpz_cmp_ui (num, 0) == 0)
{
MPFR_SET_ZERO (f);
MPFR_SET_POS (f);
MPFR_RET (0);
}
den = mpq_denref (q);
mpfr_save_emin_emax ();
prec = mpz_sizeinbase (num, 2);
if (prec < MPFR_PREC_MIN)
prec = MPFR_PREC_MIN;
mpfr_init2 (n, prec);
if (mpfr_set_z (n, num, GMP_RNDZ)) /* result is exact unless overflow */
{
mpfr_clear (n);
mpfr_restore_emin_emax ();
MPFR_SET_NAN (f);
MPFR_RET_NAN;
}
prec = mpz_sizeinbase(den, 2);
if (prec < MPFR_PREC_MIN)
prec = MPFR_PREC_MIN;
mpfr_init2 (d, prec);
if (mpfr_set_z (d, den, GMP_RNDZ)) /* result is exact unless overflow */
{
mpfr_clear (d);
mpfr_clear (n);
mpfr_restore_emin_emax ();
MPFR_SET_NAN (f);
MPFR_RET_NAN;
}
inexact = mpfr_div (f, n, d, rnd);
mpfr_clear (n);
mpfr_clear (d);
MPFR_RESTORE_RET (inexact, f, rnd);
}
int
mpfr_cos (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int K0, K, precy, m, k, l;
int inexact;
mpfr_t r, s;
mp_limb_t *rp, *sp;
mp_size_t sm;
mp_exp_t exps, cancel = 0;
TMP_DECL (marker);
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
{
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
return mpfr_set_ui (y, 1, GMP_RNDN);
}
}
mpfr_save_emin_emax ();
precy = MPFR_PREC(y);
K0 = __gmpfr_isqrt(precy / 2); /* Need K + log2(precy/K) extra bits */
m = precy + 3 * (K0 + 2 * MAX(MPFR_GET_EXP (x), 0)) + 3;
TMP_MARK(marker);
sm = (m + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
MPFR_TMP_INIT(rp, r, m, sm);
MPFR_TMP_INIT(sp, s, m, sm);
for (;;)
{
mpfr_mul (r, x, x, GMP_RNDU); /* err <= 1 ulp */
/* we need that |r| < 1 for mpfr_cos2_aux, i.e. up(x^2)/2^(2K) < 1 */
K = K0 + MAX (MPFR_GET_EXP (r), 0);
mpfr_div_2ui (r, r, 2 * K, GMP_RNDN); /* r = (x/2^K)^2, err <= 1 ulp */
/* s <- 1 - r/2! + ... + (-1)^l r^l/(2l)! */
l = mpfr_cos2_aux (s, r);
MPFR_SET_ONE (r);
for (k = 0; k < K; k++)
{
mpfr_mul (s, s, s, GMP_RNDU); /* err <= 2*olderr */
mpfr_mul_2ui (s, s, 1, GMP_RNDU); /* err <= 4*olderr */
mpfr_sub (s, s, r, GMP_RNDN);
}
/* absolute error on s is bounded by (2l+1/3)*2^(2K-m) */
for (k = 2 * K, l = 2 * l + 1; l > 1; l = (l + 1) >> 1)
k++;
/* now the error is bounded by 2^(k-m) = 2^(EXP(s)-err) */
exps = MPFR_GET_EXP(s);
if (MPFR_LIKELY(mpfr_can_round (s, exps + m - k, GMP_RNDN, GMP_RNDZ,
precy + (rnd_mode == GMP_RNDN))))
break;
m += BITS_PER_MP_LIMB;
if (exps < cancel)
{
m += cancel - exps;
cancel = exps;
}
sm = (m + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
MPFR_TMP_INIT(rp, r, m, sm);
MPFR_TMP_INIT(sp, s, m, sm);
}
mpfr_restore_emin_emax ();
inexact = mpfr_set (y, s, rnd_mode); /* FIXME: Dont' need check range? */
TMP_FREE(marker);
return inexact;
}
