Пример #1
0
int
mpfr_rint (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  int sign;
  int rnd_away;
  mpfr_exp_t exp;

  if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(u) ))
    {
      if (MPFR_IS_NAN(u))
        {
          MPFR_SET_NAN(r);
          MPFR_RET_NAN;
        }
      MPFR_SET_SAME_SIGN(r, u);
      if (MPFR_IS_INF(u))
        {
          MPFR_SET_INF(r);
          MPFR_RET(0);  /* infinity is exact */
        }
      else /* now u is zero */
        {
          MPFR_ASSERTD(MPFR_IS_ZERO(u));
          MPFR_SET_ZERO(r);
          MPFR_RET(0);  /* zero is exact */
        }
    }
  MPFR_SET_SAME_SIGN (r, u); /* Does nothing if r==u */

  sign = MPFR_INT_SIGN (u);
  exp = MPFR_GET_EXP (u);

  rnd_away =
    rnd_mode == MPFR_RNDD ? sign < 0 :
    rnd_mode == MPFR_RNDU ? sign > 0 :
    rnd_mode == MPFR_RNDZ ? 0        :
    rnd_mode == MPFR_RNDA ? 1        :
    -1; /* round to nearest-even (RNDN) or nearest-away (RNDNA) */

  /* rnd_away:
     1 if round away from zero,
     0 if round to zero,
     -1 if not decided yet.
   */

  if (MPFR_UNLIKELY (exp <= 0))  /* 0 < |u| < 1 ==> round |u| to 0 or 1 */
    {
      /* Note: in the MPFR_RNDN mode, 0.5 must be rounded to 0. */
      if (rnd_away != 0 &&
          (rnd_away > 0 ||
           (exp == 0 && (rnd_mode == MPFR_RNDNA ||
                         !mpfr_powerof2_raw (u)))))
        {
          mp_limb_t *rp;
          mp_size_t rm;

          rp = MPFR_MANT(r);
          rm = (MPFR_PREC(r) - 1) / GMP_NUMB_BITS;
          rp[rm] = MPFR_LIMB_HIGHBIT;
          MPN_ZERO(rp, rm);
          MPFR_SET_EXP (r, 1);  /* |r| = 1 */
          MPFR_RET(sign > 0 ? 2 : -2);
        }
      else
        {
          MPFR_SET_ZERO(r);  /* r = 0 */
          MPFR_RET(sign > 0 ? -2 : 2);
        }
    }
  else  /* exp > 0, |u| >= 1 */
    {
      mp_limb_t *up, *rp;
      mp_size_t un, rn, ui;
      int sh, idiff;
      int uflags;

      /*
       * uflags will contain:
       *   _ 0 if u is an integer representable in r,
       *   _ 1 if u is an integer not representable in r,
       *   _ 2 if u is not an integer.
       */

      up = MPFR_MANT(u);
      rp = MPFR_MANT(r);

      un = MPFR_LIMB_SIZE(u);
      rn = MPFR_LIMB_SIZE(r);
      MPFR_UNSIGNED_MINUS_MODULO (sh, MPFR_PREC (r));

      MPFR_SET_EXP (r, exp); /* Does nothing if r==u */

      if ((exp - 1) / GMP_NUMB_BITS >= un)
        {
          ui = un;
          idiff = 0;
          uflags = 0;  /* u is an integer, representable or not in r */
        }
      else
        {
          mp_size_t uj;

          ui = (exp - 1) / GMP_NUMB_BITS + 1;  /* #limbs of the int part */
          MPFR_ASSERTD (un >= ui);
          uj = un - ui;  /* lowest limb of the integer part */
          idiff = exp % GMP_NUMB_BITS;  /* #int-part bits in up[uj] or 0 */

          uflags = idiff == 0 || (up[uj] << idiff) == 0 ? 0 : 2;
          if (uflags == 0)
            while (uj > 0)
              if (up[--uj] != 0)
                {
                  uflags = 2;
                  break;
                }
        }

      if (ui > rn)
        {
          /* More limbs in the integer part of u than in r.
             Just round u with the precision of r. */
          MPFR_ASSERTD (rp != up && un > rn);
          MPN_COPY (rp, up + (un - rn), rn); /* r != u */
          if (rnd_away < 0)
            {
              /* This is a rounding to nearest mode (MPFR_RNDN or MPFR_RNDNA).
                 Decide the rounding direction here. */
              if (rnd_mode == MPFR_RNDN &&
                  (rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
                { /* halfway cases rounded toward zero */
                  mp_limb_t a, b;
                  /* a: rounding bit and some of the following bits */
                  /* b: boundary for a (weight of the rounding bit in a) */
                  if (sh != 0)
                    {
                      a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
                      b = MPFR_LIMB_ONE << (sh - 1);
                    }
                  else
                    {
                      a = up[un - rn - 1];
                      b = MPFR_LIMB_HIGHBIT;
                    }
                  rnd_away = a > b;
                  if (a == b)
                    {
                      mp_size_t i;
                      for (i = un - rn - 1 - (sh == 0); i >= 0; i--)
                        if (up[i] != 0)
                          {
                            rnd_away = 1;
                            break;
                          }
                    }
                }
              else  /* halfway cases rounded away from zero */
                rnd_away =  /* rounding bit */
                  ((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
                   (sh == 0 && (up[un - rn - 1] & MPFR_LIMB_HIGHBIT) != 0));
            }
          if (uflags == 0)
            { /* u is an integer; determine if it is representable in r */
              if (sh != 0 && rp[0] << (GMP_NUMB_BITS - sh) != 0)
                uflags = 1;  /* u is not representable in r */
              else
                {
                  mp_size_t i;
                  for (i = un - rn - 1; i >= 0; i--)
                    if (up[i] != 0)
                      {
                        uflags = 1;  /* u is not representable in r */
                        break;
                      }
                }
            }
        }
      else  /* ui <= rn */
        {
          mp_size_t uj, rj;
          int ush;

          uj = un - ui;  /* lowest limb of the integer part in u */
          rj = rn - ui;  /* lowest limb of the integer part in r */

          if (MPFR_LIKELY (rp != up))
            MPN_COPY(rp + rj, up + uj, ui);

          /* Ignore the lowest rj limbs, all equal to zero. */
          rp += rj;
          rn = ui;

          /* number of fractional bits in whole rp[0] */
          ush = idiff == 0 ? 0 : GMP_NUMB_BITS - idiff;

          if (rj == 0 && ush < sh)
            {
              /* If u is an integer (uflags == 0), we need to determine
                 if it is representable in r, i.e. if its sh - ush bits
                 in the non-significant part of r are all 0. */
              if (uflags == 0 && (rp[0] & ((MPFR_LIMB_ONE << sh) -
                                           (MPFR_LIMB_ONE << ush))) != 0)
                uflags = 1;  /* u is an integer not representable in r */
            }
          else  /* The integer part of u fits in r, we'll round to it. */
            sh = ush;

          if (rnd_away < 0)
            {
              /* This is a rounding to nearest mode.
                 Decide the rounding direction here. */
              if (uj == 0 && sh == 0)
                rnd_away = 0; /* rounding bit = 0 (not represented in u) */
              else if (rnd_mode == MPFR_RNDN &&
                       (rp[0] & (MPFR_LIMB_ONE << sh)) == 0)
                { /* halfway cases rounded toward zero */
                  mp_limb_t a, b;
                  /* a: rounding bit and some of the following bits */
                  /* b: boundary for a (weight of the rounding bit in a) */
                  if (sh != 0)
                    {
                      a = rp[0] & ((MPFR_LIMB_ONE << sh) - 1);
                      b = MPFR_LIMB_ONE << (sh - 1);
                    }
                  else
                    {
                      MPFR_ASSERTD (uj >= 1);  /* see above */
                      a = up[uj - 1];
                      b = MPFR_LIMB_HIGHBIT;
                    }
                  rnd_away = a > b;
                  if (a == b)
                    {
                      mp_size_t i;
                      for (i = uj - 1 - (sh == 0); i >= 0; i--)
                        if (up[i] != 0)
                          {
                            rnd_away = 1;
                            break;
                          }
                    }
                }
              else  /* halfway cases rounded away from zero */
                rnd_away =  /* rounding bit */
                  ((sh != 0 && (rp[0] & (MPFR_LIMB_ONE << (sh - 1))) != 0) ||
                   (sh == 0 && (MPFR_ASSERTD (uj >= 1),
                                up[uj - 1] & MPFR_LIMB_HIGHBIT) != 0));
            }
          /* Now we can make the low rj limbs to 0 */
          MPN_ZERO (rp-rj, rj);
        }

      if (sh != 0)
        rp[0] &= MP_LIMB_T_MAX << sh;

      /* If u is a representable integer, there is no rounding. */
      if (uflags == 0)
        MPFR_RET(0);

      MPFR_ASSERTD (rnd_away >= 0);  /* rounding direction is defined */
      if (rnd_away && mpn_add_1(rp, rp, rn, MPFR_LIMB_ONE << sh))
        {
          if (exp == __gmpfr_emax)
            return mpfr_overflow(r, rnd_mode, MPFR_SIGN(r)) >= 0 ?
              uflags : -uflags;
          else
            {
              MPFR_SET_EXP(r, exp + 1);
              rp[rn-1] = MPFR_LIMB_HIGHBIT;
            }
        }

      MPFR_RET (rnd_away ^ (sign < 0) ? uflags : -uflags);
    }  /* exp > 0, |u| >= 1 */
}
Пример #2
0
int
mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
{
  int inexact;
  mpfr_t x, t, te;
  mpfr_prec_t Nx, Ny, Nt;
  mpfr_exp_t err;
  MPFR_ZIV_DECL (loop);
  MPFR_SAVE_EXPO_DECL (expo);

  MPFR_LOG_FUNC
    (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
    ("y[%Pu]=%.*Rg inexact=%d",
     mpfr_get_prec (y), mpfr_log_prec, y, inexact));

  /* Special cases */
  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
    {
      /* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
         between -1 and 1 */
      if (MPFR_IS_NAN (xt) || MPFR_IS_INF (xt))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else /* necessarily xt is 0 */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (xt));
          MPFR_SET_ZERO (y);   /* atanh(0) = 0 */
          MPFR_SET_SAME_SIGN (y,xt);
          MPFR_RET (0);
        }
    }

  /* atanh (x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
  if (MPFR_UNLIKELY (MPFR_GET_EXP (xt) > 0))
    {
      if (MPFR_GET_EXP (xt) == 1 && mpfr_powerof2_raw (xt))
        {
          MPFR_SET_INF (y);
          MPFR_SET_SAME_SIGN (y, xt);
          MPFR_SET_DIVBY0 ();
          MPFR_RET (0);
        }
      MPFR_SET_NAN (y);
      MPFR_RET_NAN;
    }

  /* atanh(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 1,
                                    rnd_mode, {});

  MPFR_SAVE_EXPO_MARK (expo);

  /* Compute initial precision */
  Nx = MPFR_PREC (xt);
  MPFR_TMP_INIT_ABS (x, xt);
  Ny = MPFR_PREC (y);
  Nt = MAX (Nx, Ny);
  /* the optimal number of bits : see algorithms.ps */
  Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;

  /* initialize of intermediary variable */
  mpfr_init2 (t, Nt);
  mpfr_init2 (te, Nt);

  /* First computation of cosh */
  MPFR_ZIV_INIT (loop, Nt);
  for (;;)
    {
      /* compute atanh */
      mpfr_ui_sub (te, 1, x, MPFR_RNDU);   /* (1-xt)*/
      mpfr_add_ui (t,  x, 1, MPFR_RNDD);   /* (xt+1)*/
      mpfr_div (t, t, te, MPFR_RNDN);      /* (1+xt)/(1-xt)*/
      mpfr_log (t, t, MPFR_RNDN);          /* ln((1+xt)/(1-xt))*/
      mpfr_div_2ui (t, t, 1, MPFR_RNDN);   /* (1/2)*ln((1+xt)/(1-xt))*/

      /* error estimate: see algorithms.tex */
      /* FIXME: this does not correspond to the value in algorithms.tex!!! */
      /* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
      err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);

      if (MPFR_LIKELY (MPFR_IS_ZERO (t)
                       || MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
        break;

      /* reactualisation of the precision */
      MPFR_ZIV_NEXT (loop, Nt);
      mpfr_set_prec (t, Nt);
      mpfr_set_prec (te, Nt);
    }
  MPFR_ZIV_FREE (loop);

  inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));

  mpfr_clear(t);
  mpfr_clear(te);

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, inexact, rnd_mode);
}
Пример #3
0
/* set f to the rational q */
int
mpfr_set_q (mpfr_ptr f, mpq_srcptr q, mpfr_rnd_t rnd)
{
  mpz_srcptr num, den;
  mpfr_t n, d;
  int inexact;
  int cn, cd;
  long shift;
  mp_size_t sn, sd;
  MPFR_SAVE_EXPO_DECL (expo);

  num = mpq_numref (q);
  den = mpq_denref (q);
  /* NAN and INF for mpq are not really documented, but could be found */
  if (MPFR_UNLIKELY (mpz_sgn (num) == 0))
    {
      if (MPFR_UNLIKELY (mpz_sgn (den) == 0))
        {
          MPFR_SET_NAN (f);
          MPFR_RET_NAN;
        }
      else
        {
          MPFR_SET_ZERO (f);
          MPFR_SET_POS (f);
          MPFR_RET (0);
        }
    }
  if (MPFR_UNLIKELY (mpz_sgn (den) == 0))
    {
      MPFR_SET_INF (f);
      MPFR_SET_SIGN (f, mpz_sgn (num));
      MPFR_RET (0);
    }

  MPFR_SAVE_EXPO_MARK (expo);

  cn = set_z (n, num, &sn);
  cd = set_z (d, den, &sd);

  sn -= sd;
  if (MPFR_UNLIKELY (sn > MPFR_EMAX_MAX / GMP_NUMB_BITS))
    {
      MPFR_SAVE_EXPO_FREE (expo);
      inexact = mpfr_overflow (f, rnd, MPFR_SIGN (f));
      goto end;
    }
  if (MPFR_UNLIKELY (sn < MPFR_EMIN_MIN / GMP_NUMB_BITS -1))
    {
      MPFR_SAVE_EXPO_FREE (expo);
      if (rnd == MPFR_RNDN)
        rnd = MPFR_RNDZ;
      inexact = mpfr_underflow (f, rnd, MPFR_SIGN (f));
      goto end;
    }

  inexact = mpfr_div (f, n, d, rnd);
  shift = GMP_NUMB_BITS*sn+cn-cd;
  MPFR_ASSERTD (shift == GMP_NUMB_BITS*sn+cn-cd);
  cd = mpfr_mul_2si (f, f, shift, rnd);
  MPFR_SAVE_EXPO_FREE (expo);
  if (MPFR_UNLIKELY (cd != 0))
    inexact = cd;
  else
    inexact = mpfr_check_range (f, inexact, rnd);
 end:
  mpfr_clear (d);
  mpfr_clear (n);
  MPFR_RET (inexact);
}
Пример #4
0
int
main (void)
{
  mpfr_t a;
  mp_limb_t *p, tmp;
  mp_size_t s;
  mpfr_prec_t pr;
  int max;

  tests_start_mpfr ();
  for(pr = MPFR_PREC_MIN ; pr < 500 ; pr++)
    {
      mpfr_init2 (a, pr);
      if (!mpfr_check(a)) ERROR("for init");
      /* Check special cases */
      MPFR_SET_NAN(a);
      if (!mpfr_check(a)) ERROR("for nan");
      MPFR_SET_POS(a);
      MPFR_SET_INF(a);
      if (!mpfr_check(a)) ERROR("for inf");
      MPFR_SET_ZERO(a);
      if (!mpfr_check(a)) ERROR("for zero");
      /* Check var */
      mpfr_set_ui(a, 2, GMP_RNDN);
      if (!mpfr_check(a)) ERROR("for set_ui");
      mpfr_clear_overflow();
      max = 1000; /* Allows max 2^1000 bits for the exponent */
      while ((!mpfr_overflow_p()) && (max>0))
        {
          mpfr_mul(a, a, a, GMP_RNDN);
          if (!mpfr_check(a)) ERROR("for mul");
          max--;
        }
      if (max==0) ERROR("can't reach overflow");
      mpfr_set_ui(a, 2137, GMP_RNDN);
      /* Corrupt a and check for it */
      MPFR_SIGN(a) = 2;
      if (mpfr_check(a))  ERROR("sgn");
      MPFR_SET_POS(a);
      /* Check prec */
      MPFR_PREC(a) = 1;
      if (mpfr_check(a))  ERROR("precmin");
      MPFR_PREC(a) = MPFR_PREC_MAX+1;
      if (mpfr_check(a))  ERROR("precmax");
      MPFR_PREC(a) = pr;
      if (!mpfr_check(a)) ERROR("prec");
      /* Check exponent */
      MPFR_EXP(a) = MPFR_EXP_INVALID;
      if (mpfr_check(a))  ERROR("exp invalid");
      MPFR_EXP(a) = -MPFR_EXP_INVALID;
      if (mpfr_check(a))  ERROR("-exp invalid");
      MPFR_EXP(a) = 0;
      if (!mpfr_check(a)) ERROR("exp 0");
      /* Check Mantissa */
      p = MPFR_MANT(a);
      MPFR_MANT(a) = NULL;
      if (mpfr_check(a))  ERROR("Mantissa Null Ptr");
      MPFR_MANT(a) = p;
      /* Check size */
      s = MPFR_GET_ALLOC_SIZE(a);
      MPFR_SET_ALLOC_SIZE(a, 0);
      if (mpfr_check(a))  ERROR("0 size");
      MPFR_SET_ALLOC_SIZE(a, MP_SIZE_T_MIN);
      if (mpfr_check(a))  ERROR("min size");
      MPFR_SET_ALLOC_SIZE(a, MPFR_LIMB_SIZE(a)-1 );
      if (mpfr_check(a))  ERROR("size < prec");
      MPFR_SET_ALLOC_SIZE(a, s);
      /* Check normal form */
      tmp = MPFR_MANT(a)[0];
      if ((pr % BITS_PER_MP_LIMB) != 0)
        {
          MPFR_MANT(a)[0] = ~0;
          if (mpfr_check(a))  ERROR("last bits non 0");
        }
      MPFR_MANT(a)[0] = tmp;
      MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] &= MPFR_LIMB_MASK (BITS_PER_MP_LIMB-1);
      if (mpfr_check(a))  ERROR("last bits non 0");
      /* Final */
      mpfr_set_ui(a, 2137, GMP_RNDN);
      if (!mpfr_check(a)) ERROR("after last set");
      mpfr_clear (a);
      if (mpfr_check(a))  ERROR("after clear");
    }
  tests_end_mpfr ();
  return 0;
}
Пример #5
0
Файл: eint.c Проект: Kirija/XPIR
int
mpfr_eint (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
{
  int inex;
  mpfr_t tmp, ump;
  mpfr_exp_t err, te;
  mpfr_prec_t prec;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  MPFR_LOG_FUNC (
    ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd),
    ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, inex));

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      /* exp(NaN) = exp(-Inf) = NaN */
      if (MPFR_IS_NAN (x) || (MPFR_IS_INF (x) && MPFR_IS_NEG(x)))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      /* eint(+inf) = +inf */
      else if (MPFR_IS_INF (x))
        {
          MPFR_SET_INF(y);
          MPFR_SET_POS(y);
          MPFR_RET(0);
        }
      else /* eint(+/-0) = -Inf */
        {
          MPFR_SET_INF(y);
          MPFR_SET_NEG(y);
          mpfr_set_divby0 ();
          MPFR_RET(0);
        }
    }

  /* eint(x) = NaN for x < 0 */
  if (MPFR_IS_NEG(x))
    {
      MPFR_SET_NAN (y);
      MPFR_RET_NAN;
    }

  MPFR_SAVE_EXPO_MARK (expo);

  /* Since eint(x) >= exp(x)/x, we have log2(eint(x)) >= (x-log(x))/log(2).
     Let's compute k <= (x-log(x))/log(2) in a low precision. If k >= emax,
     then log2(eint(x)) >= emax, and eint(x) >= 2^emax, i.e. it overflows. */
  mpfr_init2 (tmp, 64);
  mpfr_init2 (ump, 64);
  mpfr_log (tmp, x, MPFR_RNDU);
  mpfr_sub (ump, x, tmp, MPFR_RNDD);
  mpfr_const_log2 (tmp, MPFR_RNDU);
  mpfr_div (ump, ump, tmp, MPFR_RNDD);
  /* FIXME: We really need mpfr_set_exp_t and mpfr_cmpfr_exp_t functions. */
  MPFR_ASSERTN (MPFR_EMAX_MAX <= LONG_MAX);
  if (mpfr_cmp_ui (ump, __gmpfr_emax) >= 0)
    {
      mpfr_clear (tmp);
      mpfr_clear (ump);
      MPFR_SAVE_EXPO_FREE (expo);
      return mpfr_overflow (y, rnd, 1);
    }

  /* Init stuff */
  prec = MPFR_PREC (y) + 2 * MPFR_INT_CEIL_LOG2 (MPFR_PREC (y)) + 6;

  /* eint() has a root 0.37250741078136663446..., so if x is near,
     already take more bits */
  /* FIXME: do not use native floating-point here. */
  if (MPFR_GET_EXP(x) == -1) /* 1/4 <= x < 1/2 */
    {
      double d;
      d = mpfr_get_d (x, MPFR_RNDN) - 0.37250741078136663;
      d = (d == 0.0) ? -53 : __gmpfr_ceil_log2 (d);
      prec += -d;
    }

  mpfr_set_prec (tmp, prec);
  mpfr_set_prec (ump, prec);

  MPFR_ZIV_INIT (loop, prec);            /* Initialize the ZivLoop controler */
  for (;;)                               /* Infinite loop */
    {
      /* We need that the smallest value of k!/x^k is smaller than 2^(-p).
         The minimum is obtained for x=k, and it is smaller than e*sqrt(x)/e^x
         for x>=1. */
      if (MPFR_GET_EXP (x) > 0 && mpfr_cmp_d (x, ((double) prec +
                            0.5 * (double) MPFR_GET_EXP (x)) * LOG2 + 1.0) > 0)
        err = mpfr_eint_asympt (tmp, x);
      else
        {
          err = mpfr_eint_aux (tmp, x); /* error <= 2^err ulp(tmp) */
          te = MPFR_GET_EXP(tmp);
          mpfr_const_euler (ump, MPFR_RNDN); /* 0.577 -> EXP(ump)=0 */
          mpfr_add (tmp, tmp, ump, MPFR_RNDN);
          /* error <= 1/2 + 1/2*2^(EXP(ump)-EXP(tmp)) + 2^(te-EXP(tmp)+err)
             <= 1/2 + 2^(MAX(EXP(ump), te+err+1) - EXP(tmp))
             <= 2^(MAX(0, 1 + MAX(EXP(ump), te+err+1) - EXP(tmp))) */
          err = MAX(1, te + err + 2) - MPFR_GET_EXP(tmp);
          err = MAX(0, err);
          te = MPFR_GET_EXP(tmp);
          mpfr_log (ump, x, MPFR_RNDN);
          mpfr_add (tmp, tmp, ump, MPFR_RNDN);
          /* same formula as above, except now EXP(ump) is not 0 */
          err += te + 1;
          if (MPFR_LIKELY (!MPFR_IS_ZERO (ump)))
            err = MAX (MPFR_GET_EXP (ump), err);
          err = MAX(0, err - MPFR_GET_EXP (tmp));
        }
      if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - err, MPFR_PREC (y), rnd)))
        break;
      MPFR_ZIV_NEXT (loop, prec);        /* Increase used precision */
      mpfr_set_prec (tmp, prec);
      mpfr_set_prec (ump, prec);
    }
  MPFR_ZIV_FREE (loop);                  /* Free the ZivLoop Controler */

  inex = mpfr_set (y, tmp, rnd);    /* Set y to the computed value */
  mpfr_clear (tmp);
  mpfr_clear (ump);

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, inex, rnd);
}
Пример #6
0
static void
special (void)
{
  mpfr_t x, y;

  mpfr_init (x);
  mpfr_init (y);

  MPFR_SET_INF(x);
  mpfr_set_ui (y, 1, MPFR_RNDN);
  mpfr_acosh (x, y, MPFR_RNDN);
  if (MPFR_IS_INF(x) || MPFR_IS_NAN(x) )
    {
      printf ("Inf flag not clears in acosh!\n");
      exit (1);
    }
  if (mpfr_cmp_ui (x, 0))
    {
      printf ("Error: mpfr_acosh(1) <> 0\n");
      exit (1);
    }

  MPFR_SET_NAN(x);
  mpfr_acosh (x, y, MPFR_RNDN);
  if (MPFR_IS_NAN(x) || MPFR_IS_INF(x) )
    {
      printf ("NAN flag not clears in acosh!\n");
      exit (1);
    }

  mpfr_set_ui (x, 0, MPFR_RNDN);
  mpfr_acosh (y, x, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: mpfr_acosh(0) <> NaN\n");
      exit (1);
    }

  mpfr_set_si (x, -1, MPFR_RNDN);
  mpfr_acosh (y, x, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: mpfr_acosh(-1) <> NaN\n");
      exit (1);
    }

  MPFR_SET_NAN(x);
  mpfr_acosh (y, x, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: mpfr_acosh(NaN) <> NaN\n");
      exit (1);
    }

  mpfr_set_inf (x, 1);
  mpfr_acosh (y, x, MPFR_RNDN);
  if (!mpfr_inf_p (y) || mpfr_sgn (y) < 0)
    {
      printf ("Error: mpfr_acosh(+Inf) <> +Inf\n");
      exit (1);
    }

  mpfr_set_inf (x, -1);
  mpfr_acosh (y, x, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: mpfr_acosh(-Inf) <> NaN\n");
      exit (1);
    }

  mpfr_set_ui (x, 1, MPFR_RNDN);
  mpfr_div_2exp (x, x, 1, MPFR_RNDN);
  mpfr_acosh (y, x, MPFR_RNDN);
  if (!mpfr_nan_p (y))
    {
      printf ("Error: mpfr_acosh(1/2) <> NaN\n");
      exit (1);
    }

  mpfr_set_prec (x, 32);
  mpfr_set_prec (y, 32);
  mpfr_set_str_binary (x, "1.000001101011101111001011");
  mpfr_acosh (y, x, MPFR_RNDN);
  mpfr_set_str_binary (x, "0.111010100101101001010001101001E-2");
  if (mpfr_cmp (x, y))
    {
      printf ("Error: mpfr_acosh (1)\n");
      exit (1);
    }

  mpfr_clear (x);
  mpfr_clear (y);
}