C++ MPFR_SET_NAN函数代码示例

int
mpfr_ui_div (mpfr_ptr y, unsigned long int u, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
  mpfr_t uu;
  mp_limb_t up[1];
  unsigned long cnt;

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

  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
    {
      if (MPFR_IS_NAN(x))
        {
          MPFR_SET_NAN(y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF(x)) /* u/Inf = 0 */
        {
          MPFR_SET_ZERO(y);
          MPFR_SET_SAME_SIGN(y,x);
          MPFR_RET(0);
        }
      else /* u / 0 */
        {
          MPFR_ASSERTD(MPFR_IS_ZERO(x));
          if (u)
            {
              /* u > 0, so y = sign(x) * Inf */
              MPFR_SET_SAME_SIGN(y, x);
              MPFR_SET_INF(y);
              mpfr_set_divby0 ();
              MPFR_RET(0);
            }
          else
            {
              /* 0 / 0 */
              MPFR_SET_NAN(y);
              MPFR_RET_NAN;
            }
        }
    }
  else if (MPFR_LIKELY(u != 0))
    {
      MPFR_TMP_INIT1(up, uu, GMP_NUMB_BITS);
      MPFR_ASSERTN(u == (mp_limb_t) u);
      count_leading_zeros(cnt, (mp_limb_t) u);
      up[0] = (mp_limb_t) u << cnt;
      MPFR_SET_EXP (uu, GMP_NUMB_BITS - cnt);
      return mpfr_div (y, uu, x, rnd_mode);
    }
  else /* u = 0, and x != 0 */
    {
      MPFR_SET_ZERO(y);         /* if u=0, then set y to 0 */
      MPFR_SET_SAME_SIGN(y, x); /* u considered as +0: sign(+0/x) = sign(x) */
      MPFR_RET(0);
    }
}

int
mpfr_ui_div (mpfr_ptr y, unsigned long int u, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mpfr_t uu;
  mp_limb_t up[1];
  unsigned long cnt;

  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
    {
      if (MPFR_IS_NAN(x))
        {
          MPFR_SET_NAN(y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF(x)) /* u/Inf = 0 */
        {
          MPFR_SET_ZERO(y);
          MPFR_SET_SAME_SIGN(y,x);
          MPFR_RET(0);
        }
      else /* u / 0 */
        {
          MPFR_ASSERTD(MPFR_IS_ZERO(x));
          if (u)
            {
              /* u > 0, so y = sign(x) * Inf */
              MPFR_SET_SAME_SIGN(y, x);
              MPFR_SET_INF(y);
              MPFR_RET(0);
            }
          else
            {
              /* 0 / 0 */
              MPFR_SET_NAN(y);
              MPFR_RET_NAN;
            }
        }
    }
  else if (MPFR_LIKELY(u != 0))
    {
      MPFR_TMP_INIT1(up, uu, BITS_PER_MP_LIMB);
      MPFR_ASSERTN(u == (mp_limb_t) u);
      count_leading_zeros(cnt, (mp_limb_t) u);
      up[0] = (mp_limb_t) u << cnt;
      MPFR_SET_EXP (uu, BITS_PER_MP_LIMB - cnt);
      return mpfr_div (y, uu, x, rnd_mode);
    }
  else /* u = 0, and x != 0 */
    {
      MPFR_SET_ZERO(y);         /* if u=0, then set y to 0 */
      MPFR_SET_SAME_SIGN(y, x); /* u considered as +0: sign(+0/x) = sign(x) */
      MPFR_RET(0);
    }
}

int
mpfr_root (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode)
{
  mpz_t m;
  mpfr_exp_t e, r, sh;
  mpfr_prec_t n, size_m, tmp;
  int inexact, negative;
  MPFR_SAVE_EXPO_DECL (expo);

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

  if (MPFR_UNLIKELY (k <= 1))
    {
      if (k < 1) /* k==0 => y=x^(1/0)=x^(+Inf) */
#if 0
        /* For 0 <= x < 1 => +0.
           For x = 1      => 1.
           For x > 1,     => +Inf.
           For x < 0      => NaN.
        */
        {
          if (MPFR_IS_NEG (x) && !MPFR_IS_ZERO (x))
            {
              MPFR_SET_NAN (y);
              MPFR_RET_NAN;
            }
          inexact = mpfr_cmp (x, __gmpfr_one);
          if (inexact == 0)
            return mpfr_set_ui (y, 1, rnd_mode); /* 1 may be Out of Range */
          else if (inexact < 0)
            return mpfr_set_ui (y, 0, rnd_mode); /* 0+ */
          else
            {
              mpfr_set_inf (y, 1);
              return 0;
            }
        }
#endif
      {
        MPFR_SET_NAN (y);
        MPFR_RET_NAN;
      }
      else /* y =x^(1/1)=x */
        return mpfr_set (y, x, rnd_mode);
    }

/* reldiff(b, c) = abs(b-c)/b */
void
mpfr_reldiff (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
  mpfr_t b_copy;

  if (MPFR_ARE_SINGULAR (b, c))
    {
      if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
        {
          MPFR_SET_NAN(a);
          return;
        }
      else if (MPFR_IS_INF(b))
        {
          if (MPFR_IS_INF (c) && (MPFR_SIGN (c) == MPFR_SIGN (b)))
            MPFR_SET_ZERO(a);
          else
            MPFR_SET_NAN(a);
          return;
        }
      else if (MPFR_IS_INF(c))
        {
          MPFR_SET_SAME_SIGN (a, b);
          MPFR_SET_INF (a);
          return;
        }
      else if (MPFR_IS_ZERO(b)) /* reldiff = abs(c)/c = sign(c) */
        {
          mpfr_set_si (a, MPFR_INT_SIGN (c), rnd_mode);
          return;
        }
      /* Fall through */
    }

  if (a == b)
    {
      mpfr_init2 (b_copy, MPFR_PREC(b));
      mpfr_set (b_copy, b, MPFR_RNDN);
    }

  mpfr_sub (a, b, c, rnd_mode);
  mpfr_abs (a, a, rnd_mode); /* for compatibility with MPF */
  mpfr_div (a, a, (a == b) ? b_copy : b, rnd_mode);

  if (a == b)
    mpfr_clear (b_copy);

}

int
mpfr_frexp (mpfr_exp_t *exp, mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
{
  int inex;

  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
    {
      if (MPFR_IS_NAN(x))
        {
          MPFR_SET_NAN(y);
          MPFR_RET_NAN; /* exp is unspecified */
        }
      else if (MPFR_IS_INF(x))
        {
          MPFR_SET_INF(y);
          MPFR_SET_SAME_SIGN(y,x);
          MPFR_RET(0); /* exp is unspecified */
        }
      else
        {
          MPFR_SET_ZERO(y);
          MPFR_SET_SAME_SIGN(y,x);
          *exp = 0;
          MPFR_RET(0);
        }
    }

  inex = mpfr_set (y, x, rnd);
  *exp = MPFR_GET_EXP (y);
  MPFR_SET_EXP (y, 0);
  return mpfr_check_range (y, inex, rnd);
}

int
mpfr_urandomb (mpfr_ptr rop, gmp_randstate_t rstate)
{
  mp_ptr rp;
  mp_prec_t nbits;
  mp_size_t nlimbs;
  mp_size_t k; /* number of high zero limbs */
  mp_exp_t exp;
  int cnt;

  MPFR_CLEAR_FLAGS (rop);

  rp = MPFR_MANT (rop);
  nbits = MPFR_PREC (rop);
  nlimbs = MPFR_LIMB_SIZE (rop);
  MPFR_SET_POS (rop);

  /* Uniform non-normalized significand */
  _gmp_rand (rp, rstate, nlimbs * BITS_PER_MP_LIMB);

  /* If nbits isn't a multiple of BITS_PER_MP_LIMB, mask the low bits */
  cnt = nlimbs * BITS_PER_MP_LIMB - nbits;
  if (MPFR_LIKELY (cnt != 0))
    rp[0] &= ~MPFR_LIMB_MASK (cnt);

  /* Count the null significant limbs and remaining limbs */
  exp = 0;
  k = 0;
  while (nlimbs != 0 && rp[nlimbs - 1] == 0)
    {
      k ++;
      nlimbs --;
      exp -= BITS_PER_MP_LIMB;
    }

  if (MPFR_LIKELY (nlimbs != 0)) /* otherwise value is zero */
    {
      count_leading_zeros (cnt, rp[nlimbs - 1]);
      /* Normalization */
      if (mpfr_set_exp (rop, exp - cnt))
        {
          /* If the exponent is not in the current exponent range, we
             choose to return a NaN as this is probably a user error.
             Indeed this can happen only if the exponent range has been
             reduced to a very small interval and/or the precision is
             huge (very unlikely). */
          MPFR_SET_NAN (rop);
          __gmpfr_flags |= MPFR_FLAGS_NAN; /* Can't use MPFR_RET_NAN */
          return 1;
        }
      if (cnt != 0)
        mpn_lshift (rp + k, rp, nlimbs, cnt);
      if (k != 0)
        MPN_ZERO (rp, k);
    }
  else
    MPFR_SET_ZERO (rop);

  return 0;
}

/* compute remainder as in definition:
   r = x - n * y, where n = trunc(x/y).
   warning: may change flags. */
static int
slow_fmod (mpfr_ptr r, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd)
{
  mpfr_t q;
  int inexact;
  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) || MPFR_IS_SINGULAR (y)))
    {
      if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y) || MPFR_IS_INF (x)
          || MPFR_IS_ZERO (y))
        {
          MPFR_SET_NAN (r);
          MPFR_RET_NAN;
        }
      else                      /* either y is Inf and x is 0 or non-special,
                                   or x is 0 and y is non-special,
                                   in both cases the quotient is zero. */
        return mpfr_set (r, x, rnd);
    }
  /* regular cases */
  /* if 2^(ex-1) <= |x| < 2^ex, and 2^(ey-1) <= |y| < 2^ey,
     then |x/y| < 2^(ex-ey+1) */
  mpfr_init2 (q,
              MAX (MPFR_PREC_MIN, mpfr_get_exp (x) - mpfr_get_exp (y) + 1));
  mpfr_div (q, x, y, MPFR_RNDZ);
  mpfr_trunc (q, q);                            /* may change inexact flag */
  mpfr_prec_round (q, mpfr_get_prec (q) + mpfr_get_prec (y), MPFR_RNDZ);
  inexact = mpfr_mul (q, q, y, MPFR_RNDZ);       /* exact */
  inexact = mpfr_sub (r, x, q, rnd);
  mpfr_clear (q);
  return inexact;
}

int
mpfr_max (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd_mode)
{
  if (MPFR_IS_NAN(x) && MPFR_IS_NAN(y) ) 
    {  
      MPFR_SET_NAN(z);
      MPFR_RET_NAN;
    }
  MPFR_CLEAR_NAN(z);

  if (MPFR_IS_NAN(x))
    return mpfr_set(z, y, rnd_mode);

  if (MPFR_IS_NAN(y))
    return mpfr_set(z, x, rnd_mode);

  if (MPFR_IS_FP(x) && MPFR_IS_ZERO(x) && MPFR_IS_FP(y) && MPFR_IS_ZERO(y))
    {
      if (MPFR_SIGN(x) < 0)
        return mpfr_set(z, y, rnd_mode);
      else
        return mpfr_set(z, x, rnd_mode);
    }

  if (mpfr_cmp(x,y) <= 0)
    return mpfr_set(z, y, rnd_mode);
  else
    return mpfr_set(z, x, rnd_mode);
}

int
mpfr_max (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd_mode)
{
  if (MPFR_ARE_SINGULAR(x,y))
    {
      if (MPFR_IS_NAN(x) && MPFR_IS_NAN(y) )
        {
          MPFR_SET_NAN(z);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_NAN(x))
        return mpfr_set(z, y, rnd_mode);
      else if (MPFR_IS_NAN(y))
        return mpfr_set(z, x, rnd_mode);
      else if (MPFR_IS_ZERO(x) && MPFR_IS_ZERO(y))
        {
          if (MPFR_IS_NEG(x))
            return mpfr_set(z, y, rnd_mode);
          else
            return mpfr_set(z, x, rnd_mode);
        }
    }
  if (mpfr_cmp(x,y) <= 0)
    return mpfr_set(z, y, rnd_mode);
  else
    return mpfr_set(z, x, rnd_mode);
}

void
mpfr_set_str_binary (mpfr_ptr x, const char *str)
{
  int has_sign;
  int res;

  if (*str == 'N')
    {
      MPFR_SET_NAN(x);
      __gmpfr_flags |= MPFR_FLAGS_NAN;
      return;
    }

  has_sign = *str == '-' || *str == '+';
  if (str[has_sign] == 'I')
    {
      MPFR_SET_INF(x);
      if (*str == '-')
        MPFR_SET_NEG(x);
      else
        MPFR_SET_POS(x);
      return;
    }

  res = mpfr_strtofr (x, str, 0, 2, MPFR_RNDZ);
  MPFR_ASSERTN (res == 0);
}

/* 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_urandomb (mpfr_ptr rop, gmp_randstate_t rstate)
{
    mpfr_limb_ptr rp;
    mpfr_prec_t nbits;
    mp_size_t nlimbs;
    mp_size_t k; /* number of high zero limbs */
    mpfr_exp_t exp;
    int cnt;

    rp = MPFR_MANT (rop);
    nbits = MPFR_PREC (rop);
    nlimbs = MPFR_LIMB_SIZE (rop);
    MPFR_SET_POS (rop);
    cnt = nlimbs * GMP_NUMB_BITS - nbits;

    /* Uniform non-normalized significand */
    /* generate exactly nbits so that the random generator stays in the same
       state, independent of the machine word size GMP_NUMB_BITS */
    mpfr_rand_raw (rp, rstate, nbits);
    if (MPFR_LIKELY (cnt != 0)) /* this will put the low bits to zero */
        mpn_lshift (rp, rp, nlimbs, cnt);

    /* Count the null significant limbs and remaining limbs */
    exp = 0;
    k = 0;
    while (nlimbs != 0 && rp[nlimbs - 1] == 0)
    {
        k ++;
        nlimbs --;
        exp -= GMP_NUMB_BITS;
    }

    if (MPFR_LIKELY (nlimbs != 0)) /* otherwise value is zero */
    {
        count_leading_zeros (cnt, rp[nlimbs - 1]);
        /* Normalization */
        if (mpfr_set_exp (rop, exp - cnt))
        {
            /* If the exponent is not in the current exponent range, we
               choose to return a NaN as this is probably a user error.
               Indeed this can happen only if the exponent range has been
               reduced to a very small interval and/or the precision is
               huge (very unlikely). */
            MPFR_SET_NAN (rop);
            __gmpfr_flags |= MPFR_FLAGS_NAN; /* Can't use MPFR_RET_NAN */
            return 1;
        }
        if (cnt != 0)
            mpn_lshift (rp + k, rp, nlimbs, cnt);
        if (k != 0)
            MPN_ZERO (rp, k);
    }
    else
        MPFR_SET_ZERO (rop);

    return 0;
}

static void
check_nan (void)
{
  mpfr_t  d, q;

  mpfr_init2 (d, 100L);
  mpfr_init2 (q, 100L);

  /* 1/+inf == 0 */
  MPFR_CLEAR_FLAGS (d);
  MPFR_SET_INF (d);
  MPFR_SET_POS (d);
  MPFR_ASSERTN (mpfr_ui_div (q, 1L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_number_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) == 0);

  /* 1/-inf == -0 */
  MPFR_CLEAR_FLAGS (d);
  MPFR_SET_INF (d);
  MPFR_SET_NEG (d);
  MPFR_ASSERTN (mpfr_ui_div (q, 1L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_number_p (q));
  MPFR_ASSERTN (mpfr_sgn (q) == 0);

  /* 1/nan == nan */
  MPFR_SET_NAN (d);
  MPFR_ASSERTN (mpfr_ui_div (q, 1L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_nan_p (q));

  /* 0/0 == nan */
  mpfr_set_ui (d, 0L, GMP_RNDN);
  MPFR_ASSERTN (mpfr_ui_div (q, 0L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_nan_p (q));

  /* 1/+0 = +inf */
  mpfr_set_ui (d, 0L, GMP_RNDN);
  MPFR_ASSERTN (mpfr_ui_div (q, 1L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) > 0);

  /* 1/-0 = -inf */
  mpfr_set_ui (d, 0L, GMP_RNDN);
  mpfr_neg (d, d, GMP_RNDN);
  MPFR_ASSERTN (mpfr_ui_div (q, 1L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_inf_p (q) && mpfr_sgn (q) < 0);

  /* 0/1 = +0 */
  mpfr_set_ui (d, 1L, GMP_RNDN);
  MPFR_ASSERTN (mpfr_ui_div (q, 0L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_cmp_ui (q, 0) == 0 && MPFR_IS_POS (q));

  /* 0/-1 = -0 */
  mpfr_set_si (d, -1, GMP_RNDN);
  MPFR_ASSERTN (mpfr_ui_div (q, 0L, d, GMP_RNDZ) == 0); /* exact */
  MPFR_ASSERTN (mpfr_cmp_ui (q, 0) == 0 && MPFR_IS_NEG (q));

  mpfr_clear (d);
  mpfr_clear (q);
}

/* Maybe better create its own test file ? */
static void
check_neg_special (void)
{
  mpfr_t x;
  mpfr_init (x);
  MPFR_SET_NAN (x);
  mpfr_clear_nanflag ();
  mpfr_neg (x, x, MPFR_RNDN);
  PRINT_ERROR_IF (!mpfr_nanflag_p (),
                  "ERROR: neg (NaN) doesn't set Nan flag.\n");
  mpfr_clear (x);
}

static void
set_special (mpfr_ptr x, unsigned int select)
{
  MPFR_ASSERTN (select < SPECIAL_MAX);
  switch (select)
    {
    case 0:
      MPFR_SET_NAN (x);
      break;
    case 1:
      MPFR_SET_INF (x);
      MPFR_SET_POS (x);
      break;
    case 2:
      MPFR_SET_INF (x);
      MPFR_SET_NEG (x);
      break;
    case 3:
      MPFR_SET_ZERO (x);
      MPFR_SET_POS  (x);
      break;
    case 4:
      MPFR_SET_ZERO (x);
      MPFR_SET_NEG  (x);
      break;
    case 5:
      mpfr_set_str_binary (x, "1");
      break;
    case 6:
      mpfr_set_str_binary (x, "-1");
      break;
    case 7:
      mpfr_set_str_binary (x, "1e-1");
      break;
    case 8:
      mpfr_set_str_binary (x, "1e+1");
      break;
    case 9:
      mpfr_const_pi (x, MPFR_RNDN);
      break;
    case 10:
      mpfr_const_pi (x, MPFR_RNDN);
      MPFR_SET_EXP (x, MPFR_GET_EXP (x)-1);
      break;
    default:
      mpfr_urandomb (x, RANDS);
      if (randlimb () & 1)
        mpfr_neg (x, x, MPFR_RNDN);
      break;
    }
}