Пример #1
0
int
mpfr_set_si (mpfr_ptr x, long i, mp_rnd_t rnd_mode)
{
  int inex;
  mp_size_t xn;
  unsigned int cnt, nbits;
  mp_limb_t ai, *xp;

  MPFR_CLEAR_FLAGS(x);
  if (i == 0)
    {
      MPFR_SET_ZERO(x);
      MPFR_SET_POS(x);
      MPFR_RET(0);
    }

  xn = (MPFR_PREC(x)-1)/BITS_PER_MP_LIMB;
  ai = SAFE_ABS(long, i);
  count_leading_zeros(cnt, ai);

  xp = MPFR_MANT(x);
  xp[xn] = ai << cnt;
  /* don't forget to put zero in lower limbs */
  MPN_ZERO(xp, xn);
  /* set sign */
  if ((i < 0) ^ (MPFR_SIGN(x) < 0))
    MPFR_CHANGE_SIGN(x);

  MPFR_EXP(x) = nbits = BITS_PER_MP_LIMB - cnt;
  inex = mpfr_check_range(x, rnd_mode);
  if (inex)
    return inex; /* underflow or overflow */

  /* round if MPFR_PREC(x) smaller than length of i */
  if (MPFR_PREC(x) < nbits)
    {
      int carry;

      carry = mpfr_round_raw(xp+xn, xp+xn, nbits, (i < 0), MPFR_PREC(x),
                             rnd_mode, &inex);
      if (carry)
        {
          mp_exp_t exp = MPFR_EXP(x);

          if (exp == __mpfr_emax)
            return mpfr_set_overflow(x, rnd_mode, (i < 0 ? -1 : 1));

          MPFR_EXP(x)++;
          xp[xn] = GMP_LIMB_HIGHBIT;
        }
    }

  MPFR_RET(inex);
}
Пример #2
0
int
mpfr_set_si_2exp (mpfr_ptr x, long i, mp_exp_t e, mp_rnd_t rnd_mode)
{
  if (i == 0)
    {
      MPFR_SET_ZERO (x);
      MPFR_SET_POS (x);
      MPFR_RET (0);
    }
  else
    {
      mp_size_t xn;
      unsigned int cnt, nbits;
      mp_limb_t ai, *xp;
      int inex = 0;

      /* FIXME: support int limbs (e.g. 16-bit limbs on 16-bit proc) */
      ai = SAFE_ABS (unsigned long, i);
      MPFR_ASSERTN (SAFE_ABS (unsigned long, i) == ai);

      /* Position of the highest limb */
      xn = (MPFR_PREC (x) - 1) / BITS_PER_MP_LIMB;
      count_leading_zeros (cnt, ai);
      MPFR_ASSERTD (cnt < BITS_PER_MP_LIMB);  /* OK since i != 0 */

      xp = MPFR_MANT(x);
      xp[xn] = ai << cnt;
      /* Zero the xn lower limbs. */
      MPN_ZERO(xp, xn);
      MPFR_SET_SIGN (x, i < 0 ? MPFR_SIGN_NEG : MPFR_SIGN_POS);

      nbits = BITS_PER_MP_LIMB - cnt;
      e += nbits;  /* exponent _before_ the rounding */

      /* round if MPFR_PREC(x) smaller than length of i */
      if (MPFR_UNLIKELY (MPFR_PREC (x) < nbits) &&
          MPFR_UNLIKELY (mpfr_round_raw (xp + xn, xp + xn, nbits, i < 0,
                                         MPFR_PREC (x), rnd_mode, &inex)))
        {
          e++;
          xp[xn] = MPFR_LIMB_HIGHBIT;
        }

      MPFR_CLEAR_FLAGS (x);
      MPFR_EXP (x) = e;
      return mpfr_check_range (x, inex, rnd_mode);
    }
}
int
mpfr_set_ui_2exp (mpfr_ptr x, unsigned long i, mpfr_exp_t e, mpfr_rnd_t rnd_mode)
{
  MPFR_SET_POS (x);

  if (i == 0)
    {
      MPFR_SET_ZERO (x);
      MPFR_RET (0);
    }
  else
    {
      mp_size_t xn;
      unsigned int cnt, nbits;
      mp_limb_t *xp;
      int inex = 0;

      /* FIXME: support int limbs (e.g. 16-bit limbs on 16-bit proc) */
      MPFR_ASSERTD (i == (mp_limb_t) i);

      /* Position of the highest limb */
      xn = (MPFR_PREC (x) - 1) / GMP_NUMB_BITS;
      count_leading_zeros (cnt, (mp_limb_t) i);
      MPFR_ASSERTD (cnt < GMP_NUMB_BITS);  /* OK since i != 0 */

      xp = MPFR_MANT(x);
      xp[xn] = ((mp_limb_t) i) << cnt;
      /* Zero the xn lower limbs. */
      MPN_ZERO(xp, xn);

      nbits = GMP_NUMB_BITS - cnt;
      e += nbits;  /* exponent _before_ the rounding */

      /* round if MPFR_PREC(x) smaller than length of i */
      if (MPFR_UNLIKELY (MPFR_PREC (x) < nbits) &&
          MPFR_UNLIKELY (mpfr_round_raw (xp + xn, xp + xn, nbits, 0,
                                         MPFR_PREC (x), rnd_mode, &inex)))
        {
          e++;
          xp[xn] = MPFR_LIMB_HIGHBIT;
        }

      MPFR_EXP (x) = e;
      return mpfr_check_range (x, inex, rnd_mode);
    }
}
Пример #4
0
int
mpfr_sqr (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode)
{
  int cc, inexact;
  mpfr_exp_t ax;
  mp_limb_t *tmp;
  mp_limb_t b1;
  mpfr_prec_t bq;
  mp_size_t bn, tn;
  MPFR_TMP_DECL(marker);

  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", b, b, rnd_mode),
                 ("y[%#R]=%R inexact=%d", a, a, inexact));

  /* deal with special cases */
  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(b)))
    {
      if (MPFR_IS_NAN(b))
        {
          MPFR_SET_NAN(a);
          MPFR_RET_NAN;
        }
      MPFR_SET_POS (a);
      if (MPFR_IS_INF(b))
        MPFR_SET_INF(a);
      else
        ( MPFR_ASSERTD(MPFR_IS_ZERO(b)), MPFR_SET_ZERO(a) );
      MPFR_RET(0);
    }
  ax = 2 * MPFR_GET_EXP (b);
  bq = MPFR_PREC(b);

  MPFR_ASSERTD (2 * bq > bq); /* PREC_MAX is /2 so no integer overflow */

  bn = MPFR_LIMB_SIZE(b); /* number of limbs of b */
  tn = 1 + (2 * bq - 1) / GMP_NUMB_BITS; /* number of limbs of square,
                                               2*bn or 2*bn-1 */

  MPFR_TMP_MARK(marker);
  tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) 2 * bn * BYTES_PER_MP_LIMB);

  /* Multiplies the mantissa in temporary allocated space */
  mpn_sqr_n (tmp, MPFR_MANT(b), bn);
  b1 = tmp[2 * bn - 1];

  /* now tmp[0]..tmp[2*bn-1] contains the product of both mantissa,
     with tmp[2*bn-1]>=2^(GMP_NUMB_BITS-2) */
  b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */

  /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
     then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
     and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
  tmp += 2 * bn - tn; /* +0 or +1 */
  if (MPFR_UNLIKELY(b1 == 0))
    mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */

  cc = mpfr_round_raw (MPFR_MANT (a), tmp, 2 * bq, 0,
                       MPFR_PREC (a), rnd_mode, &inexact);
  /* cc = 1 ==> result is a power of two */
  if (MPFR_UNLIKELY(cc))
    MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;

  MPFR_TMP_FREE(marker);
  {
    mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc);
    if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
      return mpfr_overflow (a, rnd_mode, MPFR_SIGN_POS);
    if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
      {
        /* In the rounding to the nearest mode, if the exponent of the exact
           result (i.e. before rounding, i.e. without taking cc into account)
           is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
           both arguments are powers of 2), then round to zero. */
        if (rnd_mode == MPFR_RNDN &&
            (ax + (mpfr_exp_t) b1 < __gmpfr_emin || mpfr_powerof2_raw (b)))
          rnd_mode = MPFR_RNDZ;
        return mpfr_underflow (a, rnd_mode, MPFR_SIGN_POS);
      }
    MPFR_SET_EXP (a, ax2);
    MPFR_SET_POS (a);
  }
  MPFR_RET (inexact);
}
Пример #5
0
Файл: mul.c Проект: gnooth/xcl
static int
mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
    /* Old implementation */
    int sign_product, cc, inexact;
    mpfr_exp_t ax;
    mp_limb_t *tmp;
    mp_limb_t b1;
    mpfr_prec_t bq, cq;
    mp_size_t bn, cn, tn, k;
    MPFR_TMP_DECL(marker);

    /* deal with special cases */
    if (MPFR_ARE_SINGULAR(b,c))
    {
        if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
        {
            MPFR_SET_NAN(a);
            MPFR_RET_NAN;
        }
        sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
        if (MPFR_IS_INF(b))
        {
            if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
            {
                MPFR_SET_SIGN(a,sign_product);
                MPFR_SET_INF(a);
                MPFR_RET(0); /* exact */
            }
            else
            {
                MPFR_SET_NAN(a);
                MPFR_RET_NAN;
            }
        }
        else if (MPFR_IS_INF(c))
        {
            if (MPFR_NOTZERO(b))
            {
                MPFR_SET_SIGN(a, sign_product);
                MPFR_SET_INF(a);
                MPFR_RET(0); /* exact */
            }
            else
            {
                MPFR_SET_NAN(a);
                MPFR_RET_NAN;
            }
        }
        else
        {
            MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
            MPFR_SET_SIGN(a, sign_product);
            MPFR_SET_ZERO(a);
            MPFR_RET(0); /* 0 * 0 is exact */
        }
    }
    sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );

    ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);

    bq = MPFR_PREC(b);
    cq = MPFR_PREC(c);

    MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */

    bn = (bq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of b */
    cn = (cq+GMP_NUMB_BITS-1)/GMP_NUMB_BITS; /* number of limbs of c */
    k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
    tn = (bq + cq + GMP_NUMB_BITS - 1) / GMP_NUMB_BITS;
    /* <= k, thus no int overflow */
    MPFR_ASSERTD(tn <= k);

    /* Check for no size_t overflow*/
    MPFR_ASSERTD((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
    MPFR_TMP_MARK(marker);
    tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);

    /* multiplies two mantissa in temporary allocated space */
    b1 = (MPFR_LIKELY(bn >= cn)) ?
         mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
         : mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);

    /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
       with tmp[k-1]>=2^(GMP_NUMB_BITS-2) */
    b1 >>= GMP_NUMB_BITS - 1; /* msb from the product */

    /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
       then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
       and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
    tmp += k - tn;
    if (MPFR_UNLIKELY(b1 == 0))
        mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
    cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq,
                         MPFR_IS_NEG_SIGN(sign_product),
                         MPFR_PREC (a), rnd_mode, &inexact);

    /* cc = 1 ==> result is a power of two */
    if (MPFR_UNLIKELY(cc))
        MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;

    MPFR_TMP_FREE(marker);

    {
        mpfr_exp_t ax2 = ax + (mpfr_exp_t) (b1 - 1 + cc);
        if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
            return mpfr_overflow (a, rnd_mode, sign_product);
        if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
        {
            /* In the rounding to the nearest mode, if the exponent of the exact
               result (i.e. before rounding, i.e. without taking cc into account)
               is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
               both arguments are powers of 2), then round to zero. */
            if (rnd_mode == MPFR_RNDN &&
                    (ax + (mpfr_exp_t) b1 < __gmpfr_emin ||
                     (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
                rnd_mode = MPFR_RNDZ;
            return mpfr_underflow (a, rnd_mode, sign_product);
        }
        MPFR_SET_EXP (a, ax2);
        MPFR_SET_SIGN(a, sign_product);
    }
    MPFR_RET (inexact);
}
Пример #6
0
int
mpfr_frac (mpfr_ptr r, mpfr_srcptr u, mpfr_rnd_t rnd_mode)
{
  mpfr_exp_t re, ue;
  mpfr_prec_t uq;
  mp_size_t un, tn, t0;
  mp_limb_t *up, *tp, k;
  int sh;
  mpfr_t tmp;
  mpfr_ptr t;
  int inex;
  MPFR_SAVE_EXPO_DECL (expo);

  /* Special cases */
  if (MPFR_UNLIKELY(MPFR_IS_NAN(u)))
    {
      MPFR_SET_NAN(r);
      MPFR_RET_NAN;
    }
  else if (MPFR_UNLIKELY(MPFR_IS_INF(u) || mpfr_integer_p (u)))
    {
      MPFR_SET_SAME_SIGN(r, u);
      MPFR_SET_ZERO(r);
      MPFR_RET(0);  /* zero is exact */
    }

  ue = MPFR_GET_EXP (u);
  if (ue <= 0)  /* |u| < 1 */
    return mpfr_set (r, u, rnd_mode);

  /* Now |u| >= 1, meaning that an overflow is not possible. */

  uq = MPFR_PREC(u);
  un = (uq - 1) / GMP_NUMB_BITS;  /* index of most significant limb */
  un -= (mp_size_t) (ue / GMP_NUMB_BITS);
  /* now the index of the MSL containing bits of the fractional part */

  up = MPFR_MANT(u);
  sh = ue % GMP_NUMB_BITS;
  k = up[un] << sh;
  /* the first bit of the fractional part is the MSB of k */

  if (k != 0)
    {
      int cnt;

      count_leading_zeros(cnt, k);
      /* first bit 1 of the fractional part -> MSB of the number */
      re = -cnt;
      sh += cnt;
      MPFR_ASSERTN (sh < GMP_NUMB_BITS);
      k <<= cnt;
    }
  else
    {
      re = sh - GMP_NUMB_BITS;
      /* searching for the first bit 1 (exists since u isn't an integer) */
      while (up[--un] == 0)
        re -= GMP_NUMB_BITS;
      MPFR_ASSERTN(un >= 0);
      k = up[un];
      count_leading_zeros(sh, k);
      re -= sh;
      k <<= sh;
    }
  /* The exponent of r will be re */
  /* un: index of the limb of u that contains the first bit 1 of the FP */

  t = (mp_size_t) (MPFR_PREC(r) - 1) / GMP_NUMB_BITS < un ?
    (mpfr_init2 (tmp, (un + 1) * GMP_NUMB_BITS), tmp) : r;
  /* t has enough precision to contain the fractional part of u */
  /* If we use a temporary variable, we take the non-significant bits
     of u into account, because of the mpn_lshift below. */
  MPFR_SET_SAME_SIGN(t, u);

  /* Put the fractional part of u into t */
  tn = (MPFR_PREC(t) - 1) / GMP_NUMB_BITS;
  MPFR_ASSERTN(tn >= un);
  t0 = tn - un;
  tp = MPFR_MANT(t);
  if (sh == 0)
    MPN_COPY_DECR(tp + t0, up, un + 1);
  else /* warning: un may be 0 here */
    tp[tn] = k | ((un) ? mpn_lshift (tp + t0, up, un, sh) : (mp_limb_t) 0);
  if (t0 > 0)
    MPN_ZERO(tp, t0);

  MPFR_SAVE_EXPO_MARK (expo);

  if (t != r)
    { /* t is tmp */
      MPFR_EXP (t) = 0;  /* should be re, but not necessarily in the range */
      inex = mpfr_set (r, t, rnd_mode);  /* no underflow */
      mpfr_clear (t);
      MPFR_EXP (r) += re;
    }
  else
    { /* There may be remaining non-significant bits in t (= r). */
      int carry;

      MPFR_EXP (r) = re;
      carry = mpfr_round_raw (tp, tp,
                              (mpfr_prec_t) (tn + 1) * GMP_NUMB_BITS,
                              MPFR_IS_NEG (r), MPFR_PREC (r), rnd_mode,
                              &inex);
      if (carry)
        {
          tp[tn] = MPFR_LIMB_HIGHBIT;
          MPFR_EXP (r) ++;
        }
    }

  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (r, inex, rnd_mode);
}
Пример #7
0
int
mpfr_set_f (mpfr_ptr y, mpf_srcptr x, mpfr_rnd_t rnd_mode)
{
  mp_limb_t *my, *mx, *tmp;
  unsigned long cnt, sx, sy;
  int inexact, carry = 0;
  MPFR_TMP_DECL(marker);

  sx = ABS(SIZ(x)); /* number of limbs of the mantissa of x */

  if (sx == 0) /* x is zero */
    {
      MPFR_SET_ZERO(y);
      MPFR_SET_POS(y);
      return 0; /* 0 is exact */
    }

  if (SIZ(x) * MPFR_FROM_SIGN_TO_INT(MPFR_SIGN(y)) < 0)
    MPFR_CHANGE_SIGN (y);

  sy = MPFR_LIMB_SIZE (y);
  my = MPFR_MANT(y);
  mx = PTR(x);

  count_leading_zeros(cnt, mx[sx - 1]);

  if (sy <= sx) /* we may have to round even when sy = sx */
    {
      unsigned long xprec = sx * GMP_NUMB_BITS;

      MPFR_TMP_MARK(marker);
      tmp = MPFR_TMP_LIMBS_ALLOC (sx);
      if (cnt)
        mpn_lshift (tmp, mx, sx, cnt);
      else
        /* FIXME: we may avoid the copy here, and directly call mpfr_round_raw
           on mx instead of tmp */
        MPN_COPY (tmp, mx, sx);
      carry = mpfr_round_raw (my, tmp, xprec, (SIZ(x) < 0), MPFR_PREC(y),
                              rnd_mode, &inexact);
      if (MPFR_UNLIKELY(carry)) /* result is a power of two */
        my[sy - 1] = MPFR_LIMB_HIGHBIT;
      MPFR_TMP_FREE(marker);
    }
  else
    {
      if (cnt)
        mpn_lshift (my + sy - sx, mx, sx, cnt);
      else
        MPN_COPY (my + sy - sx, mx, sx);
      MPN_ZERO(my, sy - sx);
      /* no rounding necessary, since y has a larger mantissa */
      inexact = 0;
    }

  /* warning: EXP(x) * GMP_NUMB_BITS may exceed the maximal exponent */
  if (EXP(x) > 1 + (__gmpfr_emax - 1) / GMP_NUMB_BITS)
    {
      /* EXP(x) >= 2 + floor((__gmpfr_emax-1)/GMP_NUMB_BITS)
         EXP(x) >= 2 + (__gmpfr_emax - GMP_NUMB_BITS) / GMP_NUMB_BITS
                >= 1 + __gmpfr_emax / GMP_NUMB_BITS
         EXP(x) * GMP_NUMB_BITS >= __gmpfr_emax + GMP_NUMB_BITS
         Since 0 <= cnt <= GMP_NUMB_BITS-1, and 0 <= carry <= 1,
         we have then EXP(x) * GMP_NUMB_BITS - cnt + carry > __gmpfr_emax */
      return mpfr_overflow (y, rnd_mode, MPFR_SIGN (y));
    }
  else
    {
      /* Do not use MPFR_SET_EXP as the exponent may be out of range. */
      MPFR_EXP (y) = EXP (x) * GMP_NUMB_BITS - (mpfr_exp_t) cnt + carry;
    }

  return mpfr_check_range (y, inexact, rnd_mode);
}