示例#1
0
文件: t-eq.c 项目: AllardJ/Tomato
void
insert_random_low_zero_limbs (mpf_t x, gmp_randstate_ptr rands)
{
  mp_size_t max = PREC(x) - SIZ(x);
  mp_size_t s;
  mpz_t ds; mpz_init (ds);
  mpz_urandomb (ds, rands, 32);
  s = mpz_get_ui (ds) % (max + 1);
  MPN_COPY_DECR (PTR(x) + s, PTR(x), SIZ(x));
  MPN_ZERO (PTR(x), s);
  SIZ(x) += s;
  mpz_clear (ds);
}
示例#2
0
void
mpz_mul_2exp (mpz_ptr w, mpz_srcptr u, unsigned long int cnt)
{
  mp_size_t usize = u->_mp_size;
  mp_size_t abs_usize = ABS (usize);
  mp_size_t wsize;
  mp_size_t limb_cnt;
  mp_ptr wp;
  mp_limb_t wlimb;

  if (usize == 0)
    {
      w->_mp_size = 0;
      return;
    }

  limb_cnt = cnt / GMP_NUMB_BITS;
  wsize = abs_usize + limb_cnt + 1;
  if (w->_mp_alloc < wsize)
    _mpz_realloc (w, wsize);

  wp = w->_mp_d;
  wsize = abs_usize + limb_cnt;

  cnt %= GMP_NUMB_BITS;
  if (cnt != 0)
    {
      wlimb = mpn_lshift (wp + limb_cnt, u->_mp_d, abs_usize, cnt);
      if (wlimb != 0)
	{
	  wp[wsize] = wlimb;
	  wsize++;
	}
    }
  else
    {
      MPN_COPY_DECR (wp + limb_cnt, u->_mp_d, abs_usize);
    }

  /* Zero all whole limbs at low end.  Do it here and not before calling
     mpn_lshift, not to lose for U == W.  */
  MPN_ZERO (wp, limb_cnt);

  w->_mp_size = usize >= 0 ? wsize : -wsize;
}
示例#3
0
void
mpi_mul_2exp( MPI w, MPI u, unsigned long cnt)
{
    mpi_size_t usize, wsize, limb_cnt;
    mpi_ptr_t wp;
    mpi_limb_t wlimb;
    int usign, wsign;

    usize = u->nlimbs;
    usign = u->sign;

    if( !usize ) {
	w->nlimbs = 0;
	w->sign = 0;
	return;
    }

    limb_cnt = cnt / BITS_PER_MPI_LIMB;
    wsize = usize + limb_cnt + 1;
    if( w->alloced < wsize )
	mpi_resize(w, wsize );
    wp = w->d;
    wsize = usize + limb_cnt;
    wsign = usign;

    cnt %= BITS_PER_MPI_LIMB;
    if( cnt ) {
	wlimb = mpihelp_lshift( wp + limb_cnt, u->d, usize, cnt );
	if( wlimb ) {
	    wp[wsize] = wlimb;
	    wsize++;
	}
    }
    else {
	MPN_COPY_DECR( wp + limb_cnt, u->d, usize );
    }

    /* Zero all whole limbs at low end.  Do it here and not before calling
     * mpn_lshift, not to lose for U == W.  */
    MPN_ZERO( wp, limb_cnt );

    w->nlimbs = wsize;
    w->sign = wsign;
}
示例#4
0
int mpi_mul_2exp(MPI w, MPI u, unsigned long cnt)
{
	mpi_size_t usize, wsize, limb_cnt;
	mpi_ptr_t wp;
	mpi_limb_t wlimb;
	int usign, wsign;

	usize = u->nlimbs;
	usign = u->sign;

	if (!usize) {
		w->nlimbs = 0;
		w->sign = 0;
		return 0;
	}

	limb_cnt = cnt / BITS_PER_MPI_LIMB;
	wsize = usize + limb_cnt + 1;
	if (w->alloced < wsize)
		if (mpi_resize(w, wsize) < 0)
			return -ENOMEM;
	wp = w->d;
	wsize = usize + limb_cnt;
	wsign = usign;

	cnt %= BITS_PER_MPI_LIMB;
	if (cnt) {
		wlimb = mpihelp_lshift(wp + limb_cnt, u->d, usize, cnt);
		if (wlimb) {
			wp[wsize] = wlimb;
			wsize++;
		}
	} else {
		MPN_COPY_DECR(wp + limb_cnt, u->d, usize);
	}

	/*                                                                    
                                         */
	MPN_ZERO(wp, limb_cnt);

	w->nlimbs = wsize;
	w->sign = wsign;
	return 0;
}
示例#5
0
文件: sub1sp.c 项目: pgundlach/LuaTeX
int
mpfr_sub1sp (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mpfr_rnd_t rnd_mode)
{
  mpfr_exp_t bx,cx;
  mpfr_uexp_t d;
  mpfr_prec_t p, sh, cnt;
  mp_size_t n;
  mp_limb_t *ap, *bp, *cp;
  mp_limb_t limb;
  int inexact;
  mp_limb_t bcp,bcp1; /* Cp and C'p+1 */
  mp_limb_t bbcp = (mp_limb_t) -1, bbcp1 = (mp_limb_t) -1; /* Cp+1 and C'p+2,
    gcc claims that they might be used uninitialized. We fill them with invalid
    values, which should produce a failure if so. See README.dev file. */

  MPFR_TMP_DECL(marker);

  MPFR_TMP_MARK(marker);

  MPFR_ASSERTD(MPFR_PREC(a) == MPFR_PREC(b) && MPFR_PREC(b) == MPFR_PREC(c));
  MPFR_ASSERTD(MPFR_IS_PURE_FP(b));
  MPFR_ASSERTD(MPFR_IS_PURE_FP(c));

  /* Read prec and num of limbs */
  p = MPFR_PREC (b);
  n = MPFR_PREC2LIMBS (p);

  /* Fast cmp of |b| and |c|*/
  bx = MPFR_GET_EXP (b);
  cx = MPFR_GET_EXP (c);
  if (MPFR_UNLIKELY(bx == cx))
    {
      mp_size_t k = n - 1;
      /* Check mantissa since exponent are equals */
      bp = MPFR_MANT(b);
      cp = MPFR_MANT(c);
      while (k>=0 && MPFR_UNLIKELY(bp[k] == cp[k]))
        k--;
      if (MPFR_UNLIKELY(k < 0))
        /* b == c ! */
        {
          /* Return exact number 0 */
          if (rnd_mode == MPFR_RNDD)
            MPFR_SET_NEG(a);
          else
            MPFR_SET_POS(a);
          MPFR_SET_ZERO(a);
          MPFR_RET(0);
        }
      else if (bp[k] > cp[k])
        goto BGreater;
      else
        {
          MPFR_ASSERTD(bp[k]<cp[k]);
          goto CGreater;
        }
    }
  else if (MPFR_UNLIKELY(bx < cx))
    {
      /* Swap b and c and set sign */
      mpfr_srcptr t;
      mpfr_exp_t tx;
    CGreater:
      MPFR_SET_OPPOSITE_SIGN(a,b);
      t  = b;  b  = c;  c  = t;
      tx = bx; bx = cx; cx = tx;
    }
  else
    {
      /* b > c */
    BGreater:
      MPFR_SET_SAME_SIGN(a,b);
    }

  /* Now b > c */
  MPFR_ASSERTD(bx >= cx);
  d = (mpfr_uexp_t) bx - cx;
  DEBUG (printf ("New with diff=%lu\n", (unsigned long) d));

  if (MPFR_UNLIKELY(d <= 1))
    {
      if (MPFR_LIKELY(d < 1))
        {
          /* <-- b -->
             <-- c --> : exact sub */
          ap = MPFR_MANT(a);
          mpn_sub_n (ap, MPFR_MANT(b), MPFR_MANT(c), n);
          /* Normalize */
        ExactNormalize:
          limb = ap[n-1];
          if (MPFR_LIKELY(limb))
            {
              /* First limb is not zero. */
              count_leading_zeros(cnt, limb);
              /* cnt could be == 0 <= SubD1Lose */
              if (MPFR_LIKELY(cnt))
                {
                  mpn_lshift(ap, ap, n, cnt); /* Normalize number */
                  bx -= cnt; /* Update final expo */
                }
              /* Last limb should be ok */
              MPFR_ASSERTD(!(ap[0] & MPFR_LIMB_MASK((unsigned int) (-p)
                                                    % GMP_NUMB_BITS)));
            }
          else
            {
              /* First limb is zero */
              mp_size_t k = n-1, len;
              /* Find the first limb not equal to zero.
                 FIXME:It is assume it exists (since |b| > |c| and same prec)*/
              do
                {
                  MPFR_ASSERTD( k > 0 );
                  limb = ap[--k];
                }
              while (limb == 0);
              MPFR_ASSERTD(limb != 0);
              count_leading_zeros(cnt, limb);
              k++;
              len = n - k; /* Number of last limb */
              MPFR_ASSERTD(k >= 0);
              if (MPFR_LIKELY(cnt))
                mpn_lshift(ap+len, ap, k, cnt); /* Normalize the High Limb*/
              else
                {
                  /* Must use DECR since src and dest may overlap & dest>=src*/
                  MPN_COPY_DECR(ap+len, ap, k);
                }
              MPN_ZERO(ap, len); /* Zeroing the last limbs */
              bx -= cnt + len*GMP_NUMB_BITS; /* Update Expo */
              /* Last limb should be ok */
              MPFR_ASSERTD(!(ap[len]&MPFR_LIMB_MASK((unsigned int) (-p)
                                                    % GMP_NUMB_BITS)));
            }
          /* Check expo underflow */
          if (MPFR_UNLIKELY(bx < __gmpfr_emin))
            {
              MPFR_TMP_FREE(marker);
              /* inexact=0 */
              DEBUG( printf("(D==0 Underflow)\n") );
              if (rnd_mode == MPFR_RNDN &&
                  (bx < __gmpfr_emin - 1 ||
                   (/*inexact >= 0 &&*/ mpfr_powerof2_raw (a))))
                rnd_mode = MPFR_RNDZ;
              return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
            }
          MPFR_SET_EXP (a, bx);
          /* No rounding is necessary since the result is exact */
          MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
          MPFR_TMP_FREE(marker);
          return 0;
        }
      else /* if (d == 1) */
        {
          /* | <-- b -->
             |  <-- c --> */
          mp_limb_t c0, mask;
          mp_size_t k;
          MPFR_UNSIGNED_MINUS_MODULO(sh, p);
          /* If we lose at least one bit, compute 2*b-c (Exact)
           * else compute b-c/2 */
          bp = MPFR_MANT(b);
          cp = MPFR_MANT(c);
          k = n-1;
          limb = bp[k] - cp[k]/2;
          if (limb > MPFR_LIMB_HIGHBIT)
            {
              /* We can't lose precision: compute b-c/2 */
              /* Shift c in the allocated temporary block */
            SubD1NoLose:
              c0 = cp[0] & (MPFR_LIMB_ONE<<sh);
              cp = MPFR_TMP_LIMBS_ALLOC (n);
              mpn_rshift(cp, MPFR_MANT(c), n, 1);
              if (MPFR_LIKELY(c0 == 0))
                {
                  /* Result is exact: no need of rounding! */
                  ap = MPFR_MANT(a);
                  mpn_sub_n (ap, bp, cp, n);
                  MPFR_SET_EXP(a, bx); /* No expo overflow! */
                  /* No truncate or normalize is needed */
                  MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
                  /* No rounding is necessary since the result is exact */
                  MPFR_TMP_FREE(marker);
                  return 0;
                }
              ap = MPFR_MANT(a);
              mask = ~MPFR_LIMB_MASK(sh);
              cp[0] &= mask; /* Delete last bit of c */
              mpn_sub_n (ap, bp, cp, n);
              MPFR_SET_EXP(a, bx);                 /* No expo overflow! */
              MPFR_ASSERTD( !(ap[0] & ~mask) );    /* Check last bits */
              /* No normalize is needed */
              MPFR_ASSERTD(ap[n-1] > ~ap[n-1]);
              /* Rounding is necessary since c0 = 1*/
              /* Cp =-1 and C'p+1=0 */
              bcp = 1; bcp1 = 0;
              if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
                {
                  /* Even Rule apply: Check Ap-1 */
                  if (MPFR_LIKELY( (ap[0] & (MPFR_LIMB_ONE<<sh)) == 0) )
                    goto truncate;
                  else
                    goto sub_one_ulp;
                }
              MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
              if (rnd_mode == MPFR_RNDZ)
                goto sub_one_ulp;
              else
                goto truncate;
            }
          else if (MPFR_LIKELY(limb < MPFR_LIMB_HIGHBIT))
            {
              /* We lose at least one bit of prec */
              /* Calcul of 2*b-c (Exact) */
              /* Shift b in the allocated temporary block */
            SubD1Lose:
              bp = MPFR_TMP_LIMBS_ALLOC (n);
              mpn_lshift (bp, MPFR_MANT(b), n, 1);
              ap = MPFR_MANT(a);
              mpn_sub_n (ap, bp, cp, n);
              bx--;
              goto ExactNormalize;
            }
          else
            {
              /* Case: limb = 100000000000 */
              /* Check while b[k] == c'[k] (C' is C shifted by 1) */
              /* If b[k]<c'[k] => We lose at least one bit*/
              /* If b[k]>c'[k] => We don't lose any bit */
              /* If k==-1 => We don't lose any bit
                 AND the result is 100000000000 0000000000 00000000000 */
              mp_limb_t carry;
              do {
                carry = cp[k]&MPFR_LIMB_ONE;
                k--;
              } while (k>=0 &&
                       bp[k]==(carry=cp[k]/2+(carry<<(GMP_NUMB_BITS-1))));
              if (MPFR_UNLIKELY(k<0))
                {
                  /*If carry then (sh==0 and Virtual c'[-1] > Virtual b[-1]) */
                  if (MPFR_UNLIKELY(carry)) /* carry = cp[0]&MPFR_LIMB_ONE */
                    {
                      /* FIXME: Can be faster? */
                      MPFR_ASSERTD(sh == 0);
                      goto SubD1Lose;
                    }
                  /* Result is a power of 2 */
                  ap = MPFR_MANT (a);
                  MPN_ZERO (ap, n);
                  ap[n-1] = MPFR_LIMB_HIGHBIT;
                  MPFR_SET_EXP (a, bx); /* No expo overflow! */
                  /* No Normalize is needed*/
                  /* No Rounding is needed */
                  MPFR_TMP_FREE (marker);
                  return 0;
                }
              /* carry = cp[k]/2+(cp[k-1]&1)<<(GMP_NUMB_BITS-1) = c'[k]*/
              else if (bp[k] > carry)
                goto SubD1NoLose;
              else
                {
                  MPFR_ASSERTD(bp[k]<carry);
                  goto SubD1Lose;
                }
            }
        }
    }
  else if (MPFR_UNLIKELY(d >= p))
    {
      ap = MPFR_MANT(a);
      MPFR_UNSIGNED_MINUS_MODULO(sh, p);
      /* We can't set A before since we use cp for rounding... */
      /* Perform rounding: check if a=b or a=b-ulp(b) */
      if (MPFR_UNLIKELY(d == p))
        {
          /* cp == -1 and c'p+1 = ? */
          bcp  = 1;
          /* We need Cp+1 later for a very improbable case. */
          bbcp = (MPFR_MANT(c)[n-1] & (MPFR_LIMB_ONE<<(GMP_NUMB_BITS-2)));
          /* We need also C'p+1 for an even more unprobable case... */
          if (MPFR_LIKELY( bbcp ))
            bcp1 = 1;
          else
            {
              cp = MPFR_MANT(c);
              if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
                {
                  mp_size_t k = n-1;
                  do {
                    k--;
                  } while (k>=0 && cp[k]==0);
                  bcp1 = (k>=0);
                }
              else
                bcp1 = 1;
            }
          DEBUG( printf("(D=P) Cp=-1 Cp+1=%d C'p+1=%d \n", bbcp!=0, bcp1!=0) );
          bp = MPFR_MANT (b);

          /* Even if src and dest overlap, it is ok using MPN_COPY */
          if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
            {
              if (MPFR_UNLIKELY( bcp && bcp1==0 ))
                /* Cp=-1 and C'p+1=0: Even rule Apply! */
                /* Check Ap-1 = Bp-1 */
                if ((bp[0] & (MPFR_LIMB_ONE<<sh)) == 0)
                  {
                    MPN_COPY(ap, bp, n);
                    goto truncate;
                  }
              MPN_COPY(ap, bp, n);
              goto sub_one_ulp;
            }
          MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
          if (rnd_mode == MPFR_RNDZ)
            {
              MPN_COPY(ap, bp, n);
              goto sub_one_ulp;
            }
          else
            {
              MPN_COPY(ap, bp, n);
              goto truncate;
            }
        }
      else
        {
          /* Cp=0, Cp+1=-1 if d==p+1, C'p+1=-1 */
          bcp = 0; bbcp = (d==p+1); bcp1 = 1;
          DEBUG( printf("(D>P) Cp=%d Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0) );
          /* Need to compute C'p+2 if d==p+1 and if rnd_mode=NEAREST
             (Because of a very improbable case) */
          if (MPFR_UNLIKELY(d==p+1 && rnd_mode==MPFR_RNDN))
            {
              cp = MPFR_MANT(c);
              if (MPFR_UNLIKELY(cp[n-1] == MPFR_LIMB_HIGHBIT))
                {
                  mp_size_t k = n-1;
                  do {
                    k--;
                  } while (k>=0 && cp[k]==0);
                  bbcp1 = (k>=0);
                }
              else
                bbcp1 = 1;
              DEBUG( printf("(D>P) C'p+2=%d\n", bbcp1!=0) );
            }
          /* Copy mantissa B in A */
          MPN_COPY(ap, MPFR_MANT(b), n);
          /* Round */
          if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
            goto truncate;
          MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
          if (rnd_mode == MPFR_RNDZ)
            goto sub_one_ulp;
          else /* rnd_mode = AWAY */
            goto truncate;
        }
    }
  else
    {
      mpfr_uexp_t dm;
      mp_size_t m;
      mp_limb_t mask;

      /* General case: 2 <= d < p */
      MPFR_UNSIGNED_MINUS_MODULO(sh, p);
      cp = MPFR_TMP_LIMBS_ALLOC (n);

      /* Shift c in temporary allocated place */
      dm = d % GMP_NUMB_BITS;
      m = d / GMP_NUMB_BITS;
      if (MPFR_UNLIKELY(dm == 0))
        {
          /* dm = 0 and m > 0: Just copy */
          MPFR_ASSERTD(m!=0);
          MPN_COPY(cp, MPFR_MANT(c)+m, n-m);
          MPN_ZERO(cp+n-m, m);
        }
      else if (MPFR_LIKELY(m == 0))
        {
          /* dm >=2 and m == 0: just shift */
          MPFR_ASSERTD(dm >= 2);
          mpn_rshift(cp, MPFR_MANT(c), n, dm);
        }
      else
        {
          /* dm > 0 and m > 0: shift and zero  */
          mpn_rshift(cp, MPFR_MANT(c)+m, n-m, dm);
          MPN_ZERO(cp+n-m, m);
        }

      DEBUG( mpfr_print_mant_binary("Before", MPFR_MANT(c), p) );
      DEBUG( mpfr_print_mant_binary("B=    ", MPFR_MANT(b), p) );
      DEBUG( mpfr_print_mant_binary("After ", cp, p) );

      /* Compute bcp=Cp and bcp1=C'p+1 */
      if (MPFR_LIKELY(sh))
        {
          /* Try to compute them from C' rather than C (FIXME: Faster?) */
          bcp = (cp[0] & (MPFR_LIMB_ONE<<(sh-1))) ;
          if (MPFR_LIKELY( cp[0] & MPFR_LIMB_MASK(sh-1) ))
            bcp1 = 1;
          else
            {
              /* We can't compute C'p+1 from C'. Compute it from C */
              /* Start from bit x=p-d+sh in mantissa C
                 (+sh since we have already looked sh bits in C'!) */
              mpfr_prec_t x = p-d+sh-1;
              if (MPFR_LIKELY(x>p))
                /* We are already looked at all the bits of c, so C'p+1 = 0*/
                bcp1 = 0;
              else
                {
                  mp_limb_t *tp = MPFR_MANT(c);
                  mp_size_t kx = n-1 - (x / GMP_NUMB_BITS);
                  mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
                  DEBUG (printf ("(First) x=%lu Kx=%ld Sx=%lu\n",
                                 (unsigned long) x, (long) kx,
                                 (unsigned long) sx));
                  /* Looks at the last bits of limb kx (if sx=0 does nothing)*/
                  if (tp[kx] & MPFR_LIMB_MASK(sx))
                    bcp1 = 1;
                  else
                    {
                      /*kx += (sx==0);*/
                      /*If sx==0, tp[kx] hasn't been checked*/
                      do {
                        kx--;
                      } while (kx>=0 && tp[kx]==0);
                      bcp1 = (kx >= 0);
                    }
                }
            }
        }
      else
        {
          /* Compute Cp and C'p+1 from C with sh=0 */
          mp_limb_t *tp = MPFR_MANT(c);
          /* Start from bit x=p-d in mantissa C */
          mpfr_prec_t  x = p-d;
          mp_size_t   kx = n-1 - (x / GMP_NUMB_BITS);
          mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
          MPFR_ASSERTD(p >= d);
          bcp = (tp[kx] & (MPFR_LIMB_ONE<<sx));
          /* Looks at the last bits of limb kx (If sx=0, does nothing)*/
          if (tp[kx] & MPFR_LIMB_MASK(sx))
            bcp1 = 1;
          else
            {
              /*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
              do {
                kx--;
              } while (kx>=0 && tp[kx]==0);
              bcp1 = (kx>=0);
            }
        }
      DEBUG( printf("sh=%lu Cp=%d C'p+1=%d\n", sh, bcp!=0, bcp1!=0) );

      /* Check if we can lose a bit, and if so compute Cp+1 and C'p+2 */
      bp = MPFR_MANT(b);
      if (MPFR_UNLIKELY((bp[n-1]-cp[n-1]) <= MPFR_LIMB_HIGHBIT))
        {
          /* We can lose a bit so we precompute Cp+1 and C'p+2 */
          /* Test for trivial case: since C'p+1=0, Cp+1=0 and C'p+2 =0 */
          if (MPFR_LIKELY(bcp1 == 0))
            {
              bbcp = 0;
              bbcp1 = 0;
            }
          else /* bcp1 != 0 */
            {
              /* We can lose a bit:
                 compute Cp+1 and C'p+2 from mantissa C */
              mp_limb_t *tp = MPFR_MANT(c);
              /* Start from bit x=(p+1)-d in mantissa C */
              mpfr_prec_t x  = p+1-d;
              mp_size_t kx = n-1 - (x/GMP_NUMB_BITS);
              mpfr_prec_t sx = GMP_NUMB_BITS-1-(x%GMP_NUMB_BITS);
              MPFR_ASSERTD(p > d);
              DEBUG (printf ("(pre) x=%lu Kx=%ld Sx=%lu\n",
                             (unsigned long) x, (long) kx,
                             (unsigned long) sx));
              bbcp = (tp[kx] & (MPFR_LIMB_ONE<<sx)) ;
              /* Looks at the last bits of limb kx (If sx=0, does nothing)*/
              /* If Cp+1=0, since C'p+1!=0, C'p+2=1 ! */
              if (MPFR_LIKELY(bbcp==0 || (tp[kx]&MPFR_LIMB_MASK(sx))))
                bbcp1 = 1;
              else
                {
                  /*kx += (sx==0);*/ /*If sx==0, tp[kx] hasn't been checked*/
                  do {
                    kx--;
                  } while (kx>=0 && tp[kx]==0);
                  bbcp1 = (kx>=0);
                  DEBUG (printf ("(Pre) Scan done for %ld\n", (long) kx));
                }
            } /*End of Bcp1 != 0*/
          DEBUG( printf("(Pre) Cp+1=%d C'p+2=%d\n", bbcp!=0, bbcp1!=0) );
        } /* End of "can lose a bit" */

      /* Clean shifted C' */
      mask = ~MPFR_LIMB_MASK (sh);
      cp[0] &= mask;

      /* Subtract the mantissa c from b in a */
      ap = MPFR_MANT(a);
      mpn_sub_n (ap, bp, cp, n);
      DEBUG( mpfr_print_mant_binary("Sub=  ", ap, p) );

     /* Normalize: we lose at max one bit*/
      if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
        {
          /* High bit is not set and we have to fix it! */
          /* Ap >= 010000xxx001 */
          mpn_lshift(ap, ap, n, 1);
          /* Ap >= 100000xxx010 */
          if (MPFR_UNLIKELY(bcp!=0)) /* Check if Cp = -1 */
            /* Since Cp == -1, we have to substract one more */
            {
              mpn_sub_1(ap, ap, n, MPFR_LIMB_ONE<<sh);
              MPFR_ASSERTD(MPFR_LIMB_MSB(ap[n-1]) != 0);
            }
          /* Ap >= 10000xxx001 */
          /* Final exponent -1 since we have shifted the mantissa */
          bx--;
          /* Update bcp and bcp1 */
          MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
          MPFR_ASSERTN(bbcp1 != (mp_limb_t) -1);
          bcp  = bbcp;
          bcp1 = bbcp1;
          /* We dont't have anymore a valid Cp+1!
             But since Ap >= 100000xxx001, the final sub can't unnormalize!*/
        }
      MPFR_ASSERTD( !(ap[0] & ~mask) );

      /* Rounding */
      if (MPFR_LIKELY(rnd_mode == MPFR_RNDN))
        {
          if (MPFR_LIKELY(bcp==0))
            goto truncate;
          else if ((bcp1) || ((ap[0] & (MPFR_LIMB_ONE<<sh)) != 0))
            goto sub_one_ulp;
          else
            goto truncate;
        }

      /* Update rounding mode */
      MPFR_UPDATE_RND_MODE(rnd_mode, MPFR_IS_NEG(a));
      if (rnd_mode == MPFR_RNDZ && (MPFR_LIKELY(bcp || bcp1)))
        goto sub_one_ulp;
      goto truncate;
    }
  MPFR_RET_NEVER_GO_HERE ();

  /* Sub one ulp to the result */
 sub_one_ulp:
  mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
  /* Result should be smaller than exact value: inexact=-1 */
  inexact = -1;
  /* Check normalisation */
  if (MPFR_UNLIKELY(MPFR_LIMB_MSB(ap[n-1]) == 0))
    {
      /* ap was a power of 2, and we lose a bit */
      /* Now it is 0111111111111111111[00000 */
      mpn_lshift(ap, ap, n, 1);
      bx--;
      /* And the lost bit x depends on Cp+1, and Cp */
      /* Compute Cp+1 if it isn't already compute (ie d==1) */
      /* FIXME: Is this case possible? */
      if (MPFR_UNLIKELY(d == 1))
        bbcp = 0;
      DEBUG( printf("(SubOneUlp)Cp=%d, Cp+1=%d C'p+1=%d\n", bcp!=0,bbcp!=0,bcp1!=0));
      /* Compute the last bit (Since we have shifted the mantissa)
         we need one more bit!*/
      MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
      if ( (rnd_mode == MPFR_RNDZ && bcp==0)
           || (rnd_mode==MPFR_RNDN && bbcp==0)
           || (bcp && bcp1==0) ) /*Exact result*/
        {
          ap[0] |= MPFR_LIMB_ONE<<sh;
          if (rnd_mode == MPFR_RNDN)
            inexact = 1;
          DEBUG( printf("(SubOneUlp) Last bit set\n") );
        }
      /* Result could be exact if C'p+1 = 0 and rnd == Zero
         since we have had one more bit to the result */
      /* Fixme: rnd_mode == MPFR_RNDZ needed ? */
      if (bcp1==0 && rnd_mode==MPFR_RNDZ)
        {
          DEBUG( printf("(SubOneUlp) Exact result\n") );
          inexact = 0;
        }
    }

  goto end_of_sub;

 truncate:
  /* Check if the result is an exact power of 2: 100000000000
     in which cases, we could have to do sub_one_ulp due to some nasty reasons:
     If Result is a Power of 2:
      + If rnd = AWAY,
      |  If Cp=-1 and C'p+1 = 0, SubOneUlp and the result is EXACT.
         If Cp=-1 and C'p+1 =-1, SubOneUlp and the result is above.
         Otherwise truncate
      + If rnd = NEAREST,
         If Cp= 0 and Cp+1  =-1 and C'p+2=-1, SubOneUlp and the result is above
         If cp=-1 and C'p+1 = 0, SubOneUlp and the result is exact.
         Otherwise truncate.
      X bit should always be set if SubOneUlp*/
  if (MPFR_UNLIKELY(ap[n-1] == MPFR_LIMB_HIGHBIT))
    {
      mp_size_t k = n-1;
      do {
        k--;
      } while (k>=0 && ap[k]==0);
      if (MPFR_UNLIKELY(k<0))
        {
          /* It is a power of 2! */
          /* Compute Cp+1 if it isn't already compute (ie d==1) */
          /* FIXME: Is this case possible? */
          if (d == 1)
            bbcp=0;
          DEBUG( printf("(Truncate) Cp=%d, Cp+1=%d C'p+1=%d C'p+2=%d\n", \
                 bcp!=0, bbcp!=0, bcp1!=0, bbcp1!=0) );
          MPFR_ASSERTN(bbcp != (mp_limb_t) -1);
          MPFR_ASSERTN((rnd_mode != MPFR_RNDN) || (bcp != 0) || (bbcp == 0) || (bbcp1 != (mp_limb_t) -1));
          if (((rnd_mode != MPFR_RNDZ) && bcp)
              ||
              ((rnd_mode == MPFR_RNDN) && (bcp == 0) && (bbcp) && (bbcp1)))
            {
              DEBUG( printf("(Truncate) Do sub\n") );
              mpn_sub_1 (ap, ap, n, MPFR_LIMB_ONE << sh);
              mpn_lshift(ap, ap, n, 1);
              ap[0] |= MPFR_LIMB_ONE<<sh;
              bx--;
              /* FIXME: Explain why it works (or why not)... */
              inexact = (bcp1 == 0) ? 0 : (rnd_mode==MPFR_RNDN) ? -1 : 1;
              goto end_of_sub;
            }
        }
    }

  /* Calcul of Inexact flag.*/
  inexact = MPFR_LIKELY(bcp || bcp1) ? 1 : 0;

 end_of_sub:
  /* Update Expo */
  /* FIXME: Is this test really useful?
      If d==0      : Exact case. This is never called.
      if 1 < d < p : bx=MPFR_EXP(b) or MPFR_EXP(b)-1 > MPFR_EXP(c) > emin
      if d == 1    : bx=MPFR_EXP(b). If we could lose any bits, the exact
                     normalisation is called.
      if d >=  p   : bx=MPFR_EXP(b) >= MPFR_EXP(c) + p > emin
     After SubOneUlp, we could have one bit less.
      if 1 < d < p : bx >= MPFR_EXP(b)-2 >= MPFR_EXP(c) > emin
      if d == 1    : bx >= MPFR_EXP(b)-1 = MPFR_EXP(c) > emin.
      if d >=  p   : bx >= MPFR_EXP(b)-1 > emin since p>=2.
  */
  MPFR_ASSERTD( bx >= __gmpfr_emin);
  /*
    if (MPFR_UNLIKELY(bx < __gmpfr_emin))
    {
      DEBUG( printf("(Final Underflow)\n") );
      if (rnd_mode == MPFR_RNDN &&
          (bx < __gmpfr_emin - 1 ||
           (inexact >= 0 && mpfr_powerof2_raw (a))))
        rnd_mode = MPFR_RNDZ;
      MPFR_TMP_FREE(marker);
      return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
    }
  */
  MPFR_SET_EXP (a, bx);

  MPFR_TMP_FREE(marker);
  MPFR_RET (inexact * MPFR_INT_SIGN (a));
}
示例#6
0
int
mpfr_set_uj_2exp (mpfr_t x, uintmax_t j, intmax_t e, mp_rnd_t rnd)
{
  unsigned int cnt, i;
  mp_size_t k, len;
  mp_limb_t limb;
  mp_limb_t yp[sizeof(uintmax_t) / sizeof(mp_limb_t)];
  mpfr_t y;
  unsigned long uintmax_bit_size = sizeof(uintmax_t) * CHAR_BIT;
  unsigned long bpml = BITS_PER_MP_LIMB % uintmax_bit_size;

  /* Special case */
  if (j == 0)
    {
      MPFR_SET_POS(x);
      MPFR_SET_ZERO(x);
      MPFR_RET(0);
    }

  MPFR_ASSERTN (sizeof(uintmax_t) % sizeof(mp_limb_t) == 0);

  /* Create an auxillary var */
  MPFR_TMP_INIT1 (yp, y, uintmax_bit_size);
  k = numberof (yp);
  if (k == 1)
    limb = yp[0] = j;
  else
    {
      /* Note: either BITS_PER_MP_LIMB = uintmax_bit_size, then k = 1 the
         shift j >>= bpml is never done, or BITS_PER_MP_LIMB < uintmax_bit_size
         and bpml = BITS_PER_MP_LIMB. */
      for (i = 0; i < k; i++, j >>= bpml)
        yp[i] = j; /* Only the low bits are copied */

      /* Find the first limb not equal to zero. */
      do
        {
          MPFR_ASSERTD (k > 0);
          limb = yp[--k];
        }
      while (limb == 0);
      k++;
    }
  count_leading_zeros(cnt, limb);
  len = numberof (yp) - k;

  /* Normalize it: len = number of last 0 limb, k number of non-zero limbs */
  if (MPFR_LIKELY(cnt))
    mpn_lshift (yp+len, yp, k, cnt);  /* Normalize the High Limb*/
  else if (len != 0)
    MPN_COPY_DECR (yp+len, yp, k);    /* Must use DECR */
  if (len != 0)
    /* Note: when numberof(yp)==1, len is constant and null, so the compiler
       can optimize out this code. */
    {
      if (len == 1)
        yp[0] = (mp_limb_t) 0;
      else
        MPN_ZERO (yp, len);   /* Zeroing the last limbs */
    }
  e += k * BITS_PER_MP_LIMB - cnt;    /* Update Expo */
  MPFR_ASSERTD (MPFR_LIMB_MSB(yp[numberof (yp) - 1]) != 0);

  /* Check expo underflow / overflow (can't use mpfr_check_range) */
  if (MPFR_UNLIKELY(e < __gmpfr_emin))
    {
      /* The following test is necessary because in the rounding to the
       * nearest mode, mpfr_underflow always rounds away from 0. In
       * this rounding mode, we need to round to 0 if:
       *   _ |x| < 2^(emin-2), or
       *   _ |x| = 2^(emin-2) and the absolute value of the exact
       *     result is <= 2^(emin-2). */
      if (rnd == GMP_RNDN && (e+1 < __gmpfr_emin || mpfr_powerof2_raw(y)))
        rnd = GMP_RNDZ;
      return mpfr_underflow (x, rnd, MPFR_SIGN_POS);
    }
  if (MPFR_UNLIKELY(e > __gmpfr_emax))
    return mpfr_overflow (x, rnd, MPFR_SIGN_POS);
  MPFR_SET_EXP (y, e);

  /* Final: set x to y (rounding if necessary) */
  return mpfr_set (x, y, rnd);
}
示例#7
0
int
mpfr_round_raw_generic(
#if flag == 0
                       mp_limb_t *yp,
#endif
                       const mp_limb_t *xp, mpfr_prec_t xprec,
                       int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode
#if use_inexp != 0
                       , int *inexp
#endif
                       )
{
  mp_size_t xsize, nw;
  mp_limb_t himask, lomask, sb;
  int rw;
#if flag == 0
  int carry;
#endif
#if use_inexp == 0
  int *inexp;
#endif

  if (use_inexp)
    MPFR_ASSERTD(inexp != ((int*) 0));
  MPFR_ASSERTD(neg == 0 || neg == 1);

  if (flag && !use_inexp &&
      (xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg)))
    return 0;

  xsize = MPFR_PREC2LIMBS (xprec);
  nw = yprec / GMP_NUMB_BITS;
  rw = yprec & (GMP_NUMB_BITS - 1);

  if (MPFR_UNLIKELY(xprec <= yprec))
    { /* No rounding is necessary. */
      /* if yp=xp, maybe an overlap: MPN_COPY_DECR is OK when src <= dst */
      if (MPFR_LIKELY(rw))
        nw++;
      MPFR_ASSERTD(nw >= 1);
      MPFR_ASSERTD(nw >= xsize);
      if (use_inexp)
        *inexp = 0;
#if flag == 0
      MPN_COPY_DECR(yp + (nw - xsize), xp, xsize);
      MPN_ZERO(yp, nw - xsize);
#endif
      return 0;
    }

  if (use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
    {
      mp_size_t k = xsize - nw - 1;

      if (MPFR_LIKELY(rw))
        {
          nw++;
          lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
          himask = ~lomask;
        }
      else
        {
          lomask = MPFR_LIMB_MAX;
          himask = MPFR_LIMB_MAX;
        }
      MPFR_ASSERTD(k >= 0);
      sb = xp[k] & lomask;  /* First non-significant bits */
      /* Rounding to nearest? */
      if (MPFR_LIKELY (rnd_mode == MPFR_RNDN || rnd_mode == MPFR_RNDNA))
        {
          /* Rounding to nearest */
          mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw);

          if ((sb & rbmask) == 0) /* rounding bit = 0 ? */
            goto rnd_RNDZ; /* yes, behave like rounding toward zero */
          /* Rounding to nearest with rounding bit = 1 */
          if (MPFR_UNLIKELY (rnd_mode == MPFR_RNDNA))
            /* FIXME: *inexp is not set. First, add a testcase that
               triggers the bug (at least with a sanitizer). */
            goto rnd_RNDN_add_one_ulp; /* like rounding away from zero */
          sb &= ~rbmask; /* first bits after the rounding bit */
          while (MPFR_UNLIKELY(sb == 0) && k > 0)
            sb = xp[--k];
          if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */
            {
              /* sb == 0 && rnd_mode == MPFR_RNDN */
              sb = xp[xsize - nw] & (himask ^ (himask << 1));
              if (sb == 0)
                {
                  if (use_inexp)
                    *inexp = 2*MPFR_EVEN_INEX*neg-MPFR_EVEN_INEX;
                  /* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX */
                  /* since neg = 0 or 1 and sb = 0 */
#if flag == 0
                  MPN_COPY_INCR(yp, xp + xsize - nw, nw);
                  yp[0] &= himask;
#endif
                  return 0; /* sb != 0 && rnd_mode != MPFR_RNDZ */
                }
              else
                {
                  /* sb != 0 && rnd_mode == MPFR_RNDN */
                  if (use_inexp)
                    *inexp = MPFR_EVEN_INEX-2*MPFR_EVEN_INEX*neg;
                  /* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX : -MPFR_EVEN_INEX */
                  /* since neg = 0 or 1 and sb != 0 */
                  goto rnd_RNDN_add_one_ulp;
                }
            }
          else /* sb != 0 && rnd_mode == MPFR_RNDN */
            {
              if (use_inexp)
                *inexp = 1-2*neg; /* neg == 0 ? 1 : -1 */
            rnd_RNDN_add_one_ulp:
#if flag == 1
              return 1; /* sb != 0 && rnd_mode != MPFR_RNDZ */
#else
              carry = mpn_add_1 (yp, xp + xsize - nw, nw,
                                 rw ?
                                 MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
                                 : MPFR_LIMB_ONE);
              yp[0] &= himask;
              return carry;
#endif
            }
        }
      /* Rounding toward zero? */
      else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
        {
          /* rnd_mode == MPFR_RNDZ */
        rnd_RNDZ:
          while (MPFR_UNLIKELY(sb == 0) && k > 0)
            sb = xp[--k];
          if (use_inexp)
            /* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */
            /* ((neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1 */
            *inexp = MPFR_UNLIKELY(sb == 0) ? 0 : (2*neg-1);
#if flag == 0
          MPN_COPY_INCR(yp, xp + xsize - nw, nw);
          yp[0] &= himask;
#endif
          return 0; /* sb != 0 && rnd_mode != MPFR_RNDZ */
        }
      else
        {
          /* Rounding away from zero */
          while (MPFR_UNLIKELY(sb == 0) && k > 0)
            sb = xp[--k];
          if (MPFR_UNLIKELY(sb == 0))
            {
              /* sb = 0 && rnd_mode != MPFR_RNDZ */
              if (use_inexp)
                /* ((neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1 */
                *inexp = 0;
#if flag == 0
              MPN_COPY_INCR(yp, xp + xsize - nw, nw);
              yp[0] &= himask;
#endif
              return 0;
            }
          else
            {
              /* sb != 0 && rnd_mode != MPFR_RNDZ */
              if (use_inexp)
                *inexp = 1-2*neg; /* neg == 0 ? 1 : -1 */
#if flag == 1
              return 1;
#else
              carry = mpn_add_1(yp, xp + xsize - nw, nw,
                                rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
                                : 1);
              yp[0] &= himask;
              return carry;
#endif
            }
        }
    }
  else
    {
      /* Rounding toward zero / no inexact flag */
#if flag == 0
      if (MPFR_LIKELY(rw))
        {
          nw++;
          himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
        }
      else
        himask = MPFR_LIMB_MAX;
      MPN_COPY_INCR(yp, xp + xsize - nw, nw);
      yp[0] &= himask;
#endif
      return 0;
    }
}
示例#8
0
mp_limb_t
mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs,
	    mp_ptr np, mp_size_t nsize,
	    mp_srcptr dp, mp_size_t dsize)
{
  mp_limb_t most_significant_q_limb = 0;

  switch (dsize)
    {
    case 0:
      /* We are asked to divide by zero, so go ahead and do it!  (To make
	 the compiler not remove this statement, return the value.)  */
      return 1 / dsize;

    case 1:
      {
	mp_size_t i;
	mp_limb_t n1;
	mp_limb_t d;

	d = dp[0];
	n1 = np[nsize - 1];

	if (n1 >= d)
	  {
	    n1 -= d;
	    most_significant_q_limb = 1;
	  }

	qp += qextra_limbs;
	for (i = nsize - 2; i >= 0; i--)
	  udiv_qrnnd (qp[i], n1, n1, np[i], d);
	qp -= qextra_limbs;

	for (i = qextra_limbs - 1; i >= 0; i--)
	  udiv_qrnnd (qp[i], n1, n1, 0, d);

	np[0] = n1;
      }
      break;

    case 2:
      {
	mp_size_t i;
	mp_limb_t n1, n0, n2;
	mp_limb_t d1, d0;

	np += nsize - 2;
	d1 = dp[1];
	d0 = dp[0];
	n1 = np[1];
	n0 = np[0];

	if (n1 >= d1 && (n1 > d1 || n0 >= d0))
	  {
	    sub_ddmmss (n1, n0, n1, n0, d1, d0);
	    most_significant_q_limb = 1;
	  }

	for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--)
	  {
	    mp_limb_t q;
	    mp_limb_t r;

	    if (i >= qextra_limbs)
	      np--;
	    else
	      np[0] = 0;

	    if (n1 == d1)
	      {
		/* Q should be either 111..111 or 111..110.  Need special
		   treatment of this rare case as normal division would
		   give overflow.  */
		q = ~(mp_limb_t) 0;

		r = n0 + d1;
		if (r < d1)	/* Carry in the addition? */
		  {
		    add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
		    qp[i] = q;
		    continue;
		  }
		n1 = d0 - (d0 != 0);
		n0 = -d0;
	      }
	    else
	      {
		udiv_qrnnd (q, r, n1, n0, d1);
		umul_ppmm (n1, n0, d0, q);
	      }

	    n2 = np[0];
	  q_test:
	    if (n1 > r || (n1 == r && n0 > n2))
	      {
		/* The estimated Q was too large.  */
		q--;

		sub_ddmmss (n1, n0, n1, n0, 0, d0);
		r += d1;
		if (r >= d1)	/* If not carry, test Q again.  */
		  goto q_test;
	      }

	    qp[i] = q;
	    sub_ddmmss (n1, n0, r, n2, n1, n0);
	  }
	np[1] = n1;
	np[0] = n0;
      }
      break;

    default:
      {
	mp_size_t i;
	mp_limb_t dX, d1, n0;

	np += nsize - dsize;
	dX = dp[dsize - 1];
	d1 = dp[dsize - 2];
	n0 = np[dsize - 1];

	if (n0 >= dX)
	  {
	    if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0)
	      {
		mpn_sub_n (np, np, dp, dsize);
		n0 = np[dsize - 1];
		most_significant_q_limb = 1;
	      }
	  }

	for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--)
	  {
	    mp_limb_t q;
	    mp_limb_t n1, n2;
	    mp_limb_t cy_limb;

	    if (i >= qextra_limbs)
	      {
		np--;
		n2 = np[dsize];
	      }
	    else
	      {
		n2 = np[dsize - 1];
		MPN_COPY_DECR (np + 1, np, dsize);
		np[0] = 0;
	      }

	    if (n0 == dX)
	      /* This might over-estimate q, but it's probably not worth
		 the extra code here to find out.  */
	      q = ~(mp_limb_t) 0;
	    else
	      {
		mp_limb_t r;

		udiv_qrnnd (q, r, n0, np[dsize - 1], dX);
		umul_ppmm (n1, n0, d1, q);

		while (n1 > r || (n1 == r && n0 > np[dsize - 2]))
		  {
		    q--;
		    r += dX;
		    if (r < dX)	/* I.e. "carry in previous addition?"  */
		      break;
		    n1 -= n0 < d1;
		    n0 -= d1;
		  }
	      }

	    /* Possible optimization: We already have (q * n0) and (1 * n1)
	       after the calculation of q.  Taking advantage of that, we
	       could make this loop make two iterations less.  */

	    cy_limb = mpn_submul_1 (np, dp, dsize, q);

	    if (n2 != cy_limb)
	      {
		mpn_add_n (np, np, dp, dsize);
		q--;
	      }

	    qp[i] = q;
	    n0 = np[dsize - 1];
	  }
      }
    }

  return most_significant_q_limb;
}
示例#9
0
void mpn_copyd(mp_ptr rp,mp_srcptr sp,mp_size_t n)
{
    MPN_COPY_DECR(rp,sp,n);
    return;
}
示例#10
0
文件: frac.c 项目: mmanley/Antares
int
mpfr_frac (mpfr_ptr r, mpfr_srcptr u, mp_rnd_t rnd_mode)
{
  mp_exp_t re, ue;
  mp_prec_t uq, fq;
  mp_size_t un, tn, t0;
  mp_limb_t *up, *tp, k;
  int sh;
  mpfr_t tmp;
  mpfr_ptr t;

  /* 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_CLEAR_FLAGS(r);
      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);

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

  up = MPFR_MANT(u);
  sh = ue % BITS_PER_MP_LIMB;
  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 < BITS_PER_MP_LIMB);
      k <<= cnt;
    }
  else
    {
      re = sh - BITS_PER_MP_LIMB;
      /* searching for the first bit 1 (exists since u isn't an integer) */
      while (up[--un] == 0)
        re -= BITS_PER_MP_LIMB;
      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 */

  ue -= re;  /* number of bits of u to discard */
  fq = uq - ue;  /* number of bits of the fractional part of u */

  /* Temporary fix */
  t = /* fq > MPFR_PREC(r) */
    (mp_size_t) (MPFR_PREC(r) - 1) / BITS_PER_MP_LIMB < un ?
    (mpfr_init2 (tmp, (un + 1) * BITS_PER_MP_LIMB), 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_CLEAR_FLAGS(t);
  MPFR_SET_SAME_SIGN(t, u);
  MPFR_SET_EXP (t, re);

  /* Put the fractional part of u into t */
  tn = (MPFR_PREC(t) - 1) / BITS_PER_MP_LIMB;
  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);

  if (t != r)
    { /* t is tmp */
      int inex;

      inex = mpfr_set (r, t, rnd_mode);
      mpfr_clear (t);
      return inex;
    }
  else
    MPFR_RET(0);
}
示例#11
0
int
mpfr_round_raw_generic(
#if flag == 0
                       mp_limb_t *yp,
#endif
                       const mp_limb_t *xp, mpfr_prec_t xprec,
                       int neg, mpfr_prec_t yprec, mpfr_rnd_t rnd_mode
#if use_inexp != 0
                       , int *inexp
#endif
                       )
{
  mp_size_t xsize, nw;
  mp_limb_t himask, lomask, sb;
  int rw;
#if flag == 0
  int carry;
#endif
#if use_inexp == 0
  int *inexp;
#endif

  if (use_inexp)
    MPFR_ASSERTD(inexp != ((int*) 0));
  MPFR_ASSERTD(neg == 0 || neg == 1);

  if (flag && !use_inexp &&
      (xprec <= yprec || MPFR_IS_LIKE_RNDZ (rnd_mode, neg)))
    return 0;

  xsize = (xprec-1)/GMP_NUMB_BITS + 1;
  nw = yprec / GMP_NUMB_BITS;
  rw = yprec & (GMP_NUMB_BITS - 1);

  if (MPFR_UNLIKELY(xprec <= yprec))
    { /* No rounding is necessary. */
      /* if yp=xp, maybe an overlap: MPN_COPY_DECR is ok when src <= dst */
      if (MPFR_LIKELY(rw))
        nw++;
      MPFR_ASSERTD(nw >= 1);
      MPFR_ASSERTD(nw >= xsize);
      if (use_inexp)
        *inexp = 0;
#if flag == 0
      MPN_COPY_DECR(yp + (nw - xsize), xp, xsize);
      MPN_ZERO(yp, nw - xsize);
#endif
      return 0;
    }

  if (use_inexp || !MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
    {
      mp_size_t k = xsize - nw - 1;

      if (MPFR_LIKELY(rw))
        {
          nw++;
          lomask = MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
          himask = ~lomask;
        }
      else
        {
          lomask = ~(mp_limb_t) 0;
          himask = ~(mp_limb_t) 0;
        }
      MPFR_ASSERTD(k >= 0);
      sb = xp[k] & lomask;  /* First non-significant bits */
      /* Rounding to nearest ? */
      if (MPFR_LIKELY( rnd_mode == MPFR_RNDN) )
        {
          /* Rounding to nearest */
          mp_limb_t rbmask = MPFR_LIMB_ONE << (GMP_NUMB_BITS - 1 - rw);
          if (sb & rbmask) /* rounding bit */
            sb &= ~rbmask; /* it is 1, clear it */
          else
            {
              /* Rounding bit is 0, behave like rounding to 0 */
              goto rnd_RNDZ;
            }
          while (MPFR_UNLIKELY(sb == 0) && k > 0)
            sb = xp[--k];
          /* rounding to nearest, with rounding bit = 1 */
          if (MPFR_UNLIKELY(sb == 0)) /* Even rounding. */
            {
              /* sb == 0 && rnd_mode == MPFR_RNDN */
              sb = xp[xsize - nw] & (himask ^ (himask << 1));
              if (sb == 0)
                {
                  if (use_inexp)
                    *inexp = 2*MPFR_EVEN_INEX*neg-MPFR_EVEN_INEX;
                  /* ((neg!=0)^(sb!=0)) ? MPFR_EVEN_INEX  : -MPFR_EVEN_INEX;*/
                  /* Since neg = 0 or 1 and sb=0*/
#if flag == 1
                  return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ */;
#else
                  MPN_COPY_INCR(yp, xp + xsize - nw, nw);
                  yp[0] &= himask;
                  return 0;
#endif
                }
              else
                {
                  /* sb != 0 && rnd_mode == MPFR_RNDN */
                  if (use_inexp)
                    *inexp = MPFR_EVEN_INEX-2*MPFR_EVEN_INEX*neg;
                  /*((neg!=0)^(sb!=0))? MPFR_EVEN_INEX  : -MPFR_EVEN_INEX; */
                  /*Since neg= 0 or 1 and sb != 0 */
                  goto rnd_RNDN_add_one_ulp;
                }
            }
          else /* sb != 0  && rnd_mode == MPFR_RNDN*/
            {
              if (use_inexp)
                /* *inexp = (neg == 0) ? 1 : -1; but since neg = 0 or 1 */
                *inexp = 1-2*neg;
            rnd_RNDN_add_one_ulp:
#if flag == 1
              return 1; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/
#else
              carry = mpn_add_1 (yp, xp + xsize - nw, nw,
                                 rw ?
                                 MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
                                 : MPFR_LIMB_ONE);
              yp[0] &= himask;
              return carry;
#endif
            }
        }
      /* Rounding to Zero ? */
      else if (MPFR_IS_LIKE_RNDZ(rnd_mode, neg))
        {
          /* rnd_mode == MPFR_RNDZ */
        rnd_RNDZ:
          while (MPFR_UNLIKELY(sb == 0) && k > 0)
            sb = xp[--k];
          if (use_inexp)
            /* rnd_mode == MPFR_RNDZ and neg = 0 or 1 */
            /* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
            *inexp = MPFR_UNLIKELY(sb == 0) ? 0 : (2*neg-1);
#if flag == 1
          return 0; /*sb != 0 && rnd_mode != MPFR_RNDZ;*/
#else
          MPN_COPY_INCR(yp, xp + xsize - nw, nw);
          yp[0] &= himask;
          return 0;
#endif
        }
      else
        {
          /* rnd_mode = Away */
          while (MPFR_UNLIKELY(sb == 0) && k > 0)
            sb = xp[--k];
          if (MPFR_UNLIKELY(sb == 0))
            {
              /* sb = 0 && rnd_mode != MPFR_RNDZ */
              if (use_inexp)
                /* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
                *inexp = 0;
#if flag == 1
              return 0;
#else
              MPN_COPY_INCR(yp, xp + xsize - nw, nw);
              yp[0] &= himask;
              return 0;
#endif
            }
          else
            {
              /* sb != 0 && rnd_mode != MPFR_RNDZ */
              if (use_inexp)
                /* (neg != 0) ^ (rnd_mode != MPFR_RNDZ)) ? 1 : -1);*/
                *inexp = 1-2*neg;
#if flag == 1
              return 1;
#else
              carry = mpn_add_1(yp, xp + xsize - nw, nw,
                                rw ? MPFR_LIMB_ONE << (GMP_NUMB_BITS - rw)
                                : 1);
              yp[0] &= himask;
              return carry;
#endif
            }
        }
    }
  else
    {
      /* Roundind mode = Zero / No inexact flag */
#if flag == 1
      return 0 /*sb != 0 && rnd_mode != MPFR_RNDZ*/;
#else
      if (MPFR_LIKELY(rw))
        {
          nw++;
          himask = ~MPFR_LIMB_MASK (GMP_NUMB_BITS - rw);
        }
      else
        himask = ~(mp_limb_t) 0;
      MPN_COPY_INCR(yp, xp + xsize - nw, nw);
      yp[0] &= himask;
      return 0;
#endif
    }
}
示例#12
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);
}