rephrase text

[official-gcc.git] / gcc / double-int.c

/* Operations with long integers.
   Copyright (C) 2006, 2007, 2009, 2010 Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3, or (at your option) any
later version.

GCC is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3.  If not see
<http://www.gnu.org/licenses/>.  */

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "tree.h"

/* We know that A1 + B1 = SUM1, using 2's complement arithmetic and ignoring
   overflow.  Suppose A, B and SUM have the same respective signs as A1, B1,
   and SUM1.  Then this yields nonzero if overflow occurred during the
   addition.

   Overflow occurs if A and B have the same sign, but A and SUM differ in
   sign.  Use `^' to test whether signs differ, and `< 0' to isolate the
   sign.  */
#define OVERFLOW_SUM_SIGN(a, b, sum) ((~((a) ^ (b)) & ((a) ^ (sum))) < 0)

/* To do constant folding on INTEGER_CST nodes requires two-word arithmetic.
   We do that by representing the two-word integer in 4 words, with only
   HOST_BITS_PER_WIDE_INT / 2 bits stored in each word, as a positive
   number.  The value of the word is LOWPART + HIGHPART * BASE.  */

#define LOWPART(x) \
  ((x) & (((unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT / 2)) - 1))
#define HIGHPART(x) \
  ((unsigned HOST_WIDE_INT) (x) >> HOST_BITS_PER_WIDE_INT / 2)
#define BASE ((unsigned HOST_WIDE_INT) 1 << HOST_BITS_PER_WIDE_INT / 2)

/* Unpack a two-word integer into 4 words.
   LOW and HI are the integer, as two `HOST_WIDE_INT' pieces.
   WORDS points to the array of HOST_WIDE_INTs.  */

static void
encode (HOST_WIDE_INT *words, unsigned HOST_WIDE_INT low, HOST_WIDE_INT hi)
{
  words[0] = LOWPART (low);
  words[1] = HIGHPART (low);
  words[2] = LOWPART (hi);
  words[3] = HIGHPART (hi);
}

/* Pack an array of 4 words into a two-word integer.
   WORDS points to the array of words.
   The integer is stored into *LOW and *HI as two `HOST_WIDE_INT' pieces.  */

static void
decode (HOST_WIDE_INT *words, unsigned HOST_WIDE_INT *low,
        HOST_WIDE_INT *hi)
{
  *low = words[0] + words[1] * BASE;
  *hi = words[2] + words[3] * BASE;
}

/* Force the double-word integer L1, H1 to be within the range of the
   integer type TYPE.  Stores the properly truncated and sign-extended
   double-word integer in *LV, *HV.  Returns true if the operation
   overflows, that is, argument and result are different.  */

int
fit_double_type (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
                 unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv, const_tree type)
{
  unsigned HOST_WIDE_INT low0 = l1;
  HOST_WIDE_INT high0 = h1;
  unsigned int prec = TYPE_PRECISION (type);
  int sign_extended_type;

  /* Size types *are* sign extended.  */
  sign_extended_type = (!TYPE_UNSIGNED (type)
                        || (TREE_CODE (type) == INTEGER_TYPE
                            && TYPE_IS_SIZETYPE (type)));

  /* First clear all bits that are beyond the type's precision.  */
  if (prec >= 2 * HOST_BITS_PER_WIDE_INT)
    ;
  else if (prec > HOST_BITS_PER_WIDE_INT)
    h1 &= ~((HOST_WIDE_INT) (-1) << (prec - HOST_BITS_PER_WIDE_INT));
  else
    {
      h1 = 0;
      if (prec < HOST_BITS_PER_WIDE_INT)
        l1 &= ~((HOST_WIDE_INT) (-1) << prec);
    }

  /* Then do sign extension if necessary.  */
  if (!sign_extended_type)
    /* No sign extension */;
  else if (prec >= 2 * HOST_BITS_PER_WIDE_INT)
    /* Correct width already.  */;
  else if (prec > HOST_BITS_PER_WIDE_INT)
    {
      /* Sign extend top half? */
      if (h1 & ((unsigned HOST_WIDE_INT)1
                << (prec - HOST_BITS_PER_WIDE_INT - 1)))
        h1 |= (HOST_WIDE_INT) (-1) << (prec - HOST_BITS_PER_WIDE_INT);
    }
  else if (prec == HOST_BITS_PER_WIDE_INT)
    {
      if ((HOST_WIDE_INT)l1 < 0)
        h1 = -1;
    }
  else
    {
      /* Sign extend bottom half? */
      if (l1 & ((unsigned HOST_WIDE_INT)1 << (prec - 1)))
        {
          h1 = -1;
          l1 |= (HOST_WIDE_INT)(-1) << prec;
        }
    }

  *lv = l1;
  *hv = h1;

  /* If the value didn't fit, signal overflow.  */
  return l1 != low0 || h1 != high0;
}

/* We force the double-int HIGH:LOW to the range of the type TYPE by
   sign or zero extending it.
   OVERFLOWABLE indicates if we are interested
   in overflow of the value, when >0 we are only interested in signed
   overflow, for <0 we are interested in any overflow.  OVERFLOWED
   indicates whether overflow has already occurred.  CONST_OVERFLOWED
   indicates whether constant overflow has already occurred.  We force
   T's value to be within range of T's type (by setting to 0 or 1 all
   the bits outside the type's range).  We set TREE_OVERFLOWED if,
        OVERFLOWED is nonzero,
        or OVERFLOWABLE is >0 and signed overflow occurs
        or OVERFLOWABLE is <0 and any overflow occurs
   We return a new tree node for the extended double-int.  The node
   is shared if no overflow flags are set.  */

tree
force_fit_type_double (tree type, unsigned HOST_WIDE_INT low,
                       HOST_WIDE_INT high, int overflowable,
                       bool overflowed)
{
  int sign_extended_type;
  bool overflow;

  /* Size types *are* sign extended.  */
  sign_extended_type = (!TYPE_UNSIGNED (type)
                        || (TREE_CODE (type) == INTEGER_TYPE
                            && TYPE_IS_SIZETYPE (type)));

  overflow = fit_double_type (low, high, &low, &high, type);

  /* If we need to set overflow flags, return a new unshared node.  */
  if (overflowed || overflow)
    {
      if (overflowed
          || overflowable < 0
          || (overflowable > 0 && sign_extended_type))
        {
          tree t = make_node (INTEGER_CST);
          TREE_INT_CST_LOW (t) = low;
          TREE_INT_CST_HIGH (t) = high;
          TREE_TYPE (t) = type;
          TREE_OVERFLOW (t) = 1;
          return t;
        }
    }

  /* Else build a shared node.  */
  return build_int_cst_wide (type, low, high);
}

/* Add two doubleword integers with doubleword result.
   Return nonzero if the operation overflows according to UNSIGNED_P.
   Each argument is given as two `HOST_WIDE_INT' pieces.
   One argument is L1 and H1; the other, L2 and H2.
   The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

int
add_double_with_sign (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
                      unsigned HOST_WIDE_INT l2, HOST_WIDE_INT h2,
                      unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv,
                      bool unsigned_p)
{
  unsigned HOST_WIDE_INT l;
  HOST_WIDE_INT h;

  l = l1 + l2;
  h = (HOST_WIDE_INT) ((unsigned HOST_WIDE_INT) h1
                       + (unsigned HOST_WIDE_INT) h2
                       + (l < l1));

  *lv = l;
  *hv = h;

  if (unsigned_p)
    return ((unsigned HOST_WIDE_INT) h < (unsigned HOST_WIDE_INT) h1
            || (h == h1
                && l < l1));
  else
    return OVERFLOW_SUM_SIGN (h1, h2, h);
}

/* Negate a doubleword integer with doubleword result.
   Return nonzero if the operation overflows, assuming it's signed.
   The argument is given as two `HOST_WIDE_INT' pieces in L1 and H1.
   The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

int
neg_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
            unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv)
{
  if (l1 == 0)
    {
      *lv = 0;
      *hv = - h1;
      return (*hv & h1) < 0;
    }
  else
    {
      *lv = -l1;
      *hv = ~h1;
      return 0;
    }
}

/* Multiply two doubleword integers with doubleword result.
   Return nonzero if the operation overflows according to UNSIGNED_P.
   Each argument is given as two `HOST_WIDE_INT' pieces.
   One argument is L1 and H1; the other, L2 and H2.
   The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

int
mul_double_with_sign (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
                      unsigned HOST_WIDE_INT l2, HOST_WIDE_INT h2,
                      unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv,
                      bool unsigned_p)
{
  HOST_WIDE_INT arg1[4];
  HOST_WIDE_INT arg2[4];
  HOST_WIDE_INT prod[4 * 2];
  unsigned HOST_WIDE_INT carry;
  int i, j, k;
  unsigned HOST_WIDE_INT toplow, neglow;
  HOST_WIDE_INT tophigh, neghigh;

  encode (arg1, l1, h1);
  encode (arg2, l2, h2);

  memset (prod, 0, sizeof prod);

  for (i = 0; i < 4; i++)
    {
      carry = 0;
      for (j = 0; j < 4; j++)
        {
          k = i + j;
          /* This product is <= 0xFFFE0001, the sum <= 0xFFFF0000.  */
          carry += arg1[i] * arg2[j];
          /* Since prod[p] < 0xFFFF, this sum <= 0xFFFFFFFF.  */
          carry += prod[k];
          prod[k] = LOWPART (carry);
          carry = HIGHPART (carry);
        }
      prod[i + 4] = carry;
    }

  decode (prod, lv, hv);
  decode (prod + 4, &toplow, &tophigh);

  /* Unsigned overflow is immediate.  */
  if (unsigned_p)
    return (toplow | tophigh) != 0;

  /* Check for signed overflow by calculating the signed representation of the
     top half of the result; it should agree with the low half's sign bit.  */
  if (h1 < 0)
    {
      neg_double (l2, h2, &neglow, &neghigh);
      add_double (neglow, neghigh, toplow, tophigh, &toplow, &tophigh);
    }
  if (h2 < 0)
    {
      neg_double (l1, h1, &neglow, &neghigh);
      add_double (neglow, neghigh, toplow, tophigh, &toplow, &tophigh);
    }
  return (*hv < 0 ? ~(toplow & tophigh) : toplow | tophigh) != 0;
}

/* Shift the doubleword integer in L1, H1 left by COUNT places
   keeping only PREC bits of result.
   Shift right if COUNT is negative.
   ARITH nonzero specifies arithmetic shifting; otherwise use logical shift.
   Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

void
lshift_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
               HOST_WIDE_INT count, unsigned int prec,
               unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv, bool arith)
{
  unsigned HOST_WIDE_INT signmask;

  if (count < 0)
    {
      rshift_double (l1, h1, -count, prec, lv, hv, arith);
      return;
    }

  if (SHIFT_COUNT_TRUNCATED)
    count %= prec;

  if (count >= 2 * HOST_BITS_PER_WIDE_INT)
    {
      /* Shifting by the host word size is undefined according to the
         ANSI standard, so we must handle this as a special case.  */
      *hv = 0;
      *lv = 0;
    }
  else if (count >= HOST_BITS_PER_WIDE_INT)
    {
      *hv = l1 << (count - HOST_BITS_PER_WIDE_INT);
      *lv = 0;
    }
  else
    {
      *hv = (((unsigned HOST_WIDE_INT) h1 << count)
             | (l1 >> (HOST_BITS_PER_WIDE_INT - count - 1) >> 1));
      *lv = l1 << count;
    }

  /* Sign extend all bits that are beyond the precision.  */

  signmask = -((prec > HOST_BITS_PER_WIDE_INT
                ? ((unsigned HOST_WIDE_INT) *hv
                   >> (prec - HOST_BITS_PER_WIDE_INT - 1))
                : (*lv >> (prec - 1))) & 1);

  if (prec >= 2 * HOST_BITS_PER_WIDE_INT)
    ;
  else if (prec >= HOST_BITS_PER_WIDE_INT)
    {
      *hv &= ~((HOST_WIDE_INT) (-1) << (prec - HOST_BITS_PER_WIDE_INT));
      *hv |= signmask << (prec - HOST_BITS_PER_WIDE_INT);
    }
  else
    {
      *hv = signmask;
      *lv &= ~((unsigned HOST_WIDE_INT) (-1) << prec);
      *lv |= signmask << prec;
    }
}

/* Shift the doubleword integer in L1, H1 right by COUNT places
   keeping only PREC bits of result.  Shift left if COUNT is negative.
   ARITH nonzero specifies arithmetic shifting; otherwise use logical shift.
   Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

void
rshift_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
               HOST_WIDE_INT count, unsigned int prec,
               unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv,
               bool arith)
{
  unsigned HOST_WIDE_INT signmask;

  if (count < 0)
    {
      lshift_double (l1, h1, -count, prec, lv, hv, arith);
      return;
    }

  signmask = (arith
              ? -((unsigned HOST_WIDE_INT) h1 >> (HOST_BITS_PER_WIDE_INT - 1))
              : 0);

  if (SHIFT_COUNT_TRUNCATED)
    count %= prec;

  if (count >= 2 * HOST_BITS_PER_WIDE_INT)
    {
      /* Shifting by the host word size is undefined according to the
         ANSI standard, so we must handle this as a special case.  */
      *hv = 0;
      *lv = 0;
    }
  else if (count >= HOST_BITS_PER_WIDE_INT)
    {
      *hv = 0;
      *lv = (unsigned HOST_WIDE_INT) h1 >> (count - HOST_BITS_PER_WIDE_INT);
    }
  else
    {
      *hv = (unsigned HOST_WIDE_INT) h1 >> count;
      *lv = ((l1 >> count)
             | ((unsigned HOST_WIDE_INT) h1
                << (HOST_BITS_PER_WIDE_INT - count - 1) << 1));
    }

  /* Zero / sign extend all bits that are beyond the precision.  */

  if (count >= (HOST_WIDE_INT)prec)
    {
      *hv = signmask;
      *lv = signmask;
    }
  else if ((prec - count) >= 2 * HOST_BITS_PER_WIDE_INT)
    ;
  else if ((prec - count) >= HOST_BITS_PER_WIDE_INT)
    {
      *hv &= ~((HOST_WIDE_INT) (-1) << (prec - count - HOST_BITS_PER_WIDE_INT));
      *hv |= signmask << (prec - count - HOST_BITS_PER_WIDE_INT);
    }
  else
    {
      *hv = signmask;
      *lv &= ~((unsigned HOST_WIDE_INT) (-1) << (prec - count));
      *lv |= signmask << (prec - count);
    }
}

/* Rotate the doubleword integer in L1, H1 left by COUNT places
   keeping only PREC bits of result.
   Rotate right if COUNT is negative.
   Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

void
lrotate_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
                HOST_WIDE_INT count, unsigned int prec,
                unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv)
{
  unsigned HOST_WIDE_INT s1l, s2l;
  HOST_WIDE_INT s1h, s2h;

  count %= prec;
  if (count < 0)
    count += prec;

  lshift_double (l1, h1, count, prec, &s1l, &s1h, 0);
  rshift_double (l1, h1, prec - count, prec, &s2l, &s2h, 0);
  *lv = s1l | s2l;
  *hv = s1h | s2h;
}

/* Rotate the doubleword integer in L1, H1 left by COUNT places
   keeping only PREC bits of result.  COUNT must be positive.
   Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV.  */

void
rrotate_double (unsigned HOST_WIDE_INT l1, HOST_WIDE_INT h1,
                HOST_WIDE_INT count, unsigned int prec,
                unsigned HOST_WIDE_INT *lv, HOST_WIDE_INT *hv)
{
  unsigned HOST_WIDE_INT s1l, s2l;
  HOST_WIDE_INT s1h, s2h;

  count %= prec;
  if (count < 0)
    count += prec;

  rshift_double (l1, h1, count, prec, &s1l, &s1h, 0);
  lshift_double (l1, h1, prec - count, prec, &s2l, &s2h, 0);
  *lv = s1l | s2l;
  *hv = s1h | s2h;
}

/* Divide doubleword integer LNUM, HNUM by doubleword integer LDEN, HDEN
   for a quotient (stored in *LQUO, *HQUO) and remainder (in *LREM, *HREM).
   CODE is a tree code for a kind of division, one of
   TRUNC_DIV_EXPR, FLOOR_DIV_EXPR, CEIL_DIV_EXPR, ROUND_DIV_EXPR
   or EXACT_DIV_EXPR
   It controls how the quotient is rounded to an integer.
   Return nonzero if the operation overflows.
   UNS nonzero says do unsigned division.  */

int
div_and_round_double (unsigned code, int uns,
                      /* num == numerator == dividend */
                      unsigned HOST_WIDE_INT lnum_orig,
                      HOST_WIDE_INT hnum_orig,
                      /* den == denominator == divisor */
                      unsigned HOST_WIDE_INT lden_orig,
                      HOST_WIDE_INT hden_orig,
                      unsigned HOST_WIDE_INT *lquo,
                      HOST_WIDE_INT *hquo, unsigned HOST_WIDE_INT *lrem,
                      HOST_WIDE_INT *hrem)
{
  int quo_neg = 0;
  HOST_WIDE_INT num[4 + 1];     /* extra element for scaling.  */
  HOST_WIDE_INT den[4], quo[4];
  int i, j;
  unsigned HOST_WIDE_INT work;
  unsigned HOST_WIDE_INT carry = 0;
  unsigned HOST_WIDE_INT lnum = lnum_orig;
  HOST_WIDE_INT hnum = hnum_orig;
  unsigned HOST_WIDE_INT lden = lden_orig;
  HOST_WIDE_INT hden = hden_orig;
  int overflow = 0;

  if (hden == 0 && lden == 0)
    overflow = 1, lden = 1;

  /* Calculate quotient sign and convert operands to unsigned.  */
  if (!uns)
    {
      if (hnum < 0)
        {
          quo_neg = ~ quo_neg;
          /* (minimum integer) / (-1) is the only overflow case.  */
          if (neg_double (lnum, hnum, &lnum, &hnum)
              && ((HOST_WIDE_INT) lden & hden) == -1)
            overflow = 1;
        }
      if (hden < 0)
        {
          quo_neg = ~ quo_neg;
          neg_double (lden, hden, &lden, &hden);
        }
    }

  if (hnum == 0 && hden == 0)
    {                           /* single precision */
      *hquo = *hrem = 0;
      /* This unsigned division rounds toward zero.  */
      *lquo = lnum / lden;
      goto finish_up;
    }

  if (hnum == 0)
    {                           /* trivial case: dividend < divisor */
      /* hden != 0 already checked.  */
      *hquo = *lquo = 0;
      *hrem = hnum;
      *lrem = lnum;
      goto finish_up;
    }

  memset (quo, 0, sizeof quo);

  memset (num, 0, sizeof num);  /* to zero 9th element */
  memset (den, 0, sizeof den);

  encode (num, lnum, hnum);
  encode (den, lden, hden);

  /* Special code for when the divisor < BASE.  */
  if (hden == 0 && lden < (unsigned HOST_WIDE_INT) BASE)
    {
      /* hnum != 0 already checked.  */
      for (i = 4 - 1; i >= 0; i--)
        {
          work = num[i] + carry * BASE;
          quo[i] = work / lden;
          carry = work % lden;
        }
    }
  else
    {
      /* Full double precision division,
         with thanks to Don Knuth's "Seminumerical Algorithms".  */
      int num_hi_sig, den_hi_sig;
      unsigned HOST_WIDE_INT quo_est, scale;

      /* Find the highest nonzero divisor digit.  */
      for (i = 4 - 1;; i--)
        if (den[i] != 0)
          {
            den_hi_sig = i;
            break;
          }

      /* Insure that the first digit of the divisor is at least BASE/2.
         This is required by the quotient digit estimation algorithm.  */

      scale = BASE / (den[den_hi_sig] + 1);
      if (scale > 1)
        {               /* scale divisor and dividend */
          carry = 0;
          for (i = 0; i <= 4 - 1; i++)
            {
              work = (num[i] * scale) + carry;
              num[i] = LOWPART (work);
              carry = HIGHPART (work);
            }

          num[4] = carry;
          carry = 0;
          for (i = 0; i <= 4 - 1; i++)
            {
              work = (den[i] * scale) + carry;
              den[i] = LOWPART (work);
              carry = HIGHPART (work);
              if (den[i] != 0) den_hi_sig = i;
            }
        }

      num_hi_sig = 4;

      /* Main loop */
      for (i = num_hi_sig - den_hi_sig - 1; i >= 0; i--)
        {
          /* Guess the next quotient digit, quo_est, by dividing the first
             two remaining dividend digits by the high order quotient digit.
             quo_est is never low and is at most 2 high.  */
          unsigned HOST_WIDE_INT tmp;

          num_hi_sig = i + den_hi_sig + 1;
          work = num[num_hi_sig] * BASE + num[num_hi_sig - 1];
          if (num[num_hi_sig] != den[den_hi_sig])
            quo_est = work / den[den_hi_sig];
          else
            quo_est = BASE - 1;

          /* Refine quo_est so it's usually correct, and at most one high.  */
          tmp = work - quo_est * den[den_hi_sig];
          if (tmp < BASE
              && (den[den_hi_sig - 1] * quo_est
                  > (tmp * BASE + num[num_hi_sig - 2])))
            quo_est--;

          /* Try QUO_EST as the quotient digit, by multiplying the
             divisor by QUO_EST and subtracting from the remaining dividend.
             Keep in mind that QUO_EST is the I - 1st digit.  */

          carry = 0;
          for (j = 0; j <= den_hi_sig; j++)
            {
              work = quo_est * den[j] + carry;
              carry = HIGHPART (work);
              work = num[i + j] - LOWPART (work);
              num[i + j] = LOWPART (work);
              carry += HIGHPART (work) != 0;
            }

          /* If quo_est was high by one, then num[i] went negative and
             we need to correct things.  */
          if (num[num_hi_sig] < (HOST_WIDE_INT) carry)
            {
              quo_est--;
              carry = 0;                /* add divisor back in */
              for (j = 0; j <= den_hi_sig; j++)
                {
                  work = num[i + j] + den[j] + carry;
                  carry = HIGHPART (work);
                  num[i + j] = LOWPART (work);
                }

              num [num_hi_sig] += carry;
            }

          /* Store the quotient digit.  */
          quo[i] = quo_est;
        }
    }

  decode (quo, lquo, hquo);

 finish_up:
  /* If result is negative, make it so.  */
  if (quo_neg)
    neg_double (*lquo, *hquo, lquo, hquo);

  /* Compute trial remainder:  rem = num - (quo * den)  */
  mul_double (*lquo, *hquo, lden_orig, hden_orig, lrem, hrem);
  neg_double (*lrem, *hrem, lrem, hrem);
  add_double (lnum_orig, hnum_orig, *lrem, *hrem, lrem, hrem);

  switch (code)
    {
    case TRUNC_DIV_EXPR:
    case TRUNC_MOD_EXPR:        /* round toward zero */
    case EXACT_DIV_EXPR:        /* for this one, it shouldn't matter */
      return overflow;

    case FLOOR_DIV_EXPR:
    case FLOOR_MOD_EXPR:        /* round toward negative infinity */
      if (quo_neg && (*lrem != 0 || *hrem != 0))   /* ratio < 0 && rem != 0 */
        {
          /* quo = quo - 1;  */
          add_double (*lquo, *hquo, (HOST_WIDE_INT) -1, (HOST_WIDE_INT)  -1,
                      lquo, hquo);
        }
      else
        return overflow;
      break;

    case CEIL_DIV_EXPR:
    case CEIL_MOD_EXPR:         /* round toward positive infinity */
      if (!quo_neg && (*lrem != 0 || *hrem != 0))  /* ratio > 0 && rem != 0 */
        {
          add_double (*lquo, *hquo, (HOST_WIDE_INT) 1, (HOST_WIDE_INT) 0,
                      lquo, hquo);
        }
      else
        return overflow;
      break;

    case ROUND_DIV_EXPR:
    case ROUND_MOD_EXPR:        /* round to closest integer */
      {
        unsigned HOST_WIDE_INT labs_rem = *lrem;
        HOST_WIDE_INT habs_rem = *hrem;
        unsigned HOST_WIDE_INT labs_den = lden, ltwice;
        HOST_WIDE_INT habs_den = hden, htwice;

        /* Get absolute values.  */
        if (*hrem < 0)
          neg_double (*lrem, *hrem, &labs_rem, &habs_rem);
        if (hden < 0)
          neg_double (lden, hden, &labs_den, &habs_den);

        /* If (2 * abs (lrem) >= abs (lden)), adjust the quotient.  */
        mul_double ((HOST_WIDE_INT) 2, (HOST_WIDE_INT) 0,
                    labs_rem, habs_rem, &ltwice, &htwice);

        if (((unsigned HOST_WIDE_INT) habs_den
             < (unsigned HOST_WIDE_INT) htwice)
            || (((unsigned HOST_WIDE_INT) habs_den
                 == (unsigned HOST_WIDE_INT) htwice)
                && (labs_den <= ltwice)))
          {
            if (*hquo < 0)
              /* quo = quo - 1;  */
              add_double (*lquo, *hquo,
                          (HOST_WIDE_INT) -1, (HOST_WIDE_INT) -1, lquo, hquo);
            else
              /* quo = quo + 1; */
              add_double (*lquo, *hquo, (HOST_WIDE_INT) 1, (HOST_WIDE_INT) 0,
                          lquo, hquo);
          }
        else
          return overflow;
      }
      break;

    default:
      gcc_unreachable ();
    }

  /* Compute true remainder:  rem = num - (quo * den)  */
  mul_double (*lquo, *hquo, lden_orig, hden_orig, lrem, hrem);
  neg_double (*lrem, *hrem, lrem, hrem);
  add_double (lnum_orig, hnum_orig, *lrem, *hrem, lrem, hrem);
  return overflow;
}


/* Returns mask for PREC bits.  */

double_int
double_int_mask (unsigned prec)
{
  unsigned HOST_WIDE_INT m;
  double_int mask;

  if (prec > HOST_BITS_PER_WIDE_INT)
    {
      prec -= HOST_BITS_PER_WIDE_INT;
      m = ((unsigned HOST_WIDE_INT) 2 << (prec - 1)) - 1;
      mask.high = (HOST_WIDE_INT) m;
      mask.low = ALL_ONES;
    }
  else
    {
      mask.high = 0;
      mask.low = ((unsigned HOST_WIDE_INT) 2 << (prec - 1)) - 1;
    }

  return mask;
}

/* Clears the bits of CST over the precision PREC.  If UNS is false, the bits
   outside of the precision are set to the sign bit (i.e., the PREC-th one),
   otherwise they are set to zero.

   This corresponds to returning the value represented by PREC lowermost bits
   of CST, with the given signedness.  */

double_int
double_int_ext (double_int cst, unsigned prec, bool uns)
{
  if (uns)
    return double_int_zext (cst, prec);
  else
    return double_int_sext (cst, prec);
}

/* The same as double_int_ext with UNS = true.  */

double_int
double_int_zext (double_int cst, unsigned prec)
{
  double_int mask = double_int_mask (prec);
  double_int r;

  r.low = cst.low & mask.low;
  r.high = cst.high & mask.high;

  return r;
}

/* The same as double_int_ext with UNS = false.  */

double_int
double_int_sext (double_int cst, unsigned prec)
{
  double_int mask = double_int_mask (prec);
  double_int r;
  unsigned HOST_WIDE_INT snum;

  if (prec <= HOST_BITS_PER_WIDE_INT)
    snum = cst.low;
  else
    {
      prec -= HOST_BITS_PER_WIDE_INT;
      snum = (unsigned HOST_WIDE_INT) cst.high;
    }
  if (((snum >> (prec - 1)) & 1) == 1)
    {
      r.low = cst.low | ~mask.low;
      r.high = cst.high | ~mask.high;
    }
  else
    {
      r.low = cst.low & mask.low;
      r.high = cst.high & mask.high;
    }

  return r;
}

/* Constructs long integer from tree CST.  The extra bits over the precision of
   the number are filled with sign bit if CST is signed, and with zeros if it
   is unsigned.  */

double_int
tree_to_double_int (const_tree cst)
{
  /* We do not need to call double_int_restrict here to ensure the semantics as
     described, as this is the default one for trees.  */
  return TREE_INT_CST (cst);
}

/* Returns true if CST fits in unsigned HOST_WIDE_INT.  */

bool
double_int_fits_in_uhwi_p (double_int cst)
{
  return cst.high == 0;
}

/* Returns true if CST fits in signed HOST_WIDE_INT.  */

bool
double_int_fits_in_shwi_p (double_int cst)
{
  if (cst.high == 0)
    return (HOST_WIDE_INT) cst.low >= 0;
  else if (cst.high == -1)
    return (HOST_WIDE_INT) cst.low < 0;
  else
    return false;
}

/* Returns true if CST fits in HOST_WIDE_INT if UNS is false, or in
   unsigned HOST_WIDE_INT if UNS is true.  */

bool
double_int_fits_in_hwi_p (double_int cst, bool uns)
{
  if (uns)
    return double_int_fits_in_uhwi_p (cst);
  else
    return double_int_fits_in_shwi_p (cst);
}

/* Returns value of CST as a signed number.  CST must satisfy
   double_int_fits_in_shwi_p.  */

HOST_WIDE_INT
double_int_to_shwi (double_int cst)
{
  return (HOST_WIDE_INT) cst.low;
}

/* Returns value of CST as an unsigned number.  CST must satisfy
   double_int_fits_in_uhwi_p.  */

unsigned HOST_WIDE_INT
double_int_to_uhwi (double_int cst)
{
  return cst.low;
}

/* Returns A * B.  */

double_int
double_int_mul (double_int a, double_int b)
{
  double_int ret;
  mul_double (a.low, a.high, b.low, b.high, &ret.low, &ret.high);
  return ret;
}

/* Returns A + B.  */

double_int
double_int_add (double_int a, double_int b)
{
  double_int ret;
  add_double (a.low, a.high, b.low, b.high, &ret.low, &ret.high);
  return ret;
}

/* Returns -A.  */

double_int
double_int_neg (double_int a)
{
  double_int ret;
  neg_double (a.low, a.high, &ret.low, &ret.high);
  return ret;
}

/* Returns A / B (computed as unsigned depending on UNS, and rounded as
   specified by CODE).  CODE is enum tree_code in fact, but double_int.h
   must be included before tree.h.  The remainder after the division is
   stored to MOD.  */

double_int
double_int_divmod (double_int a, double_int b, bool uns, unsigned code,
                   double_int *mod)
{
  double_int ret;

  div_and_round_double (code, uns, a.low, a.high,
                        b.low, b.high, &ret.low, &ret.high,
                        &mod->low, &mod->high);
  return ret;
}

/* The same as double_int_divmod with UNS = false.  */

double_int
double_int_sdivmod (double_int a, double_int b, unsigned code, double_int *mod)
{
  return double_int_divmod (a, b, false, code, mod);
}

/* The same as double_int_divmod with UNS = true.  */

double_int
double_int_udivmod (double_int a, double_int b, unsigned code, double_int *mod)
{
  return double_int_divmod (a, b, true, code, mod);
}

/* Returns A / B (computed as unsigned depending on UNS, and rounded as
   specified by CODE).  CODE is enum tree_code in fact, but double_int.h
   must be included before tree.h.  */

double_int
double_int_div (double_int a, double_int b, bool uns, unsigned code)
{
  double_int mod;

  return double_int_divmod (a, b, uns, code, &mod);
}

/* The same as double_int_div with UNS = false.  */

double_int
double_int_sdiv (double_int a, double_int b, unsigned code)
{
  return double_int_div (a, b, false, code);
}

/* The same as double_int_div with UNS = true.  */

double_int
double_int_udiv (double_int a, double_int b, unsigned code)
{
  return double_int_div (a, b, true, code);
}

/* Returns A % B (computed as unsigned depending on UNS, and rounded as
   specified by CODE).  CODE is enum tree_code in fact, but double_int.h
   must be included before tree.h.  */

double_int
double_int_mod (double_int a, double_int b, bool uns, unsigned code)
{
  double_int mod;

  double_int_divmod (a, b, uns, code, &mod);
  return mod;
}

/* The same as double_int_mod with UNS = false.  */

double_int
double_int_smod (double_int a, double_int b, unsigned code)
{
  return double_int_mod (a, b, false, code);
}

/* The same as double_int_mod with UNS = true.  */

double_int
double_int_umod (double_int a, double_int b, unsigned code)
{
  return double_int_mod (a, b, true, code);
}

/* Shift A left by COUNT places keeping only PREC bits of result.  Shift
   right if COUNT is negative.  ARITH true specifies arithmetic shifting;
   otherwise use logical shift.  */

double_int
double_int_lshift (double_int a, HOST_WIDE_INT count, unsigned int prec, bool arith)
{
  double_int ret;
  lshift_double (a.low, a.high, count, prec, &ret.low, &ret.high, arith);
  return ret;
}

/* Shift A rigth by COUNT places keeping only PREC bits of result.  Shift
   left if COUNT is negative.  ARITH true specifies arithmetic shifting;
   otherwise use logical shift.  */

double_int
double_int_rshift (double_int a, HOST_WIDE_INT count, unsigned int prec, bool arith)
{
  double_int ret;
  rshift_double (a.low, a.high, count, prec, &ret.low, &ret.high, arith);
  return ret;
}

/* Constructs tree in type TYPE from with value given by CST.  Signedness of CST
   is assumed to be the same as the signedness of TYPE.  */

tree
double_int_to_tree (tree type, double_int cst)
{
  cst = double_int_ext (cst, TYPE_PRECISION (type), TYPE_UNSIGNED (type));

  return build_int_cst_wide (type, cst.low, cst.high);
}

/* Returns true if CST fits into range of TYPE.  Signedness of CST is assumed
   to be the same as the signedness of TYPE.  */

bool
double_int_fits_to_tree_p (const_tree type, double_int cst)
{
  double_int ext = double_int_ext (cst,
                                   TYPE_PRECISION (type),
                                   TYPE_UNSIGNED (type));

  return double_int_equal_p (cst, ext);
}

/* Returns -1 if A < B, 0 if A == B and 1 if A > B.  Signedness of the
   comparison is given by UNS.  */

int
double_int_cmp (double_int a, double_int b, bool uns)
{
  if (uns)
    return double_int_ucmp (a, b);
  else
    return double_int_scmp (a, b);
}

/* Compares two unsigned values A and B.  Returns -1 if A < B, 0 if A == B,
   and 1 if A > B.  */

int
double_int_ucmp (double_int a, double_int b)
{
  if ((unsigned HOST_WIDE_INT) a.high < (unsigned HOST_WIDE_INT) b.high)
    return -1;
  if ((unsigned HOST_WIDE_INT) a.high > (unsigned HOST_WIDE_INT) b.high)
    return 1;
  if (a.low < b.low)
    return -1;
  if (a.low > b.low)
    return 1;

  return 0;
}

/* Compares two signed values A and B.  Returns -1 if A < B, 0 if A == B,
   and 1 if A > B.  */

int
double_int_scmp (double_int a, double_int b)
{
  if (a.high < b.high)
    return -1;
  if (a.high > b.high)
    return 1;
  if (a.low < b.low)
    return -1;
  if (a.low > b.low)
    return 1;

  return 0;
}

/* Splits last digit of *CST (taken as unsigned) in BASE and returns it.  */

static unsigned
double_int_split_digit (double_int *cst, unsigned base)
{
  unsigned HOST_WIDE_INT resl, reml;
  HOST_WIDE_INT resh, remh;

  div_and_round_double (FLOOR_DIV_EXPR, true, cst->low, cst->high, base, 0,
                        &resl, &resh, &reml, &remh);
  cst->high = resh;
  cst->low = resl;

  return reml;
}

/* Dumps CST to FILE.  If UNS is true, CST is considered to be unsigned,
   otherwise it is signed.  */

void
dump_double_int (FILE *file, double_int cst, bool uns)
{
  unsigned digits[100], n;
  int i;

  if (double_int_zero_p (cst))
    {
      fprintf (file, "0");
      return;
    }

  if (!uns && double_int_negative_p (cst))
    {
      fprintf (file, "-");
      cst = double_int_neg (cst);
    }

  for (n = 0; !double_int_zero_p (cst); n++)
    digits[n] = double_int_split_digit (&cst, 10);
  for (i = n - 1; i >= 0; i--)
    fprintf (file, "%u", digits[i]);
}


/* Sets RESULT to VAL, taken unsigned if UNS is true and as signed
   otherwise.  */

void
mpz_set_double_int (mpz_t result, double_int val, bool uns)
{
  bool negate = false;
  unsigned HOST_WIDE_INT vp[2];

  if (!uns && double_int_negative_p (val))
    {
      negate = true;
      val = double_int_neg (val);
    }

  vp[0] = val.low;
  vp[1] = (unsigned HOST_WIDE_INT) val.high;
  mpz_import (result, 2, -1, sizeof (HOST_WIDE_INT), 0, 0, vp);

  if (negate)
    mpz_neg (result, result);
}

/* Returns VAL converted to TYPE.  If WRAP is true, then out-of-range
   values of VAL will be wrapped; otherwise, they will be set to the
   appropriate minimum or maximum TYPE bound.  */

double_int
mpz_get_double_int (const_tree type, mpz_t val, bool wrap)
{
  unsigned HOST_WIDE_INT *vp;
  size_t count, numb;
  double_int res;

  if (!wrap)
    {
      mpz_t min, max;

      mpz_init (min);
      mpz_init (max);
      get_type_static_bounds (type, min, max);

      if (mpz_cmp (val, min) < 0)
        mpz_set (val, min);
      else if (mpz_cmp (val, max) > 0)
        mpz_set (val, max);

      mpz_clear (min);
      mpz_clear (max);
    }

  /* Determine the number of unsigned HOST_WIDE_INT that are required
     for representing the value.  The code to calculate count is
     extracted from the GMP manual, section "Integer Import and Export":
     http://gmplib.org/manual/Integer-Import-and-Export.html  */
  numb = 8*sizeof(HOST_WIDE_INT);
  count = (mpz_sizeinbase (val, 2) + numb-1) / numb;
  if (count < 2)
    count = 2;
  vp = (unsigned HOST_WIDE_INT *) alloca (count * sizeof(HOST_WIDE_INT));

  vp[0] = 0;
  vp[1] = 0;
  mpz_export (vp, &count, -1, sizeof (HOST_WIDE_INT), 0, 0, val);

  gcc_assert (wrap || count <= 2);

  res.low = vp[0];
  res.high = (HOST_WIDE_INT) vp[1];

  res = double_int_ext (res, TYPE_PRECISION (type), TYPE_UNSIGNED (type));
  if (mpz_sgn (val) < 0)
    res = double_int_neg (res);

  return res;
}