path: root/libgcc/config/libbid/bid128_add.c

/* Copyright (C) 2007, 2009  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.

Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
<http://www.gnu.org/licenses/>.  */

#include "bid_internal.h"


#if DECIMAL_CALL_BY_REFERENCE
void
bid64dq_add (UINT64 * pres, UINT64 * px, UINT128 * py
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
  UINT64 x = *px;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64dq_add (UINT64 x, UINT128 y
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
#endif
  UINT64 res = 0xbaddbaddbaddbaddull;
  UINT128 x1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qq_add (&res, &x1, py
	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	       _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid64qq_add (x1, y
		     _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		     _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qd_add (UINT64 * pres, UINT128 * px, UINT64 * py
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qd_add (UINT128 x, UINT64 y
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
#endif
  UINT64 res = 0xbaddbaddbaddbaddull;
  UINT128 y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qq_add (&res, px, &y1
	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	       _EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid64qq_add (x, y1
		     _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		     _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qq_add (UINT64 * pres, UINT128 * px, UINT128 * py
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qq_add (UINT128 x, UINT128 y
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
#endif

  UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull}
  };
  UINT64 res = 0xbaddbaddbaddbaddull;

  BID_SWAP128 (one);
#if DECIMAL_CALL_BY_REFERENCE
  bid64qqq_fma (&res, &one, &x, &y
		_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		_EXC_INFO_ARG);
#else
  res = bid64qqq_fma (one, x, y
		      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		      _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128dd_add (UINT128 * pres, UINT64 * px, UINT64 * py
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
  UINT64 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128dd_add (UINT64 x, UINT64 y
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT128 x1, y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_add (&res, &x1, &y1
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_add (x1, y1
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128dq_add (UINT128 * pres, UINT64 * px, UINT128 * py
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
  UINT64 x = *px;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128dq_add (UINT64 x, UINT128 y
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT128 x1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_add (&res, &x1, py
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_add (x1, y
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128qd_add (UINT128 * pres, UINT128 * px, UINT64 * py
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128qd_add (UINT128 x, UINT64 y
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT128 y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_add (&res, px, &y1
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_add (x, y1
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


// bid128_add stands for bid128qq_add


/*****************************************************************************
 *  BID64/BID128 sub
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid64dq_sub (UINT64 * pres, UINT64 * px, UINT128 * py
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
  UINT64 x = *px;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64dq_sub (UINT64 x, UINT128 y
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
#endif
  UINT64 res = 0xbaddbaddbaddbaddull;
  UINT128 x1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qq_sub (&res, &x1, py
	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	       _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid64qq_sub (x1, y
		     _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		     _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qd_sub (UINT64 * pres, UINT128 * px, UINT64 * py
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qd_sub (UINT128 x, UINT64 y
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
#endif
  UINT64 res = 0xbaddbaddbaddbaddull;
  UINT128 y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qq_sub (&res, px, &y1
	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	       _EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid64qq_sub (x, y1
		     _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		     _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qq_sub (UINT64 * pres, UINT128 * px, UINT128 * py
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qq_sub (UINT128 x, UINT128 y
	     _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	     _EXC_INFO_PARAM) {
#endif

  UINT128 one = { {0x0000000000000001ull, 0x3040000000000000ull}
  };
  UINT64 res = 0xbaddbaddbaddbaddull;
  UINT64 y_sign;

  BID_SWAP128 (one);
  if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) {	// y is not NAN
    // change its sign
    y_sign = y.w[HIGH_128W] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
    if (y_sign)
      y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull;
    else
      y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull;
  }
#if DECIMAL_CALL_BY_REFERENCE
  bid64qqq_fma (&res, &one, &x, &y
		_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		_EXC_INFO_ARG);
#else
  res = bid64qqq_fma (one, x, y
		      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		      _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128dd_sub (UINT128 * pres, UINT64 * px, UINT64 * py
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
  UINT64 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128dd_sub (UINT64 x, UINT64 y
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT128 x1, y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_sub (&res, &x1, &y1
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_sub (x1, y1
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128dq_sub (UINT128 * pres, UINT64 * px, UINT128 * py
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
  UINT64 x = *px;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128dq_sub (UINT64 x, UINT128 y
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT128 x1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_sub (&res, &x1, py
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_sub (x1, y
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128qd_sub (UINT128 * pres, UINT128 * px, UINT64 * py
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128qd_sub (UINT128 x, UINT64 y
	      _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	      _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT128 y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_sub (&res, px, &y1
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_sub (x, y1
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_add (UINT128 * pres, UINT128 * px, UINT128 * py
	    _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	    _EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128_add (UINT128 x, UINT128 y
	    _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	    _EXC_INFO_PARAM) {
#endif
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull}
  };
  UINT64 x_sign, y_sign, tmp_sign;
  UINT64 x_exp, y_exp, tmp_exp;	// e1 = x_exp, e2 = y_exp
  UINT64 C1_hi, C2_hi, tmp_signif_hi;
  UINT64 C1_lo, C2_lo, tmp_signif_lo;
  // Note: C1.w[1], C1.w[0] represent C1_hi, C1_lo (all UINT64)
  // Note: C2.w[1], C2.w[0] represent C2_hi, C2_lo (all UINT64)
  UINT64 tmp64, tmp64A, tmp64B;
  BID_UI64DOUBLE tmp1, tmp2;
  int x_nr_bits, y_nr_bits;
  int q1, q2, delta, scale, x1, ind, shift, tmp_inexact = 0;
  UINT64 halfulp64;
  UINT128 halfulp128;
  UINT128 C1, C2;
  UINT128 ten2m1;
  UINT128 highf2star;		// top 128 bits in f2*; low 128 bits in R256[1], R256[0]
  UINT256 P256, Q256, R256;
  int is_inexact = 0, is_midpoint_lt_even = 0, is_midpoint_gt_even = 0;
  int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  int second_pass = 0;

  BID_SWAP128 (x);
  BID_SWAP128 (y);
  x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
  y_sign = y.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative

  // check for NaN or Infinity
  if (((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL)
      || ((y.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) {
    // x is special or y is special
    if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
      // check first for non-canonical NaN payload
      if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
	  (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
	   && (x.w[0] > 0x38c15b09ffffffffull))) {
	x.w[1] = x.w[1] & 0xffffc00000000000ull;
	x.w[0] = 0x0ull;
      }
      if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
	// set invalid flag
	*pfpsf |= INVALID_EXCEPTION;
	// return quiet (x)
	res.w[1] = x.w[1] & 0xfc003fffffffffffull;
	// clear out also G[6]-G[16]
	res.w[0] = x.w[0];
      } else {	// x is QNaN
	// return x
	res.w[1] = x.w[1] & 0xfc003fffffffffffull;
	// clear out G[6]-G[16]
	res.w[0] = x.w[0];
	// if y = SNaN signal invalid exception
	if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
	  // set invalid flag
	  *pfpsf |= INVALID_EXCEPTION;
	}
      }
      BID_SWAP128 (res);
      BID_RETURN (res);
    } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
      // check first for non-canonical NaN payload
      if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
	  (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull)
	   && (y.w[0] > 0x38c15b09ffffffffull))) {
	y.w[1] = y.w[1] & 0xffffc00000000000ull;
	y.w[0] = 0x0ull;
      }
      if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
	// set invalid flag
	*pfpsf |= INVALID_EXCEPTION;
	// return quiet (y)
	res.w[1] = y.w[1] & 0xfc003fffffffffffull;
	// clear out also G[6]-G[16]
	res.w[0] = y.w[0];
      } else {	// y is QNaN
	// return y
	res.w[1] = y.w[1] & 0xfc003fffffffffffull;
	// clear out G[6]-G[16]
	res.w[0] = y.w[0];
      }
      BID_SWAP128 (res);
      BID_RETURN (res);
    } else {	// neither x not y is NaN; at least one is infinity
      if ((x.w[1] & MASK_ANY_INF) == MASK_INF) {	// x is infinity
	if ((y.w[1] & MASK_ANY_INF) == MASK_INF) {	// y is infinity
	  // if same sign, return either of them
	  if ((x.w[1] & MASK_SIGN) == (y.w[1] & MASK_SIGN)) {
	    res.w[1] = x_sign | MASK_INF;
	    res.w[0] = 0x0ull;
	  } else {	// x and y are infinities of opposite signs
	    // set invalid flag
	    *pfpsf |= INVALID_EXCEPTION;
	    // return QNaN Indefinite
	    res.w[1] = 0x7c00000000000000ull;
	    res.w[0] = 0x0000000000000000ull;
	  }
	} else {	// y is 0 or finite
	  // return x
	  res.w[1] = x_sign | MASK_INF;
	  res.w[0] = 0x0ull;
	}
      } else {	// x is not NaN or infinity, so y must be infinity
	res.w[1] = y_sign | MASK_INF;
	res.w[0] = 0x0ull;
      }
      BID_SWAP128 (res);
      BID_RETURN (res);
    }
  }
  // unpack the arguments

  // unpack x 
  C1_hi = x.w[1] & MASK_COEFF;
  C1_lo = x.w[0];
  // test for non-canonical values:
  // - values whose encoding begins with x00, x01, or x10 and whose 
  //   coefficient is larger than 10^34 -1, or
  // - values whose encoding begins with x1100, x1101, x1110 (if NaNs 
  //   and infinitis were eliminated already this test is reduced to 
  //   checking for x10x) 

  // x is not infinity; check for non-canonical values - treated as zero
  if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
    // G0_G1=11; non-canonical
    x_exp = (x.w[1] << 2) & MASK_EXP;	// biased and shifted left 49 bits
    C1_hi = 0;	// significand high
    C1_lo = 0;	// significand low
  } else {	// G0_G1 != 11
    x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bits
    if (C1_hi > 0x0001ed09bead87c0ull ||
	(C1_hi == 0x0001ed09bead87c0ull
	 && C1_lo > 0x378d8e63ffffffffull)) {
      // x is non-canonical if coefficient is larger than 10^34 -1
      C1_hi = 0;
      C1_lo = 0;
    } else {	// canonical
      ;
    }
  }

  // unpack y  
  C2_hi = y.w[1] & MASK_COEFF;
  C2_lo = y.w[0];
  // y is not infinity; check for non-canonical values - treated as zero 
  if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
    // G0_G1=11; non-canonical 
    y_exp = (y.w[1] << 2) & MASK_EXP;	// biased and shifted left 49 bits
    C2_hi = 0;	// significand high
    C2_lo = 0;	// significand low 
  } else {	// G0_G1 != 11 
    y_exp = y.w[1] & MASK_EXP;	// biased and shifted left 49 bits
    if (C2_hi > 0x0001ed09bead87c0ull ||
	(C2_hi == 0x0001ed09bead87c0ull
	 && C2_lo > 0x378d8e63ffffffffull)) {
      // y is non-canonical if coefficient is larger than 10^34 -1 
      C2_hi = 0;
      C2_lo = 0;
    } else {	// canonical
      ;
    }
  }

  if ((C1_hi == 0x0ull) && (C1_lo == 0x0ull)) {
    // x is 0 and y is not special
    // if y is 0 return 0 with the smaller exponent
    if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) {
      if (x_exp < y_exp)
	res.w[1] = x_exp;
      else
	res.w[1] = y_exp;
      if (x_sign && y_sign)
	res.w[1] = res.w[1] | x_sign;	// both negative
      else if (rnd_mode == ROUNDING_DOWN && x_sign != y_sign)
	res.w[1] = res.w[1] | 0x8000000000000000ull;	// -0
      // else; // res = +0
      res.w[0] = 0;
    } else {
      // for 0 + y return y, with the preferred exponent
      if (y_exp <= x_exp) {
	res.w[1] = y.w[1];
	res.w[0] = y.w[0];
      } else {	// if y_exp > x_exp
	// return (C2 * 10^scale) * 10^(y_exp - scale)
	// where scale = min (P34-q2, y_exp-x_exp)
	// determine q2 = nr. of decimal digits in y
	//  determine first the nr. of bits in y (y_nr_bits)

	if (C2_hi == 0) {	// y_bits is the nr. of bits in C2_lo
	  if (C2_lo >= 0x0020000000000000ull) {	// y >= 2^53
	    // split the 64-bit value in two 32-bit halves to avoid 
	    // rounding errors
	    if (C2_lo >= 0x0000000100000000ull) {	// y >= 2^32
	      tmp2.d = (double) (C2_lo >> 32);	// exact conversion
	      y_nr_bits =
		32 +
		((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
	    } else {	// y < 2^32
	      tmp2.d = (double) (C2_lo);	// exact conversion
	      y_nr_bits =
		((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
	    }
	  } else {	// if y < 2^53
	    tmp2.d = (double) C2_lo;	// exact conversion
	    y_nr_bits =
	      ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
	  }
	} else {	// C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi)
	  tmp2.d = (double) C2_hi;	// exact conversion
	  y_nr_bits =
	    64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
	q2 = nr_digits[y_nr_bits].digits;
	if (q2 == 0) {
	  q2 = nr_digits[y_nr_bits].digits1;
	  if (C2_hi > nr_digits[y_nr_bits].threshold_hi ||
	      (C2_hi == nr_digits[y_nr_bits].threshold_hi &&
	       C2_lo >= nr_digits[y_nr_bits].threshold_lo))
	    q2++;
	}
	// return (C2 * 10^scale) * 10^(y_exp - scale)
	// where scale = min (P34-q2, y_exp-x_exp)
	scale = P34 - q2;
	ind = (y_exp - x_exp) >> 49;
	if (ind < scale)
	  scale = ind;
	if (scale == 0) {
	  res.w[1] = y.w[1];
	  res.w[0] = y.w[0];
	} else if (q2 <= 19) {	// y fits in 64 bits 
	  if (scale <= 19) {	// 10^scale fits in 64 bits
	    // 64 x 64 C2_lo * ten2k64[scale]
	    __mul_64x64_to_128MACH (res, C2_lo, ten2k64[scale]);
	  } else {	// 10^scale fits in 128 bits
	    // 64 x 128 C2_lo * ten2k128[scale - 20]
	    __mul_128x64_to_128 (res, C2_lo, ten2k128[scale - 20]);
	  }
	} else {	// y fits in 128 bits, but 10^scale must fit in 64 bits 
	  // 64 x 128 ten2k64[scale] * C2
	  C2.w[1] = C2_hi;
	  C2.w[0] = C2_lo;
	  __mul_128x64_to_128 (res, ten2k64[scale], C2);
	}
	// subtract scale from the exponent
	y_exp = y_exp - ((UINT64) scale << 49);
	res.w[1] = res.w[1] | y_sign | y_exp;
      }
    }
    BID_SWAP128 (res);
    BID_RETURN (res);
  } else if ((C2_hi == 0x0ull) && (C2_lo == 0x0ull)) {
    // y is 0 and x is not special, and not zero
    // for x + 0 return x, with the preferred exponent
    if (x_exp <= y_exp) {
      res.w[1] = x.w[1];
      res.w[0] = x.w[0];
    } else {	// if x_exp > y_exp
      // return (C1 * 10^scale) * 10^(x_exp - scale)
      // where scale = min (P34-q1, x_exp-y_exp)
      // determine q1 = nr. of decimal digits in x
      //  determine first the nr. of bits in x
      if (C1_hi == 0) {	// x_bits is the nr. of bits in C1_lo
	if (C1_lo >= 0x0020000000000000ull) {	// x >= 2^53
	  // split the 64-bit value in two 32-bit halves to avoid 
	  // rounding errors
	  if (C1_lo >= 0x0000000100000000ull) {	// x >= 2^32
	    tmp1.d = (double) (C1_lo >> 32);	// exact conversion
	    x_nr_bits =
	      32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
		    0x3ff);
	  } else {	// x < 2^32
	    tmp1.d = (double) (C1_lo);	// exact conversion
	    x_nr_bits =
	      ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	  }
	} else {	// if x < 2^53
	  tmp1.d = (double) C1_lo;	// exact conversion
	  x_nr_bits =
	    ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
	tmp1.d = (double) C1_hi;	// exact conversion
	x_nr_bits =
	  64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
      q1 = nr_digits[x_nr_bits].digits;
      if (q1 == 0) {
	q1 = nr_digits[x_nr_bits].digits1;
	if (C1_hi > nr_digits[x_nr_bits].threshold_hi ||
	    (C1_hi == nr_digits[x_nr_bits].threshold_hi &&
	     C1_lo >= nr_digits[x_nr_bits].threshold_lo))
	  q1++;
      }
      // return (C1 * 10^scale) * 10^(x_exp - scale)
      // where scale = min (P34-q1, x_exp-y_exp)  
      scale = P34 - q1;
      ind = (x_exp - y_exp) >> 49;
      if (ind < scale)
	scale = ind;
      if (scale == 0) {
	res.w[1] = x.w[1];
	res.w[0] = x.w[0];
      } else if (q1 <= 19) {	// x fits in 64 bits  
	if (scale <= 19) {	// 10^scale fits in 64 bits
	  // 64 x 64 C1_lo * ten2k64[scale] 
	  __mul_64x64_to_128MACH (res, C1_lo, ten2k64[scale]);
	} else {	// 10^scale fits in 128 bits
	  // 64 x 128 C1_lo * ten2k128[scale - 20]
	  __mul_128x64_to_128 (res, C1_lo, ten2k128[scale - 20]);
	}
      } else {	// x fits in 128 bits, but 10^scale must fit in 64 bits
	// 64 x 128 ten2k64[scale] * C1
	C1.w[1] = C1_hi;
	C1.w[0] = C1_lo;
	__mul_128x64_to_128 (res, ten2k64[scale], C1);
      }
      // subtract scale from the exponent
      x_exp = x_exp - ((UINT64) scale << 49);
      res.w[1] = res.w[1] | x_sign | x_exp;
    }
    BID_SWAP128 (res);
    BID_RETURN (res);
  } else {	// x and y are not canonical, not special, and are not zero
    // note that the result may still be zero, and then it has to have the
    // preferred exponent
    if (x_exp < y_exp) {	// if exp_x < exp_y then swap x and y 
      tmp_sign = x_sign;
      tmp_exp = x_exp;
      tmp_signif_hi = C1_hi;
      tmp_signif_lo = C1_lo;
      x_sign = y_sign;
      x_exp = y_exp;
      C1_hi = C2_hi;
      C1_lo = C2_lo;
      y_sign = tmp_sign;
      y_exp = tmp_exp;
      C2_hi = tmp_signif_hi;
      C2_lo = tmp_signif_lo;
    }
    // q1 = nr. of decimal digits in x
    //  determine first the nr. of bits in x
    if (C1_hi == 0) {	// x_bits is the nr. of bits in C1_lo
      if (C1_lo >= 0x0020000000000000ull) {	// x >= 2^53
	//split the 64-bit value in two 32-bit halves to avoid rounding errors
	if (C1_lo >= 0x0000000100000000ull) {	// x >= 2^32
	  tmp1.d = (double) (C1_lo >> 32);	// exact conversion
	  x_nr_bits =
	    32 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	} else {	// x < 2^32
	  tmp1.d = (double) (C1_lo);	// exact conversion
	  x_nr_bits =
	    ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// if x < 2^53
	tmp1.d = (double) C1_lo;	// exact conversion
	x_nr_bits =
	  ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else {	// C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
      tmp1.d = (double) C1_hi;	// exact conversion
      x_nr_bits =
	64 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }

    q1 = nr_digits[x_nr_bits].digits;
    if (q1 == 0) {
      q1 = nr_digits[x_nr_bits].digits1;
      if (C1_hi > nr_digits[x_nr_bits].threshold_hi ||
	  (C1_hi == nr_digits[x_nr_bits].threshold_hi &&
	   C1_lo >= nr_digits[x_nr_bits].threshold_lo))
	q1++;
    }
    // q2 = nr. of decimal digits in y
    //  determine first the nr. of bits in y (y_nr_bits)
    if (C2_hi == 0) {	// y_bits is the nr. of bits in C2_lo
      if (C2_lo >= 0x0020000000000000ull) {	// y >= 2^53
	//split the 64-bit value in two 32-bit halves to avoid rounding errors
	if (C2_lo >= 0x0000000100000000ull) {	// y >= 2^32
	  tmp2.d = (double) (C2_lo >> 32);	// exact conversion
	  y_nr_bits =
	    32 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
	} else {	// y < 2^32
	  tmp2.d = (double) (C2_lo);	// exact conversion
	  y_nr_bits =
	    ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// if y < 2^53
	tmp2.d = (double) C2_lo;	// exact conversion
	y_nr_bits =
	  ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else {	// C2_hi != 0 => nr. bits = 64 + nr_bits (C2_hi)
      tmp2.d = (double) C2_hi;	// exact conversion
      y_nr_bits =
	64 + ((((unsigned int) (tmp2.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }

    q2 = nr_digits[y_nr_bits].digits;
    if (q2 == 0) {
      q2 = nr_digits[y_nr_bits].digits1;
      if (C2_hi > nr_digits[y_nr_bits].threshold_hi ||
	  (C2_hi == nr_digits[y_nr_bits].threshold_hi &&
	   C2_lo >= nr_digits[y_nr_bits].threshold_lo))
	q2++;
    }

    delta = q1 + (int) (x_exp >> 49) - q2 - (int) (y_exp >> 49);

    if (delta >= P34) {
      // round the result directly because 0 < C2 < ulp (C1 * 10^(x_exp-e2))
      // n = C1 * 10^e1 or n = C1 +/- 10^(q1-P34)) * 10^e1
      // the result is inexact; the preferred exponent is the least possible

      if (delta >= P34 + 1) {
	// for RN the result is the operand with the larger magnitude,
	// possibly scaled up by 10^(P34-q1)
	// an overflow cannot occur in this case (rounding to nearest)
	if (q1 < P34) {	// scale C1 up by 10^(P34-q1)
	  // Note: because delta >= P34+1 it is certain that 
	  //     x_exp - ((UINT64)scale << 49) will stay above e_min
	  scale = P34 - q1;
	  if (q1 <= 19) {	// C1 fits in 64 bits
	    // 1 <= q1 <= 19 => 15 <= scale <= 33
	    if (scale <= 19) {	// 10^scale fits in 64 bits
	      __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
	    } else {	// if 20 <= scale <= 33
	      // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
	      // (C1 * 10^(scale-19)) fits in 64 bits
	      C1_lo = C1_lo * ten2k64[scale - 19];
	      __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
	    }
	  } else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
	    // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits
	    C1.w[1] = C1_hi;
	    C1.w[0] = C1_lo;
	    // C1 = ten2k64[P34 - q1] * C1
	    __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
	  }
	  x_exp = x_exp - ((UINT64) scale << 49);
	  C1_hi = C1.w[1];
	  C1_lo = C1.w[0];
	}
	// some special cases arise: if delta = P34 + 1 and C1 = 10^(P34-1) 
	// (after scaling) and x_sign != y_sign and C2 > 5*10^(q2-1) => 
	// subtract 1 ulp
	// Note: do this only for rounding to nearest; for other rounding 
	// modes the correction will be applied next
	if ((rnd_mode == ROUNDING_TO_NEAREST
	     || rnd_mode == ROUNDING_TIES_AWAY) && delta == (P34 + 1)
	    && C1_hi == 0x0000314dc6448d93ull
	    && C1_lo == 0x38c15b0a00000000ull && x_sign != y_sign
	    && ((q2 <= 19 && C2_lo > midpoint64[q2 - 1]) || (q2 >= 20
							     && (C2_hi >
								 midpoint128
								 [q2 -
								  20].
								 w[1]
								 ||
								 (C2_hi
								  ==
								  midpoint128
								  [q2 -
								   20].
								  w[1]
								  &&
								  C2_lo
								  >
								  midpoint128
								  [q2 -
								   20].
								  w
								  [0])))))
	{
	  // C1 = 10^34 - 1 and decrement x_exp by 1 (no underflow possible)
	  C1_hi = 0x0001ed09bead87c0ull;
	  C1_lo = 0x378d8e63ffffffffull;
	  x_exp = x_exp - EXP_P1;
	}
	if (rnd_mode != ROUNDING_TO_NEAREST) {
	  if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) ||
	      (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) {
	    // add 1 ulp and then check for overflow
	    C1_lo = C1_lo + 1;
	    if (C1_lo == 0) {	// rounding overflow in the low 64 bits
	      C1_hi = C1_hi + 1;
	    }
	    if (C1_hi == 0x0001ed09bead87c0ull
		&& C1_lo == 0x378d8e6400000000ull) {
	      // C1 = 10^34 => rounding overflow
	      C1_hi = 0x0000314dc6448d93ull;
	      C1_lo = 0x38c15b0a00000000ull;	// 10^33
	      x_exp = x_exp + EXP_P1;
	      if (x_exp == EXP_MAX_P1) {	// overflow
		C1_hi = 0x7800000000000000ull;	// +inf
		C1_lo = 0x0ull;
		x_exp = 0;	// x_sign is preserved
		// set overflow flag (the inexact flag was set too)
		*pfpsf |= OVERFLOW_EXCEPTION;
	      }
	    }
	  } else if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign) ||
		     (rnd_mode == ROUNDING_UP && x_sign && !y_sign) ||
		     (rnd_mode == ROUNDING_TO_ZERO
		      && x_sign != y_sign)) {
	    // subtract 1 ulp from C1
	    // Note: because delta >= P34 + 1 the result cannot be zero
	    C1_lo = C1_lo - 1;
	    if (C1_lo == 0xffffffffffffffffull)
	      C1_hi = C1_hi - 1;
	    // if the coefficient is 10^33 - 1 then make it 10^34 - 1 and 
	    // decrease the exponent by 1 (because delta >= P34 + 1 the
	    // exponent will not become less than e_min)
	    // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff
	    // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff
	    if (C1_hi == 0x0000314dc6448d93ull
		&& C1_lo == 0x38c15b09ffffffffull) {
	      // make C1 = 10^34  - 1
	      C1_hi = 0x0001ed09bead87c0ull;
	      C1_lo = 0x378d8e63ffffffffull;
	      x_exp = x_exp - EXP_P1;
	    }
	  } else {
	    ;	// the result is already correct
	  }
	}
	// set the inexact flag
	*pfpsf |= INEXACT_EXCEPTION;
	// assemble the result
	res.w[1] = x_sign | x_exp | C1_hi;
	res.w[0] = C1_lo;
      } else {	// delta = P34 
	// in most cases, the smaller operand may be < or = or > 1/2 ulp of the
	// larger operand
	// however, the case C1 = 10^(q1-1) and x_sign != y_sign is special due
	// to accuracy loss after subtraction, and will be treated separately
	if (x_sign == y_sign || (q1 <= 20
				 && (C1_hi != 0
				     || C1_lo != ten2k64[q1 - 1]))
	    || (q1 >= 21 && (C1_hi != ten2k128[q1 - 21].w[1]
			     || C1_lo != ten2k128[q1 - 21].w[0]))) {
	  // if x_sign == y_sign or C1 != 10^(q1-1)
	  // compare C2 with 1/2 ulp = 5 * 10^(q2-1), the latter read from table
	  // Note: cases q1<=19 and q1>=20 can be coalesced at some latency cost
	  if (q2 <= 19) {	// C2 and 5*10^(q2-1) both fit in 64 bits
	    halfulp64 = midpoint64[q2 - 1];	// 5 * 10^(q2-1)
	    if (C2_lo < halfulp64) {	// n2 < 1/2 ulp (n1)
	      // for RN the result is the operand with the larger magnitude, 
	      // possibly scaled up by 10^(P34-q1)
	      // an overflow cannot occur in this case (rounding to nearest)
	      if (q1 < P34) {	// scale C1 up by 10^(P34-q1)
		// Note: because delta = P34 it is certain that
		//     x_exp - ((UINT64)scale << 49) will stay above e_min
		scale = P34 - q1;
		if (q1 <= 19) {	// C1 fits in 64 bits
		  // 1 <= q1 <= 19 => 15 <= scale <= 33
		  if (scale <= 19) {	// 10^scale fits in 64 bits
		    __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
		  } else {	// if 20 <= scale <= 33
		    // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
		    // (C1 * 10^(scale-19)) fits in 64 bits
		    C1_lo = C1_lo * ten2k64[scale - 19];
		    __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
		  }
		} else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
		  // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits
		  C1.w[1] = C1_hi;
		  C1.w[0] = C1_lo;
		  // C1 = ten2k64[P34 - q1] * C1
		  __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
		}
		x_exp = x_exp - ((UINT64) scale << 49);
		C1_hi = C1.w[1];
		C1_lo = C1.w[0];
	      }
	      if (rnd_mode != ROUNDING_TO_NEAREST) {
		if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) ||
		    (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) {
		  // add 1 ulp and then check for overflow
		  C1_lo = C1_lo + 1;
		  if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		    C1_hi = C1_hi + 1;
		  }
		  if (C1_hi == 0x0001ed09bead87c0ull
		      && C1_lo == 0x378d8e6400000000ull) {
		    // C1 = 10^34 => rounding overflow
		    C1_hi = 0x0000314dc6448d93ull;
		    C1_lo = 0x38c15b0a00000000ull;	// 10^33
		    x_exp = x_exp + EXP_P1;
		    if (x_exp == EXP_MAX_P1) {	// overflow
		      C1_hi = 0x7800000000000000ull;	// +inf
		      C1_lo = 0x0ull;
		      x_exp = 0;	// x_sign is preserved
		      // set overflow flag (the inexact flag was set too)
		      *pfpsf |= OVERFLOW_EXCEPTION;
		    }
		  }
		} else
		  if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign)
		      || (rnd_mode == ROUNDING_UP && x_sign && !y_sign)
		      || (rnd_mode == ROUNDING_TO_ZERO
			  && x_sign != y_sign)) {
		  // subtract 1 ulp from C1
		  // Note: because delta >= P34 + 1 the result cannot be zero
		  C1_lo = C1_lo - 1;
		  if (C1_lo == 0xffffffffffffffffull)
		    C1_hi = C1_hi - 1;
		  // if the coefficient is 10^33-1 then make it 10^34-1 and 
		  // decrease the exponent by 1 (because delta >= P34 + 1 the
		  // exponent will not become less than e_min)
		  // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff
		  // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff
		  if (C1_hi == 0x0000314dc6448d93ull
		      && C1_lo == 0x38c15b09ffffffffull) {
		    // make C1 = 10^34  - 1
		    C1_hi = 0x0001ed09bead87c0ull;
		    C1_lo = 0x378d8e63ffffffffull;
		    x_exp = x_exp - EXP_P1;
		  }
		} else {
		  ;	// the result is already correct
		}
	      }
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // assemble the result
	      res.w[1] = x_sign | x_exp | C1_hi;
	      res.w[0] = C1_lo;
	    } else if ((C2_lo == halfulp64)
		       && (q1 < P34 || ((C1_lo & 0x1) == 0))) {
	      // n2 = 1/2 ulp (n1) and C1 is even
	      // the result is the operand with the larger magnitude,
	      // possibly scaled up by 10^(P34-q1)
	      // an overflow cannot occur in this case (rounding to nearest)
	      if (q1 < P34) {	// scale C1 up by 10^(P34-q1)
		// Note: because delta = P34 it is certain that
		//     x_exp - ((UINT64)scale << 49) will stay above e_min
		scale = P34 - q1;
		if (q1 <= 19) {	// C1 fits in 64 bits
		  // 1 <= q1 <= 19 => 15 <= scale <= 33
		  if (scale <= 19) {	// 10^scale fits in 64 bits
		    __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
		  } else {	// if 20 <= scale <= 33 
		    // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
		    // (C1 * 10^(scale-19)) fits in 64 bits  
		    C1_lo = C1_lo * ten2k64[scale - 19];
		    __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
		  }
		} else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
		  // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits 
		  C1.w[1] = C1_hi;
		  C1.w[0] = C1_lo;
		  // C1 = ten2k64[P34 - q1] * C1 
		  __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
		}
		x_exp = x_exp - ((UINT64) scale << 49);
		C1_hi = C1.w[1];
		C1_lo = C1.w[0];
	      }
	      if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign == y_sign
		   && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_TIES_AWAY
					  && x_sign == y_sign)
		  || (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)
		  || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign)) {
		// add 1 ulp and then check for overflow
		C1_lo = C1_lo + 1;
		if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		  C1_hi = C1_hi + 1;
		}
		if (C1_hi == 0x0001ed09bead87c0ull
		    && C1_lo == 0x378d8e6400000000ull) {
		  // C1 = 10^34 => rounding overflow
		  C1_hi = 0x0000314dc6448d93ull;
		  C1_lo = 0x38c15b0a00000000ull;	// 10^33
		  x_exp = x_exp + EXP_P1;
		  if (x_exp == EXP_MAX_P1) {	// overflow
		    C1_hi = 0x7800000000000000ull;	// +inf
		    C1_lo = 0x0ull;
		    x_exp = 0;	// x_sign is preserved
		    // set overflow flag (the inexact flag was set too)
		    *pfpsf |= OVERFLOW_EXCEPTION;
		  }
		}
	      } else
		if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign
		     && (C1_lo & 0x01)) || (rnd_mode == ROUNDING_DOWN
					    && !x_sign && y_sign)
		    || (rnd_mode == ROUNDING_UP && x_sign && !y_sign)
		    || (rnd_mode == ROUNDING_TO_ZERO
			&& x_sign != y_sign)) {
		// subtract 1 ulp from C1
		// Note: because delta >= P34 + 1 the result cannot be zero
		C1_lo = C1_lo - 1;
		if (C1_lo == 0xffffffffffffffffull)
		  C1_hi = C1_hi - 1;
		// if the coefficient is 10^33 - 1 then make it 10^34 - 1
		// and decrease the exponent by 1 (because delta >= P34 + 1
		// the exponent will not become less than e_min)
		// 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff
		// 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff
		if (C1_hi == 0x0000314dc6448d93ull
		    && C1_lo == 0x38c15b09ffffffffull) {
		  // make C1 = 10^34  - 1
		  C1_hi = 0x0001ed09bead87c0ull;
		  C1_lo = 0x378d8e63ffffffffull;
		  x_exp = x_exp - EXP_P1;
		}
	      } else {
		;	// the result is already correct
	      }
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // assemble the result 
	      res.w[1] = x_sign | x_exp | C1_hi;
	      res.w[0] = C1_lo;
	    } else {	// if C2_lo > halfulp64 || 
	      // (C2_lo == halfulp64 && q1 == P34 && ((C1_lo & 0x1) == 1)), i.e.
	      // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd
	      // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0
	      if (q1 < P34) {	// then 1 ulp = 10^(e1+q1-P34) < 10^e1
		// Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1
		// because q1 < P34 we must first replace C1 by 
		// C1 * 10^(P34-q1), and must decrease the exponent by 
		// (P34-q1) (it will still be at least e_min)
		scale = P34 - q1;
		if (q1 <= 19) {	// C1 fits in 64 bits
		  // 1 <= q1 <= 19 => 15 <= scale <= 33
		  if (scale <= 19) {	// 10^scale fits in 64 bits
		    __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
		  } else {	// if 20 <= scale <= 33
		    // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
		    // (C1 * 10^(scale-19)) fits in 64 bits
		    C1_lo = C1_lo * ten2k64[scale - 19];
		    __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
		  }
		} else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
		  // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits
		  C1.w[1] = C1_hi;
		  C1.w[0] = C1_lo;
		  // C1 = ten2k64[P34 - q1] * C1
		  __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
		}
		x_exp = x_exp - ((UINT64) scale << 49);
		C1_hi = C1.w[1];
		C1_lo = C1.w[0];
		// check for rounding overflow
		if (C1_hi == 0x0001ed09bead87c0ull
		    && C1_lo == 0x378d8e6400000000ull) {
		  // C1 = 10^34 => rounding overflow 
		  C1_hi = 0x0000314dc6448d93ull;
		  C1_lo = 0x38c15b0a00000000ull;	// 10^33
		  x_exp = x_exp + EXP_P1;
		}
	      }
	      if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign)
		  || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign
		      && C2_lo != halfulp64)
		  || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign)
		  || (rnd_mode == ROUNDING_UP && x_sign && !y_sign)
		  || (rnd_mode == ROUNDING_TO_ZERO
		      && x_sign != y_sign)) {
		// the result is x - 1
		// for RN n1 * n2 < 0; underflow not possible
		C1_lo = C1_lo - 1;
		if (C1_lo == 0xffffffffffffffffull)
		  C1_hi--;
		// check if we crossed into the lower decade
		if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) {	// 10^33 - 1
		  C1_hi = 0x0001ed09bead87c0ull;	// 10^34 - 1
		  C1_lo = 0x378d8e63ffffffffull;
		  x_exp = x_exp - EXP_P1;	// no underflow, because n1 >> n2
		}
	      } else
		if ((rnd_mode == ROUNDING_TO_NEAREST
		     && x_sign == y_sign)
		    || (rnd_mode == ROUNDING_TIES_AWAY
			&& x_sign == y_sign)
		    || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign)
		    || (rnd_mode == ROUNDING_UP && !x_sign
			&& !y_sign)) {
		// the result is x + 1
		// for RN x_sign = y_sign, i.e. n1*n2 > 0
		C1_lo = C1_lo + 1;
		if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		  C1_hi = C1_hi + 1;
		}
		if (C1_hi == 0x0001ed09bead87c0ull
		    && C1_lo == 0x378d8e6400000000ull) {
		  // C1 = 10^34 => rounding overflow
		  C1_hi = 0x0000314dc6448d93ull;
		  C1_lo = 0x38c15b0a00000000ull;	// 10^33
		  x_exp = x_exp + EXP_P1;
		  if (x_exp == EXP_MAX_P1) {	// overflow
		    C1_hi = 0x7800000000000000ull;	// +inf
		    C1_lo = 0x0ull;
		    x_exp = 0;	// x_sign is preserved
		    // set the overflow flag
		    *pfpsf |= OVERFLOW_EXCEPTION;
		  }
		}
	      } else {
		;	// the result is x
	      }
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // assemble the result
	      res.w[1] = x_sign | x_exp | C1_hi;
	      res.w[0] = C1_lo;
	    }
	  } else {	// if q2 >= 20 then 5*10^(q2-1) and C2 (the latter in 
	    // most cases) fit only in more than 64 bits
	    halfulp128 = midpoint128[q2 - 20];	// 5 * 10^(q2-1)
	    if ((C2_hi < halfulp128.w[1])
		|| (C2_hi == halfulp128.w[1]
		    && C2_lo < halfulp128.w[0])) {
	      // n2 < 1/2 ulp (n1)
	      // the result is the operand with the larger magnitude,
	      // possibly scaled up by 10^(P34-q1)
	      // an overflow cannot occur in this case (rounding to nearest)
	      if (q1 < P34) {	// scale C1 up by 10^(P34-q1)
		// Note: because delta = P34 it is certain that
		//     x_exp - ((UINT64)scale << 49) will stay above e_min
		scale = P34 - q1;
		if (q1 <= 19) {	// C1 fits in 64 bits
		  // 1 <= q1 <= 19 => 15 <= scale <= 33
		  if (scale <= 19) {	// 10^scale fits in 64 bits
		    __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
		  } else {	// if 20 <= scale <= 33 
		    // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
		    // (C1 * 10^(scale-19)) fits in 64 bits  
		    C1_lo = C1_lo * ten2k64[scale - 19];
		    __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
		  }
		} else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
		  // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits 
		  C1.w[1] = C1_hi;
		  C1.w[0] = C1_lo;
		  // C1 = ten2k64[P34 - q1] * C1 
		  __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
		}
		C1_hi = C1.w[1];
		C1_lo = C1.w[0];
		x_exp = x_exp - ((UINT64) scale << 49);
	      }
	      if (rnd_mode != ROUNDING_TO_NEAREST) {
		if ((rnd_mode == ROUNDING_DOWN && x_sign && y_sign) ||
		    (rnd_mode == ROUNDING_UP && !x_sign && !y_sign)) {
		  // add 1 ulp and then check for overflow
		  C1_lo = C1_lo + 1;
		  if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		    C1_hi = C1_hi + 1;
		  }
		  if (C1_hi == 0x0001ed09bead87c0ull
		      && C1_lo == 0x378d8e6400000000ull) {
		    // C1 = 10^34 => rounding overflow
		    C1_hi = 0x0000314dc6448d93ull;
		    C1_lo = 0x38c15b0a00000000ull;	// 10^33
		    x_exp = x_exp + EXP_P1;
		    if (x_exp == EXP_MAX_P1) {	// overflow
		      C1_hi = 0x7800000000000000ull;	// +inf
		      C1_lo = 0x0ull;
		      x_exp = 0;	// x_sign is preserved
		      // set overflow flag (the inexact flag was set too)
		      *pfpsf |= OVERFLOW_EXCEPTION;
		    }
		  }
		} else
		  if ((rnd_mode == ROUNDING_DOWN && !x_sign && y_sign)
		      || (rnd_mode == ROUNDING_UP && x_sign && !y_sign)
		      || (rnd_mode == ROUNDING_TO_ZERO
			  && x_sign != y_sign)) {
		  // subtract 1 ulp from C1
		  // Note: because delta >= P34 + 1 the result cannot be zero
		  C1_lo = C1_lo - 1;
		  if (C1_lo == 0xffffffffffffffffull)
		    C1_hi = C1_hi - 1;
		  // if the coefficient is 10^33-1 then make it 10^34-1 and
		  // decrease the exponent by 1 (because delta >= P34 + 1 the
		  // exponent will not become less than e_min)
		  // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff
		  // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff
		  if (C1_hi == 0x0000314dc6448d93ull
		      && C1_lo == 0x38c15b09ffffffffull) {
		    // make C1 = 10^34  - 1
		    C1_hi = 0x0001ed09bead87c0ull;
		    C1_lo = 0x378d8e63ffffffffull;
		    x_exp = x_exp - EXP_P1;
		  }
		} else {
		  ;	// the result is already correct
		}
	      }
	      // set the inexact flag 
	      *pfpsf |= INEXACT_EXCEPTION;
	      // assemble the result 
	      res.w[1] = x_sign | x_exp | C1_hi;
	      res.w[0] = C1_lo;
	    } else if ((C2_hi == halfulp128.w[1]
			&& C2_lo == halfulp128.w[0])
		       && (q1 < P34 || ((C1_lo & 0x1) == 0))) {
	      // midpoint & lsb in C1 is 0
	      // n2 = 1/2 ulp (n1) and C1 is even
	      // the result is the operand with the larger magnitude,
	      // possibly scaled up by 10^(P34-q1)
	      // an overflow cannot occur in this case (rounding to nearest)
	      if (q1 < P34) {	// scale C1 up by 10^(P34-q1)
		// Note: because delta = P34 it is certain that
		//     x_exp - ((UINT64)scale << 49) will stay above e_min
		scale = P34 - q1;
		if (q1 <= 19) {	// C1 fits in 64 bits
		  // 1 <= q1 <= 19 => 15 <= scale <= 33
		  if (scale <= 19) {	// 10^scale fits in 64 bits
		    __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
		  } else {	// if 20 <= scale <= 33
		    // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
		    // (C1 * 10^(scale-19)) fits in 64 bits
		    C1_lo = C1_lo * ten2k64[scale - 19];
		    __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
		  }
		} else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
		  // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits
		  C1.w[1] = C1_hi;
		  C1.w[0] = C1_lo;
		  // C1 = ten2k64[P34 - q1] * C1
		  __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
		}
		x_exp = x_exp - ((UINT64) scale << 49);
		C1_hi = C1.w[1];
		C1_lo = C1.w[0];
	      }
	      if (rnd_mode != ROUNDING_TO_NEAREST) {
		if ((rnd_mode == ROUNDING_TIES_AWAY && x_sign == y_sign)
		    || (rnd_mode == ROUNDING_UP && !y_sign)) {
		  // add 1 ulp and then check for overflow
		  C1_lo = C1_lo + 1;
		  if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		    C1_hi = C1_hi + 1;
		  }
		  if (C1_hi == 0x0001ed09bead87c0ull
		      && C1_lo == 0x378d8e6400000000ull) {
		    // C1 = 10^34 => rounding overflow
		    C1_hi = 0x0000314dc6448d93ull;
		    C1_lo = 0x38c15b0a00000000ull;	// 10^33
		    x_exp = x_exp + EXP_P1;
		    if (x_exp == EXP_MAX_P1) {	// overflow
		      C1_hi = 0x7800000000000000ull;	// +inf
		      C1_lo = 0x0ull;
		      x_exp = 0;	// x_sign is preserved
		      // set overflow flag (the inexact flag was set too)
		      *pfpsf |= OVERFLOW_EXCEPTION;
		    }
		  }
		} else if ((rnd_mode == ROUNDING_DOWN && y_sign)
			   || (rnd_mode == ROUNDING_TO_ZERO
			       && x_sign != y_sign)) {
		  // subtract 1 ulp from C1
		  // Note: because delta >= P34 + 1 the result cannot be zero
		  C1_lo = C1_lo - 1;
		  if (C1_lo == 0xffffffffffffffffull)
		    C1_hi = C1_hi - 1;
		  // if the coefficient is 10^33 - 1 then make it 10^34 - 1
		  // and decrease the exponent by 1 (because delta >= P34 + 1
		  // the exponent will not become less than e_min)
		  // 10^33 - 1 = 0x0000314dc6448d9338c15b09ffffffff
		  // 10^34 - 1 = 0x0001ed09bead87c0378d8e63ffffffff
		  if (C1_hi == 0x0000314dc6448d93ull
		      && C1_lo == 0x38c15b09ffffffffull) {
		    // make C1 = 10^34  - 1
		    C1_hi = 0x0001ed09bead87c0ull;
		    C1_lo = 0x378d8e63ffffffffull;
		    x_exp = x_exp - EXP_P1;
		  }
		} else {
		  ;	// the result is already correct
		}
	      }
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // assemble the result
	      res.w[1] = x_sign | x_exp | C1_hi;
	      res.w[0] = C1_lo;
	    } else {	// if C2 > halfulp128 ||
	      // (C2 == halfulp128 && q1 == P34 && ((C1 & 0x1) == 1)), i.e.
	      // 1/2 ulp(n1) < n2 < 1 ulp(n1) or n2 = 1/2 ulp(n1) and C1 odd
	      // res = x+1 ulp if n1*n2 > 0 and res = x-1 ulp if n1*n2 < 0
	      if (q1 < P34) {	// then 1 ulp = 10^(e1+q1-P34) < 10^e1
		// Note: if (q1 == P34) then 1 ulp = 10^(e1+q1-P34) = 10^e1
		// because q1 < P34 we must first replace C1 by C1*10^(P34-q1),
		// and must decrease the exponent by (P34-q1) (it will still be
		// at least e_min)
		scale = P34 - q1;
		if (q1 <= 19) {	// C1 fits in 64 bits
		  // 1 <= q1 <= 19 => 15 <= scale <= 33
		  if (scale <= 19) {	// 10^scale fits in 64 bits
		    __mul_64x64_to_128MACH (C1, ten2k64[scale], C1_lo);
		  } else {	// if 20 <= scale <= 33
		    // C1 * 10^scale = (C1 * 10^(scale-19)) * 10^19 where
		    // (C1 * 10^(scale-19)) fits in 64 bits
		    C1_lo = C1_lo * ten2k64[scale - 19];
		    __mul_64x64_to_128MACH (C1, ten2k64[19], C1_lo);
		  }
		} else {	//if 20 <= q1 <= 33=P34-1 then C1 fits only in 128 bits
		  // => 1 <= P34 - q1 <= 14 so 10^(P34-q1) fits in 64 bits
		  C1.w[1] = C1_hi;
		  C1.w[0] = C1_lo;
		  // C1 = ten2k64[P34 - q1] * C1
		  __mul_128x64_to_128 (C1, ten2k64[P34 - q1], C1);
		}
		C1_hi = C1.w[1];
		C1_lo = C1.w[0];
		x_exp = x_exp - ((UINT64) scale << 49);
	      }
	      if ((rnd_mode == ROUNDING_TO_NEAREST && x_sign != y_sign)
		  || (rnd_mode == ROUNDING_TIES_AWAY && x_sign != y_sign
		      && (C2_hi != halfulp128.w[1]
			  || C2_lo != halfulp128.w[0]))
		  || (rnd_mode == ROUNDING_DOWN && !x_sign && y_sign)
		  || (rnd_mode == ROUNDING_UP && x_sign && !y_sign)
		  || (rnd_mode == ROUNDING_TO_ZERO
		      && x_sign != y_sign)) {
		// the result is x - 1
		// for RN n1 * n2 < 0; underflow not possible
		C1_lo = C1_lo - 1;
		if (C1_lo == 0xffffffffffffffffull)
		  C1_hi--;
		// check if we crossed into the lower decade
		if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) {	// 10^33 - 1
		  C1_hi = 0x0001ed09bead87c0ull;	// 10^34 - 1
		  C1_lo = 0x378d8e63ffffffffull;
		  x_exp = x_exp - EXP_P1;	// no underflow, because n1 >> n2
		}
	      } else
		if ((rnd_mode == ROUNDING_TO_NEAREST
		     && x_sign == y_sign)
		    || (rnd_mode == ROUNDING_TIES_AWAY
			&& x_sign == y_sign)
		    || (rnd_mode == ROUNDING_DOWN && x_sign && y_sign)
		    || (rnd_mode == ROUNDING_UP && !x_sign
			&& !y_sign)) {
		// the result is x + 1
		// for RN x_sign = y_sign, i.e. n1*n2 > 0
		C1_lo = C1_lo + 1;
		if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		  C1_hi = C1_hi + 1;
		}
		if (C1_hi == 0x0001ed09bead87c0ull
		    && C1_lo == 0x378d8e6400000000ull) {
		  // C1 = 10^34 => rounding overflow
		  C1_hi = 0x0000314dc6448d93ull;
		  C1_lo = 0x38c15b0a00000000ull;	// 10^33
		  x_exp = x_exp + EXP_P1;
		  if (x_exp == EXP_MAX_P1) {	// overflow
		    C1_hi = 0x7800000000000000ull;	// +inf
		    C1_lo = 0x0ull;
		    x_exp = 0;	// x_sign is preserved
		    // set the overflow flag
		    *pfpsf |= OVERFLOW_EXCEPTION;
		  }
		}
	      } else {
		;	// the result is x
	      }
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // assemble the result
	      res.w[1] = x_sign | x_exp | C1_hi;
	      res.w[0] = C1_lo;
	    }
	  }	// end q1 >= 20
	  // end case where C1 != 10^(q1-1)
	} else {	// C1 = 10^(q1-1) and x_sign != y_sign
	  // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34
	  // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 
	  // where x1 = q2 - 1, 0 <= x1 <= P34 - 1
	  // Because C1 = 10^(q1-1) and x_sign != y_sign, C' will have P34 
	  // digits and n = C' * 10^(e2+x1)
	  // If the result has P34+1 digits, redo the steps above with x1+1
	  // If the result has P34-1 digits or less, redo the steps above with 
	  // x1-1 but only if initially x1 >= 1
	  // NOTE: these two steps can be improved, e.g we could guess if
	  // P34+1 or P34-1 digits will be obtained by adding/subtracting 
	  // just the top 64 bits of the two operands
	  // The result cannot be zero, and it cannot overflow
	  x1 = q2 - 1;	// 0 <= x1 <= P34-1
	  // Calculate C1 * 10^(e1-e2-x1) where 1 <= e1-e2-x1 <= P34
	  // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1
	  scale = P34 - q1 + 1;	// scale=e1-e2-x1 = P34+1-q1; 1<=scale<=P34
	  // either C1 or 10^(e1-e2-x1) may not fit is 64 bits,
	  // but their product fits with certainty in 128 bits
	  if (scale >= 20) {	//10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does
	    __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]);
	  } else {	// if (scale >= 1
	    // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits
	    if (q1 <= 19) {	// C1 fits in 64 bits
	      __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]);
	    } else {	// q1 >= 20
	      C1.w[1] = C1_hi;
	      C1.w[0] = C1_lo;
	      __mul_128x64_to_128 (C1, ten2k64[scale], C1);
	    }
	  }
	  tmp64 = C1.w[0];	// C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1)

	  // now round C2 to q2-x1 = 1 decimal digit
	  // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1)
	  ind = x1 - 1;	// -1 <= ind <= P34 - 2
	  if (ind >= 0) {	// if (x1 >= 1)
	    C2.w[0] = C2_lo;
	    C2.w[1] = C2_hi;
	    if (ind <= 18) {
	      C2.w[0] = C2.w[0] + midpoint64[ind];
	      if (C2.w[0] < C2_lo)
		C2.w[1]++;
	    } else {	// 19 <= ind <= 32
	      C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0];
	      C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1];
	      if (C2.w[0] < C2_lo)
		C2.w[1]++;
	    }
	    // the approximation of 10^(-x1) was rounded up to 118 bits
	    __mul_128x128_to_256 (R256, C2, ten2mk128[ind]);	// R256 = C2*, f2*
	    // calculate C2* and f2*
	    // C2* is actually floor(C2*) in this case
	    // C2* and f2* need shifting and masking, as shown by
	    // shiftright128[] and maskhigh128[]
	    // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g.
	    // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
	    // if (0 < f2* < 10^(-x1)) then
	    //   if floor(C1+C2*) is even then C2* = floor(C2*) - logical right
	    //       shift; C2* has p decimal digits, correct by Prop. 1)
	    //   else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right
	    //       shift; C2* has p decimal digits, correct by Pr. 1)
	    // else
	    //   C2* = floor(C2*) (logical right shift; C has p decimal digits,
	    //       correct by Property 1)
	    // n = C2* * 10^(e2+x1)

	    if (ind <= 2) {
	      highf2star.w[1] = 0x0;
	      highf2star.w[0] = 0x0;	// low f2* ok
	    } else if (ind <= 21) {
	      highf2star.w[1] = 0x0;
	      highf2star.w[0] = R256.w[2] & maskhigh128[ind];	// low f2* ok
	    } else {
	      highf2star.w[1] = R256.w[3] & maskhigh128[ind];
	      highf2star.w[0] = R256.w[2];	// low f2* is ok
	    }
	    // shift right C2* by Ex-128 = shiftright128[ind]
	    if (ind >= 3) {
	      shift = shiftright128[ind];
	      if (shift < 64) {	// 3 <= shift <= 63
		R256.w[2] =
		  (R256.w[2] >> shift) | (R256.w[3] << (64 - shift));
		R256.w[3] = (R256.w[3] >> shift);
	      } else {	// 66 <= shift <= 102
		R256.w[2] = (R256.w[3] >> (shift - 64));
		R256.w[3] = 0x0ULL;
	      }
	    }
	    // redundant
	    is_inexact_lt_midpoint = 0;
	    is_inexact_gt_midpoint = 0;
	    is_midpoint_lt_even = 0;
	    is_midpoint_gt_even = 0;
	    // determine inexactness of the rounding of C2*
	    // (cannot be followed by a second rounding)
	    // if (0 < f2* - 1/2 < 10^(-x1)) then
	    //   the result is exact
	    // else (if f2* - 1/2 > T* then)
	    //   the result of is inexact
	    if (ind <= 2) {
	      if (R256.w[1] > 0x8000000000000000ull ||
		  (R256.w[1] == 0x8000000000000000ull
		   && R256.w[0] > 0x0ull)) {
		// f2* > 1/2 and the result may be exact
		tmp64A = R256.w[1] - 0x8000000000000000ull;	// f* - 1/2
		if ((tmp64A > ten2mk128trunc[ind].w[1]
		     || (tmp64A == ten2mk128trunc[ind].w[1]
			 && R256.w[0] >= ten2mk128trunc[ind].w[0]))) {
		  // set the inexact flag
		  *pfpsf |= INEXACT_EXCEPTION;
		  // this rounding is applied to C2 only!
		  // x_sign != y_sign
		  is_inexact_gt_midpoint = 1;
		}	// else the result is exact
		// rounding down, unless a midpoint in [ODD, EVEN]
	      } else {	// the result is inexact; f2* <= 1/2
		// set the inexact flag
		*pfpsf |= INEXACT_EXCEPTION;
		// this rounding is applied to C2 only!
		// x_sign != y_sign
		is_inexact_lt_midpoint = 1;
	      }
	    } else if (ind <= 21) {	// if 3 <= ind <= 21
	      if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0
					    && highf2star.w[0] >
					    onehalf128[ind])
		  || (highf2star.w[1] == 0x0
		      && highf2star.w[0] == onehalf128[ind]
		      && (R256.w[1] || R256.w[0]))) {
		// f2* > 1/2 and the result may be exact
		// Calculate f2* - 1/2
		tmp64A = highf2star.w[0] - onehalf128[ind];
		tmp64B = highf2star.w[1];
		if (tmp64A > highf2star.w[0])
		  tmp64B--;
		if (tmp64B || tmp64A
		    || R256.w[1] > ten2mk128trunc[ind].w[1]
		    || (R256.w[1] == ten2mk128trunc[ind].w[1]
			&& R256.w[0] > ten2mk128trunc[ind].w[0])) {
		  // set the inexact flag
		  *pfpsf |= INEXACT_EXCEPTION;
		  // this rounding is applied to C2 only!
		  // x_sign != y_sign
		  is_inexact_gt_midpoint = 1;
		}	// else the result is exact
	      } else {	// the result is inexact; f2* <= 1/2
		// set the inexact flag
		*pfpsf |= INEXACT_EXCEPTION;
		// this rounding is applied to C2 only!
		// x_sign != y_sign
		is_inexact_lt_midpoint = 1;
	      }
	    } else {	// if 22 <= ind <= 33
	      if (highf2star.w[1] > onehalf128[ind]
		  || (highf2star.w[1] == onehalf128[ind]
		      && (highf2star.w[0] || R256.w[1]
			  || R256.w[0]))) {
		// f2* > 1/2 and the result may be exact
		// Calculate f2* - 1/2
		// tmp64A = highf2star.w[0];
		tmp64B = highf2star.w[1] - onehalf128[ind];
		if (tmp64B || highf2star.w[0]
		    || R256.w[1] > ten2mk128trunc[ind].w[1]
		    || (R256.w[1] == ten2mk128trunc[ind].w[1]
			&& R256.w[0] > ten2mk128trunc[ind].w[0])) {
		  // set the inexact flag
		  *pfpsf |= INEXACT_EXCEPTION;
		  // this rounding is applied to C2 only!
		  // x_sign != y_sign
		  is_inexact_gt_midpoint = 1;
		}	// else the result is exact
	      } else {	// the result is inexact; f2* <= 1/2
		// set the inexact flag
		*pfpsf |= INEXACT_EXCEPTION;
		// this rounding is applied to C2 only!
		// x_sign != y_sign
		is_inexact_lt_midpoint = 1;
	      }
	    }
	    // check for midpoints after determining inexactness
	    if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0)
		&& (highf2star.w[0] == 0)
		&& (R256.w[1] < ten2mk128trunc[ind].w[1]
		    || (R256.w[1] == ten2mk128trunc[ind].w[1]
			&& R256.w[0] <= ten2mk128trunc[ind].w[0]))) {
	      // the result is a midpoint
	      if ((tmp64 + R256.w[2]) & 0x01) {	// MP in [EVEN, ODD]
		// if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0
		R256.w[2]--;
		if (R256.w[2] == 0xffffffffffffffffull)
		  R256.w[3]--;
		// this rounding is applied to C2 only!
		// x_sign != y_sign
		is_midpoint_lt_even = 1;
		is_inexact_lt_midpoint = 0;
		is_inexact_gt_midpoint = 0;
	      } else {
		// else MP in [ODD, EVEN]
		// this rounding is applied to C2 only!
		// x_sign != y_sign
		is_midpoint_gt_even = 1;
		is_inexact_lt_midpoint = 0;
		is_inexact_gt_midpoint = 0;
	      }
	    }
	  } else {	// if (ind == -1) only when x1 = 0
	    R256.w[2] = C2_lo;
	    R256.w[3] = C2_hi;
	    is_midpoint_lt_even = 0;
	    is_midpoint_gt_even = 0;
	    is_inexact_lt_midpoint = 0;
	    is_inexact_gt_midpoint = 0;
	  }
	  // and now subtract C1 * 10^(e1-e2-x1) - (C2 * 10^(-x1))rnd,P34
	  // because x_sign != y_sign this last operation is exact
	  C1.w[0] = C1.w[0] - R256.w[2];
	  C1.w[1] = C1.w[1] - R256.w[3];
	  if (C1.w[0] > tmp64)
	    C1.w[1]--;	// borrow
	  if (C1.w[1] >= 0x8000000000000000ull) {	// negative coefficient!
	    C1.w[0] = ~C1.w[0];
	    C1.w[0]++;
	    C1.w[1] = ~C1.w[1];
	    if (C1.w[0] == 0x0)
	      C1.w[1]++;
	    tmp_sign = y_sign;	// the result will have the sign of y
	  } else {
	    tmp_sign = x_sign;
	  }
	  // the difference has exactly P34 digits
	  x_sign = tmp_sign;
	  if (x1 >= 1)
	    y_exp = y_exp + ((UINT64) x1 << 49);
	  C1_hi = C1.w[1];
	  C1_lo = C1.w[0];
	  // general correction from RN to RA, RM, RP, RZ; result uses y_exp
	  if (rnd_mode != ROUNDING_TO_NEAREST) {
	    if ((!x_sign
		 && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint)
		     ||
		     ((rnd_mode == ROUNDING_TIES_AWAY
		       || rnd_mode == ROUNDING_UP)
		      && is_midpoint_gt_even))) || (x_sign
						    &&
						    ((rnd_mode ==
						      ROUNDING_DOWN
						      &&
						      is_inexact_lt_midpoint)
						     ||
						     ((rnd_mode ==
						       ROUNDING_TIES_AWAY
						       || rnd_mode ==
						       ROUNDING_DOWN)
						      &&
						      is_midpoint_gt_even))))
	    {
	      // C1 = C1 + 1
	      C1_lo = C1_lo + 1;
	      if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		C1_hi = C1_hi + 1;
	      }
	      if (C1_hi == 0x0001ed09bead87c0ull
		  && C1_lo == 0x378d8e6400000000ull) {
		// C1 = 10^34 => rounding overflow
		C1_hi = 0x0000314dc6448d93ull;
		C1_lo = 0x38c15b0a00000000ull;	// 10^33
		y_exp = y_exp + EXP_P1;
	      }
	    } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint)
		       &&
		       ((x_sign
			 && (rnd_mode == ROUNDING_UP
			     || rnd_mode == ROUNDING_TO_ZERO))
			|| (!x_sign
			    && (rnd_mode == ROUNDING_DOWN
				|| rnd_mode == ROUNDING_TO_ZERO)))) {
	      // C1 = C1 - 1
	      C1_lo = C1_lo - 1;
	      if (C1_lo == 0xffffffffffffffffull)
		C1_hi--;
	      // check if we crossed into the lower decade
	      if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) {	// 10^33 - 1
		C1_hi = 0x0001ed09bead87c0ull;	// 10^34 - 1
		C1_lo = 0x378d8e63ffffffffull;
		y_exp = y_exp - EXP_P1;
		// no underflow, because delta + q2 >= P34 + 1
	      }
	    } else {
	      ;	// exact, the result is already correct
	    }
	  }
	  // assemble the result
	  res.w[1] = x_sign | y_exp | C1_hi;
	  res.w[0] = C1_lo;
	}
      }	// end delta = P34
    } else {	// if (|delta| <= P34 - 1)
      if (delta >= 0) {	// if (0 <= delta <= P34 - 1)
	if (delta <= P34 - 1 - q2) {
	  // calculate C' directly; the result is exact
	  // in this case 1<=q1<=P34-1, 1<=q2<=P34-1 and 0 <= e1-e2 <= P34-2
	  // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the
	  // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits,
	  // but their product fits with certainty in 128 bits (actually in 113)
	  scale = delta - q1 + q2;	// scale = (int)(e1 >> 49) - (int)(e2 >> 49) 

	  if (scale >= 20) {	// 10^(e1-e2) does not fit in 64 bits, but C1 does
	    __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]);
	    C1_hi = C1.w[1];
	    C1_lo = C1.w[0];
	  } else if (scale >= 1) {
	    // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits 
	    if (q1 <= 19) {	// C1 fits in 64 bits
	      __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]);
	    } else {	// q1 >= 20
	      C1.w[1] = C1_hi;
	      C1.w[0] = C1_lo;
	      __mul_128x64_to_128 (C1, ten2k64[scale], C1);
	    }
	    C1_hi = C1.w[1];
	    C1_lo = C1.w[0];
	  } else {	// if (scale == 0) C1 is unchanged
	    C1.w[0] = C1_lo;	// C1.w[1] = C1_hi; 
	  }
	  // now add C2
	  if (x_sign == y_sign) {
	    // the result cannot overflow
	    C1_lo = C1_lo + C2_lo;
	    C1_hi = C1_hi + C2_hi;
	    if (C1_lo < C1.w[0])
	      C1_hi++;
	  } else {	// if x_sign != y_sign
	    C1_lo = C1_lo - C2_lo;
	    C1_hi = C1_hi - C2_hi;
	    if (C1_lo > C1.w[0])
	      C1_hi--;
	    // the result can be zero, but it cannot overflow
	    if (C1_lo == 0 && C1_hi == 0) {
	      // assemble the result
	      if (x_exp < y_exp)
		res.w[1] = x_exp;
	      else
		res.w[1] = y_exp;
	      res.w[0] = 0;
	      if (rnd_mode == ROUNDING_DOWN) {
		res.w[1] |= 0x8000000000000000ull;
	      }
	      BID_SWAP128 (res);
	      BID_RETURN (res);
	    }
	    if (C1_hi >= 0x8000000000000000ull) {	// negative coefficient!
	      C1_lo = ~C1_lo;
	      C1_lo++;
	      C1_hi = ~C1_hi;
	      if (C1_lo == 0x0)
		C1_hi++;
	      x_sign = y_sign;	// the result will have the sign of y
	    }
	  }
	  // assemble the result
	  res.w[1] = x_sign | y_exp | C1_hi;
	  res.w[0] = C1_lo;
	} else if (delta == P34 - q2) {
	  // calculate C' directly; the result may be inexact if it requires 
	  // P34+1 decimal digits; in this case the 'cutoff' point for addition
	  // is at the position of the lsb of C2, so 0 <= e1-e2 <= P34-1
	  // The coefficient of the result is C1 * 10^(e1-e2) + C2 and the
	  // exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits,
	  // but their product fits with certainty in 128 bits (actually in 113)
	  scale = delta - q1 + q2;	// scale = (int)(e1 >> 49) - (int)(e2 >> 49)
	  if (scale >= 20) {	// 10^(e1-e2) does not fit in 64 bits, but C1 does
	    __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]);
	  } else if (scale >= 1) {
	    // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits
	    if (q1 <= 19) {	// C1 fits in 64 bits
	      __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]);
	    } else {	// q1 >= 20
	      C1.w[1] = C1_hi;
	      C1.w[0] = C1_lo;
	      __mul_128x64_to_128 (C1, ten2k64[scale], C1);
	    }
	  } else {	// if (scale == 0) C1 is unchanged
	    C1.w[1] = C1_hi;
	    C1.w[0] = C1_lo;	// only the low part is necessary
	  }
	  C1_hi = C1.w[1];
	  C1_lo = C1.w[0];
	  // now add C2
	  if (x_sign == y_sign) {
	    // the result can overflow!
	    C1_lo = C1_lo + C2_lo;
	    C1_hi = C1_hi + C2_hi;
	    if (C1_lo < C1.w[0])
	      C1_hi++;
	    // test for overflow, possible only when C1 >= 10^34
	    if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) {	// C1 >= 10^34
	      // in this case q = P34 + 1 and x = q - P34 = 1, so multiply 
	      // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 
	      // decimal digits
	      // Calculate C'' = C' + 1/2 * 10^x
	      if (C1_lo >= 0xfffffffffffffffbull) {	// low half add has carry
		C1_lo = C1_lo + 5;
		C1_hi = C1_hi + 1;
	      } else {
		C1_lo = C1_lo + 5;
	      }
	      // the approximation of 10^(-1) was rounded up to 118 bits
	      // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129
	      // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128
	      C1.w[1] = C1_hi;
	      C1.w[0] = C1_lo;	// C''
	      ten2m1.w[1] = 0x1999999999999999ull;
	      ten2m1.w[0] = 0x9999999999999a00ull;
	      __mul_128x128_to_256 (P256, C1, ten2m1);	// P256 = C*, f*
	      // C* is actually floor(C*) in this case
	      // the top Ex = 128 bits of 10^(-1) are 
	      // T* = 0x00199999999999999999999999999999
	      // if (0 < f* < 10^(-x)) then
	      //   if floor(C*) is even then C = floor(C*) - logical right 
	      //       shift; C has p decimal digits, correct by Prop. 1)
	      //   else if floor(C*) is odd C = floor(C*) - 1 (logical right
	      //       shift; C has p decimal digits, correct by Pr. 1)
	      // else
	      //   C = floor(C*) (logical right shift; C has p decimal digits,
	      //       correct by Property 1)
	      // n = C * 10^(e2+x)
	      if ((P256.w[1] || P256.w[0])
		  && (P256.w[1] < 0x1999999999999999ull
		      || (P256.w[1] == 0x1999999999999999ull
			  && P256.w[0] <= 0x9999999999999999ull))) {
		// the result is a midpoint
		if (P256.w[2] & 0x01) {
		  is_midpoint_gt_even = 1;
		  // if floor(C*) is odd C = floor(C*) - 1; the result is not 0
		  P256.w[2]--;
		  if (P256.w[2] == 0xffffffffffffffffull)
		    P256.w[3]--;
		} else {
		  is_midpoint_lt_even = 1;
		}
	      }
	      // n = Cstar * 10^(e2+1)
	      y_exp = y_exp + EXP_P1;
	      // C* != 10^P because C* has P34 digits
	      // check for overflow
	      if (y_exp == EXP_MAX_P1
		  && (rnd_mode == ROUNDING_TO_NEAREST
		      || rnd_mode == ROUNDING_TIES_AWAY)) {
		// overflow for RN
		res.w[1] = x_sign | 0x7800000000000000ull;	// +/-inf
		res.w[0] = 0x0ull;
		// set the inexact flag
		*pfpsf |= INEXACT_EXCEPTION;
		// set the overflow flag
		*pfpsf |= OVERFLOW_EXCEPTION;
		BID_SWAP128 (res);
		BID_RETURN (res);
	      }
	      // if (0 < f* - 1/2 < 10^(-x)) then 
	      //   the result of the addition is exact 
	      // else 
	      //   the result of the addition is inexact
	      if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) {	// the result may be exact
		tmp64 = P256.w[1] - 0x8000000000000000ull;	// f* - 1/2
		if ((tmp64 > 0x1999999999999999ull
		     || (tmp64 == 0x1999999999999999ull
			 && P256.w[0] >= 0x9999999999999999ull))) {
		  // set the inexact flag
		  *pfpsf |= INEXACT_EXCEPTION;
		  is_inexact = 1;
		}	// else the result is exact
	      } else {	// the result is inexact
		// set the inexact flag
		*pfpsf |= INEXACT_EXCEPTION;
		is_inexact = 1;
	      }
	      C1_hi = P256.w[3];
	      C1_lo = P256.w[2];
	      if (!is_midpoint_gt_even && !is_midpoint_lt_even) {
		is_inexact_lt_midpoint = is_inexact
		  && (P256.w[1] & 0x8000000000000000ull);
		is_inexact_gt_midpoint = is_inexact
		  && !(P256.w[1] & 0x8000000000000000ull);
	      }
	      // general correction from RN to RA, RM, RP, RZ; 
	      // result uses y_exp
	      if (rnd_mode != ROUNDING_TO_NEAREST) {
		if ((!x_sign
		     &&
		     ((rnd_mode == ROUNDING_UP
		       && is_inexact_lt_midpoint)
		      ||
		      ((rnd_mode == ROUNDING_TIES_AWAY
			|| rnd_mode == ROUNDING_UP)
		       && is_midpoint_gt_even))) || (x_sign
						     &&
						     ((rnd_mode ==
						       ROUNDING_DOWN
						       &&
						       is_inexact_lt_midpoint)
						      ||
						      ((rnd_mode ==
							ROUNDING_TIES_AWAY
							|| rnd_mode ==
							ROUNDING_DOWN)
						       &&
						       is_midpoint_gt_even))))
		{
		  // C1 = C1 + 1
		  C1_lo = C1_lo + 1;
		  if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		    C1_hi = C1_hi + 1;
		  }
		  if (C1_hi == 0x0001ed09bead87c0ull
		      && C1_lo == 0x378d8e6400000000ull) {
		    // C1 = 10^34 => rounding overflow
		    C1_hi = 0x0000314dc6448d93ull;
		    C1_lo = 0x38c15b0a00000000ull;	// 10^33
		    y_exp = y_exp + EXP_P1;
		  }
		} else
		  if ((is_midpoint_lt_even || is_inexact_gt_midpoint)
		      &&
		      ((x_sign
			&& (rnd_mode == ROUNDING_UP
			    || rnd_mode == ROUNDING_TO_ZERO))
		       || (!x_sign
			   && (rnd_mode == ROUNDING_DOWN
			       || rnd_mode == ROUNDING_TO_ZERO)))) {
		  // C1 = C1 - 1
		  C1_lo = C1_lo - 1;
		  if (C1_lo == 0xffffffffffffffffull)
		    C1_hi--;
		  // check if we crossed into the lower decade
		  if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) {	// 10^33 - 1
		    C1_hi = 0x0001ed09bead87c0ull;	// 10^34 - 1
		    C1_lo = 0x378d8e63ffffffffull;
		    y_exp = y_exp - EXP_P1;
		    // no underflow, because delta + q2 >= P34 + 1
		  }
		} else {
		  ;	// exact, the result is already correct
		}
		// in all cases check for overflow (RN and RA solved already)
		if (y_exp == EXP_MAX_P1) {	// overflow
		  if ((rnd_mode == ROUNDING_DOWN && x_sign) ||	// RM and res < 0
		      (rnd_mode == ROUNDING_UP && !x_sign)) {	// RP and res > 0
		    C1_hi = 0x7800000000000000ull;	// +inf
		    C1_lo = 0x0ull;
		  } else {	// RM and res > 0, RP and res < 0, or RZ
		    C1_hi = 0x5fffed09bead87c0ull;
		    C1_lo = 0x378d8e63ffffffffull;
		  }
		  y_exp = 0;	// x_sign is preserved
		  // set the inexact flag (in case the exact addition was exact)
		  *pfpsf |= INEXACT_EXCEPTION;
		  // set the overflow flag
		  *pfpsf |= OVERFLOW_EXCEPTION;
		}
	      }
	    }	// else if (C1 < 10^34) then C1 is the coeff.; the result is exact
	  } else {	// if x_sign != y_sign the result is exact
	    C1_lo = C1_lo - C2_lo;
	    C1_hi = C1_hi - C2_hi;
	    if (C1_lo > C1.w[0])
	      C1_hi--;
	    // the result can be zero, but it cannot overflow
	    if (C1_lo == 0 && C1_hi == 0) {
	      // assemble the result
	      if (x_exp < y_exp)
		res.w[1] = x_exp;
	      else
		res.w[1] = y_exp;
	      res.w[0] = 0;
	      if (rnd_mode == ROUNDING_DOWN) {
		res.w[1] |= 0x8000000000000000ull;
	      }
	      BID_SWAP128 (res);
	      BID_RETURN (res);
	    }
	    if (C1_hi >= 0x8000000000000000ull) {	// negative coefficient!
	      C1_lo = ~C1_lo;
	      C1_lo++;
	      C1_hi = ~C1_hi;
	      if (C1_lo == 0x0)
		C1_hi++;
	      x_sign = y_sign;	// the result will have the sign of y
	    }
	  }
	  // assemble the result
	  res.w[1] = x_sign | y_exp | C1_hi;
	  res.w[0] = C1_lo;
	} else {	// if (delta >= P34 + 1 - q2)
	  // instead of C' = (C1 * 10^(e1-e2) + C2)rnd,P34
	  // calculate C' = C1 * 10^(e1-e2-x1) + (C2 * 10^(-x1))rnd,P34 
	  // where x1 = q1 + e1 - e2 - P34, 1 <= x1 <= P34 - 1
	  // In most cases C' will have P34 digits, and n = C' * 10^(e2+x1)
	  // If the result has P34+1 digits, redo the steps above with x1+1
	  // If the result has P34-1 digits or less, redo the steps above with 
	  // x1-1 but only if initially x1 >= 1
	  // NOTE: these two steps can be improved, e.g we could guess if
	  // P34+1 or P34-1 digits will be obtained by adding/subtracting just
	  // the top 64 bits of the two operands
	  // The result cannot be zero, but it can overflow
	  x1 = delta + q2 - P34;	// 1 <= x1 <= P34-1
	roundC2:
	  // Calculate C1 * 10^(e1-e2-x1) where 0 <= e1-e2-x1 <= P34 - 1
	  // scale = (int)(e1 >> 49) - (int)(e2 >> 49) - x1; 0 <= scale <= P34-1
	  scale = delta - q1 + q2 - x1;	// scale = e1 - e2 - x1 = P34 - q1
	  // either C1 or 10^(e1-e2-x1) may not fit is 64 bits,
	  // but their product fits with certainty in 128 bits (actually in 113)
	  if (scale >= 20) {	//10^(e1-e2-x1) doesn't fit in 64 bits, but C1 does
	    __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]);
	  } else if (scale >= 1) {
	    // if 1 <= scale <= 19 then 10^(e1-e2-x1) fits in 64 bits
	    if (q1 <= 19) {	// C1 fits in 64 bits
	      __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]);
	    } else {	// q1 >= 20
	      C1.w[1] = C1_hi;
	      C1.w[0] = C1_lo;
	      __mul_128x64_to_128 (C1, ten2k64[scale], C1);
	    }
	  } else {	// if (scale == 0) C1 is unchanged
	    C1.w[1] = C1_hi;
	    C1.w[0] = C1_lo;
	  }
	  tmp64 = C1.w[0];	// C1.w[1], C1.w[0] contains C1 * 10^(e1-e2-x1)

	  // now round C2 to q2-x1 decimal digits, where 1<=x1<=q2-1<=P34-1
	  // (but if we got here a second time after x1 = x1 - 1, then 
	  // x1 >= 0; note that for x1 = 0 C2 is unchanged)
	  // C2' = C2 + 1/2 * 10^x1 = C2 + 5 * 10^(x1-1)
	  ind = x1 - 1;	// 0 <= ind <= q2-2<=P34-2=32; but note that if x1 = 0
	  // during a second pass, then ind = -1
	  if (ind >= 0) {	// if (x1 >= 1)
	    C2.w[0] = C2_lo;
	    C2.w[1] = C2_hi;
	    if (ind <= 18) {
	      C2.w[0] = C2.w[0] + midpoint64[ind];
	      if (C2.w[0] < C2_lo)
		C2.w[1]++;
	    } else {	// 19 <= ind <= 32
	      C2.w[0] = C2.w[0] + midpoint128[ind - 19].w[0];
	      C2.w[1] = C2.w[1] + midpoint128[ind - 19].w[1];
	      if (C2.w[0] < C2_lo)
		C2.w[1]++;
	    }
	    // the approximation of 10^(-x1) was rounded up to 118 bits
	    __mul_128x128_to_256 (R256, C2, ten2mk128[ind]);	// R256 = C2*, f2*
	    // calculate C2* and f2*
	    // C2* is actually floor(C2*) in this case
	    // C2* and f2* need shifting and masking, as shown by
	    // shiftright128[] and maskhigh128[]
	    // the top Ex bits of 10^(-x1) are T* = ten2mk128trunc[ind], e.g.
	    // if x1=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
	    // if (0 < f2* < 10^(-x1)) then
	    //   if floor(C1+C2*) is even then C2* = floor(C2*) - logical right
	    //       shift; C2* has p decimal digits, correct by Prop. 1)
	    //   else if floor(C1+C2*) is odd C2* = floor(C2*)-1 (logical right
	    //       shift; C2* has p decimal digits, correct by Pr. 1)
	    // else
	    //   C2* = floor(C2*) (logical right shift; C has p decimal digits,
	    //       correct by Property 1)
	    // n = C2* * 10^(e2+x1)

	    if (ind <= 2) {
	      highf2star.w[1] = 0x0;
	      highf2star.w[0] = 0x0;	// low f2* ok
	    } else if (ind <= 21) {
	      highf2star.w[1] = 0x0;
	      highf2star.w[0] = R256.w[2] & maskhigh128[ind];	// low f2* ok
	    } else {
	      highf2star.w[1] = R256.w[3] & maskhigh128[ind];
	      highf2star.w[0] = R256.w[2];	// low f2* is ok
	    }
	    // shift right C2* by Ex-128 = shiftright128[ind]
	    if (ind >= 3) {
	      shift = shiftright128[ind];
	      if (shift < 64) {	// 3 <= shift <= 63
		R256.w[2] =
		  (R256.w[2] >> shift) | (R256.w[3] << (64 - shift));
		R256.w[3] = (R256.w[3] >> shift);
	      } else {	// 66 <= shift <= 102
		R256.w[2] = (R256.w[3] >> (shift - 64));
		R256.w[3] = 0x0ULL;
	      }
	    }
	    if (second_pass) {
	      is_inexact_lt_midpoint = 0;
	      is_inexact_gt_midpoint = 0;
	      is_midpoint_lt_even = 0;
	      is_midpoint_gt_even = 0;
	    }
	    // determine inexactness of the rounding of C2* (this may be 
	    // followed by a second rounding only if we get P34+1 
	    // decimal digits)
	    // if (0 < f2* - 1/2 < 10^(-x1)) then
	    //   the result is exact
	    // else (if f2* - 1/2 > T* then)
	    //   the result of is inexact
	    if (ind <= 2) {
	      if (R256.w[1] > 0x8000000000000000ull ||
		  (R256.w[1] == 0x8000000000000000ull
		   && R256.w[0] > 0x0ull)) {
		// f2* > 1/2 and the result may be exact
		tmp64A = R256.w[1] - 0x8000000000000000ull;	// f* - 1/2
		if ((tmp64A > ten2mk128trunc[ind].w[1]
		     || (tmp64A == ten2mk128trunc[ind].w[1]
			 && R256.w[0] >= ten2mk128trunc[ind].w[0]))) {
		  // set the inexact flag
		  // *pfpsf |= INEXACT_EXCEPTION;
		  tmp_inexact = 1;	// may be set again during a second pass
		  // this rounding is applied to C2 only!
		  if (x_sign == y_sign)
		    is_inexact_lt_midpoint = 1;
		  else	// if (x_sign != y_sign)
		    is_inexact_gt_midpoint = 1;
		}	// else the result is exact
		// rounding down, unless a midpoint in [ODD, EVEN]
	      } else {	// the result is inexact; f2* <= 1/2
		// set the inexact flag
		// *pfpsf |= INEXACT_EXCEPTION;
		tmp_inexact = 1;	// just in case we will round a second time
		// rounding up, unless a midpoint in [EVEN, ODD]
		// this rounding is applied to C2 only!
		if (x_sign == y_sign)
		  is_inexact_gt_midpoint = 1;
		else	// if (x_sign != y_sign)
		  is_inexact_lt_midpoint = 1;
	      }
	    } else if (ind <= 21) {	// if 3 <= ind <= 21
	      if (highf2star.w[1] > 0x0 || (highf2star.w[1] == 0x0
					    && highf2star.w[0] >
					    onehalf128[ind])
		  || (highf2star.w[1] == 0x0
		      && highf2star.w[0] == onehalf128[ind]
		      && (R256.w[1] || R256.w[0]))) {
		// f2* > 1/2 and the result may be exact
		// Calculate f2* - 1/2
		tmp64A = highf2star.w[0] - onehalf128[ind];
		tmp64B = highf2star.w[1];
		if (tmp64A > highf2star.w[0])
		  tmp64B--;
		if (tmp64B || tmp64A
		    || R256.w[1] > ten2mk128trunc[ind].w[1]
		    || (R256.w[1] == ten2mk128trunc[ind].w[1]
			&& R256.w[0] > ten2mk128trunc[ind].w[0])) {
		  // set the inexact flag
		  // *pfpsf |= INEXACT_EXCEPTION;
		  tmp_inexact = 1;	// may be set again during a second pass
		  // this rounding is applied to C2 only!
		  if (x_sign == y_sign)
		    is_inexact_lt_midpoint = 1;
		  else	// if (x_sign != y_sign)
		    is_inexact_gt_midpoint = 1;
		}	// else the result is exact
	      } else {	// the result is inexact; f2* <= 1/2
		// set the inexact flag
		// *pfpsf |= INEXACT_EXCEPTION;
		tmp_inexact = 1;	// may be set again during a second pass
		// rounding up, unless a midpoint in [EVEN, ODD]
		// this rounding is applied to C2 only!
		if (x_sign == y_sign)
		  is_inexact_gt_midpoint = 1;
		else	// if (x_sign != y_sign)
		  is_inexact_lt_midpoint = 1;
	      }
	    } else {	// if 22 <= ind <= 33
	      if (highf2star.w[1] > onehalf128[ind]
		  || (highf2star.w[1] == onehalf128[ind]
		      && (highf2star.w[0] || R256.w[1]
			  || R256.w[0]))) {
		// f2* > 1/2 and the result may be exact
		// Calculate f2* - 1/2
		// tmp64A = highf2star.w[0];
		tmp64B = highf2star.w[1] - onehalf128[ind];
		if (tmp64B || highf2star.w[0]
		    || R256.w[1] > ten2mk128trunc[ind].w[1]
		    || (R256.w[1] == ten2mk128trunc[ind].w[1]
			&& R256.w[0] > ten2mk128trunc[ind].w[0])) {
		  // set the inexact flag
		  // *pfpsf |= INEXACT_EXCEPTION;
		  tmp_inexact = 1;	// may be set again during a second pass
		  // this rounding is applied to C2 only!
		  if (x_sign == y_sign)
		    is_inexact_lt_midpoint = 1;
		  else	// if (x_sign != y_sign)
		    is_inexact_gt_midpoint = 1;
		}	// else the result is exact
	      } else {	// the result is inexact; f2* <= 1/2
		// set the inexact flag
		// *pfpsf |= INEXACT_EXCEPTION;
		tmp_inexact = 1;	// may be set again during a second pass
		// rounding up, unless a midpoint in [EVEN, ODD]
		// this rounding is applied to C2 only!
		if (x_sign == y_sign)
		  is_inexact_gt_midpoint = 1;
		else	// if (x_sign != y_sign)
		  is_inexact_lt_midpoint = 1;
	      }
	    }
	    // check for midpoints
	    if ((R256.w[1] || R256.w[0]) && (highf2star.w[1] == 0)
		&& (highf2star.w[0] == 0)
		&& (R256.w[1] < ten2mk128trunc[ind].w[1]
		    || (R256.w[1] == ten2mk128trunc[ind].w[1]
			&& R256.w[0] <= ten2mk128trunc[ind].w[0]))) {
	      // the result is a midpoint
	      if ((tmp64 + R256.w[2]) & 0x01) {	// MP in [EVEN, ODD]
		// if floor(C2*) is odd C = floor(C2*) - 1; the result may be 0
		R256.w[2]--;
		if (R256.w[2] == 0xffffffffffffffffull)
		  R256.w[3]--;
		// this rounding is applied to C2 only!
		if (x_sign == y_sign)
		  is_midpoint_gt_even = 1;
		else	// if (x_sign != y_sign)
		  is_midpoint_lt_even = 1;
		is_inexact_lt_midpoint = 0;
		is_inexact_gt_midpoint = 0;
	      } else {
		// else MP in [ODD, EVEN]
		// this rounding is applied to C2 only!
		if (x_sign == y_sign)
		  is_midpoint_lt_even = 1;
		else	// if (x_sign != y_sign)
		  is_midpoint_gt_even = 1;
		is_inexact_lt_midpoint = 0;
		is_inexact_gt_midpoint = 0;
	      }
	    }
	    // end if (ind >= 0)
	  } else {	// if (ind == -1); only during a 2nd pass, and when x1 = 0
	    R256.w[2] = C2_lo;
	    R256.w[3] = C2_hi;
	    tmp_inexact = 0;
	    // to correct a possible setting to 1 from 1st pass
	    if (second_pass) {
	      is_midpoint_lt_even = 0;
	      is_midpoint_gt_even = 0;
	      is_inexact_lt_midpoint = 0;
	      is_inexact_gt_midpoint = 0;
	    }
	  }
	  // and now add/subtract C1 * 10^(e1-e2-x1) +/- (C2 * 10^(-x1))rnd,P34
	  if (x_sign == y_sign) {	// addition; could overflow
	    // no second pass is possible this way (only for x_sign != y_sign)
	    C1.w[0] = C1.w[0] + R256.w[2];
	    C1.w[1] = C1.w[1] + R256.w[3];
	    if (C1.w[0] < tmp64)
	      C1.w[1]++;	// carry
	    // if the sum has P34+1 digits, i.e. C1>=10^34 redo the calculation
	    // with x1=x1+1 
	    if (C1.w[1] > 0x0001ed09bead87c0ull || (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] >= 0x378d8e6400000000ull)) {	// C1 >= 10^34
	      // chop off one more digit from the sum, but make sure there is
	      // no double-rounding error (see table - double rounding logic)
	      // now round C1 from P34+1 to P34 decimal digits
	      // C1' = C1 + 1/2 * 10 = C1 + 5
	      if (C1.w[0] >= 0xfffffffffffffffbull) {	// low half add has carry
		C1.w[0] = C1.w[0] + 5;
		C1.w[1] = C1.w[1] + 1;
	      } else {
		C1.w[0] = C1.w[0] + 5;
	      }
	      // the approximation of 10^(-1) was rounded up to 118 bits
	      __mul_128x128_to_256 (Q256, C1, ten2mk128[0]);	// Q256 = C1*, f1*
	      // C1* is actually floor(C1*) in this case
	      // the top 128 bits of 10^(-1) are
	      // T* = ten2mk128trunc[0]=0x19999999999999999999999999999999
	      // if (0 < f1* < 10^(-1)) then
	      //   if floor(C1*) is even then C1* = floor(C1*) - logical right
	      //       shift; C1* has p decimal digits, correct by Prop. 1)
	      //   else if floor(C1*) is odd C1* = floor(C1*) - 1 (logical right
	      //       shift; C1* has p decimal digits, correct by Pr. 1)
	      // else
	      //   C1* = floor(C1*) (logical right shift; C has p decimal digits
	      //       correct by Property 1)
	      // n = C1* * 10^(e2+x1+1)
	      if ((Q256.w[1] || Q256.w[0])
		  && (Q256.w[1] < ten2mk128trunc[0].w[1]
		      || (Q256.w[1] == ten2mk128trunc[0].w[1]
			  && Q256.w[0] <= ten2mk128trunc[0].w[0]))) {
		// the result is a midpoint
		if (is_inexact_lt_midpoint) {	// for the 1st rounding
		  is_inexact_gt_midpoint = 1;
		  is_inexact_lt_midpoint = 0;
		  is_midpoint_gt_even = 0;
		  is_midpoint_lt_even = 0;
		} else if (is_inexact_gt_midpoint) {	// for the 1st rounding
		  Q256.w[2]--;
		  if (Q256.w[2] == 0xffffffffffffffffull)
		    Q256.w[3]--;
		  is_inexact_gt_midpoint = 0;
		  is_inexact_lt_midpoint = 1;
		  is_midpoint_gt_even = 0;
		  is_midpoint_lt_even = 0;
		} else if (is_midpoint_gt_even) {	// for the 1st rounding
		  // Note: cannot have is_midpoint_lt_even
		  is_inexact_gt_midpoint = 0;
		  is_inexact_lt_midpoint = 1;
		  is_midpoint_gt_even = 0;
		  is_midpoint_lt_even = 0;
		} else {	// the first rounding must have been exact
		  if (Q256.w[2] & 0x01) {	// MP in [EVEN, ODD]
		    // the truncated result is correct
		    Q256.w[2]--;
		    if (Q256.w[2] == 0xffffffffffffffffull)
		      Q256.w[3]--;
		    is_inexact_gt_midpoint = 0;
		    is_inexact_lt_midpoint = 0;
		    is_midpoint_gt_even = 1;
		    is_midpoint_lt_even = 0;
		  } else {	// MP in [ODD, EVEN]
		    is_inexact_gt_midpoint = 0;
		    is_inexact_lt_midpoint = 0;
		    is_midpoint_gt_even = 0;
		    is_midpoint_lt_even = 1;
		  }
		}
		tmp_inexact = 1;	// in all cases
	      } else {	// the result is not a midpoint 
		// determine inexactness of the rounding of C1 (the sum C1+C2*)
		// if (0 < f1* - 1/2 < 10^(-1)) then
		//   the result is exact
		// else (if f1* - 1/2 > T* then)
		//   the result of is inexact
		// ind = 0
		if (Q256.w[1] > 0x8000000000000000ull
		    || (Q256.w[1] == 0x8000000000000000ull
			&& Q256.w[0] > 0x0ull)) {
		  // f1* > 1/2 and the result may be exact
		  Q256.w[1] = Q256.w[1] - 0x8000000000000000ull;	// f1* - 1/2
		  if ((Q256.w[1] > ten2mk128trunc[0].w[1]
		       || (Q256.w[1] == ten2mk128trunc[0].w[1]
			   && Q256.w[0] > ten2mk128trunc[0].w[0]))) {
		    is_inexact_gt_midpoint = 0;
		    is_inexact_lt_midpoint = 1;
		    is_midpoint_gt_even = 0;
		    is_midpoint_lt_even = 0;
		    // set the inexact flag
		    tmp_inexact = 1;
		    // *pfpsf |= INEXACT_EXCEPTION;
		  } else {	// else the result is exact for the 2nd rounding
		    if (tmp_inexact) {	// if the previous rounding was inexact
		      if (is_midpoint_lt_even) {
			is_inexact_gt_midpoint = 1;
			is_midpoint_lt_even = 0;
		      } else if (is_midpoint_gt_even) {
			is_inexact_lt_midpoint = 1;
			is_midpoint_gt_even = 0;
		      } else {
			;	// no change
		      }
		    }
		  }
		  // rounding down, unless a midpoint in [ODD, EVEN]
		} else {	// the result is inexact; f1* <= 1/2
		  is_inexact_gt_midpoint = 1;
		  is_inexact_lt_midpoint = 0;
		  is_midpoint_gt_even = 0;
		  is_midpoint_lt_even = 0;
		  // set the inexact flag
		  tmp_inexact = 1;
		  // *pfpsf |= INEXACT_EXCEPTION;
		}
	      }	// end 'the result is not a midpoint'
	      // n = C1 * 10^(e2+x1)
	      C1.w[1] = Q256.w[3];
	      C1.w[0] = Q256.w[2];
	      y_exp = y_exp + ((UINT64) (x1 + 1) << 49);
	    } else {	// C1 < 10^34
	      // C1.w[1] and C1.w[0] already set
	      // n = C1 * 10^(e2+x1)
	      y_exp = y_exp + ((UINT64) x1 << 49);
	    }
	    // check for overflow
	    if (y_exp == EXP_MAX_P1
		&& (rnd_mode == ROUNDING_TO_NEAREST
		    || rnd_mode == ROUNDING_TIES_AWAY)) {
	      res.w[1] = 0x7800000000000000ull | x_sign;	// +/-inf
	      res.w[0] = 0x0ull;
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // set the overflow flag
	      *pfpsf |= OVERFLOW_EXCEPTION;
	      BID_SWAP128 (res);
	      BID_RETURN (res);
	    }	// else no overflow
	  } else {	// if x_sign != y_sign the result of this subtract. is exact
	    C1.w[0] = C1.w[0] - R256.w[2];
	    C1.w[1] = C1.w[1] - R256.w[3];
	    if (C1.w[0] > tmp64)
	      C1.w[1]--;	// borrow
	    if (C1.w[1] >= 0x8000000000000000ull) {	// negative coefficient!
	      C1.w[0] = ~C1.w[0];
	      C1.w[0]++;
	      C1.w[1] = ~C1.w[1];
	      if (C1.w[0] == 0x0)
		C1.w[1]++;
	      tmp_sign = y_sign;
	      // the result will have the sign of y if last rnd
	    } else {
	      tmp_sign = x_sign;
	    }
	    // if the difference has P34-1 digits or less, i.e. C1 < 10^33 then
	    //   redo the calculation with x1=x1-1;
	    // redo the calculation also if C1 = 10^33 and 
	    //   (is_inexact_gt_midpoint or is_midpoint_lt_even);
	    //   (the last part should have really been 
	    //   (is_inexact_lt_midpoint or is_midpoint_gt_even) from
	    //    the rounding of C2, but the position flags have been reversed)
	    // 10^33 = 0x0000314dc6448d93 0x38c15b0a00000000
	    if ((C1.w[1] < 0x0000314dc6448d93ull || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] < 0x38c15b0a00000000ull)) || (C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b0a00000000ull && (is_inexact_gt_midpoint || is_midpoint_lt_even))) {	// C1=10^33
	      x1 = x1 - 1;	// x1 >= 0
	      if (x1 >= 0) {
		// clear position flags and tmp_inexact
		is_midpoint_lt_even = 0;
		is_midpoint_gt_even = 0;
		is_inexact_lt_midpoint = 0;
		is_inexact_gt_midpoint = 0;
		tmp_inexact = 0;
		second_pass = 1;
		goto roundC2;	// else result has less than P34 digits
	      }
	    }
	    // if the coefficient of the result is 10^34 it means that this
	    // must be the second pass, and we are done 
	    if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) {	// if  C1 = 10^34
	      C1.w[1] = 0x0000314dc6448d93ull;	// C1 = 10^33
	      C1.w[0] = 0x38c15b0a00000000ull;
	      y_exp = y_exp + ((UINT64) 1 << 49);
	    }
	    x_sign = tmp_sign;
	    if (x1 >= 1)
	      y_exp = y_exp + ((UINT64) x1 << 49);
	    // x1 = -1 is possible at the end of a second pass when the 
	    // first pass started with x1 = 1 
	  }
	  C1_hi = C1.w[1];
	  C1_lo = C1.w[0];
	  // general correction from RN to RA, RM, RP, RZ; result uses y_exp
	  if (rnd_mode != ROUNDING_TO_NEAREST) {
	    if ((!x_sign
		 && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint)
		     ||
		     ((rnd_mode == ROUNDING_TIES_AWAY
		       || rnd_mode == ROUNDING_UP)
		      && is_midpoint_gt_even))) || (x_sign
						    &&
						    ((rnd_mode ==
						      ROUNDING_DOWN
						      &&
						      is_inexact_lt_midpoint)
						     ||
						     ((rnd_mode ==
						       ROUNDING_TIES_AWAY
						       || rnd_mode ==
						       ROUNDING_DOWN)
						      &&
						      is_midpoint_gt_even))))
	    {
	      // C1 = C1 + 1
	      C1_lo = C1_lo + 1;
	      if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		C1_hi = C1_hi + 1;
	      }
	      if (C1_hi == 0x0001ed09bead87c0ull
		  && C1_lo == 0x378d8e6400000000ull) {
		// C1 = 10^34 => rounding overflow
		C1_hi = 0x0000314dc6448d93ull;
		C1_lo = 0x38c15b0a00000000ull;	// 10^33
		y_exp = y_exp + EXP_P1;
	      }
	    } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint)
		       &&
		       ((x_sign
			 && (rnd_mode == ROUNDING_UP
			     || rnd_mode == ROUNDING_TO_ZERO))
			|| (!x_sign
			    && (rnd_mode == ROUNDING_DOWN
				|| rnd_mode == ROUNDING_TO_ZERO)))) {
	      // C1 = C1 - 1
	      C1_lo = C1_lo - 1;
	      if (C1_lo == 0xffffffffffffffffull)
		C1_hi--;
	      // check if we crossed into the lower decade
	      if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) {	// 10^33 - 1
		C1_hi = 0x0001ed09bead87c0ull;	// 10^34 - 1
		C1_lo = 0x378d8e63ffffffffull;
		y_exp = y_exp - EXP_P1;
		// no underflow, because delta + q2 >= P34 + 1
	      }
	    } else {
	      ;	// exact, the result is already correct
	    }
	    // in all cases check for overflow (RN and RA solved already)
	    if (y_exp == EXP_MAX_P1) {	// overflow
	      if ((rnd_mode == ROUNDING_DOWN && x_sign) ||	// RM and res < 0
		  (rnd_mode == ROUNDING_UP && !x_sign)) {	// RP and res > 0
		C1_hi = 0x7800000000000000ull;	// +inf
		C1_lo = 0x0ull;
	      } else {	// RM and res > 0, RP and res < 0, or RZ
		C1_hi = 0x5fffed09bead87c0ull;
		C1_lo = 0x378d8e63ffffffffull;
	      }
	      y_exp = 0;	// x_sign is preserved
	      // set the inexact flag (in case the exact addition was exact)
	      *pfpsf |= INEXACT_EXCEPTION;
	      // set the overflow flag
	      *pfpsf |= OVERFLOW_EXCEPTION;
	    }
	  }
	  // assemble the result
	  res.w[1] = x_sign | y_exp | C1_hi;
	  res.w[0] = C1_lo;
	  if (tmp_inexact)
	    *pfpsf |= INEXACT_EXCEPTION;
	}
      } else {	// if (-P34 + 1 <= delta <= -1) <=> 1 <= -delta <= P34 - 1
	// NOTE: the following, up to "} else { // if x_sign != y_sign 
	// the result is exact" is identical to "else if (delta == P34 - q2) {"
	// from above; also, the code is not symmetric: a+b and b+a may take
	// different paths (need to unify eventually!) 
	// calculate C' = C2 + C1 * 10^(e1-e2) directly; the result may be 
	// inexact if it requires P34 + 1 decimal digits; in either case the 
	// 'cutoff' point for addition is at the position of the lsb of C2
	// The coefficient of the result is C1 * 10^(e1-e2) + C2 and the
	// exponent is e2; either C1 or 10^(e1-e2) may not fit is 64 bits,
	// but their product fits with certainty in 128 bits (actually in 113)
	// Note that 0 <= e1 - e2 <= P34 - 2
	//   -P34 + 1 <= delta <= -1 <=> -P34 + 1 <= delta <= -1 <=>
	//   -P34 + 1 <= q1 + e1 - q2 - e2 <= -1 <=>
	//   q2 - q1 - P34 + 1 <= e1 - e2 <= q2 - q1 - 1 <=>
	//   1 - P34 - P34 + 1 <= e1-e2 <= P34 - 1 - 1 => 0 <= e1-e2 <= P34 - 2
	scale = delta - q1 + q2;	// scale = (int)(e1 >> 49) - (int)(e2 >> 49)
	if (scale >= 20) {	// 10^(e1-e2) does not fit in 64 bits, but C1 does
	  __mul_128x64_to_128 (C1, C1_lo, ten2k128[scale - 20]);
	} else if (scale >= 1) {
	  // if 1 <= scale <= 19 then 10^(e1-e2) fits in 64 bits
	  if (q1 <= 19) {	// C1 fits in 64 bits
	    __mul_64x64_to_128MACH (C1, C1_lo, ten2k64[scale]);
	  } else {	// q1 >= 20
	    C1.w[1] = C1_hi;
	    C1.w[0] = C1_lo;
	    __mul_128x64_to_128 (C1, ten2k64[scale], C1);
	  }
	} else {	// if (scale == 0) C1 is unchanged
	  C1.w[1] = C1_hi;
	  C1.w[0] = C1_lo;	// only the low part is necessary
	}
	C1_hi = C1.w[1];
	C1_lo = C1.w[0];
	// now add C2
	if (x_sign == y_sign) {
	  // the result can overflow!
	  C1_lo = C1_lo + C2_lo;
	  C1_hi = C1_hi + C2_hi;
	  if (C1_lo < C1.w[0])
	    C1_hi++;
	  // test for overflow, possible only when C1 >= 10^34
	  if (C1_hi > 0x0001ed09bead87c0ull || (C1_hi == 0x0001ed09bead87c0ull && C1_lo >= 0x378d8e6400000000ull)) {	// C1 >= 10^34
	    // in this case q = P34 + 1 and x = q - P34 = 1, so multiply 
	    // C'' = C'+ 5 = C1 + 5 by k1 ~ 10^(-1) calculated for P34 + 1 
	    // decimal digits
	    // Calculate C'' = C' + 1/2 * 10^x
	    if (C1_lo >= 0xfffffffffffffffbull) {	// low half add has carry
	      C1_lo = C1_lo + 5;
	      C1_hi = C1_hi + 1;
	    } else {
	      C1_lo = C1_lo + 5;
	    }
	    // the approximation of 10^(-1) was rounded up to 118 bits
	    // 10^(-1) =~ 33333333333333333333333333333400 * 2^-129
	    // 10^(-1) =~ 19999999999999999999999999999a00 * 2^-128
	    C1.w[1] = C1_hi;
	    C1.w[0] = C1_lo;	// C''
	    ten2m1.w[1] = 0x1999999999999999ull;
	    ten2m1.w[0] = 0x9999999999999a00ull;
	    __mul_128x128_to_256 (P256, C1, ten2m1);	// P256 = C*, f*
	    // C* is actually floor(C*) in this case
	    // the top Ex = 128 bits of 10^(-1) are 
	    // T* = 0x00199999999999999999999999999999
	    // if (0 < f* < 10^(-x)) then
	    //   if floor(C*) is even then C = floor(C*) - logical right 
	    //       shift; C has p decimal digits, correct by Prop. 1)
	    //   else if floor(C*) is odd C = floor(C*) - 1 (logical right
	    //       shift; C has p decimal digits, correct by Pr. 1)
	    // else
	    //   C = floor(C*) (logical right shift; C has p decimal digits,
	    //       correct by Property 1)
	    // n = C * 10^(e2+x)
	    if ((P256.w[1] || P256.w[0])
		&& (P256.w[1] < 0x1999999999999999ull
		    || (P256.w[1] == 0x1999999999999999ull
			&& P256.w[0] <= 0x9999999999999999ull))) {
	      // the result is a midpoint
	      if (P256.w[2] & 0x01) {
		is_midpoint_gt_even = 1;
		// if floor(C*) is odd C = floor(C*) - 1; the result is not 0
		P256.w[2]--;
		if (P256.w[2] == 0xffffffffffffffffull)
		  P256.w[3]--;
	      } else {
		is_midpoint_lt_even = 1;
	      }
	    }
	    // n = Cstar * 10^(e2+1)
	    y_exp = y_exp + EXP_P1;
	    // C* != 10^P34 because C* has P34 digits
	    // check for overflow
	    if (y_exp == EXP_MAX_P1
		&& (rnd_mode == ROUNDING_TO_NEAREST
		    || rnd_mode == ROUNDING_TIES_AWAY)) {
	      // overflow for RN
	      res.w[1] = x_sign | 0x7800000000000000ull;	// +/-inf
	      res.w[0] = 0x0ull;
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      // set the overflow flag
	      *pfpsf |= OVERFLOW_EXCEPTION;
	      BID_SWAP128 (res);
	      BID_RETURN (res);
	    }
	    // if (0 < f* - 1/2 < 10^(-x)) then 
	    //   the result of the addition is exact 
	    // else 
	    //   the result of the addition is inexact
	    if (P256.w[1] > 0x8000000000000000ull || (P256.w[1] == 0x8000000000000000ull && P256.w[0] > 0x0ull)) {	// the result may be exact
	      tmp64 = P256.w[1] - 0x8000000000000000ull;	// f* - 1/2
	      if ((tmp64 > 0x1999999999999999ull
		   || (tmp64 == 0x1999999999999999ull
		       && P256.w[0] >= 0x9999999999999999ull))) {
		// set the inexact flag
		*pfpsf |= INEXACT_EXCEPTION;
		is_inexact = 1;
	      }	// else the result is exact
	    } else {	// the result is inexact
	      // set the inexact flag
	      *pfpsf |= INEXACT_EXCEPTION;
	      is_inexact = 1;
	    }
	    C1_hi = P256.w[3];
	    C1_lo = P256.w[2];
	    if (!is_midpoint_gt_even && !is_midpoint_lt_even) {
	      is_inexact_lt_midpoint = is_inexact
		&& (P256.w[1] & 0x8000000000000000ull);
	      is_inexact_gt_midpoint = is_inexact
		&& !(P256.w[1] & 0x8000000000000000ull);
	    }
	    // general correction from RN to RA, RM, RP, RZ; result uses y_exp
	    if (rnd_mode != ROUNDING_TO_NEAREST) {
	      if ((!x_sign
		   && ((rnd_mode == ROUNDING_UP
			&& is_inexact_lt_midpoint)
		       || ((rnd_mode == ROUNDING_TIES_AWAY
			    || rnd_mode == ROUNDING_UP)
			   && is_midpoint_gt_even))) || (x_sign
							 &&
							 ((rnd_mode ==
							   ROUNDING_DOWN
							   &&
							   is_inexact_lt_midpoint)
							  ||
							  ((rnd_mode ==
							    ROUNDING_TIES_AWAY
							    || rnd_mode
							    ==
							    ROUNDING_DOWN)
							   &&
							   is_midpoint_gt_even))))
	      {
		// C1 = C1 + 1
		C1_lo = C1_lo + 1;
		if (C1_lo == 0) {	// rounding overflow in the low 64 bits
		  C1_hi = C1_hi + 1;
		}
		if (C1_hi == 0x0001ed09bead87c0ull
		    && C1_lo == 0x378d8e6400000000ull) {
		  // C1 = 10^34 => rounding overflow
		  C1_hi = 0x0000314dc6448d93ull;
		  C1_lo = 0x38c15b0a00000000ull;	// 10^33
		  y_exp = y_exp + EXP_P1;
		}
	      } else
		if ((is_midpoint_lt_even || is_inexact_gt_midpoint) &&
		    ((x_sign && (rnd_mode == ROUNDING_UP ||
				 rnd_mode == ROUNDING_TO_ZERO)) ||
		     (!x_sign && (rnd_mode == ROUNDING_DOWN ||
				  rnd_mode == ROUNDING_TO_ZERO)))) {
		// C1 = C1 - 1
		C1_lo = C1_lo - 1;
		if (C1_lo == 0xffffffffffffffffull)
		  C1_hi--;
		// check if we crossed into the lower decade
		if (C1_hi == 0x0000314dc6448d93ull && C1_lo == 0x38c15b09ffffffffull) {	// 10^33 - 1
		  C1_hi = 0x0001ed09bead87c0ull;	// 10^34 - 1
		  C1_lo = 0x378d8e63ffffffffull;
		  y_exp = y_exp - EXP_P1;
		  // no underflow, because delta + q2 >= P34 + 1
		}
	      } else {
		;	// exact, the result is already correct
	      }
	      // in all cases check for overflow (RN and RA solved already)
	      if (y_exp == EXP_MAX_P1) {	// overflow
		if ((rnd_mode == ROUNDING_DOWN && x_sign) ||	// RM and res < 0
		    (rnd_mode == ROUNDING_UP && !x_sign)) {	// RP and res > 0
		  C1_hi = 0x7800000000000000ull;	// +inf
		  C1_lo = 0x0ull;
		} else {	// RM and res > 0, RP and res < 0, or RZ
		  C1_hi = 0x5fffed09bead87c0ull;
		  C1_lo = 0x378d8e63ffffffffull;
		}
		y_exp = 0;	// x_sign is preserved
		// set the inexact flag (in case the exact addition was exact)
		*pfpsf |= INEXACT_EXCEPTION;
		// set the overflow flag
		*pfpsf |= OVERFLOW_EXCEPTION;
	      }
	    }
	  }	// else if (C1 < 10^34) then C1 is the coeff.; the result is exact
	  // assemble the result
	  res.w[1] = x_sign | y_exp | C1_hi;
	  res.w[0] = C1_lo;
	} else {	// if x_sign != y_sign the result is exact
	  C1_lo = C2_lo - C1_lo;
	  C1_hi = C2_hi - C1_hi;
	  if (C1_lo > C2_lo)
	    C1_hi--;
	  if (C1_hi >= 0x8000000000000000ull) {	// negative coefficient!
	    C1_lo = ~C1_lo;
	    C1_lo++;
	    C1_hi = ~C1_hi;
	    if (C1_lo == 0x0)
	      C1_hi++;
	    x_sign = y_sign;	// the result will have the sign of y
	  }
	  // the result can be zero, but it cannot overflow
	  if (C1_lo == 0 && C1_hi == 0) {
	    // assemble the result
	    if (x_exp < y_exp)
	      res.w[1] = x_exp;
	    else
	      res.w[1] = y_exp;
	    res.w[0] = 0;
	    if (rnd_mode == ROUNDING_DOWN) {
	      res.w[1] |= 0x8000000000000000ull;
	    }
	    BID_SWAP128 (res);
	    BID_RETURN (res);
	  }
	  // assemble the result
	  res.w[1] = y_sign | y_exp | C1_hi;
	  res.w[0] = C1_lo;
	}
      }
    }
    BID_SWAP128 (res);
    BID_RETURN (res)
  }
}



// bid128_sub stands for bid128qq_sub

/*****************************************************************************
 *  BID128 sub
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_sub (UINT128 * pres, UINT128 * px, UINT128 * py
	    _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	    _EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128_sub (UINT128 x, UINT128 y
	    _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
	    _EXC_INFO_PARAM) {
#endif

  UINT128 res;
  UINT64 y_sign;

  if ((y.w[HIGH_128W] & MASK_NAN) != MASK_NAN) {	// y is not NAN
    // change its sign
    y_sign = y.w[HIGH_128W] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
    if (y_sign)
      y.w[HIGH_128W] = y.w[HIGH_128W] & 0x7fffffffffffffffull;
    else
      y.w[HIGH_128W] = y.w[HIGH_128W] | 0x8000000000000000ull;
  }
#if DECIMAL_CALL_BY_REFERENCE
  bid128_add (&res, &x, &y
	      _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
	      _EXC_INFO_ARG);
#else
  res = bid128_add (x, y
		    _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
		    _EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}