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  modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright notice, 
      this list of conditions and the following disclaimer.
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      notice, this list of conditions and the following disclaimer in the 
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      may be used to endorse or promote products derived from this software 
      without specific prior written permission.

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  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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******************************************************************************/

#define BID_128RES
#include "bid_internal.h"

/*****************************************************************************
 *  BID128 nextup
 ****************************************************************************/

BID128_FUNCTION_ARG1_NORND (bid128_nextup, x)

  BID_UINT128 res;
  BID_UINT64 x_sign;
  BID_UINT64 x_exp;
  int exp;
  BID_UI64DOUBLE tmp1;
  int x_nr_bits;
  int q1, ind;
  BID_UINT128 C1;			// C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (BID_UINT64)

  //BID_SWAP128 (x);
  // unpack the argument
  x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
  C1.w[1] = x.w[1] & MASK_COEFF;
  C1.w[0] = x.w[0];

  // check for NaN or Infinity
  if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
    // x is special
    if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
      // if x = NaN, then res = Q (x)
      // 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 |= BID_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];
      }
    } else {	// x is not NaN, so it must be infinity
      if (!x_sign) {	// x is +inf
	res.w[1] = 0x7800000000000000ull;	// +inf
	res.w[0] = 0x0000000000000000ull;
      } else {	// x is -inf
	res.w[1] = 0xdfffed09bead87c0ull;	// -MAXFP = -999...99 * 10^emax
	res.w[0] = 0x378d8e63ffffffffull;
      }
    }
    BID_RETURN (res);
  }
  // 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.w[1] = 0;	// significand high
    C1.w[0] = 0;	// significand low
  } else {	// G0_G1 != 11
    x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bits
    if (C1.w[1] > 0x0001ed09bead87c0ull ||
	(C1.w[1] == 0x0001ed09bead87c0ull
	 && C1.w[0] > 0x378d8e63ffffffffull)) {
      // x is non-canonical if coefficient is larger than 10^34 -1
      C1.w[1] = 0;
      C1.w[0] = 0;
    } else {	// canonical
      ;
    }
  }

  if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
    // x is +/-0
    res.w[1] = 0x0000000000000000ull;	// +1 * 10^emin
    res.w[0] = 0x0000000000000001ull;
  } else {	// x is not special and is not zero
    if (x.w[1] == 0x5fffed09bead87c0ull
	&& x.w[0] == 0x378d8e63ffffffffull) {
      // x = +MAXFP = 999...99 * 10^emax
      res.w[1] = 0x7800000000000000ull;	// +inf
      res.w[0] = 0x0000000000000000ull;
    } else if (x.w[1] == 0x8000000000000000ull
	       && x.w[0] == 0x0000000000000001ull) {
      // x = -MINFP = 1...99 * 10^emin
      res.w[1] = 0x8000000000000000ull;	// -0
      res.w[0] = 0x0000000000000000ull;
    } else {	// -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
      // can add/subtract 1 ulp to the significand

      // Note: we could check here if x >= 10^34 to speed up the case q1 = 34
      // q1 = nr. of decimal digits in x
      // determine first the nr. of bits in x
      if (C1.w[1] == 0) {
	if (C1.w[0] >= 0x0020000000000000ull) {	// x >= 2^53
	  // split the 64-bit value in two 32-bit halves to avoid rnd errors
	  if (C1.w[0] >= 0x0000000100000000ull) {	// x >= 2^32
	    tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
	    x_nr_bits =
	      33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
		    0x3ff);
	  } else {	// x < 2^32
	    tmp1.d = (double) (C1.w[0]);	// exact conversion
	    x_nr_bits =
	      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
		   0x3ff);
	  }
	} else {	// if x < 2^53
	  tmp1.d = (double) C1.w[0];	// exact conversion
	  x_nr_bits =
	    1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
	tmp1.d = (double) C1.w[1];	// exact conversion
	x_nr_bits =
	  65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
      q1 = bid_nr_digits[x_nr_bits - 1].digits;
      if (q1 == 0) {
	q1 = bid_nr_digits[x_nr_bits - 1].digits1;
	if (C1.w[1] > bid_nr_digits[x_nr_bits - 1].threshold_hi
	    || (C1.w[1] == bid_nr_digits[x_nr_bits - 1].threshold_hi
		&& C1.w[0] >= bid_nr_digits[x_nr_bits - 1].threshold_lo))
	  q1++;
      }
      // if q1 < P34 then pad the significand with zeros
      if (q1 < P34) {
	exp = (x_exp >> 49) - 6176;
	if (exp + 6176 > P34 - q1) {
	  ind = P34 - q1;	// 1 <= ind <= P34 - 1
	  // pad with P34 - q1 zeros, until exponent = emin
	  // C1 = C1 * 10^ind
	  if (q1 <= 19) {	// 64-bit C1
	    if (ind <= 19) {	// 64-bit 10^ind and 64-bit C1
	      __mul_64x64_to_128MACH (C1, C1.w[0], bid_ten2k64[ind]);
	    } else {	// 128-bit 10^ind and 64-bit C1
	      __mul_128x64_to_128 (C1, C1.w[0], bid_ten2k128[ind - 20]);
	    }
	  } else {	// C1 is (most likely) 128-bit
	    if (ind <= 14) {	// 64-bit 10^ind and 128-bit C1 (most likely)
	      __mul_128x64_to_128 (C1, bid_ten2k64[ind], C1);
	    } else if (ind <= 19) {	// 64-bit 10^ind and 64-bit C1 (q1 <= 19)
	      __mul_64x64_to_128MACH (C1, C1.w[0], bid_ten2k64[ind]);
	    } else {	// 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit)
	      __mul_128x64_to_128 (C1, C1.w[0], bid_ten2k128[ind - 20]);
	    }
	  }
	  x_exp = x_exp - ((BID_UINT64) ind << 49);
	} else {	// pad with zeros until the exponent reaches emin
	  ind = exp + 6176;
	  // C1 = C1 * 10^ind
	  if (ind <= 19) {	// 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33
	    if (q1 <= 19) {	// 64-bit C1, 64-bit 10^ind 
	      __mul_64x64_to_128MACH (C1, C1.w[0], bid_ten2k64[ind]);
	    } else {	// 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind
	      __mul_128x64_to_128 (C1, bid_ten2k64[ind], C1);
	    }
	  } else {	// if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 =>
	    // 64-bit C1, 128-bit 10^ind
	    __mul_128x64_to_128 (C1, C1.w[0], bid_ten2k128[ind - 20]);
	  }
	  x_exp = EXP_MIN;
	}
      }
      if (!x_sign) {	// x > 0
	// add 1 ulp (add 1 to the significand)
	C1.w[0]++;
	if (C1.w[0] == 0)
	  C1.w[1]++;
	if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) {	// if  C1 = 10^34
	  C1.w[1] = 0x0000314dc6448d93ull;	// C1 = 10^33
	  C1.w[0] = 0x38c15b0a00000000ull;
	  x_exp = x_exp + EXP_P1;
	}
      } else {	// x < 0
	// subtract 1 ulp (subtract 1 from the significand)
	C1.w[0]--;
	if (C1.w[0] == 0xffffffffffffffffull)
	  C1.w[1]--;
	if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) {	// if  C1 = 10^33 - 1
	  C1.w[1] = 0x0001ed09bead87c0ull;	// C1 = 10^34 - 1
	  C1.w[0] = 0x378d8e63ffffffffull;
	  x_exp = x_exp - EXP_P1;
	}
      }
      // assemble the result
      res.w[1] = x_sign | x_exp | C1.w[1];
      res.w[0] = C1.w[0];
    }	// end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
  }	// end x is not special and is not zero
  BID_RETURN (res);
}

/*****************************************************************************
 *  BID128 nextdown
 ****************************************************************************/

BID128_FUNCTION_ARG1_NORND (bid128_nextdown, x)

  BID_UINT128 res;
  BID_UINT64 x_sign;
  BID_UINT64 x_exp;
  int exp;
  BID_UI64DOUBLE tmp1;
  int x_nr_bits;
  int q1, ind;
  BID_UINT128 C1;			// C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (BID_UINT64)

  //BID_SWAP128 (x);
  // unpack the argument
  x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
  C1.w[1] = x.w[1] & MASK_COEFF;
  C1.w[0] = x.w[0];

  // check for NaN or Infinity
  if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
    // x is special
    if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
      // if x = NaN, then res = Q (x)
      // 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 |= BID_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];
      }
    } else {	// x is not NaN, so it must be infinity
      if (!x_sign) {	// x is +inf
	res.w[1] = 0x5fffed09bead87c0ull;	// +MAXFP = +999...99 * 10^emax
	res.w[0] = 0x378d8e63ffffffffull;
      } else {	// x is -inf
	res.w[1] = 0xf800000000000000ull;	// -inf
	res.w[0] = 0x0000000000000000ull;
      }
    }
    BID_RETURN (res);
  }
  // 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.w[1] = 0;	// significand high
    C1.w[0] = 0;	// significand low
  } else {	// G0_G1 != 11
    x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bits
    if (C1.w[1] > 0x0001ed09bead87c0ull ||
	(C1.w[1] == 0x0001ed09bead87c0ull
	 && C1.w[0] > 0x378d8e63ffffffffull)) {
      // x is non-canonical if coefficient is larger than 10^34 -1
      C1.w[1] = 0;
      C1.w[0] = 0;
    } else {	// canonical
      ;
    }
  }

  if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
    // x is +/-0
    res.w[1] = 0x8000000000000000ull;	// -1 * 10^emin
    res.w[0] = 0x0000000000000001ull;
  } else {	// x is not special and is not zero
    if (x.w[1] == 0xdfffed09bead87c0ull
	&& x.w[0] == 0x378d8e63ffffffffull) {
      // x = -MAXFP = -999...99 * 10^emax
      res.w[1] = 0xf800000000000000ull;	// -inf
      res.w[0] = 0x0000000000000000ull;
    } else if (x.w[1] == 0x0ull && x.w[0] == 0x0000000000000001ull) {	// +MINFP
      res.w[1] = 0x0000000000000000ull;	// +0
      res.w[0] = 0x0000000000000000ull;
    } else {	// -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
      // can add/subtract 1 ulp to the significand

      // Note: we could check here if x >= 10^34 to speed up the case q1 = 34
      // q1 = nr. of decimal digits in x
      // determine first the nr. of bits in x
      if (C1.w[1] == 0) {
	if (C1.w[0] >= 0x0020000000000000ull) {	// x >= 2^53
	  // split the 64-bit value in two 32-bit halves to avoid rnd errors
	  if (C1.w[0] >= 0x0000000100000000ull) {	// x >= 2^32
	    tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
	    x_nr_bits =
	      33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
		    0x3ff);
	  } else {	// x < 2^32
	    tmp1.d = (double) (C1.w[0]);	// exact conversion
	    x_nr_bits =
	      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) -
		   0x3ff);
	  }
	} else {	// if x < 2^53
	  tmp1.d = (double) C1.w[0];	// exact conversion
	  x_nr_bits =
	    1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
	}
      } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
	tmp1.d = (double) C1.w[1];	// exact conversion
	x_nr_bits =
	  65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
      q1 = bid_nr_digits[x_nr_bits - 1].digits;
      if (q1 == 0) {
	q1 = bid_nr_digits[x_nr_bits - 1].digits1;
	if (C1.w[1] > bid_nr_digits[x_nr_bits - 1].threshold_hi
	    || (C1.w[1] == bid_nr_digits[x_nr_bits - 1].threshold_hi
		&& C1.w[0] >= bid_nr_digits[x_nr_bits - 1].threshold_lo))
	  q1++;
      }
      // if q1 < P then pad the significand with zeros
      if (q1 < P34) {
	exp = (x_exp >> 49) - 6176;
	if (exp + 6176 > P34 - q1) {
	  ind = P34 - q1;	// 1 <= ind <= P34 - 1
	  // pad with P34 - q1 zeros, until exponent = emin
	  // C1 = C1 * 10^ind
	  if (q1 <= 19) {	// 64-bit C1
	    if (ind <= 19) {	// 64-bit 10^ind and 64-bit C1
	      __mul_64x64_to_128MACH (C1, C1.w[0], bid_ten2k64[ind]);
	    } else {	// 128-bit 10^ind and 64-bit C1
	      __mul_128x64_to_128 (C1, C1.w[0], bid_ten2k128[ind - 20]);
	    }
	  } else {	// C1 is (most likely) 128-bit
	    if (ind <= 14) {	// 64-bit 10^ind and 128-bit C1 (most likely)
	      __mul_128x64_to_128 (C1, bid_ten2k64[ind], C1);
	    } else if (ind <= 19) {	// 64-bit 10^ind and 64-bit C1 (q1 <= 19)
	      __mul_64x64_to_128MACH (C1, C1.w[0], bid_ten2k64[ind]);
	    } else {	// 128-bit 10^ind and 64-bit C1 (C1 must be 64-bit)
	      __mul_128x64_to_128 (C1, C1.w[0], bid_ten2k128[ind - 20]);
	    }
	  }
	  x_exp = x_exp - ((BID_UINT64) ind << 49);
	} else {	// pad with zeros until the exponent reaches emin
	  ind = exp + 6176;
	  // C1 = C1 * 10^ind
	  if (ind <= 19) {	// 1 <= P34 - q1 <= 19 <=> 15 <= q1 <= 33
	    if (q1 <= 19) {	// 64-bit C1, 64-bit 10^ind 
	      __mul_64x64_to_128MACH (C1, C1.w[0], bid_ten2k64[ind]);
	    } else {	// 20 <= q1 <= 33 => 128-bit C1, 64-bit 10^ind
	      __mul_128x64_to_128 (C1, bid_ten2k64[ind], C1);
	    }
	  } else {	// if 20 <= P34 - q1 <= 33 <=> 1 <= q1 <= 14 =>
	    // 64-bit C1, 128-bit 10^ind
	    __mul_128x64_to_128 (C1, C1.w[0], bid_ten2k128[ind - 20]);
	  }
	  x_exp = EXP_MIN;
	}
      }
      if (x_sign) {	// x < 0
	// add 1 ulp (add 1 to the significand)
	C1.w[0]++;
	if (C1.w[0] == 0)
	  C1.w[1]++;
	if (C1.w[1] == 0x0001ed09bead87c0ull && C1.w[0] == 0x378d8e6400000000ull) {	// if  C1 = 10^34
	  C1.w[1] = 0x0000314dc6448d93ull;	// C1 = 10^33
	  C1.w[0] = 0x38c15b0a00000000ull;
	  x_exp = x_exp + EXP_P1;
	}
      } else {	// x > 0
	// subtract 1 ulp (subtract 1 from the significand)
	C1.w[0]--;
	if (C1.w[0] == 0xffffffffffffffffull)
	  C1.w[1]--;
	if (x_exp != 0 && C1.w[1] == 0x0000314dc6448d93ull && C1.w[0] == 0x38c15b09ffffffffull) {	// if  C1 = 10^33 - 1
	  C1.w[1] = 0x0001ed09bead87c0ull;	// C1 = 10^34 - 1
	  C1.w[0] = 0x378d8e63ffffffffull;
	  x_exp = x_exp - EXP_P1;
	}
      }
      // assemble the result
      res.w[1] = x_sign | x_exp | C1.w[1];
      res.w[0] = C1.w[0];
    }	// end -MAXFP <= x <= -MINFP - 1 ulp OR MINFP <= x <= MAXFP - 1 ulp
  }	// end x is not special and is not zero
  BID_RETURN (res);
}

/*****************************************************************************
 *  BID128 nextafter
 ****************************************************************************/

BID128_FUNCTION_ARG2_NORND (bid128_nextafter, x, y)

  BID_UINT128 xnswp = x;
  BID_UINT128 ynswp = y;
  BID_UINT128 res;
  BID_UINT128 tmp1, tmp2, tmp3;
  BID_FPSC tmp_fpsf = 0;		// dummy fpsf for calls to comparison functions
  int res1, res2;
  BID_UINT64 x_exp;


  BID_SWAP128 (xnswp);
  BID_SWAP128 (ynswp);
  // check for NaNs
  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
      // if x = NaN, then res = Q (x)
      // 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 |= BID_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.w[1] & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
	  // set invalid flag
	  *pfpsf |= BID_INVALID_EXCEPTION;
	}
      }
      BID_RETURN (res)
    } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
      // if x = NaN, then res = Q (x)
      // 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 |= BID_INVALID_EXCEPTION;
	// return quiet (x)
	res.w[1] = y.w[1] & 0xfc003fffffffffffull;	// clear out also G[6]-G[16]
	res.w[0] = y.w[0];
      } else {	// x is QNaN
	// return x
	res.w[1] = y.w[1] & 0xfc003fffffffffffull;	// clear out G[6]-G[16]
	res.w[0] = y.w[0];
      }
      BID_RETURN (res)
    } else {	// at least one is infinity
      if ((x.w[1] & MASK_ANY_INF) == MASK_INF) {	// x = inf
	x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
	x.w[0] = 0x0ull;
      }
      if ((y.w[1] & MASK_ANY_INF) == MASK_INF) {	// y = inf
	y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
	y.w[0] = 0x0ull;
      }
    }
  }
  // neither x nor y is NaN

  // if not infinity, check for non-canonical values x (treated as zero)
  if ((x.w[1] & MASK_ANY_INF) != MASK_INF) {	// x != inf
    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
      x.w[1] = (x.w[1] & MASK_SIGN) | x_exp;
      x.w[0] = 0x0ull;
    } else {	// G0_G1 != 11
      x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bits
      if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
	  ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
	   && x.w[0] > 0x378d8e63ffffffffull)) {
	// x is non-canonical if coefficient is larger than 10^34 -1
	x.w[1] = (x.w[1] & MASK_SIGN) | x_exp;
	x.w[0] = 0x0ull;
      } else {	// canonical
	;
      }
    }
  }
  // no need to check for non-canonical y

  // neither x nor y is NaN
  tmp_fpsf = *pfpsf;	// save fpsf
#if DECIMAL_CALL_BY_REFERENCE
  bid128_quiet_equal (&res1, &xnswp,
		      &ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
		      _EXC_INFO_ARG);
  bid128_quiet_greater (&res2, &xnswp,
			&ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
			_EXC_INFO_ARG);
#else
  res1 =
    bid128_quiet_equal (xnswp,
			ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
			_EXC_INFO_ARG);
  res2 =
    bid128_quiet_greater (xnswp,
			  ynswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
			  _EXC_INFO_ARG);
#endif
  *pfpsf = tmp_fpsf;	// restore fpsf

  if (res1) {	// x = y
    // return x with the sign of y
    res.w[1] =
      (x.w[1] & 0x7fffffffffffffffull) | (y.
					  w[1] & 0x8000000000000000ull);
    res.w[0] = x.w[0];
  } else if (res2) {	// x > y
#if DECIMAL_CALL_BY_REFERENCE
    bid128_nextdown (&res,
		     &xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
		     _EXC_INFO_ARG);
#else
    res =
      bid128_nextdown (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG
		       _EXC_INFO_ARG);
#endif
    BID_SWAP128 (res);
  } else {	// x < y
#if DECIMAL_CALL_BY_REFERENCE
    bid128_nextup (&res,
		   &xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#else
    res =
      bid128_nextup (xnswp _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
#endif
    BID_SWAP128 (res);
  }
  // if the operand x is finite but the result is infinite, signal 
  // overflow and inexact
  if (((x.w[1] & MASK_SPECIAL) != MASK_SPECIAL)
      && ((res.w[1] & MASK_SPECIAL) == MASK_SPECIAL)) {
    // set the inexact flag
    *pfpsf |= BID_INEXACT_EXCEPTION;
    // set the overflow flag
    *pfpsf |= BID_OVERFLOW_EXCEPTION;
  }
  // if the result is in (-10^emin, 10^emin), and is different from the
  // operand x, signal underflow and inexact
  tmp1.w[BID_HIGH_128W] = 0x0000314dc6448d93ull;
  tmp1.w[BID_LOW_128W] = 0x38c15b0a00000000ull;	// +100...0[34] * 10^emin
  tmp2.w[BID_HIGH_128W] = res.w[1] & 0x7fffffffffffffffull;
  tmp2.w[BID_LOW_128W] = res.w[0];
  tmp3.w[BID_HIGH_128W] = res.w[1];
  tmp3.w[BID_LOW_128W] = res.w[0];
  tmp_fpsf = *pfpsf;	// save fpsf
#if DECIMAL_CALL_BY_REFERENCE
  bid128_quiet_greater (&res1, &tmp1,
			&tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
			_EXC_INFO_ARG);
  bid128_quiet_not_equal (&res2, &xnswp,
			  &tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG
			  _EXC_INFO_ARG);
#else
  res1 =
    bid128_quiet_greater (tmp1,
			  tmp2 _EXC_FLAGS_ARG _EXC_MASKS_ARG
			  _EXC_INFO_ARG);
  res2 =
    bid128_quiet_not_equal (xnswp,
			    tmp3 _EXC_FLAGS_ARG _EXC_MASKS_ARG
			    _EXC_INFO_ARG);
#endif
  *pfpsf = tmp_fpsf;	// restore fpsf
  if (res1 && res2) {
    // set the inexact flag 
    *pfpsf |= BID_INEXACT_EXCEPTION;
    // set the underflow flag 
    *pfpsf |= BID_UNDERFLOW_EXCEPTION;
  }
  BID_RETURN (res);
}
