gcc/libgcc/config/libbid/bid64_compare.c

/* Copyright (C) 2007  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 2, or (at your option) any later
version.

In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file.  (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)

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

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING.  If not, write to the Free
Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA.  */

#include "bid_internal.h"

static const UINT64 mult_factor[16] = {
  1ull, 10ull, 100ull, 1000ull,
  10000ull, 100000ull, 1000000ull, 10000000ull,
  100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,
  1000000000000ull, 10000000000000ull,
  100000000000000ull, 1000000000000000ull
};

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_equal (int *pres, UINT64 * px,
		   UINT64 *
		   py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		   _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_equal (UINT64 x,
		   UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		   _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y, exp_t;
  UINT64 sig_x, sig_y, sig_t;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  // rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equivalent.
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) {
    res = (((x ^ y) & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // ONE INFINITY (CASE3')
  if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) {
    res = 0;
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //    therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  } else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
    res = 0;
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ => not equal : return 0
  if ((x ^ y) & MASK_SIGN) {
    res = 0;
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  if (exp_x > exp_y) {	// to simplify the loop below,
    SWAP (exp_x, exp_y, exp_t);	// put the larger exp in y,
    SWAP (sig_x, sig_y, sig_t);	// and the smaller exp in x
  }
  if (exp_y - exp_x > 15) {
    res = 0;	// difference cannot be greater than 10^15
    BID_RETURN (res);
  }
  for (lcv = 0; lcv < (exp_y - exp_x); lcv++) {
    // recalculate y's significand upwards
    sig_y = sig_y * 10;
    if (sig_y > 9999999999999999ull) {
      res = 0;
      BID_RETURN (res);
    }
  }
  res = (sig_y == sig_x);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_greater (int *pres, UINT64 * px,
		     UINT64 *
		     py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		     _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_greater (UINT64 x,
		     UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		     _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, rather than equal : 
  // return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, there is no way it is greater than y, return 0
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 0;
      BID_RETURN (res);
    } else {
      // x is pos infinity, it is greater, unless y is positive 
      // infinity => return y!=pos_infinity
      res = (((y & MASK_INF) != MASK_INF)
	     || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 0
    //                 if y is negative infinity, then x is greater, return 1
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  //(+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //(ZERO x 10^A == ZERO x 10^B) for any valid A, B => therefore ignore the 
  // exponent field
  // (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  } else if (x_is_zero) {
    // is x is zero, it is greater if Y is negative
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  } else if (y_is_zero) {
    // is y is zero, X is greater if it is positive
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is greater if y is negative
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
  if (sig_x > sig_y && exp_x > exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x < exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {	// difference cannot be greater than 10^15
    if (x & MASK_SIGN)	// if both are negative
      res = 0;
    else	// if both are positive
      res = 1;
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    if (x & MASK_SIGN)	// if both are negative
      res = 1;
    else	// if both are positive
      res = 0;
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // if postitive, return whichever significand is larger (converse if neg.)
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }
    res = (((sig_n_prime.w[1] > 0)
	    || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);
  // if postitive, return whichever significand is larger 
  //     (converse if negative)
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  res = (((sig_n_prime.w[1] == 0)
	  && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_greater_equal (int *pres, UINT64 * px,
			   UINT64 *
			   py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			   _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_greater_equal (UINT64 x,
			   UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			   _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 1
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN) {
      // x is -inf, so it is less than y unless y is -inf
      res = (((y & MASK_INF) == MASK_INF)
	     && (y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    } else {	// x is pos_inf, no way for it to be less than y
      res = 1;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //   therefore ignore the exponent field
  //  (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  if (x_is_zero && y_is_zero) {
    // if both numbers are zero, they are equal
    res = 1;
    BID_RETURN (res);
  } else if (x_is_zero) {
    // if x is zero, it is lessthan if Y is positive
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  } else if (y_is_zero) {
    // if y is zero, X is less if it is negative
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    // difference cannot be greater than 10^15
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // return 1 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    // (converse if negative)
    res = (((sig_n_prime.w[1] == 0)
	    && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
					    MASK_SIGN));
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);
  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  // (converse if negative)
  res = (((sig_n_prime.w[1] > 0)
	  || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
					    MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_greater_unordered (int *pres, UINT64 * px,
			       UINT64 *
			       py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			       _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_greater_unordered (UINT64 x,
			       UINT64 y _EXC_FLAGS_PARAM
			       _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, rather than equal : 
  // return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, there is no way it is greater than y, return 0
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 0;
      BID_RETURN (res);
    } else {
      // x is pos infinity, it is greater, unless y is positive infinity => 
      // return y!=pos_infinity
      res = (((y & MASK_INF) != MASK_INF)
	     || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 0
    //                 if y is negative infinity, then x is greater, return 1
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  // therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  } else if (x_is_zero) {
    // is x is zero, it is greater if Y is negative
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  } else if (y_is_zero) {
    // is y is zero, X is greater if it is positive
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is greater if y is negative
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    // difference cannot be greater than 10^15
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }
    res = (((sig_n_prime.w[1] > 0)
	    || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);
  // if postitive, return whichever significand is larger (converse if negative)
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  res = (((sig_n_prime.w[1] == 0)
	  && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_less (int *pres, UINT64 * px,
		  UINT64 *
		  py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) 
{
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_less (UINT64 x,
		  UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		  _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN) {
      // x is -inf, so it is less than y unless y is -inf
      res = (((y & MASK_INF) != MASK_INF)
	     || (y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    } else {
      // x is pos_inf, no way for it to be less than y
      res = 0;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //  therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  if (x_is_zero && y_is_zero) {
    // if both numbers are zero, they are equal
    res = 0;
    BID_RETURN (res);
  } else if (x_is_zero) {
    // if x is zero, it is lessthan if Y is positive
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  } else if (y_is_zero) {
    // if y is zero, X is less if it is negative
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    // difference cannot be greater than 10^15
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // return 0 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    // (converse if negative)
    res = (((sig_n_prime.w[1] == 0)
	    && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);
  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  // (converse if negative)
  res = (((sig_n_prime.w[1] > 0)
	  || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_less_equal (int *pres, UINT64 * px,
			UINT64 *
			py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			_EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_less_equal (UINT64 x,
			UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			_EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, rather than equal : 
  //     return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (LESSEQUAL).
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      // if x is neg infinity, it must be lessthan or equal to y return 1
      res = 1;
      BID_RETURN (res);
    } else {
      // x is pos infinity, it is greater, unless y is positive infinity => 
      // return y==pos_infinity
      res = !(((y & MASK_INF) != MASK_INF)
	      || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 1
    //                 if y is negative infinity, then x is greater, return 0
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //     therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  if (x_is_zero && y_is_zero) {
    // if both numbers are zero, they are equal -> return 1
    res = 1;
    BID_RETURN (res);
  } else if (x_is_zero) {
    // if x is zero, it is lessthan if Y is positive
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  } else if (y_is_zero) {
    // if y is zero, X is less if it is negative
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    // difference cannot be greater than 10^15
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // return 1 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    res = (((sig_n_prime.w[1] == 0)
	    && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);
  // return 1 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  res = (((sig_n_prime.w[1] > 0)
	  || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_less_unordered (int *pres, UINT64 * px,
			    UINT64 *
			    py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			    _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_less_unordered (UINT64 x,
			    UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			    _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN) {
      // x is -inf, so it is less than y unless y is -inf
      res = (((y & MASK_INF) != MASK_INF)
	     || (y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    } else {
      // x is pos_inf, no way for it to be less than y
      res = 0;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }
  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  // (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //     therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  if (x_is_zero && y_is_zero) {
    // if both numbers are zero, they are equal
    res = 0;
    BID_RETURN (res);
  } else if (x_is_zero) {
    // if x is zero, it is lessthan if Y is positive
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  } else if (y_is_zero) {
    // if y is zero, X is less if it is negative
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    // difference cannot be greater than 10^15
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // return 0 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    res = (((sig_n_prime.w[1] == 0)
	    && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);
  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  res = (((sig_n_prime.w[1] > 0)
	  || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					    MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_not_equal (int *pres, UINT64 * px,
		       UINT64 *
		       py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		       _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_not_equal (UINT64 x,
		       UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		       _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y, exp_t;
  UINT64 sig_x, sig_y, sig_t;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y, lcv;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  // rather than equal : return 1
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equivalent.
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if (((x & MASK_INF) == MASK_INF) && ((y & MASK_INF) == MASK_INF)) {
    res = (((x ^ y) & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // ONE INFINITY (CASE3')
  if (((x & MASK_INF) == MASK_INF) || ((y & MASK_INF) == MASK_INF)) {
    res = 1;
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //        therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }

  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  } else if ((x_is_zero && !y_is_zero) || (!x_is_zero && y_is_zero)) {
    res = 1;
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ => not equal : return 1
  if ((x ^ y) & MASK_SIGN) {
    res = 1;
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  if (exp_x > exp_y) {	// to simplify the loop below,
    SWAP (exp_x, exp_y, exp_t);	// put the larger exp in y,
    SWAP (sig_x, sig_y, sig_t);	// and the smaller exp in x
  }

  if (exp_y - exp_x > 15) {
    res = 1;
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^16

  for (lcv = 0; lcv < (exp_y - exp_x); lcv++) {

    // recalculate y's significand upwards
    sig_y = sig_y * 10;
    if (sig_y > 9999999999999999ull) {
      res = 1;
      BID_RETURN (res);
    }
  }

  {
    res = sig_y != sig_x;
    BID_RETURN (res);
  }

}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_not_greater (int *pres, UINT64 * px,
			 UINT64 *
			 py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			 _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_not_greater (UINT64 x,
			 UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			 _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  //   rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (LESSEQUAL).
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, it must be lessthan or equal to y return 1
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 1;
      BID_RETURN (res);
    }
    // x is pos infinity, it is greater, unless y is positive 
    // infinity => return y==pos_infinity
    else {
      res = !(((y & MASK_INF) != MASK_INF)
	      || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 1
    //                 if y is negative infinity, then x is greater, return 0
    {
      res = ((y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither 
  //         number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //         therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal -> return 1
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 1 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 1 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_not_less (int *pres, UINT64 * px,
		      UINT64 *
		      py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		      _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_not_less (UINT64 x,
		      UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		      _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 1
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN)
      // x is -inf, so it is less than y unless y is -inf
    {
      res = (((y & MASK_INF) == MASK_INF)
	     && (y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    } else
      // x is pos_inf, no way for it to be less than y
    {
      res = 1;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    {
      res = ((y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither 
  //        number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //        therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 0 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_ordered (int *pres, UINT64 * px,
		     UINT64 *
		     py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		     _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_ordered (UINT64 x,
		     UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		     _EXC_INFO_PARAM) {
#endif
  int res;

  // NaN (CASE1)
  // if either number is NAN, the comparison is ordered, rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 0;
    BID_RETURN (res);
  } else {
    res = 1;
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_quiet_unordered (int *pres, UINT64 * px,
		       UINT64 *
		       py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		       _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_quiet_unordered (UINT64 x,
		       UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		       _EXC_INFO_PARAM) {
#endif
  int res;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  //     rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    if ((x & MASK_SNAN) == MASK_SNAN || (y & MASK_SNAN) == MASK_SNAN) {
      *pfpsf |= INVALID_EXCEPTION;	// set exception if sNaN
    }
    res = 1;
    BID_RETURN (res);
  } else {
    res = 0;
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_greater (int *pres, UINT64 * px,
			 UINT64 *
			 py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			 _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_greater (UINT64 x,
			 UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			 _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  //     rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, there is no way it is greater than y, return 0
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 0;
      BID_RETURN (res);
    }
    // x is pos infinity, it is greater, 
    // unless y is positive infinity => return y!=pos_infinity
    else {
      res = (((y & MASK_INF) != MASK_INF)
	     || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 0
    //                 if y is negative infinity, then x is greater, return 1
    {
      res = ((y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  }
  // is x is zero, it is greater if Y is negative
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // is y is zero, X is greater if it is positive
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is greater if y is negative
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)

  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);


    // if postitive, return whichever significand is larger 
    //     (converse if negative)
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }

    {
      res = (((sig_n_prime.w[1] > 0)
	      || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // if postitive, return whichever significand is larger 
  //     (converse if negative)
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  {
    res = (((sig_n_prime.w[1] == 0)
	    && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_greater_equal (int *pres, UINT64 * px,
			       UINT64 *
			       py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			       _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_greater_equal (UINT64 x,
			       UINT64 y _EXC_FLAGS_PARAM
			       _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 1
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN)
      // x is -inf, so it is less than y unless y is -inf
    {
      res = (((y & MASK_INF) == MASK_INF)
	     && (y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    } else
      // x is pos_inf, no way for it to be less than y
    {
      res = 1;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    {
      res = ((y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 1 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_greater_unordered (int *pres, UINT64 * px,
				   UINT64 *
				   py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
				   _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_greater_unordered (UINT64 x,
				   UINT64 y _EXC_FLAGS_PARAM
				   _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  // rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, there is no way it is greater than y, return 0
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 0;
      BID_RETURN (res);
    }
    // x is pos infinity, it is greater, 
    // unless y is positive infinity => return y!=pos_infinity
    else {
      res = (((y & MASK_INF) != MASK_INF)
	     || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 0
    //                 if y is negative infinity, then x is greater, return 1
    {
      res = ((y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  }
  // is x is zero, it is greater if Y is negative
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // is y is zero, X is greater if it is positive
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is greater if y is negative
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)

  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // if postitive, return whichever significand is larger 
    //     (converse if negative)
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }

    {
      res = (((sig_n_prime.w[1] > 0)
	      || sig_n_prime.w[0] > sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // if postitive, return whichever significand is larger 
  //     (converse if negative)
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  {
    res = (((sig_n_prime.w[1] == 0)
	    && (sig_x > sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_less (int *pres, UINT64 * px,
		      UINT64 *
		      py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		      _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_less (UINT64 x,
		      UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
		      _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN)
      // x is -inf, so it is less than y unless y is -inf
    {
      res = (((y & MASK_INF) != MASK_INF)
	     || (y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    } else
      // x is pos_inf, no way for it to be less than y
    {
      res = 0;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    {
      res = ((y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal
  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 0 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_less_equal (int *pres, UINT64 * px,
			    UINT64 *
			    py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			    _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_less_equal (UINT64 x,
			    UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			    _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  // rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 0;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (LESSEQUAL).
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, it must be lessthan or equal to y return 1
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 1;
      BID_RETURN (res);
    }
    // x is pos infinity, it is greater, 
    // unless y is positive infinity => return y==pos_infinity
    else {
      res = !(((y & MASK_INF) != MASK_INF)
	      || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 1
    //                 if y is negative infinity, then x is greater, return 0
    {
      res = ((y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal -> return 1
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 1 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 1 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_less_unordered (int *pres, UINT64 * px,
				UINT64 *
				py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
				_EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_less_unordered (UINT64 x,
				UINT64 y _EXC_FLAGS_PARAM
				_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 0;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?0:1; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN)
      // x is -inf, so it is less than y unless y is -inf
    {
      res = (((y & MASK_INF) != MASK_INF)
	     || (y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    } else
      // x is pos_inf, no way for it to be less than y
    {
      res = 0;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    {
      res = ((y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal
  if (x_is_zero && y_is_zero) {
    res = 0;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 0 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 0;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 0;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_not_greater (int *pres, UINT64 * px,
			     UINT64 *
			     py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			     _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_not_greater (UINT64 x,
			     UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			     _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered, 
  // rather than equal : return 0
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (LESSEQUAL).
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x is neg infinity, it must be lessthan or equal to y return 1
    if (((x & MASK_SIGN) == MASK_SIGN)) {
      res = 1;
      BID_RETURN (res);
    }
    // x is pos infinity, it is greater, 
    // unless y is positive infinity => return y==pos_infinity
    else {
      res = !(((y & MASK_INF) != MASK_INF)
	      || ((y & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so if y is positive infinity, then x is less, return 1
    //                 if y is negative infinity, then x is greater, return 0
    {
      res = ((y & MASK_SIGN) != MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal -> return 1
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 1 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 1 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					      MASK_SIGN));
    BID_RETURN (res);
  }
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_signaling_not_less (int *pres, UINT64 * px,
			  UINT64 *
			  py _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			  _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_signaling_not_less (UINT64 x,
			  UINT64 y _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
			  _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT64 sig_x, sig_y;
  UINT128 sig_n_prime;
  char x_is_zero = 0, y_is_zero = 0, non_canon_x, non_canon_y;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 1
  if (((x & MASK_NAN) == MASK_NAN) || ((y & MASK_NAN) == MASK_NAN)) {
    *pfpsf |= INVALID_EXCEPTION;	// set invalid exception if NaN
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
  if (x == y) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
    if ((x & MASK_SIGN) == MASK_SIGN)
      // x is -inf, so it is less than y unless y is -inf
    {
      res = (((y & MASK_INF) == MASK_INF)
	     && (y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    } else
      // x is pos_inf, no way for it to be less than y
    {
      res = 1;
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    {
      res = ((y & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;
    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_x > 9999999999999999ull) {
      non_canon_x = 1;
    } else {
      non_canon_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;
    sig_x = (x & MASK_BINARY_SIG1);
    non_canon_x = 0;
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>
  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {
    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;
    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;
    if (sig_y > 9999999999999999ull) {
      non_canon_y = 1;
    } else {
      non_canon_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;
    sig_y = (y & MASK_BINARY_SIG1);
    non_canon_y = 0;
  }

  // ZERO (CASE4)
  // some properties:
  // (+ZERO==-ZERO) => therefore ignore the sign, and neither number is greater
  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => 
  //      therefore ignore the exponent field
  //    (Any non-canonical # is considered 0)
  if (non_canon_x || sig_x == 0) {
    x_is_zero = 1;
  }
  if (non_canon_y || sig_y == 0) {
    y_is_zero = 1;
  }
  // if both numbers are zero, they are equal
  if (x_is_zero && y_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if x is zero, it is lessthan if Y is positive
  else if (x_is_zero) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, X is less if it is negative
  else if (y_is_zero) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // OPPOSITE SIGN (CASE5)
  // now, if the sign bits differ, x is less than if y is positive
  if (((x ^ y) & MASK_SIGN) == MASK_SIGN) {
    res = ((y & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, no need for compensation
  if (exp_x - exp_y > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // difference cannot be greater than 10^15

  // if exp_x is 15 less than exp_y, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down to the compensated significand
  if (exp_x > exp_y) {	// to simplify the loop below,

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // return 0 if values are equal
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      res = 1;
      BID_RETURN (res);
    }
    // if postitive, return whichever significand abs is smaller 
    //     (converse if negative)
    {
      res = (((sig_n_prime.w[1] == 0)
	      && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) !=
					      MASK_SIGN));
      BID_RETURN (res);
    }
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // return 0 if values are equal
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = 1;
    BID_RETURN (res);
  }
  // if positive, return whichever significand abs is smaller 
  //     (converse if negative)
  {
    res = (((sig_n_prime.w[1] > 0)
	    || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) !=
					      MASK_SIGN));
    BID_RETURN (res);
  }
}