Merge -r 127928:132243 from trunk

[official-gcc.git] / libgcc / config / libbid / bid128_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"

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_equal, x, y)

     int res;
     int exp_x, exp_y, exp_t;
     UINT128 sig_x, sig_y, sig_t;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equivalent.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  if ((y.w[1] & MASK_INF) == MASK_INF) {
    res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  } else {
    res = 0;
    BID_RETURN (res);
  }
}
if ((y.w[1] & MASK_INF) == MASK_INF) {
  res = 0;
  BID_RETURN (res);
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //   If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  // If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  non_canon_y = 0;

  // 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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] ^ y.w[1]) & 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.w[1], sig_y.w[1], sig_t.w[1]);    // and the smaller exp in x
  SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]);    // and the smaller exp in x
}


if (exp_y - exp_x > 33) {
  res = 0;
  BID_RETURN (res);
}       // difference cannot be greater than 10^33

if (exp_y - exp_x > 19) {
  // recalculate y's significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y,
                        ten2k128[exp_y - exp_x - 20]);
  {
    res = ((sig_n_prime256.w[3] == 0) && (sig_n_prime256.w[2] == 0)
           && (sig_n_prime256.w[1] == sig_x.w[1])
           && (sig_n_prime256.w[0] == sig_x.w[0]));
    BID_RETURN (res);
  }

}
  //else{
  // recalculate y's significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
{
  res = ((sig_n_prime192.w[2] == 0)
         && (sig_n_prime192.w[1] == sig_x.w[1])
         && (sig_n_prime192.w[0] == sig_x.w[0]));
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_greater, x,
                                          y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 0
  if (((x.w[1] & 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.w[1] & MASK_INF) != MASK_INF)
           || ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);

    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0) ||
            (sig_n_prime192.w[1] > sig_y.w[1]) ||
            (sig_n_prime192.w[1] == sig_y.w[1] &&
             sig_n_prime192.w[0] > sig_y.w[0])) ^
           ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0 ||
            (sig_n_prime256.w[1] > sig_x.w[1] ||
             (sig_n_prime256.w[1] == sig_x.w[1] &&
              sig_n_prime256.w[0] > sig_x.w[0]))) ^
           ((x.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_quiet_greater_equal, x,
                                          y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) == MASK_INF)
           && (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison of the 
  // significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
    && exp_x > exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
    && exp_x < exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 1
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
            && (sig_n_prime256.w[1] < sig_x.w[1]
                || (sig_n_prime256.w[1] == sig_x.w[1]
                    && sig_n_prime256.w[0] <
                    sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
                                     MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 1
{
  res = (sig_n_prime192.w[2] == 0
         && (sig_n_prime192.w[1] < sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] <
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_quiet_greater_unordered,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 0
  if (((x.w[1] & 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.w[1] & MASK_INF) != MASK_INF)
           || ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison of the 
  // significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
    && exp_x > exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
    && exp_x < exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
            && (sig_n_prime256.w[1] < sig_x.w[1]
                || (sig_n_prime256.w[1] == sig_x.w[1]
                    && sig_n_prime256.w[0] <
                    sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
                                     MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] == 0
         && (sig_n_prime192.w[1] < sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] <
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less, x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) != MASK_INF)
           || (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison of the 
  // significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res = ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
            || (sig_n_prime256.w[1] > sig_x.w[1]
                || (sig_n_prime256.w[1] == sig_x.w[1]
                    && sig_n_prime256.w[0] >
                    sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) ==
                                     MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_less_equal,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 1
  if (((x.w[1] & 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.w[1] & MASK_INF) == MASK_INF)
           && ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison of the 
  // significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1]) || (sig_x.w[1] == sig_y.w[1] &&
                                        sig_x.w[0] >=
                                        sig_y.w[0])) ^ ((x.
                                                         w[1] &
                                                         MASK_SIGN) !=
                                                        MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
      // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_quiet_less_unordered,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) != MASK_INF)
           || (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_equal,
                                          x, y)

     int res;
     int exp_x, exp_y, exp_t;
     UINT128 sig_x, sig_y, sig_t;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equivalent.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  if ((y.w[1] & MASK_INF) == MASK_INF) {
    res = (((x.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  } else {
    res = 1;
    BID_RETURN (res);
  }
}
if ((y.w[1] & MASK_INF) == MASK_INF) {
  res = 1;
  BID_RETURN (res);
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  non_canon_y = 0;

  // 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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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 0
if ((x.w[1] ^ y.w[1]) & 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.w[1], sig_y.w[1], sig_t.w[1]);    // and the smaller exp in x
  SWAP (sig_x.w[0], sig_y.w[0], sig_t.w[0]);    // and the smaller exp in x
}


if (exp_y - exp_x > 33) {
  res = 1;
  BID_RETURN (res);
}       // difference cannot be greater than 10^33

if (exp_y - exp_x > 19) {
  // recalculate y's significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y,
                        ten2k128[exp_y - exp_x - 20]);
  {
    res = ((sig_n_prime256.w[3] != 0) || (sig_n_prime256.w[2] != 0)
           || (sig_n_prime256.w[1] != sig_x.w[1])
           || (sig_n_prime256.w[0] != sig_x.w[0]));
    BID_RETURN (res);
  }

}
  //else{
  // recalculate y's significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
{
  res = ((sig_n_prime192.w[2] != 0)
         || (sig_n_prime192.w[1] != sig_x.w[1])
         || (sig_n_prime192.w[0] != sig_x.w[0]));
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_greater,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 1
  if (((x.w[1] & 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.w[1] & MASK_INF) == MASK_INF)
           && ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //    If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_not_less, x,
                                          y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) == MASK_INF)
           && (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)

  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
    && exp_x > exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
    && exp_x < exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 1
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res =
      ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
        && (sig_n_prime256.w[1] < sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] <
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 1
{
  res = (sig_n_prime192.w[2] == 0
         && (sig_n_prime192.w[1] < sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] <
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_ordered, x,
                                          y)

     int res;

  // NaN (CASE1)
  // if either number is NAN, the comparison is ordered : return 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 0;
  BID_RETURN (res);
}
}
{
  res = 1;
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_quiet_unordered,
                                          x, y)

     int res;

  // NaN (CASE1)
  // if either number is NAN, the comparison is unordered : return 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
if ((x.w[1] & MASK_SNAN) == MASK_SNAN
    || (y.w[1] & MASK_SNAN) == MASK_SNAN) {
  *pfpsf |= INVALID_EXCEPTION;
}
{
  res = 1;
  BID_RETURN (res);
}
}
{
  res = 0;
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_greater,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 0
  if (((x.w[1] & 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.w[1] & MASK_INF) != MASK_INF)
           || ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);

    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_signaling_greater_equal,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) == MASK_INF)
           && (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
    && exp_x > exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
    && exp_x < exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 1
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res =
      ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
        && (sig_n_prime256.w[1] < sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] <
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 1
{
  res = (sig_n_prime192.w[2] == 0
         && (sig_n_prime192.w[1] < sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] <
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_signaling_greater_unordered,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 0
  if (((x.w[1] & 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.w[1] & MASK_INF) != MASK_INF)
           || ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
    && exp_x > exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
    && exp_x < exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res =
      ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
        && (sig_n_prime256.w[1] < sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] <
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] == 0
         && (sig_n_prime192.w[1] < sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] <
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int, bid128_signaling_less, x,
                                          y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) != MASK_INF)
           || (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, |x| < |y|, return 1 if positive
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_signaling_less_equal,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 0;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 1
  if (((x.w[1] & 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.w[1] & MASK_INF) == MASK_INF)
           && ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_signaling_less_unordered,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal.
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 0;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) != MASK_INF)
           || (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 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.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 0;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 0;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 0;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_signaling_not_greater,
                                          x, y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x is neg infinity, there is no way it is greater than y, return 1
  if (((x.w[1] & 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.w[1] & MASK_INF) == MASK_INF)
           && ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
} else if ((y.w[1] & 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.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) !=
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if ((sig_x.w[1] > sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] > sig_y.w[0]))
    && exp_x >= exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
if ((sig_x.w[1] < sig_y.w[1]
     || (sig_x.w[1] == sig_y.w[1] && sig_x.w[0] < sig_y.w[0]))
    && exp_x <= exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 0
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) != MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 0
  {
    res =
      ((sig_n_prime256.w[3] != 0 || sig_n_prime256.w[2] != 0
        || (sig_n_prime256.w[1] > sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] >
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 0
{
  res = (sig_n_prime192.w[2] != 0
         || (sig_n_prime192.w[1] > sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] >
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}

BID128_FUNCTION_ARG2_NORND_CUSTOMRESTYPE (int,
                                          bid128_signaling_not_less, x,
                                          y)

     int res;
     int exp_x, exp_y;
     int diff;
     UINT128 sig_x, sig_y;
     UINT192 sig_n_prime192;
     UINT256 sig_n_prime256;
     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 1
if (((x.w[1] & MASK_NAN) == MASK_NAN)
    || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
*pfpsf |= INVALID_EXCEPTION;
{
  res = 1;
  BID_RETURN (res);
}
}
  // SIMPLE (CASE2)
  // if all the bits are the same, these numbers are equal (not Greater).
if (x.w[0] == y.w[0] && x.w[1] == y.w[1]) {
  res = 1;
  BID_RETURN (res);
}
  // INFINITY (CASE3)
if ((x.w[1] & MASK_INF) == MASK_INF) {
  // if x==neg_inf, { res = (y == neg_inf)?1:0; BID_RETURN (res) }
  if ((x.w[1] & MASK_SIGN) == MASK_SIGN)
    // x is -inf, so it is less than y unless y is -inf
  {
    res = (((y.w[1] & MASK_INF) == MASK_INF)
           && (y.w[1] & 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.w[1] & 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.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
}
  // CONVERT X
sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
sig_x.w[0] = x.w[0];
exp_x = (x.w[1] >> 49) & 0x000000000003fffull;

  // CHECK IF X IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
        && (sig_x.w[0] > 0x378d8e63ffffffffull))
    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_x = 1;
else
  non_canon_x = 0;

  // CONVERT Y
exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
sig_y.w[0] = y.w[0];

  // CHECK IF Y IS CANONICAL
  // 9999999999999999999999999999999999(decimal) = 
  //   1ed09_bead87c0_378d8e63_ffffffff(hexadecimal)
  // [0, 10^34) is the 754r supported canonical range.  
  //     If the value exceeds that, it is interpreted as 0.
if ((sig_y.w[1] > 0x0001ed09bead87c0ull)
    || ((sig_y.w[1] == 0x0001ed09bead87c0ull)
        && (sig_y.w[0] > 0x378d8e63ffffffffull))
    || ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull))
  non_canon_y = 1;
else
  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.w[1] == 0) && (sig_x.w[0] == 0))) {
  x_is_zero = 1;
}
if (non_canon_y || ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
  y_is_zero = 1;
}
  // if both numbers are zero, neither is greater => return NOTGREATERTHAN
if (x_is_zero && y_is_zero) {
  res = 1;
  BID_RETURN (res);
}
  // is x is zero, it is greater if Y is negative
else if (x_is_zero) {
  res = ((y.w[1] & 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.w[1] & 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.w[1] ^ y.w[1]) & MASK_SIGN) == MASK_SIGN) {
  res = ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
  // REDUNDANT REPRESENTATIONS (CASE6)

  // if exponents are the same, then we have a simple comparison 
  // of the significands
if (exp_y == exp_x) {
  res = (((sig_x.w[1] > sig_y.w[1])
          || (sig_x.w[1] == sig_y.w[1]
              && sig_x.w[0] >= sig_y.w[0])) ^ ((x.w[1] & MASK_SIGN) ==
                                               MASK_SIGN));
  BID_RETURN (res);
}
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
if (sig_x.w[1] >= sig_y.w[1] && sig_x.w[0] >= sig_y.w[0]
    && exp_x > exp_y) {
  res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
  BID_RETURN (res);
}
if (sig_x.w[1] <= sig_y.w[1] && sig_x.w[0] <= sig_y.w[0]
    && exp_x < exp_y) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

diff = exp_x - exp_y;

  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
if (diff > 0) { // to simplify the loop below,

  // if exp_x is 33 greater than exp_y, no need for compensation
  if (diff > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }     // difference cannot be greater than 10^33

  if (diff > 19) {      //128 by 128 bit multiply -> 256 bits
    __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);


    // if postitive, return whichever significand is larger 
    // (converse if negative)
    if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
        && sig_n_prime256.w[1] == sig_y.w[1]
        && (sig_n_prime256.w[0] == sig_y.w[0])) {
      res = 1;
      BID_RETURN (res);
    }   // if equal, return 1
    {
      res = ((((sig_n_prime256.w[3] > 0) || sig_n_prime256.w[2] > 0)
              || (sig_n_prime256.w[1] > sig_y.w[1])
              || (sig_n_prime256.w[1] == sig_y.w[1]
                  && sig_n_prime256.w[0] >
                  sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
      BID_RETURN (res);
    }
  }
  //else { //128 by 64 bit multiply -> 192 bits
  __mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_x);

  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_y.w[1]
      && (sig_n_prime192.w[0] == sig_y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res = (((sig_n_prime192.w[2] > 0)
            || (sig_n_prime192.w[1] > sig_y.w[1])
            || (sig_n_prime192.w[1] == sig_y.w[1]
                && sig_n_prime192.w[0] >
                sig_y.w[0])) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}

diff = exp_y - exp_x;

  // if exp_x is 33 less than exp_y, no need for compensation
if (diff > 33) {
  res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

if (diff > 19) {        //128 by 128 bit multiply -> 256 bits
  // adjust the y significand upwards
  __mul_128x128_to_256 (sig_n_prime256, sig_y, ten2k128[diff - 20]);


  // if postitive, return whichever significand is larger 
  // (converse if negative)
  if (sig_n_prime256.w[3] == 0 && (sig_n_prime256.w[2] == 0)
      && sig_n_prime256.w[1] == sig_x.w[1]
      && (sig_n_prime256.w[0] == sig_x.w[0])) {
    res = 1;
    BID_RETURN (res);
  }     // if equal, return 1
  {
    res =
      ((sig_n_prime256.w[3] == 0 && sig_n_prime256.w[2] == 0
        && (sig_n_prime256.w[1] < sig_x.w[1]
            || (sig_n_prime256.w[1] == sig_x.w[1]
                && sig_n_prime256.w[0] <
                sig_x.w[0]))) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
}
  //else { //128 by 64 bit multiply -> 192 bits
  // adjust the y significand upwards
__mul_64x128_to192 (sig_n_prime192, ten2k64[diff], sig_y);

  // if postitive, return whichever significand is larger (converse if negative)
if ((sig_n_prime192.w[2] == 0) && sig_n_prime192.w[1] == sig_x.w[1]
    && (sig_n_prime192.w[0] == sig_x.w[0])) {
  res = 1;
  BID_RETURN (res);
}       // if equal, return 1
{
  res = (sig_n_prime192.w[2] == 0
         && (sig_n_prime192.w[1] < sig_x.w[1]
             || (sig_n_prime192.w[1] == sig_x.w[1]
                 && sig_n_prime192.w[0] <
                 sig_x.w[0]))) ^ ((y.w[1] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}
}