--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libgcc/config/libbid/bid128_compare.c	Fri Jul 17 14:47:48 2009 +0900
@@ -0,0 +1,4346 @@
+/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
+
+This file is part of GCC.
+
+GCC is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation; either version 3, or (at your option) any later
+version.
+
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+for more details.
+
+Under Section 7 of GPL version 3, you are granted additional
+permissions described in the GCC Runtime Library Exception, version
+3.1, as published by the Free Software Foundation.
+
+You should have received a copy of the GNU General Public License and
+a copy of the GCC Runtime Library Exception along with this program;
+see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+<http://www.gnu.org/licenses/>.  */
+
+#include "bid_internal.h"
+
+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);
+}
+}