X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=libgcc%2Fconfig%2Flibbid%2Fbid128_minmax.c;fp=libgcc%2Fconfig%2Flibbid%2Fbid128_minmax.c;h=2bb049b13d21d76b5792c70e3bfda07dff9b640f;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git

diff --git a/libgcc/config/libbid/bid128_minmax.c b/libgcc/config/libbid/bid128_minmax.c
new file mode 100644
index 00000000..2bb049b1
--- /dev/null
+++ b/libgcc/config/libbid/bid128_minmax.c
@@ -0,0 +1,1095 @@
+/* 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/>.  */
+
+#define BID_128RES
+#include "bid_internal.h"
+
+/*****************************************************************************
+ *  BID128 minimum number
+ *****************************************************************************/
+
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128_minnum (UINT128 * pres, UINT128 * px,
+	       UINT128 * py _EXC_FLAGS_PARAM) {
+  UINT128 x = *px;
+  UINT128 y = *py;
+#else
+UINT128
+bid128_minnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
+#endif
+
+  UINT128 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;
+
+  BID_SWAP128 (x);
+  BID_SWAP128 (y);
+
+  // check for non-canonical x
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    x.w[1] = x.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (x.w[0] > 0x38c15b09ffffffffull))) {
+      x.w[1] = x.w[1] & 0xffffc00000000000ull;
+      x.w[0] = 0x0ull;
+    }
+  } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) {	// x = inf
+    x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
+    x.w[0] = 0x0ull;
+  } else {	// x is not special
+    // check for non-canonical values - treated as zero
+    if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
+      x.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && x.w[0] > 0x378d8e63ffffffffull)) {
+	// x is non-canonical if coefficient is larger than 10^34 -1
+	x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
+	x.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+  // check for non-canonical y
+  if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+    y.w[1] = y.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (y.w[0] > 0x38c15b09ffffffffull))) {
+      y.w[1] = y.w[1] & 0xffffc00000000000ull;
+      y.w[0] = 0x0ull;
+    }
+  } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) {	// y = inf
+    y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
+    y.w[0] = 0x0ull;
+  } else {	// y is not special
+    // check for non-canonical values - treated as zero
+    if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
+      y.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && y.w[0] > 0x378d8e63ffffffffull)) {
+	// y is non-canonical if coefficient is larger than 10^34 -1
+	y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
+	y.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+
+  // NaN (CASE1)
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNaN
+      // if x is SNAN, then return quiet (x)
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      x.w[1] = x.w[1] & 0xfdffffffffffffffull;	// quietize x
+      res = x;
+    } else {	// x is QNaN
+      if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+	if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
+	  *pfpsf |= INVALID_EXCEPTION;	// set invalid flag
+	}
+	res = x;
+      } else {
+	res = y;
+      }
+    }
+    BID_RETURN (res);
+  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NaN, but x is not
+    if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      y.w[1] = y.w[1] & 0xfdffffffffffffffull;	// quietize y
+      res = y;
+    } else {
+      // will return x (which is not NaN)
+      res = x;
+    }
+    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 = x;
+    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
+    res = (((x.w[1] & MASK_SIGN) == MASK_SIGN)) ? x : y;
+    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) ? y : x;
+    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;
+
+  // CONVERT Y
+  exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
+  sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
+  sig_y.w[0] = y.w[0];
+
+  // ZERO (CASE4)
+  // some properties:
+  //    (+ZERO == -ZERO) => therefore ignore the sign
+  //    (ZERO x 10^A == ZERO x 10^B) for any valid A, B => ignore the exponent 
+  //    field
+  //    (Any non-canonical # is considered 0)
+  if ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
+    x_is_zero = 1;
+  }
+  if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
+    y_is_zero = 1;
+  }
+
+  if (x_is_zero && y_is_zero) {
+    // if both numbers are zero, neither is greater => return either number
+    res = x;
+    BID_RETURN (res);
+  } else if (x_is_zero) {
+    // is x is zero, it is greater if Y is negative
+    res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
+    BID_RETURN (res);
+  } else if (y_is_zero) {
+    // is y is zero, X is greater if it is positive
+    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
+    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) ? y : x;
+    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)) ? y : x;
+    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) ? y : x;
+    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) ? y : x;
+    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) {
+      // difference cannot be greater than 10^33
+      res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? y : x;
+      BID_RETURN (res);
+    }
+    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)
+      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)) ? y : x;
+      BID_RETURN (res);
+    }
+    __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
+    // if postitive, return whichever significand is larger 
+    // (converse if negative)
+    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)) ? y : x;
+    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) ? y : x;
+    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)
+    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)) ? x : y;
+    BID_RETURN (res);
+  }
+  // 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)
+  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)) ? x : y;
+  BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128 minimum magnitude function - returns greater of two numbers
+ *****************************************************************************/
+
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128_minnum_mag (UINT128 * pres, UINT128 * px,
+		   UINT128 * py _EXC_FLAGS_PARAM) {
+  UINT128 x = *px;
+  UINT128 y = *py;
+#else
+UINT128
+bid128_minnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
+#endif
+
+  UINT128 res;
+  int exp_x, exp_y;
+  int diff;
+  UINT128 sig_x, sig_y;
+  UINT192 sig_n_prime192;
+  UINT256 sig_n_prime256;
+
+  BID_SWAP128 (x);
+  BID_SWAP128 (y);
+
+  // check for non-canonical x
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    x.w[1] = x.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (x.w[0] > 0x38c15b09ffffffffull))) {
+      x.w[1] = x.w[1] & 0xffffc00000000000ull;
+      x.w[0] = 0x0ull;
+    }
+  } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) {	// x = inf
+    x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
+    x.w[0] = 0x0ull;
+  } else {	// x is not special
+    // check for non-canonical values - treated as zero
+    if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
+      x.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && x.w[0] > 0x378d8e63ffffffffull)) {
+	// x is non-canonical if coefficient is larger than 10^34 -1
+	x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
+	x.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+  // check for non-canonical y
+  if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+    y.w[1] = y.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (y.w[0] > 0x38c15b09ffffffffull))) {
+      y.w[1] = y.w[1] & 0xffffc00000000000ull;
+      y.w[0] = 0x0ull;
+    }
+  } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) {	// y = inf
+    y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
+    y.w[0] = 0x0ull;
+  } else {	// y is not special
+    // check for non-canonical values - treated as zero
+    if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
+      y.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && y.w[0] > 0x378d8e63ffffffffull)) {
+	// y is non-canonical if coefficient is larger than 10^34 -1
+	y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
+	y.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+
+  // NaN (CASE1)
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNaN
+      // if x is SNAN, then return quiet (x)
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      x.w[1] = x.w[1] & 0xfdffffffffffffffull;	// quietize x
+      res = x;
+    } else {	// x is QNaN
+      if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+	if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
+	  *pfpsf |= INVALID_EXCEPTION;	// set invalid flag
+	}
+	res = x;
+      } else {
+	res = y;
+      }
+    }
+    BID_RETURN (res);
+  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NaN, but x is not
+    if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      y.w[1] = y.w[1] & 0xfdffffffffffffffull;	// quietize y
+      res = y;
+    } else {
+      // will return x (which is not NaN)
+      res = x;
+    }
+    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 = y;
+    BID_RETURN (res);
+  }
+  // INFINITY (CASE3)
+  if ((x.w[1] & MASK_INF) == MASK_INF) {
+    // if x infinity, it has maximum magnitude.
+    // Check if magnitudes are equal.  If x is negative, return it.
+    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
+	   && (y.w[1] & MASK_INF) == MASK_INF) ? x : y;
+    BID_RETURN (res);
+  } else if ((y.w[1] & MASK_INF) == MASK_INF) {
+    // x is finite, so if y is infinity, then x is less in magnitude
+    res = x;
+    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;
+
+  // CONVERT Y
+  exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
+  sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
+  sig_y.w[0] = y.w[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 ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
+    res = x;
+    BID_RETURN (res);
+  }
+  if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
+    res = y;
+    BID_RETURN (res);
+  }
+  // REDUNDANT REPRESENTATIONS (CASE6)
+  // check if exponents are the same and significands are the same
+  if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
+      && sig_x.w[0] == sig_y.w[0]) {
+    if (x.w[1] & 0x8000000000000000ull) {	// x is negative
+      res = x;
+      BID_RETURN (res);
+    } else {
+      res = y;
+      BID_RETURN (res);
+    }
+  } else 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)
+	     || ((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)) {
+    // if both components are either bigger or smaller, it is clear what 
+    // needs to be done; also if the magnitudes are equal
+    res = y;
+    BID_RETURN (res);
+  } else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
+					   && sig_y.w[0] > sig_x.w[0]))
+	      && exp_y == exp_x)
+	     || ((sig_y.w[1] > sig_x.w[1]
+		  || (sig_y.w[1] == sig_x.w[1]
+		      && sig_y.w[0] >= sig_x.w[0]))
+		 && exp_y > exp_x)) {
+    res = x;
+    BID_RETURN (res);
+  } else {
+    ;	// continue
+  }
+  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 = y;	// difference cannot be greater than 10^33
+      BID_RETURN (res);
+    }
+    if (diff > 19) {	//128 by 128 bit multiply -> 256 bits
+      __mul_128x128_to_256 (sig_n_prime256, sig_x, ten2k128[diff - 20]);
+      // if positive, 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 = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;	// if equal
+	BID_RETURN (res);
+      }
+      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 : x;
+      BID_RETURN (res);
+    }
+    __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
+    // if positive, 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])) {
+      // if = in magnitude, return +, (if possible)
+      res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
+      BID_RETURN (res);
+    }
+    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 : x;
+    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;
+    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 positive, 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])) {
+      // if = in magnitude, return +, (if possible)
+      res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
+      BID_RETURN (res);
+    }
+    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]))) ? y : x;
+    BID_RETURN (res);
+  }
+  // adjust the y significand upwards
+  __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_y);
+  // if positive, 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])) {
+    // if = in magnitude, return +, if possible)
+    res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
+    BID_RETURN (res);
+  }
+  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 : x;
+  BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128 maximum function - returns greater of two numbers
+ *****************************************************************************/
+
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128_maxnum (UINT128 * pres, UINT128 * px,
+	       UINT128 * py _EXC_FLAGS_PARAM) {
+  UINT128 x = *px;
+  UINT128 y = *py;
+#else
+UINT128
+bid128_maxnum (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
+#endif
+
+  UINT128 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;
+
+  BID_SWAP128 (x);
+  BID_SWAP128 (y);
+
+  // check for non-canonical x
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    x.w[1] = x.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (x.w[0] > 0x38c15b09ffffffffull))) {
+      x.w[1] = x.w[1] & 0xffffc00000000000ull;
+      x.w[0] = 0x0ull;
+    }
+  } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) {	// x = inf
+    x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
+    x.w[0] = 0x0ull;
+  } else {	// x is not special
+    // check for non-canonical values - treated as zero
+    if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
+      x.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && x.w[0] > 0x378d8e63ffffffffull)) {
+	// x is non-canonical if coefficient is larger than 10^34 -1
+	x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
+	x.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+  // check for non-canonical y
+  if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+    y.w[1] = y.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (y.w[0] > 0x38c15b09ffffffffull))) {
+      y.w[1] = y.w[1] & 0xffffc00000000000ull;
+      y.w[0] = 0x0ull;
+    }
+  } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) {	// y = inf
+    y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
+    y.w[0] = 0x0ull;
+  } else {	// y is not special
+    // check for non-canonical values - treated as zero
+    if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
+      y.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && y.w[0] > 0x378d8e63ffffffffull)) {
+	// y is non-canonical if coefficient is larger than 10^34 -1
+	y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
+	y.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+
+  // NaN (CASE1)
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNaN
+      // if x is SNAN, then return quiet (x)
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      x.w[1] = x.w[1] & 0xfdffffffffffffffull;	// quietize x
+      res = x;
+    } else {	// x is QNaN
+      if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+	if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
+	  *pfpsf |= INVALID_EXCEPTION;	// set invalid flag
+	}
+	res = x;
+      } else {
+	res = y;
+      }
+    }
+    BID_RETURN (res);
+  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NaN, but x is not
+    if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      y.w[1] = y.w[1] & 0xfdffffffffffffffull;	// quietize y
+      res = y;
+    } else {
+      // will return x (which is not NaN)
+      res = x;
+    }
+    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 = x;
+    BID_RETURN (res);
+  }
+  // INFINITY (CASE3)
+  if ((x.w[1] & MASK_INF) == MASK_INF) {
+    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? y : x;
+    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) ? x : y;
+    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;
+
+  // CONVERT Y
+  exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
+  sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
+  sig_y.w[0] = y.w[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 ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
+    x_is_zero = 1;
+  }
+  if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
+    y_is_zero = 1;
+  }
+
+  if (x_is_zero && y_is_zero) {
+    // if both numbers are zero, neither is greater => return either number
+    res = x;
+    BID_RETURN (res);
+  } else if (x_is_zero) {
+    // is x is zero, it is greater if Y is negative
+    res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
+    BID_RETURN (res);
+  } else if (y_is_zero) {
+    // is y is zero, X is greater if it is positive
+    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
+    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) ? x : y;
+    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)) ? x : y;
+    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) ? x : y;
+    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) ? x : y;
+    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) {
+      // difference cannot be greater than 10^33
+      res = ((x.w[1] & MASK_SIGN) != MASK_SIGN) ? x : y;
+      BID_RETURN (res);
+    }
+    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)
+      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)) ? x : y;
+      BID_RETURN (res);
+    }
+    __mul_64x128_to_192 (sig_n_prime192, ten2k64[diff], sig_x);
+    // if postitive, return whichever significand is larger 
+    // (converse if negative)
+    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)) ? x : y;
+    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) ? x : y;
+    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)
+    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)) ? x : y;
+    BID_RETURN (res);
+  }
+  // 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)
+  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)) ? x : y;
+  BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128 maximum magnitude function - returns greater of two numbers
+ *****************************************************************************/
+
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128_maxnum_mag (UINT128 * pres, UINT128 * px,
+		   UINT128 * py _EXC_FLAGS_PARAM) {
+  UINT128 x = *px;
+  UINT128 y = *py;
+#else
+UINT128
+bid128_maxnum_mag (UINT128 x, UINT128 y _EXC_FLAGS_PARAM) {
+#endif
+
+  UINT128 res;
+  int exp_x, exp_y;
+  int diff;
+  UINT128 sig_x, sig_y;
+  UINT192 sig_n_prime192;
+  UINT256 sig_n_prime256;
+
+  BID_SWAP128 (x);
+  BID_SWAP128 (y);
+
+  // check for non-canonical x
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    x.w[1] = x.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (x.w[0] > 0x38c15b09ffffffffull))) {
+      x.w[1] = x.w[1] & 0xffffc00000000000ull;
+      x.w[0] = 0x0ull;
+    }
+  } else if ((x.w[1] & MASK_ANY_INF) == MASK_INF) {	// x = inf
+    x.w[1] = x.w[1] & (MASK_SIGN | MASK_INF);
+    x.w[0] = 0x0ull;
+  } else {	// x is not special
+    // check for non-canonical values - treated as zero
+    if ((x.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      x.w[1] = (x.w[1] & MASK_SIGN) | ((x.w[1] << 2) & MASK_EXP);
+      x.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((x.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((x.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull
+	   && x.w[0] > 0x378d8e63ffffffffull)) {
+	// x is non-canonical if coefficient is larger than 10^34 -1
+	x.w[1] = (x.w[1] & MASK_SIGN) | (x.w[1] & MASK_EXP);
+	x.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+  // check for non-canonical y
+  if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+    y.w[1] = y.w[1] & 0xfe003fffffffffffull;	// clear out G[6]-G[16]
+    // check for non-canonical NaN payload
+    if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+	(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+	 (y.w[0] > 0x38c15b09ffffffffull))) {
+      y.w[1] = y.w[1] & 0xffffc00000000000ull;
+      y.w[0] = 0x0ull;
+    }
+  } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) {	// y = inf
+    y.w[1] = y.w[1] & (MASK_SIGN | MASK_INF);
+    y.w[0] = 0x0ull;
+  } else {	// y is not special
+    // check for non-canonical values - treated as zero
+    if ((y.w[1] & MASK_STEERING_BITS) == MASK_STEERING_BITS) {	// G0_G1=11
+      // non-canonical
+      y.w[1] = (y.w[1] & MASK_SIGN) | ((y.w[1] << 2) & MASK_EXP);
+      y.w[0] = 0x0ull;
+    } else {	// G0_G1 != 11
+      if ((y.w[1] & MASK_COEFF) > 0x0001ed09bead87c0ull ||
+	  ((y.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull &&
+	   y.w[0] > 0x378d8e63ffffffffull)) {
+	// y is non-canonical if coefficient is larger than 10^34 -1
+	y.w[1] = (y.w[1] & MASK_SIGN) | (y.w[1] & MASK_EXP);
+	y.w[0] = 0x0ull;
+      } else {	// canonical
+	;
+      }
+    }
+  }
+
+  // NaN (CASE1)
+  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNaN
+      // if x is SNAN, then return quiet (x)
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      x.w[1] = x.w[1] & 0xfdffffffffffffffull;	// quietize x
+      res = x;
+    } else {	// x is QNaN
+      if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NAN
+	if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {	// y is SNAN
+	  *pfpsf |= INVALID_EXCEPTION;	// set invalid flag
+	}
+	res = x;
+      } else {
+	res = y;
+      }
+    }
+    BID_RETURN (res);
+  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {	// y is NaN, but x is not
+    if ((y.w[1] & MASK_SNAN) == MASK_SNAN) {
+      *pfpsf |= INVALID_EXCEPTION;	// set exception if SNaN
+      y.w[1] = y.w[1] & 0xfdffffffffffffffull;	// quietize y
+      res = y;
+    } else {
+      // will return x (which is not NaN)
+      res = x;
+    }
+    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 = y;
+    BID_RETURN (res);
+  }
+  // INFINITY (CASE3)
+  if ((x.w[1] & MASK_INF) == MASK_INF) {
+    // if x infinity, it has maximum magnitude
+    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN
+	   && (y.w[1] & MASK_INF) == MASK_INF) ? y : x;
+    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;
+    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;
+
+  // CONVERT Y
+  exp_y = (y.w[1] >> 49) & 0x0000000000003fffull;
+  sig_y.w[1] = y.w[1] & 0x0001ffffffffffffull;
+  sig_y.w[0] = y.w[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 ((sig_x.w[1] == 0) && (sig_x.w[0] == 0)) {
+    res = y;
+    BID_RETURN (res);
+  }
+  if ((sig_y.w[1] == 0) && (sig_y.w[0] == 0)) {
+    res = x;
+    BID_RETURN (res);
+  }
+  // REDUNDANT REPRESENTATIONS (CASE6)
+  if (exp_y == exp_x && sig_x.w[1] == sig_y.w[1]
+      && sig_x.w[0] == sig_y.w[0]) {
+    // check if exponents are the same and significands are the same
+    if (x.w[1] & 0x8000000000000000ull) {	// x is negative
+      res = y;
+      BID_RETURN (res);
+    } else {
+      res = x;
+      BID_RETURN (res);
+    }
+  } else 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)
+	     || ((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)) {
+    // if both components are either bigger or smaller, it is clear what 
+    // needs to be done; also if the magnitudes are equal
+    res = x;
+    BID_RETURN (res);
+  } else if (((sig_y.w[1] > sig_x.w[1] || (sig_y.w[1] == sig_x.w[1]
+					   && sig_y.w[0] > sig_x.w[0]))
+	      && exp_y == exp_x)
+	     || ((sig_y.w[1] > sig_x.w[1]
+		  || (sig_y.w[1] == sig_x.w[1]
+		      && sig_y.w[0] >= sig_x.w[0]))
+		 && exp_y > exp_x)) {
+    res = y;
+    BID_RETURN (res);
+  } else {
+    ;	// continue
+  }
+  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;	// difference cannot be greater than 10^33
+      BID_RETURN (res);
+    }
+    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 = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;	// if equal
+	BID_RETURN (res);
+      }
+      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])) ? x : y;
+      BID_RETURN (res);
+    }
+    __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])) {
+      // if equal, return positive magnitude
+      res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
+      BID_RETURN (res);
+    }
+    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])) ? x : y;
+    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 = y;
+    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])) {
+      // if equal, return positive (if possible)
+      res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
+      BID_RETURN (res);
+    }
+    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 : y;
+    BID_RETURN (res);
+  }
+  // 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])) {
+    // if equal, return positive (if possible)
+    res = ((y.w[1] & MASK_SIGN) == MASK_SIGN) ? x : y;
+    BID_RETURN (res);
+  }
+  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]))) ? x : y;
+  BID_RETURN (res);
+}