gcc/libgcc/config/libbid/bid128_noncomp.c

/* Copyright (C) 2007  Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2, or (at your option) any later
version.

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

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

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

#include "bid_internal.h"

/*****************************************************************************
 *
 *    BID128 non-computational functions:
 *         - bid128_isSigned
 *         - bid128_isNormal
 *         - bid128_isSubnormal
 *         - bid128_isFinite
 *         - bid128_isZero
 *         - bid128_isInf
 *         - bid128_isSignaling
 *         - bid128_isCanonical
 *         - bid128_isNaN
 *         - bid128_copy
 *         - bid128_negate
 *         - bid128_abs
 *         - bid128_copySign
 *         - bid128_class
 *         - bid128_totalOrder
 *         - bid128_totalOrderMag
 *         - bid128_sameQuantum
 *         - bid128_radix
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isSigned (int *pres,
		 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isSigned (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x.w[HIGH_128W] & MASK_SIGN) == MASK_SIGN);
  BID_RETURN (res);
}

// return 1 iff x is not zero, nor NaN nor subnormal nor infinity
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isNormal (int *pres,
		 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isNormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  UINT64 x_exp, C1_hi, C1_lo;
  BID_UI64DOUBLE tmp1;
  int exp, q, x_nr_bits;

  BID_SWAP128 (x);
  // test for special values - infinity or NaN
  if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
    // x is special
    res = 0;
    BID_RETURN (res);
  }
  // unpack x 
  x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
  C1_hi = x.w[1] & MASK_COEFF;
  C1_lo = x.w[0];
  // test for zero
  if (C1_hi == 0 && C1_lo == 0) {
    res = 0;
    BID_RETURN (res);
  }
  // test for non-canonical values of the argument x
  if ((((C1_hi > 0x0001ed09bead87c0ull)
	|| ((C1_hi == 0x0001ed09bead87c0ull)
	    && (C1_lo > 0x378d8e63ffffffffull)))
       && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
      || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
    res = 0;
    BID_RETURN (res);
  }
  // x is subnormal or normal
  // determine the number of digits q in the significand
  // q = nr. of decimal digits in x
  // determine first the nr. of bits in x
  if (C1_hi == 0) {
    if (C1_lo >= 0x0020000000000000ull) {	// x >= 2^53
      // split the 64-bit value in two 32-bit halves to avoid rounding errors
      if (C1_lo >= 0x0000000100000000ull) {	// x >= 2^32
	tmp1.d = (double) (C1_lo >> 32);	// exact conversion
	x_nr_bits =
	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      } else {	// x < 2^32
	tmp1.d = (double) (C1_lo);	// exact conversion
	x_nr_bits =
	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else {	// if x < 2^53
      tmp1.d = (double) C1_lo;	// exact conversion
      x_nr_bits =
	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }
  } else {	// C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
    tmp1.d = (double) C1_hi;	// exact conversion
    x_nr_bits =
      65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
  }
  q = nr_digits[x_nr_bits - 1].digits;
  if (q == 0) {
    q = nr_digits[x_nr_bits - 1].digits1;
    if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
	(C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
	 C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
      q++;
  }
  exp = (int) (x_exp >> 49) - 6176;
  // test for subnormal values of x
  if (exp + q <= -6143) {
    res = 0;
    BID_RETURN (res);
  } else {
    res = 1;
    BID_RETURN (res);
  }
}

// return 1 iff x is not zero, nor NaN nor normal nor infinity
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isSubnormal (int *pres,
		    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isSubnormal (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  UINT64 x_exp, C1_hi, C1_lo;
  BID_UI64DOUBLE tmp1;
  int exp, q, x_nr_bits;

  BID_SWAP128 (x);
  // test for special values - infinity or NaN
  if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
    // x is special
    res = 0;
    BID_RETURN (res);
  }
  // unpack x 
  x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
  C1_hi = x.w[1] & MASK_COEFF;
  C1_lo = x.w[0];
  // test for zero
  if (C1_hi == 0 && C1_lo == 0) {
    res = 0;
    BID_RETURN (res);
  }
  // test for non-canonical values of the argument x
  if ((((C1_hi > 0x0001ed09bead87c0ull)
	|| ((C1_hi == 0x0001ed09bead87c0ull)
	    && (C1_lo > 0x378d8e63ffffffffull)))
       && ((x.w[1] & 0x6000000000000000ull) != 0x6000000000000000ull))
      || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
    res = 0;
    BID_RETURN (res);
  }
  // x is subnormal or normal
  // determine the number of digits q in the significand
  // q = nr. of decimal digits in x
  // determine first the nr. of bits in x
  if (C1_hi == 0) {
    if (C1_lo >= 0x0020000000000000ull) {	// x >= 2^53
      // split the 64-bit value in two 32-bit halves to avoid rounding errors
      if (C1_lo >= 0x0000000100000000ull) {	// x >= 2^32
	tmp1.d = (double) (C1_lo >> 32);	// exact conversion
	x_nr_bits =
	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      } else {	// x < 2^32
	tmp1.d = (double) (C1_lo);	// exact conversion
	x_nr_bits =
	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else {	// if x < 2^53
      tmp1.d = (double) C1_lo;	// exact conversion
      x_nr_bits =
	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }
  } else {	// C1_hi != 0 => nr. bits = 64 + nr_bits (C1_hi)
    tmp1.d = (double) C1_hi;	// exact conversion
    x_nr_bits =
      65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
  }
  q = nr_digits[x_nr_bits - 1].digits;
  if (q == 0) {
    q = nr_digits[x_nr_bits - 1].digits1;
    if (C1_hi > nr_digits[x_nr_bits - 1].threshold_hi ||
	(C1_hi == nr_digits[x_nr_bits - 1].threshold_hi &&
	 C1_lo >= nr_digits[x_nr_bits - 1].threshold_lo))
      q++;
  }
  exp = (int) (x_exp >> 49) - 6176;
  // test for subnormal values of x
  if (exp + q <= -6143) {
    res = 1;
  } else {
    res = 0;
  }
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isFinite (int *pres,
		 UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isFinite (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  res = ((x.w[HIGH_128W] & MASK_INF) != MASK_INF);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isZero (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isZero (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  UINT128 sig_x;

  BID_SWAP128 (x);
  if ((x.w[1] & MASK_INF) == MASK_INF) {
    res = 0;
    BID_RETURN (res);
  }
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
  sig_x.w[0] = x.w[0];
  if ((sig_x.w[1] > 0x0001ed09bead87c0ull) ||	// significand is non-canonical
      ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) ||	// significand is non-canonical
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull && (x.w[1] & MASK_INF) != MASK_INF) ||	// significand is non-canonical
      (sig_x.w[1] == 0 && sig_x.w[0] == 0)) {	// significand is 0
    res = 1;
    BID_RETURN (res);
  }
  res = 0;
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isInf (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isInf (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  res = ((x.w[HIGH_128W] & MASK_INF) == MASK_INF)
    && ((x.w[HIGH_128W] & MASK_NAN) != MASK_NAN);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isSignaling (int *pres,
		    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isSignaling (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x.w[HIGH_128W] & MASK_SNAN) == MASK_SNAN);
  BID_RETURN (res);
}

// return 1 iff x is a canonical number ,infinity, or NaN.
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isCanonical (int *pres,
		    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isCanonical (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  UINT128 sig_x;

  BID_SWAP128 (x);
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// NaN
    if (x.w[1] & 0x01ffc00000000000ull) {
      res = 0;
      BID_RETURN (res);
    }
    sig_x.w[1] = x.w[1] & 0x00003fffffffffffull;	// 46 bits
    sig_x.w[0] = x.w[0];	// 64 bits
    // payload must be < 10^33 = 0x0000314dc6448d93_38c15b0a00000000
    if (sig_x.w[1] < 0x0000314dc6448d93ull
	|| (sig_x.w[1] == 0x0000314dc6448d93ull
	    && sig_x.w[0] < 0x38c15b0a00000000ull)) {
      res = 1;
    } else {
      res = 0;
    }
    BID_RETURN (res);
  } else if ((x.w[1] & MASK_INF) == MASK_INF) {	// infinity
    if ((x.w[1] & 0x03ffffffffffffffull) || x.w[0]) {
      res = 0;
    } else {
      res = 1;
    }
    BID_RETURN (res);
  }
  // not NaN or infinity; extract significand to ensure it is canonical
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
  sig_x.w[0] = x.w[0];
  // a canonical number has a coefficient < 10^34 
  //    (0x0001ed09_bead87c0_378d8e64_00000000)
  if ((sig_x.w[1] > 0x0001ed09bead87c0ull) ||	// significand is non-canonical
      ((sig_x.w[1] == 0x0001ed09bead87c0ull) && (sig_x.w[0] > 0x378d8e63ffffffffull)) ||	// significand is non-canonical
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
    res = 0;
  } else {
    res = 1;
  }
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_isNaN (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_isNaN (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x.w[HIGH_128W] & MASK_NAN) == MASK_NAN);
  BID_RETURN (res);
}

// copies a floating-point operand x to destination y, with no change
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_copy (UINT128 * pres,
	     UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
UINT128
bid128_copy (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  UINT128 res;

  res = x;
  BID_RETURN (res);
}

// copies a floating-point operand x to destination y, reversing the sign
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_negate (UINT128 * pres,
	       UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
UINT128
bid128_negate (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  UINT128 res;

  x.w[HIGH_128W] ^= MASK_SIGN;
  res = x;
  BID_RETURN (res);
}

// copies a floating-point operand x to destination y, changing the sign to positive
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_abs (UINT128 * pres,
	    UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
UINT128
bid128_abs (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  UINT128 res;

  x.w[HIGH_128W] &= ~MASK_SIGN;
  res = x;
  BID_RETURN (res);
}

// copies operand x to destination in the same format as x, but with the sign of y
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_copySign (UINT128 * pres, UINT128 * px,
		 UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
  UINT128 y = *py;
#else
UINT128
bid128_copySign (UINT128 x, UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  UINT128 res;

  x.w[HIGH_128W] =
    (x.w[HIGH_128W] & ~MASK_SIGN) | (y.w[HIGH_128W] & MASK_SIGN);
  res = x;
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_class (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_class (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  UINT256 sig_x_prime256;
  UINT192 sig_x_prime192;
  UINT128 sig_x;
  int exp_x;

  BID_SWAP128 (x);
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {
    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {
      res = signalingNaN;
    } else {
      res = quietNaN;
    }
    BID_RETURN (res);
  }
  if ((x.w[1] & MASK_INF) == MASK_INF) {
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
      res = negativeInfinity;
    } else {
      res = positiveInfinity;
    }
    BID_RETURN (res);
  }
  // decode number into exponent and significand
  sig_x.w[1] = x.w[1] & 0x0001ffffffffffffull;
  sig_x.w[0] = x.w[0];
  // check for zero or non-canonical
  if ((sig_x.w[1] > 0x0001ed09bead87c0ull)
      || ((sig_x.w[1] == 0x0001ed09bead87c0ull)
	  && (sig_x.w[0] > 0x378d8e63ffffffffull))
      || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)
      || ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
      res = negativeZero;
    } else {
      res = positiveZero;
    }
    BID_RETURN (res);
  }
  exp_x = (x.w[1] >> 49) & 0x000000000003fffull;
  // if exponent is less than -6176, the number may be subnormal 
  // (less than the smallest normal value)
  //  the smallest normal value is 1 x 10^-6143 = 10^33 x 10^-6176
  //  if (exp_x - 6176 < -6143)
  if (exp_x < 33) {	// sig_x * 10^exp_x
    if (exp_x > 19) {
      __mul_128x128_to_256 (sig_x_prime256, sig_x,
			    ten2k128[exp_x - 20]);
      // 10^33 = 0x0000314dc6448d93_38c15b0a00000000
      if ((sig_x_prime256.w[3] == 0) && (sig_x_prime256.w[2] == 0)
	  && ((sig_x_prime256.w[1] < 0x0000314dc6448d93ull)
	      || ((sig_x_prime256.w[1] == 0x0000314dc6448d93ull)
		  && (sig_x_prime256.w[0] < 0x38c15b0a00000000ull)))) {
	res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal :
	  positiveSubnormal;
	BID_RETURN (res);
      }
    } else {
      __mul_64x128_to_192 (sig_x_prime192, ten2k64[exp_x], sig_x);
      // 10^33 = 0x0000314dc6448d93_38c15b0a00000000
      if ((sig_x_prime192.w[2] == 0)
	  && ((sig_x_prime192.w[1] < 0x0000314dc6448d93ull)
	      || ((sig_x_prime192.w[1] == 0x0000314dc6448d93ull)
		  && (sig_x_prime192.w[0] < 0x38c15b0a00000000ull)))) {
	res = ((x.w[1] & MASK_SIGN) == MASK_SIGN) ? negativeSubnormal :
	  positiveSubnormal;
	BID_RETURN (res);
      }
    }
  }
  // otherwise, normal number, determine the sign
  res =
    ((x.w[1] & MASK_SIGN) ==
     MASK_SIGN) ? negativeNormal : positiveNormal;
  BID_RETURN (res);
}

// true if the exponents of x and y are the same, false otherwise.
// The special cases of sameQuantum(NaN, NaN) and sameQuantum(Inf, Inf) are true
// If exactly one operand is infinite or exactly one operand is NaN, then false
#if DECIMAL_CALL_BY_REFERENCE
void
bid128_sameQuantum (int *pres, UINT128 * px,
		    UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
  UINT128 y = *py;
#else
int
bid128_sameQuantum (UINT128 x,
		    UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  UINT64 x_exp, y_exp;

  BID_SWAP128 (x);
  BID_SWAP128 (y);
  // if both operands are NaN, return true
  if ((x.w[1] & MASK_NAN) == MASK_NAN
      || ((y.w[1] & MASK_NAN) == MASK_NAN)) {
    res = ((x.w[1] & MASK_NAN) == MASK_NAN
	   && (y.w[1] & MASK_NAN) == MASK_NAN);
    BID_RETURN (res);
  }
  // if both operands are INF, return true
  if ((x.w[1] & MASK_INF) == MASK_INF
      || (y.w[1] & MASK_INF) == MASK_INF) {
    res = ((x.w[1] & MASK_INF) == MASK_INF)
      && ((y.w[1] & MASK_INF) == MASK_INF);
    BID_RETURN (res);
  }
  // decode exponents for both numbers, and return true if they match
  if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {	// G0_G1=11
    x_exp = (x.w[1] << 2) & MASK_EXP;	// biased and shifted left 49 bits
  } else {	// G0_G1 != 11
    x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bits
  }
  if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {	// G0_G1=11
    y_exp = (y.w[1] << 2) & MASK_EXP;	// biased and shifted left 49 bits
  } else {	// G0_G1 != 11
    y_exp = y.w[1] & MASK_EXP;	// biased and shifted left 49 bits
  }
  res = (x_exp == y_exp);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_totalOrder (int *pres, UINT128 * px,
		   UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
  UINT128 y = *py;
#else
int
bid128_totalOrder (UINT128 x,
		   UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT128 sig_x, sig_y, pyld_y, pyld_x;
  UINT192 sig_n_prime192;
  UINT256 sig_n_prime256;
  char x_is_zero = 0, y_is_zero = 0;

  BID_SWAP128 (x);
  BID_SWAP128 (y);
  // NaN (CASE 1)
  // if x and y are unordered numerically because either operand is NaN
  //    (1) totalOrder(-NaN, number) is true
  //    (2) totalOrder(number, +NaN) is true
  //    (3) if x and y are both NaN:
  //       i) negative sign bit < positive sign bit
  //       ii) signaling < quiet for +NaN, reverse for -NaN
  //       iii) lesser payload < greater payload for +NaN (reverse for -NaN)
  //       iv) else if bitwise identical (in canonical form), return 1
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {
    // if x is -NaN
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
      // return true, unless y is -NaN also
      if ((y.w[1] & MASK_NAN) != MASK_NAN
	  || (y.w[1] & MASK_SIGN) != MASK_SIGN) {
	res = 1;	// y is a number, return 1
	BID_RETURN (res);
      } else {	// if y and x are both -NaN
	pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
	pyld_x.w[0] = x.w[0];
	pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
	pyld_y.w[0] = y.w[0];
	if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
	    || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
		&& (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
	  pyld_x.w[1] = 0;
	  pyld_x.w[0] = 0;
	}
	if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
	    || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
		&& (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
	  pyld_y.w[1] = 0;
	  pyld_y.w[0] = 0;
	}
	// if x and y are both -SNaN or both -QNaN, we have to compare payloads
	// this statement evaluates to true if both are SNaN or QNaN
	if (!
	    (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
	     ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
	  // it comes down to the payload.  we want to return true if x has a
	  // larger payload, or if the payloads are equal (canonical forms
	  // are bitwise identical)
	  if ((pyld_x.w[1] > pyld_y.w[1]) ||
	      ((pyld_x.w[1] == pyld_y.w[1])
	       && (pyld_x.w[0] >= pyld_y.w[0])))
	    res = 1;
	  else
	    res = 0;
	  BID_RETURN (res);
	} else {
	  // either x = -SNaN and y = -QNaN or x = -QNaN and y = -SNaN
	  res = ((y.w[1] & MASK_SNAN) == MASK_SNAN);
	  // totalOrder (-QNaN, -SNaN) == 1
	  BID_RETURN (res);
	}
      }
    } else {	// x is +NaN
      // return false, unless y is +NaN also
      if ((y.w[1] & MASK_NAN) != MASK_NAN
	  || (y.w[1] & MASK_SIGN) == MASK_SIGN) {
	res = 0;	// y is a number, return 1
	BID_RETURN (res);
      } else {
	// x and y are both +NaN; 
	pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
	pyld_x.w[0] = x.w[0];
	pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
	pyld_y.w[0] = y.w[0];
	if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
	    || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
		&& (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
	  pyld_x.w[1] = 0;
	  pyld_x.w[0] = 0;
	}
	if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
	    || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
		&& (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
	  pyld_y.w[1] = 0;
	  pyld_y.w[0] = 0;
	}
	// if x and y are both +SNaN or both +QNaN, we have to compare payloads
	// this statement evaluates to true if both are SNaN or QNaN
	if (!
	    (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
	     ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
	  // it comes down to the payload.  we want to return true if x has a
	  // smaller payload, or if the payloads are equal (canonical forms
	  // are bitwise identical)
	  if ((pyld_x.w[1] < pyld_y.w[1]) ||
	      ((pyld_x.w[1] == pyld_y.w[1])
	       && (pyld_x.w[0] <= pyld_y.w[0])))
	    res = 1;
	  else
	    res = 0;
	  BID_RETURN (res);
	} else {
	  // either x = SNaN and y = QNaN or x = QNaN and y = SNaN
	  res = ((x.w[1] & MASK_SNAN) == MASK_SNAN);
	  // totalOrder (-QNaN, -SNaN) == 1
	  BID_RETURN (res);
	}
      }
    }
  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {
    // x is certainly not NAN in this case.
    // return true if y is positive
    res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // SIMPLE (CASE 2)
  // if all the bits are the same, the numbers are equal.
  if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }
  // OPPOSITE SIGNS (CASE 3)
  // if signs are opposite, return 1 if x is negative 
  // (if x < y, totalOrder is true)
  if (((x.w[1] & MASK_SIGN) == MASK_SIGN) ^ ((y.w[1] & MASK_SIGN) ==
					     MASK_SIGN)) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // INFINITY (CASE 4)
  if ((x.w[1] & MASK_INF) == MASK_INF) {
    // if x == neg_inf, return (y == neg_inf);
    if ((x.w[1] & MASK_SIGN) == MASK_SIGN) {
      res = 1;
      BID_RETURN (res);
    } else {
      // x is positive infinity, only return1 if y is positive infinity as well
      res = ((y.w[1] & MASK_INF) == MASK_INF);
      BID_RETURN (res);
      // && (y & MASK_SIGN) != MASK_SIGN); (we know y has same sign as x)
    }
  } else if ((y.w[1] & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    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)) ||
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
      ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
    x_is_zero = 1;
    // check for the case where the exponent is shifted right by 2 bits!
    if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
      exp_x = (x.w[1] >> 47) & 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];

  // 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)) ||
      ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
      ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
    y_is_zero = 1;
    // check for the case where the exponent is shifted right by 2 bits!
    if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
      exp_y = (y.w[1] >> 47) & 0x000000000003fffull;
    }
  }
  // ZERO (CASE 5)
  // if x and y represent the same entities, and both are negative 
  // return true iff exp_x <= exp_y
  if (x_is_zero && y_is_zero) {
    // we know that signs must be the same because we would have caught it 
    // in case3 if signs were different
    // totalOrder(x,y) iff exp_x >= exp_y for negative numbers
    // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
    if (exp_x == exp_y) {
      res = 1;
      BID_RETURN (res);
    }
    res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
    BID_RETURN (res);
  }
  // if x is zero and y isn't, clearly x has the smaller payload
  if (x_is_zero) {
    res = ((y.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if y is zero, and x isn't, clearly y has the smaller payload
  if (y_is_zero) {
    res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE 6)
  // if both components are either bigger or smaller
  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);
  }
  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
  if (exp_x > exp_y) {
    // if exp_x is 33 greater than exp_y, it is definitely larger, 
    // so no need for compensation
    if (exp_x - exp_y > 33) {
      res = ((x.w[1] & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
      // difference cannot be greater than 10^33
    }
    // otherwise adjust the x significand upwards
    if (exp_x - exp_y > 19) {
      __mul_128x128_to_256 (sig_n_prime256, sig_x,
			    ten2k128[exp_x - exp_y - 20]);
      // the compensated significands are equal (ie "x and y represent the same
      // entities") return 1 if (negative && expx > expy) || 
      // (positive && expx < expy)
      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])) {
	// the case exp_x == exp_y  cannot occur, because all bits must be 
	// the same - would have been caught if (x == y)
	res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
	BID_RETURN (res);
      }
      // if positive, return 1 if adjusted x is smaller than y
      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.w[1] & MASK_SIGN) ==
				       MASK_SIGN));
      BID_RETURN (res);
    }
    __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], 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])) {
      res = ((exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
      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.w[1] & MASK_SIGN) ==
				     MASK_SIGN));
    BID_RETURN (res);
  }
  // if exp_x is 33 less than exp_y, it is definitely smaller, 
  // no need for compensation
  if (exp_y - exp_x > 33) {
    res = ((x.w[1] & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  if (exp_y - exp_x > 19) {
    // adjust the y significand upwards
    __mul_128x128_to_256 (sig_n_prime256, sig_y,
			  ten2k128[exp_y - exp_x - 20]);
    // if x and y represent the same entities and both are negative
    // return true iff exp_x <= exp_y
    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 = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
    // values are not equal, for positive numbers return 1 if x is less than y
    // and 0 otherwise
    res = (((sig_n_prime256.w[3] != 0) ||
	    // if upper128 bits of compensated y are non-zero, y is bigger
	    (sig_n_prime256.w[2] != 0) ||
	    // if upper128 bits of compensated y are non-zero, y is bigger
	    (sig_n_prime256.w[1] > sig_x.w[1]) ||
	    // if compensated y is bigger, y is bigger
	    (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);
  }
  __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
  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 = (exp_x <= exp_y) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  res = (((sig_n_prime192.w[2] != 0) ||
	  // if upper128 bits of compensated y are non-zero, y is bigger
	  (sig_n_prime192.w[1] > sig_x.w[1]) ||
	  // if compensated y is bigger, y is bigger
	  (sig_n_prime192.w[1] == sig_x.w[1]
	   && sig_n_prime192.w[0] >
	   sig_x.w[0])) ^ ((x.w[1] & MASK_SIGN) == MASK_SIGN));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_totalOrderMag (int *pres, UINT128 * px,
		      UINT128 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
  UINT128 y = *py;
#else
int
bid128_totalOrderMag (UINT128 x,
		      UINT128 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  UINT128 sig_x, sig_y, pyld_y, pyld_x;
  UINT192 sig_n_prime192;
  UINT256 sig_n_prime256;
  char x_is_zero = 0, y_is_zero = 0;

  BID_SWAP128 (x);
  BID_SWAP128 (y);
  x.w[1] = x.w[1] & 0x7fffffffffffffffull;
  y.w[1] = y.w[1] & 0x7fffffffffffffffull;

  // NaN (CASE 1)
  // if x and y are unordered numerically because either operand is NaN
  //    (1) totalOrder(number, +NaN) is true
  //    (2) if x and y are both NaN:
  //       i) signaling < quiet for +NaN
  //       ii) lesser payload < greater payload for +NaN
  //       iii) else if bitwise identical (in canonical form), return 1
  if ((x.w[1] & MASK_NAN) == MASK_NAN) {
    // x is +NaN
    // return false, unless y is +NaN also
    if ((y.w[1] & MASK_NAN) != MASK_NAN) {
      res = 0;	// y is a number, return 0
      BID_RETURN (res);
    } else {
      // x and y are both +NaN; 
      pyld_x.w[1] = x.w[1] & 0x00003fffffffffffull;
      pyld_x.w[0] = x.w[0];
      pyld_y.w[1] = y.w[1] & 0x00003fffffffffffull;
      pyld_y.w[0] = y.w[0];
      if ((pyld_x.w[1] > 0x0000314dc6448d93ull)
	  || ((pyld_x.w[1] == 0x0000314dc6448d93ull)
	      && (pyld_x.w[0] > 0x38c15b09ffffffffull))) {
	pyld_x.w[1] = 0;
	pyld_x.w[0] = 0;
      }
      if ((pyld_y.w[1] > 0x0000314dc6448d93ull)
	  || ((pyld_y.w[1] == 0x0000314dc6448d93ull)
	      && (pyld_y.w[0] > 0x38c15b09ffffffffull))) {
	pyld_y.w[1] = 0;
	pyld_y.w[0] = 0;
      }
      // if x and y are both +SNaN or both +QNaN, we have to compare payloads
      // this statement evaluates to true if both are SNaN or QNaN
      if (!
	  (((y.w[1] & MASK_SNAN) == MASK_SNAN) ^
	   ((x.w[1] & MASK_SNAN) == MASK_SNAN))) {
	// it comes down to the payload.  we want to return true if x has a
	// smaller payload, or if the payloads are equal (canonical forms
	// are bitwise identical)
	if ((pyld_x.w[1] < pyld_y.w[1]) ||
	    ((pyld_x.w[1] == pyld_y.w[1])
	     && (pyld_x.w[0] <= pyld_y.w[0]))) {
	  res = 1;
	} else {
	  res = 0;
	}
	BID_RETURN (res);
      } else {
	// either x = SNaN and y = QNaN or x = QNaN and y = SNaN
	res = ((x.w[1] & MASK_SNAN) == MASK_SNAN);
	// totalOrder (-QNaN, -SNaN) == 1
	BID_RETURN (res);
      }
    }
  } else if ((y.w[1] & MASK_NAN) == MASK_NAN) {
    // x is certainly not NAN in this case.
    // return true because y is positive
    res = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE 2)
  // if all the bits are the same, the numbers are equal.
  if ((x.w[1] == y.w[1]) && (x.w[0] == y.w[0])) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE 3)
  if ((x.w[1] & MASK_INF) == MASK_INF) {
    // x is positive infinity, only return 1 if y is positive infinity as well
    res = ((y.w[1] & MASK_INF) == MASK_INF);
    BID_RETURN (res);
    // (we know y has same sign as x)
  } else if ((y.w[1] & MASK_INF) == MASK_INF) {
    // x is finite, so:
    //    since y is +inf, x<y
    res = 1;
    BID_RETURN (res);
  } else {
    ;	// continue
  }

  // 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)) ||
      ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
      ((sig_x.w[1] == 0) && (sig_x.w[0] == 0))) {
    x_is_zero = 1;
    // check for the case where the exponent is shifted right by 2 bits!
    if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
      exp_x = (x.w[1] >> 47) & 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];

  // 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)) ||
      ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) ||
      ((sig_y.w[1] == 0) && (sig_y.w[0] == 0))) {
    y_is_zero = 1;
    // check for the case where the exponent is shifted right by 2 bits!
    if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) {
      exp_y = (y.w[1] >> 47) & 0x000000000003fffull;
    }
  }
  // ZERO (CASE 4)
  if (x_is_zero && y_is_zero) {
    // we know that signs must be the same because we would have caught it 
    // in case3 if signs were different
    // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
    if (exp_x == exp_y) {
      res = 1;
      BID_RETURN (res);
    }
    res = (exp_x <= exp_y);
    BID_RETURN (res);
  }
  // if x is zero and y isn't, clearly x has the smaller payload
  if (x_is_zero) {
    res = 1;
    BID_RETURN (res);
  }
  // if y is zero, and x isn't, clearly y has the smaller payload
  if (y_is_zero) {
    res = 0;
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE 5)
  // if both components are either bigger or smaller
  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 = 0;
    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 = 1;
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 33, it comes down to the compensated significand
  if (exp_x > exp_y) {
    // if exp_x is 33 greater than exp_y, it is definitely larger, 
    // so no need for compensation
    if (exp_x - exp_y > 33) {
      res = 0;	// difference cannot be greater than 10^33
      BID_RETURN (res);
    }
    // otherwise adjust the x significand upwards
    if (exp_x - exp_y > 19) {
      __mul_128x128_to_256 (sig_n_prime256, sig_x,
			    ten2k128[exp_x - exp_y - 20]);
      // the compensated significands are equal (ie "x and y represent the same
      // entities") return 1 if (negative && expx > expy) || 
      // (positive && expx < expy)
      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])) {
	// the case (exp_x == exp_y) cannot occur, because all bits must be 
	// the same - would have been caught if (x == y)
	res = (exp_x <= exp_y);
	BID_RETURN (res);
      }
      // since positive, return 1 if adjusted x is smaller than y
      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])));
      BID_RETURN (res);
    }
    __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_x - exp_y], 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])) {
      res = (exp_x <= exp_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])));
    BID_RETURN (res);
  }
  // if exp_x is 33 less than exp_y, it is definitely smaller, 
  // no need for compensation
  if (exp_y - exp_x > 33) {
    res = 1;
    BID_RETURN (res);
  }
  if (exp_y - exp_x > 19) {
    // adjust the y significand upwards
    __mul_128x128_to_256 (sig_n_prime256, sig_y,
			  ten2k128[exp_y - exp_x - 20]);
    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 = (exp_x <= exp_y);
      BID_RETURN (res);
    }
    // values are not equal, for positive numbers return 1 if x is less than y
    // and 0 otherwise
    res = ((sig_n_prime256.w[3] != 0) ||
	   // if upper128 bits of compensated y are non-zero, y is bigger
	   (sig_n_prime256.w[2] != 0) ||
	   // if upper128 bits of compensated y are non-zero, y is bigger
	   (sig_n_prime256.w[1] > sig_x.w[1]) ||
	   // if compensated y is bigger, y is bigger
	   (sig_n_prime256.w[1] == sig_x.w[1]
	    && sig_n_prime256.w[0] > sig_x.w[0]));
    BID_RETURN (res);
  }
  __mul_64x128_to_192 (sig_n_prime192, ten2k64[exp_y - exp_x], sig_y);
  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 = (exp_x <= exp_y);
    BID_RETURN (res);
  }
  res = ((sig_n_prime192.w[2] != 0) ||
	 // if upper128 bits of compensated y are non-zero, y is bigger
	 (sig_n_prime192.w[1] > sig_x.w[1]) ||
	 // if compensated y is bigger, y is bigger
	 (sig_n_prime192.w[1] == sig_x.w[1]
	  && sig_n_prime192.w[0] > sig_x.w[0]));
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid128_radix (int *pres, UINT128 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT128 x = *px;
#else
int
bid128_radix (UINT128 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  if (x.w[LOW_128W])	// dummy test
    res = 10;
  else
    res = 10;
  BID_RETURN (res);
}