gcc/libgcc/config/libbid/bid128_noncomp.c

/* Copyright (C) 2007-2022 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 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);
}