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/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under

the terms of the GNU General Public License as published by the Free

Software Foundation; either version 3, or (at your option) any later

version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY

WARRANTY; without even the implied warranty of MERCHANTABILITY or

FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

for more details.

Under Section 7 of GPL version 3, you are granted additional

permissions described in the GCC Runtime Library Exception, version

3.1, as published by the Free Software Foundation.

You should have received a copy of the GNU General Public License and

a copy of the GCC Runtime Library Exception along with this program;

see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see

<http://www.gnu.org/licenses/>.  */

#include "bid_internal.h"

static const UINT64 mult_factor[16] = {

  1ull, 10ull, 100ull, 1000ull,

  10000ull, 100000ull, 1000000ull, 10000000ull,

  100000000ull, 1000000000ull, 10000000000ull, 100000000000ull,

  1000000000000ull, 10000000000000ull,

  100000000000000ull, 1000000000000000ull

};

/*****************************************************************************

 *    BID64 non-computational functions:

 *         - bid64_isSigned

 *         - bid64_isNormal

 *         - bid64_isSubnormal

 *         - bid64_isFinite

 *         - bid64_isZero

 *         - bid64_isInf

 *         - bid64_isSignaling

 *         - bid64_isCanonical

 *         - bid64_isNaN

 *         - bid64_copy

 *         - bid64_negate

 *         - bid64_abs

 *         - bid64_copySign

 *         - bid64_class

 *         - bid64_sameQuantum

 *         - bid64_totalOrder

 *         - bid64_totalOrderMag

 *         - bid64_radix

 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isSigned (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isSigned (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  res = ((x & 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

bid64_isNormal (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isNormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  UINT128 sig_x_prime;

  UINT64 sig_x;

  unsigned int exp_x;

  if ((x & MASK_INF) == MASK_INF) {     // x is either INF or NaN

    res = 0;

  } else {

    // decode number into exponent and significand

    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

      sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

      // check for zero or non-canonical

      if (sig_x > 9999999999999999ull || sig_x == 0) {

        res = 0; // zero or non-canonical

        BID_RETURN (res);

      }

      exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;

    } else {

      sig_x = (x & MASK_BINARY_SIG1);

      if (sig_x == 0) {

        res = 0; // zero

        BID_RETURN (res);

      }

      exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;

    }

    // if exponent is less than -383, the number may be subnormal

    // if (exp_x - 398 = -383) the number may be subnormal

    if (exp_x < 15) {

      __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);

      if (sig_x_prime.w[1] == 0

          && sig_x_prime.w[0] < 1000000000000000ull) {

        res = 0; // subnormal

      } else {

        res = 1;        // normal

      }

    } else {

      res = 1;  // normal

    }

  }

  BID_RETURN (res);

}

// return 1 iff x is not zero, nor NaN nor normal nor infinity

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isSubnormal (int *pres,

                   UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isSubnormal (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  UINT128 sig_x_prime;

  UINT64 sig_x;

  unsigned int exp_x;

  if ((x & MASK_INF) == MASK_INF) {     // x is either INF or NaN

    res = 0;

  } else {

    // decode number into exponent and significand

    if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

      sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

      // check for zero or non-canonical

      if (sig_x > 9999999999999999ull || sig_x == 0) {

        res = 0; // zero or non-canonical

        BID_RETURN (res);

      }

      exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;

    } else {

      sig_x = (x & MASK_BINARY_SIG1);

      if (sig_x == 0) {

        res = 0; // zero

        BID_RETURN (res);

      }

      exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;

    }

    // if exponent is less than -383, the number may be subnormal

    // if (exp_x - 398 = -383) the number may be subnormal

    if (exp_x < 15) {

      __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);

      if (sig_x_prime.w[1] == 0

          && sig_x_prime.w[0] < 1000000000000000ull) {

        res = 1;        // subnormal

      } else {

        res = 0; // normal

      }

    } else {

      res = 0;   // normal

    }

  }

  BID_RETURN (res);

}

//iff x is zero, subnormal or normal (not infinity or NaN)

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isFinite (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isFinite (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  res = ((x & MASK_INF) != MASK_INF);

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isZero (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isZero (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  // if infinity or nan, return 0

  if ((x & MASK_INF) == MASK_INF) {

    res = 0;

  } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

    // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1]

    // => sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

    // if(sig_x > 9999999999999999ull) {return 1;}

    res =

      (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) >

       9999999999999999ull);

  } else {

    res = ((x & MASK_BINARY_SIG1) == 0);

  }

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isInf (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isInf (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  res = ((x & MASK_INF) == MASK_INF) && ((x & MASK_NAN) != MASK_NAN);

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isSignaling (int *pres,

                   UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isSignaling (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  res = ((x & MASK_SNAN) == MASK_SNAN);

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isCanonical (int *pres,

                   UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isCanonical (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  if ((x & MASK_NAN) == MASK_NAN) {     // NaN

    if (x & 0x01fc000000000000ull) {

      res = 0;

    } else if ((x & 0x0003ffffffffffffull) > 999999999999999ull) {      // payload

      res = 0;

    } else {

      res = 1;

    }

  } else if ((x & MASK_INF) == MASK_INF) {

    if (x & 0x03ffffffffffffffull) {

      res = 0;

    } else {

      res = 1;

    }

  } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {  // 54-bit coeff.

    res =

      (((x & MASK_BINARY_SIG2) | MASK_BINARY_OR2) <=

       9999999999999999ull);

  } else {      // 53-bit coeff.

    res = 1;

  }

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_isNaN (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_isNaN (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  res = ((x & 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

bid64_copy (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_copy (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  res = x;

  BID_RETURN (res);

}

// copies a floating-point operand x to destination y, reversing the sign

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_negate (UINT64 * pres,

              UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_negate (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  res = x ^ MASK_SIGN;

  BID_RETURN (res);

}

// copies a floating-point operand x to destination y, changing the sign to positive

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_abs (UINT64 * pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_abs (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  res = x & ~MASK_SIGN;

  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

bid64_copySign (UINT64 * pres, UINT64 * px,

                UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

  UINT64 y = *py;

#else

UINT64

bid64_copySign (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  res = (x & ~MASK_SIGN) | (y & MASK_SIGN);

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_class (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

int

bid64_class (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  UINT128 sig_x_prime;

  UINT64 sig_x;

  int exp_x;

  if ((x & MASK_NAN) == MASK_NAN) {

    // is the NaN signaling?

    if ((x & MASK_SNAN) == MASK_SNAN) {

      res = signalingNaN;

      BID_RETURN (res);

    }

    // if NaN and not signaling, must be quietNaN

    res = quietNaN;

    BID_RETURN (res);

  } else if ((x & MASK_INF) == MASK_INF) {

    // is the Infinity negative?

    if ((x & MASK_SIGN) == MASK_SIGN) {

      res = negativeInfinity;

    } else {

      // otherwise, must be positive infinity

      res = positiveInfinity;

    }

    BID_RETURN (res);

  } else if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

    // decode number into exponent and significand

    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

    // check for zero or non-canonical

    if (sig_x > 9999999999999999ull || sig_x == 0) {

      if ((x & MASK_SIGN) == MASK_SIGN) {

        res = negativeZero;

      } else {

        res = positiveZero;

      }

      BID_RETURN (res);

    }

    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;

  } else {

    sig_x = (x & MASK_BINARY_SIG1);

    if (sig_x == 0) {

      res =

        ((x & MASK_SIGN) == MASK_SIGN) ? negativeZero : positiveZero;

      BID_RETURN (res);

    }

    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;

  }

  // if exponent is less than -383, number may be subnormal

  //  if (exp_x - 398 < -383)

  if (exp_x < 15) {     // sig_x *10^exp_x

    __mul_64x64_to_128MACH (sig_x_prime, sig_x, mult_factor[exp_x]);

    if (sig_x_prime.w[1] == 0

        && (sig_x_prime.w[0] < 1000000000000000ull)) {

      res =

        ((x & MASK_SIGN) ==

         MASK_SIGN) ? negativeSubnormal : positiveSubnormal;

      BID_RETURN (res);

    }

  }

  // otherwise, normal number, determine the sign

  res =

    ((x & 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

bid64_sameQuantum (int *pres, UINT64 * px,

                   UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

  UINT64 y = *py;

#else

int

bid64_sameQuantum (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  unsigned int exp_x, exp_y;

  // if both operands are NaN, return true; if just one is NaN, return false

  if ((x & MASK_NAN) == MASK_NAN || ((y & MASK_NAN) == MASK_NAN)) {

    res = ((x & MASK_NAN) == MASK_NAN && (y & MASK_NAN) == MASK_NAN);

    BID_RETURN (res);

  }

  // if both operands are INF, return true; if just one is INF, return false

  if ((x & MASK_INF) == MASK_INF || (y & MASK_INF) == MASK_INF) {

    res = ((x & MASK_INF) == MASK_INF && (y & MASK_INF) == MASK_INF);

    BID_RETURN (res);

  }

  // decode exponents for both numbers, and return true if they match

  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;

  } else {

    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;

  }

  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;

  } else {

    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;

  }

  res = (exp_x == exp_y);

  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_totalOrder (int *pres, UINT64 * px,

                  UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

  UINT64 x = *px;

  UINT64 y = *py;

#else

int

bid64_totalOrder (UINT64 x, UINT64 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  int res;

  int exp_x, exp_y;

  UINT64 sig_x, sig_y, pyld_y, pyld_x;

  UINT128 sig_n_prime;

  char x_is_zero = 0, y_is_zero = 0;

  // NaN (CASE1)

  // 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 & MASK_NAN) == MASK_NAN) {

    // if x is -NaN

    if ((x & MASK_SIGN) == MASK_SIGN) {

      // return true, unless y is -NaN also

      if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) != MASK_SIGN) {

        res = 1;        // y is a number, return 1

        BID_RETURN (res);

      } else {  // if y and x are both -NaN

        // if x and y are both -sNaN or both -qNaN, we have to compare payloads

        // this xnor statement evaluates to true if both are sNaN or qNaN

        if (!

            (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & 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)

          pyld_y = y & 0x0003ffffffffffffull;

          pyld_x = x & 0x0003ffffffffffffull;

          if (pyld_y > 999999999999999ull || pyld_y == 0) {

            // if y is zero, x must be less than or numerically equal

            // y's payload is 0

            res = 1;

            BID_RETURN (res);

          }

          // if x is zero and y isn't, x has the smaller payload

          // definitely (since we know y isn't 0 at this point)

          if (pyld_x > 999999999999999ull || pyld_x == 0) {

            // x's payload is 0

            res = 0;

            BID_RETURN (res);

          }

          res = (pyld_x >= pyld_y);

          BID_RETURN (res);

        } else {

          // either x = -sNaN and y = -qNaN or x = -qNaN and y = -sNaN

          res = (y & MASK_SNAN) == MASK_SNAN;   // totalOrder(-qNaN, -sNaN) == 1

          BID_RETURN (res);

        }

      }

    } else {    // x is +NaN

      // return false, unless y is +NaN also

      if ((y & MASK_NAN) != MASK_NAN || (y & MASK_SIGN) == MASK_SIGN) {

        res = 0; // y is a number, return 1

        BID_RETURN (res);

      } else {

        // x and y are both +NaN; 

        // must investigate payload if both quiet or both signaling

        // this xnor statement will be true if both x and y are +qNaN or +sNaN

        if (!

            (((y & MASK_SNAN) == MASK_SNAN) ^ ((x & 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)

          pyld_y = y & 0x0003ffffffffffffull;

          pyld_x = x & 0x0003ffffffffffffull;

          // if x is zero and y isn't, x has the smaller 

          // payload definitely (since we know y isn't 0 at this point)

          if (pyld_x > 999999999999999ull || pyld_x == 0) {

            res = 1;

            BID_RETURN (res);

          }

          if (pyld_y > 999999999999999ull || pyld_y == 0) {

            // if y is zero, x must be less than or numerically equal

            res = 0;

            BID_RETURN (res);

          }

          res = (pyld_x <= pyld_y);

          BID_RETURN (res);

        } else {

          // return true if y is +qNaN and x is +sNaN 

          // (we know they're different bc of xor if_stmt above)

          res = ((x & MASK_SNAN) == MASK_SNAN);

          BID_RETURN (res);

        }

      }

    }

  } else if ((y & MASK_NAN) == MASK_NAN) {

    // x is certainly not NAN in this case.

    // return true if y is positive

    res = ((y & MASK_SIGN) != MASK_SIGN);

    BID_RETURN (res);

  }

  // SIMPLE (CASE2)

  // if all the bits are the same, these numbers are equal.

  if (x == y) {

    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 & MASK_SIGN) == MASK_SIGN) ^ ((y & MASK_SIGN) == MASK_SIGN)) {

    res = (x & MASK_SIGN) == MASK_SIGN;

    BID_RETURN (res);

  }

  // INFINITY (CASE4)

  if ((x & MASK_INF) == MASK_INF) {

    // if x==neg_inf, return (y == neg_inf)?1:0;

    if ((x & MASK_SIGN) == MASK_SIGN) {

      res = 1;

      BID_RETURN (res);

    } else {

      // x is positive infinity, only return1 if y 

      // is positive infinity as well

      // (we know y has same sign as x)

      res = ((y & MASK_INF) == MASK_INF);

      BID_RETURN (res);

    }

  } else if ((y & MASK_INF) == MASK_INF) {

    // x is finite, so:

    //    if y is +inf, x<y

    //    if y is -inf, x>y

    res = ((y & MASK_SIGN) != MASK_SIGN);

    BID_RETURN (res);

  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>

  if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

    exp_x = (x & MASK_BINARY_EXPONENT2) >> 51;

    sig_x = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

    if (sig_x > 9999999999999999ull || sig_x == 0) {

      x_is_zero = 1;

    }

  } else {

    exp_x = (x & MASK_BINARY_EXPONENT1) >> 53;

    sig_x = (x & MASK_BINARY_SIG1);

    if (sig_x == 0) {

      x_is_zero = 1;

    }

  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] =>

  if ((y & MASK_STEERING_BITS) == MASK_STEERING_BITS) {

    exp_y = (y & MASK_BINARY_EXPONENT2) >> 51;

    sig_y = (y & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

    if (sig_y > 9999999999999999ull || sig_y == 0) {

      y_is_zero = 1;

    }

  } else {

    exp_y = (y & MASK_BINARY_EXPONENT1) >> 53;

    sig_y = (y & MASK_BINARY_SIG1);

    if (sig_y == 0) {

      y_is_zero = 1;

    }

  }

  // 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) {

    if (!((x & MASK_SIGN) == MASK_SIGN) ^

        ((y & MASK_SIGN) == MASK_SIGN)) {

      // if signs are the same:

      // 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 & MASK_SIGN) == MASK_SIGN);

      BID_RETURN (res);

    } else {

      // signs are different.

      // totalOrder(-0, +0) is true

      // totalOrder(+0, -0) is false

      res = ((x & 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 & 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 & MASK_SIGN) == MASK_SIGN);