libgcc/config/libbid/bid64_noncomp.c

/* Copyright (C) 2007-2023 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);
    BID_RETURN (res);
  }
  // REDUNDANT REPRESENTATIONS (CASE6)
  // if both components are either bigger or smaller, 
  // it is clear what needs to be done
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, it is 
  // definitely larger, so no need for compensation
  if (exp_x - exp_y > 15) {
    // difference cannot be greater than 10^15
    res = ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, it is 
  // definitely smaller, no need for compensation
  if (exp_y - exp_x > 15) {
    res = ((x & MASK_SIGN) != MASK_SIGN);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down 
  // to the compensated significand
  if (exp_x > exp_y) {
    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);
    // if x and y represent the same entities, 
    // and both are negative, return true iff exp_x <= exp_y
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      // case cannot occure, because all bits must 
      // be the same - would have been caught if (x==y)
      res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
      BID_RETURN (res);
    }
    // if positive, return 1 if adjusted x is smaller than y
    res = ((sig_n_prime.w[1] == 0)
	   && sig_n_prime.w[0] < sig_y) ^ ((x & MASK_SIGN) ==
					   MASK_SIGN);
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // if x and y represent the same entities, 
  // and both are negative, return true iff exp_x <= exp_y
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    // Cannot occur, because all bits must be the same. 
    // Case would have been caught if (x==y)
    res = (exp_x <= exp_y) ^ ((x & MASK_SIGN) == MASK_SIGN);
    BID_RETURN (res);
  }
  // values are not equal, for positive numbers return 1 
  // if x is less than y.  0 otherwise
  res = ((sig_n_prime.w[1] > 0)
	 || (sig_x < sig_n_prime.w[0])) ^ ((x & MASK_SIGN) ==
					   MASK_SIGN);
  BID_RETURN (res);
}

// totalOrderMag is TotalOrder(abs(x), abs(y))
#if DECIMAL_CALL_BY_REFERENCE
void
bid64_totalOrderMag (int *pres, UINT64 * px,
		     UINT64 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT64 x = *px;
  UINT64 y = *py;
#else
int
bid64_totalOrderMag (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 (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 & MASK_NAN) == MASK_NAN) {
    // x is +NaN

    // return false, unless y is +NaN also
    if ((y & MASK_NAN) != MASK_NAN) {
      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 = 1;
    BID_RETURN (res);
  }
  // SIMPLE (CASE2)
  // if all the bits (except sign bit) are the same, 
  // these numbers are equal.
  if ((x & ~MASK_SIGN) == (y & ~MASK_SIGN)) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF) == MASK_INF) {
    // x is positive infinity, only return1 
    // if y is positive infinity as well
    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
    res = 1;
    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) {
    // totalOrder(x,y) iff exp_x <= exp_y for positive numbers
    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 (CASE6)
  // if both components are either bigger or smaller
  if (sig_x > sig_y && exp_x >= exp_y) {
    res = 0;
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = 1;
    BID_RETURN (res);
  }
  // if exp_x is 15 greater than exp_y, it is definitely 
  // larger, so no need for compensation
  if (exp_x - exp_y > 15) {
    res = 0;	// difference cannot be greater than 10^15
    BID_RETURN (res);
  }
  // if exp_x is 15 less than exp_y, it is definitely 
  // smaller, no need for compensation
  if (exp_y - exp_x > 15) {
    res = 1;
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 15, it comes down 
  // to the compensated significand
  if (exp_x > exp_y) {

    // otherwise adjust the x significand upwards
    __mul_64x64_to_128MACH (sig_n_prime, sig_x,
			    mult_factor[exp_x - exp_y]);

    // if x and y represent the same entities, 
    // and both are negative, return true iff exp_x <= exp_y
    if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_y)) {
      // case cannot occur, because all bits 
      // must be the same - would have been caught if (x==y)
      res = (exp_x <= exp_y);
      BID_RETURN (res);
    }
    // if positive, return 1 if adjusted x is smaller than y
    res = ((sig_n_prime.w[1] == 0) && sig_n_prime.w[0] < sig_y);
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  __mul_64x64_to_128MACH (sig_n_prime, sig_y,
			  mult_factor[exp_y - exp_x]);

  // if x and y represent the same entities, 
  // and both are negative, return true iff exp_x <= exp_y
  if (sig_n_prime.w[1] == 0 && (sig_n_prime.w[0] == sig_x)) {
    res = (exp_x <= exp_y);
    BID_RETURN (res);
  }
  // values are not equal, for positive numbers 
  // return 1 if x is less than y.  0 otherwise
  res = ((sig_n_prime.w[1] > 0) || (sig_x < sig_n_prime.w[0]));
  BID_RETURN (res);

}

#if DECIMAL_CALL_BY_REFERENCE
void
bid64_radix (int *pres, UINT64 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  UINT64 x = *px;
#else
int
bid64_radix (UINT64 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  if (x)	// dummy test
    res = 10;
  else
    res = 10;
  BID_RETURN (res);
}