path: root/src/third_party/IntelRDFPMathLib20U1/LIBRARY/src/bid32_noncomp.c

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  Copyright (c) 2007-2011, Intel Corp.
  All rights reserved.

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  modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright notice, 
      this list of conditions and the following disclaimer.
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      notice, this list of conditions and the following disclaimer in the 
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      may be used to endorse or promote products derived from this software 
      without specific prior written permission.

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#include "bid_internal.h"

static const BID_UINT32 bid_mult_factor[7] = {
  1, 10, 100, 1000, 10000, 100000, 1000000
};

/*****************************************************************************
 *    BID32 non-computational functions:
 *         - bid32_isSigned
 *         - bid32_isNormal
 *         - bid32_isSubnormal
 *         - bid32_isFinite
 *         - bid32_isZero
 *         - bid32_isInf
 *         - bid32_isSignaling
 *         - bid32_isCanonical
 *         - bid32_isNaN
 *         - bid32_copy
 *         - bid32_negate
 *         - bid32_abs
 *         - bid32_copySign
 *         - bid32_class
 *         - bid32_sameQuantum
 *         - bid32_totalOrder
 *         - bid32_totalOrderMag
 *         - bid32_radix
 ****************************************************************************/

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isSigned (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isSigned, 32)
int
bid32_isSigned (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x & MASK_SIGN32) == MASK_SIGN32);
  BID_RETURN (res);
}

// return 1 iff x is not zero, nor NaN nor subnormal nor infinity
#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isNormal (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isNormal, 32)
int
bid32_isNormal (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  BID_UINT64 sig_x_prime;
  BID_UINT32 sig_x;
  unsigned int exp_x;

  if ((x & MASK_INF32) == MASK_INF32) {	// x is either INF or NaN
    res = 0;
  } else {
    // decode number into exponent and significand
    if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
      sig_x = (x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
      // check for zero or non-canonical
      if (sig_x > 9999999 || sig_x == 0) {
	res = 0; // zero or non-canonical
	BID_RETURN (res);
      }
      exp_x = (x & MASK_BINARY_EXPONENT2_32) >> 21;
    } else {
      sig_x = (x & MASK_BINARY_SIG1_32);
      if (sig_x == 0) {
	res = 0; // zero
	BID_RETURN (res);
      }
      exp_x = (x & MASK_BINARY_EXPONENT1_32) >> 23;
    }
    // if exponent is less than -95, the number may be subnormal
    // if (exp_x - 101 = -95) the number may be subnormal
    if (exp_x < 6) {
      sig_x_prime = (BID_UINT64)sig_x * (BID_UINT64)bid_mult_factor[exp_x];
      if (sig_x_prime < 1000000ull) {
	res = 0; // subnormal
      } else {
	res = 1; // normal
      }
    } else {
      res = 1; // normal
    }
  }
  BID_RETURN (res);
}

// return 1 iff x is not zero, NaN, normal, or infinity
#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isSubnormal (int *pres, BID_UINT32 * px 
    _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isSubnormal, 32)
int
bid32_isSubnormal (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  BID_UINT64 sig_x_prime;
  BID_UINT32 sig_x;
  unsigned int exp_x;

  if ((x & MASK_INF32) == MASK_INF32) {	// x is either INF or NaN
    res = 0;
  } else {
    // decode number into exponent and significand
    if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
      sig_x = (x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
      // check for zero or non-canonical
      if (sig_x > 9999999 || sig_x == 0) {
	res = 0; // zero or non-canonical
	BID_RETURN (res);
      }
      exp_x = (x & MASK_BINARY_EXPONENT2_32) >> 21;
    } else {
      sig_x = (x & MASK_BINARY_SIG1_32);
      if (sig_x == 0) {
	res = 0; // zero
	BID_RETURN (res);
      }
      exp_x = (x & MASK_BINARY_EXPONENT1_32) >> 23;
    }
    // if exponent is less than -95, the number may be subnormal
    // if (exp_x - 101 = -95) the number may be subnormal
    if (exp_x < 6) {
      sig_x_prime = (BID_UINT64)sig_x * (BID_UINT64)bid_mult_factor[exp_x];
      if (sig_x_prime < 1000000ull) {
        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
bid32_isFinite (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isFinite, 32)
int
bid32_isFinite (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x & MASK_INF32) != MASK_INF32);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isZero (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isZero, 32)
int
bid32_isZero (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  // if infinity or nan, return 0
  if ((x & MASK_INF32) == MASK_INF32) {
    res = 0;
  } else if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
    // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1]
    // => sig_x = (x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
    // if(sig_x > 9999999) {return 1;}
    res =
      (((x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32) >
       9999999);
  } else {
    res = ((x & MASK_BINARY_SIG1_32) == 0);
  }
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isInf (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isInf, 32)
int
bid32_isInf (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x & MASK_INF32) == MASK_INF32) && ((x & MASK_NAN32) != MASK_NAN32);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isSignaling (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isSignaling, 32)
int
bid32_isSignaling (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x & MASK_SNAN32) == MASK_SNAN32);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isCanonical (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isCanonical, 32)
int
bid32_isCanonical (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  if ((x & MASK_NAN32) == MASK_NAN32) {	// NaN
    if (x & 0x01f00000) {
      res = 0;
    } else if ((x & 0x000fffff) > 999999) { // payload
      res = 0;
    } else {
      res = 1;
    }
  } else if ((x & MASK_INF32) == MASK_INF32) {
    if (x & 0x03ffffff) {
      res = 0;
    } else {
      res = 1;
    }
  } else if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) { // 24-bit
    res = (((x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32) <= 9999999);
  } else { // 23-bit coeff.
    res = 1;
  }
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_isNaN (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_isNaN, 32)
int
bid32_isNaN (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;

  res = ((x & MASK_NAN32) == MASK_NAN32);
  BID_RETURN (res);
}

// copies a floating-point operand x to destination y, with no change
#if DECIMAL_CALL_BY_REFERENCE
void
bid32_copy (BID_UINT32 * pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
DFP_WRAPFN_DFP(32, bid32_copy, 32)
BID_UINT32
bid32_copy (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  BID_UINT32 res;

  res = x;
  BID_RETURN (res);
}

// copies a floating-point operand x to destination y, reversing the sign
#if DECIMAL_CALL_BY_REFERENCE
void
bid32_negate (BID_UINT32 * pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
DFP_WRAPFN_DFP(32, bid32_negate, 32)
BID_UINT32
bid32_negate (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  BID_UINT32 res;

  res = x ^ MASK_SIGN32;
  BID_RETURN (res);
}

// copies a floating-point operand x to destination y, changing the sign to positive
#if DECIMAL_CALL_BY_REFERENCE
void
bid32_abs (BID_UINT32 * pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
DFP_WRAPFN_DFP(32, bid32_abs, 32)
BID_UINT32
bid32_abs (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  BID_UINT32 res;

  res = x & ~MASK_SIGN32;
  BID_RETURN (res);
}

// copies operand x to destination in the same format as x, but 
// with the sign of y
DFP_WRAPFN_DFP_DFP(32, bid32_copySign, 32, 32);   

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_copySign (BID_UINT32 * pres, BID_UINT32 * px,
		BID_UINT32 * py _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
  BID_UINT32 y = *py;
#else
BID_UINT32
bid32_copySign (BID_UINT32 x, BID_UINT32 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  BID_UINT32 res;

  res = (x & ~MASK_SIGN32) | (y & MASK_SIGN32);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_class (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_class, 32)
int
bid32_class (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  BID_UINT64 sig_x_prime;
  BID_UINT32 sig_x;
  int exp_x;

  if ((x & MASK_NAN32) == MASK_NAN32) {
    // is the NaN signaling?
    if ((x & MASK_SNAN32) == MASK_SNAN32) {
      res = signalingNaN;
      BID_RETURN (res);
    }
    // if NaN and not signaling, must be quietNaN
    res = quietNaN;
    BID_RETURN (res);
  } else if ((x & MASK_INF32) == MASK_INF32) {
    // is the Infinity negative?
    if ((x & MASK_SIGN32) == MASK_SIGN32) {
      res = negativeInfinity;
    } else {
      // otherwise, must be positive infinity
      res = positiveInfinity;
    }
    BID_RETURN (res);
  } else if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
    // decode number into exponent and significand
    sig_x = (x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
    // check for zero or non-canonical
    if (sig_x > 9999999 || sig_x == 0) {
      if ((x & MASK_SIGN32) == MASK_SIGN32) {
	res = negativeZero;
      } else {
	res = positiveZero;
      }
      BID_RETURN (res);
    }
    exp_x = (x & MASK_BINARY_EXPONENT2_32) >> 21;
  } else {
    sig_x = (x & MASK_BINARY_SIG1_32);
    if (sig_x == 0) {
      res = ((x & MASK_SIGN32) == MASK_SIGN32) ? negativeZero : positiveZero;
      BID_RETURN (res);
    }
    exp_x = (x & MASK_BINARY_EXPONENT1_32) >> 23;
  }
  // if exponent is less than -95, number may be subnormal
  //  if (exp_x - 101 < -95)
  if (exp_x < 6) { // sig_x *10^exp_x
    sig_x_prime = (BID_UINT64)sig_x * (BID_UINT64)bid_mult_factor[exp_x];
    if (sig_x_prime < 1000000ull) {
      res = ((x & MASK_SIGN32) ==
          MASK_SIGN32) ? negativeSubnormal : positiveSubnormal;
      BID_RETURN (res);
    }
  }
  // otherwise, normal number, determine the sign
  res = ((x & MASK_SIGN32) == MASK_SIGN32) ? 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
bid32_sameQuantum (int *pres, BID_UINT32 * px, BID_UINT32 * py 
    _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
  BID_UINT32 y = *py;
#else
RES_WRAPFN_DFP_DFP(int, bid32_sameQuantum, 32, 32)
int
bid32_sameQuantum (BID_UINT32 x, BID_UINT32 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_NAN32) == MASK_NAN32 || ((y & MASK_NAN32) == MASK_NAN32)) {
    res = ((x & MASK_NAN32) == MASK_NAN32 && (y & MASK_NAN32) == MASK_NAN32);
    BID_RETURN (res);
  }
  // if both operands are INF, return true; if just one is INF, return false
  if ((x & MASK_INF32) == MASK_INF32 || (y & MASK_INF32) == MASK_INF32) {
    res = ((x & MASK_INF32) == MASK_INF32 && (y & MASK_INF32) == MASK_INF32);
    BID_RETURN (res);
  }
  // decode exponents for both numbers, and return true if they match
  if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
    exp_x = (x & MASK_BINARY_EXPONENT2_32) >> 21;
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1_32) >> 23;
  }
  if ((y & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
    exp_y = (y & MASK_BINARY_EXPONENT2_32) >> 21;
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1_32) >> 23;
  }
  res = (exp_x == exp_y);
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void
bid32_totalOrder (int *pres, BID_UINT32 * px, BID_UINT32 * py 
    _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
  BID_UINT32 y = *py;
#else
RES_WRAPFN_DFP_DFP(int, bid32_totalOrder, 32, 32)
int
bid32_totalOrder (BID_UINT32 x, BID_UINT32 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  BID_UINT32 sig_x, sig_y, pyld_y, pyld_x;
  BID_UINT64 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_NAN32) == MASK_NAN32) {
    // if x is -NaN
    if ((x & MASK_SIGN32) == MASK_SIGN32) {
      // return true, unless y is -NaN also
      if ((y & MASK_NAN32) != MASK_NAN32 || (y & MASK_SIGN32) != MASK_SIGN32) {
	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_SNAN32) == MASK_SNAN32) ^ 
            ((x & MASK_SNAN32) == MASK_SNAN32))) {
	  // 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 & 0x000fffff;
	  pyld_x = x & 0x000fffff;
	  if (pyld_y > 999999 || 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 > 999999 || 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_SNAN32) == MASK_SNAN32; // totalOrder(-qNaN,-sNaN)==1
	  BID_RETURN (res);
	}
      }
    } else { // x is +NaN
      // return false, unless y is +NaN also
      if ((y & MASK_NAN32) != MASK_NAN32 || (y & MASK_SIGN32) == MASK_SIGN32) {
	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_SNAN32) == MASK_SNAN32) ^ 
            ((x & MASK_SNAN32) == MASK_SNAN32))) {
	  // 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 & 0x000fffff;
	  pyld_x = x & 0x000fffff;
	  // 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 > 999999 || pyld_x == 0) {
	    res = 1;
	    BID_RETURN (res);
	  }
	  if (pyld_y > 999999 || 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_SNAN32) == MASK_SNAN32);
	  BID_RETURN (res);
	}
      }
    }
  } else if ((y & MASK_NAN32) == MASK_NAN32) {
    // x is certainly not NAN in this case.
    // return true if y is positive
    res = ((y & MASK_SIGN32) != MASK_SIGN32);
    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_SIGN32) == MASK_SIGN32) ^ 
        ((y & MASK_SIGN32) == MASK_SIGN32)) {
    res = (x & MASK_SIGN32) == MASK_SIGN32;
    BID_RETURN (res);
  } // from this point on x and y have the same sign
  // INFINITY (CASE4)
  if ((x & MASK_INF32) == MASK_INF32) {
    // if x==neg_inf, return (y == neg_inf)?1:0;
    if ((x & MASK_SIGN32) == MASK_SIGN32) {
      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_INF32) == MASK_INF32);
      BID_RETURN (res);
    }
  } else if ((y & MASK_INF32) == MASK_INF32) {
    // x is finite, so:
    //    if y is +inf, x<y
    //    if y is -inf, x>y
    res = ((y & MASK_SIGN32) != MASK_SIGN32);
    BID_RETURN (res);
  }
  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1]
  if ((x & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
    exp_x = (x & MASK_BINARY_EXPONENT2_32) >> 21;
    sig_x = (x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
    if (sig_x > 9999999 || sig_x == 0) {
      x_is_zero = 1;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1_32) >> 23;
    sig_x = (x & MASK_BINARY_SIG1_32);
    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_BITS32) == MASK_STEERING_BITS32) {
    exp_y = (y & MASK_BINARY_EXPONENT2_32) >> 21;
    sig_y = (y & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
    if (sig_y > 9999999 || sig_y == 0) {
      y_is_zero = 1;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1_32) >> 23;
    sig_y = (y & MASK_BINARY_SIG1_32);
    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) {
    // the 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_SIGN32) == MASK_SIGN32);
    BID_RETURN (res);
  }
  // if x is zero and y isn't, clearly x has the smaller payload.
  if (x_is_zero) {
    res = ((y & MASK_SIGN32) != MASK_SIGN32);
    BID_RETURN (res);
  }
  // if y is zero, and x isn't, clearly y has the smaller payload.
  if (y_is_zero) {
    res = ((x & MASK_SIGN32) == MASK_SIGN32);
    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_SIGN32) == MASK_SIGN32);
    BID_RETURN (res);
  }
  if (sig_x < sig_y && exp_x <= exp_y) {
    res = ((x & MASK_SIGN32) != MASK_SIGN32);
    BID_RETURN (res);
  }
  // if exp_x is 6 greater than exp_y, it is 
  // definitely larger, so no need for compensation
  if (exp_x - exp_y > 6) {
    // difference cannot be greater than 10^6
    res = ((x & MASK_SIGN32) == MASK_SIGN32);
    BID_RETURN (res);
  }
  // if exp_x is 6 less than exp_y, it is 
  // definitely smaller, no need for compensation
  if (exp_y - exp_x > 6) {
    res = ((x & MASK_SIGN32) != MASK_SIGN32);
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 6, it comes down 
  // to the compensated significand
  if (exp_x > exp_y) {
    // otherwise adjust the x significand upwards
    sig_n_prime = (BID_UINT64)sig_x * (BID_UINT64)bid_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 == (BID_UINT64)sig_y) {
      // case cannot occur, because all bits must 
      // be the same - would have been caught if (x==y)
      res = (exp_x <= exp_y) ^ ((x & MASK_SIGN32) == MASK_SIGN32);
      BID_RETURN (res);
    }
    // if positive, return 1 if adjusted x is smaller than y
    res = (sig_n_prime < (BID_UINT64)sig_y) ^ ((x & MASK_SIGN32) == MASK_SIGN32);
    BID_RETURN (res);
  }
  // adjust the y significand upwards
  sig_n_prime = (BID_UINT64)sig_y * (BID_UINT64)bid_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 == (BID_UINT64)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_SIGN32) == MASK_SIGN32);
    BID_RETURN (res);
  }
  // values are not equal, for positive numbers return 1 
  // if x is less than y.  0 otherwise
  res = ((BID_UINT64)sig_x < sig_n_prime) ^ ((x & MASK_SIGN32) == MASK_SIGN32);
  BID_RETURN (res);
}


// totalOrderMag is TotalOrder(abs(x), abs(y))
#if DECIMAL_CALL_BY_REFERENCE
void
bid32_totalOrderMag (int *pres, BID_UINT32 * px, BID_UINT32 * py 
    _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
  BID_UINT32 y = *py;
#else
RES_WRAPFN_DFP_DFP(int, bid32_totalOrderMag, 32, 32)
int
bid32_totalOrderMag (BID_UINT32 x, BID_UINT32 y _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  int exp_x, exp_y;
  BID_UINT32 sig_x, sig_y, pyld_y, pyld_x;
  BID_UINT64 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_NAN32) == MASK_NAN32) {
    // x is +NaN

    // return false, unless y is +NaN also
    if ((y & MASK_NAN32) != MASK_NAN32) {
      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_SNAN32) == MASK_SNAN32) ^ 
          ((x & MASK_SNAN32) == MASK_SNAN32))) {
	// 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 & 0x000fffff;
	pyld_x = x & 0x000fffff;
	// 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 > 999999 || pyld_x == 0) {
	  res = 1;
	  BID_RETURN (res);
	}

	if (pyld_y > 999999 || 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_SNAN32) == MASK_SNAN32);
	BID_RETURN (res);
      }
    }

  } else if ((y & MASK_NAN32) == MASK_NAN32) {
    // 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_SIGN32) == (y & ~MASK_SIGN32)) {
    res = 1;
    BID_RETURN (res);
  }
  // INFINITY (CASE3)
  if ((x & MASK_INF32) == MASK_INF32) {
    // x is positive infinity; return 1 only 
    // if y is positive infinity as well
    res = ((y & MASK_INF32) == MASK_INF32);
    BID_RETURN (res);
  } else if ((y & MASK_INF32) == MASK_INF32) {
    // 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_BITS32) == MASK_STEERING_BITS32) {
    exp_x = (x & MASK_BINARY_EXPONENT2_32) >> 21;
    sig_x = (x & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
    if (sig_x > 9999999 || sig_x == 0) {
      x_is_zero = 1;
      sig_x = 0;
    }
  } else {
    exp_x = (x & MASK_BINARY_EXPONENT1_32) >> 23;
    sig_x = (x & MASK_BINARY_SIG1_32);
    if (sig_x == 0) {
      x_is_zero = 1;
      sig_x = 0;
    }
  }

  // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1]
  if ((y & MASK_STEERING_BITS32) == MASK_STEERING_BITS32) {
    exp_y = (y & MASK_BINARY_EXPONENT2_32) >> 21;
    sig_y = (y & MASK_BINARY_SIG2_32) | MASK_BINARY_OR2_32;
    if (sig_y > 9999999 || sig_y == 0) {
      y_is_zero = 1;
      sig_y = 0;
    }
  } else {
    exp_y = (y & MASK_BINARY_EXPONENT1_32) >> 23;
    sig_y = (y & MASK_BINARY_SIG1_32);
    if (sig_y == 0) {
      y_is_zero = 1;
      sig_y = 0;
    }
  }

  // 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 6 greater than exp_y, it is definitely 
  // larger, so no need for compensation
  if (exp_x - exp_y > 6) {
    res = 0;	// difference cannot be greater than 10^6
    BID_RETURN (res);
  }
  // if exp_x is 6 less than exp_y, it is definitely 
  // smaller, no need for compensation
  if (exp_y - exp_x > 6) {
    res = 1;
    BID_RETURN (res);
  }
  // if |exp_x - exp_y| < 6, it comes down 
  // to the compensated significand
  if (exp_x > exp_y) {
    // adjust the x significand upwards
    sig_n_prime = (BID_UINT64)sig_x * (BID_UINT64)bid_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 == (BID_UINT64)sig_y) {
      // case cannot occur, because all bits 
      // must be the same - would have been caught if (x==y)
      res = 0; // res = (exp_x <= exp_y); but 0 < exp_x - exp_y <= 5
      BID_RETURN (res);
    }
    // if positive, return 1 if adjusted x is smaller than y
    res = (sig_n_prime < (BID_UINT64)sig_y);
    BID_RETURN (res);
  } // from this point on -5 <= exp_x - exp_y <= 0
  // adjust the y significand upwards
  sig_n_prime = (BID_UINT64)sig_y * (BID_UINT64)bid_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 == (BID_UINT64)sig_x) {
    res = 1; // res = (exp_x <= exp_y); but -5 <= exp_x - exp_y <= 0
    BID_RETURN (res);
  }
  // values are not equal, for positive numbers 
  // return 1 if x is less than y, and 0 otherwise
  res = ((BID_UINT64)sig_x < sig_n_prime);
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid32_radix (int *pres, BID_UINT32 * px _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
  BID_UINT32 x = *px;
#else
RES_WRAPFN_DFP(int, bid32_radix, 32)
int
bid32_radix (BID_UINT32 x _EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif
  int res;
  if (x) // dummy test
    res = 10;
  else
    res = 10;
  BID_RETURN (res);
}

#if DECIMAL_CALL_BY_REFERENCE
void bid32_inf (BID_UINT32 *pres) {
#else
BID_UINT32 bid32_inf (void) {
#endif
 
  BID_UINT32 res; 
  res = 0x78000000; // + inf
  BID_RETURN(res);
}


DFP_WRAPFN_OTHERTYPE(32, bid32_nan, const char *);

#if DECIMAL_CALL_BY_REFERENCE
void bid32_nan (BID_UINT32 *pres, const char *tagp) {
#else
BID_UINT32 bid32_nan (const char *tagp) {
#endif
 
  BID_UINT32 res, x;

#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = BID_ROUNDING_TO_NEAREST;
#endif
#if !DECIMAL_GLOBAL_EXCEPTION_FLAGS
  unsigned int fpsf;
  unsigned int *pfpsf = &fpsf;
#endif

  res = 0x7c000000; // +QNaN
  if (!tagp) BID_RETURN(res);

#if DECIMAL_CALL_BY_REFERENCE
  bid32_from_string (&x, (char *)tagp _RND_MODE_ARG _EXC_FLAGS_ARG);
#else      
  x = bid32_from_string ((char *)tagp _RND_MODE_ARG _EXC_FLAGS_ARG);
#endif
  x = x & 0x000fffff; // valid values fit in 20 bits
  res = res | x;

  BID_RETURN(res);
}