gcc/libgcc/config/libbid/bid128_fma.c

/* Copyright (C) 2007-2016 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/>.  */

/*****************************************************************************
 * 
 *  BID128 fma   x * y + z
 * 
 ****************************************************************************/

#include "bid_internal.h"

static void
rounding_correction (unsigned int rnd_mode,
        	     unsigned int is_inexact_lt_midpoint,
        	     unsigned int is_inexact_gt_midpoint,
        	     unsigned int is_midpoint_lt_even,
        	     unsigned int is_midpoint_gt_even,
        	     int unbexp,
        	     UINT128 * ptrres, _IDEC_flags * ptrfpsf) {
  // unbiased true exponent unbexp may be larger than emax

  UINT128 res = *ptrres; // expected to have the correct sign and coefficient
  // (the exponent field is ignored, as unbexp is used instead)
  UINT64 sign, exp;
  UINT64 C_hi, C_lo;

  // general correction from RN to RA, RM, RP, RZ
  // Note: if the result is negative, then is_inexact_lt_midpoint, 
  // is_inexact_gt_midpoint, is_midpoint_lt_even, and is_midpoint_gt_even 
  // have to be considered as if determined for the absolute value of the 
  // result (so they seem to be reversed)

  if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
      is_midpoint_lt_even || is_midpoint_gt_even) {
    *ptrfpsf |= INEXACT_EXCEPTION;
  }
  // apply correction to result calculated with unbounded exponent
  sign = res.w[1] & MASK_SIGN;
  exp = (UINT64) (unbexp + 6176) << 49; // valid only if expmin<=unbexp<=expmax
  C_hi = res.w[1] & MASK_COEFF;
  C_lo = res.w[0];
  if ((!sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) ||
      ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) && 
      is_midpoint_gt_even))) || 
      (sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) ||
      ((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) && 
      is_midpoint_gt_even)))) {
    // C = C + 1
    C_lo = C_lo + 1;
    if (C_lo == 0)
      C_hi = C_hi + 1;
    if (C_hi == 0x0001ed09bead87c0ull && C_lo == 0x378d8e6400000000ull) {
      // C = 10^34 => rounding overflow
      C_hi = 0x0000314dc6448d93ull;
      C_lo = 0x38c15b0a00000000ull; // 10^33
      // exp = exp + EXP_P1;
      unbexp = unbexp + 1;
      exp = (UINT64) (unbexp + 6176) << 49;
    }
  } else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) &&
      ((sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) ||
      (!sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) {
    // C = C - 1
    C_lo = C_lo - 1;
    if (C_lo == 0xffffffffffffffffull)
      C_hi--;
    // check if we crossed into the lower decade
    if (C_hi == 0x0000314dc6448d93ull && C_lo == 0x38c15b09ffffffffull) { 
      // C = 10^33 - 1
      if (exp > 0) {
        C_hi = 0x0001ed09bead87c0ull; // 10^34 - 1
        C_lo = 0x378d8e63ffffffffull;
        // exp = exp - EXP_P1;
        unbexp = unbexp - 1;
        exp = (UINT64) (unbexp + 6176) << 49;
      } else { // if exp = 0 the result is tiny & inexact
        *ptrfpsf |= UNDERFLOW_EXCEPTION;
      }
    }
  } else {
    ; // the result is already correct
  }
  if (unbexp > expmax) { // 6111
    *ptrfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
    exp = 0;
    if (!sign) { // result is positive
      if (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TIES_AWAY) { // +inf
        C_hi = 0x7800000000000000ull;
        C_lo = 0x0000000000000000ull;
      } else { // res = +MAXFP = (10^34-1) * 10^emax
        C_hi = 0x5fffed09bead87c0ull;
        C_lo = 0x378d8e63ffffffffull;
      }
    } else { // result is negative
      if (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TIES_AWAY) { // -inf
        C_hi = 0xf800000000000000ull;
        C_lo = 0x0000000000000000ull;
      } else { // res = -MAXFP = -(10^34-1) * 10^emax
        C_hi = 0xdfffed09bead87c0ull;
        C_lo = 0x378d8e63ffffffffull;
      }
    }
  }
  // assemble the result
  res.w[1] = sign | exp | C_hi;
  res.w[0] = C_lo;
  *ptrres = res;
}

static void
add256 (UINT256 x, UINT256 y, UINT256 * pz) {
  // *z = x + yl assume the sum fits in 256 bits
  UINT256 z;
  z.w[0] = x.w[0] + y.w[0];
  if (z.w[0] < x.w[0]) {
    x.w[1]++;
    if (x.w[1] == 0x0000000000000000ull) {
      x.w[2]++;
      if (x.w[2] == 0x0000000000000000ull) {
        x.w[3]++;
      }
    }
  }
  z.w[1] = x.w[1] + y.w[1];
  if (z.w[1] < x.w[1]) {
    x.w[2]++;
    if (x.w[2] == 0x0000000000000000ull) {
      x.w[3]++;
    }
  }
  z.w[2] = x.w[2] + y.w[2];
  if (z.w[2] < x.w[2]) {
    x.w[3]++;
  }
  z.w[3] = x.w[3] + y.w[3]; // it was assumed that no carry is possible
  *pz = z;
}

static void
sub256 (UINT256 x, UINT256 y, UINT256 * pz) {
  // *z = x - y; assume x >= y
  UINT256 z;
  z.w[0] = x.w[0] - y.w[0];
  if (z.w[0] > x.w[0]) {
    x.w[1]--;
    if (x.w[1] == 0xffffffffffffffffull) {
      x.w[2]--;
      if (x.w[2] == 0xffffffffffffffffull) {
        x.w[3]--;
      }
    }
  }
  z.w[1] = x.w[1] - y.w[1];
  if (z.w[1] > x.w[1]) {
    x.w[2]--;
    if (x.w[2] == 0xffffffffffffffffull) {
      x.w[3]--;
    }
  }
  z.w[2] = x.w[2] - y.w[2];
  if (z.w[2] > x.w[2]) {
    x.w[3]--;
  }
  z.w[3] = x.w[3] - y.w[3]; // no borrow possible, because x >= y
  *pz = z;
}


static int
nr_digits256 (UINT256 R256) {
  int ind;
  // determine the number of decimal digits in R256
  if (R256.w[3] == 0x0 && R256.w[2] == 0x0 && R256.w[1] == 0x0) {
    // between 1 and 19 digits
    for (ind = 1; ind <= 19; ind++) {
      if (R256.w[0] < ten2k64[ind]) {
        break;
      }
    }
    // ind digits
  } else if (R256.w[3] == 0x0 && R256.w[2] == 0x0 &&
             (R256.w[1] < ten2k128[0].w[1] ||
              (R256.w[1] == ten2k128[0].w[1]
               && R256.w[0] < ten2k128[0].w[0]))) {
    // 20 digits
    ind = 20;
  } else if (R256.w[3] == 0x0 && R256.w[2] == 0x0) {
    // between 21 and 38 digits
    for (ind = 1; ind <= 18; ind++) {
      if (R256.w[1] < ten2k128[ind].w[1] ||
          (R256.w[1] == ten2k128[ind].w[1] &&
           R256.w[0] < ten2k128[ind].w[0])) {
        break;
      }
    }
    // ind + 20 digits
    ind = ind + 20;
  } else if (R256.w[3] == 0x0 &&
             (R256.w[2] < ten2k256[0].w[2] ||
              (R256.w[2] == ten2k256[0].w[2] &&
               R256.w[1] < ten2k256[0].w[1]) ||
              (R256.w[2] == ten2k256[0].w[2] &&
               R256.w[1] == ten2k256[0].w[1] &&
               R256.w[0] < ten2k256[0].w[0]))) {
    // 39 digits
    ind = 39;
  } else {
    // between 40 and 68 digits
    for (ind = 1; ind <= 29; ind++) {
      if (R256.w[3] < ten2k256[ind].w[3] ||
          (R256.w[3] == ten2k256[ind].w[3] &&
           R256.w[2] < ten2k256[ind].w[2]) ||
          (R256.w[3] == ten2k256[ind].w[3] &&
           R256.w[2] == ten2k256[ind].w[2] &&
           R256.w[1] < ten2k256[ind].w[1]) ||
          (R256.w[3] == ten2k256[ind].w[3] &&
           R256.w[2] == ten2k256[ind].w[2] &&
           R256.w[1] == ten2k256[ind].w[1] &&
           R256.w[0] < ten2k256[ind].w[0])) {
        break;
      }
    }
    // ind + 39 digits
    ind = ind + 39;
  }
  return (ind);
}

// add/subtract C4 and C3 * 10^scale; this may follow a previous rounding, so
// use the rounding information from ptr_is_* to avoid a double rounding error
static void
add_and_round (int q3,
               int q4,
               int e4,
               int delta,
               int p34,
               UINT64 z_sign,
               UINT64 p_sign,
               UINT128 C3,
               UINT256 C4,
               int rnd_mode,
               int *ptr_is_midpoint_lt_even,
               int *ptr_is_midpoint_gt_even,
               int *ptr_is_inexact_lt_midpoint,
               int *ptr_is_inexact_gt_midpoint,
               _IDEC_flags * ptrfpsf, UINT128 * ptrres) {

  int scale;
  int x0;
  int ind;
  UINT64 R64;
  UINT128 P128, R128;
  UINT192 P192, R192;
  UINT256 R256;
  int is_midpoint_lt_even = 0;
  int is_midpoint_gt_even = 0;
  int is_inexact_lt_midpoint = 0;
  int is_inexact_gt_midpoint = 0;
  int is_midpoint_lt_even0 = 0;
  int is_midpoint_gt_even0 = 0;
  int is_inexact_lt_midpoint0 = 0;
  int is_inexact_gt_midpoint0 = 0;
  int incr_exp = 0;
  int is_tiny = 0;
  int lt_half_ulp = 0;
  int eq_half_ulp = 0;
  // int gt_half_ulp = 0;
  UINT128 res = *ptrres;

  // scale C3 up by 10^(q4-delta-q3), 0 <= q4-delta-q3 <= 2*P34-2 = 66
  scale = q4 - delta - q3; // 0 <= scale <= 66 (or 0 <= scale <= 68 if this
  // comes from Cases (2), (3), (4), (5), (6), with 0 <= |delta| <= 1

  // calculate C3 * 10^scale in R256 (it has at most 67 decimal digits for
  // Cases (15),(16),(17) and at most 69 for Cases (2),(3),(4),(5),(6))
  if (scale == 0) {
    R256.w[3] = 0x0ull;
    R256.w[2] = 0x0ull;
    R256.w[1] = C3.w[1];
    R256.w[0] = C3.w[0];
  } else if (scale <= 19) { // 10^scale fits in 64 bits
    P128.w[1] = 0;
    P128.w[0] = ten2k64[scale];
    __mul_128x128_to_256 (R256, P128, C3);
  } else if (scale <= 38) { // 10^scale fits in 128 bits
    __mul_128x128_to_256 (R256, ten2k128[scale - 20], C3);
  } else if (scale <= 57) { // 39 <= scale <= 57 
    // 10^scale fits in 192 bits but C3 * 10^scale fits in 223 or 230 bits
    // (10^67 has 223 bits; 10^69 has 230 bits);  
    // must split the computation:  
    // 10^scale * C3 = 10*38 * 10^(scale-38) * C3 where 10^38 takes 127
    // bits and so 10^(scale-38) * C3 fits in 128 bits with certainty
    // Note that 1 <= scale - 38 <= 19 => 10^(scale-38) fits in 64 bits
    __mul_64x128_to_128 (R128, ten2k64[scale - 38], C3);
    // now multiply R128 by 10^38
    __mul_128x128_to_256 (R256, R128, ten2k128[18]);
  } else { // 58 <= scale <= 66
    // 10^scale takes between 193 and 220 bits,
    // and C3 * 10^scale fits in 223 bits (10^67/10^69 has 223/230 bits)
    // must split the computation: 
    // 10^scale * C3 = 10*38 * 10^(scale-38) * C3 where 10^38 takes 127
    // bits and so 10^(scale-38) * C3 fits in 128 bits with certainty 
    // Note that 20 <= scale - 38 <= 30 => 10^(scale-38) fits in 128 bits
    // Calculate first 10^(scale-38) * C3, which fits in 128 bits; because
    // 10^(scale-38) takes more than 64 bits, C3 will take less than 64
    __mul_64x128_to_128 (R128, C3.w[0], ten2k128[scale - 58]);
    // now calculate 10*38 * 10^(scale-38) * C3 
    __mul_128x128_to_256 (R256, R128, ten2k128[18]);
  }
  // C3 * 10^scale is now in R256 

  // for Cases (15), (16), (17) C4 > C3 * 10^scale because C4 has at least 
  // one extra digit; for Cases (2), (3), (4), (5), or (6) any order is 
  // possible 
  // add/subtract C4 and C3 * 10^scale; the exponent is e4
  if (p_sign == z_sign) { // R256 = C4 + R256
    // calculate R256 = C4 + C3 * 10^scale = C4 + R256 which is exact,
    // but may require rounding
    add256 (C4, R256, &R256);
  } else { // if (p_sign != z_sign) { // R256 = C4 - R256
    // calculate R256 = C4 - C3 * 10^scale = C4 - R256 or
    // R256 = C3 * 10^scale - C4 = R256 - C4 which is exact,
    // but may require rounding

    // compare first R256 = C3 * 10^scale and C4 
    if (R256.w[3] > C4.w[3] || (R256.w[3] == C4.w[3] && R256.w[2] > C4.w[2]) ||
        (R256.w[3] == C4.w[3] && R256.w[2] == C4.w[2] && R256.w[1] > C4.w[1]) ||
        (R256.w[3] == C4.w[3] && R256.w[2] == C4.w[2] && R256.w[1] == C4.w[1] &&
        R256.w[0] >= C4.w[0])) { // C3 * 10^scale >= C4
      // calculate R256 = C3 * 10^scale - C4 = R256 - C4, which is exact,
      // but may require rounding 
      sub256 (R256, C4, &R256);
      // flip p_sign too, because the result has the sign of z 
      p_sign = z_sign;
    } else { // if C4 > C3 * 10^scale
      // calculate R256 = C4 - C3 * 10^scale = C4 - R256, which is exact,
      // but may require rounding  
      sub256 (C4, R256, &R256);
    }
    // if the result is pure zero, the sign depends on the rounding mode
    // (x*y and z had opposite signs) 
    if (R256.w[3] == 0x0ull && R256.w[2] == 0x0ull &&
        R256.w[1] == 0x0ull && R256.w[0] == 0x0ull) {
      if (rnd_mode != ROUNDING_DOWN)
        p_sign = 0x0000000000000000ull;
      else
        p_sign = 0x8000000000000000ull;
      // the exponent is max (e4, expmin)
      if (e4 < -6176)
        e4 = expmin;
      // assemble result 
      res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49);
      res.w[0] = 0x0;
      *ptrres = res;
      return;
    }
  }

  // determine the number of decimal digits in R256
  ind = nr_digits256 (R256);

  // the exact result is (-1)^p_sign * R256 * 10^e4 where q (R256) = ind;
  // round to the destination precision, with unbounded exponent

  if (ind <= p34) {
    // result rounded to the destination precision with unbounded exponent
    // is exact
    if (ind + e4 < p34 + expmin) {
      is_tiny = 1; // applies to all rounding modes
    }
    res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | R256.w[1];
    res.w[0] = R256.w[0];
    // Note: res is correct only if expmin <= e4 <= expmax
  } else { // if (ind > p34)
    // if more than P digits, round to nearest to P digits
    // round R256 to p34 digits
    x0 = ind - p34; // 1 <= x0 <= 34 as 35 <= ind <= 68
    if (ind <= 38) {
      P128.w[1] = R256.w[1];
      P128.w[0] = R256.w[0];
      round128_19_38 (ind, x0, P128, &R128, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
    } else if (ind <= 57) {
      P192.w[2] = R256.w[2];
      P192.w[1] = R256.w[1];
      P192.w[0] = R256.w[0];
      round192_39_57 (ind, x0, P192, &R192, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
      R128.w[1] = R192.w[1];
      R128.w[0] = R192.w[0];
    } else { // if (ind <= 68)
      round256_58_76 (ind, x0, R256, &R256, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
      R128.w[1] = R256.w[1];
      R128.w[0] = R256.w[0];
    }
    // the rounded result has p34 = 34 digits
    e4 = e4 + x0 + incr_exp;
    if (rnd_mode == ROUNDING_TO_NEAREST) {
      if (e4 < expmin) {
        is_tiny = 1; // for other rounding modes apply correction
      }
    } else {
      // for RM, RP, RZ, RA apply correction in order to determine tininess
      // but do not save the result; apply the correction to 
      // (-1)^p_sign * significand * 10^0
      P128.w[1] = p_sign | 0x3040000000000000ull | R128.w[1];
      P128.w[0] = R128.w[0];
      rounding_correction (rnd_mode,
        		   is_inexact_lt_midpoint,
        		   is_inexact_gt_midpoint, is_midpoint_lt_even,
        		   is_midpoint_gt_even, 0, &P128, ptrfpsf);
      scale = ((P128.w[1] & MASK_EXP) >> 49) - 6176; // -1, 0, or +1
      // the number of digits in the significand is p34 = 34
      if (e4 + scale < expmin) {
        is_tiny = 1;
      }
    }
    ind = p34; // the number of decimal digits in the signifcand of res
    res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | R128.w[1]; // RN
    res.w[0] = R128.w[0];
    // Note: res is correct only if expmin <= e4 <= expmax
    // set the inexact flag after rounding with bounded exponent, if any
  }
  // at this point we have the result rounded with unbounded exponent in
  // res and we know its tininess:
  // res = (-1)^p_sign * significand * 10^e4, 
  // where q (significand) = ind <= p34
  // Note: res is correct only if expmin <= e4 <= expmax

  // check for overflow if RN
  if (rnd_mode == ROUNDING_TO_NEAREST && (ind + e4) > (p34 + expmax)) {
    res.w[1] = p_sign | 0x7800000000000000ull;
    res.w[0] = 0x0000000000000000ull;
    *ptrres = res;
    *ptrfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
    return; // BID_RETURN (res)
  } // else not overflow or not RN, so continue

  // if (e4 >= expmin) we have the result rounded with bounded exponent
  if (e4 < expmin) {
    x0 = expmin - e4; // x0 >= 1; the number of digits to chop off of res
    // where the result rounded [at most] once is
    //   (-1)^p_sign * significand_res * 10^e4

    // avoid double rounding error
    is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
    is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
    is_midpoint_lt_even0 = is_midpoint_lt_even;
    is_midpoint_gt_even0 = is_midpoint_gt_even;
    is_inexact_lt_midpoint = 0;
    is_inexact_gt_midpoint = 0;
    is_midpoint_lt_even = 0;
    is_midpoint_gt_even = 0;

    if (x0 > ind) {
      // nothing is left of res when moving the decimal point left x0 digits
      is_inexact_lt_midpoint = 1;
      res.w[1] = p_sign | 0x0000000000000000ull;
      res.w[0] = 0x0000000000000000ull;
      e4 = expmin;
    } else if (x0 == ind) { // 1 <= x0 = ind <= p34 = 34
      // this is <, =, or > 1/2 ulp
      // compare the ind-digit value in the significand of res with
      // 1/2 ulp = 5*10^(ind-1), i.e. determine whether it is 
      // less than, equal to, or greater than 1/2 ulp (significand of res)
      R128.w[1] = res.w[1] & MASK_COEFF;
      R128.w[0] = res.w[0];
      if (ind <= 19) {
        if (R128.w[0] < midpoint64[ind - 1]) { // < 1/2 ulp
          lt_half_ulp = 1;
          is_inexact_lt_midpoint = 1;
        } else if (R128.w[0] == midpoint64[ind - 1]) { // = 1/2 ulp
          eq_half_ulp = 1;
          is_midpoint_gt_even = 1;
        } else { // > 1/2 ulp
          // gt_half_ulp = 1;
          is_inexact_gt_midpoint = 1;
        }
      } else { // if (ind <= 38) {
        if (R128.w[1] < midpoint128[ind - 20].w[1] || 
            (R128.w[1] == midpoint128[ind - 20].w[1] && 
            R128.w[0] < midpoint128[ind - 20].w[0])) { // < 1/2 ulp
          lt_half_ulp = 1;
          is_inexact_lt_midpoint = 1;
        } else if (R128.w[1] == midpoint128[ind - 20].w[1] && 
            R128.w[0] == midpoint128[ind - 20].w[0]) { // = 1/2 ulp
          eq_half_ulp = 1;
          is_midpoint_gt_even = 1;
        } else { // > 1/2 ulp
          // gt_half_ulp = 1;
          is_inexact_gt_midpoint = 1;
        }
      }
      if (lt_half_ulp || eq_half_ulp) {
        // res = +0.0 * 10^expmin
        res.w[1] = 0x0000000000000000ull;
        res.w[0] = 0x0000000000000000ull;
      } else { // if (gt_half_ulp)
        // res = +1 * 10^expmin
        res.w[1] = 0x0000000000000000ull;
        res.w[0] = 0x0000000000000001ull;
      }
      res.w[1] = p_sign | res.w[1];
      e4 = expmin;
    } else { // if (1 <= x0 <= ind - 1 <= 33)
      // round the ind-digit result to ind - x0 digits

      if (ind <= 18) { // 2 <= ind <= 18
        round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
        res.w[1] = 0x0;
        res.w[0] = R64;
      } else if (ind <= 38) {
        P128.w[1] = res.w[1] & MASK_COEFF;
        P128.w[0] = res.w[0];
        round128_19_38 (ind, x0, P128, &res, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
      }
      e4 = e4 + x0; // expmin
      // we want the exponent to be expmin, so if incr_exp = 1 then
      // multiply the rounded result by 10 - it will still fit in 113 bits
      if (incr_exp) {
        // 64 x 128 -> 128
        P128.w[1] = res.w[1] & MASK_COEFF;
        P128.w[0] = res.w[0];
        __mul_64x128_to_128 (res, ten2k64[1], P128);
      }
      res.w[1] =
        p_sign | ((UINT64) (e4 + 6176) << 49) | (res.w[1] & MASK_COEFF);
      // avoid a double rounding error
      if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
          is_midpoint_lt_even) { // double rounding error upward
        // res = res - 1
        res.w[0]--;
        if (res.w[0] == 0xffffffffffffffffull)
          res.w[1]--;
        // Note: a double rounding error upward is not possible; for this
        // the result after the first rounding would have to be 99...95
        // (35 digits in all), possibly followed by a number of zeros; this
        // is not possible in Cases (2)-(6) or (15)-(17) which may get here
        is_midpoint_lt_even = 0;
        is_inexact_lt_midpoint = 1;
      } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
          is_midpoint_gt_even) { // double rounding error downward
        // res = res + 1
        res.w[0]++;
        if (res.w[0] == 0)
          res.w[1]++;
        is_midpoint_gt_even = 0;
        is_inexact_gt_midpoint = 1;
      } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	 !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
        // if this second rounding was exact the result may still be 
        // inexact because of the first rounding
        if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
          is_inexact_gt_midpoint = 1;
        }
        if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
          is_inexact_lt_midpoint = 1;
        }
      } else if (is_midpoint_gt_even &&
        	 (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
        // pulled up to a midpoint
        is_inexact_lt_midpoint = 1;
        is_inexact_gt_midpoint = 0;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
      } else if (is_midpoint_lt_even &&
        	 (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
        // pulled down to a midpoint
        is_inexact_lt_midpoint = 0;
        is_inexact_gt_midpoint = 1;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
      } else {
        ;
      }
    }
  }
  // res contains the correct result
  // apply correction if not rounding to nearest
  if (rnd_mode != ROUNDING_TO_NEAREST) {
    rounding_correction (rnd_mode,
        		 is_inexact_lt_midpoint, is_inexact_gt_midpoint,
        		 is_midpoint_lt_even, is_midpoint_gt_even,
        		 e4, &res, ptrfpsf);
  }
  if (is_midpoint_lt_even || is_midpoint_gt_even ||
      is_inexact_lt_midpoint || is_inexact_gt_midpoint) {
    // set the inexact flag
    *ptrfpsf |= INEXACT_EXCEPTION;
    if (is_tiny)
      *ptrfpsf |= UNDERFLOW_EXCEPTION;
  }

  *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
  *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
  *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
  *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
  *ptrres = res;
  return;
}


#if DECIMAL_CALL_BY_REFERENCE
static void
bid128_ext_fma (int *ptr_is_midpoint_lt_even,
        	int *ptr_is_midpoint_gt_even,
        	int *ptr_is_inexact_lt_midpoint,
        	int *ptr_is_inexact_gt_midpoint, UINT128 * pres,
        	UINT128 * px, UINT128 * py,
        	UINT128 *
        	pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
        	_EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
static UINT128
bid128_ext_fma (int *ptr_is_midpoint_lt_even,
        	int *ptr_is_midpoint_gt_even,
        	int *ptr_is_inexact_lt_midpoint,
        	int *ptr_is_inexact_gt_midpoint, UINT128 x, UINT128 y,
        	UINT128 z _RND_MODE_PARAM _EXC_FLAGS_PARAM
        	_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
#endif

  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT64 x_sign, y_sign, z_sign, p_sign, tmp_sign;
  UINT64 x_exp = 0, y_exp = 0, z_exp = 0, p_exp;
  int true_p_exp;
  UINT128 C1, C2, C3;
  UINT256 C4;
  int q1 = 0, q2 = 0, q3 = 0, q4;
  int e1, e2, e3, e4;
  int scale, ind, delta, x0;
  int p34 = P34; // used to modify the limit on the number of digits
  BID_UI64DOUBLE tmp;
  int x_nr_bits, y_nr_bits, z_nr_bits;
  unsigned int save_fpsf;
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0;
  int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  int is_midpoint_lt_even0 = 0, is_midpoint_gt_even0 = 0;
  int is_inexact_lt_midpoint0 = 0, is_inexact_gt_midpoint0 = 0;
  int incr_exp = 0;
  int lsb;
  int lt_half_ulp = 0;
  int eq_half_ulp = 0;
  int gt_half_ulp = 0;
  int is_tiny = 0;
  UINT64 R64, tmp64;
  UINT128 P128, R128;
  UINT192 P192, R192;
  UINT256 R256;

  // the following are based on the table of special cases for fma; the NaN
  // behavior is similar to that of the IA-64 Architecture fma 

  // identify cases where at least one operand is NaN

  BID_SWAP128 (x);
  BID_SWAP128 (y);
  BID_SWAP128 (z);
  if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
    // if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y)
    // check first for non-canonical NaN payload
    if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
        (((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
         (y.w[0] > 0x38c15b09ffffffffull))) {
      y.w[1] = y.w[1] & 0xffffc00000000000ull;
      y.w[0] = 0x0ull;
    }
    if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
      // set invalid flag
      *pfpsf |= INVALID_EXCEPTION;
      // return quiet (y)
      res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
      res.w[0] = y.w[0];
    } else { // y is QNaN
      // return y
      res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
      res.w[0] = y.w[0];
      // if z = SNaN or x = SNaN signal invalid exception
      if ((z.w[1] & MASK_SNAN) == MASK_SNAN ||
          (x.w[1] & MASK_SNAN) == MASK_SNAN) {
        // set invalid flag
        *pfpsf |= INVALID_EXCEPTION;
      }
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  } else if ((z.w[1] & MASK_NAN) == MASK_NAN) { // z is NAN
    // if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z)
    // check first for non-canonical NaN payload
    if (((z.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
        (((z.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
         (z.w[0] > 0x38c15b09ffffffffull))) {
      z.w[1] = z.w[1] & 0xffffc00000000000ull;
      z.w[0] = 0x0ull;
    }
    if ((z.w[1] & MASK_SNAN) == MASK_SNAN) { // z is SNAN 
      // set invalid flag 
      *pfpsf |= INVALID_EXCEPTION;
      // return quiet (z) 
      res.w[1] = z.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
      res.w[0] = z.w[0];
    } else { // z is QNaN 
      // return z  
      res.w[1] = z.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
      res.w[0] = z.w[0];
      // if x = SNaN signal invalid exception
      if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {
        // set invalid flag
        *pfpsf |= INVALID_EXCEPTION;
      }
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  } else if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
    // if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x)
    // check first for non-canonical NaN payload
    if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
        (((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
         (x.w[0] > 0x38c15b09ffffffffull))) {
      x.w[1] = x.w[1] & 0xffffc00000000000ull;
      x.w[0] = 0x0ull;
    }
    if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN 
      // set invalid flag 
      *pfpsf |= INVALID_EXCEPTION;
      // return quiet (x) 
      res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
      res.w[0] = x.w[0];
    } else { // x is QNaN 
      // return x  
      res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
      res.w[0] = x.w[0];
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  }
  // x, y, z are 0, f, or inf but not NaN => unpack the arguments and check
  // for non-canonical values

  x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
  C1.w[1] = x.w[1] & MASK_COEFF;
  C1.w[0] = x.w[0];
  if ((x.w[1] & MASK_ANY_INF) != MASK_INF) { // x != inf
    // if x is not infinity check for non-canonical values - treated as zero
    if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
      // non-canonical
      x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
      C1.w[1] = 0; // significand high
      C1.w[0] = 0; // significand low
    } else { // G0_G1 != 11
      x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
      if (C1.w[1] > 0x0001ed09bead87c0ull ||
          (C1.w[1] == 0x0001ed09bead87c0ull &&
           C1.w[0] > 0x378d8e63ffffffffull)) {
        // x is non-canonical if coefficient is larger than 10^34 -1
        C1.w[1] = 0;
        C1.w[0] = 0;
      } else { // canonical          
        ;
      }
    }
  }
  y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
  C2.w[1] = y.w[1] & MASK_COEFF;
  C2.w[0] = y.w[0];
  if ((y.w[1] & MASK_ANY_INF) != MASK_INF) { // y != inf
    // if y is not infinity check for non-canonical values - treated as zero
    if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
      // non-canonical
      y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
      C2.w[1] = 0; // significand high
      C2.w[0] = 0; // significand low 
    } else { // G0_G1 != 11
      y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits
      if (C2.w[1] > 0x0001ed09bead87c0ull ||
          (C2.w[1] == 0x0001ed09bead87c0ull &&
           C2.w[0] > 0x378d8e63ffffffffull)) {
        // y is non-canonical if coefficient is larger than 10^34 -1
        C2.w[1] = 0;
        C2.w[0] = 0;
      } else { // canonical
        ;
      }
    }
  }
  z_sign = z.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
  C3.w[1] = z.w[1] & MASK_COEFF;
  C3.w[0] = z.w[0];
  if ((z.w[1] & MASK_ANY_INF) != MASK_INF) { // z != inf
    // if z is not infinity check for non-canonical values - treated as zero
    if ((z.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
      // non-canonical
      z_exp = (z.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
      C3.w[1] = 0; // significand high
      C3.w[0] = 0; // significand low 
    } else { // G0_G1 != 11
      z_exp = z.w[1] & MASK_EXP; // biased and shifted left 49 bits
      if (C3.w[1] > 0x0001ed09bead87c0ull ||
          (C3.w[1] == 0x0001ed09bead87c0ull &&
           C3.w[0] > 0x378d8e63ffffffffull)) {
        // z is non-canonical if coefficient is larger than 10^34 -1
        C3.w[1] = 0;
        C3.w[0] = 0;
      } else { // canonical
        ;
      }
    }
  }

  p_sign = x_sign ^ y_sign; // sign of the product

  // identify cases where at least one operand is infinity

  if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
    if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
      if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
        if (p_sign == z_sign) {
          res.w[1] = z_sign | MASK_INF;
          res.w[0] = 0x0;
        } else {
          // return QNaN Indefinite
          res.w[1] = 0x7c00000000000000ull;
          res.w[0] = 0x0000000000000000ull;
          // set invalid flag
          *pfpsf |= INVALID_EXCEPTION;
        }
      } else { // z = 0 or z = f
        res.w[1] = p_sign | MASK_INF;
        res.w[0] = 0x0;
      }
    } else if (C2.w[1] != 0 || C2.w[0] != 0) { // y = f
      if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
        if (p_sign == z_sign) {
          res.w[1] = z_sign | MASK_INF;
          res.w[0] = 0x0;
        } else {
          // return QNaN Indefinite 
          res.w[1] = 0x7c00000000000000ull;
          res.w[0] = 0x0000000000000000ull;
          // set invalid flag
          *pfpsf |= INVALID_EXCEPTION;
        }
      } else { // z = 0 or z = f
        res.w[1] = p_sign | MASK_INF;
        res.w[0] = 0x0;
      }
    } else { // y = 0
      // return QNaN Indefinite
      res.w[1] = 0x7c00000000000000ull;
      res.w[0] = 0x0000000000000000ull;
      // set invalid flag
      *pfpsf |= INVALID_EXCEPTION;
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  } else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
    if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
      // x = f, necessarily
      if ((p_sign != z_sign)
          || (C1.w[1] == 0x0ull && C1.w[0] == 0x0ull)) {
        // return QNaN Indefinite
        res.w[1] = 0x7c00000000000000ull;
        res.w[0] = 0x0000000000000000ull;
        // set invalid flag
        *pfpsf |= INVALID_EXCEPTION;
      } else {
        res.w[1] = z_sign | MASK_INF;
        res.w[0] = 0x0;
      }
    } else if (C1.w[1] == 0x0 && C1.w[0] == 0x0) { // x = 0
      // z = 0, f, inf
      // return QNaN Indefinite
      res.w[1] = 0x7c00000000000000ull;
      res.w[0] = 0x0000000000000000ull;
      // set invalid flag
      *pfpsf |= INVALID_EXCEPTION;
    } else {
      // x = f and z = 0, f, necessarily
      res.w[1] = p_sign | MASK_INF;
      res.w[0] = 0x0;
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  } else if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
    // x = 0, f and y = 0, f, necessarily
    res.w[1] = z_sign | MASK_INF;
    res.w[0] = 0x0;
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  }

  true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176;
  if (true_p_exp < -6176)
    p_exp = 0; // cannot be less than EXP_MIN
  else
    p_exp = (UINT64) (true_p_exp + 6176) << 49;

  if (((C1.w[1] == 0x0 && C1.w[0] == 0x0) || (C2.w[1] == 0x0 && C2.w[0] == 0x0)) && C3.w[1] == 0x0 && C3.w[0] == 0x0) { // (x = 0 or y = 0) and z = 0
    // the result is 0
    if (p_exp < z_exp)
      res.w[1] = p_exp; // preferred exponent
    else
      res.w[1] = z_exp; // preferred exponent
    if (p_sign == z_sign) {
      res.w[1] |= z_sign;
      res.w[0] = 0x0;
    } else { // x * y and z have opposite signs
      if (rnd_mode == ROUNDING_DOWN) {
        // res = -0.0
        res.w[1] |= MASK_SIGN;
        res.w[0] = 0x0;
      } else {
        // res = +0.0
        // res.w[1] |= 0x0;
        res.w[0] = 0x0;
      }
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  }
  // from this point on, we may need to know the number of decimal digits
  // in the significands of x, y, z when x, y, z != 0

  if (C1.w[1] != 0 || C1.w[0] != 0) { // x = f (non-zero finite)
    // q1 = nr. of decimal digits in x
    // determine first the nr. of bits in x
    if (C1.w[1] == 0) {
      if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
        // split the 64-bit value in two 32-bit halves to avoid rounding errors
        if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
          tmp.d = (double) (C1.w[0] >> 32); // exact conversion
          x_nr_bits =
            33 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
        } else { // x < 2^32
          tmp.d = (double) (C1.w[0]); // exact conversion
          x_nr_bits =
            1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
        }
      } else { // if x < 2^53
        tmp.d = (double) C1.w[0]; // exact conversion
        x_nr_bits =
          1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
      tmp.d = (double) C1.w[1]; // exact conversion
      x_nr_bits =
        65 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }
    q1 = nr_digits[x_nr_bits - 1].digits;
    if (q1 == 0) {
      q1 = nr_digits[x_nr_bits - 1].digits1;
      if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
          (C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
           C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
        q1++;
    }
  }

  if (C2.w[1] != 0 || C2.w[0] != 0) { // y = f (non-zero finite)
    if (C2.w[1] == 0) {
      if (C2.w[0] >= 0x0020000000000000ull) { // y >= 2^53
        // split the 64-bit value in two 32-bit halves to avoid rounding errors
        if (C2.w[0] >= 0x0000000100000000ull) { // y >= 2^32
          tmp.d = (double) (C2.w[0] >> 32); // exact conversion
          y_nr_bits =
            32 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
        } else { // y < 2^32
          tmp.d = (double) C2.w[0]; // exact conversion
          y_nr_bits =
            ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
        }
      } else { // if y < 2^53
        tmp.d = (double) C2.w[0]; // exact conversion
        y_nr_bits =
          ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else { // C2.w[1] != 0 => nr. bits = 64 + nr_bits (C2.w[1])
      tmp.d = (double) C2.w[1]; // exact conversion
      y_nr_bits =
        64 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }

    q2 = nr_digits[y_nr_bits].digits;
    if (q2 == 0) {
      q2 = nr_digits[y_nr_bits].digits1;
      if (C2.w[1] > nr_digits[y_nr_bits].threshold_hi ||
          (C2.w[1] == nr_digits[y_nr_bits].threshold_hi &&
           C2.w[0] >= nr_digits[y_nr_bits].threshold_lo))
        q2++;
    }
  }

  if (C3.w[1] != 0 || C3.w[0] != 0) { // z = f (non-zero finite)
    if (C3.w[1] == 0) {
      if (C3.w[0] >= 0x0020000000000000ull) { // z >= 2^53
        // split the 64-bit value in two 32-bit halves to avoid rounding errors
        if (C3.w[0] >= 0x0000000100000000ull) { // z >= 2^32
          tmp.d = (double) (C3.w[0] >> 32); // exact conversion
          z_nr_bits =
            32 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
        } else { // z < 2^32
          tmp.d = (double) C3.w[0]; // exact conversion
          z_nr_bits =
            ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
        }
      } else { // if z < 2^53
        tmp.d = (double) C3.w[0]; // exact conversion
        z_nr_bits =
          ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else { // C3.w[1] != 0 => nr. bits = 64 + nr_bits (C3.w[1])
      tmp.d = (double) C3.w[1]; // exact conversion
      z_nr_bits =
        64 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }

    q3 = nr_digits[z_nr_bits].digits;
    if (q3 == 0) {
      q3 = nr_digits[z_nr_bits].digits1;
      if (C3.w[1] > nr_digits[z_nr_bits].threshold_hi ||
          (C3.w[1] == nr_digits[z_nr_bits].threshold_hi &&
           C3.w[0] >= nr_digits[z_nr_bits].threshold_lo))
        q3++;
    }
  }

  if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) ||
      (C2.w[1] == 0x0 && C2.w[0] == 0x0)) {
    // x = 0 or y = 0
    // z = f, necessarily; for 0 + z return z, with the preferred exponent
    // the result is z, but need to get the preferred exponent
    if (z_exp <= p_exp) { // the preferred exponent is z_exp
      res.w[1] = z_sign | (z_exp & MASK_EXP) | C3.w[1];
      res.w[0] = C3.w[0];
    } else { // if (p_exp < z_exp) the preferred exponent is p_exp
      // return (C3 * 10^scale) * 10^(z_exp - scale)
      // where scale = min (p34-q3, (z_exp-p_exp) >> 49)
      scale = p34 - q3;
      ind = (z_exp - p_exp) >> 49;
      if (ind < scale)
        scale = ind;
      if (scale == 0) {
        res.w[1] = z.w[1]; // & MASK_COEFF, which is redundant
        res.w[0] = z.w[0];
      } else if (q3 <= 19) { // z fits in 64 bits 
        if (scale <= 19) { // 10^scale fits in 64 bits
          // 64 x 64 C3.w[0] * ten2k64[scale]
          __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
        } else { // 10^scale fits in 128 bits
          // 64 x 128 C3.w[0] * ten2k128[scale - 20]
          __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
        }
      } else { // z fits in 128 bits, but 10^scale must fit in 64 bits 
        // 64 x 128 ten2k64[scale] * C3
        __mul_128x64_to_128 (res, ten2k64[scale], C3);
      }
      // subtract scale from the exponent
      z_exp = z_exp - ((UINT64) scale << 49);
      res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
    }
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  } else {
    ; // continue with x = f, y = f, z = 0 or x = f, y = f, z = f
  }

  e1 = (x_exp >> 49) - 6176; // unbiased exponent of x 
  e2 = (y_exp >> 49) - 6176; // unbiased exponent of y 
  e3 = (z_exp >> 49) - 6176; // unbiased exponent of z
  e4 = e1 + e2; // unbiased exponent of the exact x * y

  // calculate C1 * C2 and its number of decimal digits, q4

  // the exact product has either q1 + q2 - 1 or q1 + q2 decimal digits
  // where 2 <= q1 + q2 <= 68
  // calculate C4 = C1 * C2 and determine q
  C4.w[3] = C4.w[2] = C4.w[1] = C4.w[0] = 0;
  if (q1 + q2 <= 19) { // if 2 <= q1 + q2 <= 19, C4 = C1 * C2 fits in 64 bits
    C4.w[0] = C1.w[0] * C2.w[0];
    // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
    if (C4.w[0] < ten2k64[q1 + q2 - 1])
      q4 = q1 + q2 - 1; // q4 in [1, 18]
    else
      q4 = q1 + q2; // q4 in [2, 19]
    // length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
  } else if (q1 + q2 == 20) { // C4 = C1 * C2 fits in 64 or 128 bits
    // q1 <= 19 and q2 <= 19 so both C1 and C2 fit in 64 bits
    __mul_64x64_to_128MACH (C4, C1.w[0], C2.w[0]);
    // if C4 < 10^(q1+q2-1) = 10^19 then q4 = q1+q2-1 = 19 else q4 = q1+q2 = 20
    if (C4.w[1] == 0 && C4.w[0] < ten2k64[19]) { // 19 = q1+q2-1
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
      q4 = 19; // 19 = q1 + q2 - 1
    } else {
      // if (C4.w[1] == 0)
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
      // else
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
      q4 = 20; // 20 = q1 + q2
    }
  } else if (q1 + q2 <= 38) { // 21 <= q1 + q2 <= 38
    // C4 = C1 * C2 fits in 64 or 128 bits
    // (64 bits possibly, but only when q1 + q2 = 21 and C4 has 20 digits)
    // at least one of C1, C2 has at most 19 decimal digits & fits in 64 bits
    if (q1 <= 19) {
      __mul_128x64_to_128 (C4, C1.w[0], C2);
    } else { // q2 <= 19
      __mul_128x64_to_128 (C4, C2.w[0], C1);
    }
    // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
    if (C4.w[1] < ten2k128[q1 + q2 - 21].w[1] ||
        (C4.w[1] == ten2k128[q1 + q2 - 21].w[1] &&
         C4.w[0] < ten2k128[q1 + q2 - 21].w[0])) {
      // if (C4.w[1] == 0) // q4 = 20, necessarily
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
      // else
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
      q4 = q1 + q2 - 1; // q4 in [20, 37]
    } else {
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
      q4 = q1 + q2; // q4 in [21, 38]
    }
  } else if (q1 + q2 == 39) { // C4 = C1 * C2 fits in 128 or 192 bits
    // both C1 and C2 fit in 128 bits (actually in 113 bits)
    // may replace this by 128x128_to192
    __mul_128x128_to_256 (C4, C1, C2); // C4.w[3] is 0
    // if C4 < 10^(q1+q2-1) = 10^38 then q4 = q1+q2-1 = 38 else q4 = q1+q2 = 39
    if (C4.w[2] == 0 && (C4.w[1] < ten2k128[18].w[1] ||
        		 (C4.w[1] == ten2k128[18].w[1]
        		  && C4.w[0] < ten2k128[18].w[0]))) {
      // 18 = 38 - 20 = q1+q2-1 - 20
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
      q4 = 38; // 38 = q1 + q2 - 1
    } else {
      // if (C4.w[2] == 0)
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
      // else
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
      q4 = 39; // 39 = q1 + q2
    }
  } else if (q1 + q2 <= 57) { // 40 <= q1 + q2 <= 57
    // C4 = C1 * C2 fits in 128 or 192 bits
    // (128 bits possibly, but only when q1 + q2 = 40 and C4 has 39 digits)
    // both C1 and C2 fit in 128 bits (actually in 113 bits); at most one
    // may fit in 64 bits
    if (C1.w[1] == 0) { // C1 fits in 64 bits
      // __mul_64x128_full (REShi64, RESlo128, A64, B128)
      __mul_64x128_full (C4.w[2], C4, C1.w[0], C2);
    } else if (C2.w[1] == 0) { // C2 fits in 64 bits
      // __mul_64x128_full (REShi64, RESlo128, A64, B128)
      __mul_64x128_full (C4.w[2], C4, C2.w[0], C1);
    } else { // both C1 and C2 require 128 bits
      // may use __mul_128x128_to_192 (C4.w[2], C4.w[0], C2.w[0], C1);
      __mul_128x128_to_256 (C4, C1, C2); // C4.w[3] = 0
    }
    // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
    if (C4.w[2] < ten2k256[q1 + q2 - 40].w[2] ||
        (C4.w[2] == ten2k256[q1 + q2 - 40].w[2] &&
         (C4.w[1] < ten2k256[q1 + q2 - 40].w[1] ||
          (C4.w[1] == ten2k256[q1 + q2 - 40].w[1] &&
           C4.w[0] < ten2k256[q1 + q2 - 40].w[0])))) {
      // if (C4.w[2] == 0) // q4 = 39, necessarily
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
      // else
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
      q4 = q1 + q2 - 1; // q4 in [39, 56]
    } else {
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
      q4 = q1 + q2; // q4 in [40, 57]
    }
  } else if (q1 + q2 == 58) { // C4 = C1 * C2 fits in 192 or 256 bits
    // both C1 and C2 fit in 128 bits (actually in 113 bits); at most one
    // may fit in 64 bits
    if (C1.w[1] == 0) { // C1 * C2 will fit in 192 bits
      __mul_64x128_full (C4.w[2], C4, C1.w[0], C2); // may use 64x128_to_192
    } else if (C2.w[1] == 0) { // C1 * C2 will fit in 192 bits
      __mul_64x128_full (C4.w[2], C4, C2.w[0], C1); // may use 64x128_to_192
    } else { // C1 * C2 will fit in 192 bits or in 256 bits
      __mul_128x128_to_256 (C4, C1, C2);
    }
    // if C4 < 10^(q1+q2-1) = 10^57 then q4 = q1+q2-1 = 57 else q4 = q1+q2 = 58
    if (C4.w[3] == 0 && (C4.w[2] < ten2k256[18].w[2] ||
        		 (C4.w[2] == ten2k256[18].w[2]
        		  && (C4.w[1] < ten2k256[18].w[1]
        		      || (C4.w[1] == ten2k256[18].w[1]
        			  && C4.w[0] < ten2k256[18].w[0]))))) {
      // 18 = 57 - 39 = q1+q2-1 - 39
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
      q4 = 57; // 57 = q1 + q2 - 1
    } else {
      // if (C4.w[3] == 0)
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
      // else
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 256;
      q4 = 58; // 58 = q1 + q2
    }
  } else { // if 59 <= q1 + q2 <= 68
    // C4 = C1 * C2 fits in 192 or 256 bits
    // (192 bits possibly, but only when q1 + q2 = 59 and C4 has 58 digits)
    // both C1 and C2 fit in 128 bits (actually in 113 bits); none fits in
    // 64 bits
    // may use __mul_128x128_to_192 (C4.w[2], C4.w[0], C2.w[0], C1);
    __mul_128x128_to_256 (C4, C1, C2); // C4.w[3] = 0
    // if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
    if (C4.w[3] < ten2k256[q1 + q2 - 40].w[3] ||
        (C4.w[3] == ten2k256[q1 + q2 - 40].w[3] &&
         (C4.w[2] < ten2k256[q1 + q2 - 40].w[2] ||
          (C4.w[2] == ten2k256[q1 + q2 - 40].w[2] &&
           (C4.w[1] < ten2k256[q1 + q2 - 40].w[1] ||
            (C4.w[1] == ten2k256[q1 + q2 - 40].w[1] &&
             C4.w[0] < ten2k256[q1 + q2 - 40].w[0])))))) {
      // if (C4.w[3] == 0) // q4 = 58, necessarily
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
      // else
      //   length of C1 * C2 rounded up to a multiple of 64 bits is len = 256;
      q4 = q1 + q2 - 1; // q4 in [58, 67]
    } else {
      // length of C1 * C2 rounded up to a multiple of 64 bits is len = 256;
      q4 = q1 + q2; // q4 in [59, 68]
    }
  }

  if (C3.w[1] == 0x0 && C3.w[0] == 0x0) { // x = f, y = f, z = 0
    save_fpsf = *pfpsf; // sticky bits - caller value must be preserved
    *pfpsf = 0;

    if (q4 > p34) {

      // truncate C4 to p34 digits into res
      // x = q4-p34, 1 <= x <= 34 because 35 <= q4 <= 68
      x0 = q4 - p34;
      if (q4 <= 38) {
        P128.w[1] = C4.w[1];
        P128.w[0] = C4.w[0];
        round128_19_38 (q4, x0, P128, &res, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
      } else if (q4 <= 57) { // 35 <= q4 <= 57
        P192.w[2] = C4.w[2];
        P192.w[1] = C4.w[1];
        P192.w[0] = C4.w[0];
        round192_39_57 (q4, x0, P192, &R192, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
        res.w[0] = R192.w[0];
        res.w[1] = R192.w[1];
      } else { // if (q4 <= 68)
        round256_58_76 (q4, x0, C4, &R256, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
        res.w[0] = R256.w[0];
        res.w[1] = R256.w[1];
      }
      e4 = e4 + x0;
      if (incr_exp) {
        e4 = e4 + 1;
      }
      q4 = p34;
      // res is now the coefficient of the result rounded to the destination 
      // precision, with unbounded exponent; the exponent is e4; q4=digits(res)
    } else { // if (q4 <= p34)
      // C4 * 10^e4 is the result rounded to the destination precision, with  
      // unbounded exponent (which is exact)

      if ((q4 + e4 <= p34 + expmax) && (e4 > expmax)) {
        // e4 is too large, but can be brought within range by scaling up C4
        scale = e4 - expmax; // 1 <= scale < P-q4 <= P-1 => 1 <= scale <= P-2
        // res = (C4 * 10^scale) * 10^expmax
        if (q4 <= 19) { // C4 fits in 64 bits
          if (scale <= 19) { // 10^scale fits in 64 bits
            // 64 x 64 C4.w[0] * ten2k64[scale]
            __mul_64x64_to_128MACH (res, C4.w[0], ten2k64[scale]);
          } else { // 10^scale fits in 128 bits
            // 64 x 128 C4.w[0] * ten2k128[scale - 20]
            __mul_128x64_to_128 (res, C4.w[0], ten2k128[scale - 20]);
          }
        } else { // C4 fits in 128 bits, but 10^scale must fit in 64 bits
          // 64 x 128 ten2k64[scale] * CC43
          __mul_128x64_to_128 (res, ten2k64[scale], C4);
        }
        e4 = e4 - scale; // expmax
        q4 = q4 + scale;
      } else {
        res.w[1] = C4.w[1];
        res.w[0] = C4.w[0];
      }
      // res is the coefficient of the result rounded to the destination 
      // precision, with unbounded exponent (it has q4 digits); the exponent 
      // is e4 (exact result)
    }

    // check for overflow
    if (q4 + e4 > p34 + expmax) {
      if (rnd_mode == ROUNDING_TO_NEAREST) {
        res.w[1] = p_sign | 0x7800000000000000ull; // +/-inf
        res.w[0] = 0x0000000000000000ull;
        *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
      } else {
        res.w[1] = p_sign | res.w[1];
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     e4, &res, pfpsf);
      }
      *pfpsf |= save_fpsf;
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)
    }
    // check for underflow
    if (q4 + e4 < expmin + P34) {
      is_tiny = 1; // the result is tiny
      if (e4 < expmin) {
        // if e4 < expmin, we must truncate more of res
        x0 = expmin - e4; // x0 >= 1
        is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
        is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
        is_midpoint_lt_even0 = is_midpoint_lt_even;
        is_midpoint_gt_even0 = is_midpoint_gt_even;
        is_inexact_lt_midpoint = 0;
        is_inexact_gt_midpoint = 0;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
        // the number of decimal digits in res is q4
        if (x0 < q4) { // 1 <= x0 <= q4-1 => round res to q4 - x0 digits
          if (q4 <= 18) { // 2 <= q4 <= 18, 1 <= x0 <= 17
            round64_2_18 (q4, x0, res.w[0], &R64, &incr_exp,
        		  &is_midpoint_lt_even, &is_midpoint_gt_even,
        		  &is_inexact_lt_midpoint,
        		  &is_inexact_gt_midpoint);
            if (incr_exp) {
              // R64 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 17
              R64 = ten2k64[q4 - x0];
            }
            // res.w[1] = 0; (from above)
            res.w[0] = R64;
          } else { // if (q4 <= 34)
            // 19 <= q4 <= 38
            P128.w[1] = res.w[1];
            P128.w[0] = res.w[0];
            round128_19_38 (q4, x0, P128, &res, &incr_exp,
        		    &is_midpoint_lt_even, &is_midpoint_gt_even,
        		    &is_inexact_lt_midpoint,
        		    &is_inexact_gt_midpoint);
            if (incr_exp) {
              // increase coefficient by a factor of 10; this will be <= 10^33
              // R128 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 37
              if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
        	// res.w[1] = 0;
        	res.w[0] = ten2k64[q4 - x0];
              } else { // 20 <= q4 - x0 <= 37
        	res.w[0] = ten2k128[q4 - x0 - 20].w[0];
        	res.w[1] = ten2k128[q4 - x0 - 20].w[1];
              }
            }
          }
          e4 = e4 + x0; // expmin 
        } else if (x0 == q4) {
          // the second rounding is for 0.d(0)d(1)...d(q4-1) * 10^emin
          // determine relationship with 1/2 ulp
          if (q4 <= 19) {
            if (res.w[0] < midpoint64[q4 - 1]) { // < 1/2 ulp
              lt_half_ulp = 1;
              is_inexact_lt_midpoint = 1;
            } else if (res.w[0] == midpoint64[q4 - 1]) { // = 1/2 ulp
              eq_half_ulp = 1;
              is_midpoint_gt_even = 1;
            } else { // > 1/2 ulp
              // gt_half_ulp = 1;
              is_inexact_gt_midpoint = 1;
            }
          } else { // if (q4 <= 34)
            if (res.w[1] < midpoint128[q4 - 20].w[1] || 
                (res.w[1] == midpoint128[q4 - 20].w[1] && 
                res.w[0] < midpoint128[q4 - 20].w[0])) { // < 1/2 ulp
              lt_half_ulp = 1;
              is_inexact_lt_midpoint = 1;
            } else if (res.w[1] == midpoint128[q4 - 20].w[1] && 
                res.w[0] == midpoint128[q4 - 20].w[0]) { // = 1/2 ulp
              eq_half_ulp = 1;
              is_midpoint_gt_even = 1;
            } else { // > 1/2 ulp
              // gt_half_ulp = 1;
              is_inexact_gt_midpoint = 1;
            }
          }
          if (lt_half_ulp || eq_half_ulp) {
            // res = +0.0 * 10^expmin
            res.w[1] = 0x0000000000000000ull;
            res.w[0] = 0x0000000000000000ull;
          } else { // if (gt_half_ulp)
            // res = +1 * 10^expmin
            res.w[1] = 0x0000000000000000ull;
            res.w[0] = 0x0000000000000001ull;
          }
          e4 = expmin;
        } else { // if (x0 > q4)
          // the second rounding is for 0.0...d(0)d(1)...d(q4-1) * 10^emin
          res.w[1] = 0;
          res.w[0] = 0;
          e4 = expmin;
          is_inexact_lt_midpoint = 1;
        }
        // avoid a double rounding error
        if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
            is_midpoint_lt_even) { // double rounding error upward
          // res = res - 1
          res.w[0]--;
          if (res.w[0] == 0xffffffffffffffffull)
            res.w[1]--;
          // Note: a double rounding error upward is not possible; for this
          // the result after the first rounding would have to be 99...95
          // (35 digits in all), possibly followed by a number of zeros; this
          // not possible for f * f + 0
          is_midpoint_lt_even = 0;
          is_inexact_lt_midpoint = 1;
        } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
            is_midpoint_gt_even) { // double rounding error downward
          // res = res + 1
          res.w[0]++;
          if (res.w[0] == 0)
            res.w[1]++;
          is_midpoint_gt_even = 0;
          is_inexact_gt_midpoint = 1;
        } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	   !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
          // if this second rounding was exact the result may still be 
          // inexact because of the first rounding
          if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
            is_inexact_gt_midpoint = 1;
          }
          if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
            is_inexact_lt_midpoint = 1;
          }
        } else if (is_midpoint_gt_even &&
        	   (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
          // pulled up to a midpoint
          is_inexact_lt_midpoint = 1;
          is_inexact_gt_midpoint = 0;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
        } else if (is_midpoint_lt_even &&
        	   (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
          // pulled down to a midpoint
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 1;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
        } else {
          ;
        }
      } else { // if e4 >= emin then q4 < P and the result is tiny and exact
        if (e3 < e4) {
          // if (e3 < e4) the preferred exponent is e3
          // return (C4 * 10^scale) * 10^(e4 - scale)
          // where scale = min (p34-q4, (e4 - e3))
          scale = p34 - q4;
          ind = e4 - e3;
          if (ind < scale)
            scale = ind;
          if (scale == 0) {
            ; // res and e4 are unchanged
          } else if (q4 <= 19) { // C4 fits in 64 bits
            if (scale <= 19) { // 10^scale fits in 64 bits
              // 64 x 64 res.w[0] * ten2k64[scale]
              __mul_64x64_to_128MACH (res, res.w[0], ten2k64[scale]);
            } else { // 10^scale fits in 128 bits
              // 64 x 128 res.w[0] * ten2k128[scale - 20]
              __mul_128x64_to_128 (res, res.w[0], ten2k128[scale - 20]);
            }
          } else { // res fits in 128 bits, but 10^scale must fit in 64 bits
            // 64 x 128 ten2k64[scale] * C3
            __mul_128x64_to_128 (res, ten2k64[scale], res);
          }
          // subtract scale from the exponent
          e4 = e4 - scale;
        }
      }

      // check for inexact result
      if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
          is_midpoint_lt_even || is_midpoint_gt_even) {
        // set the inexact flag and the underflow flag
        *pfpsf |= INEXACT_EXCEPTION;
        *pfpsf |= UNDERFLOW_EXCEPTION;
      }
      res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1];
      if (rnd_mode != ROUNDING_TO_NEAREST) {
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     e4, &res, pfpsf);
      }
      *pfpsf |= save_fpsf;
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)
    }
    // no overflow, and no underflow for rounding to nearest
    res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1];

    if (rnd_mode != ROUNDING_TO_NEAREST) {
      rounding_correction (rnd_mode,
        		   is_inexact_lt_midpoint,
        		   is_inexact_gt_midpoint,
        		   is_midpoint_lt_even, is_midpoint_gt_even,
        		   e4, &res, pfpsf);
      // if e4 = expmin && significand < 10^33 => result is tiny (for RD, RZ)
      if (e4 == expmin) {
        if ((res.w[1] & MASK_COEFF) < 0x0000314dc6448d93ull ||
            ((res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull &&
             res.w[0] < 0x38c15b0a00000000ull)) {
          is_tiny = 1;
        }
      }
    }

    if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
        is_midpoint_lt_even || is_midpoint_gt_even) {
      // set the inexact flag
      *pfpsf |= INEXACT_EXCEPTION;
      if (is_tiny)
        *pfpsf |= UNDERFLOW_EXCEPTION;
    }

    if ((*pfpsf & INEXACT_EXCEPTION) == 0) { // x * y is exact
      // need to ensure that the result has the preferred exponent
      p_exp = res.w[1] & MASK_EXP;
      if (z_exp < p_exp) { // the preferred exponent is z_exp
        // signficand of res in C3
        C3.w[1] = res.w[1] & MASK_COEFF;
        C3.w[0] = res.w[0];
        // the number of decimal digits of x * y is q4 <= 34
        // Note: the coefficient fits in 128 bits

        // return (C3 * 10^scale) * 10^(p_exp - scale)
        // where scale = min (p34-q4, (p_exp-z_exp) >> 49)
        scale = p34 - q4;
        ind = (p_exp - z_exp) >> 49;
        if (ind < scale)
          scale = ind;
        // subtract scale from the exponent
        p_exp = p_exp - ((UINT64) scale << 49);
        if (scale == 0) {
          ; // leave res unchanged
        } else if (q4 <= 19) { // x * y fits in 64 bits
          if (scale <= 19) { // 10^scale fits in 64 bits
            // 64 x 64 C3.w[0] * ten2k64[scale] 
            __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
          } else { // 10^scale fits in 128 bits 
            // 64 x 128 C3.w[0] * ten2k128[scale - 20]
            __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
          }
          res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1];
        } else { // x * y fits in 128 bits, but 10^scale must fit in 64 bits
          // 64 x 128 ten2k64[scale] * C3 
          __mul_128x64_to_128 (res, ten2k64[scale], C3);
          res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1];
        }
      } // else leave the result as it is, because p_exp <= z_exp
    }
    *pfpsf |= save_fpsf;
    *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
    *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
    *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
    *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
    BID_SWAP128 (res);
    BID_RETURN (res)
  } // else we have f * f + f

  // continue with x = f, y = f, z = f

  delta = q3 + e3 - q4 - e4;
delta_ge_zero:
  if (delta >= 0) {

    if (p34 <= delta - 1 ||	// Case (1')
        (p34 == delta && e3 + 6176 < p34 - q3)) { // Case (1''A)
      // check for overflow, which can occur only in Case (1')
      if ((q3 + e3) > (p34 + expmax) && p34 <= delta - 1) {
        // e3 > expmax implies p34 <= delta-1 and e3 > expmax is a necessary
        // condition for (q3 + e3) > (p34 + expmax)
        if (rnd_mode == ROUNDING_TO_NEAREST) {
          res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
          res.w[0] = 0x0000000000000000ull;
          *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
        } else {
          if (p_sign == z_sign) {
            is_inexact_lt_midpoint = 1;
          } else {
            is_inexact_gt_midpoint = 1;
          }
          // q3 <= p34; if (q3 < p34) scale C3 up by 10^(p34-q3)
          scale = p34 - q3;
          if (scale == 0) {
            res.w[1] = z_sign | C3.w[1];
            res.w[0] = C3.w[0];
          } else {
            if (q3 <= 19) { // C3 fits in 64 bits
              if (scale <= 19) { // 10^scale fits in 64 bits
        	// 64 x 64 C3.w[0] * ten2k64[scale]
        	__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
              } else { // 10^scale fits in 128 bits
        	// 64 x 128 C3.w[0] * ten2k128[scale - 20]
        	__mul_128x64_to_128 (res, C3.w[0],
        			     ten2k128[scale - 20]);
              }
            } else { // C3 fits in 128 bits, but 10^scale must fit in 64 bits
              // 64 x 128 ten2k64[scale] * C3
              __mul_128x64_to_128 (res, ten2k64[scale], C3);
            }
            // the coefficient in res has q3 + scale = p34 digits
          }
          e3 = e3 - scale;
          res.w[1] = z_sign | res.w[1];
          rounding_correction (rnd_mode,
        		       is_inexact_lt_midpoint,
        		       is_inexact_gt_midpoint,
        		       is_midpoint_lt_even, is_midpoint_gt_even,
        		       e3, &res, pfpsf);
        }
        *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
        *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
        *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
        *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
        BID_SWAP128 (res);
        BID_RETURN (res)
      }
      // res = z
      if (q3 < p34) { // the preferred exponent is z_exp - (p34 - q3)
        // return (C3 * 10^scale) * 10^(z_exp - scale)
        // where scale = min (p34-q3, z_exp-EMIN)
        scale = p34 - q3;
        ind = e3 + 6176;
        if (ind < scale)
          scale = ind;
        if (scale == 0) {
          res.w[1] = C3.w[1];
          res.w[0] = C3.w[0];
        } else if (q3 <= 19) { // z fits in 64 bits
          if (scale <= 19) { // 10^scale fits in 64 bits
            // 64 x 64 C3.w[0] * ten2k64[scale]
            __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
          } else { // 10^scale fits in 128 bits
            // 64 x 128 C3.w[0] * ten2k128[scale - 20]
            __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
          }
        } else { // z fits in 128 bits, but 10^scale must fit in 64 bits
          // 64 x 128 ten2k64[scale] * C3
          __mul_128x64_to_128 (res, ten2k64[scale], C3);
        }
        // the coefficient in res has q3 + scale digits
        // subtract scale from the exponent
        z_exp = z_exp - ((UINT64) scale << 49);
        e3 = e3 - scale;
        res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
        if (scale + q3 < p34)
          *pfpsf |= UNDERFLOW_EXCEPTION;
      } else {
        scale = 0;
        res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | C3.w[1];
        res.w[0] = C3.w[0];
      }

      // use the following to avoid double rounding errors when operating on
      // mixed formats in rounding to nearest, and for correcting the result
      // if not rounding to nearest
      if ((p_sign != z_sign) && (delta == (q3 + scale + 1))) {
        // there is a gap of exactly one digit between the scaled C3 and C4
        // C3 * 10^ scale = 10^(q3+scale-1) <=> C3 = 10^(q3-1) is special case
        if ((q3 <= 19 && C3.w[0] != ten2k64[q3 - 1]) ||
            (q3 == 20 && (C3.w[1] != 0 || C3.w[0] != ten2k64[19])) ||
            (q3 >= 21 && (C3.w[1] != ten2k128[q3 - 21].w[1] ||
        		  C3.w[0] != ten2k128[q3 - 21].w[0]))) {
          // C3 * 10^ scale != 10^(q3-1)
          // if ((res.w[1] & MASK_COEFF) != 0x0000314dc6448d93ull ||
          // res.w[0] != 0x38c15b0a00000000ull) { // C3 * 10^scale != 10^33
          is_inexact_gt_midpoint = 1; // if (z_sign), set as if for abs. value
        } else { // if C3 * 10^scale = 10^(q3+scale-1)
          // ok from above e3 = (z_exp >> 49) - 6176;
          // the result is always inexact
          if (q4 == 1) {
            R64 = C4.w[0];
          } else {
            // if q4 > 1 then truncate C4 from q4 digits to 1 digit; 
            // x = q4-1, 1 <= x <= 67 and check if this operation is exact
            if (q4 <= 18) { // 2 <= q4 <= 18
              round64_2_18 (q4, q4 - 1, C4.w[0], &R64, &incr_exp,
        		    &is_midpoint_lt_even, &is_midpoint_gt_even,
        		    &is_inexact_lt_midpoint,
        		    &is_inexact_gt_midpoint);
            } else if (q4 <= 38) {
              P128.w[1] = C4.w[1];
              P128.w[0] = C4.w[0];
              round128_19_38 (q4, q4 - 1, P128, &R128, &incr_exp,
        		      &is_midpoint_lt_even,
        		      &is_midpoint_gt_even,
        		      &is_inexact_lt_midpoint,
        		      &is_inexact_gt_midpoint);
              R64 = R128.w[0]; // one decimal digit
            } else if (q4 <= 57) {
              P192.w[2] = C4.w[2];
              P192.w[1] = C4.w[1];
              P192.w[0] = C4.w[0];
              round192_39_57 (q4, q4 - 1, P192, &R192, &incr_exp,
        		      &is_midpoint_lt_even,
        		      &is_midpoint_gt_even,
        		      &is_inexact_lt_midpoint,
        		      &is_inexact_gt_midpoint);
              R64 = R192.w[0]; // one decimal digit
            } else { // if (q4 <= 68)
              round256_58_76 (q4, q4 - 1, C4, &R256, &incr_exp,
        		      &is_midpoint_lt_even,
        		      &is_midpoint_gt_even,
        		      &is_inexact_lt_midpoint,
        		      &is_inexact_gt_midpoint);
              R64 = R256.w[0]; // one decimal digit
            }
            if (incr_exp) {
              R64 = 10;
            }
          }
          if (q4 == 1 && C4.w[0] == 5) {
            is_inexact_lt_midpoint = 0;
            is_inexact_gt_midpoint = 0;
            is_midpoint_lt_even = 1;
            is_midpoint_gt_even = 0;
          } else if ((e3 == expmin) ||
        	     R64 < 5 || (R64 == 5 && is_inexact_gt_midpoint)) {
            // result does not change
            is_inexact_lt_midpoint = 0;
            is_inexact_gt_midpoint = 1;
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 0;
          } else {
            is_inexact_lt_midpoint = 1;
            is_inexact_gt_midpoint = 0;
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 0;
            // result decremented is 10^(q3+scale) - 1
            if ((q3 + scale) <= 19) {
              res.w[1] = 0;
              res.w[0] = ten2k64[q3 + scale];
            } else { // if ((q3 + scale + 1) <= 35)
              res.w[1] = ten2k128[q3 + scale - 20].w[1];
              res.w[0] = ten2k128[q3 + scale - 20].w[0];
            }
            res.w[0] = res.w[0] - 1; // borrow never occurs
            z_exp = z_exp - EXP_P1;
            e3 = e3 - 1;
            res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1];
          }
          if (e3 == expmin) {
            if (R64 < 5 || (R64 == 5 && !is_inexact_lt_midpoint)) {
              ; // result not tiny (in round-to-nearest mode)
            } else {
              *pfpsf |= UNDERFLOW_EXCEPTION;
            }
          }
        } // end 10^(q3+scale-1)
        // set the inexact flag
        *pfpsf |= INEXACT_EXCEPTION;
      } else {
        if (p_sign == z_sign) {
          // if (z_sign), set as if for absolute value
          is_inexact_lt_midpoint = 1;
        } else { // if (p_sign != z_sign)
          // if (z_sign), set as if for absolute value
          is_inexact_gt_midpoint = 1;
        }
        *pfpsf |= INEXACT_EXCEPTION;
      }
      // the result is always inexact => set the inexact flag
      // Determine tininess:
      //    if (exp > expmin)
      //      the result is not tiny
      //    else // if exp = emin
      //      if (q3 + scale < p34)
      //        the result is tiny
      //      else // if (q3 + scale = p34)
      //        if (C3 * 10^scale > 10^33)
      //          the result is not tiny
      //        else // if C3 * 10^scale = 10^33
      //          if (xy * z > 0)
      //            the result is not tiny
      //          else // if (xy * z < 0)
      //            if (z > 0)
      //              if rnd_mode != RP
      //                the result is tiny
      //              else // if RP
      //                the result is not tiny
      //            else // if (z < 0)
      //              if rnd_mode != RM
      //                the result is tiny
      //              else // if RM
      //                the result is not tiny
      //              endif
      //            endif
      //          endif
      //        endif
      //      endif
      //    endif 
      if ((e3 == expmin && (q3 + scale) < p34) || 
          (e3 == expmin && (q3 + scale) == p34 && 
          (res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull &&	// 10^33_high
          res.w[0] == 0x38c15b0a00000000ull &&	// 10^33_low
          z_sign != p_sign && ((!z_sign && rnd_mode != ROUNDING_UP) || 
          (z_sign && rnd_mode != ROUNDING_DOWN)))) {
        *pfpsf |= UNDERFLOW_EXCEPTION;
      }
      if (rnd_mode != ROUNDING_TO_NEAREST) {
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     e3, &res, pfpsf);
      }
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    } else if (p34 == delta) { // Case (1''B)

      // because Case (1''A) was treated above, e3 + 6176 >= p34 - q3
      // and C3 can be scaled up to p34 digits if needed

      // scale C3 to p34 digits if needed
      scale = p34 - q3; // 0 <= scale <= p34 - 1
      if (scale == 0) {
        res.w[1] = C3.w[1];
        res.w[0] = C3.w[0];
      } else if (q3 <= 19) { // z fits in 64 bits
        if (scale <= 19) { // 10^scale fits in 64 bits
          // 64 x 64 C3.w[0] * ten2k64[scale]
          __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
        } else { // 10^scale fits in 128 bits
          // 64 x 128 C3.w[0] * ten2k128[scale - 20]
          __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
        }
      } else { // z fits in 128 bits, but 10^scale must fit in 64 bits
        // 64 x 128 ten2k64[scale] * C3
        __mul_128x64_to_128 (res, ten2k64[scale], C3);
      }
      // subtract scale from the exponent
      z_exp = z_exp - ((UINT64) scale << 49);
      e3 = e3 - scale;
      // now z_sign, z_exp, and res correspond to a z scaled to p34 = 34 digits

      // determine whether x * y is less than, equal to, or greater than 
      // 1/2 ulp (z)
      if (q4 <= 19) {
        if (C4.w[0] < midpoint64[q4 - 1]) { // < 1/2 ulp
          lt_half_ulp = 1;
        } else if (C4.w[0] == midpoint64[q4 - 1]) { // = 1/2 ulp
          eq_half_ulp = 1;
        } else { // > 1/2 ulp
          gt_half_ulp = 1;
        }
      } else if (q4 <= 38) {
        if (C4.w[2] == 0 && (C4.w[1] < midpoint128[q4 - 20].w[1] || 
            (C4.w[1] == midpoint128[q4 - 20].w[1] && 
            C4.w[0] < midpoint128[q4 - 20].w[0]))) { // < 1/2 ulp
          lt_half_ulp = 1;
        } else if (C4.w[2] == 0 && C4.w[1] == midpoint128[q4 - 20].w[1] && 
            C4.w[0] == midpoint128[q4 - 20].w[0]) { // = 1/2 ulp
          eq_half_ulp = 1;
        } else { // > 1/2 ulp
          gt_half_ulp = 1;
        }
      } else if (q4 <= 58) {
        if (C4.w[3] == 0 && (C4.w[2] < midpoint192[q4 - 39].w[2] || 
            (C4.w[2] == midpoint192[q4 - 39].w[2] && 
            C4.w[1] < midpoint192[q4 - 39].w[1]) || 
            (C4.w[2] == midpoint192[q4 - 39].w[2] && 
            C4.w[1] == midpoint192[q4 - 39].w[1] && 
            C4.w[0] < midpoint192[q4 - 39].w[0]))) { // < 1/2 ulp
          lt_half_ulp = 1;
        } else if (C4.w[3] == 0 && C4.w[2] == midpoint192[q4 - 39].w[2] && 
            C4.w[1] == midpoint192[q4 - 39].w[1] && 
            C4.w[0] == midpoint192[q4 - 39].w[0]) { // = 1/2 ulp
          eq_half_ulp = 1;
        } else { // > 1/2 ulp
          gt_half_ulp = 1;
        }
      } else {
        if (C4.w[3] < midpoint256[q4 - 59].w[3] || 
            (C4.w[3] == midpoint256[q4 - 59].w[3] && 
            C4.w[2] < midpoint256[q4 - 59].w[2]) || 
            (C4.w[3] == midpoint256[q4 - 59].w[3] && 
            C4.w[2] == midpoint256[q4 - 59].w[2] && 
            C4.w[1] < midpoint256[q4 - 59].w[1]) || 
            (C4.w[3] == midpoint256[q4 - 59].w[3] && 
            C4.w[2] == midpoint256[q4 - 59].w[2] && 
            C4.w[1] == midpoint256[q4 - 59].w[1] && 
            C4.w[0] < midpoint256[q4 - 59].w[0])) { // < 1/2 ulp
          lt_half_ulp = 1;
        } else if (C4.w[3] == midpoint256[q4 - 59].w[3] && 
            C4.w[2] == midpoint256[q4 - 59].w[2] && 
            C4.w[1] == midpoint256[q4 - 59].w[1] && 
            C4.w[0] == midpoint256[q4 - 59].w[0]) { // = 1/2 ulp
          eq_half_ulp = 1;
        } else { // > 1/2 ulp
          gt_half_ulp = 1;
        }
      }

      if (p_sign == z_sign) {
        if (lt_half_ulp) {
          res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
          // use the following to avoid double rounding errors when operating on
          // mixed formats in rounding to nearest
          is_inexact_lt_midpoint = 1; // if (z_sign), as if for absolute value
        } else if ((eq_half_ulp && (res.w[0] & 0x01)) || gt_half_ulp) {
          // add 1 ulp to the significand
          res.w[0]++;
          if (res.w[0] == 0x0ull)
            res.w[1]++;
          // check for rounding overflow, when coeff == 10^34
          if ((res.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull && 
              res.w[0] == 0x378d8e6400000000ull) { // coefficient = 10^34
            e3 = e3 + 1;
            // coeff = 10^33
            z_exp = ((UINT64) (e3 + 6176) << 49) & MASK_EXP;
            res.w[1] = 0x0000314dc6448d93ull;
            res.w[0] = 0x38c15b0a00000000ull;
          }
          // end add 1 ulp
          res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
          if (eq_half_ulp) {
            is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value
          } else {
            is_inexact_gt_midpoint = 1; // if (z_sign), as if for absolute value
          }
        } else { // if (eq_half_ulp && !(res.w[0] & 0x01))
          // leave unchanged 
          res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
          is_midpoint_gt_even = 1; // if (z_sign), as if for absolute value
        }
        // the result is always inexact, and never tiny
        // set the inexact flag
        *pfpsf |= INEXACT_EXCEPTION;
        // check for overflow
        if (e3 > expmax && rnd_mode == ROUNDING_TO_NEAREST) {
          res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
          res.w[0] = 0x0000000000000000ull;
          *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
          *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
          *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
          *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
          *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
          BID_SWAP128 (res);
          BID_RETURN (res)
        }
        if (rnd_mode != ROUNDING_TO_NEAREST) {
          rounding_correction (rnd_mode,
        		       is_inexact_lt_midpoint,
        		       is_inexact_gt_midpoint,
        		       is_midpoint_lt_even, is_midpoint_gt_even,
        		       e3, &res, pfpsf);
          z_exp = res.w[1] & MASK_EXP;
        }
      } else { // if (p_sign != z_sign)
        // consider two cases, because C3 * 10^scale = 10^33 is a special case
        if (res.w[1] != 0x0000314dc6448d93ull || 
            res.w[0] != 0x38c15b0a00000000ull) { // C3 * 10^scale != 10^33
          if (lt_half_ulp) {
            res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
            // use the following to avoid double rounding errors when operating
            // on mixed formats in rounding to nearest
            is_inexact_gt_midpoint = 1; // if (z_sign), as if for absolute value
          } else if ((eq_half_ulp && (res.w[0] & 0x01)) || gt_half_ulp) {
            // subtract 1 ulp from the significand
            res.w[0]--;
            if (res.w[0] == 0xffffffffffffffffull)
              res.w[1]--;
            res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
            if (eq_half_ulp) {
              is_midpoint_gt_even = 1; // if (z_sign), as if for absolute value
            } else {
              is_inexact_lt_midpoint = 1; //if(z_sign), as if for absolute value
            }
          } else { // if (eq_half_ulp && !(res.w[0] & 0x01))
            // leave unchanged
            res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
            is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value
          }
          // the result is always inexact, and never tiny
          // check for overflow for RN
          if (e3 > expmax) {
            if (rnd_mode == ROUNDING_TO_NEAREST) {
              res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
              res.w[0] = 0x0000000000000000ull;
              *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
            } else {
              rounding_correction (rnd_mode,
        			   is_inexact_lt_midpoint,
        			   is_inexact_gt_midpoint,
        			   is_midpoint_lt_even,
        			   is_midpoint_gt_even, e3, &res,
        			   pfpsf);
            }
            *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
            *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
            *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
            *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
            BID_SWAP128 (res);
            BID_RETURN (res)
          }
          // set the inexact flag
          *pfpsf |= INEXACT_EXCEPTION;
          if (rnd_mode != ROUNDING_TO_NEAREST) {
            rounding_correction (rnd_mode,
        			 is_inexact_lt_midpoint,
        			 is_inexact_gt_midpoint,
        			 is_midpoint_lt_even,
        			 is_midpoint_gt_even, e3, &res, pfpsf);
          }
          z_exp = res.w[1] & MASK_EXP;
        } else { // if C3 * 10^scale = 10^33
          e3 = (z_exp >> 49) - 6176;
          if (e3 > expmin) {
            // the result is exact if exp > expmin and C4 = d*10^(q4-1), 
            // where d = 1, 2, 3, ..., 9; it could be tiny too, but exact
            if (q4 == 1) {
              // if q4 = 1 the result is exact
              // result coefficient = 10^34 - C4
              res.w[1] = 0x0001ed09bead87c0ull;
              res.w[0] = 0x378d8e6400000000ull - C4.w[0];
              z_exp = z_exp - EXP_P1;
              e3 = e3 - 1;
              res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
            } else {
              // if q4 > 1 then truncate C4 from q4 digits to 1 digit; 
              // x = q4-1, 1 <= x <= 67 and check if this operation is exact
              if (q4 <= 18) { // 2 <= q4 <= 18
        	round64_2_18 (q4, q4 - 1, C4.w[0], &R64, &incr_exp,
        		      &is_midpoint_lt_even,
        		      &is_midpoint_gt_even,
        		      &is_inexact_lt_midpoint,
        		      &is_inexact_gt_midpoint);
              } else if (q4 <= 38) {
        	P128.w[1] = C4.w[1];
        	P128.w[0] = C4.w[0];
        	round128_19_38 (q4, q4 - 1, P128, &R128, &incr_exp,
        			&is_midpoint_lt_even,
        			&is_midpoint_gt_even,
        			&is_inexact_lt_midpoint,
        			&is_inexact_gt_midpoint);
        	R64 = R128.w[0]; // one decimal digit
              } else if (q4 <= 57) {
        	P192.w[2] = C4.w[2];
        	P192.w[1] = C4.w[1];
        	P192.w[0] = C4.w[0];
        	round192_39_57 (q4, q4 - 1, P192, &R192, &incr_exp,
        			&is_midpoint_lt_even,
        			&is_midpoint_gt_even,
        			&is_inexact_lt_midpoint,
        			&is_inexact_gt_midpoint);
        	R64 = R192.w[0]; // one decimal digit
              } else { // if (q4 <= 68)
        	round256_58_76 (q4, q4 - 1, C4, &R256, &incr_exp,
        			&is_midpoint_lt_even,
        			&is_midpoint_gt_even,
        			&is_inexact_lt_midpoint,
        			&is_inexact_gt_midpoint);
        	R64 = R256.w[0]; // one decimal digit
              }
              if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	  !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
        	// the result is exact: 10^34 - R64
        	// incr_exp = 0 with certainty
        	z_exp = z_exp - EXP_P1;
        	e3 = e3 - 1;
        	res.w[1] =
        	  z_sign | (z_exp & MASK_EXP) | 0x0001ed09bead87c0ull;
        	res.w[0] = 0x378d8e6400000000ull - R64;
              } else {
        	// We want R64 to be the top digit of C4, but we actually 
        	// obtained (C4 * 10^(-q4+1))RN; a correction may be needed,
        	// because the top digit is (C4 * 10^(-q4+1))RZ
        	// however, if incr_exp = 1 then R64 = 10 with certainty
        	if (incr_exp) {
        	  R64 = 10;
        	}
        	// the result is inexact as C4 has more than 1 significant digit
        	// and C3 * 10^scale = 10^33
        	// example of case that is treated here:
        	// 100...0 * 10^e3 - 0.41 * 10^e3 =
        	// 0999...9.59 * 10^e3 -> rounds to 99...96*10^(e3-1)
        	// note that (e3 > expmin}
        	// in order to round, subtract R64 from 10^34 and then compare
        	// C4 - R64 * 10^(q4-1) with 1/2 ulp
        	// calculate 10^34 - R64
        	res.w[1] = 0x0001ed09bead87c0ull;
        	res.w[0] = 0x378d8e6400000000ull - R64;
        	z_exp = z_exp - EXP_P1; // will be OR-ed with sign & significand
        	// calculate C4 - R64 * 10^(q4-1); this is a rare case and
        	// R64 is small, 1 <= R64 <= 9
        	e3 = e3 - 1;
        	if (is_inexact_lt_midpoint) {
        	  is_inexact_lt_midpoint = 0;
        	  is_inexact_gt_midpoint = 1;
        	} else if (is_inexact_gt_midpoint) {
        	  is_inexact_gt_midpoint = 0;
        	  is_inexact_lt_midpoint = 1;
        	} else if (is_midpoint_lt_even) {
        	  is_midpoint_lt_even = 0;
        	  is_midpoint_gt_even = 1;
        	} else if (is_midpoint_gt_even) {
        	  is_midpoint_gt_even = 0;
        	  is_midpoint_lt_even = 1;
        	} else {
        	  ;
        	}
        	// the result is always inexact, and never tiny
        	// check for overflow for RN
        	if (e3 > expmax) {
        	  if (rnd_mode == ROUNDING_TO_NEAREST) {
        	    res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
        	    res.w[0] = 0x0000000000000000ull;
        	    *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
        	  } else {
        	    rounding_correction (rnd_mode,
        				 is_inexact_lt_midpoint,
        				 is_inexact_gt_midpoint,
        				 is_midpoint_lt_even,
        				 is_midpoint_gt_even, e3, &res,
        				 pfpsf);
        	  }
        	  *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
        	  *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
        	  *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
        	  *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
        	  BID_SWAP128 (res);
        	  BID_RETURN (res)
        	}
        	// set the inexact flag
        	*pfpsf |= INEXACT_EXCEPTION;
        	res.w[1] =
        	  z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1];
        	if (rnd_mode != ROUNDING_TO_NEAREST) {
        	  rounding_correction (rnd_mode,
        			       is_inexact_lt_midpoint,
        			       is_inexact_gt_midpoint,
        			       is_midpoint_lt_even,
        			       is_midpoint_gt_even, e3, &res,
        			       pfpsf);
        	}
        	z_exp = res.w[1] & MASK_EXP;
              } // end result is inexact
            } // end q4 > 1
          } else { // if (e3 = emin)
            // if e3 = expmin the result is also tiny (the condition for
            // tininess is C4 > 050...0 [q4 digits] which is met because
            // the msd of C4 is not zero)
            // the result is tiny and inexact in all rounding modes;
            // it is either 100...0 or 0999...9 (use lt_half_ulp, eq_half_ulp, 
            // gt_half_ulp to calculate)
            // if (lt_half_ulp || eq_half_ulp) res = 10^33 stays unchanged

            // p_sign != z_sign so swap gt_half_ulp and lt_half_ulp
            if (gt_half_ulp) { // res = 10^33 - 1
              res.w[1] = 0x0000314dc6448d93ull;
              res.w[0] = 0x38c15b09ffffffffull;
            } else {
              res.w[1] = 0x0000314dc6448d93ull;
              res.w[0] = 0x38c15b0a00000000ull;
            }
            res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
            *pfpsf |= UNDERFLOW_EXCEPTION; // inexact is set later

            if (eq_half_ulp) {
              is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value
            } else if (lt_half_ulp) {
              is_inexact_gt_midpoint = 1; //if(z_sign), as if for absolute value
            } else { // if (gt_half_ulp)
              is_inexact_lt_midpoint = 1; //if(z_sign), as if for absolute value
            }

            if (rnd_mode != ROUNDING_TO_NEAREST) {
              rounding_correction (rnd_mode,
                  is_inexact_lt_midpoint,
                  is_inexact_gt_midpoint,
                  is_midpoint_lt_even,
                  is_midpoint_gt_even, e3, &res,
                  pfpsf);
              z_exp = res.w[1] & MASK_EXP;
            }
          } // end e3 = emin
          // set the inexact flag (if the result was not exact)
          if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
              is_midpoint_lt_even || is_midpoint_gt_even)
            *pfpsf |= INEXACT_EXCEPTION;
        } // end 10^33
      } // end if (p_sign != z_sign)
      res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    } else if (((q3 <= delta && delta < p34 && p34 < delta + q4) || // Case (2)
        (q3 <= delta && delta + q4 <= p34) || // Case (3)
        (delta < q3 && p34 < delta + q4) || // Case (4)
        (delta < q3 && q3 <= delta + q4 && delta + q4 <= p34) || // Case (5)
        (delta + q4 < q3)) && // Case (6)
        !(delta <= 1 && p_sign != z_sign)) { // Case (2), (3), (4), (5) or (6)

      // the result has the sign of z

      if ((q3 <= delta && delta < p34 && p34 < delta + q4) || // Case (2)
          (delta < q3 && p34 < delta + q4)) { // Case (4)
        // round first the sum x * y + z with unbounded exponent
        // scale C3 up by scale = p34 - q3, 1 <= scale <= p34-1, 
        // 1 <= scale <= 33
        // calculate res = C3 * 10^scale
        scale = p34 - q3;
        x0 = delta + q4 - p34;
      } else if (delta + q4 < q3) { // Case (6)
        // make Case (6) look like Case (3) or Case (5) with scale = 0
        // by scaling up C4 by 10^(q3 - delta - q4) 
        scale = q3 - delta - q4; // 1 <= scale <= 33
        if (q4 <= 19) { // 1 <= scale <= 19; C4 fits in 64 bits
          if (scale <= 19) { // 10^scale fits in 64 bits
            // 64 x 64 C4.w[0] * ten2k64[scale]
            __mul_64x64_to_128MACH (P128, C4.w[0], ten2k64[scale]);
          } else { // 10^scale fits in 128 bits
            // 64 x 128 C4.w[0] * ten2k128[scale - 20]
            __mul_128x64_to_128 (P128, C4.w[0], ten2k128[scale - 20]);
          }
        } else { // C4 fits in 128 bits, but 10^scale must fit in 64 bits
          // 64 x 128 ten2k64[scale] * C4
          __mul_128x64_to_128 (P128, ten2k64[scale], C4);
        }
        C4.w[0] = P128.w[0];
        C4.w[1] = P128.w[1];
        // e4 does not need adjustment, as it is not used from this point on
        scale = 0;
        x0 = 0;
        // now Case (6) looks like Case (3) or Case (5) with scale = 0 
      } else { // if Case (3) or Case (5)
        // Note: Case (3) is similar to Case (2), but scale differs and the
        // result is exact, unless it is tiny (so x0 = 0 when calculating the
        // result with unbounded exponent)

        // calculate first the sum x * y + z with unbounded exponent (exact)
        // scale C3 up by scale = delta + q4 - q3, 1 <= scale <= p34-1,
        // 1 <= scale <= 33
        // calculate res = C3 * 10^scale
        scale = delta + q4 - q3;
        x0 = 0;
        // Note: the comments which follow refer [mainly] to Case (2)]
      }

    case2_repeat:
      if (scale == 0) { // this could happen e.g. if we return to case2_repeat
        // or in Case (4)
        res.w[1] = C3.w[1];
        res.w[0] = C3.w[0];
      } else if (q3 <= 19) { // 1 <= scale <= 19; z fits in 64 bits
        if (scale <= 19) { // 10^scale fits in 64 bits
          // 64 x 64 C3.w[0] * ten2k64[scale]
          __mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
        } else { // 10^scale fits in 128 bits
          // 64 x 128 C3.w[0] * ten2k128[scale - 20]
          __mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
        }
      } else { // z fits in 128 bits, but 10^scale must fit in 64 bits
        // 64 x 128 ten2k64[scale] * C3
        __mul_128x64_to_128 (res, ten2k64[scale], C3);
      }
      // e3 is already calculated
      e3 = e3 - scale;
      // now res = C3 * 10^scale and e3 = e3 - scale
      // Note: C3 * 10^scale could be 10^34 if we returned to case2_repeat
      // because the result was too small

      // round C4 to nearest to q4 - x0 digits, where x0 = delta + q4 - p34,
      // 1 <= x0 <= min (q4 - 1, 2 * p34 - 1) <=> 1 <= x0 <= min (q4 - 1, 67)
      // Also: 1 <= q4 - x0 <= p34 -1 => 1 <= q4 - x0 <= 33 (so the result of
      // the rounding fits in 128 bits!)
      // x0 = delta + q4 - p34 (calculated before reaching case2_repeat)
      // because q3 + q4 - x0 <= P => x0 >= q3 + q4 - p34
      if (x0 == 0) { // this could happen only if we return to case2_repeat, or
        // for Case (3) or Case (6)
        R128.w[1] = C4.w[1];
        R128.w[0] = C4.w[0];
      } else if (q4 <= 18) {
        // 2 <= q4 <= 18, max(1, q3+q4-p34) <= x0 <= q4 - 1, 1 <= x0 <= 17
        round64_2_18 (q4, x0, C4.w[0], &R64, &incr_exp,
            &is_midpoint_lt_even, &is_midpoint_gt_even,
            &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
        if (incr_exp) {
          // R64 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 17
          R64 = ten2k64[q4 - x0];
        }
        R128.w[1] = 0;
        R128.w[0] = R64;
      } else if (q4 <= 38) {
        // 19 <= q4 <= 38, max(1, q3+q4-p34) <= x0 <= q4 - 1, 1 <= x0 <= 37
        P128.w[1] = C4.w[1];
        P128.w[0] = C4.w[0];
        round128_19_38 (q4, x0, P128, &R128, &incr_exp,
            &is_midpoint_lt_even, &is_midpoint_gt_even,
            &is_inexact_lt_midpoint,
            &is_inexact_gt_midpoint);
        if (incr_exp) {
          // R128 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 37
          if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
            R128.w[0] = ten2k64[q4 - x0];
            // R128.w[1] stays 0
          } else { // 20 <= q4 - x0 <= 37
            R128.w[0] = ten2k128[q4 - x0 - 20].w[0];
            R128.w[1] = ten2k128[q4 - x0 - 20].w[1];
          }
        }
      } else if (q4 <= 57) {
        // 38 <= q4 <= 57, max(1, q3+q4-p34) <= x0 <= q4 - 1, 5 <= x0 <= 56
        P192.w[2] = C4.w[2];
        P192.w[1] = C4.w[1];
        P192.w[0] = C4.w[0];
        round192_39_57 (q4, x0, P192, &R192, &incr_exp,
            &is_midpoint_lt_even, &is_midpoint_gt_even,
            &is_inexact_lt_midpoint,
            &is_inexact_gt_midpoint);
        // R192.w[2] is always 0
        if (incr_exp) {
          // R192 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 5, 1 <= q4 - x0 <= 52
          if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
            R192.w[0] = ten2k64[q4 - x0];
            // R192.w[1] stays 0
            // R192.w[2] stays 0
          } else { // 20 <= q4 - x0 <= 33
            R192.w[0] = ten2k128[q4 - x0 - 20].w[0];
            R192.w[1] = ten2k128[q4 - x0 - 20].w[1];
            // R192.w[2] stays 0
          }
        }
        R128.w[1] = R192.w[1];
        R128.w[0] = R192.w[0];
      } else {
        // 58 <= q4 <= 68, max(1, q3+q4-p34) <= x0 <= q4 - 1, 25 <= x0 <= 67
        round256_58_76 (q4, x0, C4, &R256, &incr_exp,
            &is_midpoint_lt_even, &is_midpoint_gt_even,
            &is_inexact_lt_midpoint,
            &is_inexact_gt_midpoint);
        // R256.w[3] and R256.w[2] are always 0
        if (incr_exp) {
          // R256 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 25, 1 <= q4 - x0 <= 43
          if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19  
            R256.w[0] = ten2k64[q4 - x0];
            // R256.w[1] stays 0
            // R256.w[2] stays 0
            // R256.w[3] stays 0
          } else { // 20 <= q4 - x0 <= 33 
            R256.w[0] = ten2k128[q4 - x0 - 20].w[0];
            R256.w[1] = ten2k128[q4 - x0 - 20].w[1];
            // R256.w[2] stays 0
            // R256.w[3] stays 0
          }
        }
        R128.w[1] = R256.w[1];
        R128.w[0] = R256.w[0];
      }
      // now add C3 * 10^scale in res and the signed top (q4-x0) digits of C4,
      // rounded to nearest, which were copied into R128
      if (z_sign == p_sign) {
        lsb = res.w[0] & 0x01; // lsb of C3 * 10^scale
        // the sum can result in [up to] p34 or p34 + 1 digits
        res.w[0] = res.w[0] + R128.w[0];
        res.w[1] = res.w[1] + R128.w[1];
        if (res.w[0] < R128.w[0])
          res.w[1]++; // carry
        // if res > 10^34 - 1 need to increase x0 and decrease scale by 1
        if (res.w[1] > 0x0001ed09bead87c0ull ||
            (res.w[1] == 0x0001ed09bead87c0ull &&
             res.w[0] > 0x378d8e63ffffffffull)) {
          // avoid double rounding error
          is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
          is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
          is_midpoint_lt_even0 = is_midpoint_lt_even;
          is_midpoint_gt_even0 = is_midpoint_gt_even;
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 0;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
          P128.w[1] = res.w[1];
          P128.w[0] = res.w[0];
          round128_19_38 (35, 1, P128, &res, &incr_exp,
              &is_midpoint_lt_even, &is_midpoint_gt_even,
              &is_inexact_lt_midpoint,
              &is_inexact_gt_midpoint);
          // incr_exp is 0 with certainty in this case
          // avoid a double rounding error
          if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
              is_midpoint_lt_even) { // double rounding error upward
            // res = res - 1
            res.w[0]--;
            if (res.w[0] == 0xffffffffffffffffull)
              res.w[1]--;
            // Note: a double rounding error upward is not possible; for this
            // the result after the first rounding would have to be 99...95
            // (35 digits in all), possibly followed by a number of zeros; this
            // not possible in Cases (2)-(6) or (15)-(17) which may get here
            is_midpoint_lt_even = 0;
            is_inexact_lt_midpoint = 1;
          } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
              is_midpoint_gt_even) { // double rounding error downward
            // res = res + 1
            res.w[0]++;
            if (res.w[0] == 0)
              res.w[1]++;
            is_midpoint_gt_even = 0;
            is_inexact_gt_midpoint = 1;
          } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	     !is_inexact_lt_midpoint
        	     && !is_inexact_gt_midpoint) {
            // if this second rounding was exact the result may still be 
            // inexact because of the first rounding
            if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
              is_inexact_gt_midpoint = 1;
            }
            if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
              is_inexact_lt_midpoint = 1;
            }
          } else if (is_midpoint_gt_even &&
        	     (is_inexact_gt_midpoint0
        	      || is_midpoint_lt_even0)) {
            // pulled up to a midpoint
            is_inexact_lt_midpoint = 1;
            is_inexact_gt_midpoint = 0;
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 0;
          } else if (is_midpoint_lt_even &&
        	     (is_inexact_lt_midpoint0
        	      || is_midpoint_gt_even0)) {
            // pulled down to a midpoint
            is_inexact_lt_midpoint = 0;
            is_inexact_gt_midpoint = 1;
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 0;
          } else {
            ;
          }
          // adjust exponent
          e3 = e3 + 1;
          if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
              !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
            if (is_midpoint_lt_even0 || is_midpoint_gt_even0 ||
        	is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0) {
              is_inexact_lt_midpoint = 1;
            }
          }
        } else {
          // this is the result rounded with unbounded exponent, unless a
          // correction is needed
          res.w[1] = res.w[1] & MASK_COEFF;
          if (lsb == 1) {
            if (is_midpoint_gt_even) {
              // res = res + 1
              is_midpoint_gt_even = 0;
              is_midpoint_lt_even = 1;
              res.w[0]++;
              if (res.w[0] == 0x0)
        	res.w[1]++;
              // check for rounding overflow
              if (res.w[1] == 0x0001ed09bead87c0ull &&
        	  res.w[0] == 0x378d8e6400000000ull) {
        	// res = 10^34 => rounding overflow
        	res.w[1] = 0x0000314dc6448d93ull;
        	res.w[0] = 0x38c15b0a00000000ull; // 10^33
        	e3++;
              }
            } else if (is_midpoint_lt_even) {
              // res = res - 1
              is_midpoint_lt_even = 0;
              is_midpoint_gt_even = 1;
              res.w[0]--;
              if (res.w[0] == 0xffffffffffffffffull)
        	res.w[1]--;
              // if the result is pure zero, the sign depends on the rounding 
              // mode (x*y and z had opposite signs)
              if (res.w[1] == 0x0ull && res.w[0] == 0x0ull) {
        	if (rnd_mode != ROUNDING_DOWN)
        	  z_sign = 0x0000000000000000ull;
        	else
        	  z_sign = 0x8000000000000000ull;
        	// the exponent is max (e3, expmin)
        	res.w[1] = 0x0;
        	res.w[0] = 0x0;
        	*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
        	*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
        	*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
        	*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
        	BID_SWAP128 (res);
        	BID_RETURN (res)
              }
            } else {
              ;
            }
          }
        }
      } else { // if (z_sign != p_sign)
        lsb = res.w[0] & 0x01; // lsb of C3 * 10^scale; R128 contains rounded C4
        // used to swap rounding indicators if p_sign != z_sign
        // the sum can result in [up to] p34 or p34 - 1 digits
        tmp64 = res.w[0];
        res.w[0] = res.w[0] - R128.w[0];
        res.w[1] = res.w[1] - R128.w[1];
        if (res.w[0] > tmp64)
          res.w[1]--; // borrow
        // if res < 10^33 and exp > expmin need to decrease x0 and 
        // increase scale by 1
        if (e3 > expmin && ((res.w[1] < 0x0000314dc6448d93ull ||
        		     (res.w[1] == 0x0000314dc6448d93ull &&
        		      res.w[0] < 0x38c15b0a00000000ull)) ||
        		    (is_inexact_lt_midpoint
        		     && res.w[1] == 0x0000314dc6448d93ull
        		     && res.w[0] == 0x38c15b0a00000000ull))
            && x0 >= 1) {
          x0 = x0 - 1;
          // first restore e3, otherwise it will be too small
          e3 = e3 + scale;
          scale = scale + 1;
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 0;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
          incr_exp = 0;
          goto case2_repeat;
        }
        // else this is the result rounded with unbounded exponent;
        // because the result has opposite sign to that of C4 which was 
        // rounded, need to change the rounding indicators
        if (is_inexact_lt_midpoint) {
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 1;
        } else if (is_inexact_gt_midpoint) {
          is_inexact_gt_midpoint = 0;
          is_inexact_lt_midpoint = 1;
        } else if (lsb == 0) {
          if (is_midpoint_lt_even) {
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 1;
          } else if (is_midpoint_gt_even) {
            is_midpoint_gt_even = 0;
            is_midpoint_lt_even = 1;
          } else {
            ;
          }
        } else if (lsb == 1) {
          if (is_midpoint_lt_even) {
            // res = res + 1
            res.w[0]++;
            if (res.w[0] == 0x0)
              res.w[1]++;
            // check for rounding overflow
            if (res.w[1] == 0x0001ed09bead87c0ull &&
        	res.w[0] == 0x378d8e6400000000ull) {
              // res = 10^34 => rounding overflow
              res.w[1] = 0x0000314dc6448d93ull;
              res.w[0] = 0x38c15b0a00000000ull; // 10^33
              e3++;
            }
          } else if (is_midpoint_gt_even) {
            // res = res - 1
            res.w[0]--;
            if (res.w[0] == 0xffffffffffffffffull)
              res.w[1]--;
            // if the result is pure zero, the sign depends on the rounding 
            // mode (x*y and z had opposite signs)
            if (res.w[1] == 0x0ull && res.w[0] == 0x0ull) {
              if (rnd_mode != ROUNDING_DOWN)
        	z_sign = 0x0000000000000000ull;
              else
        	z_sign = 0x8000000000000000ull;
              // the exponent is max (e3, expmin)
              res.w[1] = 0x0;
              res.w[0] = 0x0;
              *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
              *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
              *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
              *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
              BID_SWAP128 (res);
              BID_RETURN (res)
            }
          } else {
            ;
          }
        } else {
          ;
        }
      }
      // check for underflow
      if (e3 == expmin) { // and if significand < 10^33 => result is tiny
        if ((res.w[1] & MASK_COEFF) < 0x0000314dc6448d93ull ||
            ((res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull &&
             res.w[0] < 0x38c15b0a00000000ull)) {
          is_tiny = 1;
        }
      } else if (e3 < expmin) {
        // the result is tiny, so we must truncate more of res
        is_tiny = 1;
        x0 = expmin - e3;
        is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
        is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
        is_midpoint_lt_even0 = is_midpoint_lt_even;
        is_midpoint_gt_even0 = is_midpoint_gt_even;
        is_inexact_lt_midpoint = 0;
        is_inexact_gt_midpoint = 0;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
        // determine the number of decimal digits in res
        if (res.w[1] == 0x0) {
          // between 1 and 19 digits
          for (ind = 1; ind <= 19; ind++) {
            if (res.w[0] < ten2k64[ind]) {
              break;
            }
          }
          // ind digits
        } else if (res.w[1] < ten2k128[0].w[1] ||
        	   (res.w[1] == ten2k128[0].w[1]
        	    && res.w[0] < ten2k128[0].w[0])) {
          // 20 digits
          ind = 20;
        } else { // between 21 and 38 digits
          for (ind = 1; ind <= 18; ind++) {
            if (res.w[1] < ten2k128[ind].w[1] ||
        	(res.w[1] == ten2k128[ind].w[1] &&
        	 res.w[0] < ten2k128[ind].w[0])) {
              break;
            }
          }
          // ind + 20 digits
          ind = ind + 20;
        }

        // at this point ind >= x0; because delta >= 2 on this path, the case
        // ind = x0 can occur only in Case (2) or case (3), when C3 has one
        // digit (q3 = 1) equal to 1 (C3 = 1), e3 is expmin (e3 = expmin), 
        // the signs of x * y and z are opposite, and through cancellation 
        // the most significant decimal digit in res has the weight
        // 10^(emin-1); however, it is clear that in this case the most
        // significant digit is 9, so the result before rounding is
        // 0.9... * 10^emin
        // Otherwise, ind > x0 because there are non-zero decimal digits in the
        // result with weight of at least 10^emin, and correction for underflow
        //  can be carried out using the round*_*_2_* () routines
        if (x0 == ind) { // the result before rounding is 0.9... * 10^emin
          res.w[1] = 0x0;
          res.w[0] = 0x1;
          is_inexact_gt_midpoint = 1;
        } else if (ind <= 18) { // check that 2 <= ind
          // 2 <= ind <= 18, 1 <= x0 <= 17
          round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
          if (incr_exp) {
            // R64 = 10^(ind-x0), 1 <= ind - x0 <= ind - 1, 1 <= ind - x0 <= 17
            R64 = ten2k64[ind - x0];
          }
          res.w[1] = 0;
          res.w[0] = R64;
        } else if (ind <= 38) {
          // 19 <= ind <= 38
          P128.w[1] = res.w[1];
          P128.w[0] = res.w[0];
          round128_19_38 (ind, x0, P128, &res, &incr_exp,
        		  &is_midpoint_lt_even, &is_midpoint_gt_even,
        		  &is_inexact_lt_midpoint,
        		  &is_inexact_gt_midpoint);
          if (incr_exp) {
            // R128 = 10^(ind-x0), 1 <= ind - x0 <= ind - 1, 1 <= ind - x0 <= 37
            if (ind - x0 <= 19) { // 1 <= ind - x0 <= 19
              res.w[0] = ten2k64[ind - x0];
              // res.w[1] stays 0
            } else { // 20 <= ind - x0 <= 37
              res.w[0] = ten2k128[ind - x0 - 20].w[0];
              res.w[1] = ten2k128[ind - x0 - 20].w[1];
            }
          }
        }
        // avoid a double rounding error
        if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
            is_midpoint_lt_even) { // double rounding error upward
          // res = res - 1
          res.w[0]--;
          if (res.w[0] == 0xffffffffffffffffull)
            res.w[1]--;
          // Note: a double rounding error upward is not possible; for this
          // the result after the first rounding would have to be 99...95
          // (35 digits in all), possibly followed by a number of zeros; this
          // not possible in Cases (2)-(6) which may get here
          is_midpoint_lt_even = 0;
          is_inexact_lt_midpoint = 1;
        } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
            is_midpoint_gt_even) { // double rounding error downward
          // res = res + 1
          res.w[0]++;
          if (res.w[0] == 0)
            res.w[1]++;
          is_midpoint_gt_even = 0;
          is_inexact_gt_midpoint = 1;
        } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	   !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
          // if this second rounding was exact the result may still be 
          // inexact because of the first rounding
          if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
            is_inexact_gt_midpoint = 1;
          }
          if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
            is_inexact_lt_midpoint = 1;
          }
        } else if (is_midpoint_gt_even &&
        	   (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
          // pulled up to a midpoint
          is_inexact_lt_midpoint = 1;
          is_inexact_gt_midpoint = 0;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
        } else if (is_midpoint_lt_even &&
        	   (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
          // pulled down to a midpoint
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 1;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
        } else {
          ;
        }
        // adjust exponent
        e3 = e3 + x0;
        if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
            !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
          if (is_midpoint_lt_even0 || is_midpoint_gt_even0 ||
              is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0) {
            is_inexact_lt_midpoint = 1;
          }
        }
      } else {
        ; // not underflow
      }
      // check for inexact result
      if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
          is_midpoint_lt_even || is_midpoint_gt_even) {
        // set the inexact flag
        *pfpsf |= INEXACT_EXCEPTION;
        if (is_tiny)
          *pfpsf |= UNDERFLOW_EXCEPTION;
      }
      // now check for significand = 10^34 (may have resulted from going
      // back to case2_repeat)
      if (res.w[1] == 0x0001ed09bead87c0ull && 
          res.w[0] == 0x378d8e6400000000ull) { // if  res = 10^34
        res.w[1] = 0x0000314dc6448d93ull; // res = 10^33
        res.w[0] = 0x38c15b0a00000000ull;
        e3 = e3 + 1;
      }
      res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1];
      // check for overflow
      if (rnd_mode == ROUNDING_TO_NEAREST && e3 > expmax) {
        res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
        res.w[0] = 0x0000000000000000ull;
        *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
      }
      if (rnd_mode != ROUNDING_TO_NEAREST) {
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     e3, &res, pfpsf);
      }
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    } else {

      // we get here only if delta <= 1 in Cases (2), (3), (4), (5), or (6) and
      // the signs of x*y and z are opposite; in these cases massive
      // cancellation can occur, so it is better to scale either C3 or C4 and 
      // to perform the subtraction before rounding; rounding is performed 
      // next, depending on the number of decimal digits in the result and on 
      // the exponent value
      // Note: overlow is not possible in this case
      // this is similar to Cases (15), (16), and (17)

      if (delta + q4 < q3) { // from Case (6) 
        // Case (6) with 0<= delta <= 1 is similar to Cases (15), (16), and 
        // (17) if we swap (C3, C4), (q3, q4), (e3, e4), (z_sign, p_sign)
        // and call add_and_round; delta stays positive
        // C4.w[3] = 0 and C4.w[2] = 0, so swap just the low part of C4 with C3
        P128.w[1] = C3.w[1];
        P128.w[0] = C3.w[0];
        C3.w[1] = C4.w[1];
        C3.w[0] = C4.w[0];
        C4.w[1] = P128.w[1];
        C4.w[0] = P128.w[0];
        ind = q3;
        q3 = q4;
        q4 = ind;
        ind = e3;
        e3 = e4;
        e4 = ind;
        tmp_sign = z_sign;
        z_sign = p_sign;
        p_sign = tmp_sign;
      } else { // from Cases (2), (3), (4), (5)
        // In Cases (2), (3), (4), (5) with 0 <= delta <= 1 C3 has to be 
        // scaled up by q4 + delta - q3; this is the same as in Cases (15), 
        // (16), and (17) if we just change the sign of delta
        delta = -delta;
      }
      add_and_round (q3, q4, e4, delta, p34, z_sign, p_sign, C3, C4,
        	     rnd_mode, &is_midpoint_lt_even,
        	     &is_midpoint_gt_even, &is_inexact_lt_midpoint,
        	     &is_inexact_gt_midpoint, pfpsf, &res);
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    }

  } else { // if delta < 0

    delta = -delta;

    if (p34 < q4 && q4 <= delta) { // Case (7)

      // truncate C4 to p34 digits into res
      // x = q4-p34, 1 <= x <= 34 because 35 <= q4 <= 68
      x0 = q4 - p34;
      if (q4 <= 38) {
        P128.w[1] = C4.w[1];
        P128.w[0] = C4.w[0];
        round128_19_38 (q4, x0, P128, &res, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
      } else if (q4 <= 57) { // 35 <= q4 <= 57
        P192.w[2] = C4.w[2];
        P192.w[1] = C4.w[1];
        P192.w[0] = C4.w[0];
        round192_39_57 (q4, x0, P192, &R192, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
        res.w[0] = R192.w[0];
        res.w[1] = R192.w[1];
      } else { // if (q4 <= 68)
        round256_58_76 (q4, x0, C4, &R256, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
        res.w[0] = R256.w[0];
        res.w[1] = R256.w[1];
      }
      e4 = e4 + x0;
      if (incr_exp) {
        e4 = e4 + 1;
      }
      if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
          !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
        // if C4 rounded to p34 digits is exact then the result is inexact,
        // in a way that depends on the signs of x * y and z
        if (p_sign == z_sign) {
          is_inexact_lt_midpoint = 1;
        } else { // if (p_sign != z_sign)
          if (res.w[1] != 0x0000314dc6448d93ull || 
              res.w[0] != 0x38c15b0a00000000ull) { // res != 10^33
            is_inexact_gt_midpoint = 1;
          } else { // res = 10^33 and exact is a special case
            // if C3 < 1/2 ulp then res = 10^33 and is_inexact_gt_midpoint = 1
            // if C3 = 1/2 ulp then res = 10^33 and is_midpoint_lt_even = 1
            // if C3 > 1/2 ulp then res = 10^34-1 and is_inexact_lt_midpoint = 1
            // Note: ulp is really ulp/10 (after borrow which propagates to msd)
            if (delta > p34 + 1) { // C3 < 1/2
              // res = 10^33, unchanged
              is_inexact_gt_midpoint = 1;
            } else { // if (delta == p34 + 1)
              if (q3 <= 19) {
        	if (C3.w[0] < midpoint64[q3 - 1]) { // C3 < 1/2 ulp
        	  // res = 10^33, unchanged
        	  is_inexact_gt_midpoint = 1;
        	} else if (C3.w[0] == midpoint64[q3 - 1]) { // C3 = 1/2 ulp
        	  // res = 10^33, unchanged
        	  is_midpoint_lt_even = 1;
        	} else { // if (C3.w[0] > midpoint64[q3-1]), C3 > 1/2 ulp
        	  res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
        	  res.w[0] = 0x378d8e63ffffffffull;
        	  e4 = e4 - 1;
        	  is_inexact_lt_midpoint = 1;
        	}
              } else { // if (20 <= q3 <=34)
        	if (C3.w[1] < midpoint128[q3 - 20].w[1] || 
                    (C3.w[1] == midpoint128[q3 - 20].w[1] && 
                    C3.w[0] < midpoint128[q3 - 20].w[0])) { // C3 < 1/2 ulp
        	  // res = 10^33, unchanged
        	  is_inexact_gt_midpoint = 1;
        	} else if (C3.w[1] == midpoint128[q3 - 20].w[1] && 
                    C3.w[0] == midpoint128[q3 - 20].w[0]) { // C3 = 1/2 ulp
        	  // res = 10^33, unchanged
        	  is_midpoint_lt_even = 1;
        	} else { // if (C3 > midpoint128[q3-20]), C3 > 1/2 ulp
        	  res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
        	  res.w[0] = 0x378d8e63ffffffffull;
        	  e4 = e4 - 1;
        	  is_inexact_lt_midpoint = 1;
        	}
              }
            }
          }
        }
      } else if (is_midpoint_lt_even) {
        if (z_sign != p_sign) {
          // needs correction: res = res - 1
          res.w[0] = res.w[0] - 1;
          if (res.w[0] == 0xffffffffffffffffull)
            res.w[1]--;
          // if it is (10^33-1)*10^e4 then the corect result is 
          // (10^34-1)*10(e4-1)
          if (res.w[1] == 0x0000314dc6448d93ull &&
              res.w[0] == 0x38c15b09ffffffffull) {
            res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
            res.w[0] = 0x378d8e63ffffffffull;
            e4 = e4 - 1;
          }
          is_midpoint_lt_even = 0;
          is_inexact_lt_midpoint = 1;
        } else { // if (z_sign == p_sign)
          is_midpoint_lt_even = 0;
          is_inexact_gt_midpoint = 1;
        }
      } else if (is_midpoint_gt_even) {
        if (z_sign == p_sign) {
          // needs correction: res = res + 1 (cannot cross in the next binade)
          res.w[0] = res.w[0] + 1;
          if (res.w[0] == 0x0000000000000000ull)
            res.w[1]++;
          is_midpoint_gt_even = 0;
          is_inexact_gt_midpoint = 1;
        } else { // if (z_sign != p_sign)
          is_midpoint_gt_even = 0;
          is_inexact_lt_midpoint = 1;
        }
      } else {
        ; // the rounded result is already correct
      }
      // check for overflow
      if (rnd_mode == ROUNDING_TO_NEAREST && e4 > expmax) {
        res.w[1] = p_sign | 0x7800000000000000ull;
        res.w[0] = 0x0000000000000000ull;
        *pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
      } else { // no overflow or not RN
        p_exp = ((UINT64) (e4 + 6176) << 49);
        res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1];
      }
      if (rnd_mode != ROUNDING_TO_NEAREST) {
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     e4, &res, pfpsf);
      }
      if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
          is_midpoint_lt_even || is_midpoint_gt_even) {
        // set the inexact flag
        *pfpsf |= INEXACT_EXCEPTION;
      }
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    } else if ((q4 <= p34 && p34 <= delta) || // Case (8)
        (q4 <= delta && delta < p34 && p34 < delta + q3) || // Case (9)
        (q4 <= delta && delta + q3 <= p34) || // Case (10)
        (delta < q4 && q4 <= p34 && p34 < delta + q3) || // Case (13)
        (delta < q4 && q4 <= delta + q3 && delta + q3 <= p34) || // Case (14)
        (delta + q3 < q4 && q4 <= p34)) { // Case (18)

      // Case (8) is similar to Case (1), with C3 and C4 swapped
      // Case (9) is similar to Case (2), with C3 and C4 swapped
      // Case (10) is similar to Case (3), with C3 and C4 swapped
      // Case (13) is similar to Case (4), with C3 and C4 swapped
      // Case (14) is similar to Case (5), with C3 and C4 swapped
      // Case (18) is similar to Case (6), with C3 and C4 swapped

      // swap (C3, C4), (q3, q4), (e3, 34), (z_sign, p_sign), (z_exp, p_exp)
      // and go back to delta_ge_zero
      // C4.w[3] = 0 and C4.w[2] = 0, so swap just the low part of C4 with C3
      P128.w[1] = C3.w[1];
      P128.w[0] = C3.w[0];
      C3.w[1] = C4.w[1];
      C3.w[0] = C4.w[0];
      C4.w[1] = P128.w[1];
      C4.w[0] = P128.w[0];
      ind = q3;
      q3 = q4;
      q4 = ind;
      ind = e3;
      e3 = e4;
      e4 = ind;
      tmp_sign = z_sign;
      z_sign = p_sign;
      p_sign = tmp_sign;
      tmp.ui64 = z_exp;
      z_exp = p_exp;
      p_exp = tmp.ui64;
      goto delta_ge_zero;

    } else if ((p34 <= delta && delta < q4 && q4 < delta + q3) || // Case (11)
               (delta < p34 && p34 < q4 && q4 < delta + q3)) { // Case (12)

      // round C3 to nearest to q3 - x0 digits, where x0 = e4 - e3,
      // 1 <= x0 <= q3 - 1 <= p34 - 1 
      x0 = e4 - e3; // or x0 = delta + q3 - q4
      if (q3 <= 18) { // 2 <= q3 <= 18
        round64_2_18 (q3, x0, C3.w[0], &R64, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
        // C3.w[1] = 0;
        C3.w[0] = R64;
      } else if (q3 <= 38) {
        round128_19_38 (q3, x0, C3, &R128, &incr_exp,
        		&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint);
        C3.w[1] = R128.w[1];
        C3.w[0] = R128.w[0];
      }
      // the rounded result has q3 - x0 digits
      // we want the exponent to be e4, so if incr_exp = 1 then
      // multiply the rounded result by 10 - it will still fit in 113 bits
      if (incr_exp) {
        // 64 x 128 -> 128
        P128.w[1] = C3.w[1];
        P128.w[0] = C3.w[0];
        __mul_64x128_to_128 (C3, ten2k64[1], P128);
      }
      e3 = e3 + x0; // this is e4
      // now add/subtract the 256-bit C4 and the new (and shorter) 128-bit C3; 
      // the result will have the sign of x * y; the exponent is e4
      R256.w[3] = 0;
      R256.w[2] = 0;
      R256.w[1] = C3.w[1];
      R256.w[0] = C3.w[0];
      if (p_sign == z_sign) { // R256 = C4 + R256
        add256 (C4, R256, &R256);
      } else { // if (p_sign != z_sign) { // R256 = C4 - R256
        sub256 (C4, R256, &R256); // the result cannot be pure zero
        // because the result has opposite sign to that of R256 which was 
        // rounded, need to change the rounding indicators
        lsb = C4.w[0] & 0x01;
        if (is_inexact_lt_midpoint) {
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 1;
        } else if (is_inexact_gt_midpoint) {
          is_inexact_gt_midpoint = 0;
          is_inexact_lt_midpoint = 1;
        } else if (lsb == 0) {
          if (is_midpoint_lt_even) {
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 1;
          } else if (is_midpoint_gt_even) {
            is_midpoint_gt_even = 0;
            is_midpoint_lt_even = 1;
          } else {
            ;
          }
        } else if (lsb == 1) {
          if (is_midpoint_lt_even) {
            // res = res + 1
            R256.w[0]++;
            if (R256.w[0] == 0x0) {
              R256.w[1]++;
              if (R256.w[1] == 0x0) {
        	R256.w[2]++;
        	if (R256.w[2] == 0x0) {
        	  R256.w[3]++;
        	}
              }
            }
            // no check for rounding overflow - R256 was a difference
          } else if (is_midpoint_gt_even) {
            // res = res - 1
            R256.w[0]--;
            if (R256.w[0] == 0xffffffffffffffffull) {
              R256.w[1]--;
              if (R256.w[1] == 0xffffffffffffffffull) {
        	R256.w[2]--;
        	if (R256.w[2] == 0xffffffffffffffffull) {
        	  R256.w[3]--;
        	}
              }
            }
          } else {
            ;
          }
        } else {
          ;
        }
      }
      // determine the number of decimal digits in R256
      ind = nr_digits256 (R256); // ind >= p34
      // if R256 is sum, then ind > p34; if R256 is a difference, then 
      // ind >= p34; this means that we can calculate the result rounded to
      // the destination precision, with unbounded exponent, starting from R256
      // and using the indicators from the rounding of C3 to avoid a double
      // rounding error 

      if (ind < p34) {
        ;
      } else if (ind == p34) {
        // the result rounded to the destination precision with 
        // unbounded exponent
        // is (-1)^p_sign * R256 * 10^e4
        res.w[1] = R256.w[1];
        res.w[0] = R256.w[0];
      } else { // if (ind > p34)
        // if more than P digits, round to nearest to P digits
        // round R256 to p34 digits
        x0 = ind - p34; // 1 <= x0 <= 34 as 35 <= ind <= 68
        // save C3 rounding indicators to help avoid double rounding error
        is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
        is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
        is_midpoint_lt_even0 = is_midpoint_lt_even;
        is_midpoint_gt_even0 = is_midpoint_gt_even;
        // initialize rounding indicators
        is_inexact_lt_midpoint = 0;
        is_inexact_gt_midpoint = 0;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
        // round to p34 digits; the result fits in 113 bits
        if (ind <= 38) {
          P128.w[1] = R256.w[1];
          P128.w[0] = R256.w[0];
          round128_19_38 (ind, x0, P128, &R128, &incr_exp,
        		  &is_midpoint_lt_even, &is_midpoint_gt_even,
        		  &is_inexact_lt_midpoint,
        		  &is_inexact_gt_midpoint);
        } else if (ind <= 57) {
          P192.w[2] = R256.w[2];
          P192.w[1] = R256.w[1];
          P192.w[0] = R256.w[0];
          round192_39_57 (ind, x0, P192, &R192, &incr_exp,
        		  &is_midpoint_lt_even, &is_midpoint_gt_even,
        		  &is_inexact_lt_midpoint,
        		  &is_inexact_gt_midpoint);
          R128.w[1] = R192.w[1];
          R128.w[0] = R192.w[0];
        } else { // if (ind <= 68)
          round256_58_76 (ind, x0, R256, &R256, &incr_exp,
        		  &is_midpoint_lt_even, &is_midpoint_gt_even,
        		  &is_inexact_lt_midpoint,
        		  &is_inexact_gt_midpoint);
          R128.w[1] = R256.w[1];
          R128.w[0] = R256.w[0];
        }
        // the rounded result has p34 = 34 digits
        e4 = e4 + x0 + incr_exp;

        res.w[1] = R128.w[1];
        res.w[0] = R128.w[0];

        // avoid a double rounding error
        if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
            is_midpoint_lt_even) { // double rounding error upward
          // res = res - 1
          res.w[0]--;
          if (res.w[0] == 0xffffffffffffffffull)
            res.w[1]--;
          is_midpoint_lt_even = 0;
          is_inexact_lt_midpoint = 1;
          // Note: a double rounding error upward is not possible; for this
          // the result after the first rounding would have to be 99...95
          // (35 digits in all), possibly followed by a number of zeros; this
          // not possible in Cases (2)-(6) or (15)-(17) which may get here
          // if this is 10^33 - 1 make it 10^34 - 1 and decrement exponent
          if (res.w[1] == 0x0000314dc6448d93ull && 
            res.w[0] == 0x38c15b09ffffffffull) { // 10^33 - 1
            res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
            res.w[0] = 0x378d8e63ffffffffull;
            e4--;
          }
        } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
            is_midpoint_gt_even) { // double rounding error downward
          // res = res + 1 
          res.w[0]++;
          if (res.w[0] == 0)
            res.w[1]++;
          is_midpoint_gt_even = 0;
          is_inexact_gt_midpoint = 1;
        } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	   !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
          // if this second rounding was exact the result may still be
          // inexact because of the first rounding
          if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
            is_inexact_gt_midpoint = 1;
          }
          if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
            is_inexact_lt_midpoint = 1;
          }
        } else if (is_midpoint_gt_even &&
        	   (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
          // pulled up to a midpoint
          is_inexact_lt_midpoint = 1;
          is_inexact_gt_midpoint = 0;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
        } else if (is_midpoint_lt_even &&
        	   (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
          // pulled down to a midpoint
          is_inexact_lt_midpoint = 0;
          is_inexact_gt_midpoint = 1;
          is_midpoint_lt_even = 0;
          is_midpoint_gt_even = 0;
        } else {
          ;
        }
      }

      // determine tininess
      if (rnd_mode == ROUNDING_TO_NEAREST) {
        if (e4 < expmin) {
          is_tiny = 1; // for other rounding modes apply correction
        }
      } else {
        // for RM, RP, RZ, RA apply correction in order to determine tininess
        // but do not save the result; apply the correction to 
        // (-1)^p_sign * res * 10^0
        P128.w[1] = p_sign | 0x3040000000000000ull | res.w[1];
        P128.w[0] = res.w[0];
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     0, &P128, pfpsf);
        scale = ((P128.w[1] & MASK_EXP) >> 49) - 6176; // -1, 0, or +1
        // the number of digits in the significand is p34 = 34
        if (e4 + scale < expmin) {
          is_tiny = 1;
        }
      }

      // the result rounded to the destination precision with unbounded exponent
      // is (-1)^p_sign * res * 10^e4
      res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1]; // RN
      // res.w[0] unchanged;
      // Note: res is correct only if expmin <= e4 <= expmax
      ind = p34; // the number of decimal digits in the signifcand of res

      // at this point we have the result rounded with unbounded exponent in
      // res and we know its tininess:
      // res = (-1)^p_sign * significand * 10^e4, 
      // where q (significand) = ind = p34
      // Note: res is correct only if expmin <= e4 <= expmax

      // check for overflow if RN
      if (rnd_mode == ROUNDING_TO_NEAREST
          && (ind + e4) > (p34 + expmax)) {
        res.w[1] = p_sign | 0x7800000000000000ull;
        res.w[0] = 0x0000000000000000ull;
        *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
        *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
        *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
        *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
        *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
        BID_SWAP128 (res);
        BID_RETURN (res)
      } // else not overflow or not RN, so continue

      // from this point on this is similar to the last part of the computation
      // for Cases (15), (16), (17)

      // if (e4 >= expmin) we have the result rounded with bounded exponent
      if (e4 < expmin) {
        x0 = expmin - e4; // x0 >= 1; the number of digits to chop off of res
        // where the result rounded [at most] once is
        //   (-1)^p_sign * significand_res * 10^e4

        // avoid double rounding error
        is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
        is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
        is_midpoint_lt_even0 = is_midpoint_lt_even;
        is_midpoint_gt_even0 = is_midpoint_gt_even;
        is_inexact_lt_midpoint = 0;
        is_inexact_gt_midpoint = 0;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;

        if (x0 > ind) {
          // nothing is left of res when moving the decimal point left x0 digits
          is_inexact_lt_midpoint = 1;
          res.w[1] = p_sign | 0x0000000000000000ull;
          res.w[0] = 0x0000000000000000ull;
          e4 = expmin;
        } else if (x0 == ind) { // 1 <= x0 = ind <= p34 = 34
          // this is <, =, or > 1/2 ulp
          // compare the ind-digit value in the significand of res with
          // 1/2 ulp = 5*10^(ind-1), i.e. determine whether it is 
          // less than, equal to, or greater than 1/2 ulp (significand of res)
          R128.w[1] = res.w[1] & MASK_COEFF;
          R128.w[0] = res.w[0];
          if (ind <= 19) {
            if (R128.w[0] < midpoint64[ind - 1]) { // < 1/2 ulp
              lt_half_ulp = 1;
              is_inexact_lt_midpoint = 1;
            } else if (R128.w[0] == midpoint64[ind - 1]) { // = 1/2 ulp
              eq_half_ulp = 1;
              is_midpoint_gt_even = 1;
            } else { // > 1/2 ulp
              gt_half_ulp = 1;
              is_inexact_gt_midpoint = 1;
            }
          } else { // if (ind <= 38)
            if (R128.w[1] < midpoint128[ind - 20].w[1] || 
                (R128.w[1] == midpoint128[ind - 20].w[1] && 
                R128.w[0] < midpoint128[ind - 20].w[0])) { // < 1/2 ulp
              lt_half_ulp = 1;
              is_inexact_lt_midpoint = 1;
            } else if (R128.w[1] == midpoint128[ind - 20].w[1] && 
                R128.w[0] == midpoint128[ind - 20].w[0]) { // = 1/2 ulp
              eq_half_ulp = 1;
              is_midpoint_gt_even = 1;
            } else { // > 1/2 ulp
              gt_half_ulp = 1;
              is_inexact_gt_midpoint = 1;
            }
          }
          if (lt_half_ulp || eq_half_ulp) {
            // res = +0.0 * 10^expmin
            res.w[1] = 0x0000000000000000ull;
            res.w[0] = 0x0000000000000000ull;
          } else { // if (gt_half_ulp)
            // res = +1 * 10^expmin
            res.w[1] = 0x0000000000000000ull;
            res.w[0] = 0x0000000000000001ull;
          }
          res.w[1] = p_sign | res.w[1];
          e4 = expmin;
        } else { // if (1 <= x0 <= ind - 1 <= 33)
          // round the ind-digit result to ind - x0 digits

          if (ind <= 18) { // 2 <= ind <= 18
            round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp,
        		  &is_midpoint_lt_even, &is_midpoint_gt_even,
        		  &is_inexact_lt_midpoint,
        		  &is_inexact_gt_midpoint);
            res.w[1] = 0x0;
            res.w[0] = R64;
          } else if (ind <= 38) {
            P128.w[1] = res.w[1] & MASK_COEFF;
            P128.w[0] = res.w[0];
            round128_19_38 (ind, x0, P128, &res, &incr_exp,
        		    &is_midpoint_lt_even, &is_midpoint_gt_even,
        		    &is_inexact_lt_midpoint,
        		    &is_inexact_gt_midpoint);
          }
          e4 = e4 + x0; // expmin
          // we want the exponent to be expmin, so if incr_exp = 1 then
          // multiply the rounded result by 10 - it will still fit in 113 bits
          if (incr_exp) {
            // 64 x 128 -> 128
            P128.w[1] = res.w[1] & MASK_COEFF;
            P128.w[0] = res.w[0];
            __mul_64x128_to_128 (res, ten2k64[1], P128);
          }
          res.w[1] =
            p_sign | ((UINT64) (e4 + 6176) << 49) | (res.
        					     w[1] & MASK_COEFF);
          // avoid a double rounding error
          if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
                is_midpoint_lt_even) { // double rounding error upward
            // res = res - 1
            res.w[0]--;
            if (res.w[0] == 0xffffffffffffffffull)
              res.w[1]--;
            // Note: a double rounding error upward is not possible; for this
            // the result after the first rounding would have to be 99...95
            // (35 digits in all), possibly followed by a number of zeros; this
            // not possible in this underflow case
            is_midpoint_lt_even = 0;
            is_inexact_lt_midpoint = 1;
          } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
                is_midpoint_gt_even) { // double rounding error downward
            // res = res + 1
            res.w[0]++;
            if (res.w[0] == 0)
              res.w[1]++;
            is_midpoint_gt_even = 0;
            is_inexact_gt_midpoint = 1;
          } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	     !is_inexact_lt_midpoint
        	     && !is_inexact_gt_midpoint) {
            // if this second rounding was exact the result may still be 
            // inexact because of the first rounding
            if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
              is_inexact_gt_midpoint = 1;
            }
            if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
              is_inexact_lt_midpoint = 1;
            }
          } else if (is_midpoint_gt_even &&
        	     (is_inexact_gt_midpoint0
        	      || is_midpoint_lt_even0)) {
            // pulled up to a midpoint
            is_inexact_lt_midpoint = 1;
            is_inexact_gt_midpoint = 0;
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 0;
          } else if (is_midpoint_lt_even &&
        	     (is_inexact_lt_midpoint0
        	      || is_midpoint_gt_even0)) {
            // pulled down to a midpoint
            is_inexact_lt_midpoint = 0;
            is_inexact_gt_midpoint = 1;
            is_midpoint_lt_even = 0;
            is_midpoint_gt_even = 0;
          } else {
            ;
          }
        }
      }
      // res contains the correct result
      // apply correction if not rounding to nearest
      if (rnd_mode != ROUNDING_TO_NEAREST) {
        rounding_correction (rnd_mode,
        		     is_inexact_lt_midpoint,
        		     is_inexact_gt_midpoint,
        		     is_midpoint_lt_even, is_midpoint_gt_even,
        		     e4, &res, pfpsf);
      }
      if (is_midpoint_lt_even || is_midpoint_gt_even ||
          is_inexact_lt_midpoint || is_inexact_gt_midpoint) {
        // set the inexact flag
        *pfpsf |= INEXACT_EXCEPTION;
        if (is_tiny)
          *pfpsf |= UNDERFLOW_EXCEPTION;
      }
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    } else if ((p34 <= delta && delta + q3 <= q4) || // Case (15)
        (delta < p34 && p34 < delta + q3 && delta + q3 <= q4) || //Case (16)
        (delta + q3 <= p34 && p34 < q4)) { // Case (17)

      // calculate first the result rounded to the destination precision, with
      // unbounded exponent

      add_and_round (q3, q4, e4, delta, p34, z_sign, p_sign, C3, C4,
              rnd_mode, &is_midpoint_lt_even,
              &is_midpoint_gt_even, &is_inexact_lt_midpoint,
              &is_inexact_gt_midpoint, pfpsf, &res);
      *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
      *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
      *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
      *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
      BID_SWAP128 (res);
      BID_RETURN (res)

    } else {
      ;
    }

  } // end if delta < 0

  *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
  *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
  *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
  *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
  BID_SWAP128 (res);
  BID_RETURN (res)

}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128_fma (UINT128 * pres, UINT128 * px, UINT128 * py, UINT128 * pz
            _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
            _EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128_fma (UINT128 x, UINT128 y, UINT128 z
            _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
            _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even, is_midpoint_gt_even,
    is_inexact_lt_midpoint, is_inexact_gt_midpoint;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };

#if DECIMAL_CALL_BY_REFERENCE
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, &x, &y, &z
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x, y,
        		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128ddd_fma (UINT128 * pres, UINT64 * px, UINT64 * py, UINT64 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 x = *px, y = *py, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128ddd_fma (UINT64 x, UINT64 y, UINT64 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 x1, y1, z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, &x1, &y1, &z1
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x1, y1,
        		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128ddq_fma (UINT128 * pres, UINT64 * px, UINT64 * py, UINT128 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 x = *px, y = *py;
  UINT128 z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128ddq_fma (UINT64 x, UINT64 y, UINT128 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 x1, y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, &x1, &y1, &z
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x1, y1,
        		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128dqd_fma (UINT128 * pres, UINT64 * px, UINT128 * py, UINT64 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 x = *px, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128dqd_fma (UINT64 x, UINT128 y, UINT64 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 x1, z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, &x1, py, &z1
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x1, y,
        		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128dqq_fma (UINT128 * pres, UINT64 * px, UINT128 * py, UINT128 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 x = *px;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128dqq_fma (UINT64 x, UINT128 y, UINT128 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 x1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, &x1, py, pz
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x1, y,
        		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128qdd_fma (UINT128 * pres, UINT128 * px, UINT64 * py, UINT64 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 y = *py, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128qdd_fma (UINT128 x, UINT64 y, UINT64 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 y1, z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, px, &y1, &z1
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x, y1,
        		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128qdq_fma (UINT128 * pres, UINT128 * px, UINT64 * py, UINT128 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128qdq_fma (UINT128 x, UINT64 y, UINT128 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, px, &y1, pz
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x, y1,
        		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid128qqd_fma (UINT128 * pres, UINT128 * px, UINT128 * py, UINT64 * pz
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
  UINT64 z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT128
bid128qqd_fma (UINT128 x, UINT128 y, UINT64 z
               _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
               _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
        	  &res, px, py, &z1
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
        		&is_inexact_lt_midpoint,
        		&is_inexact_gt_midpoint, x, y,
        		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif
  BID_RETURN (res);
}

// Note: bid128qqq_fma is represented by bid128_fma

// Note: bid64ddd_fma is represented by bid64_fma

#if DECIMAL_CALL_BY_REFERENCE
void
bid64ddq_fma (UINT64 * pres, UINT64 * px, UINT64 * py, UINT128 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT64 x = *px, y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64ddq_fma (UINT64 x, UINT64 y, UINT128 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  UINT128 x1, y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qqq_fma (&res1, &x1, &y1, pz
        	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	_EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res1 = bid64qqq_fma (x1, y1, z
        	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	       _EXC_INFO_ARG);
#endif
  BID_RETURN (res1);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64dqd_fma (UINT64 * pres, UINT64 * px, UINT128 * py, UINT64 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT64 x = *px, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64dqd_fma (UINT64 x, UINT128 y, UINT64 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  UINT128 x1, z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qqq_fma (&res1, &x1, py, &z1
        	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	_EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res1 = bid64qqq_fma (x1, y, z1
        	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	       _EXC_INFO_ARG);
#endif
  BID_RETURN (res1);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64dqq_fma (UINT64 * pres, UINT64 * px, UINT128 * py, UINT128 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT64 x = *px;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64dqq_fma (UINT64 x, UINT128 y, UINT128 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  UINT128 x1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qqq_fma (&res1, &x1, py, pz
        	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	_EXC_INFO_ARG);
#else
  x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res1 = bid64qqq_fma (x1, y, z
        	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	       _EXC_INFO_ARG);
#endif
  BID_RETURN (res1);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qdd_fma (UINT64 * pres, UINT128 * px, UINT64 * py, UINT64 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT64 y = *py, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qdd_fma (UINT128 x, UINT64 y, UINT64 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  UINT128 y1, z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qqq_fma (&res1, px, &y1, &z1
        	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	_EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res1 = bid64qqq_fma (x, y1, z1
        	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	       _EXC_INFO_ARG);
#endif
  BID_RETURN (res1);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qdq_fma (UINT64 * pres, UINT128 * px, UINT64 * py, UINT128 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT64 y = *py;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qdq_fma (UINT128 x, UINT64 y, UINT128 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  UINT128 y1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qqq_fma (&res1, px, &y1, pz
        	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	_EXC_INFO_ARG);
#else
  y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res1 = bid64qqq_fma (x, y1, z
        	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	       _EXC_INFO_ARG);
#endif
  BID_RETURN (res1);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qqd_fma (UINT64 * pres, UINT128 * px, UINT128 * py, UINT64 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT64 z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qqd_fma (UINT128 x, UINT128 y, UINT64 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  UINT128 z1;

#if DECIMAL_CALL_BY_REFERENCE
  bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  bid64qqq_fma (&res1, px, py, &z1
        	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	_EXC_INFO_ARG);
#else
  z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
  res1 = bid64qqq_fma (x, y, z1
        	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	       _EXC_INFO_ARG);
#endif
  BID_RETURN (res1);
}


#if DECIMAL_CALL_BY_REFERENCE
void
bid64qqq_fma (UINT64 * pres, UINT128 * px, UINT128 * py, UINT128 * pz
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
  UINT128 x = *px, y = *py, z = *pz;
#if !DECIMAL_GLOBAL_ROUNDING
  unsigned int rnd_mode = *prnd_mode;
#endif
#else
UINT64
bid64qqq_fma (UINT128 x, UINT128 y, UINT128 z
              _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
              _EXC_INFO_PARAM) {
#endif
  int is_midpoint_lt_even0 = 0, is_midpoint_gt_even0 = 0,
    is_inexact_lt_midpoint0 = 0, is_inexact_gt_midpoint0 = 0;
  int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
    is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
  int incr_exp;
  UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT128 res128 = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
  UINT64 res1 = 0xbaddbaddbaddbaddull;
  unsigned int save_fpsf; // needed because of the call to bid128_ext_fma
  UINT64 sign;
  UINT64 exp;
  int unbexp;
  UINT128 C;
  BID_UI64DOUBLE tmp;
  int nr_bits;
  int q, x0;
  int scale;
  int lt_half_ulp = 0, eq_half_ulp = 0;

  // Note: for rounding modes other than RN or RA, the result can be obtained
  // by rounding first to BID128 and then to BID64

  save_fpsf = *pfpsf; // sticky bits - caller value must be preserved
  *pfpsf = 0;

#if DECIMAL_CALL_BY_REFERENCE
  bid128_ext_fma (&is_midpoint_lt_even0, &is_midpoint_gt_even0,
        	  &is_inexact_lt_midpoint0, &is_inexact_gt_midpoint0,
        	  &res, &x, &y, &z
        	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        	  _EXC_INFO_ARG);
#else
  res = bid128_ext_fma (&is_midpoint_lt_even0, &is_midpoint_gt_even0,
        		&is_inexact_lt_midpoint0,
        		&is_inexact_gt_midpoint0, x, y,
        		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
        		_EXC_INFO_ARG);
#endif

  if ((rnd_mode == ROUNDING_DOWN) || (rnd_mode == ROUNDING_UP) || 
      (rnd_mode == ROUNDING_TO_ZERO) || // no double rounding error is possible
      ((res.w[HIGH_128W] & MASK_NAN) == MASK_NAN) || //res=QNaN (cannot be SNaN)
      ((res.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF)) { // result is infinity  
#if DECIMAL_CALL_BY_REFERENCE
    bid128_to_bid64 (&res1, &res _RND_MODE_ARG _EXC_FLAGS_ARG);
#else
    res1 = bid128_to_bid64 (res _RND_MODE_ARG _EXC_FLAGS_ARG);
#endif
    // determine the unbiased exponent of the result
    unbexp = ((res1 >> 53) & 0x3ff) - 398;

    // if subnormal, res1  must have exp = -398
    // if tiny and inexact set underflow and inexact status flags
    if (!((res1 & MASK_NAN) == MASK_NAN) &&	// res1 not NaN
        (unbexp == -398)
        && ((res1 & MASK_BINARY_SIG1) < 1000000000000000ull)
        && (is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0
            || is_midpoint_lt_even0 || is_midpoint_gt_even0)) {
      // set the inexact flag and the underflow flag
      *pfpsf |= (INEXACT_EXCEPTION | UNDERFLOW_EXCEPTION);
    } else if (is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 ||
               is_midpoint_lt_even0 || is_midpoint_gt_even0) {
      // set the inexact flag and the underflow flag
      *pfpsf |= INEXACT_EXCEPTION;
    }

    *pfpsf |= save_fpsf;
    BID_RETURN (res1);
  } // else continue, and use rounding to nearest to round to 16 digits

  // at this point the result is rounded to nearest (even or away) to 34 digits
  // (or less if exact), and it is zero or finite non-zero canonical [sub]normal
  sign = res.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
  exp = res.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits
  unbexp = (exp >> 49) - 6176;
  C.w[1] = res.w[HIGH_128W] & MASK_COEFF;
  C.w[0] = res.w[LOW_128W];

  if ((C.w[1] == 0x0 && C.w[0] == 0x0) ||	// result is zero
      (unbexp <= (-398 - 35)) || (unbexp >= (369 + 16))) { 
      // clear under/overflow
#if DECIMAL_CALL_BY_REFERENCE
    bid128_to_bid64 (&res1, &res _RND_MODE_ARG _EXC_FLAGS_ARG);
#else
    res1 = bid128_to_bid64 (res _RND_MODE_ARG _EXC_FLAGS_ARG);
#endif
    *pfpsf |= save_fpsf;
    BID_RETURN (res1);
  } // else continue

  // -398 - 34 <= unbexp <= 369 + 15
  if (rnd_mode == ROUNDING_TIES_AWAY) {
    // apply correction, if needed, to make the result rounded to nearest-even
    if (is_midpoint_gt_even) {
      // res = res - 1
      res1--; // res1 is now even
    } // else the result is already correctly rounded to nearest-even
  }
  // at this point the result is finite, non-zero canonical normal or subnormal,
  // and in most cases overflow or underflow will not occur

  // determine the number of digits q in the result
  // q = nr. of decimal digits in x
  // determine first the nr. of bits in x
  if (C.w[1] == 0) {
    if (C.w[0] >= 0x0020000000000000ull) { // x >= 2^53
      // split the 64-bit value in two 32-bit halves to avoid rounding errors
      if (C.w[0] >= 0x0000000100000000ull) { // x >= 2^32
        tmp.d = (double) (C.w[0] >> 32); // exact conversion
        nr_bits =
          33 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
      } else { // x < 2^32
        tmp.d = (double) (C.w[0]); // exact conversion
        nr_bits =
          1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
      }
    } else { // if x < 2^53
      tmp.d = (double) C.w[0]; // exact conversion
      nr_bits =
        1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
    }
  } else { // C.w[1] != 0 => nr. bits = 64 + nr_bits (C.w[1])
    tmp.d = (double) C.w[1]; // exact conversion
    nr_bits =
      65 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
  }
  q = nr_digits[nr_bits - 1].digits;
  if (q == 0) {
    q = nr_digits[nr_bits - 1].digits1;
    if (C.w[1] > nr_digits[nr_bits - 1].threshold_hi ||
        (C.w[1] == nr_digits[nr_bits - 1].threshold_hi &&
         C.w[0] >= nr_digits[nr_bits - 1].threshold_lo))
      q++;
  }
  // if q > 16, round to nearest even to 16 digits (but for underflow it may 
  // have to be truncated even more)
  if (q > 16) {
    x0 = q - 16;
    if (q <= 18) {
      round64_2_18 (q, x0, C.w[0], &res1, &incr_exp,
        	    &is_midpoint_lt_even, &is_midpoint_gt_even,
        	    &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
    } else { // 19 <= q <= 34
      round128_19_38 (q, x0, C, &res128, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
      res1 = res128.w[0]; // the result fits in 64 bits
    }
    unbexp = unbexp + x0;
    if (incr_exp)
      unbexp++;
    q = 16; // need to set in case denormalization is necessary
  } else {
    // the result does not require a second rounding (and it must have 
    // been exact in the first rounding, since q <= 16)
    res1 = C.w[0];
  }

  // avoid a double rounding error
  if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
      is_midpoint_lt_even) { // double rounding error upward
    // res = res - 1 
    res1--; // res1 becomes odd 
    is_midpoint_lt_even = 0;
    is_inexact_lt_midpoint = 1;
    if (res1 == 0x00038d7ea4c67fffull) { // 10^15 - 1
      res1 = 0x002386f26fc0ffffull; // 10^16 - 1 
      unbexp--;
    }
  } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
      is_midpoint_gt_even) { // double rounding error downward
    // res = res + 1
    res1++; // res1 becomes odd (so it cannot be 10^16)
    is_midpoint_gt_even = 0;
    is_inexact_gt_midpoint = 1;
  } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
             !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
    // if this second rounding was exact the result may still be 
    // inexact because of the first rounding
    if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
      is_inexact_gt_midpoint = 1;
    }
    if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
      is_inexact_lt_midpoint = 1;
    }
  } else if (is_midpoint_gt_even &&
             (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
    // pulled up to a midpoint 
    is_inexact_lt_midpoint = 1;
    is_inexact_gt_midpoint = 0;
    is_midpoint_lt_even = 0;
    is_midpoint_gt_even = 0;
  } else if (is_midpoint_lt_even &&
             (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
    // pulled down to a midpoint 
    is_inexact_lt_midpoint = 0;
    is_inexact_gt_midpoint = 1;
    is_midpoint_lt_even = 0;
    is_midpoint_gt_even = 0;
  } else {
    ;
  }
  // this is the result rounded correctly to nearest even, with unbounded exp. 

  // check for overflow
  if (q + unbexp > P16 + expmax16) {
    res1 = sign | 0x7800000000000000ull;
    *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
    *pfpsf |= save_fpsf;
    BID_RETURN (res1)
  } else if (unbexp > expmax16) { // q + unbexp <= P16 + expmax16
    // not overflow; the result must be exact, and we can multiply res1 by
    // 10^(unbexp - expmax16) and the product will fit in 16 decimal digits
    scale = unbexp - expmax16;
    res1 = res1 * ten2k64[scale]; // res1 * 10^scale
    unbexp = expmax16; // unbexp - scale 
  } else {
    ; // continue
  }

  // check for underflow
  if (q + unbexp < P16 + expmin16) {
    if (unbexp < expmin16) {
      // we must truncate more of res
      x0 = expmin16 - unbexp; // x0 >= 1
      is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
      is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
      is_midpoint_lt_even0 = is_midpoint_lt_even;
      is_midpoint_gt_even0 = is_midpoint_gt_even;
      is_inexact_lt_midpoint = 0;
      is_inexact_gt_midpoint = 0;
      is_midpoint_lt_even = 0;
      is_midpoint_gt_even = 0;
      // the number of decimal digits in res1 is q
      if (x0 < q) { // 1 <= x0 <= q-1 => round res to q - x0 digits
        // 2 <= q <= 16, 1 <= x0 <= 15
        round64_2_18 (q, x0, res1, &res1, &incr_exp,
        	      &is_midpoint_lt_even, &is_midpoint_gt_even,
        	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
        if (incr_exp) {
          // res1 = 10^(q-x0), 1 <= q - x0 <= q - 1, 1 <= q - x0 <= 15
          res1 = ten2k64[q - x0];
        }
        unbexp = unbexp + x0; // expmin16
      } else if (x0 == q) {
        // the second rounding is for 0.d(0)d(1)...d(q-1) * 10^emin
        // determine relationship with 1/2 ulp
        // q <= 16
        if (res1 < midpoint64[q - 1]) { // < 1/2 ulp
          lt_half_ulp = 1;
          is_inexact_lt_midpoint = 1;
        } else if (res1 == midpoint64[q - 1]) { // = 1/2 ulp
          eq_half_ulp = 1;
          is_midpoint_gt_even = 1;
        } else { // > 1/2 ulp
          // gt_half_ulp = 1;
          is_inexact_gt_midpoint = 1;
        }
        if (lt_half_ulp || eq_half_ulp) {
          // res = +0.0 * 10^expmin16
          res1 = 0x0000000000000000ull;
        } else { // if (gt_half_ulp)
          // res = +1 * 10^expmin16
          res1 = 0x0000000000000001ull;
        }
        unbexp = expmin16;
      } else { // if (x0 > q)
        // the second rounding is for 0.0...d(0)d(1)...d(q-1) * 10^emin
        res1 = 0x0000000000000000ull;
        unbexp = expmin16;
        is_inexact_lt_midpoint = 1;
      }
      // avoid a double rounding error
      if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) && 
          is_midpoint_lt_even) { // double rounding error upward
        // res = res - 1
        res1--; // res1 becomes odd
        is_midpoint_lt_even = 0;
        is_inexact_lt_midpoint = 1;
      } else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) && 
          is_midpoint_gt_even) { // double rounding error downward
        // res = res + 1
        res1++; // res1 becomes odd
        is_midpoint_gt_even = 0;
        is_inexact_gt_midpoint = 1;
      } else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
        	 !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
        // if this rounding was exact the result may still be 
        // inexact because of the previous roundings
        if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
          is_inexact_gt_midpoint = 1;
        }
        if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
          is_inexact_lt_midpoint = 1;
        }
      } else if (is_midpoint_gt_even &&
        	 (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
        // pulled up to a midpoint
        is_inexact_lt_midpoint = 1;
        is_inexact_gt_midpoint = 0;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
      } else if (is_midpoint_lt_even &&
        	 (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
        // pulled down to a midpoint
        is_inexact_lt_midpoint = 0;
        is_inexact_gt_midpoint = 1;
        is_midpoint_lt_even = 0;
        is_midpoint_gt_even = 0;
      } else {
        ;
      }
    }
    // else if unbexp >= emin then q < P (because q + unbexp < P16 + expmin16)
    // and the result is tiny and exact

    // check for inexact result
    if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
        is_midpoint_lt_even || is_midpoint_gt_even ||
        is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 ||
        is_midpoint_lt_even0 || is_midpoint_gt_even0) {
      // set the inexact flag and the underflow flag
      *pfpsf |= (INEXACT_EXCEPTION | UNDERFLOW_EXCEPTION);
    }
  } else if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
             is_midpoint_lt_even || is_midpoint_gt_even) {
    *pfpsf |= INEXACT_EXCEPTION;
  }
  // this is the result rounded correctly to nearest, with bounded exponent

  if (rnd_mode == ROUNDING_TIES_AWAY && is_midpoint_gt_even) { // correction
    // res = res + 1
    res1++; // res1 is now odd
  } // else the result is already correct

  // assemble the result
  if (res1 < 0x0020000000000000ull) { // res < 2^53
    res1 = sign | ((UINT64) (unbexp + 398) << 53) | res1;
  } else { // res1 >= 2^53
    res1 = sign | MASK_STEERING_BITS |
      ((UINT64) (unbexp + 398) << 51) | (res1 & MASK_BINARY_SIG2);
  }
  *pfpsf |= save_fpsf;
  BID_RETURN (res1);
}