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

This file is part of GCC.

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

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

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

version.

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

WARRANTY; without even the implied warranty of MERCHANTABILITY or

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

for more details.

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

permissions described in the GCC Runtime Library Exception, version

3.1, as published by the Free Software Foundation.

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

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

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

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

#include "bid_internal.h"

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

 *  BID64_round_integral_exact

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

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_round_integral_exact (UINT64 * pres,

                            UINT64 *

                            px _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

bid64_round_integral_exact (UINT64 x _RND_MODE_PARAM _EXC_FLAGS_PARAM

                            _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  UINT64 res = 0xbaddbaddbaddbaddull;

  UINT64 x_sign;

  int exp;                      // unbiased exponent

  // Note: C1 represents the significand (UINT64)

  BID_UI64DOUBLE tmp1;

  int x_nr_bits;

  int q, ind, shift;

  UINT64 C1;

  // UINT64 res is C* at first - represents up to 16 decimal digits <= 54 bits

  UINT128 fstar = { {0x0ull, 0x0ull} };

  UINT128 P128;

  x_sign = x & MASK_SIGN;       // 0 for positive, MASK_SIGN for negative

  // check for NaNs and infinities

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

    if ((x & 0x0003ffffffffffffull) > 999999999999999ull)

      x = x & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits

    else

      x = x & 0xfe03ffffffffffffull;    // clear G6-G12

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

      // set invalid flag

      *pfpsf |= INVALID_EXCEPTION;

      // return quiet (SNaN)

      res = x & 0xfdffffffffffffffull;

    } else {    // QNaN

      res = x;

    }

    BID_RETURN (res);

  } else if ((x & MASK_INF) == MASK_INF) {      // check for Infinity

    res = x_sign | 0x7800000000000000ull;

    BID_RETURN (res);

  }

  // unpack x

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

    // if the steering bits are 11 (condition will be 0), then 

    // the exponent is G[0:w+1]

    exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;

    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

    if (C1 > 9999999999999999ull) {     // non-canonical

      C1 = 0;

    }

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

    exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;

    C1 = (x & MASK_BINARY_SIG1);

  }

  // if x is 0 or non-canonical return 0 preserving the sign bit and 

  // the preferred exponent of MAX(Q(x), 0)

  if (C1 == 0) {

    if (exp < 0)

      exp = 0;

    res = x_sign | (((UINT64) exp + 398) << 53);

    BID_RETURN (res);

  }

  // x is a finite non-zero number (not 0, non-canonical, or special)

  switch (rnd_mode) {

  case ROUNDING_TO_NEAREST:

  case ROUNDING_TIES_AWAY:

    // return 0 if (exp <= -(p+1))

    if (exp <= -17) {

      res = x_sign | 0x31c0000000000000ull;

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_DOWN:

    // return 0 if (exp <= -p)

    if (exp <= -16) {

      if (x_sign) {

        res = 0xb1c0000000000001ull;

      } else {

        res = 0x31c0000000000000ull;

      }

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_UP:

    // return 0 if (exp <= -p)

    if (exp <= -16) {

      if (x_sign) {

        res = 0xb1c0000000000000ull;

      } else {

        res = 0x31c0000000000001ull;

      }

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_TO_ZERO:

    // return 0 if (exp <= -p) 

    if (exp <= -16) {

      res = x_sign | 0x31c0000000000000ull;

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  }     // end switch ()

  // q = nr. of decimal digits in x (1 <= q <= 54)

  //  determine first the nr. of bits in x

  if (C1 >= 0x0020000000000000ull) {    // x >= 2^53

    q = 16;

  } else {      // if x < 2^53

    tmp1.d = (double) C1;       // exact conversion

    x_nr_bits =

      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);

    q = nr_digits[x_nr_bits - 1].digits;

    if (q == 0) {

      q = nr_digits[x_nr_bits - 1].digits1;

      if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)

        q++;

    }

  }

  if (exp >= 0) {        // -exp <= 0

    // the argument is an integer already

    res = x;

    BID_RETURN (res);

  }

  switch (rnd_mode) {

  case ROUNDING_TO_NEAREST:

    if ((q + exp) >= 0) {        // exp < 0 and 1 <= -exp <= q

      // need to shift right -exp digits from the coefficient; exp will be 0

      ind = -exp;       // 1 <= ind <= 16; ind is a synonym for 'x'

      // chop off ind digits from the lower part of C1 

      // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits

      // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate

      C1 = C1 + midpoint64[ind - 1];

      // calculate C* and f*

      // C* is actually floor(C*) in this case

      // C* and f* need shifting and masking, as shown by

      // shiftright128[] and maskhigh128[]

      // 1 <= x <= 16

      // kx = 10^(-x) = ten2mk64[ind - 1]

      // C* = (C1 + 1/2 * 10^x) * 10^(-x)

      // the approximation of 10^(-x) was rounded up to 64 bits

      __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);

      // if (0 < f* < 10^(-x)) then the result is a midpoint

      //   if floor(C*) is even then C* = floor(C*) - logical right

      //       shift; C* has p decimal digits, correct by Prop. 1)

      //   else if floor(C*) is odd C* = floor(C*)-1 (logical right

      //       shift; C* has p decimal digits, correct by Pr. 1)

      // else  

      //   C* = floor(C*) (logical right shift; C has p decimal digits,

      //       correct by Property 1)

      // n = C* * 10^(e+x)  

      if (ind - 1 <= 2) {       // 0 <= ind - 1 <= 2 => shift = 0

        res = P128.w[1];

        fstar.w[1] = 0;

        fstar.w[0] = P128.w[0];

      } else if (ind - 1 <= 21) {       // 3 <= ind - 1 <= 21 => 3 <= shift <= 63

        shift = shiftright128[ind - 1]; // 3 <= shift <= 63

        res = (P128.w[1] >> shift);

        fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];

        fstar.w[0] = P128.w[0];

      }

      // if (0 < f* < 10^(-x)) then the result is a midpoint

      // since round_to_even, subtract 1 if current result is odd

      if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0)

          && (fstar.w[0] < ten2mk64[ind - 1])) {

        res--;

      }

      // determine inexactness of the rounding of C*

      // if (0 < f* - 1/2 < 10^(-x)) then

      //   the result is exact

      // else // if (f* - 1/2 > T*) then

      //   the result is inexact

      if (ind - 1 <= 2) {

        if (fstar.w[0] > 0x8000000000000000ull) {

          // f* > 1/2 and the result may be exact

          // fstar.w[0] - 0x8000000000000000ull is f* - 1/2

          if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) {

            // set the inexact flag

            *pfpsf |= INEXACT_EXCEPTION;

          }     // else the result is exact

        } else {        // the result is inexact; f2* <= 1/2

          // set the inexact flag

          *pfpsf |= INEXACT_EXCEPTION;

        }

      } else {  // if 3 <= ind - 1 <= 21

        if (fstar.w[1] > onehalf128[ind - 1] ||

            (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {

          // f2* > 1/2 and the result may be exact

          // Calculate f2* - 1/2

          if (fstar.w[1] > onehalf128[ind - 1]

              || fstar.w[0] > ten2mk64[ind - 1]) {

            // set the inexact flag

            *pfpsf |= INEXACT_EXCEPTION;

          }     // else the result is exact

        } else {        // the result is inexact; f2* <= 1/2

          // set the inexact flag

          *pfpsf |= INEXACT_EXCEPTION;

        }

      }

      // set exponent to zero as it was negative before.

      res = x_sign | 0x31c0000000000000ull | res;

      BID_RETURN (res);

    } else {    // if exp < 0 and q + exp < 0

      // the result is +0 or -0

      res = x_sign | 0x31c0000000000000ull;

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_TIES_AWAY:

    if ((q + exp) >= 0) {        // exp < 0 and 1 <= -exp <= q

      // need to shift right -exp digits from the coefficient; exp will be 0

      ind = -exp;       // 1 <= ind <= 16; ind is a synonym for 'x'

      // chop off ind digits from the lower part of C1 

      // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits

      // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate

      C1 = C1 + midpoint64[ind - 1];

      // calculate C* and f*

      // C* is actually floor(C*) in this case

      // C* and f* need shifting and masking, as shown by

      // shiftright128[] and maskhigh128[]

      // 1 <= x <= 16

      // kx = 10^(-x) = ten2mk64[ind - 1]

      // C* = (C1 + 1/2 * 10^x) * 10^(-x)

      // the approximation of 10^(-x) was rounded up to 64 bits

      __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);

      // if (0 < f* < 10^(-x)) then the result is a midpoint

      //   C* = floor(C*) - logical right shift; C* has p decimal digits, 

      //       correct by Prop. 1)

      // else

      //   C* = floor(C*) (logical right shift; C has p decimal digits,

      //       correct by Property 1)

      // n = C* * 10^(e+x)

      if (ind - 1 <= 2) {       // 0 <= ind - 1 <= 2 => shift = 0

        res = P128.w[1];

        fstar.w[1] = 0;

        fstar.w[0] = P128.w[0];

      } else if (ind - 1 <= 21) {       // 3 <= ind - 1 <= 21 => 3 <= shift <= 63

        shift = shiftright128[ind - 1]; // 3 <= shift <= 63

        res = (P128.w[1] >> shift);

        fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];

        fstar.w[0] = P128.w[0];

      }

      // midpoints are already rounded correctly

      // determine inexactness of the rounding of C*

      // if (0 < f* - 1/2 < 10^(-x)) then

      //   the result is exact

      // else // if (f* - 1/2 > T*) then

      //   the result is inexact

      if (ind - 1 <= 2) {

        if (fstar.w[0] > 0x8000000000000000ull) {

          // f* > 1/2 and the result may be exact 

          // fstar.w[0] - 0x8000000000000000ull is f* - 1/2

          if ((fstar.w[0] - 0x8000000000000000ull) > ten2mk64[ind - 1]) {

            // set the inexact flag

            *pfpsf |= INEXACT_EXCEPTION;

          }     // else the result is exact

        } else {        // the result is inexact; f2* <= 1/2

          // set the inexact flag

          *pfpsf |= INEXACT_EXCEPTION;

        }

      } else {  // if 3 <= ind - 1 <= 21

        if (fstar.w[1] > onehalf128[ind - 1] ||

            (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) {

          // f2* > 1/2 and the result may be exact

          // Calculate f2* - 1/2

          if (fstar.w[1] > onehalf128[ind - 1]

              || fstar.w[0] > ten2mk64[ind - 1]) {

            // set the inexact flag

            *pfpsf |= INEXACT_EXCEPTION;

          }     // else the result is exact

        } else {        // the result is inexact; f2* <= 1/2

          // set the inexact flag

          *pfpsf |= INEXACT_EXCEPTION;

        }

      }

      // set exponent to zero as it was negative before.

      res = x_sign | 0x31c0000000000000ull | res;

      BID_RETURN (res);

    } else {    // if exp < 0 and q + exp < 0

      // the result is +0 or -0

      res = x_sign | 0x31c0000000000000ull;

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_DOWN:

    if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q

      // need to shift right -exp digits from the coefficient; exp will be 0

      ind = -exp;       // 1 <= ind <= 16; ind is a synonym for 'x'

      // chop off ind digits from the lower part of C1 

      // C1 fits in 64 bits

      // calculate C* and f*

      // C* is actually floor(C*) in this case

      // C* and f* need shifting and masking, as shown by

      // shiftright128[] and maskhigh128[]

      // 1 <= x <= 16

      // kx = 10^(-x) = ten2mk64[ind - 1]

      // C* = C1 * 10^(-x)

      // the approximation of 10^(-x) was rounded up to 64 bits

      __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);

      // C* = floor(C*) (logical right shift; C has p decimal digits,

      //       correct by Property 1)

      // if (0 < f* < 10^(-x)) then the result is exact

      // n = C* * 10^(e+x)  

      if (ind - 1 <= 2) {       // 0 <= ind - 1 <= 2 => shift = 0

        res = P128.w[1];

        fstar.w[1] = 0;

        fstar.w[0] = P128.w[0];

      } else if (ind - 1 <= 21) {       // 3 <= ind - 1 <= 21 => 3 <= shift <= 63

        shift = shiftright128[ind - 1]; // 3 <= shift <= 63

        res = (P128.w[1] >> shift);

        fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];

        fstar.w[0] = P128.w[0];

      }

      // if (f* > 10^(-x)) then the result is inexact

      if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) {

        if (x_sign) {

          // if negative and not exact, increment magnitude

          res++;

        }

        *pfpsf |= INEXACT_EXCEPTION;

      }

      // set exponent to zero as it was negative before.

      res = x_sign | 0x31c0000000000000ull | res;

      BID_RETURN (res);

    } else {    // if exp < 0 and q + exp <= 0

      // the result is +0 or -1

      if (x_sign) {

        res = 0xb1c0000000000001ull;

      } else {

        res = 0x31c0000000000000ull;

      }

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_UP:

    if ((q + exp) > 0) { // exp < 0 and 1 <= -exp < q

      // need to shift right -exp digits from the coefficient; exp will be 0

      ind = -exp;       // 1 <= ind <= 16; ind is a synonym for 'x'

      // chop off ind digits from the lower part of C1 

      // C1 fits in 64 bits

      // calculate C* and f*

      // C* is actually floor(C*) in this case

      // C* and f* need shifting and masking, as shown by

      // shiftright128[] and maskhigh128[]

      // 1 <= x <= 16

      // kx = 10^(-x) = ten2mk64[ind - 1]

      // C* = C1 * 10^(-x)

      // the approximation of 10^(-x) was rounded up to 64 bits

      __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);

      // C* = floor(C*) (logical right shift; C has p decimal digits,

      //       correct by Property 1)

      // if (0 < f* < 10^(-x)) then the result is exact

      // n = C* * 10^(e+x)  

      if (ind - 1 <= 2) {       // 0 <= ind - 1 <= 2 => shift = 0

        res = P128.w[1];

        fstar.w[1] = 0;

        fstar.w[0] = P128.w[0];

      } else if (ind - 1 <= 21) {       // 3 <= ind - 1 <= 21 => 3 <= shift <= 63

        shift = shiftright128[ind - 1]; // 3 <= shift <= 63

        res = (P128.w[1] >> shift);

        fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];

        fstar.w[0] = P128.w[0];

      }

      // if (f* > 10^(-x)) then the result is inexact

      if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) {

        if (!x_sign) {

          // if positive and not exact, increment magnitude

          res++;

        }

        *pfpsf |= INEXACT_EXCEPTION;

      }

      // set exponent to zero as it was negative before.

      res = x_sign | 0x31c0000000000000ull | res;

      BID_RETURN (res);

    } else {    // if exp < 0 and q + exp <= 0

      // the result is -0 or +1

      if (x_sign) {

        res = 0xb1c0000000000000ull;

      } else {

        res = 0x31c0000000000001ull;

      }

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  case ROUNDING_TO_ZERO:

    if ((q + exp) >= 0) {        // exp < 0 and 1 <= -exp <= q

      // need to shift right -exp digits from the coefficient; exp will be 0

      ind = -exp;       // 1 <= ind <= 16; ind is a synonym for 'x'

      // chop off ind digits from the lower part of C1 

      // C1 fits in 127 bits

      // calculate C* and f*

      // C* is actually floor(C*) in this case

      // C* and f* need shifting and masking, as shown by

      // shiftright128[] and maskhigh128[]

      // 1 <= x <= 16

      // kx = 10^(-x) = ten2mk64[ind - 1]

      // C* = C1 * 10^(-x)

      // the approximation of 10^(-x) was rounded up to 64 bits

      __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);

      // C* = floor(C*) (logical right shift; C has p decimal digits,

      //       correct by Property 1)

      // if (0 < f* < 10^(-x)) then the result is exact

      // n = C* * 10^(e+x)  

      if (ind - 1 <= 2) {       // 0 <= ind - 1 <= 2 => shift = 0

        res = P128.w[1];

        fstar.w[1] = 0;

        fstar.w[0] = P128.w[0];

      } else if (ind - 1 <= 21) {       // 3 <= ind - 1 <= 21 => 3 <= shift <= 63

        shift = shiftright128[ind - 1]; // 3 <= shift <= 63

        res = (P128.w[1] >> shift);

        fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];

        fstar.w[0] = P128.w[0];

      }

      // if (f* > 10^(-x)) then the result is inexact

      if ((fstar.w[1] != 0) || (fstar.w[0] >= ten2mk64[ind - 1])) {

        *pfpsf |= INEXACT_EXCEPTION;

      }

      // set exponent to zero as it was negative before.

      res = x_sign | 0x31c0000000000000ull | res;

      BID_RETURN (res);

    } else {    // if exp < 0 and q + exp < 0

      // the result is +0 or -0

      res = x_sign | 0x31c0000000000000ull;

      *pfpsf |= INEXACT_EXCEPTION;

      BID_RETURN (res);

    }

    break;

  }     // end switch ()

  BID_RETURN (res);

}

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

 *  BID64_round_integral_nearest_even

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

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_round_integral_nearest_even (UINT64 * pres,

                                   UINT64 *

                                   px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                                   _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_round_integral_nearest_even (UINT64 x _EXC_FLAGS_PARAM

                                   _EXC_MASKS_PARAM _EXC_INFO_PARAM) {

#endif

  UINT64 res = 0xbaddbaddbaddbaddull;

  UINT64 x_sign;

  int exp;                      // unbiased exponent

  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)

  BID_UI64DOUBLE tmp1;

  int x_nr_bits;

  int q, ind, shift;

  UINT64 C1;

  UINT128 fstar;

  UINT128 P128;

  x_sign = x & MASK_SIGN;       // 0 for positive, MASK_SIGN for negative

  // check for NaNs and infinities

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

    if ((x & 0x0003ffffffffffffull) > 999999999999999ull)

      x = x & 0xfe00000000000000ull;    // clear G6-G12 and the payload bits

    else

      x = x & 0xfe03ffffffffffffull;    // clear G6-G12 

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

      // set invalid flag 

      *pfpsf |= INVALID_EXCEPTION;

      // return quiet (SNaN) 

      res = x & 0xfdffffffffffffffull;

    } else {    // QNaN

      res = x;

    }

    BID_RETURN (res);

  } else if ((x & MASK_INF) == MASK_INF) {      // check for Infinity

    res = x_sign | 0x7800000000000000ull;

    BID_RETURN (res);

  }

  // unpack x

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

    // if the steering bits are 11 (condition will be 0), then

    // the exponent is G[0:w+1]

    exp = ((x & MASK_BINARY_EXPONENT2) >> 51) - 398;

    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

    if (C1 > 9999999999999999ull) {     // non-canonical

      C1 = 0;

    }

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

    exp = ((x & MASK_BINARY_EXPONENT1) >> 53) - 398;

    C1 = (x & MASK_BINARY_SIG1);

  }

  // if x is 0 or non-canonical

  if (C1 == 0) {

    if (exp < 0)

      exp = 0;

    res = x_sign | (((UINT64) exp + 398) << 53);

    BID_RETURN (res);

  }

  // x is a finite non-zero number (not 0, non-canonical, or special)

  // return 0 if (exp <= -(p+1))

  if (exp <= -17) {

    res = x_sign | 0x31c0000000000000ull;

    BID_RETURN (res);

  }

  // q = nr. of decimal digits in x (1 <= q <= 54)

  //  determine first the nr. of bits in x

  if (C1 >= 0x0020000000000000ull) {    // x >= 2^53

    q = 16;

  } else {      // if x < 2^53

    tmp1.d = (double) C1;       // exact conversion

    x_nr_bits =

      1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);

    q = nr_digits[x_nr_bits - 1].digits;

    if (q == 0) {

      q = nr_digits[x_nr_bits - 1].digits1;

      if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo)

        q++;

    }

  }

  if (exp >= 0) {        // -exp <= 0

    // the argument is an integer already

    res = x;

    BID_RETURN (res);

  } else if ((q + exp) >= 0) {   // exp < 0 and 1 <= -exp <= q

    // need to shift right -exp digits from the coefficient; the exp will be 0

    ind = -exp; // 1 <= ind <= 16; ind is a synonym for 'x'

    // chop off ind digits from the lower part of C1 

    // C1 = C1 + 1/2 * 10^x where the result C1 fits in 64 bits

    // FOR ROUND_TO_NEAREST, WE ADD 1/2 ULP(y) then truncate

    C1 = C1 + midpoint64[ind - 1];

    // calculate C* and f*

    // C* is actually floor(C*) in this case

    // C* and f* need shifting and masking, as shown by

    // shiftright128[] and maskhigh128[]

    // 1 <= x <= 16

    // kx = 10^(-x) = ten2mk64[ind - 1]

    // C* = (C1 + 1/2 * 10^x) * 10^(-x)

    // the approximation of 10^(-x) was rounded up to 64 bits

    __mul_64x64_to_128 (P128, C1, ten2mk64[ind - 1]);

    // if (0 < f* < 10^(-x)) then the result is a midpoint

    //   if floor(C*) is even then C* = floor(C*) - logical right

    //       shift; C* has p decimal digits, correct by Prop. 1)

    //   else if floor(C*) is odd C* = floor(C*)-1 (logical right

    //       shift; C* has p decimal digits, correct by Pr. 1)

    // else  

    //   C* = floor(C*) (logical right shift; C has p decimal digits,

    //       correct by Property 1)

    // n = C* * 10^(e+x)  

    if (ind - 1 <= 2) { // 0 <= ind - 1 <= 2 => shift = 0

      res = P128.w[1];

      fstar.w[1] = 0;

      fstar.w[0] = P128.w[0];

    } else if (ind - 1 <= 21) { // 3 <= ind - 1 <= 21 => 3 <= shift <= 63

      shift = shiftright128[ind - 1];   // 3 <= shift <= 63

      res = (P128.w[1] >> shift);

      fstar.w[1] = P128.w[1] & maskhigh128[ind - 1];

      fstar.w[0] = P128.w[0];

    }

    // if (0 < f* < 10^(-x)) then the result is a midpoint

    // since round_to_even, subtract 1 if current result is odd

    if ((res & 0x0000000000000001ull) && (fstar.w[1] == 0)

        && (fstar.w[0] < ten2mk64[ind - 1])) {

      res--;

    }

    // set exponent to zero as it was negative before.

    res = x_sign | 0x31c0000000000000ull | res;

    BID_RETURN (res);

  } else {      // if exp < 0 and q + exp < 0

    // the result is +0 or -0

    res = x_sign | 0x31c0000000000000ull;

    BID_RETURN (res);