Subversion Repositories openrisc

/* 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_to_uint64_rnint

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

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_to_uint64_rnint (UINT64 * pres, UINT64 * px

                       _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                       _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_to_uint64_rnint (UINT64 x

                       _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                       _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  UINT64 x_sign;

  UINT64 x_exp;

  int exp;                      // unbiased exponent

  // Note: C1 represents x_significand (UINT64)

  BID_UI64DOUBLE tmp1;

  unsigned int x_nr_bits;

  int q, ind, shift;

  UINT64 C1;

  UINT128 C;

  UINT64 Cstar;                 // C* represents up to 16 decimal digits ~ 54 bits

  UINT128 fstar;

  UINT128 P128;

  // check for NaN or Infinity

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

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    BID_RETURN (res);

  }

  // unpack x

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

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

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

    x_exp = (x & MASK_BINARY_EXPONENT2) >> 51;  // biased

    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

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

      x_exp = 0;

      C1 = 0;

    }

  } else {

    x_exp = (x & MASK_BINARY_EXPONENT1) >> 53;  // biased

    C1 = x & MASK_BINARY_SIG1;

  }

  // check for zeros (possibly from non-canonical values)

  if (C1 == 0x0ull) {

    // x is 0

    res = 0x0000000000000000ull;

    BID_RETURN (res);

  }

  // x is not special and is not zero

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

  //  determine first the nr. of bits in x

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

    // split the 64-bit value in two 32-bit halves to avoid rounding errors

    if (C1 >= 0x0000000100000000ull) {  // x >= 2^32

      tmp1.d = (double) (C1 >> 32);     // exact conversion

      x_nr_bits =

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

    } else {    // x < 2^32

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

      x_nr_bits =

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

    }

  } 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++;

  }

  exp = x_exp - 398;    // unbiased exponent

  if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    BID_RETURN (res);

  } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)

    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...

    // so x rounded to an integer may or may not fit in an unsigned 64-bit int

    // the cases that do not fit are identified here; the ones that fit

    // fall through and will be handled with other cases further,

    // under '1 <= q + exp <= 20'

    if (x_sign) {       // if n < 0 and q + exp = 20 then x is much less than -1/2

      // => set invalid flag

      *pfpsf |= INVALID_EXCEPTION;

      // return Integer Indefinite

      res = 0x8000000000000000ull;

      BID_RETURN (res);

    } else {    // if n > 0 and q + exp = 20

      // if n >= 2^64 - 1/2 then n is too large

      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2

      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2

      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)

      // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16

      if (q == 1) {

        // C * 10^20 >= 0x9fffffffffffffffb

        __mul_128x64_to_128 (C, C1, ten2k128[0]);        // 10^20 * C

        if (C.w[1] > 0x09 ||

            (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) {

          // set invalid flag

          *pfpsf |= INVALID_EXCEPTION;

          // return Integer Indefinite

          res = 0x8000000000000000ull;

          BID_RETURN (res);

        }

        // else cases that can be rounded to a 64-bit int fall through

        // to '1 <= q + exp <= 20'

      } else {  // if (2 <= q <= 16) => 5 <= 21 - q <= 19

        // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb 

        // has 21 digits

        __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]);

        if (C.w[1] > 0x09 ||

            (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) {

          // set invalid flag

          *pfpsf |= INVALID_EXCEPTION;

          // return Integer Indefinite

          res = 0x8000000000000000ull;

          BID_RETURN (res);

        }

        // else cases that can be rounded to a 64-bit int fall through

        // to '1 <= q + exp <= 20'

      }

    }

  }

  // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2

  // Note: some of the cases tested for above fall through to this point

  if ((q + exp) < 0) {   // n = +/-0.0...c(0)c(1)...c(q-1)

    // return 0

    res = 0x0000000000000000ull;

    BID_RETURN (res);

  } else if ((q + exp) == 0) {   // n = +/-0.c(0)c(1)...c(q-1)

    // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)

    //   res = 0

    // else if x > 0

    //   res = +1

    // else // if x < 0

    //   invalid exc

    ind = q - 1;        // 0 <= ind <= 15

    if (C1 <= midpoint64[ind]) {

      res = 0x0000000000000000ull;      // return 0

    } else if (!x_sign) {       // n > 0

      res = 0x0000000000000001ull;      // return +1

    } else {    // if n < 0

      res = 0x8000000000000000ull;

      *pfpsf |= INVALID_EXCEPTION;

      BID_RETURN (res);

    }

  } else {      // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19)

    // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded

    // to nearest to a 64-bit unsigned signed integer

    if (x_sign) {       // x <= -1

      // set invalid flag

      *pfpsf |= INVALID_EXCEPTION;

      // return Integer Indefinite

      res = 0x8000000000000000ull;

      BID_RETURN (res);

    }

    // 1 <= x < 2^64-1/2 so x can be rounded

    // to nearest to a 64-bit unsigned integer

    if (exp < 0) {       // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20

      ind = -exp;       // 1 <= ind <= 15; ind is a synonym for 'x'

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

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

      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 <= 15 

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

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

      // the approximation of 10^(-x) was rounded up to 54 bits

      __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);

      Cstar = P128.w[1];

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

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

      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.

      // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999

      // 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)

      // shift right C* by Ex-64 = shiftright128[ind]

      shift = shiftright128[ind - 1];   // 0 <= shift <= 39

      Cstar = Cstar >> shift;

      // if the result was a midpoint it was rounded away from zero, so

      // it will need a correction

      // check for midpoints

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

          (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {

        // ten2mk128trunc[ind -1].w[1] is identical to 

        // ten2mk128[ind -1].w[1]

        // the result is a midpoint; round to nearest

        if (Cstar & 0x01) {     // Cstar is odd; MP in [EVEN, ODD]

          // if floor(C*) is odd C = floor(C*) - 1; the result >= 1

          Cstar--;      // Cstar is now even

        }       // else MP in [ODD, EVEN]

      }

      res = Cstar;      // the result is positive

    } else if (exp == 0) {

      // 1 <= q <= 10

      // res = +C (exact)

      res = C1; // the result is positive

    } else {    // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10

      // res = +C * 10^exp (exact)

      res = C1 * ten2k64[exp];  // the result is positive

    }

  }

  BID_RETURN (res);

}

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

 *  BID64_to_uint64_xrnint

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

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_to_uint64_xrnint (UINT64 * pres, UINT64 * px

                        _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                        _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_to_uint64_xrnint (UINT64 x

                        _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                        _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  UINT64 x_sign;

  UINT64 x_exp;

  int exp;                      // unbiased exponent

  // Note: C1 represents x_significand (UINT64)

  UINT64 tmp64;

  BID_UI64DOUBLE tmp1;

  unsigned int x_nr_bits;

  int q, ind, shift;

  UINT64 C1;

  UINT128 C;

  UINT64 Cstar;                 // C* represents up to 16 decimal digits ~ 54 bits

  UINT128 fstar;

  UINT128 P128;

  // check for NaN or Infinity

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

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    BID_RETURN (res);

  }

  // unpack x

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

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

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

    x_exp = (x & MASK_BINARY_EXPONENT2) >> 51;  // biased

    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

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

      x_exp = 0;

      C1 = 0;

    }

  } else {

    x_exp = (x & MASK_BINARY_EXPONENT1) >> 53;  // biased

    C1 = x & MASK_BINARY_SIG1;

  }

  // check for zeros (possibly from non-canonical values)

  if (C1 == 0x0ull) {

    // x is 0

    res = 0x0000000000000000ull;

    BID_RETURN (res);

  }

  // x is not special and is not zero

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

  //  determine first the nr. of bits in x

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

    // split the 64-bit value in two 32-bit halves to avoid rounding errors

    if (C1 >= 0x0000000100000000ull) {  // x >= 2^32

      tmp1.d = (double) (C1 >> 32);     // exact conversion

      x_nr_bits =

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

    } else {    // x < 2^32

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

      x_nr_bits =

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

    }

  } 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++;

  }

  exp = x_exp - 398;    // unbiased exponent

  if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    BID_RETURN (res);

  } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)

    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...

    // so x rounded to an integer may or may not fit in an unsigned 64-bit int

    // the cases that do not fit are identified here; the ones that fit

    // fall through and will be handled with other cases further,

    // under '1 <= q + exp <= 20'

    if (x_sign) {       // if n < 0 and q + exp = 20 then x is much less than -1/2

      // => set invalid flag

      *pfpsf |= INVALID_EXCEPTION;

      // return Integer Indefinite

      res = 0x8000000000000000ull;

      BID_RETURN (res);

    } else {    // if n > 0 and q + exp = 20

      // if n >= 2^64 - 1/2 then n is too large

      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2

      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2

      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)

      // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=16

      if (q == 1) {

        // C * 10^20 >= 0x9fffffffffffffffb

        __mul_128x64_to_128 (C, C1, ten2k128[0]);        // 10^20 * C

        if (C.w[1] > 0x09 ||

            (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) {

          // set invalid flag

          *pfpsf |= INVALID_EXCEPTION;

          // return Integer Indefinite

          res = 0x8000000000000000ull;

          BID_RETURN (res);

        }

        // else cases that can be rounded to a 64-bit int fall through

        // to '1 <= q + exp <= 20'

      } else {  // if (2 <= q <= 16) => 5 <= 21 - q <= 19

        // Note: C * 10^(21-q) has 20 or 21 digits; 0x9fffffffffffffffb 

        // has 21 digits

        __mul_64x64_to_128MACH (C, C1, ten2k64[21 - q]);

        if (C.w[1] > 0x09 ||

            (C.w[1] == 0x09 && C.w[0] >= 0xfffffffffffffffbull)) {

          // set invalid flag

          *pfpsf |= INVALID_EXCEPTION;

          // return Integer Indefinite

          res = 0x8000000000000000ull;

          BID_RETURN (res);

        }

        // else cases that can be rounded to a 64-bit int fall through

        // to '1 <= q + exp <= 20'

      }

    }

  }

  // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2

  // Note: some of the cases tested for above fall through to this point

  if ((q + exp) < 0) {   // n = +/-0.0...c(0)c(1)...c(q-1)

    // set inexact flag

    *pfpsf |= INEXACT_EXCEPTION;

    // return 0

    res = 0x0000000000000000ull;

    BID_RETURN (res);

  } else if ((q + exp) == 0) {   // n = +/-0.c(0)c(1)...c(q-1)

    // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)

    //   res = 0

    // else if x > 0

    //   res = +1

    // else // if x < 0

    //   invalid exc

    ind = q - 1;        // 0 <= ind <= 15

    if (C1 <= midpoint64[ind]) {

      res = 0x0000000000000000ull;      // return 0

    } else if (!x_sign) {       // n > 0

      res = 0x0000000000000001ull;      // return +1

    } else {    // if n < 0

      res = 0x8000000000000000ull;

      *pfpsf |= INVALID_EXCEPTION;

      BID_RETURN (res);

    }

    // set inexact flag

    *pfpsf |= INEXACT_EXCEPTION;

  } else {      // if (1 <= q + exp <= 20, 1 <= q <= 16, -15 <= exp <= 19)

    // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded

    // to nearest to a 64-bit unsigned signed integer

    if (x_sign) {       // x <= -1

      // set invalid flag

      *pfpsf |= INVALID_EXCEPTION;

      // return Integer Indefinite

      res = 0x8000000000000000ull;

      BID_RETURN (res);

    }

    // 1 <= x < 2^64-1/2 so x can be rounded

    // to nearest to a 64-bit unsigned integer

    if (exp < 0) {       // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 20

      ind = -exp;       // 1 <= ind <= 15; ind is a synonym for 'x'

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

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

      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 <= 15 

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

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

      // the approximation of 10^(-x) was rounded up to 54 bits

      __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]);

      Cstar = P128.w[1];

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

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

      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g.

      // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999

      // 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)

      // shift right C* by Ex-64 = shiftright128[ind]

      shift = shiftright128[ind - 1];   // 0 <= shift <= 39

      Cstar = Cstar >> shift;

      // 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) {       // fstar.w[1] is 0

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

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

          tmp64 = fstar.w[0] - 0x8000000000000000ull;    // f* - 1/2

          if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) {

            // ten2mk128trunc[ind -1].w[1] is identical to

            // ten2mk128[ind -1].w[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 <= 14

        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

          tmp64 = fstar.w[1] - onehalf128[ind - 1];

          if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) {

            // ten2mk128trunc[ind -1].w[1] is identical to

            // ten2mk128[ind -1].w[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;

        }

      }

      // if the result was a midpoint it was rounded away from zero, so

      // it will need a correction

      // check for midpoints

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

          (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) {

        // ten2mk128trunc[ind -1].w[1] is identical to 

        // ten2mk128[ind -1].w[1]

        // the result is a midpoint; round to nearest

        if (Cstar & 0x01) {     // Cstar is odd; MP in [EVEN, ODD]

          // if floor(C*) is odd C = floor(C*) - 1; the result >= 1

          Cstar--;      // Cstar is now even

        }       // else MP in [ODD, EVEN]

      }

      res = Cstar;      // the result is positive

    } else if (exp == 0) {

      // 1 <= q <= 10

      // res = +C (exact)

      res = C1; // the result is positive

    } else {    // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10

      // res = +C * 10^exp (exact)

      res = C1 * ten2k64[exp];  // the result is positive

    }

  }

  BID_RETURN (res);

}

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

 *  BID64_to_uint64_floor

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

#if DECIMAL_CALL_BY_REFERENCE

void

bid64_to_uint64_floor (UINT64 * pres, UINT64 * px

                       _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                       _EXC_INFO_PARAM) {

  UINT64 x = *px;

#else

UINT64

bid64_to_uint64_floor (UINT64 x

                       _EXC_FLAGS_PARAM _EXC_MASKS_PARAM

                       _EXC_INFO_PARAM) {

#endif

  UINT64 res;

  UINT64 x_sign;

  UINT64 x_exp;

  int exp;                      // unbiased exponent

  // Note: C1 represents x_significand (UINT64)

  BID_UI64DOUBLE tmp1;

  unsigned int x_nr_bits;

  int q, ind, shift;

  UINT64 C1;

  UINT128 C;

  UINT64 Cstar;                 // C* represents up to 16 decimal digits ~ 54 bits

  UINT128 P128;

  // check for NaN or Infinity

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

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    BID_RETURN (res);

  }

  // unpack x

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

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

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

    x_exp = (x & MASK_BINARY_EXPONENT2) >> 51;  // biased

    C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2;

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

      x_exp = 0;

      C1 = 0;

    }

  } else {

    x_exp = (x & MASK_BINARY_EXPONENT1) >> 53;  // biased

    C1 = x & MASK_BINARY_SIG1;

  }

  // check for zeros (possibly from non-canonical values)

  if (C1 == 0x0ull) {

    // x is 0

    res = 0x0000000000000000ull;

    BID_RETURN (res);

  }

  // x is not special and is not zero

  if (x_sign) { // if n < 0 the conversion is invalid

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    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

    // split the 64-bit value in two 32-bit halves to avoid rounding errors

    if (C1 >= 0x0000000100000000ull) {  // x >= 2^32

      tmp1.d = (double) (C1 >> 32);     // exact conversion

      x_nr_bits =

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

    } else {    // x < 2^32

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

      x_nr_bits =

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

    }

  } 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++;

  }

  exp = x_exp - 398;    // unbiased exponent

  if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)

    // set invalid flag

    *pfpsf |= INVALID_EXCEPTION;

    // return Integer Indefinite

    res = 0x8000000000000000ull;

    BID_RETURN (res);

  } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)

    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...

    // so x rounded to an integer may or may not fit in an unsigned 64-bit int

    // the cases that do not fit are identified here; the ones that fit

    // fall through and will be handled with other cases further,

    // under '1 <= q + exp <= 20'

    // n > 0 and q + exp = 20

    // if n >= 2^64 then n is too large

    // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64

    // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64

    // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65)

    // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=16

    if (q == 1) {

      // C * 10^20 >= 0xa0000000000000000

      __mul_128x64_to_128 (C, C1, ten2k128[0]);  // 10^20 * C

      if (C.w[1] >= 0x0a) {

        // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {

        // set invalid flag

        *pfpsf |= INVALID_EXCEPTION;