--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/libgcc/config/libbid/bid128_to_int32.c	Fri Jul 17 14:47:48 2009 +0900
@@ -0,0 +1,3659 @@
+/* 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"
+
+/*****************************************************************************
+ *  BID128_to_int32_rnint 
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_rnint, x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n < -2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 > 0x500000005ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005 <=>
+	// C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1/2 up)
+	tmp64 = 0x500000005ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x4fffffffbull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=>
+	// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31-1/2 up)
+	tmp64 = 0x4fffffffbull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 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 = 0x00000000;
+    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
+    //   res = +/-1
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    } else {	// 19 <= ind <= 33
+      if ((C1.w[1] < midpoint128[ind - 19].w[1])
+	  || ((C1.w[1] == midpoint128[ind - 19].w[1])
+	      && (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    }
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded
+    // to nearest to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	}	// else MP in [ODD, EVEN]
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_xrnint
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xrnint,
+					  x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n < -2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31+1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 > 0x500000005ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000005 <=>
+	// C > 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1/2 up)
+	tmp64 = 0x500000005ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x4fffffffbull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=>
+	// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31-1/2 up)
+	tmp64 = 0x4fffffffbull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 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 = 0x00000000;
+    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
+    //   res = +/-1
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    } else {	// 19 <= ind <= 33
+      if ((C1.w[1] < midpoint128[ind - 19].w[1])
+	  || ((C1.w[1] == midpoint128[ind - 19].w[1])
+	      && (C1.w[0] <= midpoint128[ind - 19].w[0]))) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    }
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1/2 <= x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded
+    // to nearest to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if (tmp64 > ten2mk128trunc[ind - 1].w[1]
+	      || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
+	    // 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 (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // 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 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // 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[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	}	// else MP in [ODD, EVEN]
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_floor
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_floor, x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+     int is_inexact_lt_midpoint = 0;
+     int is_inexact_gt_midpoint = 0;
+     int is_midpoint_lt_even = 0;
+     int is_midpoint_gt_even = 0;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n < -2^31 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 > 0x500000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000 <=>
+	// C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31 up)
+	tmp64 = 0x500000000ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x500000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=>
+	// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31 up)
+	tmp64 = 0x500000000ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 <= n < 2^31
+  // 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) or n = +/-0.c(0)c(1)...c(q-1)
+    // return 0
+    if (x_sign)
+      res = 0xffffffff;
+    else
+      res = 0x00000000;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31 <= x <= -1 or 1 <= x < 2^31 so x can be rounded
+    // toward negative infinity to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if (tmp64 > ten2mk128trunc[ind - 1].w[1]
+	      || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      }
+
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	  is_midpoint_gt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	} else {	// else MP in [ODD, EVEN]
+	  is_midpoint_lt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	}
+      }
+      // general correction for RM
+      if (x_sign && (is_midpoint_gt_even || is_inexact_lt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] + 1;
+      } else if (!x_sign
+		 && (is_midpoint_lt_even || is_inexact_gt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] - 1;
+      } else {
+	;	// the result is already correct
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+
+/*****************************************************************************
+ *  BID128_to_int32_xfloor
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xfloor,
+					  x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+     int is_inexact_lt_midpoint = 0;
+     int is_inexact_gt_midpoint = 0;
+     int is_midpoint_lt_even = 0;
+     int is_midpoint_gt_even = 0;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n < -2^31 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 > 0x500000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 > 0x500000000 <=>
+	// C > 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31 up)
+	tmp64 = 0x500000000ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x500000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=>
+	// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31 up)
+	tmp64 = 0x500000000ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 <= n < 2^31
+  // 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) or n = +/-0.c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
+    if (x_sign)
+      res = 0xffffffff;
+    else
+      res = 0x00000000;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31 <= x <= -1 or 1 <= x < 2^31 so x can be rounded
+    // toward negative infinity to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if (tmp64 > ten2mk128trunc[ind - 1].w[1]
+	      || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
+	    // set the inexact flag
+	    *pfpsf |= INEXACT_EXCEPTION;
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // set the inexact flag
+	    *pfpsf |= INEXACT_EXCEPTION;
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // set the inexact flag
+	    *pfpsf |= INEXACT_EXCEPTION;
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	  is_inexact_gt_midpoint = 1;
+	}
+      }
+
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	  is_midpoint_gt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	} else {	// else MP in [ODD, EVEN]
+	  is_midpoint_lt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	}
+      }
+      // general correction for RM
+      if (x_sign && (is_midpoint_gt_even || is_inexact_lt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] + 1;
+      } else if (!x_sign
+		 && (is_midpoint_lt_even || is_inexact_gt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] - 1;
+      } else {
+	;	// the result is already correct
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_ceil
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_ceil, x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+     int is_inexact_lt_midpoint = 0;
+     int is_inexact_gt_midpoint = 0;
+     int is_midpoint_lt_even = 0;
+     int is_midpoint_gt_even = 0;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n <= -2^31-1 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x50000000aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=>
+	// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1 up)
+	tmp64 = 0x50000000aull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n > 2^31 - 1 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 > 0x4fffffff6ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6 <=>
+	// C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31 up)
+	tmp64 = 0x4fffffff6ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31-1 < n <= 2^31-1
+  // 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) or n = +/-0.c(0)c(1)...c(q-1)
+    // return 0
+    if (x_sign)
+      res = 0x00000000;
+    else
+      res = 0x00000001;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded
+    // toward positive infinity to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if (tmp64 > ten2mk128trunc[ind - 1].w[1]
+	      || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      }
+
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	  is_midpoint_gt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	} else {	// else MP in [ODD, EVEN]
+	  is_midpoint_lt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	}
+      }
+      // general correction for RM
+      if (x_sign && (is_midpoint_lt_even || is_inexact_gt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] - 1;
+      } else if (!x_sign
+		 && (is_midpoint_gt_even || is_inexact_lt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] + 1;
+      } else {
+	;	// the result is already correct
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_xceil
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xceil, x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+     int is_inexact_lt_midpoint = 0;
+     int is_inexact_gt_midpoint = 0;
+     int is_midpoint_lt_even = 0;
+     int is_midpoint_gt_even = 0;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n <= -2^31-1 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x50000000aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=>
+	// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1 up)
+	tmp64 = 0x50000000aull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n > 2^31 - 1 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^31 - 1
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 > 0x4fffffff6ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 > 0x4fffffff6 <=>
+	// C > 0x4fffffff6 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31 up)
+	tmp64 = 0x4fffffff6ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] > C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31-1 < n <= 2^31-1
+  // 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) or n = +/-0.c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
+    if (x_sign)
+      res = 0x00000000;
+    else
+      res = 0x00000001;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1 < x <= -1 or 1 <= x <= 2^31-1 so x can be rounded
+    // toward positive infinity to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if (tmp64 > ten2mk128trunc[ind - 1].w[1]
+	      || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
+	    // set the inexact flag
+	    *pfpsf |= INEXACT_EXCEPTION;
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // set the inexact flag
+	    *pfpsf |= INEXACT_EXCEPTION;
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // set the inexact flag
+	    *pfpsf |= INEXACT_EXCEPTION;
+	    is_inexact_lt_midpoint = 1;
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	  is_inexact_gt_midpoint = 1;
+	}
+      }
+
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	  is_midpoint_gt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	} else {	// else MP in [ODD, EVEN]
+	  is_midpoint_lt_even = 1;
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 0;
+	}
+      }
+      // general correction for RM
+      if (x_sign && (is_midpoint_lt_even || is_inexact_gt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] - 1;
+      } else if (!x_sign
+		 && (is_midpoint_gt_even || is_inexact_lt_midpoint)) {
+	Cstar.w[0] = Cstar.w[0] + 1;
+      } else {
+	;	// the result is already correct
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_int
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_int, x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+     int is_inexact_gt_midpoint = 0;
+     int is_midpoint_lt_even = 0;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n <= -2^31 - 1 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x50000000aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=>
+	// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1 up)
+	tmp64 = 0x50000000aull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x500000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=>
+	// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31-1/2 up)
+	tmp64 = 0x500000000ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 - 1 < n < 2^31
+  // 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) or n = +/-0.c(0)c(1)...c(q-1)
+    // return 0
+    res = 0x00000000;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded
+    // toward zero to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if ((tmp64 > ten2mk128trunc[ind - 1].w[1]
+	       || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		   && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0]))) {
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	  }	// else the result is exact
+	} else {	// the result is inexact; f2* <= 1/2
+	  is_inexact_gt_midpoint = 1;
+	}
+      }
+
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0) &&
+	  (fstar.w[1] || fstar.w[0]) &&
+	  (fstar.w[1] < ten2mk128trunc[ind - 1].w[1] ||
+	   (fstar.w[1] == ten2mk128trunc[ind - 1].w[1] &&
+	    fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	  is_inexact_gt_midpoint = 0;
+	} else {	// else MP in [ODD, EVEN]
+	  is_midpoint_lt_even = 1;
+	  is_inexact_gt_midpoint = 0;
+	}
+      }
+      // general correction for RZ
+      if (is_midpoint_lt_even || is_inexact_gt_midpoint) {
+	Cstar.w[0] = Cstar.w[0] - 1;
+      } else {
+	;	// exact, the result is already correct
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_xint
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xint, x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+     int is_inexact_gt_midpoint = 0;
+     int is_midpoint_lt_even = 0;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n <= -2^31 - 1 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x50000000aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x50000000a <=>
+	// C >= 0x50000000a * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1 up)
+	tmp64 = 0x50000000aull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x500000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000000 <=>
+	// C >= 0x500000000 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31-1/2 up)
+	tmp64 = 0x500000000ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 - 1 < n < 2^31
+  // 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) or n = +/-0.c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
+    res = 0x00000000;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1 < x <= -1 or 1 <= x < 2^31 so x can be rounded
+    // toward zero to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if (tmp64 > ten2mk128trunc[ind - 1].w[1]
+	      || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0])) {
+	    // 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;
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // 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;
+	  is_inexact_gt_midpoint = 1;
+	}
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] && (fstar.w[2] ||
+						   fstar.w[1]
+						   || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2]
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // 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;
+	  is_inexact_gt_midpoint = 1;
+	}
+      }
+
+      // if the result was a midpoint it was rounded away from zero, so
+      // it will need a correction
+      // check for midpoints
+      if ((fstar.w[3] == 0) && (fstar.w[2] == 0)
+	  && (fstar.w[1] || fstar.w[0])
+	  && (fstar.w[1] < ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] <= ten2mk128trunc[ind - 1].w[0]))) {
+	// the result is a midpoint; round to nearest
+	if (Cstar.w[0] & 0x01) {	// Cstar.w[0] is odd; MP in [EVEN, ODD]
+	  // if floor(C*) is odd C = floor(C*) - 1; the result >= 1
+	  Cstar.w[0]--;	// Cstar.w[0] is now even
+	  is_inexact_gt_midpoint = 0;
+	} else {	// else MP in [ODD, EVEN]
+	  is_midpoint_lt_even = 1;
+	  is_inexact_gt_midpoint = 0;
+	}
+      }
+      // general correction for RZ
+      if (is_midpoint_lt_even || is_inexact_gt_midpoint) {
+	Cstar.w[0] = Cstar.w[0] - 1;
+      } else {
+	;	// exact, the result is already correct
+      }
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_rninta
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_rninta,
+					  x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 P256;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n <= -2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x500000005ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005 <=>
+	// C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1/2 up)
+	tmp64 = 0x500000005ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x4fffffffbull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=>
+	// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31-1/2 up)
+	tmp64 = 0x4fffffffbull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 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 = 0x00000000;
+    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
+    //   res = +/-1
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    } else {	// 19 <= ind <= 33
+      if ((C1.w[1] < midpoint128[ind - 19].w[1])
+	  || ((C1.w[1] == midpoint128[ind - 19].w[1])
+	      && (C1.w[0] < midpoint128[ind - 19].w[0]))) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    }
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1/2 < x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded
+    // to nearest-away to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // if the result was a midpoint, it was already rounded away from zero
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+      // no need to check for midpoints - already rounded away from zero!
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_int32_xrninta
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (int, bid128_to_int32_xrninta,
+					  x)
+
+     int res;
+     UINT64 x_sign;
+     UINT64 x_exp;
+     int exp;			// unbiased exponent
+  // Note: C1.w[1], C1.w[0] represent x_signif_hi, x_signif_lo (all are UINT64)
+     UINT64 tmp64, tmp64A;
+     BID_UI64DOUBLE tmp1;
+     unsigned int x_nr_bits;
+     int q, ind, shift;
+     UINT128 C1, C;
+     UINT128 Cstar;		// C* represents up to 34 decimal digits ~ 113 bits
+     UINT256 fstar;
+     UINT256 P256;
+
+  // unpack x
+x_sign = x.w[1] & MASK_SIGN;	// 0 for positive, MASK_SIGN for negative
+x_exp = x.w[1] & MASK_EXP;	// biased and shifted left 49 bit positions
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+
+  // check for NaN or Infinity
+if ((x.w[1] & MASK_SPECIAL) == MASK_SPECIAL) {
+    // x is special
+if ((x.w[1] & MASK_NAN) == MASK_NAN) {	// x is NAN
+  if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {	// x is SNAN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+} else {	// x is not a NaN, so it must be infinity
+  if (!x_sign) {	// x is +inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+  }
+  BID_RETURN (res);
+}
+}
+  // check for non-canonical values (after the check for special values)
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x00000000;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x00000000;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // q = 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
+	tmp1.d = (double) (C1.w[0] >> 32);	// exact conversion
+	x_nr_bits =
+	  33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      } else {	// x < 2^32
+	tmp1.d = (double) (C1.w[0]);	// exact conversion
+	x_nr_bits =
+	  1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+      }
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+    }
+  } else {	// C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+    tmp1.d = (double) C1.w[1];	// exact conversion
+    x_nr_bits =
+      65 + ((((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.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))
+      q++;
+  }
+  exp = (x_exp >> 49) - 6176;
+  if ((q + exp) > 10) {	// x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x80000000;
+    BID_RETURN (res);
+  } else if ((q + exp) == 10) {	// x = c(0)c(1)...c(9).c(10)...c(q-1)
+    // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2...
+    // so x rounded to an integer may or may not fit in a signed 32-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 <= 10'
+    if (x_sign) {	// if n < 0 and q + exp = 10
+      // if n <= -2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31+1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x500000005ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x500000005 <=>
+	// C >= 0x500000005 * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31+1/2 up)
+	tmp64 = 0x500000005ull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    } else {	// if n > 0 and q + exp = 10
+      // if n >= 2^31 - 1/2 then n is too large
+      // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^31-1/2
+      // too large if 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb, 1<=q<=34
+      if (q <= 11) {
+	tmp64 = C1.w[0] * ten2k64[11 - q];	// C scaled up to 11-digit int
+	// c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits)
+	if (tmp64 >= 0x4fffffffbull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      } else {	// if (q > 11), i.e. 12 <= q <= 34 and so -24 <= exp <= -2
+	// 0.c(0)c(1)...c(q-1) * 10^11 >= 0x4fffffffb <=>
+	// C >= 0x4fffffffb * 10^(q-11) where 1 <= q - 11 <= 23
+	// (scale 2^31-1/2 up)
+	tmp64 = 0x4fffffffbull;
+	if (q - 11 <= 19) {	// 1 <= q - 11 <= 19; 10^(q-11) requires 64 bits
+	  __mul_64x64_to_128MACH (C, tmp64, ten2k64[q - 11]);
+	} else {	// 20 <= q - 11 <= 23, and 10^(q-11) requires 128 bits
+	  __mul_128x64_to_128 (C, tmp64, ten2k128[q - 31]);
+	}
+	if (C1.w[1] > C.w[1]
+	    || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x80000000;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 32-bit int fall through
+	// to '1 <= q + exp <= 10'
+      }
+    }
+  }
+  // n is not too large to be converted to int32: -2^31 - 1/2 < n < 2^31 - 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 = 0x00000000;
+    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
+    //   res = +/-1
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    } else {	// 19 <= ind <= 33
+      if ((C1.w[1] < midpoint128[ind - 19].w[1])
+	  || ((C1.w[1] == midpoint128[ind - 19].w[1])
+	      && (C1.w[0] < midpoint128[ind - 19].w[0]))) {
+	res = 0x00000000;	// return 0
+      } else if (x_sign) {	// n < 0
+	res = 0xffffffff;	// return -1
+      } else {	// n > 0
+	res = 0x00000001;	// return +1
+      }
+    }
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+  } else {	// if (1 <= q + exp <= 10, 1 <= q <= 34, -33 <= exp <= 9)
+    // -2^31-1/2 < x <= -1 or 1 <= x < 2^31-1/2 so x can be rounded
+    // to nearest-away to a 32-bit signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 10
+      ind = -exp;	// 1 <= ind <= 33; 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 127 bits
+      tmp64 = C1.w[0];
+      if (ind <= 19) {
+	C1.w[0] = C1.w[0] + midpoint64[ind - 1];
+      } else {
+	C1.w[0] = C1.w[0] + midpoint128[ind - 20].w[0];
+	C1.w[1] = C1.w[1] + midpoint128[ind - 20].w[1];
+      }
+      if (C1.w[0] < tmp64)
+	C1.w[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 <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = (C1 + 1/2 * 10^x) * 10^(-x)
+      // the approximation of 10^(-x) was rounded up to 118 bits
+      __mul_128x128_to_256 (P256, C1, ten2mk128[ind - 1]);
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[1] = P256.w[3];
+	Cstar.w[0] = P256.w[2];
+	fstar.w[3] = 0;
+	fstar.w[2] = P256.w[2] & maskhigh128[ind - 1];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[1] = 0;
+	Cstar.w[0] = P256.w[3];
+	fstar.w[3] = P256.w[3] & maskhigh128[ind - 1];
+	fstar.w[2] = P256.w[2];
+	fstar.w[1] = P256.w[1];
+	fstar.w[0] = P256.w[0];
+      }
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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-128 = shiftright128[ind]
+      shift = shiftright128[ind - 1];	// 0 <= shift <= 102
+      if (ind - 1 <= 21) {	// 0 <= ind - 1 <= 21
+	Cstar.w[0] =
+	  (Cstar.w[0] >> shift) | (Cstar.w[1] << (64 - shift));
+	// redundant, it will be 0! Cstar.w[1] = (Cstar.w[1] >> shift);
+      } else {	// 22 <= ind - 1 <= 33
+	Cstar.w[0] = (Cstar.w[0] >> (shift - 64));	// 2 <= shift - 64 <= 38
+      }
+      // if the result was a midpoint, it was already rounded away from zero
+      if (x_sign)
+	res = -Cstar.w[0];
+      else
+	res = Cstar.w[0];
+      // 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[1] > 0x8000000000000000ull || (fstar.w[1] == 0x8000000000000000ull && fstar.w[0] > 0x0ull)) {	// f* > 1/2 and the result may be exact
+	  tmp64 = fstar.w[1] - 0x8000000000000000ull;	// f* - 1/2
+	  if ((tmp64 > ten2mk128trunc[ind - 1].w[1]
+	       || (tmp64 == ten2mk128trunc[ind - 1].w[1]
+		   && fstar.w[0] >= ten2mk128trunc[ind - 1].w[0]))) {
+	    // 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 (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (fstar.w[3] > 0x0 ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] > onehalf128[ind - 1]) ||
+	    (fstar.w[3] == 0x0 && fstar.w[2] == onehalf128[ind - 1] &&
+	     (fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[2] - onehalf128[ind - 1];
+	  tmp64A = fstar.w[3];
+	  if (tmp64 > fstar.w[2])
+	    tmp64A--;
+	  if (tmp64A || tmp64
+	      || fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // 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 22 <= ind <= 33
+	if (fstar.w[3] > onehalf128[ind - 1] ||
+	    (fstar.w[3] == onehalf128[ind - 1] &&
+	     (fstar.w[2] || fstar.w[1] || fstar.w[0]))) {
+	  // f2* > 1/2 and the result may be exact
+	  // Calculate f2* - 1/2
+	  tmp64 = fstar.w[3] - onehalf128[ind - 1];
+	  if (tmp64 || fstar.w[2] ||
+	      fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	      || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		  && fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	    // 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;
+	}
+      }
+      // no need to check for midpoints - already rounded away from zero!
+    } else if (exp == 0) {
+      // 1 <= q <= 10
+      // res = +/-C (exact)
+      if (x_sign)
+	res = -C1.w[0];
+      else
+	res = C1.w[0];
+    } else {	// if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10
+      // res = +/-C * 10^exp (exact)
+      if (x_sign)
+	res = -C1.w[0] * ten2k64[exp];
+      else
+	res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}