Makefile.in (dfp-filenames): Replace decimal_globals...

libgcc/

2007-09-27  H.J. Lu  <hongjiu.lu@intel.com>

	* Makefile.in (dfp-filenames): Replace decimal_globals,
	decimal_data, binarydecimal and convert_data with
	bid_decimal_globals, bid_decimal_data, bid_binarydecimal
	and bid_convert_data, respectively.

libgcc/config/libbid/

2007-09-27  H.J. Lu  <hongjiu.lu@intel.com>

	* bid128_fromstring.c: Removed.

	* bid_dpd.c: New from libbid 2007-09-26.
	* bid128_to_int16.c: Likewise.
	* bid128_to_int8.c: Likewise.
	* bid128_to_uint8.c: Likewise.
	* bid128_to_uint16.c: Likewise.
	* bid64_to_int16.c: Likewise.
	* bid64_to_int8.c: Likewise.
	* bid64_to_uint16.c: Likewise.
	* bid64_to_uint8.c: Likewise.

	* bid128_2_str.h: Updated from libbid 2007-09-26.
	* bid128_2_str_macros.h: Likewise.
	* bid128_2_str_tables.c: Likewise.
	* bid128_add.c: Likewise.
	* bid128.c: Likewise.
	* bid128_compare.c: Likewise.
	* bid128_div.c: Likewise.
	* bid128_fma.c: Likewise.
	* bid128_logb.c: Likewise.
	* bid128_minmax.c: Likewise.
	* bid128_mul.c: Likewise.
	* bid128_next.c: Likewise.
	* bid128_noncomp.c: Likewise.
	* bid128_quantize.c: Likewise.
	* bid128_rem.c: Likewise.
	* bid128_round_integral.c: Likewise.
	* bid128_scalb.c: Likewise.
	* bid128_sqrt.c: Likewise.
	* bid128_string.c: Likewise.
	* bid128_to_int32.c: Likewise.
	* bid128_to_int64.c: Likewise.
	* bid128_to_uint32.c: Likewise.
	* bid128_to_uint64.c: Likewise.
	* bid32_to_bid128.c: Likewise.
	* bid32_to_bid64.c: Likewise.
	* bid64_add.c: Likewise.
	* bid64_compare.c: Likewise.
	* bid64_div.c: Likewise.
	* bid64_fma.c: Likewise.
	* bid64_logb.c: Likewise.
	* bid64_minmax.c: Likewise.
	* bid64_mul.c: Likewise.
	* bid64_next.c: Likewise.
	* bid64_noncomp.c: Likewise.
	* bid64_quantize.c: Likewise.
	* bid64_rem.c: Likewise.
	* bid64_round_integral.c: Likewise.
	* bid64_scalb.c: Likewise.
	* bid64_sqrt.c: Likewise.
	* bid64_string.c: Likewise.
	* bid64_to_bid128.c: Likewise.
	* bid64_to_int32.c: Likewise.
	* bid64_to_int64.c: Likewise.
	* bid64_to_uint32.c: Likewise.
	* bid64_to_uint64.c: Likewise.
	* bid_b2d.h: Likewise.
	* bid_binarydecimal.c: Likewise.
	* bid_conf.h: Likewise.
	* bid_convert_data.c: Likewise.
	* bid_decimal_data.c: Likewise.
	* bid_decimal_globals.c: Likewise.
	* bid_div_macros.h: Likewise.
	* bid_flag_operations.c: Likewise.
	* bid_from_int.c: Likewise.
	* bid_functions.h: Likewise.
	* bid_gcc_intrinsics.h: Likewise.
	* bid_inline_add.h: Likewise.
	* bid_internal.h: Likewise.
	* bid_round.c: Likewise.
	* bid_sqrt_macros.h: Likewise.
	* _addsub_dd.c: Likewise.
	* _addsub_sd.c: Likewise.
	* _addsub_td.c: Likewise.
	* _dd_to_df.c: Likewise.
	* _dd_to_di.c: Likewise.
	* _dd_to_sd.c: Likewise.
	* _dd_to_sf.c: Likewise.
	* _dd_to_si.c: Likewise.
	* _dd_to_td.c: Likewise.
	* _dd_to_tf.c: Likewise.
	* _dd_to_udi.c: Likewise.
	* _dd_to_usi.c: Likewise.
	* _dd_to_xf.c: Likewise.
	* _df_to_dd.c: Likewise.
	* _df_to_sd.c: Likewise.
	* _df_to_td.c: Likewise.
	* _di_to_dd.c: Likewise.
	* _di_to_sd.c: Likewise.
	* _di_to_td.c: Likewise.
	* _div_dd.c: Likewise.
	* _div_sd.c: Likewise.
	* _div_td.c: Likewise.
	* _eq_dd.c: Likewise.
	* _eq_sd.c: Likewise.
	* _eq_td.c: Likewise.
	* _ge_dd.c: Likewise.
	* _ge_sd.c: Likewise.
	* _ge_td.c: Likewise.
	* _gt_dd.c: Likewise.
	* _gt_sd.c: Likewise.
	* _gt_td.c: Likewise.
	* _isinfd128.c: Likewise.
	* _isinfd32.c: Likewise.
	* _isinfd64.c: Likewise.
	* _le_dd.c: Likewise.
	* _le_sd.c: Likewise.
	* _le_td.c: Likewise.
	* _lt_dd.c: Likewise.
	* _lt_sd.c: Likewise.
	* _lt_td.c: Likewise.
	* _mul_dd.c: Likewise.
	* _mul_sd.c: Likewise.
	* _mul_td.c: Likewise.
	* _ne_dd.c: Likewise.
	* _ne_sd.c: Likewise.
	* _ne_td.c: Likewise.
	* _sd_to_dd.c: Likewise.
	* _sd_to_df.c: Likewise.
	* _sd_to_di.c: Likewise.
	* _sd_to_sf.c: Likewise.
	* _sd_to_si.c: Likewise.
	* _sd_to_td.c: Likewise.
	* _sd_to_tf.c: Likewise.
	* _sd_to_udi.c: Likewise.
	* _sd_to_usi.c: Likewise.
	* _sd_to_xf.c: Likewise.
	* _sf_to_dd.c: Likewise.
	* _sf_to_sd.c: Likewise.
	* _sf_to_td.c: Likewise.
	* _si_to_dd.c: Likewise.
	* _si_to_sd.c: Likewise.
	* _si_to_td.c: Likewise.
	* _td_to_dd.c: Likewise.
	* _td_to_df.c: Likewise.
	* _td_to_di.c: Likewise.
	* _td_to_sd.c: Likewise.
	* _td_to_sf.c: Likewise.
	* _td_to_si.c: Likewise.
	* _td_to_tf.c: Likewise.
	* _td_to_udi.c: Likewise.
	* _td_to_usi.c: Likewise.
	* _td_to_xf.c: Likewise.
	* _tf_to_dd.c: Likewise.
	* _tf_to_sd.c: Likewise.
	* _tf_to_td.c: Likewise.
	* _udi_to_dd.c: Likewise.
	* _udi_to_sd.c: Likewise.
	* _udi_to_td.c: Likewise.
	* _unord_dd.c: Likewise.
	* _unord_sd.c: Likewise.
	* _unord_td.c: Likewise.
	* _usi_to_dd.c: Likewise.
	* _usi_to_sd.c: Likewise.
	* _usi_to_td.c: Likewise.
	* _xf_to_dd.c: Likewise.
	* _xf_to_sd.c: Likewise.
	* _xf_to_td.c: Likewise.

2007-09-27  H.J. Lu  <hongjiu.lu@intel.com>

	* b2d.h: Renamed to ...
	* bid_b2d.h: This.

	* bid128_to_string.c: Renamed to ...
	* bid128_string.c: This.

	* bid_intrinsics.h: Renamed to ...
	* bid_gcc_intrinsics.h: This.

	* bid_string.c: Renamed to ...
	* bid64_string.c: This.

	* binarydecimal.c: Renamed to ...
	* bid_decimal_globals.c: This.

	* convert_data.c: Renamed to ...
	* bid_convert_data.c: This.

	* decimal_data.c: Renamed to ...
	* bid_decimal_data.c: This.

	* decimal_globals.c: Renamed to ...
	* bid_decimal_globals.c: This.

	* div_macros.h: Renamed to ...
	* bid_div_macros.h: This.

	* inline_bid_add.h: Renamed to ...
	* bid_inline_add.h: This.

	* sqrt_macros.h: Renamed to ...
	* bid_sqrt_macros.h: This.

From-SVN: r128841

1 files changed, 2907 insertions, 2883 deletions

diff --git a/libgcc/config/libbid/bid128_to_uint64.c b/libgcc/config/libbid/bid128_to_uint64.c
index de6fd60e295..d8ec7110079 100644
--- a/libgcc/config/libbid/bid128_to_uint64.c
+++ b/libgcc/config/libbid/bid128_to_uint64.c
@@ -32,912 +32,1488 @@ Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
  *  BID128_to_uint64_rnint
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_rnint, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_rnint, x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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;
+     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];
+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) {
+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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      BID_RETURN (res);
-    }
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
   }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
-      tmp1.d = (double) C1.w[1]; // exact conversion
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
       x_nr_bits =
-	65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    q = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
-    }
-    exp = (x_exp >> 49) - 6176;
+  } 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) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n < -1/2 then n cannot be converted to uint64 with RN
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34
-	// <=> C * 10^(21-q) > 0x05, 1<=q<=34
-	if (q == 21) {
-	  // C > 5 
-	  if (C1.w[1] != 0 || C1.w[0] > 0x05ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //   C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
+  if ((q + exp) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n < -1/2 then n cannot be converted to uint64 with RN
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34
+      // <=> C * 10^(21-q) > 0x05, 1<=q<=34
+      if (q == 21) {
+	// C > 5 
+	if (C1.w[1] != 0 || C1.w[0] > 0x05ull) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // if n > 0 and q + exp = 20
-	// if n >= 2^64 - 1/2 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
-	// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 >= 0x9fffffffffffffffb
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) >= 0x9fffffffffffffffb
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
-	  C.w[0] = C1.w[0] + C1.w[0];
-	  C.w[1] = C1.w[1] + C1.w[1];
-	  if (C.w[0] < C1.w[0])
-	    C.w[1]++;
-	  if (C.w[1] > 0x01 || (C.w[1] == 0x01
-	      && C.w[0] >= 0xffffffffffffffffull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C >= 0x9fffffffffffffffb
-	  if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
-	      && C1.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
-	  C.w[1] = 0x09;
-	  C.w[0] = 0xfffffffffffffffbull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//   C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-    }
-    // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
-      // return 0
-      res = 0x0000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
-      // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
-      //   res = 0
-      // else if x > 0
-      //   res = +1
-      // else // if x < 0
-      //   invalid exc
-      ind = q - 1;
-      if (ind <= 18) { // 0 <= ind <= 18
-	if ((C1.w[1] == 0) && (C1.w[0] <= __bid_midpoint64[ind])) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
+    } else {	// if n > 0 and q + exp = 20
+      // if n >= 2^64 - 1/2 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
+      // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
+      if (q == 1) {
+	// C * 10^20 >= 0x9fffffffffffffffb
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q <= 19) {
+	// C * 10^(21-q) >= 0x9fffffffffffffffb
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 20) {
+	// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
+	C.w[0] = C1.w[0] + C1.w[0];
+	C.w[1] = C1.w[1] + C1.w[1];
+	if (C.w[0] < C1.w[0])
+	  C.w[1]++;
+	if (C.w[1] > 0x01 || (C.w[1] == 0x01
+			      && C.w[0] >= 0xffffffffffffffffull)) {
+	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-      } else { // 19 <= ind <= 33
-	if ((C1.w[1] < __bid_midpoint128[ind - 19].w[1])
-	    || ((C1.w[1] == __bid_midpoint128[ind - 19].w[1])
-	    && (C1.w[0] <= __bid_midpoint128[ind - 19].w[0]))) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 21) {
+	// C >= 0x9fffffffffffffffb
+	if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
+			       && C1.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
+	C.w[1] = 0x09;
+	C.w[0] = 0xfffffffffffffffbull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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 = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
       }
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
-      // to nearest to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
-	// set invalid flag
+    }
+  }
+  // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) < 0) {	// n = +/-0.0...c(0)c(1)...c(q-1)
+    // return 0
+    res = 0x0000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 0) {	// n = +/-0.c(0)c(1)...c(q-1)
+    // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
+    //   res = 0
+    // else if x > 0
+    //   res = +1
+    // else // if x < 0
+    //   invalid exc
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
+	res = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
+	res = 0x8000000000000000ull;
 	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
+      }
+    } 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 = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
 	res = 0x8000000000000000ull;
-	BID_RETURN (res);
+	*pfpsf |= INVALID_EXCEPTION;
       }
-      // 1 <= x < 2^64-1/2 so x can be rounded
-      // to nearest to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	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] + __bid_midpoint64[ind - 1];
-	} else {
-	  C1.w[0] = C1.w[0] + __bid_midpoint128[ind - 20].w[0];
-	  C1.w[1] = C1.w[1] + __bid_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
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_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, __bid_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] & __bid_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] & __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_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 = __bid_shiftright128[ind]
-	shift = __bid_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] < __bid_ten2mk128trunc[ind - 1].w[1]
-		|| (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-		&& fstar.w[0] <= __bid_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]
-	}
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
+    }
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
+    // to nearest to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
+      // set invalid flag
+      *pfpsf |= INVALID_EXCEPTION;
+      // return Integer Indefinite
+      res = 0x8000000000000000ull;
+      BID_RETURN (res);
+    }
+    // 1 <= x < 2^64-1/2 so x can be rounded
+    // to nearest to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      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 {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+	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]
       }
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }
 
 /*****************************************************************************
  *  BID128_to_uint64_xrnint
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xrnint, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_xrnint, x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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;
+     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];
+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) {
+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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      BID_RETURN (res);
-    }
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
   }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
-      tmp1.d = (double) C1.w[1]; // exact conversion
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
       x_nr_bits =
-	65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
-    }
-    q = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    exp = (x_exp >> 49) - 6176;
+  } 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) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n < -1/2 then n cannot be converted to uint64 with RN
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34
-	// <=> C * 10^(21-q) > 0x05, 1<=q<=34
-	if (q == 21) {
-	  // C > 5 
-	  if (C1.w[1] != 0 || C1.w[0] > 0x05ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //   C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
+  if ((q + exp) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n < -1/2 then n cannot be converted to uint64 with RN
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 > 0x05, 1<=q<=34
+      // <=> C * 10^(21-q) > 0x05, 1<=q<=34
+      if (q == 21) {
+	// C > 5 
+	if (C1.w[1] != 0 || C1.w[0] > 0x05ull) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // if n > 0 and q + exp = 20
-	// if n >= 2^64 - 1/2 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
-	// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 >= 0x9fffffffffffffffb
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) >= 0x9fffffffffffffffb
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
-	  C.w[0] = C1.w[0] + C1.w[0];
-	  C.w[1] = C1.w[1] + C1.w[1];
-	  if (C.w[0] < C1.w[0])
-	    C.w[1]++;
-	  if (C.w[1] > 0x01 || (C.w[1] == 0x01
-	      && C.w[0] >= 0xffffffffffffffffull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C >= 0x9fffffffffffffffb
-	  if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
-	      && C1.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
-	  C.w[1] = 0x09;
-	  C.w[0] = 0xfffffffffffffffbull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) > 5 is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//   C > 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-    }
-    // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-      // return 0
-      res = 0x0000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
-      // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
-      //   res = 0
-      // else if x > 0
-      //   res = +1
-      // else // if x < 0
-      //   invalid exc
-      ind = q - 1;
-      if (ind <= 18) { // 0 <= ind <= 18
-	if ((C1.w[1] == 0) && (C1.w[0] <= __bid_midpoint64[ind])) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
+    } else {	// if n > 0 and q + exp = 20
+      // if n >= 2^64 - 1/2 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
+      // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
+      if (q == 1) {
+	// C * 10^20 >= 0x9fffffffffffffffb
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q <= 19) {
+	// C * 10^(21-q) >= 0x9fffffffffffffffb
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // 19 <= ind <= 33
-	if ((C1.w[1] < __bid_midpoint128[ind - 19].w[1])
-	    || ((C1.w[1] == __bid_midpoint128[ind - 19].w[1])
-	    && (C1.w[0] <= __bid_midpoint128[ind - 19].w[0]))) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 20) {
+	// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
+	C.w[0] = C1.w[0] + C1.w[0];
+	C.w[1] = C1.w[1] + C1.w[1];
+	if (C.w[0] < C1.w[0])
+	  C.w[1]++;
+	if (C.w[1] > 0x01 || (C.w[1] == 0x01
+			      && C.w[0] >= 0xffffffffffffffffull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 21) {
+	// C >= 0x9fffffffffffffffb
+	if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
+			       && C1.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
+	C.w[1] = 0x09;
+	C.w[0] = 0xfffffffffffffffbull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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 = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
       }
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
-      // to nearest to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
-	// set invalid flag
+    }
+  }
+  // n is not too large to be converted to int64 if -1/2 <= n < 2^64 - 1/2
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) < 0) {	// n = +/-0.0...c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
+    res = 0x0000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 0) {	// n = +/-0.c(0)c(1)...c(q-1)
+    // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1)
+    //   res = 0
+    // else if x > 0
+    //   res = +1
+    // else // if x < 0
+    //   invalid exc
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] <= midpoint64[ind])) {
+	res = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
+	res = 0x8000000000000000ull;
 	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
+	BID_RETURN (res);
+      }
+    } 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 = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
 	res = 0x8000000000000000ull;
+	*pfpsf |= INVALID_EXCEPTION;
 	BID_RETURN (res);
       }
-      // 1 <= x < 2^64-1/2 so x can be rounded
-      // to nearest to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	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] + __bid_midpoint64[ind - 1];
-	} else {
-	  C1.w[0] = C1.w[0] + __bid_midpoint128[ind - 20].w[0];
-	  C1.w[1] = C1.w[1] + __bid_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
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_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, __bid_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] & __bid_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] & __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_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 = __bid_shiftright128[ind]
-	shift = __bid_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 > __bid_ten2mk128trunc[ind - 1].w[1]
-		 || (tmp64 == __bid_ten2mk128trunc[ind - 1].w[1]
-		 && fstar.w[0] >= __bid_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 inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
+    // to nearest to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
+      // set invalid flag
+      *pfpsf |= INVALID_EXCEPTION;
+      // return Integer Indefinite
+      res = 0x8000000000000000ull;
+      BID_RETURN (res);
+    }
+    // 1 <= x < 2^64-1/2 so x can be rounded
+    // to nearest to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      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 if (ind - 1 <= 21) { // if 3 <= ind <= 21
-	  if (fstar.w[3] > 0x0 || (fstar.w[3] == 0x0
-	      && fstar.w[2] > __bid_one_half128[ind - 1]) || (fstar.w[3] == 0x0
-	      && fstar.w[2] == __bid_one_half128[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] - __bid_one_half128[ind - 1];
-	    tmp64A = fstar.w[3];
-	    if (tmp64 > fstar.w[2])
-	      tmp64A--;
-	    if (tmp64A || tmp64
-		|| fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-		|| (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-		&& fstar.w[0] > __bid_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
+	  }	// 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 { // if 22 <= ind <= 33
-	  if (fstar.w[3] > __bid_one_half128[ind - 1]
-	      || (fstar.w[3] == __bid_one_half128[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] - __bid_one_half128[ind - 1];
-	    if (tmp64 || fstar.w[2]
-		|| fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-		|| (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-		&& fstar.w[0] > __bid_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
+	  }	// 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] < __bid_ten2mk128trunc[ind - 1].w[1]
-		|| (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-		&& fstar.w[0] <= __bid_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]
-	}
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+      // 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]
       }
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }
 
 /*****************************************************************************
  *  BID128_to_uint64_floor
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_floor, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_floor, x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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)
-  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;
+     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];
+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) {
+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
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // if n < 0 then n cannot be converted to uint64 with RM
+  if (x_sign) {	// if n < 0 and q + exp = 20
+    // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  }
+  // 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    // if n > 0 and q + exp = 20
+    // if n >= 2^64 then n is too large
+    // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
+    // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
+    // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
+    // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
+    if (q == 1) {
+      // C * 10^20 >= 0xa0000000000000000
+      __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+      if (C.w[1] >= 0x0a) {
+	// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
-      } else { // x is QNaN
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else if (q <= 19) {
+      // C * 10^(21-q) >= 0xa0000000000000000
+      __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+      if (C.w[1] >= 0x0a) {
+	// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-      BID_RETURN (res);
-    } else { // x is not a NaN, so it must be infinity
-      if (!x_sign) { // x is +inf
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else if (q == 20) {
+      // C >= 0x10000000000000000
+      if (C1.w[1] >= 0x01) {
+	// actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else if (q == 21) {
+      // C >= 0xa0000000000000000
+      if (C1.w[1] >= 0x0a) {
+	// actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
-      } else { // x is -inf
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+      // C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
+      C.w[1] = 0x0a;
+      C.w[0] = 0x0000000000000000ull;
+      __mul_128x64_to_128 (C, ten2k64[q - 21], C);
+      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 = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-      BID_RETURN (res);
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
     }
   }
-  // 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)) {
+  // n is not too large to be converted to int64 if 0 <= n < 2^64
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) <= 0) {	// n = +0.[0...0]c(0)c(1)...c(q-1)
+    // return 0
     res = 0x0000000000000000ull;
     BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // 1 <= x < 2^64 so x can be rounded
+    // down to a 64-bit unsigned signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      ind = -exp;	// 1 <= ind <= 33; ind is a synonym for 'x'
+      // chop off ind digits from the lower part of C1
+      // C1 fits in 127 bits
+      // calculate C* and f*
+      // C* is actually floor(C*) in this case
+      // C* and f* need shifting and masking, as shown by
+      // shiftright128[] and maskhigh128[]
+      // 1 <= x <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = C1 * 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
+      // 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
+      }
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_uint64_xfloor
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_xfloor, x)
+
+     UINT64 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)
+     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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else {	// x is not special and is not zero
+
+  // if n < 0 then n cannot be converted to uint64 with RM
+  if (x_sign) {	// if n < 0 and q + exp = 20
+    // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  }
+  // 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    // if n > 0 and q + exp = 20
+    // if n >= 2^64 then n is too large
+    // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
+    // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
+    // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
+    // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
+    if (q == 1) {
+      // C * 10^20 >= 0xa0000000000000000
+      __mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+      if (C.w[1] >= 0x0a) {
+	// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else if (q <= 19) {
+      // C * 10^(21-q) >= 0xa0000000000000000
+      __mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+      if (C.w[1] >= 0x0a) {
+	// actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else if (q == 20) {
+      // C >= 0x10000000000000000
+      if (C1.w[1] >= 0x01) {
+	// actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else if (q == 21) {
+      // C >= 0xa0000000000000000
+      if (C1.w[1] >= 0x0a) {
+	// actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+      // C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
+      C.w[1] = 0x0a;
+      C.w[0] = 0x0000000000000000ull;
+      __mul_128x64_to_128 (C, ten2k64[q - 21], C);
+      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 = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+      // else cases that can be rounded to a 64-bit int fall through
+      // to '1 <= q + exp <= 20'
+    }
+  }
+  // n is not too large to be converted to int64 if 0 <= n < 2^64
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) <= 0) {	// n = +0.[0...0]c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
     res = 0x0000000000000000ull;
     BID_RETURN (res);
-  } else { // x is not special and is not zero
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // 1 <= x < 2^64 so x can be rounded
+    // down to a 64-bit unsigned signed integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      ind = -exp;	// 1 <= ind <= 33; ind is a synonym for 'x'
+      // chop off ind digits from the lower part of C1
+      // C1 fits in 127 bits
+      // calculate C* and f*
+      // C* is actually floor(C*) in this case
+      // C* and f* need shifting and masking, as shown by
+      // shiftright128[] and maskhigh128[]
+      // 1 <= x <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = C1 * 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
+      // 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* < 10^(-x)) then
+      //   the result is exact
+      // else // if (f* > T*) then
+      //   the result is inexact
+      if (ind - 1 <= 2) {
+	if (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 if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (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 {	// if 22 <= ind <= 33
+	if (fstar.w[3] || 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
+      }
 
-    // if n < 0 then n cannot be converted to uint64 with RM
-    if (x_sign) { // if n < 0 and q + exp = 20
-      // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
-    // 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
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_uint64_ceil
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_ceil,
+					  x)
+
+     UINT64 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)
+     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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
-      tmp1.d = (double) C1.w[1]; // exact conversion
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
       x_nr_bits =
-	65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    q = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
-    }
-    exp = (x_exp >> 49) - 6176;
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      // if n > 0 and q + exp = 20
-      // if n >= 2^64 then n is too large
-      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
-      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
-      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
-      // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
+  } 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n <= -1 then n cannot be converted to uint64 with RZ
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
+      // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
+      if (q == 21) {
+	// C >= a 
+	if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+    } else {	// if n > 0 and q + exp = 20
+      // if n > 2^64 - 1 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) 
+      // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34
       if (q == 1) {
-	// C * 10^20 >= 0xa0000000000000000
-	__mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	if (C.w[1] >= 0x0a) {
-	  // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
+	// C * 10^20 > 0x9fffffffffffffff6
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] > 0xfffffffffffffff6ull)) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
@@ -947,10 +1523,10 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_floor, x)
 	// else cases that can be rounded to a 64-bit int fall through
 	// to '1 <= q + exp <= 20'
       } else if (q <= 19) {
-	// C * 10^(21-q) >= 0xa0000000000000000
-	__mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	if (C.w[1] >= 0x0a) {
-	  // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
+	// C * 10^(21-q) > 0x9fffffffffffffff6
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] > 0xfffffffffffffff6ull)) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
@@ -960,9 +1536,8 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_floor, x)
 	// else cases that can be rounded to a 64-bit int fall through
 	// to '1 <= q + exp <= 20'
       } else if (q == 20) {
-	// C >= 0x10000000000000000
-	if (C1.w[1] >= 0x01) {
-	  // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
+	// C > 0xffffffffffffffff
+	if (C1.w[1]) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
@@ -972,9 +1547,9 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_floor, x)
 	// else cases that can be rounded to a 64-bit int fall through
 	// to '1 <= q + exp <= 20'
       } else if (q == 21) {
-	// C >= 0xa0000000000000000
-	if (C1.w[1] >= 0x0a) {
-	  // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
+	// C > 0x9fffffffffffffff6
+	if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
+			       && C1.w[0] > 0xfffffffffffffff6ull)) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
@@ -983,12 +1558,12 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_floor, x)
 	}
 	// else cases that can be rounded to a 64-bit int fall through
 	// to '1 <= q + exp <= 20'
-      } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	// C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
-	C.w[1] = 0x0a;
-	C.w[0] = 0x0000000000000000ull;
-	__mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits
+	C.w[1] = 0x09;
+	C.w[0] = 0xfffffffffffffff6ull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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
@@ -999,189 +1574,612 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_floor, x)
 	// to '1 <= q + exp <= 20'
       }
     }
-    // n is not too large to be converted to int64 if 0 <= n < 2^64
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1)
-      // return 0
+  }
+  // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) <= 0) {	// n = +/-0.[0...0]c(0)c(1)...c(q-1)
+    // return 0 or 1
+    if (x_sign)
       res = 0x0000000000000000ull;
+    else
+      res = 0x0000000000000001ull;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
+    // to zero to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
+      // set invalid flag
+      *pfpsf |= INVALID_EXCEPTION;
+      // return Integer Indefinite
+      res = 0x8000000000000000ull;
       BID_RETURN (res);
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // 1 <= x < 2^64 so x can be rounded
-      // down to a 64-bit unsigned signed integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
-	// chop off ind digits from the lower part of C1
-	// C1 fits in 127 bits
-	// calculate C* and f*
-	// C* is actually floor(C*) in this case
-	// C* and f* need shifting and masking, as shown by
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_ten2mk128[ind - 1]
-	// C* = C1 * 10^(-x)
-	// the approximation of 10^(-x) was rounded up to 118 bits
-	__mul_128x128_to_256 (P256, C1, __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_ten2mk128trunc[0]=0x19999999999999999999999999999999
-	// 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 = __bid_shiftright128[ind]
-	shift = __bid_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
-	}
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+    }
+    // 1 <= x <= 2^64 - 1 so x can be rounded
+    // to zero to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      ind = -exp;	// 1 <= ind <= 33; ind is a synonym for 'x'
+      // chop off ind digits from the lower part of C1
+      // C1 fits in 127 bits
+      // calculate C* and f*
+      // C* is actually floor(C*) in this case
+      // C* and f* need shifting and masking, as shown by
+      // shiftright128[] and maskhigh128[]
+      // 1 <= x <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = C1 * 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
+      // 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 is positive and inexact, need to add 1 to it
+
+      // determine inexactness of the rounding of C*
+      // if (0 < f* < 10^(-x)) then
+      //   the result is exact
+      // else // if (f* > T*) then
+      //   the result is inexact
+      if (ind - 1 <= 2) {
+	if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	    || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	  if (!x_sign) {	// positive and inexact
+	    Cstar.w[0]++;
+	    if (Cstar.w[0] == 0x0)
+	      Cstar.w[1]++;
+	  }
+	}	// else the result is exact
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (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])) {
+	  if (!x_sign) {	// positive and inexact
+	    Cstar.w[0]++;
+	    if (Cstar.w[0] == 0x0)
+	      Cstar.w[1]++;
+	  }
+	}	// else the result is exact
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] || 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])) {
+	  if (!x_sign) {	// positive and inexact
+	    Cstar.w[0]++;
+	    if (Cstar.w[0] == 0x0)
+	      Cstar.w[1]++;
+	  }
+	}	// else the result is exact
       }
+
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }
 
 /*****************************************************************************
- *  BID128_to_uint64_xfloor
+ *  BID128_to_uint64_xceil
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xfloor, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_xceil, x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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)
-  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;
+     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];
+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) {
+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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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);
       }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
+    } 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n <= -1 then n cannot be converted to uint64 with RZ
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
+      // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
+      if (q == 21) {
+	// C >= a 
+	if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+    } else {	// if n > 0 and q + exp = 20
+      // if n > 2^64 - 1 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) 
+      // <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34
+      if (q == 1) {
+	// C * 10^20 > 0x9fffffffffffffff6
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] > 0xfffffffffffffff6ull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q <= 19) {
+	// C * 10^(21-q) > 0x9fffffffffffffff6
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] > 0xfffffffffffffff6ull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 20) {
+	// C > 0xffffffffffffffff
+	if (C1.w[1]) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 21) {
+	// C > 0x9fffffffffffffff6
+	if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
+			       && C1.w[0] > 0xfffffffffffffff6ull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits
+	C.w[1] = 0x09;
+	C.w[0] = 0xfffffffffffffff6ull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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 = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
       }
-      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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
+  // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) <= 0) {	// n = +/-0.[0...0]c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0 or 1
+    if (x_sign)
+      res = 0x0000000000000000ull;
+    else
+      res = 0x0000000000000001ull;
     BID_RETURN (res);
-  } else { // x is not special and is not zero
-
-    // if n < 0 then n cannot be converted to uint64 with RM
-    if (x_sign) { // if n < 0 and q + exp = 20
-      // too large if c(0)c(1)...c(19).c(20)...c(q-1) > 0
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
+    // to zero to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
       // set invalid flag
       *pfpsf |= INVALID_EXCEPTION;
       // return Integer Indefinite
       res = 0x8000000000000000ull;
       BID_RETURN (res);
     }
-    // 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
+    // 1 <= x <= 2^64 - 1 so x can be rounded
+    // to zero to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      ind = -exp;	// 1 <= ind <= 33; ind is a synonym for 'x'
+      // chop off ind digits from the lower part of C1
+      // C1 fits in 127 bits
+      // calculate C* and f*
+      // C* is actually floor(C*) in this case
+      // C* and f* need shifting and masking, as shown by
+      // shiftright128[] and maskhigh128[]
+      // 1 <= x <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = C1 * 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
+      // 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 is positive and inexact, need to add 1 to it
+
+      // determine inexactness of the rounding of C*
+      // if (0 < f* < 10^(-x)) then
+      //   the result is exact
+      // else // if (f* > T*) then
+      //   the result is inexact
+      if (ind - 1 <= 2) {
+	if (fstar.w[1] > ten2mk128trunc[ind - 1].w[1]
+	    || (fstar.w[1] == ten2mk128trunc[ind - 1].w[1]
+		&& fstar.w[0] > ten2mk128trunc[ind - 1].w[0])) {
+	  if (!x_sign) {	// positive and inexact
+	    Cstar.w[0]++;
+	    if (Cstar.w[0] == 0x0)
+	      Cstar.w[1]++;
+	  }
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	}	// else the result is exact
+      } else if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (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])) {
+	  if (!x_sign) {	// positive and inexact
+	    Cstar.w[0]++;
+	    if (Cstar.w[0] == 0x0)
+	      Cstar.w[1]++;
+	  }
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	}	// else the result is exact
+      } else {	// if 22 <= ind <= 33
+	if (fstar.w[3] || 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])) {
+	  if (!x_sign) {	// positive and inexact
+	    Cstar.w[0]++;
+	    if (Cstar.w[0] == 0x0)
+	      Cstar.w[1]++;
+	  }
+	  // set the inexact flag
+	  *pfpsf |= INEXACT_EXCEPTION;
+	}	// else the result is exact
+      }
+
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
+    }
+  }
+}
+
+BID_RETURN (res);
+}
+
+/*****************************************************************************
+ *  BID128_to_uint64_int
+ ****************************************************************************/
+
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_int,
+					  x)
+
+     UINT64 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)
+     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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
-      tmp1.d = (double) C1.w[1]; // exact conversion
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
       x_nr_bits =
-	65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    q = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
-    }
-    exp = (x_exp >> 49) - 6176;
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      // if n > 0 and q + exp = 20
+  } 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n <= -1 then n cannot be converted to uint64 with RZ
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
+      // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
+      if (q == 21) {
+	// C >= a 
+	if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
+      }
+    } else {	// if n > 0 and q + exp = 20
       // if n >= 2^64 then n is too large
       // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
       // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
@@ -1189,7 +2187,7 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xfloor, x)
       // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
       if (q == 1) {
 	// C * 10^20 >= 0xa0000000000000000
-	__mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
 	if (C.w[1] >= 0x0a) {
 	  // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
 	  // set invalid flag
@@ -1202,7 +2200,7 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xfloor, x)
 	// to '1 <= q + exp <= 20'
       } else if (q <= 19) {
 	// C * 10^(21-q) >= 0xa0000000000000000
-	__mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
 	if (C.w[1] >= 0x0a) {
 	  // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
 	  // set invalid flag
@@ -1237,12 +2235,13 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xfloor, x)
 	}
 	// else cases that can be rounded to a 64-bit int fall through
 	// to '1 <= q + exp <= 20'
-      } else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
 	// C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
 	C.w[1] = 0x0a;
 	C.w[0] = 0x0000000000000000ull;
-	__mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	if (C1.w[1] > C.w[1] || (C1.w[1] == C.w[1] && C1.w[0] >= C.w[0])) {
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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
@@ -1253,2130 +2252,1155 @@ BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xfloor, x)
 	// to '1 <= q + exp <= 20'
       }
     }
-    // n is not too large to be converted to int64 if 0 <= n < 2^64
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1)
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-      // return 0
-      res = 0x0000000000000000ull;
+  }
+  // n is not too large to be converted to int64 if -1 < n < 2^64
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) <= 0) {	// n = +/-0.[0...0]c(0)c(1)...c(q-1)
+    // return 0
+    res = 0x0000000000000000ull;
+    BID_RETURN (res);
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
+    // to zero to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
+      // set invalid flag
+      *pfpsf |= INVALID_EXCEPTION;
+      // return Integer Indefinite
+      res = 0x8000000000000000ull;
       BID_RETURN (res);
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // 1 <= x < 2^64 so x can be rounded
-      // down to a 64-bit unsigned signed integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
-	// chop off ind digits from the lower part of C1
-	// C1 fits in 127 bits
-	// calculate C* and f*
-	// C* is actually floor(C*) in this case
-	// C* and f* need shifting and masking, as shown by
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_ten2mk128[ind - 1]
-	// C* = C1 * 10^(-x)
-	// the approximation of 10^(-x) was rounded up to 118 bits
-	__mul_128x128_to_256 (P256, C1, __bid_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] & __bid_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] & __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_ten2mk128trunc[0]=0x19999999999999999999999999999999
-	// 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 = __bid_shiftright128[ind]
-	shift = __bid_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* < 10^(-x)) then
-	//   the result is exact
-	// else // if (f* > T*) then
-	//   the result is inexact
-	if (ind - 1 <= 2) {
-	  if (fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
-	  if (fstar.w[2] || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	} else { // if 22 <= ind <= 33
-	  if (fstar.w[3] || fstar.w[2]
-	      || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	}
-
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+    }
+    // 1 <= x < 2^64 so x can be rounded
+    // to zero to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      ind = -exp;	// 1 <= ind <= 33; ind is a synonym for 'x'
+      // chop off ind digits from the lower part of C1
+      // C1 fits in 127 bits
+      // calculate C* and f*
+      // C* is actually floor(C*) in this case
+      // C* and f* need shifting and masking, as shown by
+      // shiftright128[] and maskhigh128[]
+      // 1 <= x <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = C1 * 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
+      // 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
       }
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }
 
 /*****************************************************************************
- *  BID128_to_uint64_ceil
+ *  BID128_to_uint64_xint
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_ceil, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64, bid128_to_uint64_xint,
+					  x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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)
-  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;
+     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];
+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) {
+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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      BID_RETURN (res);
-    }
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
   }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
-      tmp1.d = (double) C1.w[1]; // exact conversion
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
       x_nr_bits =
-	65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    q = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
-    }
-    exp = (x_exp >> 49) - 6176;
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n <= -1 then n cannot be converted to uint64 with RZ
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
-	// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
-	if (q == 21) {
-	  // C >= a 
-	  if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
+  } 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n <= -1 then n cannot be converted to uint64 with RZ
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
+      // <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
+      if (q == 21) {
+	// C >= a 
+	if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // if n > 0 and q + exp = 20
-	// if n > 2^64 - 1 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) 
-	// <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 > 0x9fffffffffffffff6
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] > 0xfffffffffffffff6ull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) > 0x9fffffffffffffff6
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] > 0xfffffffffffffff6ull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C > 0xffffffffffffffff
-	  if (C1.w[1] > 0x0 || (C1.w[1] == 0x0
-	      && C1.w[0] > 0xffffffffffffffffull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C > 0x9fffffffffffffff6
-	  if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
-	      && C1.w[0] > 0xfffffffffffffff6ull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits
-	  C.w[1] = 0x09;
-	  C.w[0] = 0xfffffffffffffff6ull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
-      }
-    }
-    // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
-      // return 0 or 1
-      if (x_sign)
-	res = 0x0000000000000000ull;
-      else
-	res = 0x0000000000000001ull;
-      BID_RETURN (res);
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
-      // to zero to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
 	BID_RETURN (res);
       }
-      // 1 <= x <= 2^64 - 1 so x can be rounded
-      // to zero to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
-	// chop off ind digits from the lower part of C1
-	// C1 fits in 127 bits
-	// calculate C* and f*
-	// C* is actually floor(C*) in this case
-	// C* and f* need shifting and masking, as shown by
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_ten2mk128[ind - 1]
-	// C* = C1 * 10^(-x)
-	// the approximation of 10^(-x) was rounded up to 118 bits
-	__mul_128x128_to_256 (P256, C1, __bid_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] & __bid_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] & __bid_maskhigh128[ind - 1];
-	  fstar.w[2] = P256.w[2];
-	  fstar.w[1] = P256.w[1];
-	  fstar.w[0] = P256.w[0];
+    } else {	// if n > 0 and q + exp = 20
+      // if n >= 2^64 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
+      // <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
+      if (q == 1) {
+	// C * 10^20 >= 0xa0000000000000000
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] >= 0x0a) {
+	  // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-	// the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_ten2mk128trunc[0]=0x19999999999999999999999999999999
-	// 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 = __bid_shiftright128[ind]
-	shift = __bid_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
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q <= 19) {
+	// C * 10^(21-q) >= 0xa0000000000000000
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] >= 0x0a) {
+	  // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-	// if the result is positive and inexact, need to add 1 to it
-
-	// determine inexactness of the rounding of C*
-	// if (0 < f* < 10^(-x)) then
-	//   the result is exact
-	// else // if (f* > T*) then
-	//   the result is inexact
-	if (ind - 1 <= 2) {
-	  if (fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    if (!x_sign) { // positive and inexact
-	      Cstar.w[0]++;
-	      if (Cstar.w[0] == 0x0)
-		Cstar.w[1]++;
-	    }
-	  } // else the result is exact
-	} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
-	  if (fstar.w[2] || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    if (!x_sign) { // positive and inexact
-	      Cstar.w[0]++;
-	      if (Cstar.w[0] == 0x0)
-		Cstar.w[1]++;
-	    }
-	  } // else the result is exact
-	} else { // if 22 <= ind <= 33
-	  if (fstar.w[3] || fstar.w[2]
-	      || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    if (!x_sign) { // positive and inexact
-	      Cstar.w[0]++;
-	      if (Cstar.w[0] == 0x0)
-		Cstar.w[1]++;
-	    }
-	  } // else the result is exact
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 20) {
+	// C >= 0x10000000000000000
+	if (C1.w[1] >= 0x01) {
+	  // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
-      }
-    }
-  }
-  BID_RETURN (res);
-}
-
-/*****************************************************************************
- *  BID128_to_uint64_xceil
- ****************************************************************************/
-
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xceil, x)
-
-  UINT64 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)
-  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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 21) {
+	// C >= 0xa0000000000000000
+	if (C1.w[1] >= 0x0a) {
+	  // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
+	C.w[1] = 0x0a;
+	C.w[0] = 0x0000000000000000ull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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 = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
       }
-      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)) {
+  // n is not too large to be converted to int64 if -1 < n < 2^64
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) <= 0) {	// n = +/-0.[0...0]c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
     res = 0x0000000000000000ull;
     BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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 = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
-    }
-    exp = (x_exp >> 49) - 6176;
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
+    // to zero to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
       // set invalid flag
       *pfpsf |= INVALID_EXCEPTION;
       // return Integer Indefinite
       res = 0x8000000000000000ull;
       BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n <= -1 then n cannot be converted to uint64 with RZ
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
-	// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
-	if (q == 21) {
-	  // C >= a 
-	  if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
-	  // set invalid flag
-	  *pfpsf |= INVALID_EXCEPTION;
-	  // return Integer Indefinite
-	  res = 0x8000000000000000ull;
-	  BID_RETURN (res);
-	}
-      } else { // if n > 0 and q + exp = 20
-	// if n > 2^64 - 1 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) > 2^64 - 1
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 > 2^64 - 1
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 > 10 * (2^64 - 1) 
-	// <=> C * 10^(21-q) > 0x9fffffffffffffff6, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 > 0x9fffffffffffffff6
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] > 0xfffffffffffffff6ull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) > 0x9fffffffffffffff6
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] > 0xfffffffffffffff6ull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C > 0xffffffffffffffff
-	  if (C1.w[1] > 0x0 || (C1.w[1] == 0x0
-	      && C1.w[0] > 0xffffffffffffffffull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C > 0x9fffffffffffffff6
-	  if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
-	      && C1.w[0] > 0xfffffffffffffff6ull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  > 10^(q-21) * 0x9fffffffffffffff6 max 44 bits x 68 bits
-	  C.w[1] = 0x09;
-	  C.w[0] = 0xfffffffffffffff6ull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
-      }
     }
-    // n is not too large to be converted to int64 if -1 < n <= 2^64 - 1
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-      // return 0 or 1
-      if (x_sign)
-	res = 0x0000000000000000ull;
-      else
-	res = 0x0000000000000001ull;
-      BID_RETURN (res);
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
-      // to zero to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-	BID_RETURN (res);
+    // 1 <= x < 2^64 so x can be rounded
+    // to zero to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      ind = -exp;	// 1 <= ind <= 33; ind is a synonym for 'x'
+      // chop off ind digits from the lower part of C1
+      // C1 fits in 127 bits
+      // calculate C* and f*
+      // C* is actually floor(C*) in this case
+      // C* and f* need shifting and masking, as shown by
+      // shiftright128[] and maskhigh128[]
+      // 1 <= x <= 33
+      // kx = 10^(-x) = ten2mk128[ind - 1]
+      // C* = C1 * 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];
       }
-      // 1 <= x <= 2^64 - 1 so x can be rounded
-      // to zero to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
-	// chop off ind digits from the lower part of C1
-	// C1 fits in 127 bits
-	// calculate C* and f*
-	// C* is actually floor(C*) in this case
-	// C* and f* need shifting and masking, as shown by
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_ten2mk128[ind - 1]
-	// C* = C1 * 10^(-x)
-	// the approximation of 10^(-x) was rounded up to 118 bits
-	__mul_128x128_to_256 (P256, C1, __bid_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] & __bid_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] & __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_ten2mk128trunc[0]=0x19999999999999999999999999999999
-	// 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 = __bid_shiftright128[ind]
-	shift = __bid_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 is positive and inexact, need to add 1 to it
-
-	// determine inexactness of the rounding of C*
-	// if (0 < f* < 10^(-x)) then
-	//   the result is exact
-	// else // if (f* > T*) then
-	//   the result is inexact
-	if (ind - 1 <= 2) {
-	  if (fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    if (!x_sign) { // positive and inexact
-	      Cstar.w[0]++;
-	      if (Cstar.w[0] == 0x0)
-		Cstar.w[1]++;
-	    }
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
-	  if (fstar.w[2] || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    if (!x_sign) { // positive and inexact
-	      Cstar.w[0]++;
-	      if (Cstar.w[0] == 0x0)
-		Cstar.w[1]++;
-	    }
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	} else { // if 22 <= ind <= 33
-	  if (fstar.w[3] || fstar.w[2]
-	      || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    if (!x_sign) { // positive and inexact
-	      Cstar.w[0]++;
-	      if (Cstar.w[0] == 0x0)
-		Cstar.w[1]++;
-	    }
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	}
-
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+      // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind], e.g.
+      // if x=1, T*=ten2mk128trunc[0]=0x19999999999999999999999999999999
+      // 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* < 10^(-x)) then
+      //   the result is exact
+      // else // if (f* > T*) then
+      //   the result is inexact
+      if (ind - 1 <= 2) {
+	if (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 if (ind - 1 <= 21) {	// if 3 <= ind <= 21
+	if (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 {	// if 22 <= ind <= 33
+	if (fstar.w[3] || 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
+      }
+
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }
 
 /*****************************************************************************
- *  BID128_to_uint64_int
+ *  BID128_to_uint64_rninta
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_int, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_rninta, x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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)
-  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;
+     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];
+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) {
+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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      BID_RETURN (res);
-    }
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
   }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
-      tmp1.d = (double) C1.w[1]; // exact conversion
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
       x_nr_bits =
-	65 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
-    }
-    q = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    exp = (x_exp >> 49) - 6176;
-
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n <= -1 then n cannot be converted to uint64 with RZ
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
-	// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
-	if (q == 21) {
-	  // C >= a 
-	  if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
+  } 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n <= -1/2 then n cannot be converted to uint64 with RN
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34
+      // <=> C * 10^(21-q) >= 0x05, 1<=q<=34
+      if (q == 21) {
+	// C >= 5 
+	if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // if n > 0 and q + exp = 20
-	// if n >= 2^64 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
-	// <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 >= 0xa0000000000000000
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] >= 0x0a) {
-	    // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) >= 0xa0000000000000000
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] >= 0x0a) {
-	    // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C >= 0x10000000000000000
-	  if (C1.w[1] >= 0x01) {
-	    // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C >= 0xa0000000000000000
-	  if (C1.w[1] >= 0x0a) {
-	    // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
-	  C.w[1] = 0x0a;
-	  C.w[0] = 0x0000000000000000ull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
-      }
-    }
-    // n is not too large to be converted to int64 if -1 < n < 2^64
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
-      // return 0
-      res = 0x0000000000000000ull;
-      BID_RETURN (res);
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
-      // to zero to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//  C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
 	BID_RETURN (res);
       }
-      // 1 <= x < 2^64 so x can be rounded
-      // to zero to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
-	// chop off ind digits from the lower part of C1
-	// C1 fits in 127 bits
-	// calculate C* and f*
-	// C* is actually floor(C*) in this case
-	// C* and f* need shifting and masking, as shown by
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_ten2mk128[ind - 1]
-	// C* = C1 * 10^(-x)
-	// the approximation of 10^(-x) was rounded up to 118 bits
-	__mul_128x128_to_256 (P256, C1, __bid_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];
+    } else {	// if n > 0 and q + exp = 20
+      // if n >= 2^64 - 1/2 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
+      // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
+      if (q == 1) {
+	// C * 10^20 >= 0x9fffffffffffffffb
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-	// the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_ten2mk128trunc[0]=0x19999999999999999999999999999999
-	// 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 = __bid_shiftright128[ind]
-	shift = __bid_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
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q <= 19) {
+	// C * 10^(21-q) >= 0x9fffffffffffffffb
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 20) {
+	// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
+	C.w[0] = C1.w[0] + C1.w[0];
+	C.w[1] = C1.w[1] + C1.w[1];
+	if (C.w[0] < C1.w[0])
+	  C.w[1]++;
+	if (C.w[1] > 0x01 || (C.w[1] == 0x01
+			      && C.w[0] >= 0xffffffffffffffffull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 21) {
+	// C >= 0x9fffffffffffffffb
+	if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
+			       && C1.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
+	C.w[1] = 0x09;
+	C.w[0] = 0xfffffffffffffffbull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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 = 0x8000000000000000ull;
+	  BID_RETURN (res);
+	}
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
       }
     }
   }
-  BID_RETURN (res);
-}
-
-/*****************************************************************************
- *  BID128_to_uint64_xint
- ****************************************************************************/
-
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xint, x)
-
-  UINT64 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)
-  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 = 0x8000000000000000ull;
-      } else { // x is QNaN
+  // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) < 0) {	// n = +/-0.0...c(0)c(1)...c(q-1)
+    // return 0
+    res = 0x0000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 0) {	// n = +/-0.c(0)c(1)...c(q-1)
+    // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
+    //   res = 0
+    // else if x > 0
+    //   res = +1
+    // else // if x < 0
+    //   invalid exc
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
+	res = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
+    } 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 = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-      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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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 = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
     }
-    exp = (x_exp >> 49) - 6176;
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
+    // to nearest to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
       // set invalid flag
       *pfpsf |= INVALID_EXCEPTION;
       // return Integer Indefinite
       res = 0x8000000000000000ull;
       BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n <= -1 then n cannot be converted to uint64 with RZ
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x0a, 1<=q<=34
-	// <=> C * 10^(21-q) >= 0x0a, 1<=q<=34
-	if (q == 21) {
-	  // C >= a 
-	  if (C1.w[1] != 0 || C1.w[0] >= 0x0aull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) >= a is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //  C >= a * 10^(q-21) is true because C > 2^64 and a*10^(q-21) < 2^64
-	  // set invalid flag
-	  *pfpsf |= INVALID_EXCEPTION;
-	  // return Integer Indefinite
-	  res = 0x8000000000000000ull;
-	  BID_RETURN (res);
-	}
-      } else { // if n > 0 and q + exp = 20
-	// if n >= 2^64 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*2^65
-	// <=> C * 10^(21-q) >= 0xa0000000000000000, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 >= 0xa0000000000000000
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] >= 0x0a) {
-	    // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) >= 0xa0000000000000000
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] >= 0x0a) {
-	    // actually C.w[1] == 0x0a && C.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C >= 0x10000000000000000
-	  if (C1.w[1] >= 0x01) {
-	    // actually C1.w[1] == 0x01 && C1.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C >= 0xa0000000000000000
-	  if (C1.w[1] >= 0x0a) {
-	    // actually C1.w[1] == 0x0a && C1.w[0] >= 0x0000000000000000ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  >= 10^(q-21) * 0xa0000000000000000 max 44 bits x 68 bits
-	  C.w[1] = 0x0a;
-	  C.w[0] = 0x0000000000000000ull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
-      }
     }
-    // n is not too large to be converted to int64 if -1 < n < 2^64
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1)
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-      // return 0
-      res = 0x0000000000000000ull;
-      BID_RETURN (res);
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64 so if positive x can be rounded
-      // to zero to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-	BID_RETURN (res);
-      }
-      // 1 <= x < 2^64 so x can be rounded
-      // to zero to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	ind = -exp; // 1 <= ind <= 33; ind is a synonym for 'x'
-	// chop off ind digits from the lower part of C1
-	// C1 fits in 127 bits
-	// calculate C* and f*
-	// C* is actually floor(C*) in this case
-	// C* and f* need shifting and masking, as shown by
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_ten2mk128[ind - 1]
-	// C* = C1 * 10^(-x)
-	// the approximation of 10^(-x) was rounded up to 118 bits
-	__mul_128x128_to_256 (P256, C1, __bid_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] & __bid_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] & __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_ten2mk128trunc[0]=0x19999999999999999999999999999999
-	// 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 = __bid_shiftright128[ind]
-	shift = __bid_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* < 10^(-x)) then
-	//   the result is exact
-	// else // if (f* > T*) then
-	//   the result is inexact
-	if (ind - 1 <= 2) {
-	  if (fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	} else if (ind - 1 <= 21) { // if 3 <= ind <= 21
-	  if (fstar.w[2] || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	} else { // if 22 <= ind <= 33
-	  if (fstar.w[3] || fstar.w[2]
-	      || fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-	      || (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-	      && fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[0])) {
-	    // set the inexact flag
-	    *pfpsf |= INEXACT_EXCEPTION;
-	  } // else the result is exact
-	}
-
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
+    // 1 <= x < 2^64-1/2 so x can be rounded
+    // to nearest to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      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 {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+	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 rounded away from zero
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }
 
 /*****************************************************************************
- *  BID128_to_uint64_rninta
+ *  BID128_to_uint64_xrninta
  ****************************************************************************/
 
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_rninta, x)
+BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE (UINT64,
+					  bid128_to_uint64_xrninta, x)
 
-  UINT64 res;
-  UINT64 x_sign;
-  UINT64 x_exp;
-  int exp; 	// unbiased exponent
+     UINT64 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;
+     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];
+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) {
+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 = 0x8000000000000000ull;
-      } else { // x is QNaN
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      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 = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-      }
-      BID_RETURN (res);
-    }
+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 = 0x8000000000000000ull;
+  } else {	// x is QNaN
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
   }
+  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 = 0x8000000000000000ull;
+  } else {	// x is -inf
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+  }
+  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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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
+if ((C1.w[1] > 0x0001ed09bead87c0ull)
+    || (C1.w[1] == 0x0001ed09bead87c0ull
+	&& (C1.w[0] > 0x378d8e63ffffffffull))
+    || ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull)) {
+  res = 0x0000000000000000ull;
+  BID_RETURN (res);
+} else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
+  // x is 0
+  res = 0x0000000000000000ull;
+  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 { // 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 = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
+    } else {	// if x < 2^53
+      tmp1.d = (double) C1.w[0];	// exact conversion
+      x_nr_bits =
+	1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff);
     }
-    exp = (x_exp >> 49) - 6176;
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
-      // set invalid flag
-      *pfpsf |= INVALID_EXCEPTION;
-      // return Integer Indefinite
-      res = 0x8000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n <= -1/2 then n cannot be converted to uint64 with RN
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34
-	// <=> C * 10^(21-q) >= 0x05, 1<=q<=34
-	if (q == 21) {
-	  // C >= 5 
-	  if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //  C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
+  } 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) > 20) {	// x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set invalid flag
+    *pfpsf |= INVALID_EXCEPTION;
+    // return Integer Indefinite
+    res = 0x8000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 20) {	// x = c(0)c(1)...c(19).c(20)...c(q-1)
+    // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
+    // so x rounded to an integer may or may not fit in an unsigned 64-bit int
+    // the cases that do not fit are identified here; the ones that fit
+    // fall through and will be handled with other cases further,
+    // under '1 <= q + exp <= 20'
+    if (x_sign) {	// if n < 0 and q + exp = 20
+      // if n <= -1/2 then n cannot be converted to uint64 with RN
+      // too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2
+      // <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34
+      // <=> C * 10^(21-q) >= 0x05, 1<=q<=34
+      if (q == 21) {
+	// C >= 5 
+	if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // if n > 0 and q + exp = 20
-	// if n >= 2^64 - 1/2 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
-	// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 >= 0x9fffffffffffffffb
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) >= 0x9fffffffffffffffb
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
-	  C.w[0] = C1.w[0] + C1.w[0];
-	  C.w[1] = C1.w[1] + C1.w[1];
-	  if (C.w[0] < C1.w[0])
-	    C.w[1]++;
-	  if (C.w[1] > 0x01 || (C.w[1] == 0x01
-	      && C.w[0] >= 0xffffffffffffffffull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C >= 0x9fffffffffffffffb
-	  if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
-	      && C1.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
-	  C.w[1] = 0x09;
-	  C.w[0] = 0xfffffffffffffffbull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
+	// else cases that can be rounded to 64-bit unsigned int fall through
+	// to '1 <= q + exp <= 20'
+      } else {
+	// if 1 <= q <= 20
+	//   C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10
+	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	//  C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
+	// set invalid flag
+	*pfpsf |= INVALID_EXCEPTION;
+	// return Integer Indefinite
+	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-    }
-    // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
-      // return 0
-      res = 0x0000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
-      // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
-      //   res = 0
-      // else if x > 0
-      //   res = +1
-      // else // if x < 0
-      //   invalid exc
-      ind = q - 1;
-      if (ind <= 18) { // 0 <= ind <= 18
-	if ((C1.w[1] == 0) && (C1.w[0] < __bid_midpoint64[ind])) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
+    } else {	// if n > 0 and q + exp = 20
+      // if n >= 2^64 - 1/2 then n is too large
+      // <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
+      // <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
+      // <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
+      if (q == 1) {
+	// C * 10^20 >= 0x9fffffffffffffffb
+	__mul_128x64_to_128 (C, C1.w[0], ten2k128[0]);	// 10^20 * C
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      } else { // 19 <= ind <= 33
-	if ((C1.w[1] < __bid_midpoint128[ind - 19].w[1])
-	    || ((C1.w[1] == __bid_midpoint128[ind - 19].w[1])
-	    && (C1.w[0] < __bid_midpoint128[ind - 19].w[0]))) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q <= 19) {
+	// C * 10^(21-q) >= 0x9fffffffffffffffb
+	__mul_64x64_to_128MACH (C, C1.w[0], ten2k64[21 - q]);
+	if (C.w[1] > 0x09 || (C.w[1] == 0x09
+			      && C.w[0] >= 0xfffffffffffffffbull)) {
 	  // set invalid flag
 	  *pfpsf |= INVALID_EXCEPTION;
 	  // return Integer Indefinite
 	  res = 0x8000000000000000ull;
 	  BID_RETURN (res);
 	}
-      }
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
-      // to nearest to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-	BID_RETURN (res);
-      }
-      // 1 <= x < 2^64-1/2 so x can be rounded
-      // to nearest to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	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] + __bid_midpoint64[ind - 1];
-	} else {
-	  C1.w[0] = C1.w[0] + __bid_midpoint128[ind - 20].w[0];
-	  C1.w[1] = C1.w[1] + __bid_midpoint128[ind - 20].w[1];
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 20) {
+	// C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
+	C.w[0] = C1.w[0] + C1.w[0];
+	C.w[1] = C1.w[1] + C1.w[1];
+	if (C.w[0] < C1.w[0])
+	  C.w[1]++;
+	if (C.w[1] > 0x01 || (C.w[1] == 0x01
+			      && C.w[0] >= 0xffffffffffffffffull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-	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
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_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, __bid_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];
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else if (q == 21) {
+	// C >= 0x9fffffffffffffffb
+	if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
+			       && C1.w[0] >= 0xfffffffffffffffbull)) {
+	  // set invalid flag
+	  *pfpsf |= INVALID_EXCEPTION;
+	  // return Integer Indefinite
+	  res = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-	// the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_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 = __bid_shiftright128[ind]
-	shift = __bid_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
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
+      } else {	// if 22 <= q <= 34 => 1 <= q - 21 <= 13
+	// C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
+	C.w[1] = 0x09;
+	C.w[0] = 0xfffffffffffffffbull;
+	__mul_128x64_to_128 (C, ten2k64[q - 21], C);
+	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 = 0x8000000000000000ull;
+	  BID_RETURN (res);
 	}
-
-	// if the result was a midpoint it was rounded away from zero
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
+	// else cases that can be rounded to a 64-bit int fall through
+	// to '1 <= q + exp <= 20'
       }
     }
   }
-  BID_RETURN (res);
-}
-
-/*****************************************************************************
- *  BID128_to_uint64_xrninta
- ****************************************************************************/
-
-BID128_FUNCTION_ARG1_NORND_CUSTOMRESTYPE(UINT64, __bid128_to_uint64_xrninta, x)
-
-  UINT64 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
+  // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2
+  // Note: some of the cases tested for above fall through to this point
+  if ((q + exp) < 0) {	// n = +/-0.0...c(0)c(1)...c(q-1)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+    // return 0
+    res = 0x0000000000000000ull;
+    BID_RETURN (res);
+  } else if ((q + exp) == 0) {	// n = +/-0.c(0)c(1)...c(q-1)
+    // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
+    //   res = 0
+    // else if x > 0
+    //   res = +1
+    // else // if x < 0
+    //   invalid exc
+    ind = q - 1;
+    if (ind <= 18) {	// 0 <= ind <= 18
+      if ((C1.w[1] == 0) && (C1.w[0] < midpoint64[ind])) {
+	res = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
 	res = 0x8000000000000000ull;
-      } else { // x is QNaN
 	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-      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
+    } 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 = 0x0000000000000000ull;	// return 0
+      } else if (!x_sign) {	// n > 0
+	res = 0x00000001;	// return +1
+      } else {
 	res = 0x8000000000000000ull;
-      } else { // x is -inf
-	// set invalid flag
 	*pfpsf |= INVALID_EXCEPTION;
 	// return Integer Indefinite
 	res = 0x8000000000000000ull;
+	BID_RETURN (res);
       }
-      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 = 0x0000000000000000ull;
-    BID_RETURN (res);
-  } else if ((C1.w[1] == 0x0ull) && (C1.w[0] == 0x0ull)) {
-    // x is 0
-    res = 0x0000000000000000ull;
-    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 = __bid_nr_digits[x_nr_bits - 1].digits;
-    if (q == 0) {
-      q = __bid_nr_digits[x_nr_bits - 1].digits1;
-      if (C1.w[1] > __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  || (C1.w[1] == __bid_nr_digits[x_nr_bits - 1].threshold_hi
-	  && C1.w[0] >= __bid_nr_digits[x_nr_bits - 1].threshold_lo))
-	q++;
     }
-    exp = (x_exp >> 49) - 6176;
-
-    if ((q + exp) > 20) { // x >= 10^20 ~= 2^66.45... (cannot fit in 64 bits)
+    // set inexact flag
+    *pfpsf |= INEXACT_EXCEPTION;
+  } else {	// if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
+    // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
+    // to nearest to a 64-bit unsigned signed integer
+    if (x_sign) {	// x <= -1
       // set invalid flag
       *pfpsf |= INVALID_EXCEPTION;
       // return Integer Indefinite
       res = 0x8000000000000000ull;
       BID_RETURN (res);
-    } else if ((q + exp) == 20) { // x = c(0)c(1)...c(19).c(20)...c(q-1)
-      // in this case 2^63.11... ~= 10^19 <= x < 10^20 ~= 2^66.43...
-      // so x rounded to an integer may or may not fit in an unsigned 64-bit int
-      // the cases that do not fit are identified here; the ones that fit
-      // fall through and will be handled with other cases further,
-      // under '1 <= q + exp <= 20'
-      if (x_sign) { // if n < 0 and q + exp = 20
-	// if n <= -1/2 then n cannot be converted to uint64 with RN
-	// too large if c(0)c(1)...c(19).c(20)...c(q-1) >= 1/2
-	// <=> 0.c(0)c(1)...c(q-1) * 10^21 >= 0x05, 1<=q<=34
-	// <=> C * 10^(21-q) >= 0x05, 1<=q<=34
-	if (q == 21) {
-	  // C >= 5 
-	  if (C1.w[1] != 0 || C1.w[0] >= 0x05ull) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to 64-bit unsigned int fall through
-	  // to '1 <= q + exp <= 20'
-	} else {
-	  // if 1 <= q <= 20
-	  //   C * 10^(21-q) >= 5 is true because C >= 1 and 10^(21-q) >= 10
-	  // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  //  C >= 5 * 10^(q-21) is true because C > 2^64 and 5*10^(q-21) < 2^64
-	  // set invalid flag
-	  *pfpsf |= INVALID_EXCEPTION;
-	  // return Integer Indefinite
-	  res = 0x8000000000000000ull;
-	  BID_RETURN (res);
-	}
-      } else { // if n > 0 and q + exp = 20
-	// if n >= 2^64 - 1/2 then n is too large
-	// <=> c(0)c(1)...c(19).c(20)...c(q-1) >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^20 >= 2^64-1/2
-	// <=> 0.c(0)c(1)...c(19)c(20)...c(q-1) * 10^21 >= 5*(2^65-1)
-	// <=> C * 10^(21-q) >= 0x9fffffffffffffffb, 1<=q<=34
-	if (q == 1) {
-	  // C * 10^20 >= 0x9fffffffffffffffb
-	  __mul_128x64_to_128 (C, C1.w[0], __bid_ten2k128[0]); // 10^20 * C
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q <= 19) {
-	  // C * 10^(21-q) >= 0x9fffffffffffffffb
-	  __mul_64x64_to_128MACH (C, C1.w[0], __bid_ten2k64[21 - q]);
-	  if (C.w[1] > 0x09 || (C.w[1] == 0x09
-	      && C.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 20) {
-	  // C * 10 >= 0x9fffffffffffffffb <=> C * 2 > 1ffffffffffffffff
-	  C.w[0] = C1.w[0] + C1.w[0];
-	  C.w[1] = C1.w[1] + C1.w[1];
-	  if (C.w[0] < C1.w[0])
-	    C.w[1]++;
-	  if (C.w[1] > 0x01 || (C.w[1] == 0x01
-	      && C.w[0] >= 0xffffffffffffffffull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else if (q == 21) {
-	  // C >= 0x9fffffffffffffffb
-	  if (C1.w[1] > 0x09 || (C1.w[1] == 0x09
-	      && C1.w[0] >= 0xfffffffffffffffbull)) {
-	    // set invalid flag
-	    *pfpsf |= INVALID_EXCEPTION;
-	    // return Integer Indefinite
-	    res = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	} else { // if 22 <= q <= 34 => 1 <= q - 21 <= 13
-	  // C  >= 10^(q-21) * 0x9fffffffffffffffb max 44 bits x 68 bits
-	  C.w[1] = 0x09;
-	  C.w[0] = 0xfffffffffffffffbull;
-	  __mul_128x64_to_128 (C, __bid_ten2k64[q - 21], C);
-	  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 = 0x8000000000000000ull;
-	    BID_RETURN (res);
-	  }
-	  // else cases that can be rounded to a 64-bit int fall through
-	  // to '1 <= q + exp <= 20'
-	}
-      }
     }
-    // n is not too large to be converted to int64 if -1/2 < n < 2^64 - 1/2
-    // Note: some of the cases tested for above fall through to this point
-    if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1)
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-      // return 0
-      res = 0x0000000000000000ull;
-      BID_RETURN (res);
-    } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1)
-      // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1)
-      //   res = 0
-      // else if x > 0
-      //   res = +1
-      // else // if x < 0
-      //   invalid exc
-      ind = q - 1;
-      if (ind <= 18) { // 0 <= ind <= 18
-	if ((C1.w[1] == 0) && (C1.w[0] < __bid_midpoint64[ind])) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
-	  res = 0x8000000000000000ull;
-	  // set invalid flag
-	  *pfpsf |= INVALID_EXCEPTION;
-	  // return Integer Indefinite
-	  res = 0x8000000000000000ull;
-	  BID_RETURN (res);
-	}
-      } else { // 19 <= ind <= 33
-	if ((C1.w[1] < __bid_midpoint128[ind - 19].w[1])
-	    || ((C1.w[1] == __bid_midpoint128[ind - 19].w[1])
-	    && (C1.w[0] < __bid_midpoint128[ind - 19].w[0]))) {
-	  res = 0x0000000000000000ull; // return 0
-	} else if (!x_sign) { // n > 0
-	  res = 0x00000001; // return +1
-	} else {
-	  res = 0x8000000000000000ull;
-	  *pfpsf |= INVALID_EXCEPTION;
-	  // return Integer Indefinite
-	  res = 0x8000000000000000ull;
-	  BID_RETURN (res);
-	}
+    // 1 <= x < 2^64-1/2 so x can be rounded
+    // to nearest to a 64-bit unsigned integer
+    if (exp < 0) {	// 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
+      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];
       }
-      // set inexact flag
-      *pfpsf |= INEXACT_EXCEPTION;
-    } else { // if (1 <= q + exp <= 20, 1 <= q <= 34, -33 <= exp <= 19)
-      // x <= -1 or 1 <= x < 2^64-1/2 so if positive x can be rounded
-      // to nearest to a 64-bit unsigned signed integer
-      if (x_sign) { // x <= -1
-	// set invalid flag
-	*pfpsf |= INVALID_EXCEPTION;
-	// return Integer Indefinite
-	res = 0x8000000000000000ull;
-	BID_RETURN (res);
+      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];
       }
-      // 1 <= x < 2^64-1/2 so x can be rounded
-      // to nearest to a 64-bit unsigned integer
-      if (exp < 0) { // 2 <= q <= 34, -33 <= exp <= -1, 1 <= q + exp <= 20
-	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] + __bid_midpoint64[ind - 1];
-	} else {
-	  C1.w[0] = C1.w[0] + __bid_midpoint128[ind - 20].w[0];
-	  C1.w[1] = C1.w[1] + __bid_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
-	// __bid_shiftright128[] and __bid_maskhigh128[]
-	// 1 <= x <= 33
-	// kx = 10^(-x) = __bid_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, __bid_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] & __bid_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] & __bid_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* = __bid_ten2mk128trunc[ind], e.g.
-	// if x=1, T*=__bid_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 = __bid_shiftright128[ind]
-	shift = __bid_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 > __bid_ten2mk128trunc[ind - 1].w[1]
-		 || (tmp64 == __bid_ten2mk128trunc[ind - 1].w[1]
-		 && fstar.w[0] >= __bid_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
+      // 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 if (ind - 1 <= 21) { // if 3 <= ind <= 21
-	  if (fstar.w[3] > 0x0 || (fstar.w[3] == 0x0
-	      && fstar.w[2] > __bid_one_half128[ind - 1]) || (fstar.w[3] == 0x0
-	      && fstar.w[2] == __bid_one_half128[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] - __bid_one_half128[ind - 1];
-	    tmp64A = fstar.w[3];
-	    if (tmp64 > fstar.w[2])
-	      tmp64A--;
-	    if (tmp64A || tmp64
-		|| fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-		|| (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-		&& fstar.w[0] > __bid_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
+	  }	// 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 { // if 22 <= ind <= 33
-	  if (fstar.w[3] > __bid_one_half128[ind - 1] || 
-              (fstar.w[3] == __bid_one_half128[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] - __bid_one_half128[ind - 1];
-	    if (tmp64 || fstar.w[2]
-		|| fstar.w[1] > __bid_ten2mk128trunc[ind - 1].w[1]
-		|| (fstar.w[1] == __bid_ten2mk128trunc[ind - 1].w[1]
-		&& fstar.w[0] > __bid_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
+	  }	// 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
-	res = Cstar.w[0]; // the result is positive
-      } else if (exp == 0) {
-	// 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
-	// res = C (exact)
-	res = C1.w[0];
-      } else {
-	// if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
-	// res = C * 10^exp (exact) - must fit in 64 bits
-	res = C1.w[0] * __bid_ten2k64[exp];
       }
+
+      // if the result was a midpoint it was rounded away from zero
+      res = Cstar.w[0];	// the result is positive
+    } else if (exp == 0) {
+      // 1 <= q <= 20, but x < 2^64 - 1/2 so in this case C1.w[1] has to be 0
+      // res = C (exact)
+      res = C1.w[0];
+    } else {
+      // if (exp > 0) => 1 <= exp <= 19, 1 <= q < 19, 2 <= q + exp <= 20
+      // res = C * 10^exp (exact) - must fit in 64 bits
+      res = C1.w[0] * ten2k64[exp];
     }
   }
-  BID_RETURN (res);
+}
+
+BID_RETURN (res);
 }