CbC/CbC_gcc: libgcc/config/libbid/bid128

comparison libgcc/config/libbid/bid128_fma.c @ 0:a06113de4d67

first commit

author	kent <kent@cr.ie.u-ryukyu.ac.jp>
date	Fri, 17 Jul 2009 14:47:48 +0900
parents
children	04ced10e8804

comparison

equal deleted inserted replaced

--1:000000000000
+:a06113de4d67
+/* Copyright (C) 2007, 2009  Free Software Foundation, Inc.
+This file is part of GCC.
+GCC is free software; you can redistribute it and/or modify it under
+the terms of the GNU General Public License as published by the Free
+Software Foundation; either version 3, or (at your option) any later
+version.
+GCC is distributed in the hope that it will be useful, but WITHOUT ANY
+WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+for more details.
+Under Section 7 of GPL version 3, you are granted additional
+permissions described in the GCC Runtime Library Exception, version
+3.1, as published by the Free Software Foundation.
+You should have received a copy of the GNU General Public License and
+a copy of the GCC Runtime Library Exception along with this program;
+see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
+<http://www.gnu.org/licenses/>.  */
+/*****************************************************************************
+*
+*  BID128 fma   x * y + z
+*
+****************************************************************************/
+#include "bid_internal.h"
+static void
+rounding_correction (unsigned int rnd_mode,
+	     unsigned int is_inexact_lt_midpoint,
+	     unsigned int is_inexact_gt_midpoint,
+	     unsigned int is_midpoint_lt_even,
+	     unsigned int is_midpoint_gt_even,
+	     int unbexp,
+	     UINT128 * ptrres, _IDEC_flags * ptrfpsf) {
+// unbiased true exponent unbexp may be larger than emax
+UINT128 res = *ptrres; // expected to have the correct sign and coefficient
+// (the exponent field is ignored, as unbexp is used instead)
+UINT64 sign, exp;
+UINT64 C_hi, C_lo;
+// general correction from RN to RA, RM, RP, RZ
+// Note: if the result is negative, then is_inexact_lt_midpoint,
+// is_inexact_gt_midpoint, is_midpoint_lt_even, and is_midpoint_gt_even
+// have to be considered as if determined for the absolute value of the
+// result (so they seem to be reversed)
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even) {
+*ptrfpsf |= INEXACT_EXCEPTION;
+}
+// apply correction to result calculated with unbounded exponent
+sign = res.w[1] & MASK_SIGN;
+exp = (UINT64) (unbexp + 6176) << 49; // valid only if expmin<=unbexp<=expmax
+C_hi = res.w[1] & MASK_COEFF;
+C_lo = res.w[0];
+if ((!sign && ((rnd_mode == ROUNDING_UP && is_inexact_lt_midpoint) ||
+((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_UP) &&
+is_midpoint_gt_even))) ||
+(sign && ((rnd_mode == ROUNDING_DOWN && is_inexact_lt_midpoint) ||
+((rnd_mode == ROUNDING_TIES_AWAY || rnd_mode == ROUNDING_DOWN) &&
+is_midpoint_gt_even)))) {
+// C = C + 1
+C_lo = C_lo + 1;
+if (C_lo == 0)
+C_hi = C_hi + 1;
+if (C_hi == 0x0001ed09bead87c0ull && C_lo == 0x378d8e6400000000ull) {
+// C = 10^34 => rounding overflow
+C_hi = 0x0000314dc6448d93ull;
+C_lo = 0x38c15b0a00000000ull; // 10^33
+// exp = exp + EXP_P1;
+unbexp = unbexp + 1;
+exp = (UINT64) (unbexp + 6176) << 49;
+}
+} else if ((is_midpoint_lt_even || is_inexact_gt_midpoint) &&
+((sign && (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TO_ZERO)) ||
+(!sign && (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TO_ZERO)))) {
+// C = C - 1
+C_lo = C_lo - 1;
+if (C_lo == 0xffffffffffffffffull)
+C_hi--;
+// check if we crossed into the lower decade
+if (C_hi == 0x0000314dc6448d93ull && C_lo == 0x38c15b09ffffffffull) {
+// C = 10^33 - 1
+if (exp > 0) {
+C_hi = 0x0001ed09bead87c0ull; // 10^34 - 1
+C_lo = 0x378d8e63ffffffffull;
+// exp = exp - EXP_P1;
+unbexp = unbexp - 1;
+exp = (UINT64) (unbexp + 6176) << 49;
+} else { // if exp = 0
+if (is_midpoint_lt_even || is_midpoint_lt_even ||
+is_inexact_gt_midpoint || is_inexact_gt_midpoint) // tiny & inexact
+*ptrfpsf |= UNDERFLOW_EXCEPTION;
+}
+}
+} else {
+; // the result is already correct
+}
+if (unbexp > expmax) { // 6111
+*ptrfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+exp = 0;
+if (!sign) { // result is positive
+if (rnd_mode == ROUNDING_UP || rnd_mode == ROUNDING_TIES_AWAY) { // +inf
+C_hi = 0x7800000000000000ull;
+C_lo = 0x0000000000000000ull;
+} else { // res = +MAXFP = (10^34-1) * 10^emax
+C_hi = 0x5fffed09bead87c0ull;
+C_lo = 0x378d8e63ffffffffull;
+}
+} else { // result is negative
+if (rnd_mode == ROUNDING_DOWN || rnd_mode == ROUNDING_TIES_AWAY) { // -inf
+C_hi = 0xf800000000000000ull;
+C_lo = 0x0000000000000000ull;
+} else { // res = -MAXFP = -(10^34-1) * 10^emax
+C_hi = 0xdfffed09bead87c0ull;
+C_lo = 0x378d8e63ffffffffull;
+}
+}
+}
+// assemble the result
+res.w[1] = sign | exp | C_hi;
+res.w[0] = C_lo;
+*ptrres = res;
+}
+static void
+add256 (UINT256 x, UINT256 y, UINT256 * pz) {
+// *z = x + yl assume the sum fits in 256 bits
+UINT256 z;
+z.w[0] = x.w[0] + y.w[0];
+if (z.w[0] < x.w[0]) {
+x.w[1]++;
+if (x.w[1] == 0x0000000000000000ull) {
+x.w[2]++;
+if (x.w[2] == 0x0000000000000000ull) {
+x.w[3]++;
+}
+}
+}
+z.w[1] = x.w[1] + y.w[1];
+if (z.w[1] < x.w[1]) {
+x.w[2]++;
+if (x.w[2] == 0x0000000000000000ull) {
+x.w[3]++;
+}
+}
+z.w[2] = x.w[2] + y.w[2];
+if (z.w[2] < x.w[2]) {
+x.w[3]++;
+}
+z.w[3] = x.w[3] + y.w[3]; // it was assumed that no carry is possible
+*pz = z;
+}
+static void
+sub256 (UINT256 x, UINT256 y, UINT256 * pz) {
+// *z = x - y; assume x >= y
+UINT256 z;
+z.w[0] = x.w[0] - y.w[0];
+if (z.w[0] > x.w[0]) {
+x.w[1]--;
+if (x.w[1] == 0xffffffffffffffffull) {
+x.w[2]--;
+if (x.w[2] == 0xffffffffffffffffull) {
+x.w[3]--;
+}
+}
+}
+z.w[1] = x.w[1] - y.w[1];
+if (z.w[1] > x.w[1]) {
+x.w[2]--;
+if (x.w[2] == 0xffffffffffffffffull) {
+x.w[3]--;
+}
+}
+z.w[2] = x.w[2] - y.w[2];
+if (z.w[2] > x.w[2]) {
+x.w[3]--;
+}
+z.w[3] = x.w[3] - y.w[3]; // no borrow possible, because x >= y
+*pz = z;
+}
+static int
+nr_digits256 (UINT256 R256) {
+int ind;
+// determine the number of decimal digits in R256
+if (R256.w[3] == 0x0 && R256.w[2] == 0x0 && R256.w[1] == 0x0) {
+// between 1 and 19 digits
+for (ind = 1; ind <= 19; ind++) {
+if (R256.w[0] < ten2k64[ind]) {
+break;
+}
+}
+// ind digits
+} else if (R256.w[3] == 0x0 && R256.w[2] == 0x0 &&
+(R256.w[1] < ten2k128[0].w[1] ||
+(R256.w[1] == ten2k128[0].w[1]
+&& R256.w[0] < ten2k128[0].w[0]))) {
+// 20 digits
+ind = 20;
+} else if (R256.w[3] == 0x0 && R256.w[2] == 0x0) {
+// between 21 and 38 digits
+for (ind = 1; ind <= 18; ind++) {
+if (R256.w[1] < ten2k128[ind].w[1] ||
+(R256.w[1] == ten2k128[ind].w[1] &&
+R256.w[0] < ten2k128[ind].w[0])) {
+break;
+}
+}
+// ind + 20 digits
+ind = ind + 20;
+} else if (R256.w[3] == 0x0 &&
+(R256.w[2] < ten2k256[0].w[2] ||
+(R256.w[2] == ten2k256[0].w[2] &&
+R256.w[1] < ten2k256[0].w[1]) ||
+(R256.w[2] == ten2k256[0].w[2] &&
+R256.w[1] == ten2k256[0].w[1] &&
+R256.w[0] < ten2k256[0].w[0]))) {
+// 39 digits
+ind = 39;
+} else {
+// between 40 and 68 digits
+for (ind = 1; ind <= 29; ind++) {
+if (R256.w[3] < ten2k256[ind].w[3] ||
+(R256.w[3] == ten2k256[ind].w[3] &&
+R256.w[2] < ten2k256[ind].w[2]) ||
+(R256.w[3] == ten2k256[ind].w[3] &&
+R256.w[2] == ten2k256[ind].w[2] &&
+R256.w[1] < ten2k256[ind].w[1]) ||
+(R256.w[3] == ten2k256[ind].w[3] &&
+R256.w[2] == ten2k256[ind].w[2] &&
+R256.w[1] == ten2k256[ind].w[1] &&
+R256.w[0] < ten2k256[ind].w[0])) {
+break;
+}
+}
+// ind + 39 digits
+ind = ind + 39;
+}
+return (ind);
+}
+// add/subtract C4 and C3 * 10^scale; this may follow a previous rounding, so
+// use the rounding information from ptr_is_* to avoid a double rounding error
+static void
+add_and_round (int q3,
+int q4,
+int e4,
+int delta,
+int p34,
+UINT64 z_sign,
+UINT64 p_sign,
+UINT128 C3,
+UINT256 C4,
+int rnd_mode,
+int *ptr_is_midpoint_lt_even,
+int *ptr_is_midpoint_gt_even,
+int *ptr_is_inexact_lt_midpoint,
+int *ptr_is_inexact_gt_midpoint,
+_IDEC_flags * ptrfpsf, UINT128 * ptrres) {
+int scale;
+int x0;
+int ind;
+UINT64 R64;
+UINT128 P128, R128;
+UINT192 P192, R192;
+UINT256 R256;
+int is_midpoint_lt_even = 0;
+int is_midpoint_gt_even = 0;
+int is_inexact_lt_midpoint = 0;
+int is_inexact_gt_midpoint = 0;
+int is_midpoint_lt_even0 = 0;
+int is_midpoint_gt_even0 = 0;
+int is_inexact_lt_midpoint0 = 0;
+int is_inexact_gt_midpoint0 = 0;
+int incr_exp = 0;
+int is_tiny = 0;
+int lt_half_ulp = 0;
+int eq_half_ulp = 0;
+// int gt_half_ulp = 0;
+UINT128 res = *ptrres;
+// scale C3 up by 10^(q4-delta-q3), 0 <= q4-delta-q3 <= 2*P34-2 = 66
+scale = q4 - delta - q3; // 0 <= scale <= 66 (or 0 <= scale <= 68 if this
+// comes from Cases (2), (3), (4), (5), (6), with 0 <= |delta| <= 1
+// calculate C3 * 10^scale in R256 (it has at most 67 decimal digits for
+// Cases (15),(16),(17) and at most 69 for Cases (2),(3),(4),(5),(6))
+if (scale == 0) {
+R256.w[3] = 0x0ull;
+R256.w[2] = 0x0ull;
+R256.w[1] = C3.w[1];
+R256.w[0] = C3.w[0];
+} else if (scale <= 19) { // 10^scale fits in 64 bits
+P128.w[1] = 0;
+P128.w[0] = ten2k64[scale];
+__mul_128x128_to_256 (R256, P128, C3);
+} else if (scale <= 38) { // 10^scale fits in 128 bits
+__mul_128x128_to_256 (R256, ten2k128[scale - 20], C3);
+} else if (scale <= 57) { // 39 <= scale <= 57
+// 10^scale fits in 192 bits but C3 * 10^scale fits in 223 or 230 bits
+// (10^67 has 223 bits; 10^69 has 230 bits);
+// must split the computation:
+// 10^scale * C3 = 10*38 * 10^(scale-38) * C3 where 10^38 takes 127
+// bits and so 10^(scale-38) * C3 fits in 128 bits with certainty
+// Note that 1 <= scale - 38 <= 19 => 10^(scale-38) fits in 64 bits
+__mul_64x128_to_128 (R128, ten2k64[scale - 38], C3);
+// now multiply R128 by 10^38
+__mul_128x128_to_256 (R256, R128, ten2k128[18]);
+} else { // 58 <= scale <= 66
+// 10^scale takes between 193 and 220 bits,
+// and C3 * 10^scale fits in 223 bits (10^67/10^69 has 223/230 bits)
+// must split the computation:
+// 10^scale * C3 = 10*38 * 10^(scale-38) * C3 where 10^38 takes 127
+// bits and so 10^(scale-38) * C3 fits in 128 bits with certainty
+// Note that 20 <= scale - 38 <= 30 => 10^(scale-38) fits in 128 bits
+// Calculate first 10^(scale-38) * C3, which fits in 128 bits; because
+// 10^(scale-38) takes more than 64 bits, C3 will take less than 64
+__mul_64x128_to_128 (R128, C3.w[0], ten2k128[scale - 58]);
+// now calculate 10*38 * 10^(scale-38) * C3
+__mul_128x128_to_256 (R256, R128, ten2k128[18]);
+}
+// C3 * 10^scale is now in R256
+// for Cases (15), (16), (17) C4 > C3 * 10^scale because C4 has at least
+// one extra digit; for Cases (2), (3), (4), (5), or (6) any order is
+// possible
+// add/subtract C4 and C3 * 10^scale; the exponent is e4
+if (p_sign == z_sign) { // R256 = C4 + R256
+// calculate R256 = C4 + C3 * 10^scale = C4 + R256 which is exact,
+// but may require rounding
+add256 (C4, R256, &R256);
+} else { // if (p_sign != z_sign) { // R256 = C4 - R256
+// calculate R256 = C4 - C3 * 10^scale = C4 - R256 or
+// R256 = C3 * 10^scale - C4 = R256 - C4 which is exact,
+// but may require rounding
+// compare first R256 = C3 * 10^scale and C4
+if (R256.w[3] > C4.w[3] || (R256.w[3] == C4.w[3] && R256.w[2] > C4.w[2]) ||
+(R256.w[3] == C4.w[3] && R256.w[2] == C4.w[2] && R256.w[1] > C4.w[1]) ||
+(R256.w[3] == C4.w[3] && R256.w[2] == C4.w[2] && R256.w[1] == C4.w[1] &&
+R256.w[0] >= C4.w[0])) { // C3 * 10^scale >= C4
+// calculate R256 = C3 * 10^scale - C4 = R256 - C4, which is exact,
+// but may require rounding
+sub256 (R256, C4, &R256);
+// flip p_sign too, because the result has the sign of z
+p_sign = z_sign;
+} else { // if C4 > C3 * 10^scale
+// calculate R256 = C4 - C3 * 10^scale = C4 - R256, which is exact,
+// but may require rounding
+sub256 (C4, R256, &R256);
+}
+// if the result is pure zero, the sign depends on the rounding mode
+// (x*y and z had opposite signs)
+if (R256.w[3] == 0x0ull && R256.w[2] == 0x0ull &&
+R256.w[1] == 0x0ull && R256.w[0] == 0x0ull) {
+if (rnd_mode != ROUNDING_DOWN)
+p_sign = 0x0000000000000000ull;
+else
+p_sign = 0x8000000000000000ull;
+// the exponent is max (e4, expmin)
+if (e4 < -6176)
+e4 = expmin;
+// assemble result
+res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49);
+res.w[0] = 0x0;
+*ptrres = res;
+return;
+}
+}
+// determine the number of decimal digits in R256
+ind = nr_digits256 (R256);
+// the exact result is (-1)^p_sign * R256 * 10^e4 where q (R256) = ind;
+// round to the destination precision, with unbounded exponent
+if (ind <= p34) {
+// result rounded to the destination precision with unbounded exponent
+// is exact
+if (ind + e4 < p34 + expmin) {
+is_tiny = 1; // applies to all rounding modes
+}
+res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | R256.w[1];
+res.w[0] = R256.w[0];
+// Note: res is correct only if expmin <= e4 <= expmax
+} else { // if (ind > p34)
+// if more than P digits, round to nearest to P digits
+// round R256 to p34 digits
+x0 = ind - p34; // 1 <= x0 <= 34 as 35 <= ind <= 68
+if (ind <= 38) {
+P128.w[1] = R256.w[1];
+P128.w[0] = R256.w[0];
+round128_19_38 (ind, x0, P128, &R128, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+} else if (ind <= 57) {
+P192.w[2] = R256.w[2];
+P192.w[1] = R256.w[1];
+P192.w[0] = R256.w[0];
+round192_39_57 (ind, x0, P192, &R192, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+R128.w[1] = R192.w[1];
+R128.w[0] = R192.w[0];
+} else { // if (ind <= 68)
+round256_58_76 (ind, x0, R256, &R256, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+R128.w[1] = R256.w[1];
+R128.w[0] = R256.w[0];
+}
+// the rounded result has p34 = 34 digits
+e4 = e4 + x0 + incr_exp;
+if (rnd_mode == ROUNDING_TO_NEAREST) {
+if (e4 < expmin) {
+is_tiny = 1; // for other rounding modes apply correction
+}
+} else {
+// for RM, RP, RZ, RA apply correction in order to determine tininess
+// but do not save the result; apply the correction to
+// (-1)^p_sign * significand * 10^0
+P128.w[1] = p_sign | 0x3040000000000000ull | R128.w[1];
+P128.w[0] = R128.w[0];
+rounding_correction (rnd_mode,
+		   is_inexact_lt_midpoint,
+		   is_inexact_gt_midpoint, is_midpoint_lt_even,
+		   is_midpoint_gt_even, 0, &P128, ptrfpsf);
+scale = ((P128.w[1] & MASK_EXP) >> 49) - 6176; // -1, 0, or +1
+// the number of digits in the significand is p34 = 34
+if (e4 + scale < expmin) {
+is_tiny = 1;
+}
+}
+ind = p34; // the number of decimal digits in the signifcand of res
+res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | R128.w[1]; // RN
+res.w[0] = R128.w[0];
+// Note: res is correct only if expmin <= e4 <= expmax
+// set the inexact flag after rounding with bounded exponent, if any
+}
+// at this point we have the result rounded with unbounded exponent in
+// res and we know its tininess:
+// res = (-1)^p_sign * significand * 10^e4,
+// where q (significand) = ind <= p34
+// Note: res is correct only if expmin <= e4 <= expmax
+// check for overflow if RN
+if (rnd_mode == ROUNDING_TO_NEAREST && (ind + e4) > (p34 + expmax)) {
+res.w[1] = p_sign | 0x7800000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+*ptrres = res;
+*ptrfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+return; // BID_RETURN (res)
+} // else not overflow or not RN, so continue
+// if (e4 >= expmin) we have the result rounded with bounded exponent
+if (e4 < expmin) {
+x0 = expmin - e4; // x0 >= 1; the number of digits to chop off of res
+// where the result rounded [at most] once is
+//   (-1)^p_sign * significand_res * 10^e4
+// avoid double rounding error
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+if (x0 > ind) {
+// nothing is left of res when moving the decimal point left x0 digits
+is_inexact_lt_midpoint = 1;
+res.w[1] = p_sign | 0x0000000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+e4 = expmin;
+} else if (x0 == ind) { // 1 <= x0 = ind <= p34 = 34
+// this is <, =, or > 1/2 ulp
+// compare the ind-digit value in the significand of res with
+// 1/2 ulp = 5*10^(ind-1), i.e. determine whether it is
+// less than, equal to, or greater than 1/2 ulp (significand of res)
+R128.w[1] = res.w[1] & MASK_COEFF;
+R128.w[0] = res.w[0];
+if (ind <= 19) {
+if (R128.w[0] < midpoint64[ind - 1]) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (R128.w[0] == midpoint64[ind - 1]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+// gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+} else { // if (ind <= 38) {
+if (R128.w[1] < midpoint128[ind - 20].w[1] ||
+(R128.w[1] == midpoint128[ind - 20].w[1] &&
+R128.w[0] < midpoint128[ind - 20].w[0])) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (R128.w[1] == midpoint128[ind - 20].w[1] &&
+R128.w[0] == midpoint128[ind - 20].w[0]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+// gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+}
+if (lt_half_ulp || eq_half_ulp) {
+// res = +0.0 * 10^expmin
+res.w[1] = 0x0000000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+} else { // if (gt_half_ulp)
+// res = +1 * 10^expmin
+res.w[1] = 0x0000000000000000ull;
+res.w[0] = 0x0000000000000001ull;
+}
+res.w[1] = p_sign | res.w[1];
+e4 = expmin;
+} else { // if (1 <= x0 <= ind - 1 <= 33)
+// round the ind-digit result to ind - x0 digits
+if (ind <= 18) { // 2 <= ind <= 18
+round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+res.w[1] = 0x0;
+res.w[0] = R64;
+} else if (ind <= 38) {
+P128.w[1] = res.w[1] & MASK_COEFF;
+P128.w[0] = res.w[0];
+round128_19_38 (ind, x0, P128, &res, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+}
+e4 = e4 + x0; // expmin
+// we want the exponent to be expmin, so if incr_exp = 1 then
+// multiply the rounded result by 10 - it will still fit in 113 bits
+if (incr_exp) {
+// 64 x 128 -> 128
+P128.w[1] = res.w[1] & MASK_COEFF;
+P128.w[0] = res.w[0];
+__mul_64x128_to_128 (res, ten2k64[1], P128);
+}
+res.w[1] =
+p_sign | ((UINT64) (e4 + 6176) << 49) | (res.w[1] & MASK_COEFF);
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// Note: a double rounding error upward is not possible; for this
+// the result after the first rounding would have to be 99...95
+// (35 digits in all), possibly followed by a number of zeros; this
+// is not possible in Cases (2)-(6) or (15)-(17) which may get here
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	 !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	 (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	 (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+}
+}
+// res contains the correct result
+// apply correction if not rounding to nearest
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		 is_inexact_lt_midpoint, is_inexact_gt_midpoint,
+		 is_midpoint_lt_even, is_midpoint_gt_even,
+		 e4, &res, ptrfpsf);
+}
+if (is_midpoint_lt_even || is_midpoint_gt_even ||
+is_inexact_lt_midpoint || is_inexact_gt_midpoint) {
+// set the inexact flag
+*ptrfpsf |= INEXACT_EXCEPTION;
+if (is_tiny)
+*ptrfpsf |= UNDERFLOW_EXCEPTION;
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+*ptrres = res;
+return;
+}
+#if DECIMAL_CALL_BY_REFERENCE
+static void
+bid128_ext_fma (int *ptr_is_midpoint_lt_even,
+	int *ptr_is_midpoint_gt_even,
+	int *ptr_is_inexact_lt_midpoint,
+	int *ptr_is_inexact_gt_midpoint, UINT128 * pres,
+	UINT128 * px, UINT128 * py,
+	UINT128 *
+	pz _RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+	_EXC_INFO_PARAM) {
+UINT128 x = *px, y = *py, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+static UINT128
+bid128_ext_fma (int *ptr_is_midpoint_lt_even,
+	int *ptr_is_midpoint_gt_even,
+	int *ptr_is_inexact_lt_midpoint,
+	int *ptr_is_inexact_gt_midpoint, UINT128 x, UINT128 y,
+	UINT128 z _RND_MODE_PARAM _EXC_FLAGS_PARAM
+	_EXC_MASKS_PARAM _EXC_INFO_PARAM) {
+#endif
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT64 x_sign, y_sign, z_sign, p_sign, tmp_sign;
+UINT64 x_exp = 0, y_exp = 0, z_exp = 0, p_exp;
+int true_p_exp;
+UINT128 C1, C2, C3;
+UINT256 C4;
+int q1 = 0, q2 = 0, q3 = 0, q4;
+int e1, e2, e3, e4;
+int scale, ind, delta, x0;
+int p34 = P34; // used to modify the limit on the number of digits
+BID_UI64DOUBLE tmp;
+int x_nr_bits, y_nr_bits, z_nr_bits;
+unsigned int save_fpsf;
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0;
+int is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+int is_midpoint_lt_even0 = 0, is_midpoint_gt_even0 = 0;
+int is_inexact_lt_midpoint0 = 0, is_inexact_gt_midpoint0 = 0;
+int incr_exp = 0;
+int lsb;
+int lt_half_ulp = 0;
+int eq_half_ulp = 0;
+int gt_half_ulp = 0;
+int is_tiny = 0;
+UINT64 R64, tmp64;
+UINT128 P128, R128;
+UINT192 P192, R192;
+UINT256 R256;
+// the following are based on the table of special cases for fma; the NaN
+// behavior is similar to that of the IA-64 Architecture fma
+// identify cases where at least one operand is NaN
+BID_SWAP128 (x);
+BID_SWAP128 (y);
+BID_SWAP128 (z);
+if ((y.w[1] & MASK_NAN) == MASK_NAN) { // y is NAN
+// if x = {0, f, inf, NaN}, y = NaN, z = {0, f, inf, NaN} then res = Q (y)
+// check first for non-canonical NaN payload
+if (((y.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+(((y.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+(y.w[0] > 0x38c15b09ffffffffull))) {
+y.w[1] = y.w[1] & 0xffffc00000000000ull;
+y.w[0] = 0x0ull;
+}
+if ((y.w[1] & MASK_SNAN) == MASK_SNAN) { // y is SNAN
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+// return quiet (y)
+res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
+res.w[0] = y.w[0];
+} else { // y is QNaN
+// return y
+res.w[1] = y.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
+res.w[0] = y.w[0];
+// if z = SNaN or x = SNaN signal invalid exception
+if ((z.w[1] & MASK_SNAN) == MASK_SNAN ||
+(x.w[1] & MASK_SNAN) == MASK_SNAN) {
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+}
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if ((z.w[1] & MASK_NAN) == MASK_NAN) { // z is NAN
+// if x = {0, f, inf, NaN}, y = {0, f, inf}, z = NaN then res = Q (z)
+// check first for non-canonical NaN payload
+if (((z.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+(((z.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+(z.w[0] > 0x38c15b09ffffffffull))) {
+z.w[1] = z.w[1] & 0xffffc00000000000ull;
+z.w[0] = 0x0ull;
+}
+if ((z.w[1] & MASK_SNAN) == MASK_SNAN) { // z is SNAN
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+// return quiet (z)
+res.w[1] = z.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
+res.w[0] = z.w[0];
+} else { // z is QNaN
+// return z
+res.w[1] = z.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
+res.w[0] = z.w[0];
+// if x = SNaN signal invalid exception
+if ((x.w[1] & MASK_SNAN) == MASK_SNAN) {
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+}
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if ((x.w[1] & MASK_NAN) == MASK_NAN) { // x is NAN
+// if x = NaN, y = {0, f, inf}, z = {0, f, inf} then res = Q (x)
+// check first for non-canonical NaN payload
+if (((x.w[1] & 0x00003fffffffffffull) > 0x0000314dc6448d93ull) ||
+(((x.w[1] & 0x00003fffffffffffull) == 0x0000314dc6448d93ull) &&
+(x.w[0] > 0x38c15b09ffffffffull))) {
+x.w[1] = x.w[1] & 0xffffc00000000000ull;
+x.w[0] = 0x0ull;
+}
+if ((x.w[1] & MASK_SNAN) == MASK_SNAN) { // x is SNAN
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+// return quiet (x)
+res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out also G[6]-G[16]
+res.w[0] = x.w[0];
+} else { // x is QNaN
+// return x
+res.w[1] = x.w[1] & 0xfc003fffffffffffull; // clear out G[6]-G[16]
+res.w[0] = x.w[0];
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+// x, y, z are 0, f, or inf but not NaN => unpack the arguments and check
+// for non-canonical values
+x_sign = x.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+C1.w[1] = x.w[1] & MASK_COEFF;
+C1.w[0] = x.w[0];
+if ((x.w[1] & MASK_ANY_INF) != MASK_INF) { // x != inf
+// if x is not infinity check for non-canonical values - treated as zero
+if ((x.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
+// non-canonical
+x_exp = (x.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
+C1.w[1] = 0; // significand high
+C1.w[0] = 0; // significand low
+} else { // G0_G1 != 11
+x_exp = x.w[1] & MASK_EXP; // biased and shifted left 49 bits
+if (C1.w[1] > 0x0001ed09bead87c0ull ||
+(C1.w[1] == 0x0001ed09bead87c0ull &&
+C1.w[0] > 0x378d8e63ffffffffull)) {
+// x is non-canonical if coefficient is larger than 10^34 -1
+C1.w[1] = 0;
+C1.w[0] = 0;
+} else { // canonical
+;
+}
+}
+}
+y_sign = y.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+C2.w[1] = y.w[1] & MASK_COEFF;
+C2.w[0] = y.w[0];
+if ((y.w[1] & MASK_ANY_INF) != MASK_INF) { // y != inf
+// if y is not infinity check for non-canonical values - treated as zero
+if ((y.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
+// non-canonical
+y_exp = (y.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
+C2.w[1] = 0; // significand high
+C2.w[0] = 0; // significand low
+} else { // G0_G1 != 11
+y_exp = y.w[1] & MASK_EXP; // biased and shifted left 49 bits
+if (C2.w[1] > 0x0001ed09bead87c0ull ||
+(C2.w[1] == 0x0001ed09bead87c0ull &&
+C2.w[0] > 0x378d8e63ffffffffull)) {
+// y is non-canonical if coefficient is larger than 10^34 -1
+C2.w[1] = 0;
+C2.w[0] = 0;
+} else { // canonical
+;
+}
+}
+}
+z_sign = z.w[1] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+C3.w[1] = z.w[1] & MASK_COEFF;
+C3.w[0] = z.w[0];
+if ((z.w[1] & MASK_ANY_INF) != MASK_INF) { // z != inf
+// if z is not infinity check for non-canonical values - treated as zero
+if ((z.w[1] & 0x6000000000000000ull) == 0x6000000000000000ull) { // G0_G1=11
+// non-canonical
+z_exp = (z.w[1] << 2) & MASK_EXP; // biased and shifted left 49 bits
+C3.w[1] = 0; // significand high
+C3.w[0] = 0; // significand low
+} else { // G0_G1 != 11
+z_exp = z.w[1] & MASK_EXP; // biased and shifted left 49 bits
+if (C3.w[1] > 0x0001ed09bead87c0ull ||
+(C3.w[1] == 0x0001ed09bead87c0ull &&
+C3.w[0] > 0x378d8e63ffffffffull)) {
+// z is non-canonical if coefficient is larger than 10^34 -1
+C3.w[1] = 0;
+C3.w[0] = 0;
+} else { // canonical
+;
+}
+}
+}
+p_sign = x_sign ^ y_sign; // sign of the product
+// identify cases where at least one operand is infinity
+if ((x.w[1] & MASK_ANY_INF) == MASK_INF) { // x = inf
+if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
+if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
+if (p_sign == z_sign) {
+res.w[1] = z_sign | MASK_INF;
+res.w[0] = 0x0;
+} else {
+// return QNaN Indefinite
+res.w[1] = 0x7c00000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+}
+} else { // z = 0 or z = f
+res.w[1] = p_sign | MASK_INF;
+res.w[0] = 0x0;
+}
+} else if (C2.w[1] != 0 || C2.w[0] != 0) { // y = f
+if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
+if (p_sign == z_sign) {
+res.w[1] = z_sign | MASK_INF;
+res.w[0] = 0x0;
+} else {
+// return QNaN Indefinite
+res.w[1] = 0x7c00000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+}
+} else { // z = 0 or z = f
+res.w[1] = p_sign | MASK_INF;
+res.w[0] = 0x0;
+}
+} else { // y = 0
+// return QNaN Indefinite
+res.w[1] = 0x7c00000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if ((y.w[1] & MASK_ANY_INF) == MASK_INF) { // y = inf
+if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
+// x = f, necessarily
+if ((p_sign != z_sign)
+|| (C1.w[1] == 0x0ull && C1.w[0] == 0x0ull)) {
+// return QNaN Indefinite
+res.w[1] = 0x7c00000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+} else {
+res.w[1] = z_sign | MASK_INF;
+res.w[0] = 0x0;
+}
+} else if (C1.w[1] == 0x0 && C1.w[0] == 0x0) { // x = 0
+// z = 0, f, inf
+// return QNaN Indefinite
+res.w[1] = 0x7c00000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+// set invalid flag
+*pfpsf |= INVALID_EXCEPTION;
+} else {
+// x = f and z = 0, f, necessarily
+res.w[1] = p_sign | MASK_INF;
+res.w[0] = 0x0;
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if ((z.w[1] & MASK_ANY_INF) == MASK_INF) { // z = inf
+// x = 0, f and y = 0, f, necessarily
+res.w[1] = z_sign | MASK_INF;
+res.w[0] = 0x0;
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+true_p_exp = (x_exp >> 49) - 6176 + (y_exp >> 49) - 6176;
+if (true_p_exp < -6176)
+p_exp = 0; // cannot be less than EXP_MIN
+else
+p_exp = (UINT64) (true_p_exp + 6176) << 49;
+if (((C1.w[1] == 0x0 && C1.w[0] == 0x0) || (C2.w[1] == 0x0 && C2.w[0] == 0x0)) && C3.w[1] == 0x0 && C3.w[0] == 0x0) { // (x = 0 or y = 0) and z = 0
+// the result is 0
+if (p_exp < z_exp)
+res.w[1] = p_exp; // preferred exponent
+else
+res.w[1] = z_exp; // preferred exponent
+if (p_sign == z_sign) {
+res.w[1] |= z_sign;
+res.w[0] = 0x0;
+} else { // x * y and z have opposite signs
+if (rnd_mode == ROUNDING_DOWN) {
+// res = -0.0
+res.w[1] |= MASK_SIGN;
+res.w[0] = 0x0;
+} else {
+// res = +0.0
+// res.w[1] |= 0x0;
+res.w[0] = 0x0;
+}
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+// from this point on, we may need to know the number of decimal digits
+// in the significands of x, y, z when x, y, z != 0
+if (C1.w[1] != 0 || C1.w[0] != 0) { // x = f (non-zero finite)
+// q1 = nr. of decimal digits in x
+// determine first the nr. of bits in x
+if (C1.w[1] == 0) {
+if (C1.w[0] >= 0x0020000000000000ull) { // x >= 2^53
+// split the 64-bit value in two 32-bit halves to avoid rounding errors
+if (C1.w[0] >= 0x0000000100000000ull) { // x >= 2^32
+tmp.d = (double) (C1.w[0] >> 32); // exact conversion
+x_nr_bits =
+33 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+} else { // x < 2^32
+tmp.d = (double) (C1.w[0]); // exact conversion
+x_nr_bits =
+1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // if x < 2^53
+tmp.d = (double) C1.w[0]; // exact conversion
+x_nr_bits =
+1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // C1.w[1] != 0 => nr. bits = 64 + nr_bits (C1.w[1])
+tmp.d = (double) C1.w[1]; // exact conversion
+x_nr_bits =
+65 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+q1 = nr_digits[x_nr_bits - 1].digits;
+if (q1 == 0) {
+q1 = nr_digits[x_nr_bits - 1].digits1;
+if (C1.w[1] > nr_digits[x_nr_bits - 1].threshold_hi ||
+(C1.w[1] == nr_digits[x_nr_bits - 1].threshold_hi &&
+C1.w[0] >= nr_digits[x_nr_bits - 1].threshold_lo))
+q1++;
+}
+}
+if (C2.w[1] != 0 || C2.w[0] != 0) { // y = f (non-zero finite)
+if (C2.w[1] == 0) {
+if (C2.w[0] >= 0x0020000000000000ull) { // y >= 2^53
+// split the 64-bit value in two 32-bit halves to avoid rounding errors
+if (C2.w[0] >= 0x0000000100000000ull) { // y >= 2^32
+tmp.d = (double) (C2.w[0] >> 32); // exact conversion
+y_nr_bits =
+32 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+} else { // y < 2^32
+tmp.d = (double) C2.w[0]; // exact conversion
+y_nr_bits =
+((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // if y < 2^53
+tmp.d = (double) C2.w[0]; // exact conversion
+y_nr_bits =
+((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // C2.w[1] != 0 => nr. bits = 64 + nr_bits (C2.w[1])
+tmp.d = (double) C2.w[1]; // exact conversion
+y_nr_bits =
+64 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+q2 = nr_digits[y_nr_bits].digits;
+if (q2 == 0) {
+q2 = nr_digits[y_nr_bits].digits1;
+if (C2.w[1] > nr_digits[y_nr_bits].threshold_hi ||
+(C2.w[1] == nr_digits[y_nr_bits].threshold_hi &&
+C2.w[0] >= nr_digits[y_nr_bits].threshold_lo))
+q2++;
+}
+}
+if (C3.w[1] != 0 || C3.w[0] != 0) { // z = f (non-zero finite)
+if (C3.w[1] == 0) {
+if (C3.w[0] >= 0x0020000000000000ull) { // z >= 2^53
+// split the 64-bit value in two 32-bit halves to avoid rounding errors
+if (C3.w[0] >= 0x0000000100000000ull) { // z >= 2^32
+tmp.d = (double) (C3.w[0] >> 32); // exact conversion
+z_nr_bits =
+32 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+} else { // z < 2^32
+tmp.d = (double) C3.w[0]; // exact conversion
+z_nr_bits =
+((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // if z < 2^53
+tmp.d = (double) C3.w[0]; // exact conversion
+z_nr_bits =
+((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // C3.w[1] != 0 => nr. bits = 64 + nr_bits (C3.w[1])
+tmp.d = (double) C3.w[1]; // exact conversion
+z_nr_bits =
+64 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+q3 = nr_digits[z_nr_bits].digits;
+if (q3 == 0) {
+q3 = nr_digits[z_nr_bits].digits1;
+if (C3.w[1] > nr_digits[z_nr_bits].threshold_hi ||
+(C3.w[1] == nr_digits[z_nr_bits].threshold_hi &&
+C3.w[0] >= nr_digits[z_nr_bits].threshold_lo))
+q3++;
+}
+}
+if ((C1.w[1] == 0x0 && C1.w[0] == 0x0) ||
+(C2.w[1] == 0x0 && C2.w[0] == 0x0)) {
+// x = 0 or y = 0
+// z = f, necessarily; for 0 + z return z, with the preferred exponent
+// the result is z, but need to get the preferred exponent
+if (z_exp <= p_exp) { // the preferred exponent is z_exp
+res.w[1] = z_sign | (z_exp & MASK_EXP) | C3.w[1];
+res.w[0] = C3.w[0];
+} else { // if (p_exp < z_exp) the preferred exponent is p_exp
+// return (C3 * 10^scale) * 10^(z_exp - scale)
+// where scale = min (p34-q3, (z_exp-p_exp) >> 49)
+scale = p34 - q3;
+ind = (z_exp - p_exp) >> 49;
+if (ind < scale)
+scale = ind;
+if (scale == 0) {
+res.w[1] = z.w[1]; // & MASK_COEFF, which is redundant
+res.w[0] = z.w[0];
+} else if (q3 <= 19) { // z fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C3.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C3.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
+}
+} else { // z fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], C3);
+}
+// subtract scale from the exponent
+z_exp = z_exp - ((UINT64) scale << 49);
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else {
+; // continue with x = f, y = f, z = 0 or x = f, y = f, z = f
+}
+e1 = (x_exp >> 49) - 6176; // unbiased exponent of x
+e2 = (y_exp >> 49) - 6176; // unbiased exponent of y
+e3 = (z_exp >> 49) - 6176; // unbiased exponent of z
+e4 = e1 + e2; // unbiased exponent of the exact x * y
+// calculate C1 * C2 and its number of decimal digits, q4
+// the exact product has either q1 + q2 - 1 or q1 + q2 decimal digits
+// where 2 <= q1 + q2 <= 68
+// calculate C4 = C1 * C2 and determine q
+C4.w[3] = C4.w[2] = C4.w[1] = C4.w[0] = 0;
+if (q1 + q2 <= 19) { // if 2 <= q1 + q2 <= 19, C4 = C1 * C2 fits in 64 bits
+C4.w[0] = C1.w[0] * C2.w[0];
+// if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
+if (C4.w[0] < ten2k64[q1 + q2 - 1])
+q4 = q1 + q2 - 1; // q4 in [1, 18]
+else
+q4 = q1 + q2; // q4 in [2, 19]
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
+} else if (q1 + q2 == 20) { // C4 = C1 * C2 fits in 64 or 128 bits
+// q1 <= 19 and q2 <= 19 so both C1 and C2 fit in 64 bits
+__mul_64x64_to_128MACH (C4, C1.w[0], C2.w[0]);
+// if C4 < 10^(q1+q2-1) = 10^19 then q4 = q1+q2-1 = 19 else q4 = q1+q2 = 20
+if (C4.w[1] == 0 && C4.w[0] < ten2k64[19]) { // 19 = q1+q2-1
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
+q4 = 19; // 19 = q1 + q2 - 1
+} else {
+// if (C4.w[1] == 0)
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
+// else
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
+q4 = 20; // 20 = q1 + q2
+}
+} else if (q1 + q2 <= 38) { // 21 <= q1 + q2 <= 38
+// C4 = C1 * C2 fits in 64 or 128 bits
+// (64 bits possibly, but only when q1 + q2 = 21 and C4 has 20 digits)
+// at least one of C1, C2 has at most 19 decimal digits & fits in 64 bits
+if (q1 <= 19) {
+__mul_128x64_to_128 (C4, C1.w[0], C2);
+} else { // q2 <= 19
+__mul_128x64_to_128 (C4, C2.w[0], C1);
+}
+// if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
+if (C4.w[1] < ten2k128[q1 + q2 - 21].w[1] ||
+(C4.w[1] == ten2k128[q1 + q2 - 21].w[1] &&
+C4.w[0] < ten2k128[q1 + q2 - 21].w[0])) {
+// if (C4.w[1] == 0) // q4 = 20, necessarily
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 64;
+// else
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
+q4 = q1 + q2 - 1; // q4 in [20, 37]
+} else {
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
+q4 = q1 + q2; // q4 in [21, 38]
+}
+} else if (q1 + q2 == 39) { // C4 = C1 * C2 fits in 128 or 192 bits
+// both C1 and C2 fit in 128 bits (actually in 113 bits)
+// may replace this by 128x128_to192
+__mul_128x128_to_256 (C4, C1, C2); // C4.w[3] is 0
+// if C4 < 10^(q1+q2-1) = 10^38 then q4 = q1+q2-1 = 38 else q4 = q1+q2 = 39
+if (C4.w[2] == 0 && (C4.w[1] < ten2k128[18].w[1] ||
+		 (C4.w[1] == ten2k128[18].w[1]
+		  && C4.w[0] < ten2k128[18].w[0]))) {
+// 18 = 38 - 20 = q1+q2-1 - 20
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
+q4 = 38; // 38 = q1 + q2 - 1
+} else {
+// if (C4.w[2] == 0)
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
+// else
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
+q4 = 39; // 39 = q1 + q2
+}
+} else if (q1 + q2 <= 57) { // 40 <= q1 + q2 <= 57
+// C4 = C1 * C2 fits in 128 or 192 bits
+// (128 bits possibly, but only when q1 + q2 = 40 and C4 has 39 digits)
+// both C1 and C2 fit in 128 bits (actually in 113 bits); at most one
+// may fit in 64 bits
+if (C1.w[1] == 0) { // C1 fits in 64 bits
+// __mul_64x128_full (REShi64, RESlo128, A64, B128)
+__mul_64x128_full (C4.w[2], C4, C1.w[0], C2);
+} else if (C2.w[1] == 0) { // C2 fits in 64 bits
+// __mul_64x128_full (REShi64, RESlo128, A64, B128)
+__mul_64x128_full (C4.w[2], C4, C2.w[0], C1);
+} else { // both C1 and C2 require 128 bits
+// may use __mul_128x128_to_192 (C4.w[2], C4.w[0], C2.w[0], C1);
+__mul_128x128_to_256 (C4, C1, C2); // C4.w[3] = 0
+}
+// if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
+if (C4.w[2] < ten2k256[q1 + q2 - 40].w[2] ||
+(C4.w[2] == ten2k256[q1 + q2 - 40].w[2] &&
+(C4.w[1] < ten2k256[q1 + q2 - 40].w[1] ||
+(C4.w[1] == ten2k256[q1 + q2 - 40].w[1] &&
+C4.w[0] < ten2k256[q1 + q2 - 40].w[0])))) {
+// if (C4.w[2] == 0) // q4 = 39, necessarily
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 128;
+// else
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
+q4 = q1 + q2 - 1; // q4 in [39, 56]
+} else {
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
+q4 = q1 + q2; // q4 in [40, 57]
+}
+} else if (q1 + q2 == 58) { // C4 = C1 * C2 fits in 192 or 256 bits
+// both C1 and C2 fit in 128 bits (actually in 113 bits); at most one
+// may fit in 64 bits
+if (C1.w[1] == 0) { // C1 * C2 will fit in 192 bits
+__mul_64x128_full (C4.w[2], C4, C1.w[0], C2); // may use 64x128_to_192
+} else if (C2.w[1] == 0) { // C1 * C2 will fit in 192 bits
+__mul_64x128_full (C4.w[2], C4, C2.w[0], C1); // may use 64x128_to_192
+} else { // C1 * C2 will fit in 192 bits or in 256 bits
+__mul_128x128_to_256 (C4, C1, C2);
+}
+// if C4 < 10^(q1+q2-1) = 10^57 then q4 = q1+q2-1 = 57 else q4 = q1+q2 = 58
+if (C4.w[3] == 0 && (C4.w[2] < ten2k256[18].w[2] ||
+		 (C4.w[2] == ten2k256[18].w[2]
+		  && (C4.w[1] < ten2k256[18].w[1]
+		      || (C4.w[1] == ten2k256[18].w[1]
+			  && C4.w[0] < ten2k256[18].w[0]))))) {
+// 18 = 57 - 39 = q1+q2-1 - 39
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
+q4 = 57; // 57 = q1 + q2 - 1
+} else {
+// if (C4.w[3] == 0)
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
+// else
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 256;
+q4 = 58; // 58 = q1 + q2
+}
+} else { // if 59 <= q1 + q2 <= 68
+// C4 = C1 * C2 fits in 192 or 256 bits
+// (192 bits possibly, but only when q1 + q2 = 59 and C4 has 58 digits)
+// both C1 and C2 fit in 128 bits (actually in 113 bits); none fits in
+// 64 bits
+// may use __mul_128x128_to_192 (C4.w[2], C4.w[0], C2.w[0], C1);
+__mul_128x128_to_256 (C4, C1, C2); // C4.w[3] = 0
+// if C4 < 10^(q1+q2-1) then q4 = q1 + q2 - 1 else q4 = q1 + q2
+if (C4.w[3] < ten2k256[q1 + q2 - 40].w[3] ||
+(C4.w[3] == ten2k256[q1 + q2 - 40].w[3] &&
+(C4.w[2] < ten2k256[q1 + q2 - 40].w[2] ||
+(C4.w[2] == ten2k256[q1 + q2 - 40].w[2] &&
+(C4.w[1] < ten2k256[q1 + q2 - 40].w[1] ||
+(C4.w[1] == ten2k256[q1 + q2 - 40].w[1] &&
+C4.w[0] < ten2k256[q1 + q2 - 40].w[0])))))) {
+// if (C4.w[3] == 0) // q4 = 58, necessarily
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 192;
+// else
+//   length of C1 * C2 rounded up to a multiple of 64 bits is len = 256;
+q4 = q1 + q2 - 1; // q4 in [58, 67]
+} else {
+// length of C1 * C2 rounded up to a multiple of 64 bits is len = 256;
+q4 = q1 + q2; // q4 in [59, 68]
+}
+}
+if (C3.w[1] == 0x0 && C3.w[0] == 0x0) { // x = f, y = f, z = 0
+save_fpsf = *pfpsf; // sticky bits - caller value must be preserved
+*pfpsf = 0;
+if (q4 > p34) {
+// truncate C4 to p34 digits into res
+// x = q4-p34, 1 <= x <= 34 because 35 <= q4 <= 68
+x0 = q4 - p34;
+if (q4 <= 38) {
+P128.w[1] = C4.w[1];
+P128.w[0] = C4.w[0];
+round128_19_38 (q4, x0, P128, &res, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+} else if (q4 <= 57) { // 35 <= q4 <= 57
+P192.w[2] = C4.w[2];
+P192.w[1] = C4.w[1];
+P192.w[0] = C4.w[0];
+round192_39_57 (q4, x0, P192, &R192, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+res.w[0] = R192.w[0];
+res.w[1] = R192.w[1];
+} else { // if (q4 <= 68)
+round256_58_76 (q4, x0, C4, &R256, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+res.w[0] = R256.w[0];
+res.w[1] = R256.w[1];
+}
+e4 = e4 + x0;
+if (incr_exp) {
+e4 = e4 + 1;
+}
+q4 = p34;
+// res is now the coefficient of the result rounded to the destination
+// precision, with unbounded exponent; the exponent is e4; q4=digits(res)
+} else { // if (q4 <= p34)
+// C4 * 10^e4 is the result rounded to the destination precision, with
+// unbounded exponent (which is exact)
+if ((q4 + e4 <= p34 + expmax) && (e4 > expmax)) {
+// e4 is too large, but can be brought within range by scaling up C4
+scale = e4 - expmax; // 1 <= scale < P-q4 <= P-1 => 1 <= scale <= P-2
+// res = (C4 * 10^scale) * 10^expmax
+if (q4 <= 19) { // C4 fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C4.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, C4.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C4.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, C4.w[0], ten2k128[scale - 20]);
+}
+} else { // C4 fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * CC43
+__mul_128x64_to_128 (res, ten2k64[scale], C4);
+}
+e4 = e4 - scale; // expmax
+q4 = q4 + scale;
+} else {
+res.w[1] = C4.w[1];
+res.w[0] = C4.w[0];
+}
+// res is the coefficient of the result rounded to the destination
+// precision, with unbounded exponent (it has q4 digits); the exponent
+// is e4 (exact result)
+}
+// check for overflow
+if (q4 + e4 > p34 + expmax) {
+if (rnd_mode == ROUNDING_TO_NEAREST) {
+res.w[1] = p_sign | 0x7800000000000000ull; // +/-inf
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+} else {
+res.w[1] = p_sign | res.w[1];
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     e4, &res, pfpsf);
+}
+*pfpsf |= save_fpsf;
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+// check for underflow
+if (q4 + e4 < expmin + P34) {
+is_tiny = 1; // the result is tiny
+if (e4 < expmin) {
+// if e4 < expmin, we must truncate more of res
+x0 = expmin - e4; // x0 >= 1
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+// the number of decimal digits in res is q4
+if (x0 < q4) { // 1 <= x0 <= q4-1 => round res to q4 - x0 digits
+if (q4 <= 18) { // 2 <= q4 <= 18, 1 <= x0 <= 17
+round64_2_18 (q4, x0, res.w[0], &R64, &incr_exp,
+		  &is_midpoint_lt_even, &is_midpoint_gt_even,
+		  &is_inexact_lt_midpoint,
+		  &is_inexact_gt_midpoint);
+if (incr_exp) {
+// R64 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 17
+R64 = ten2k64[q4 - x0];
+}
+// res.w[1] = 0; (from above)
+res.w[0] = R64;
+} else { // if (q4 <= 34)
+// 19 <= q4 <= 38
+P128.w[1] = res.w[1];
+P128.w[0] = res.w[0];
+round128_19_38 (q4, x0, P128, &res, &incr_exp,
+		    &is_midpoint_lt_even, &is_midpoint_gt_even,
+		    &is_inexact_lt_midpoint,
+		    &is_inexact_gt_midpoint);
+if (incr_exp) {
+// increase coefficient by a factor of 10; this will be <= 10^33
+// R128 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 37
+if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
+	// res.w[1] = 0;
+	res.w[0] = ten2k64[q4 - x0];
+} else { // 20 <= q4 - x0 <= 37
+	res.w[0] = ten2k128[q4 - x0 - 20].w[0];
+	res.w[1] = ten2k128[q4 - x0 - 20].w[1];
+}
+}
+}
+e4 = e4 + x0; // expmin
+} else if (x0 == q4) {
+// the second rounding is for 0.d(0)d(1)...d(q4-1) * 10^emin
+// determine relationship with 1/2 ulp
+if (q4 <= 19) {
+if (res.w[0] < midpoint64[q4 - 1]) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (res.w[0] == midpoint64[q4 - 1]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+// gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+} else { // if (q4 <= 34)
+if (res.w[1] < midpoint128[q4 - 20].w[1] ||
+(res.w[1] == midpoint128[q4 - 20].w[1] &&
+res.w[0] < midpoint128[q4 - 20].w[0])) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (res.w[1] == midpoint128[q4 - 20].w[1] &&
+res.w[0] == midpoint128[q4 - 20].w[0]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+// gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+}
+if (lt_half_ulp || eq_half_ulp) {
+// res = +0.0 * 10^expmin
+res.w[1] = 0x0000000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+} else { // if (gt_half_ulp)
+// res = +1 * 10^expmin
+res.w[1] = 0x0000000000000000ull;
+res.w[0] = 0x0000000000000001ull;
+}
+e4 = expmin;
+} else { // if (x0 > q4)
+// the second rounding is for 0.0...d(0)d(1)...d(q4-1) * 10^emin
+res.w[1] = 0;
+res.w[0] = 0;
+e4 = expmin;
+is_inexact_lt_midpoint = 1;
+}
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// Note: a double rounding error upward is not possible; for this
+// the result after the first rounding would have to be 99...95
+// (35 digits in all), possibly followed by a number of zeros; this
+// not possible for f * f + 0
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	   !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	   (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	   (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+} else { // if e4 >= emin then q4 < P and the result is tiny and exact
+if (e3 < e4) {
+// if (e3 < e4) the preferred exponent is e3
+// return (C4 * 10^scale) * 10^(e4 - scale)
+// where scale = min (p34-q4, (e4 - e3))
+scale = p34 - q4;
+ind = e4 - e3;
+if (ind < scale)
+scale = ind;
+if (scale == 0) {
+; // res and e4 are unchanged
+} else if (q4 <= 19) { // C4 fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 res.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, res.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 res.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, res.w[0], ten2k128[scale - 20]);
+}
+} else { // res fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], res);
+}
+// subtract scale from the exponent
+e4 = e4 - scale;
+}
+}
+// check for inexact result
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even) {
+// set the inexact flag and the underflow flag
+*pfpsf |= INEXACT_EXCEPTION;
+*pfpsf |= UNDERFLOW_EXCEPTION;
+}
+res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1];
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     e4, &res, pfpsf);
+}
+*pfpsf |= save_fpsf;
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+// no overflow, and no underflow for rounding to nearest
+res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1];
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		   is_inexact_lt_midpoint,
+		   is_inexact_gt_midpoint,
+		   is_midpoint_lt_even, is_midpoint_gt_even,
+		   e4, &res, pfpsf);
+// if e4 = expmin && significand < 10^33 => result is tiny (for RD, RZ)
+if (e4 == expmin) {
+if ((res.w[1] & MASK_COEFF) < 0x0000314dc6448d93ull ||
+((res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull &&
+res.w[0] < 0x38c15b0a00000000ull)) {
+is_tiny = 1;
+}
+}
+}
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even) {
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+if (is_tiny)
+*pfpsf |= UNDERFLOW_EXCEPTION;
+}
+if ((*pfpsf & INEXACT_EXCEPTION) == 0) { // x * y is exact
+// need to ensure that the result has the preferred exponent
+p_exp = res.w[1] & MASK_EXP;
+if (z_exp < p_exp) { // the preferred exponent is z_exp
+// signficand of res in C3
+C3.w[1] = res.w[1] & MASK_COEFF;
+C3.w[0] = res.w[0];
+// the number of decimal digits of x * y is q4 <= 34
+// Note: the coefficient fits in 128 bits
+// return (C3 * 10^scale) * 10^(p_exp - scale)
+// where scale = min (p34-q4, (p_exp-z_exp) >> 49)
+scale = p34 - q4;
+ind = (p_exp - z_exp) >> 49;
+if (ind < scale)
+scale = ind;
+// subtract scale from the exponent
+p_exp = p_exp - ((UINT64) scale << 49);
+if (scale == 0) {
+; // leave res unchanged
+} else if (q4 <= 19) { // x * y fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C3.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C3.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
+}
+res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1];
+} else { // x * y fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], C3);
+res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1];
+}
+} // else leave the result as it is, because p_exp <= z_exp
+}
+*pfpsf |= save_fpsf;
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} // else we have f * f + f
+// continue with x = f, y = f, z = f
+delta = q3 + e3 - q4 - e4;
+delta_ge_zero:
+if (delta >= 0) {
+if (p34 <= delta - 1 ||	// Case (1')
+(p34 == delta && e3 + 6176 < p34 - q3)) { // Case (1''A)
+// check for overflow, which can occur only in Case (1')
+if ((q3 + e3) > (p34 + expmax) && p34 <= delta - 1) {
+// e3 > expmax implies p34 <= delta-1 and e3 > expmax is a necessary
+// condition for (q3 + e3) > (p34 + expmax)
+if (rnd_mode == ROUNDING_TO_NEAREST) {
+res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+} else {
+if (p_sign == z_sign) {
+is_inexact_lt_midpoint = 1;
+} else {
+is_inexact_gt_midpoint = 1;
+}
+// q3 <= p34; if (q3 < p34) scale C3 up by 10^(p34-q3)
+scale = p34 - q3;
+if (scale == 0) {
+res.w[1] = z_sign | C3.w[1];
+res.w[0] = C3.w[0];
+} else {
+if (q3 <= 19) { // C3 fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+	// 64 x 64 C3.w[0] * ten2k64[scale]
+	__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+	// 64 x 128 C3.w[0] * ten2k128[scale - 20]
+	__mul_128x64_to_128 (res, C3.w[0],
+			     ten2k128[scale - 20]);
+}
+} else { // C3 fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], C3);
+}
+// the coefficient in res has q3 + scale = p34 digits
+}
+e3 = e3 - scale;
+res.w[1] = z_sign | res.w[1];
+rounding_correction (rnd_mode,
+		       is_inexact_lt_midpoint,
+		       is_inexact_gt_midpoint,
+		       is_midpoint_lt_even, is_midpoint_gt_even,
+		       e3, &res, pfpsf);
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+// res = z
+if (q3 < p34) { // the preferred exponent is z_exp - (p34 - q3)
+// return (C3 * 10^scale) * 10^(z_exp - scale)
+// where scale = min (p34-q3, z_exp-EMIN)
+scale = p34 - q3;
+ind = e3 + 6176;
+if (ind < scale)
+scale = ind;
+if (scale == 0) {
+res.w[1] = C3.w[1];
+res.w[0] = C3.w[0];
+} else if (q3 <= 19) { // z fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C3.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C3.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
+}
+} else { // z fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], C3);
+}
+// the coefficient in res has q3 + scale digits
+// subtract scale from the exponent
+z_exp = z_exp - ((UINT64) scale << 49);
+e3 = e3 - scale;
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+if (scale + q3 < p34)
+*pfpsf |= UNDERFLOW_EXCEPTION;
+} else {
+scale = 0;
+res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | C3.w[1];
+res.w[0] = C3.w[0];
+}
+// use the following to avoid double rounding errors when operating on
+// mixed formats in rounding to nearest, and for correcting the result
+// if not rounding to nearest
+if ((p_sign != z_sign) && (delta == (q3 + scale + 1))) {
+// there is a gap of exactly one digit between the scaled C3 and C4
+// C3 * 10^ scale = 10^(q3+scale-1) <=> C3 = 10^(q3-1) is special case
+if ((q3 <= 19 && C3.w[0] != ten2k64[q3 - 1]) ||
+(q3 == 20 && (C3.w[1] != 0 || C3.w[0] != ten2k64[19])) ||
+(q3 >= 21 && (C3.w[1] != ten2k128[q3 - 21].w[1] ||
+		  C3.w[0] != ten2k128[q3 - 21].w[0]))) {
+// C3 * 10^ scale != 10^(q3-1)
+// if ((res.w[1] & MASK_COEFF) != 0x0000314dc6448d93ull ||
+// res.w[0] != 0x38c15b0a00000000ull) { // C3 * 10^scale != 10^33
+is_inexact_gt_midpoint = 1; // if (z_sign), set as if for abs. value
+} else { // if C3 * 10^scale = 10^(q3+scale-1)
+// ok from above e3 = (z_exp >> 49) - 6176;
+// the result is always inexact
+if (q4 == 1) {
+R64 = C4.w[0];
+} else {
+// if q4 > 1 then truncate C4 from q4 digits to 1 digit;
+// x = q4-1, 1 <= x <= 67 and check if this operation is exact
+if (q4 <= 18) { // 2 <= q4 <= 18
+round64_2_18 (q4, q4 - 1, C4.w[0], &R64, &incr_exp,
+		    &is_midpoint_lt_even, &is_midpoint_gt_even,
+		    &is_inexact_lt_midpoint,
+		    &is_inexact_gt_midpoint);
+} else if (q4 <= 38) {
+P128.w[1] = C4.w[1];
+P128.w[0] = C4.w[0];
+round128_19_38 (q4, q4 - 1, P128, &R128, &incr_exp,
+		      &is_midpoint_lt_even,
+		      &is_midpoint_gt_even,
+		      &is_inexact_lt_midpoint,
+		      &is_inexact_gt_midpoint);
+R64 = R128.w[0]; // one decimal digit
+} else if (q4 <= 57) {
+P192.w[2] = C4.w[2];
+P192.w[1] = C4.w[1];
+P192.w[0] = C4.w[0];
+round192_39_57 (q4, q4 - 1, P192, &R192, &incr_exp,
+		      &is_midpoint_lt_even,
+		      &is_midpoint_gt_even,
+		      &is_inexact_lt_midpoint,
+		      &is_inexact_gt_midpoint);
+R64 = R192.w[0]; // one decimal digit
+} else { // if (q4 <= 68)
+round256_58_76 (q4, q4 - 1, C4, &R256, &incr_exp,
+		      &is_midpoint_lt_even,
+		      &is_midpoint_gt_even,
+		      &is_inexact_lt_midpoint,
+		      &is_inexact_gt_midpoint);
+R64 = R256.w[0]; // one decimal digit
+}
+if (incr_exp) {
+R64 = 10;
+}
+}
+if (q4 == 1 && C4.w[0] == 5) {
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 1;
+is_midpoint_gt_even = 0;
+} else if ((e3 == expmin) ||
+	     R64 < 5 || (R64 == 5 && is_inexact_gt_midpoint)) {
+// result does not change
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+// result decremented is 10^(q3+scale) - 1
+if ((q3 + scale) <= 19) {
+res.w[1] = 0;
+res.w[0] = ten2k64[q3 + scale];
+} else { // if ((q3 + scale + 1) <= 35)
+res.w[1] = ten2k128[q3 + scale - 20].w[1];
+res.w[0] = ten2k128[q3 + scale - 20].w[0];
+}
+res.w[0] = res.w[0] - 1; // borrow never occurs
+z_exp = z_exp - EXP_P1;
+e3 = e3 - 1;
+res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1];
+}
+if (e3 == expmin) {
+if (R64 < 5 || (R64 == 5 && !is_inexact_lt_midpoint)) {
+; // result not tiny (in round-to-nearest mode)
+} else {
+*pfpsf |= UNDERFLOW_EXCEPTION;
+}
+}
+} // end 10^(q3+scale-1)
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+} else {
+if (p_sign == z_sign) {
+// if (z_sign), set as if for absolute value
+is_inexact_lt_midpoint = 1;
+} else { // if (p_sign != z_sign)
+// if (z_sign), set as if for absolute value
+is_inexact_gt_midpoint = 1;
+}
+*pfpsf |= INEXACT_EXCEPTION;
+}
+// the result is always inexact => set the inexact flag
+// Determine tininess:
+//    if (exp > expmin)
+//      the result is not tiny
+//    else // if exp = emin
+//      if (q3 + scale < p34)
+//        the result is tiny
+//      else // if (q3 + scale = p34)
+//        if (C3 * 10^scale > 10^33)
+//          the result is not tiny
+//        else // if C3 * 10^scale = 10^33
+//          if (xy * z > 0)
+//            the result is not tiny
+//          else // if (xy * z < 0)
+//            if (z > 0)
+//              if rnd_mode != RP
+//                the result is tiny
+//              else // if RP
+//                the result is not tiny
+//            else // if (z < 0)
+//              if rnd_mode != RM
+//                the result is tiny
+//              else // if RM
+//                the result is not tiny
+//              endif
+//            endif
+//          endif
+//        endif
+//      endif
+//    endif
+if ((e3 == expmin && (q3 + scale) < p34) ||
+(e3 == expmin && (q3 + scale) == p34 &&
+(res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull &&	// 10^33_high
+res.w[0] == 0x38c15b0a00000000ull &&	// 10^33_low
+z_sign != p_sign && ((!z_sign && rnd_mode != ROUNDING_UP) ||
+(z_sign && rnd_mode != ROUNDING_DOWN)))) {
+*pfpsf |= UNDERFLOW_EXCEPTION;
+}
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     e3, &res, pfpsf);
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if (p34 == delta) { // Case (1''B)
+// because Case (1''A) was treated above, e3 + 6176 >= p34 - q3
+// and C3 can be scaled up to p34 digits if needed
+// scale C3 to p34 digits if needed
+scale = p34 - q3; // 0 <= scale <= p34 - 1
+if (scale == 0) {
+res.w[1] = C3.w[1];
+res.w[0] = C3.w[0];
+} else if (q3 <= 19) { // z fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C3.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C3.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
+}
+} else { // z fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], C3);
+}
+// subtract scale from the exponent
+z_exp = z_exp - ((UINT64) scale << 49);
+e3 = e3 - scale;
+// now z_sign, z_exp, and res correspond to a z scaled to p34 = 34 digits
+// determine whether x * y is less than, equal to, or greater than
+// 1/2 ulp (z)
+if (q4 <= 19) {
+if (C4.w[0] < midpoint64[q4 - 1]) { // < 1/2 ulp
+lt_half_ulp = 1;
+} else if (C4.w[0] == midpoint64[q4 - 1]) { // = 1/2 ulp
+eq_half_ulp = 1;
+} else { // > 1/2 ulp
+gt_half_ulp = 1;
+}
+} else if (q4 <= 38) {
+if (C4.w[2] == 0 && (C4.w[1] < midpoint128[q4 - 20].w[1] ||
+(C4.w[1] == midpoint128[q4 - 20].w[1] &&
+C4.w[0] < midpoint128[q4 - 20].w[0]))) { // < 1/2 ulp
+lt_half_ulp = 1;
+} else if (C4.w[2] == 0 && C4.w[1] == midpoint128[q4 - 20].w[1] &&
+C4.w[0] == midpoint128[q4 - 20].w[0]) { // = 1/2 ulp
+eq_half_ulp = 1;
+} else { // > 1/2 ulp
+gt_half_ulp = 1;
+}
+} else if (q4 <= 58) {
+if (C4.w[3] == 0 && (C4.w[2] < midpoint192[q4 - 39].w[2] ||
+(C4.w[2] == midpoint192[q4 - 39].w[2] &&
+C4.w[1] < midpoint192[q4 - 39].w[1]) ||
+(C4.w[2] == midpoint192[q4 - 39].w[2] &&
+C4.w[1] == midpoint192[q4 - 39].w[1] &&
+C4.w[0] < midpoint192[q4 - 39].w[0]))) { // < 1/2 ulp
+lt_half_ulp = 1;
+} else if (C4.w[3] == 0 && C4.w[2] == midpoint192[q4 - 39].w[2] &&
+C4.w[1] == midpoint192[q4 - 39].w[1] &&
+C4.w[0] == midpoint192[q4 - 39].w[0]) { // = 1/2 ulp
+eq_half_ulp = 1;
+} else { // > 1/2 ulp
+gt_half_ulp = 1;
+}
+} else {
+if (C4.w[3] < midpoint256[q4 - 59].w[3] ||
+(C4.w[3] == midpoint256[q4 - 59].w[3] &&
+C4.w[2] < midpoint256[q4 - 59].w[2]) ||
+(C4.w[3] == midpoint256[q4 - 59].w[3] &&
+C4.w[2] == midpoint256[q4 - 59].w[2] &&
+C4.w[1] < midpoint256[q4 - 59].w[1]) ||
+(C4.w[3] == midpoint256[q4 - 59].w[3] &&
+C4.w[2] == midpoint256[q4 - 59].w[2] &&
+C4.w[1] == midpoint256[q4 - 59].w[1] &&
+C4.w[0] < midpoint256[q4 - 59].w[0])) { // < 1/2 ulp
+lt_half_ulp = 1;
+} else if (C4.w[3] == midpoint256[q4 - 59].w[3] &&
+C4.w[2] == midpoint256[q4 - 59].w[2] &&
+C4.w[1] == midpoint256[q4 - 59].w[1] &&
+C4.w[0] == midpoint256[q4 - 59].w[0]) { // = 1/2 ulp
+eq_half_ulp = 1;
+} else { // > 1/2 ulp
+gt_half_ulp = 1;
+}
+}
+if (p_sign == z_sign) {
+if (lt_half_ulp) {
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+// use the following to avoid double rounding errors when operating on
+// mixed formats in rounding to nearest
+is_inexact_lt_midpoint = 1; // if (z_sign), as if for absolute value
+} else if ((eq_half_ulp && (res.w[0] & 0x01)) || gt_half_ulp) {
+// add 1 ulp to the significand
+res.w[0]++;
+if (res.w[0] == 0x0ull)
+res.w[1]++;
+// check for rounding overflow, when coeff == 10^34
+if ((res.w[1] & MASK_COEFF) == 0x0001ed09bead87c0ull &&
+res.w[0] == 0x378d8e6400000000ull) { // coefficient = 10^34
+e3 = e3 + 1;
+// coeff = 10^33
+z_exp = ((UINT64) (e3 + 6176) << 49) & MASK_EXP;
+res.w[1] = 0x0000314dc6448d93ull;
+res.w[0] = 0x38c15b0a00000000ull;
+}
+// end add 1 ulp
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+if (eq_half_ulp) {
+is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value
+} else {
+is_inexact_gt_midpoint = 1; // if (z_sign), as if for absolute value
+}
+} else { // if (eq_half_ulp && !(res.w[0] & 0x01))
+// leave unchanged
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+is_midpoint_gt_even = 1; // if (z_sign), as if for absolute value
+}
+// the result is always inexact, and never tiny
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+// check for overflow
+if (e3 > expmax && rnd_mode == ROUNDING_TO_NEAREST) {
+res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		       is_inexact_lt_midpoint,
+		       is_inexact_gt_midpoint,
+		       is_midpoint_lt_even, is_midpoint_gt_even,
+		       e3, &res, pfpsf);
+z_exp = res.w[1] & MASK_EXP;
+}
+} else { // if (p_sign != z_sign)
+// consider two cases, because C3 * 10^scale = 10^33 is a special case
+if (res.w[1] != 0x0000314dc6448d93ull ||
+res.w[0] != 0x38c15b0a00000000ull) { // C3 * 10^scale != 10^33
+if (lt_half_ulp) {
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+// use the following to avoid double rounding errors when operating
+// on mixed formats in rounding to nearest
+is_inexact_gt_midpoint = 1; // if (z_sign), as if for absolute value
+} else if ((eq_half_ulp && (res.w[0] & 0x01)) || gt_half_ulp) {
+// subtract 1 ulp from the significand
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+if (eq_half_ulp) {
+is_midpoint_gt_even = 1; // if (z_sign), as if for absolute value
+} else {
+is_inexact_lt_midpoint = 1; //if(z_sign), as if for absolute value
+}
+} else { // if (eq_half_ulp && !(res.w[0] & 0x01))
+// leave unchanged
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value
+}
+// the result is always inexact, and never tiny
+// check for overflow for RN
+if (e3 > expmax) {
+if (rnd_mode == ROUNDING_TO_NEAREST) {
+res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+} else {
+rounding_correction (rnd_mode,
+			   is_inexact_lt_midpoint,
+			   is_inexact_gt_midpoint,
+			   is_midpoint_lt_even,
+			   is_midpoint_gt_even, e3, &res,
+			   pfpsf);
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+			 is_inexact_lt_midpoint,
+			 is_inexact_gt_midpoint,
+			 is_midpoint_lt_even,
+			 is_midpoint_gt_even, e3, &res, pfpsf);
+}
+z_exp = res.w[1] & MASK_EXP;
+} else { // if C3 * 10^scale = 10^33
+e3 = (z_exp >> 49) - 6176;
+if (e3 > expmin) {
+// the result is exact if exp > expmin and C4 = d*10^(q4-1),
+// where d = 1, 2, 3, ..., 9; it could be tiny too, but exact
+if (q4 == 1) {
+// if q4 = 1 the result is exact
+// result coefficient = 10^34 - C4
+res.w[1] = 0x0001ed09bead87c0ull;
+res.w[0] = 0x378d8e6400000000ull - C4.w[0];
+z_exp = z_exp - EXP_P1;
+e3 = e3 - 1;
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+} else {
+// if q4 > 1 then truncate C4 from q4 digits to 1 digit;
+// x = q4-1, 1 <= x <= 67 and check if this operation is exact
+if (q4 <= 18) { // 2 <= q4 <= 18
+	round64_2_18 (q4, q4 - 1, C4.w[0], &R64, &incr_exp,
+		      &is_midpoint_lt_even,
+		      &is_midpoint_gt_even,
+		      &is_inexact_lt_midpoint,
+		      &is_inexact_gt_midpoint);
+} else if (q4 <= 38) {
+	P128.w[1] = C4.w[1];
+	P128.w[0] = C4.w[0];
+	round128_19_38 (q4, q4 - 1, P128, &R128, &incr_exp,
+			&is_midpoint_lt_even,
+			&is_midpoint_gt_even,
+			&is_inexact_lt_midpoint,
+			&is_inexact_gt_midpoint);
+	R64 = R128.w[0]; // one decimal digit
+} else if (q4 <= 57) {
+	P192.w[2] = C4.w[2];
+	P192.w[1] = C4.w[1];
+	P192.w[0] = C4.w[0];
+	round192_39_57 (q4, q4 - 1, P192, &R192, &incr_exp,
+			&is_midpoint_lt_even,
+			&is_midpoint_gt_even,
+			&is_inexact_lt_midpoint,
+			&is_inexact_gt_midpoint);
+	R64 = R192.w[0]; // one decimal digit
+} else { // if (q4 <= 68)
+	round256_58_76 (q4, q4 - 1, C4, &R256, &incr_exp,
+			&is_midpoint_lt_even,
+			&is_midpoint_gt_even,
+			&is_inexact_lt_midpoint,
+			&is_inexact_gt_midpoint);
+	R64 = R256.w[0]; // one decimal digit
+}
+if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	  !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+	// the result is exact: 10^34 - R64
+	// incr_exp = 0 with certainty
+	z_exp = z_exp - EXP_P1;
+	e3 = e3 - 1;
+	res.w[1] =
+	  z_sign | (z_exp & MASK_EXP) | 0x0001ed09bead87c0ull;
+	res.w[0] = 0x378d8e6400000000ull - R64;
+} else {
+	// We want R64 to be the top digit of C4, but we actually
+	// obtained (C4 * 10^(-q4+1))RN; a correction may be needed,
+	// because the top digit is (C4 * 10^(-q4+1))RZ
+	// however, if incr_exp = 1 then R64 = 10 with certainty
+	if (incr_exp) {
+	  R64 = 10;
+	}
+	// the result is inexact as C4 has more than 1 significant digit
+	// and C3 * 10^scale = 10^33
+	// example of case that is treated here:
+	// 100...0 * 10^e3 - 0.41 * 10^e3 =
+	// 0999...9.59 * 10^e3 -> rounds to 99...96*10^(e3-1)
+	// note that (e3 > expmin}
+	// in order to round, subtract R64 from 10^34 and then compare
+	// C4 - R64 * 10^(q4-1) with 1/2 ulp
+	// calculate 10^34 - R64
+	res.w[1] = 0x0001ed09bead87c0ull;
+	res.w[0] = 0x378d8e6400000000ull - R64;
+	z_exp = z_exp - EXP_P1; // will be OR-ed with sign & significand
+	// calculate C4 - R64 * 10^(q4-1); this is a rare case and
+	// R64 is small, 1 <= R64 <= 9
+	e3 = e3 - 1;
+	if (is_inexact_lt_midpoint) {
+	  is_inexact_lt_midpoint = 0;
+	  is_inexact_gt_midpoint = 1;
+	} else if (is_inexact_gt_midpoint) {
+	  is_inexact_gt_midpoint = 0;
+	  is_inexact_lt_midpoint = 1;
+	} else if (is_midpoint_lt_even) {
+	  is_midpoint_lt_even = 0;
+	  is_midpoint_gt_even = 1;
+	} else if (is_midpoint_gt_even) {
+	  is_midpoint_gt_even = 0;
+	  is_midpoint_lt_even = 1;
+	} else {
+	  ;
+	}
+	// the result is always inexact, and never tiny
+	// check for overflow for RN
+	if (e3 > expmax) {
+	  if (rnd_mode == ROUNDING_TO_NEAREST) {
+	    res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
+	    res.w[0] = 0x0000000000000000ull;
+	    *pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+	  } else {
+	    rounding_correction (rnd_mode,
+				 is_inexact_lt_midpoint,
+				 is_inexact_gt_midpoint,
+				 is_midpoint_lt_even,
+				 is_midpoint_gt_even, e3, &res,
+				 pfpsf);
+	  }
+	  *ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+	  *ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+	  *ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+	  *ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+	  BID_SWAP128 (res);
+	  BID_RETURN (res)
+	}
+	// set the inexact flag
+	*pfpsf |= INEXACT_EXCEPTION;
+	res.w[1] =
+	  z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1];
+	if (rnd_mode != ROUNDING_TO_NEAREST) {
+	  rounding_correction (rnd_mode,
+			       is_inexact_lt_midpoint,
+			       is_inexact_gt_midpoint,
+			       is_midpoint_lt_even,
+			       is_midpoint_gt_even, e3, &res,
+			       pfpsf);
+	}
+	z_exp = res.w[1] & MASK_EXP;
+} // end result is inexact
+} // end q4 > 1
+} else { // if (e3 = emin)
+// if e3 = expmin the result is also tiny (the condition for
+// tininess is C4 > 050...0 [q4 digits] which is met because
+// the msd of C4 is not zero)
+// the result is tiny and inexact in all rounding modes;
+// it is either 100...0 or 0999...9 (use lt_half_ulp, eq_half_ulp,
+// gt_half_ulp to calculate)
+// if (lt_half_ulp || eq_half_ulp) res = 10^33 stays unchanged
+// p_sign != z_sign so swap gt_half_ulp and lt_half_ulp
+if (gt_half_ulp) { // res = 10^33 - 1
+res.w[1] = 0x0000314dc6448d93ull;
+res.w[0] = 0x38c15b09ffffffffull;
+} else {
+res.w[1] = 0x0000314dc6448d93ull;
+res.w[0] = 0x38c15b0a00000000ull;
+}
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+*pfpsf |= UNDERFLOW_EXCEPTION; // inexact is set later
+if (eq_half_ulp) {
+is_midpoint_lt_even = 1; // if (z_sign), as if for absolute value
+} else if (lt_half_ulp) {
+is_inexact_gt_midpoint = 1; //if(z_sign), as if for absolute value
+} else { // if (gt_half_ulp)
+is_inexact_lt_midpoint = 1; //if(z_sign), as if for absolute value
+}
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+is_inexact_lt_midpoint,
+is_inexact_gt_midpoint,
+is_midpoint_lt_even,
+is_midpoint_gt_even, e3, &res,
+pfpsf);
+z_exp = res.w[1] & MASK_EXP;
+}
+} // end e3 = emin
+// set the inexact flag (if the result was not exact)
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even)
+*pfpsf |= INEXACT_EXCEPTION;
+} // end 10^33
+} // end if (p_sign != z_sign)
+res.w[1] = z_sign | (z_exp & MASK_EXP) | res.w[1];
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if (((q3 <= delta && delta < p34 && p34 < delta + q4) || // Case (2)
+(q3 <= delta && delta + q4 <= p34) || // Case (3)
+(delta < q3 && p34 < delta + q4) || // Case (4)
+(delta < q3 && q3 <= delta + q4 && delta + q4 <= p34) || // Case (5)
+(delta + q4 < q3)) && // Case (6)
+!(delta <= 1 && p_sign != z_sign)) { // Case (2), (3), (4), (5) or (6)
+// the result has the sign of z
+if ((q3 <= delta && delta < p34 && p34 < delta + q4) || // Case (2)
+(delta < q3 && p34 < delta + q4)) { // Case (4)
+// round first the sum x * y + z with unbounded exponent
+// scale C3 up by scale = p34 - q3, 1 <= scale <= p34-1,
+// 1 <= scale <= 33
+// calculate res = C3 * 10^scale
+scale = p34 - q3;
+x0 = delta + q4 - p34;
+} else if (delta + q4 < q3) { // Case (6)
+// make Case (6) look like Case (3) or Case (5) with scale = 0
+// by scaling up C4 by 10^(q3 - delta - q4)
+scale = q3 - delta - q4; // 1 <= scale <= 33
+if (q4 <= 19) { // 1 <= scale <= 19; C4 fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C4.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (P128, C4.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C4.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (P128, C4.w[0], ten2k128[scale - 20]);
+}
+} else { // C4 fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C4
+__mul_128x64_to_128 (P128, ten2k64[scale], C4);
+}
+C4.w[0] = P128.w[0];
+C4.w[1] = P128.w[1];
+// e4 does not need adjustment, as it is not used from this point on
+scale = 0;
+x0 = 0;
+// now Case (6) looks like Case (3) or Case (5) with scale = 0
+} else { // if Case (3) or Case (5)
+// Note: Case (3) is similar to Case (2), but scale differs and the
+// result is exact, unless it is tiny (so x0 = 0 when calculating the
+// result with unbounded exponent)
+// calculate first the sum x * y + z with unbounded exponent (exact)
+// scale C3 up by scale = delta + q4 - q3, 1 <= scale <= p34-1,
+// 1 <= scale <= 33
+// calculate res = C3 * 10^scale
+scale = delta + q4 - q3;
+x0 = 0;
+// Note: the comments which follow refer [mainly] to Case (2)]
+}
+case2_repeat:
+if (scale == 0) { // this could happen e.g. if we return to case2_repeat
+// or in Case (4)
+res.w[1] = C3.w[1];
+res.w[0] = C3.w[0];
+} else if (q3 <= 19) { // 1 <= scale <= 19; z fits in 64 bits
+if (scale <= 19) { // 10^scale fits in 64 bits
+// 64 x 64 C3.w[0] * ten2k64[scale]
+__mul_64x64_to_128MACH (res, C3.w[0], ten2k64[scale]);
+} else { // 10^scale fits in 128 bits
+// 64 x 128 C3.w[0] * ten2k128[scale - 20]
+__mul_128x64_to_128 (res, C3.w[0], ten2k128[scale - 20]);
+}
+} else { // z fits in 128 bits, but 10^scale must fit in 64 bits
+// 64 x 128 ten2k64[scale] * C3
+__mul_128x64_to_128 (res, ten2k64[scale], C3);
+}
+// e3 is already calculated
+e3 = e3 - scale;
+// now res = C3 * 10^scale and e3 = e3 - scale
+// Note: C3 * 10^scale could be 10^34 if we returned to case2_repeat
+// because the result was too small
+// round C4 to nearest to q4 - x0 digits, where x0 = delta + q4 - p34,
+// 1 <= x0 <= min (q4 - 1, 2 * p34 - 1) <=> 1 <= x0 <= min (q4 - 1, 67)
+// Also: 1 <= q4 - x0 <= p34 -1 => 1 <= q4 - x0 <= 33 (so the result of
+// the rounding fits in 128 bits!)
+// x0 = delta + q4 - p34 (calculated before reaching case2_repeat)
+// because q3 + q4 - x0 <= P => x0 >= q3 + q4 - p34
+if (x0 == 0) { // this could happen only if we return to case2_repeat, or
+// for Case (3) or Case (6)
+R128.w[1] = C4.w[1];
+R128.w[0] = C4.w[0];
+} else if (q4 <= 18) {
+// 2 <= q4 <= 18, max(1, q3+q4-p34) <= x0 <= q4 - 1, 1 <= x0 <= 17
+round64_2_18 (q4, x0, C4.w[0], &R64, &incr_exp,
+&is_midpoint_lt_even, &is_midpoint_gt_even,
+&is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+if (incr_exp) {
+// R64 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 17
+R64 = ten2k64[q4 - x0];
+}
+R128.w[1] = 0;
+R128.w[0] = R64;
+} else if (q4 <= 38) {
+// 19 <= q4 <= 38, max(1, q3+q4-p34) <= x0 <= q4 - 1, 1 <= x0 <= 37
+P128.w[1] = C4.w[1];
+P128.w[0] = C4.w[0];
+round128_19_38 (q4, x0, P128, &R128, &incr_exp,
+&is_midpoint_lt_even, &is_midpoint_gt_even,
+&is_inexact_lt_midpoint,
+&is_inexact_gt_midpoint);
+if (incr_exp) {
+// R128 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 1, 1 <= q4 - x0 <= 37
+if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
+R128.w[0] = ten2k64[q4 - x0];
+// R128.w[1] stays 0
+} else { // 20 <= q4 - x0 <= 37
+R128.w[0] = ten2k128[q4 - x0 - 20].w[0];
+R128.w[1] = ten2k128[q4 - x0 - 20].w[1];
+}
+}
+} else if (q4 <= 57) {
+// 38 <= q4 <= 57, max(1, q3+q4-p34) <= x0 <= q4 - 1, 5 <= x0 <= 56
+P192.w[2] = C4.w[2];
+P192.w[1] = C4.w[1];
+P192.w[0] = C4.w[0];
+round192_39_57 (q4, x0, P192, &R192, &incr_exp,
+&is_midpoint_lt_even, &is_midpoint_gt_even,
+&is_inexact_lt_midpoint,
+&is_inexact_gt_midpoint);
+// R192.w[2] is always 0
+if (incr_exp) {
+// R192 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 5, 1 <= q4 - x0 <= 52
+if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
+R192.w[0] = ten2k64[q4 - x0];
+// R192.w[1] stays 0
+// R192.w[2] stays 0
+} else { // 20 <= q4 - x0 <= 33
+R192.w[0] = ten2k128[q4 - x0 - 20].w[0];
+R192.w[1] = ten2k128[q4 - x0 - 20].w[1];
+// R192.w[2] stays 0
+}
+}
+R128.w[1] = R192.w[1];
+R128.w[0] = R192.w[0];
+} else {
+// 58 <= q4 <= 68, max(1, q3+q4-p34) <= x0 <= q4 - 1, 25 <= x0 <= 67
+round256_58_76 (q4, x0, C4, &R256, &incr_exp,
+&is_midpoint_lt_even, &is_midpoint_gt_even,
+&is_inexact_lt_midpoint,
+&is_inexact_gt_midpoint);
+// R256.w[3] and R256.w[2] are always 0
+if (incr_exp) {
+// R256 = 10^(q4-x0), 1 <= q4 - x0 <= q4 - 25, 1 <= q4 - x0 <= 43
+if (q4 - x0 <= 19) { // 1 <= q4 - x0 <= 19
+R256.w[0] = ten2k64[q4 - x0];
+// R256.w[1] stays 0
+// R256.w[2] stays 0
+// R256.w[3] stays 0
+} else { // 20 <= q4 - x0 <= 33
+R256.w[0] = ten2k128[q4 - x0 - 20].w[0];
+R256.w[1] = ten2k128[q4 - x0 - 20].w[1];
+// R256.w[2] stays 0
+// R256.w[3] stays 0
+}
+}
+R128.w[1] = R256.w[1];
+R128.w[0] = R256.w[0];
+}
+// now add C3 * 10^scale in res and the signed top (q4-x0) digits of C4,
+// rounded to nearest, which were copied into R128
+if (z_sign == p_sign) {
+lsb = res.w[0] & 0x01; // lsb of C3 * 10^scale
+// the sum can result in [up to] p34 or p34 + 1 digits
+res.w[0] = res.w[0] + R128.w[0];
+res.w[1] = res.w[1] + R128.w[1];
+if (res.w[0] < R128.w[0])
+res.w[1]++; // carry
+// if res > 10^34 - 1 need to increase x0 and decrease scale by 1
+if (res.w[1] > 0x0001ed09bead87c0ull ||
+(res.w[1] == 0x0001ed09bead87c0ull &&
+res.w[0] > 0x378d8e63ffffffffull)) {
+// avoid double rounding error
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+P128.w[1] = res.w[1];
+P128.w[0] = res.w[0];
+round128_19_38 (35, 1, P128, &res, &incr_exp,
+&is_midpoint_lt_even, &is_midpoint_gt_even,
+&is_inexact_lt_midpoint,
+&is_inexact_gt_midpoint);
+// incr_exp is 0 with certainty in this case
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// Note: a double rounding error upward is not possible; for this
+// the result after the first rounding would have to be 99...95
+// (35 digits in all), possibly followed by a number of zeros; this
+// not possible in Cases (2)-(6) or (15)-(17) which may get here
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	     !is_inexact_lt_midpoint
+	     && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	     (is_inexact_gt_midpoint0
+	      || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	     (is_inexact_lt_midpoint0
+	      || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+// adjust exponent
+e3 = e3 + 1;
+if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+!is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+if (is_midpoint_lt_even0 || is_midpoint_gt_even0 ||
+	is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0) {
+is_inexact_lt_midpoint = 1;
+}
+}
+} else {
+// this is the result rounded with unbounded exponent, unless a
+// correction is needed
+res.w[1] = res.w[1] & MASK_COEFF;
+if (lsb == 1) {
+if (is_midpoint_gt_even) {
+// res = res + 1
+is_midpoint_gt_even = 0;
+is_midpoint_lt_even = 1;
+res.w[0]++;
+if (res.w[0] == 0x0)
+	res.w[1]++;
+// check for rounding overflow
+if (res.w[1] == 0x0001ed09bead87c0ull &&
+	  res.w[0] == 0x378d8e6400000000ull) {
+	// res = 10^34 => rounding overflow
+	res.w[1] = 0x0000314dc6448d93ull;
+	res.w[0] = 0x38c15b0a00000000ull; // 10^33
+	e3++;
+}
+} else if (is_midpoint_lt_even) {
+// res = res - 1
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 1;
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+	res.w[1]--;
+// if the result is pure zero, the sign depends on the rounding
+// mode (x*y and z had opposite signs)
+if (res.w[1] == 0x0ull && res.w[0] == 0x0ull) {
+	if (rnd_mode != ROUNDING_DOWN)
+	  z_sign = 0x0000000000000000ull;
+	else
+	  z_sign = 0x8000000000000000ull;
+	// the exponent is max (e3, expmin)
+	res.w[1] = 0x0;
+	res.w[0] = 0x0;
+	*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+	*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+	*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+	*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+	BID_SWAP128 (res);
+	BID_RETURN (res)
+}
+} else {
+;
+}
+}
+}
+} else { // if (z_sign != p_sign)
+lsb = res.w[0] & 0x01; // lsb of C3 * 10^scale; R128 contains rounded C4
+// used to swap rounding indicators if p_sign != z_sign
+// the sum can result in [up to] p34 or p34 - 1 digits
+tmp64 = res.w[0];
+res.w[0] = res.w[0] - R128.w[0];
+res.w[1] = res.w[1] - R128.w[1];
+if (res.w[0] > tmp64)
+res.w[1]--; // borrow
+// if res < 10^33 and exp > expmin need to decrease x0 and
+// increase scale by 1
+if (e3 > expmin && ((res.w[1] < 0x0000314dc6448d93ull ||
+		     (res.w[1] == 0x0000314dc6448d93ull &&
+		      res.w[0] < 0x38c15b0a00000000ull)) ||
+		    (is_inexact_lt_midpoint
+		     && res.w[1] == 0x0000314dc6448d93ull
+		     && res.w[0] == 0x38c15b0a00000000ull))
+&& x0 >= 1) {
+x0 = x0 - 1;
+// first restore e3, otherwise it will be too small
+e3 = e3 + scale;
+scale = scale + 1;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+incr_exp = 0;
+goto case2_repeat;
+}
+// else this is the result rounded with unbounded exponent;
+// because the result has opposite sign to that of C4 which was
+// rounded, need to change the rounding indicators
+if (is_inexact_lt_midpoint) {
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+} else if (is_inexact_gt_midpoint) {
+is_inexact_gt_midpoint = 0;
+is_inexact_lt_midpoint = 1;
+} else if (lsb == 0) {
+if (is_midpoint_lt_even) {
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 1;
+} else if (is_midpoint_gt_even) {
+is_midpoint_gt_even = 0;
+is_midpoint_lt_even = 1;
+} else {
+;
+}
+} else if (lsb == 1) {
+if (is_midpoint_lt_even) {
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0x0)
+res.w[1]++;
+// check for rounding overflow
+if (res.w[1] == 0x0001ed09bead87c0ull &&
+	res.w[0] == 0x378d8e6400000000ull) {
+// res = 10^34 => rounding overflow
+res.w[1] = 0x0000314dc6448d93ull;
+res.w[0] = 0x38c15b0a00000000ull; // 10^33
+e3++;
+}
+} else if (is_midpoint_gt_even) {
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// if the result is pure zero, the sign depends on the rounding
+// mode (x*y and z had opposite signs)
+if (res.w[1] == 0x0ull && res.w[0] == 0x0ull) {
+if (rnd_mode != ROUNDING_DOWN)
+	z_sign = 0x0000000000000000ull;
+else
+	z_sign = 0x8000000000000000ull;
+// the exponent is max (e3, expmin)
+res.w[1] = 0x0;
+res.w[0] = 0x0;
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+} else {
+;
+}
+} else {
+;
+}
+}
+// check for underflow
+if (e3 == expmin) { // and if significand < 10^33 => result is tiny
+if ((res.w[1] & MASK_COEFF) < 0x0000314dc6448d93ull ||
+((res.w[1] & MASK_COEFF) == 0x0000314dc6448d93ull &&
+res.w[0] < 0x38c15b0a00000000ull)) {
+is_tiny = 1;
+}
+} else if (e3 < expmin) {
+// the result is tiny, so we must truncate more of res
+is_tiny = 1;
+x0 = expmin - e3;
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+// determine the number of decimal digits in res
+if (res.w[1] == 0x0) {
+// between 1 and 19 digits
+for (ind = 1; ind <= 19; ind++) {
+if (res.w[0] < ten2k64[ind]) {
+break;
+}
+}
+// ind digits
+} else if (res.w[1] < ten2k128[0].w[1] ||
+	   (res.w[1] == ten2k128[0].w[1]
+	    && res.w[0] < ten2k128[0].w[0])) {
+// 20 digits
+ind = 20;
+} else { // between 21 and 38 digits
+for (ind = 1; ind <= 18; ind++) {
+if (res.w[1] < ten2k128[ind].w[1] ||
+	(res.w[1] == ten2k128[ind].w[1] &&
+	 res.w[0] < ten2k128[ind].w[0])) {
+break;
+}
+}
+// ind + 20 digits
+ind = ind + 20;
+}
+// at this point ind >= x0; because delta >= 2 on this path, the case
+// ind = x0 can occur only in Case (2) or case (3), when C3 has one
+// digit (q3 = 1) equal to 1 (C3 = 1), e3 is expmin (e3 = expmin),
+// the signs of x * y and z are opposite, and through cancellation
+// the most significant decimal digit in res has the weight
+// 10^(emin-1); however, it is clear that in this case the most
+// significant digit is 9, so the result before rounding is
+// 0.9... * 10^emin
+// Otherwise, ind > x0 because there are non-zero decimal digits in the
+// result with weight of at least 10^emin, and correction for underflow
+//  can be carried out using the round*_*_2_* () routines
+if (x0 == ind) { // the result before rounding is 0.9... * 10^emin
+res.w[1] = 0x0;
+res.w[0] = 0x1;
+is_inexact_gt_midpoint = 1;
+} else if (ind <= 18) { // check that 2 <= ind
+// 2 <= ind <= 18, 1 <= x0 <= 17
+round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+if (incr_exp) {
+// R64 = 10^(ind-x0), 1 <= ind - x0 <= ind - 1, 1 <= ind - x0 <= 17
+R64 = ten2k64[ind - x0];
+}
+res.w[1] = 0;
+res.w[0] = R64;
+} else if (ind <= 38) {
+// 19 <= ind <= 38
+P128.w[1] = res.w[1];
+P128.w[0] = res.w[0];
+round128_19_38 (ind, x0, P128, &res, &incr_exp,
+		  &is_midpoint_lt_even, &is_midpoint_gt_even,
+		  &is_inexact_lt_midpoint,
+		  &is_inexact_gt_midpoint);
+if (incr_exp) {
+// R128 = 10^(ind-x0), 1 <= ind - x0 <= ind - 1, 1 <= ind - x0 <= 37
+if (ind - x0 <= 19) { // 1 <= ind - x0 <= 19
+res.w[0] = ten2k64[ind - x0];
+// res.w[1] stays 0
+} else { // 20 <= ind - x0 <= 37
+res.w[0] = ten2k128[ind - x0 - 20].w[0];
+res.w[1] = ten2k128[ind - x0 - 20].w[1];
+}
+}
+}
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// Note: a double rounding error upward is not possible; for this
+// the result after the first rounding would have to be 99...95
+// (35 digits in all), possibly followed by a number of zeros; this
+// not possible in Cases (2)-(6) which may get here
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	   !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	   (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	   (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+// adjust exponent
+e3 = e3 + x0;
+if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+!is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+if (is_midpoint_lt_even0 || is_midpoint_gt_even0 ||
+is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0) {
+is_inexact_lt_midpoint = 1;
+}
+}
+} else {
+; // not underflow
+}
+// check for inexact result
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even) {
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+if (is_tiny)
+*pfpsf |= UNDERFLOW_EXCEPTION;
+}
+// now check for significand = 10^34 (may have resulted from going
+// back to case2_repeat)
+if (res.w[1] == 0x0001ed09bead87c0ull &&
+res.w[0] == 0x378d8e6400000000ull) { // if  res = 10^34
+res.w[1] = 0x0000314dc6448d93ull; // res = 10^33
+res.w[0] = 0x38c15b0a00000000ull;
+e3 = e3 + 1;
+}
+res.w[1] = z_sign | ((UINT64) (e3 + 6176) << 49) | res.w[1];
+// check for overflow
+if (rnd_mode == ROUNDING_TO_NEAREST && e3 > expmax) {
+res.w[1] = z_sign | 0x7800000000000000ull; // +/-inf
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+}
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     e3, &res, pfpsf);
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else {
+// we get here only if delta <= 1 in Cases (2), (3), (4), (5), or (6) and
+// the signs of x*y and z are opposite; in these cases massive
+// cancellation can occur, so it is better to scale either C3 or C4 and
+// to perform the subtraction before rounding; rounding is performed
+// next, depending on the number of decimal digits in the result and on
+// the exponent value
+// Note: overlow is not possible in this case
+// this is similar to Cases (15), (16), and (17)
+if (delta + q4 < q3) { // from Case (6)
+// Case (6) with 0<= delta <= 1 is similar to Cases (15), (16), and
+// (17) if we swap (C3, C4), (q3, q4), (e3, e4), (z_sign, p_sign)
+// and call add_and_round; delta stays positive
+// C4.w[3] = 0 and C4.w[2] = 0, so swap just the low part of C4 with C3
+P128.w[1] = C3.w[1];
+P128.w[0] = C3.w[0];
+C3.w[1] = C4.w[1];
+C3.w[0] = C4.w[0];
+C4.w[1] = P128.w[1];
+C4.w[0] = P128.w[0];
+ind = q3;
+q3 = q4;
+q4 = ind;
+ind = e3;
+e3 = e4;
+e4 = ind;
+tmp_sign = z_sign;
+z_sign = p_sign;
+p_sign = tmp_sign;
+} else { // from Cases (2), (3), (4), (5)
+// In Cases (2), (3), (4), (5) with 0 <= delta <= 1 C3 has to be
+// scaled up by q4 + delta - q3; this is the same as in Cases (15),
+// (16), and (17) if we just change the sign of delta
+delta = -delta;
+}
+add_and_round (q3, q4, e4, delta, p34, z_sign, p_sign, C3, C4,
+	     rnd_mode, &is_midpoint_lt_even,
+	     &is_midpoint_gt_even, &is_inexact_lt_midpoint,
+	     &is_inexact_gt_midpoint, pfpsf, &res);
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+} else { // if delta < 0
+delta = -delta;
+if (p34 < q4 && q4 <= delta) { // Case (7)
+// truncate C4 to p34 digits into res
+// x = q4-p34, 1 <= x <= 34 because 35 <= q4 <= 68
+x0 = q4 - p34;
+if (q4 <= 38) {
+P128.w[1] = C4.w[1];
+P128.w[0] = C4.w[0];
+round128_19_38 (q4, x0, P128, &res, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+} else if (q4 <= 57) { // 35 <= q4 <= 57
+P192.w[2] = C4.w[2];
+P192.w[1] = C4.w[1];
+P192.w[0] = C4.w[0];
+round192_39_57 (q4, x0, P192, &R192, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+res.w[0] = R192.w[0];
+res.w[1] = R192.w[1];
+} else { // if (q4 <= 68)
+round256_58_76 (q4, x0, C4, &R256, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+res.w[0] = R256.w[0];
+res.w[1] = R256.w[1];
+}
+e4 = e4 + x0;
+if (incr_exp) {
+e4 = e4 + 1;
+}
+if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+!is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if C4 rounded to p34 digits is exact then the result is inexact,
+// in a way that depends on the signs of x * y and z
+if (p_sign == z_sign) {
+is_inexact_lt_midpoint = 1;
+} else { // if (p_sign != z_sign)
+if (res.w[1] != 0x0000314dc6448d93ull ||
+res.w[0] != 0x38c15b0a00000000ull) { // res != 10^33
+is_inexact_gt_midpoint = 1;
+} else { // res = 10^33 and exact is a special case
+// if C3 < 1/2 ulp then res = 10^33 and is_inexact_gt_midpoint = 1
+// if C3 = 1/2 ulp then res = 10^33 and is_midpoint_lt_even = 1
+// if C3 > 1/2 ulp then res = 10^34-1 and is_inexact_lt_midpoint = 1
+// Note: ulp is really ulp/10 (after borrow which propagates to msd)
+if (delta > p34 + 1) { // C3 < 1/2
+// res = 10^33, unchanged
+is_inexact_gt_midpoint = 1;
+} else { // if (delta == p34 + 1)
+if (q3 <= 19) {
+	if (C3.w[0] < midpoint64[q3 - 1]) { // C3 < 1/2 ulp
+	  // res = 10^33, unchanged
+	  is_inexact_gt_midpoint = 1;
+	} else if (C3.w[0] == midpoint64[q3 - 1]) { // C3 = 1/2 ulp
+	  // res = 10^33, unchanged
+	  is_midpoint_lt_even = 1;
+	} else { // if (C3.w[0] > midpoint64[q3-1]), C3 > 1/2 ulp
+	  res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
+	  res.w[0] = 0x378d8e63ffffffffull;
+	  e4 = e4 - 1;
+	  is_inexact_lt_midpoint = 1;
+	}
+} else { // if (20 <= q3 <=34)
+	if (C3.w[1] < midpoint128[q3 - 20].w[1] ||
+(C3.w[1] == midpoint128[q3 - 20].w[1] &&
+C3.w[0] < midpoint128[q3 - 20].w[0])) { // C3 < 1/2 ulp
+	  // res = 10^33, unchanged
+	  is_inexact_gt_midpoint = 1;
+	} else if (C3.w[1] == midpoint128[q3 - 20].w[1] &&
+C3.w[0] == midpoint128[q3 - 20].w[0]) { // C3 = 1/2 ulp
+	  // res = 10^33, unchanged
+	  is_midpoint_lt_even = 1;
+	} else { // if (C3 > midpoint128[q3-20]), C3 > 1/2 ulp
+	  res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
+	  res.w[0] = 0x378d8e63ffffffffull;
+	  e4 = e4 - 1;
+	  is_inexact_lt_midpoint = 1;
+	}
+}
+}
+}
+}
+} else if (is_midpoint_lt_even) {
+if (z_sign != p_sign) {
+// needs correction: res = res - 1
+res.w[0] = res.w[0] - 1;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// if it is (10^33-1)*10^e4 then the corect result is
+// (10^34-1)*10(e4-1)
+if (res.w[1] == 0x0000314dc6448d93ull &&
+res.w[0] == 0x38c15b09ffffffffull) {
+res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
+res.w[0] = 0x378d8e63ffffffffull;
+e4 = e4 - 1;
+}
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else { // if (z_sign == p_sign)
+is_midpoint_lt_even = 0;
+is_inexact_gt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even) {
+if (z_sign == p_sign) {
+// needs correction: res = res + 1 (cannot cross in the next binade)
+res.w[0] = res.w[0] + 1;
+if (res.w[0] == 0x0000000000000000ull)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else { // if (z_sign != p_sign)
+is_midpoint_gt_even = 0;
+is_inexact_lt_midpoint = 1;
+}
+} else {
+; // the rounded result is already correct
+}
+// check for overflow
+if (rnd_mode == ROUNDING_TO_NEAREST && e4 > expmax) {
+res.w[1] = p_sign | 0x7800000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (OVERFLOW_EXCEPTION | INEXACT_EXCEPTION);
+} else { // no overflow or not RN
+p_exp = ((UINT64) (e4 + 6176) << 49);
+res.w[1] = p_sign | (p_exp & MASK_EXP) | res.w[1];
+}
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     e4, &res, pfpsf);
+}
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even) {
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if ((q4 <= p34 && p34 <= delta) || // Case (8)
+(q4 <= delta && delta < p34 && p34 < delta + q3) || // Case (9)
+(q4 <= delta && delta + q3 <= p34) || // Case (10)
+(delta < q4 && q4 <= p34 && p34 < delta + q3) || // Case (13)
+(delta < q4 && q4 <= delta + q3 && delta + q3 <= p34) || // Case (14)
+(delta + q3 < q4 && q4 <= p34)) { // Case (18)
+// Case (8) is similar to Case (1), with C3 and C4 swapped
+// Case (9) is similar to Case (2), with C3 and C4 swapped
+// Case (10) is similar to Case (3), with C3 and C4 swapped
+// Case (13) is similar to Case (4), with C3 and C4 swapped
+// Case (14) is similar to Case (5), with C3 and C4 swapped
+// Case (18) is similar to Case (6), with C3 and C4 swapped
+// swap (C3, C4), (q3, q4), (e3, 34), (z_sign, p_sign), (z_exp, p_exp)
+// and go back to delta_ge_zero
+// C4.w[3] = 0 and C4.w[2] = 0, so swap just the low part of C4 with C3
+P128.w[1] = C3.w[1];
+P128.w[0] = C3.w[0];
+C3.w[1] = C4.w[1];
+C3.w[0] = C4.w[0];
+C4.w[1] = P128.w[1];
+C4.w[0] = P128.w[0];
+ind = q3;
+q3 = q4;
+q4 = ind;
+ind = e3;
+e3 = e4;
+e4 = ind;
+tmp_sign = z_sign;
+z_sign = p_sign;
+p_sign = tmp_sign;
+tmp.ui64 = z_exp;
+z_exp = p_exp;
+p_exp = tmp.ui64;
+goto delta_ge_zero;
+} else if ((p34 <= delta && delta < q4 && q4 < delta + q3) || // Case (11)
+(delta < p34 && p34 < q4 && q4 < delta + q3)) { // Case (12)
+// round C3 to nearest to q3 - x0 digits, where x0 = e4 - e3,
+// 1 <= x0 <= q3 - 1 <= p34 - 1
+x0 = e4 - e3; // or x0 = delta + q3 - q4
+if (q3 <= 18) { // 2 <= q3 <= 18
+round64_2_18 (q3, x0, C3.w[0], &R64, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+// C3.w[1] = 0;
+C3.w[0] = R64;
+} else if (q3 <= 38) {
+round128_19_38 (q3, x0, C3, &R128, &incr_exp,
+		&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint);
+C3.w[1] = R128.w[1];
+C3.w[0] = R128.w[0];
+}
+// the rounded result has q3 - x0 digits
+// we want the exponent to be e4, so if incr_exp = 1 then
+// multiply the rounded result by 10 - it will still fit in 113 bits
+if (incr_exp) {
+// 64 x 128 -> 128
+P128.w[1] = C3.w[1];
+P128.w[0] = C3.w[0];
+__mul_64x128_to_128 (C3, ten2k64[1], P128);
+}
+e3 = e3 + x0; // this is e4
+// now add/subtract the 256-bit C4 and the new (and shorter) 128-bit C3;
+// the result will have the sign of x * y; the exponent is e4
+R256.w[3] = 0;
+R256.w[2] = 0;
+R256.w[1] = C3.w[1];
+R256.w[0] = C3.w[0];
+if (p_sign == z_sign) { // R256 = C4 + R256
+add256 (C4, R256, &R256);
+} else { // if (p_sign != z_sign) { // R256 = C4 - R256
+sub256 (C4, R256, &R256); // the result cannot be pure zero
+// because the result has opposite sign to that of R256 which was
+// rounded, need to change the rounding indicators
+lsb = C4.w[0] & 0x01;
+if (is_inexact_lt_midpoint) {
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+} else if (is_inexact_gt_midpoint) {
+is_inexact_gt_midpoint = 0;
+is_inexact_lt_midpoint = 1;
+} else if (lsb == 0) {
+if (is_midpoint_lt_even) {
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 1;
+} else if (is_midpoint_gt_even) {
+is_midpoint_gt_even = 0;
+is_midpoint_lt_even = 1;
+} else {
+;
+}
+} else if (lsb == 1) {
+if (is_midpoint_lt_even) {
+// res = res + 1
+R256.w[0]++;
+if (R256.w[0] == 0x0) {
+R256.w[1]++;
+if (R256.w[1] == 0x0) {
+	R256.w[2]++;
+	if (R256.w[2] == 0x0) {
+	  R256.w[3]++;
+	}
+}
+}
+// no check for rounding overflow - R256 was a difference
+} else if (is_midpoint_gt_even) {
+// res = res - 1
+R256.w[0]--;
+if (R256.w[0] == 0xffffffffffffffffull) {
+R256.w[1]--;
+if (R256.w[1] == 0xffffffffffffffffull) {
+	R256.w[2]--;
+	if (R256.w[2] == 0xffffffffffffffffull) {
+	  R256.w[3]--;
+	}
+}
+}
+} else {
+;
+}
+} else {
+;
+}
+}
+// determine the number of decimal digits in R256
+ind = nr_digits256 (R256); // ind >= p34
+// if R256 is sum, then ind > p34; if R256 is a difference, then
+// ind >= p34; this means that we can calculate the result rounded to
+// the destination precision, with unbounded exponent, starting from R256
+// and using the indicators from the rounding of C3 to avoid a double
+// rounding error
+if (ind < p34) {
+;
+} else if (ind == p34) {
+// the result rounded to the destination precision with
+// unbounded exponent
+// is (-1)^p_sign * R256 * 10^e4
+res.w[1] = R256.w[1];
+res.w[0] = R256.w[0];
+} else { // if (ind > p34)
+// if more than P digits, round to nearest to P digits
+// round R256 to p34 digits
+x0 = ind - p34; // 1 <= x0 <= 34 as 35 <= ind <= 68
+// save C3 rounding indicators to help avoid double rounding error
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+// initialize rounding indicators
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+// round to p34 digits; the result fits in 113 bits
+if (ind <= 38) {
+P128.w[1] = R256.w[1];
+P128.w[0] = R256.w[0];
+round128_19_38 (ind, x0, P128, &R128, &incr_exp,
+		  &is_midpoint_lt_even, &is_midpoint_gt_even,
+		  &is_inexact_lt_midpoint,
+		  &is_inexact_gt_midpoint);
+} else if (ind <= 57) {
+P192.w[2] = R256.w[2];
+P192.w[1] = R256.w[1];
+P192.w[0] = R256.w[0];
+round192_39_57 (ind, x0, P192, &R192, &incr_exp,
+		  &is_midpoint_lt_even, &is_midpoint_gt_even,
+		  &is_inexact_lt_midpoint,
+		  &is_inexact_gt_midpoint);
+R128.w[1] = R192.w[1];
+R128.w[0] = R192.w[0];
+} else { // if (ind <= 68)
+round256_58_76 (ind, x0, R256, &R256, &incr_exp,
+		  &is_midpoint_lt_even, &is_midpoint_gt_even,
+		  &is_inexact_lt_midpoint,
+		  &is_inexact_gt_midpoint);
+R128.w[1] = R256.w[1];
+R128.w[0] = R256.w[0];
+}
+// the rounded result has p34 = 34 digits
+e4 = e4 + x0 + incr_exp;
+res.w[1] = R128.w[1];
+res.w[0] = R128.w[0];
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+// Note: a double rounding error upward is not possible; for this
+// the result after the first rounding would have to be 99...95
+// (35 digits in all), possibly followed by a number of zeros; this
+// not possible in Cases (2)-(6) or (15)-(17) which may get here
+// if this is 10^33 - 1 make it 10^34 - 1 and decrement exponent
+if (res.w[1] == 0x0000314dc6448d93ull &&
+res.w[0] == 0x38c15b09ffffffffull) { // 10^33 - 1
+res.w[1] = 0x0001ed09bead87c0ull; // 10^34 - 1
+res.w[0] = 0x378d8e63ffffffffull;
+e4--;
+}
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	   !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	   (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	   (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+}
+// determine tininess
+if (rnd_mode == ROUNDING_TO_NEAREST) {
+if (e4 < expmin) {
+is_tiny = 1; // for other rounding modes apply correction
+}
+} else {
+// for RM, RP, RZ, RA apply correction in order to determine tininess
+// but do not save the result; apply the correction to
+// (-1)^p_sign * res * 10^0
+P128.w[1] = p_sign | 0x3040000000000000ull | res.w[1];
+P128.w[0] = res.w[0];
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     0, &P128, pfpsf);
+scale = ((P128.w[1] & MASK_EXP) >> 49) - 6176; // -1, 0, or +1
+// the number of digits in the significand is p34 = 34
+if (e4 + scale < expmin) {
+is_tiny = 1;
+}
+}
+// the result rounded to the destination precision with unbounded exponent
+// is (-1)^p_sign * res * 10^e4
+res.w[1] = p_sign | ((UINT64) (e4 + 6176) << 49) | res.w[1]; // RN
+// res.w[0] unchanged;
+// Note: res is correct only if expmin <= e4 <= expmax
+ind = p34; // the number of decimal digits in the signifcand of res
+// at this point we have the result rounded with unbounded exponent in
+// res and we know its tininess:
+// res = (-1)^p_sign * significand * 10^e4,
+// where q (significand) = ind = p34
+// Note: res is correct only if expmin <= e4 <= expmax
+// check for overflow if RN
+if (rnd_mode == ROUNDING_TO_NEAREST
+&& (ind + e4) > (p34 + expmax)) {
+res.w[1] = p_sign | 0x7800000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} // else not overflow or not RN, so continue
+// from this point on this is similar to the last part of the computation
+// for Cases (15), (16), (17)
+// if (e4 >= expmin) we have the result rounded with bounded exponent
+if (e4 < expmin) {
+x0 = expmin - e4; // x0 >= 1; the number of digits to chop off of res
+// where the result rounded [at most] once is
+//   (-1)^p_sign * significand_res * 10^e4
+// avoid double rounding error
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+if (x0 > ind) {
+// nothing is left of res when moving the decimal point left x0 digits
+is_inexact_lt_midpoint = 1;
+res.w[1] = p_sign | 0x0000000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+e4 = expmin;
+} else if (x0 == ind) { // 1 <= x0 = ind <= p34 = 34
+// this is <, =, or > 1/2 ulp
+// compare the ind-digit value in the significand of res with
+// 1/2 ulp = 5*10^(ind-1), i.e. determine whether it is
+// less than, equal to, or greater than 1/2 ulp (significand of res)
+R128.w[1] = res.w[1] & MASK_COEFF;
+R128.w[0] = res.w[0];
+if (ind <= 19) {
+if (R128.w[0] < midpoint64[ind - 1]) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (R128.w[0] == midpoint64[ind - 1]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+} else { // if (ind <= 38)
+if (R128.w[1] < midpoint128[ind - 20].w[1] ||
+(R128.w[1] == midpoint128[ind - 20].w[1] &&
+R128.w[0] < midpoint128[ind - 20].w[0])) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (R128.w[1] == midpoint128[ind - 20].w[1] &&
+R128.w[0] == midpoint128[ind - 20].w[0]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+}
+if (lt_half_ulp || eq_half_ulp) {
+// res = +0.0 * 10^expmin
+res.w[1] = 0x0000000000000000ull;
+res.w[0] = 0x0000000000000000ull;
+} else { // if (gt_half_ulp)
+// res = +1 * 10^expmin
+res.w[1] = 0x0000000000000000ull;
+res.w[0] = 0x0000000000000001ull;
+}
+res.w[1] = p_sign | res.w[1];
+e4 = expmin;
+} else { // if (1 <= x0 <= ind - 1 <= 33)
+// round the ind-digit result to ind - x0 digits
+if (ind <= 18) { // 2 <= ind <= 18
+round64_2_18 (ind, x0, res.w[0], &R64, &incr_exp,
+		  &is_midpoint_lt_even, &is_midpoint_gt_even,
+		  &is_inexact_lt_midpoint,
+		  &is_inexact_gt_midpoint);
+res.w[1] = 0x0;
+res.w[0] = R64;
+} else if (ind <= 38) {
+P128.w[1] = res.w[1] & MASK_COEFF;
+P128.w[0] = res.w[0];
+round128_19_38 (ind, x0, P128, &res, &incr_exp,
+		    &is_midpoint_lt_even, &is_midpoint_gt_even,
+		    &is_inexact_lt_midpoint,
+		    &is_inexact_gt_midpoint);
+}
+e4 = e4 + x0; // expmin
+// we want the exponent to be expmin, so if incr_exp = 1 then
+// multiply the rounded result by 10 - it will still fit in 113 bits
+if (incr_exp) {
+// 64 x 128 -> 128
+P128.w[1] = res.w[1] & MASK_COEFF;
+P128.w[0] = res.w[0];
+__mul_64x128_to_128 (res, ten2k64[1], P128);
+}
+res.w[1] =
+p_sign | ((UINT64) (e4 + 6176) << 49) | (res.
+					     w[1] & MASK_COEFF);
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res.w[0]--;
+if (res.w[0] == 0xffffffffffffffffull)
+res.w[1]--;
+// Note: a double rounding error upward is not possible; for this
+// the result after the first rounding would have to be 99...95
+// (35 digits in all), possibly followed by a number of zeros; this
+// not possible in this underflow case
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res.w[0]++;
+if (res.w[0] == 0)
+res.w[1]++;
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	     !is_inexact_lt_midpoint
+	     && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	     (is_inexact_gt_midpoint0
+	      || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	     (is_inexact_lt_midpoint0
+	      || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+}
+}
+// res contains the correct result
+// apply correction if not rounding to nearest
+if (rnd_mode != ROUNDING_TO_NEAREST) {
+rounding_correction (rnd_mode,
+		     is_inexact_lt_midpoint,
+		     is_inexact_gt_midpoint,
+		     is_midpoint_lt_even, is_midpoint_gt_even,
+		     e4, &res, pfpsf);
+}
+if (is_midpoint_lt_even || is_midpoint_gt_even ||
+is_inexact_lt_midpoint || is_inexact_gt_midpoint) {
+// set the inexact flag
+*pfpsf |= INEXACT_EXCEPTION;
+if (is_tiny)
+*pfpsf |= UNDERFLOW_EXCEPTION;
+}
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else if ((p34 <= delta && delta + q3 <= q4) || // Case (15)
+(delta < p34 && p34 < delta + q3 && delta + q3 <= q4) || //Case (16)
+(delta + q3 <= p34 && p34 < q4)) { // Case (17)
+// calculate first the result rounded to the destination precision, with
+// unbounded exponent
+add_and_round (q3, q4, e4, delta, p34, z_sign, p_sign, C3, C4,
+rnd_mode, &is_midpoint_lt_even,
+&is_midpoint_gt_even, &is_inexact_lt_midpoint,
+&is_inexact_gt_midpoint, pfpsf, &res);
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+} else {
+;
+}
+} // end if delta < 0
+*ptr_is_midpoint_lt_even = is_midpoint_lt_even;
+*ptr_is_midpoint_gt_even = is_midpoint_gt_even;
+*ptr_is_inexact_lt_midpoint = is_inexact_lt_midpoint;
+*ptr_is_inexact_gt_midpoint = is_inexact_gt_midpoint;
+BID_SWAP128 (res);
+BID_RETURN (res)
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128_fma (UINT128 * pres, UINT128 * px, UINT128 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT128 x = *px, y = *py, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128_fma (UINT128 x, UINT128 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even, is_midpoint_gt_even,
+is_inexact_lt_midpoint, is_inexact_gt_midpoint;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+#if DECIMAL_CALL_BY_REFERENCE
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, &x, &y, &z
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x, y,
+		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128ddd_fma (UINT128 * pres, UINT64 * px, UINT64 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px, y = *py, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128ddd_fma (UINT64 x, UINT64 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 x1, y1, z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, &x1, &y1, &z1
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x1, y1,
+		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128ddq_fma (UINT128 * pres, UINT64 * px, UINT64 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px, y = *py;
+UINT128 z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128ddq_fma (UINT64 x, UINT64 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 x1, y1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, &x1, &y1, &z
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x1, y1,
+		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128dqd_fma (UINT128 * pres, UINT64 * px, UINT128 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128dqd_fma (UINT64 x, UINT128 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 x1, z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, &x1, py, &z1
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x1, y,
+		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128dqq_fma (UINT128 * pres, UINT64 * px, UINT128 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128dqq_fma (UINT64 x, UINT128 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 x1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, &x1, py, pz
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x1, y,
+		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128qdd_fma (UINT128 * pres, UINT128 * px, UINT64 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 y = *py, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128qdd_fma (UINT128 x, UINT64 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 y1, z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, px, &y1, &z1
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x, y1,
+		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128qdq_fma (UINT128 * pres, UINT128 * px, UINT64 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 y = *py;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128qdq_fma (UINT128 x, UINT64 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 y1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, px, &y1, pz
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x, y1,
+		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid128qqd_fma (UINT128 * pres, UINT128 * px, UINT128 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT128
+bid128qqd_fma (UINT128 x, UINT128 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+	  &is_inexact_lt_midpoint, &is_inexact_gt_midpoint,
+	  &res, px, py, &z1
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res = bid128_ext_fma (&is_midpoint_lt_even, &is_midpoint_gt_even,
+		&is_inexact_lt_midpoint,
+		&is_inexact_gt_midpoint, x, y,
+		z1 _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+BID_RETURN (res);
+}
+// Note: bid128qqq_fma is represented by bid128_fma
+// Note: bid64ddd_fma is represented by bid64_fma
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64ddq_fma (UINT64 * pres, UINT64 * px, UINT64 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px, y = *py;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64ddq_fma (UINT64 x, UINT64 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+UINT128 x1, y1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64qqq_fma (&res1, &x1, &y1, pz
+	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	_EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res1 = bid64qqq_fma (x1, y1, z
+	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	       _EXC_INFO_ARG);
+#endif
+BID_RETURN (res1);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64dqd_fma (UINT64 * pres, UINT64 * px, UINT128 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64dqd_fma (UINT64 x, UINT128 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+UINT128 x1, z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64qqq_fma (&res1, &x1, py, &z1
+	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	_EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res1 = bid64qqq_fma (x1, y, z1
+	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	       _EXC_INFO_ARG);
+#endif
+BID_RETURN (res1);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64dqq_fma (UINT64 * pres, UINT64 * px, UINT128 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 x = *px;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64dqq_fma (UINT64 x, UINT128 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+UINT128 x1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&x1, &x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64qqq_fma (&res1, &x1, py, pz
+	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	_EXC_INFO_ARG);
+#else
+x1 = bid64_to_bid128 (x _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res1 = bid64qqq_fma (x1, y, z
+	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	       _EXC_INFO_ARG);
+#endif
+BID_RETURN (res1);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64qdd_fma (UINT64 * pres, UINT128 * px, UINT64 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 y = *py, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64qdd_fma (UINT128 x, UINT64 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+UINT128 y1, z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64qqq_fma (&res1, px, &y1, &z1
+	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	_EXC_INFO_ARG);
+#else
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res1 = bid64qqq_fma (x, y1, z1
+	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	       _EXC_INFO_ARG);
+#endif
+BID_RETURN (res1);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64qdq_fma (UINT64 * pres, UINT128 * px, UINT64 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 y = *py;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64qdq_fma (UINT128 x, UINT64 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+UINT128 y1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&y1, &y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64qqq_fma (&res1, px, &y1, pz
+	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	_EXC_INFO_ARG);
+#else
+y1 = bid64_to_bid128 (y _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res1 = bid64qqq_fma (x, y1, z
+	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	       _EXC_INFO_ARG);
+#endif
+BID_RETURN (res1);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64qqd_fma (UINT64 * pres, UINT128 * px, UINT128 * py, UINT64 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT64 z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64qqd_fma (UINT128 x, UINT128 y, UINT64 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+UINT128 z1;
+#if DECIMAL_CALL_BY_REFERENCE
+bid64_to_bid128 (&z1, &z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+bid64qqq_fma (&res1, px, py, &z1
+	_RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	_EXC_INFO_ARG);
+#else
+z1 = bid64_to_bid128 (z _EXC_FLAGS_ARG _EXC_MASKS_ARG _EXC_INFO_ARG);
+res1 = bid64qqq_fma (x, y, z1
+	       _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	       _EXC_INFO_ARG);
+#endif
+BID_RETURN (res1);
+}
+#if DECIMAL_CALL_BY_REFERENCE
+void
+bid64qqq_fma (UINT64 * pres, UINT128 * px, UINT128 * py, UINT128 * pz
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+UINT128 x = *px, y = *py, z = *pz;
+#if !DECIMAL_GLOBAL_ROUNDING
+unsigned int rnd_mode = *prnd_mode;
+#endif
+#else
+UINT64
+bid64qqq_fma (UINT128 x, UINT128 y, UINT128 z
+_RND_MODE_PARAM _EXC_FLAGS_PARAM _EXC_MASKS_PARAM
+_EXC_INFO_PARAM) {
+#endif
+int is_midpoint_lt_even0 = 0, is_midpoint_gt_even0 = 0,
+is_inexact_lt_midpoint0 = 0, is_inexact_gt_midpoint0 = 0;
+int is_midpoint_lt_even = 0, is_midpoint_gt_even = 0,
+is_inexact_lt_midpoint = 0, is_inexact_gt_midpoint = 0;
+int incr_exp;
+UINT128 res = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT128 res128 = { {0xbaddbaddbaddbaddull, 0xbaddbaddbaddbaddull} };
+UINT64 res1 = 0xbaddbaddbaddbaddull;
+unsigned int save_fpsf; // needed because of the call to bid128_ext_fma
+UINT64 sign;
+UINT64 exp;
+int unbexp;
+UINT128 C;
+BID_UI64DOUBLE tmp;
+int nr_bits;
+int q, x0;
+int scale;
+int lt_half_ulp = 0, eq_half_ulp = 0;
+// Note: for rounding modes other than RN or RA, the result can be obtained
+// by rounding first to BID128 and then to BID64
+save_fpsf = *pfpsf; // sticky bits - caller value must be preserved
+*pfpsf = 0;
+#if DECIMAL_CALL_BY_REFERENCE
+bid128_ext_fma (&is_midpoint_lt_even0, &is_midpoint_gt_even0,
+	  &is_inexact_lt_midpoint0, &is_inexact_gt_midpoint0,
+	  &res, &x, &y, &z
+	  _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+	  _EXC_INFO_ARG);
+#else
+res = bid128_ext_fma (&is_midpoint_lt_even0, &is_midpoint_gt_even0,
+		&is_inexact_lt_midpoint0,
+		&is_inexact_gt_midpoint0, x, y,
+		z _RND_MODE_ARG _EXC_FLAGS_ARG _EXC_MASKS_ARG
+		_EXC_INFO_ARG);
+#endif
+if ((rnd_mode == ROUNDING_DOWN) || (rnd_mode == ROUNDING_UP) ||
+(rnd_mode == ROUNDING_TO_ZERO) || // no double rounding error is possible
+((res.w[HIGH_128W] & MASK_NAN) == MASK_NAN) || //res=QNaN (cannot be SNaN)
+((res.w[HIGH_128W] & MASK_ANY_INF) == MASK_INF)) { // result is infinity
+#if DECIMAL_CALL_BY_REFERENCE
+bid128_to_bid64 (&res1, &res _RND_MODE_ARG _EXC_FLAGS_ARG);
+#else
+res1 = bid128_to_bid64 (res _RND_MODE_ARG _EXC_FLAGS_ARG);
+#endif
+// determine the unbiased exponent of the result
+unbexp = ((res1 >> 53) & 0x3ff) - 398;
+// if subnormal, res1  must have exp = -398
+// if tiny and inexact set underflow and inexact status flags
+if (!((res1 & MASK_NAN) == MASK_NAN) &&	// res1 not NaN
+(unbexp == -398)
+&& ((res1 & MASK_BINARY_SIG1) < 1000000000000000ull)
+&& (is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0
+|| is_midpoint_lt_even0 || is_midpoint_gt_even0)) {
+// set the inexact flag and the underflow flag
+*pfpsf |= (INEXACT_EXCEPTION | UNDERFLOW_EXCEPTION);
+} else if (is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 ||
+is_midpoint_lt_even0 || is_midpoint_gt_even0) {
+// set the inexact flag and the underflow flag
+*pfpsf |= INEXACT_EXCEPTION;
+}
+*pfpsf |= save_fpsf;
+BID_RETURN (res1);
+} // else continue, and use rounding to nearest to round to 16 digits
+// at this point the result is rounded to nearest (even or away) to 34 digits
+// (or less if exact), and it is zero or finite non-zero canonical [sub]normal
+sign = res.w[HIGH_128W] & MASK_SIGN; // 0 for positive, MASK_SIGN for negative
+exp = res.w[HIGH_128W] & MASK_EXP; // biased and shifted left 49 bits
+unbexp = (exp >> 49) - 6176;
+C.w[1] = res.w[HIGH_128W] & MASK_COEFF;
+C.w[0] = res.w[LOW_128W];
+if ((C.w[1] == 0x0 && C.w[0] == 0x0) ||	// result is zero
+(unbexp <= (-398 - 35)) || (unbexp >= (369 + 16))) {
+// clear under/overflow
+#if DECIMAL_CALL_BY_REFERENCE
+bid128_to_bid64 (&res1, &res _RND_MODE_ARG _EXC_FLAGS_ARG);
+#else
+res1 = bid128_to_bid64 (res _RND_MODE_ARG _EXC_FLAGS_ARG);
+#endif
+*pfpsf |= save_fpsf;
+BID_RETURN (res1);
+} // else continue
+// -398 - 34 <= unbexp <= 369 + 15
+if (rnd_mode == ROUNDING_TIES_AWAY) {
+// apply correction, if needed, to make the result rounded to nearest-even
+if (is_midpoint_gt_even) {
+// res = res - 1
+res1--; // res1 is now even
+} // else the result is already correctly rounded to nearest-even
+}
+// at this point the result is finite, non-zero canonical normal or subnormal,
+// and in most cases overflow or underflow will not occur
+// determine the number of digits q in the result
+// q = nr. of decimal digits in x
+// determine first the nr. of bits in x
+if (C.w[1] == 0) {
+if (C.w[0] >= 0x0020000000000000ull) { // x >= 2^53
+// split the 64-bit value in two 32-bit halves to avoid rounding errors
+if (C.w[0] >= 0x0000000100000000ull) { // x >= 2^32
+tmp.d = (double) (C.w[0] >> 32); // exact conversion
+nr_bits =
+33 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+} else { // x < 2^32
+tmp.d = (double) (C.w[0]); // exact conversion
+nr_bits =
+1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // if x < 2^53
+tmp.d = (double) C.w[0]; // exact conversion
+nr_bits =
+1 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+} else { // C.w[1] != 0 => nr. bits = 64 + nr_bits (C.w[1])
+tmp.d = (double) C.w[1]; // exact conversion
+nr_bits =
+65 + ((((unsigned int) (tmp.ui64 >> 52)) & 0x7ff) - 0x3ff);
+}
+q = nr_digits[nr_bits - 1].digits;
+if (q == 0) {
+q = nr_digits[nr_bits - 1].digits1;
+if (C.w[1] > nr_digits[nr_bits - 1].threshold_hi ||
+(C.w[1] == nr_digits[nr_bits - 1].threshold_hi &&
+C.w[0] >= nr_digits[nr_bits - 1].threshold_lo))
+q++;
+}
+// if q > 16, round to nearest even to 16 digits (but for underflow it may
+// have to be truncated even more)
+if (q > 16) {
+x0 = q - 16;
+if (q <= 18) {
+round64_2_18 (q, x0, C.w[0], &res1, &incr_exp,
+	    &is_midpoint_lt_even, &is_midpoint_gt_even,
+	    &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+} else { // 19 <= q <= 34
+round128_19_38 (q, x0, C, &res128, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+res1 = res128.w[0]; // the result fits in 64 bits
+}
+unbexp = unbexp + x0;
+if (incr_exp)
+unbexp++;
+q = 16; // need to set in case denormalization is necessary
+} else {
+// the result does not require a second rounding (and it must have
+// been exact in the first rounding, since q <= 16)
+res1 = C.w[0];
+}
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res1--; // res1 becomes odd
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+if (res1 == 0x00038d7ea4c67fffull) { // 10^15 - 1
+res1 = 0x002386f26fc0ffffull; // 10^16 - 1
+unbexp--;
+}
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res1++; // res1 becomes odd (so it cannot be 10^16)
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+!is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if this second rounding was exact the result may still be
+// inexact because of the first rounding
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+(is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+(is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+// this is the result rounded correctly to nearest even, with unbounded exp.
+// check for overflow
+if (q + unbexp > P16 + expmax16) {
+res1 = sign | 0x7800000000000000ull;
+*pfpsf |= (INEXACT_EXCEPTION | OVERFLOW_EXCEPTION);
+*pfpsf |= save_fpsf;
+BID_RETURN (res1)
+} else if (unbexp > expmax16) { // q + unbexp <= P16 + expmax16
+// not overflow; the result must be exact, and we can multiply res1 by
+// 10^(unbexp - expmax16) and the product will fit in 16 decimal digits
+scale = unbexp - expmax16;
+res1 = res1 * ten2k64[scale]; // res1 * 10^scale
+unbexp = expmax16; // unbexp - scale
+} else {
+; // continue
+}
+// check for underflow
+if (q + unbexp < P16 + expmin16) {
+if (unbexp < expmin16) {
+// we must truncate more of res
+x0 = expmin16 - unbexp; // x0 >= 1
+is_inexact_lt_midpoint0 = is_inexact_lt_midpoint;
+is_inexact_gt_midpoint0 = is_inexact_gt_midpoint;
+is_midpoint_lt_even0 = is_midpoint_lt_even;
+is_midpoint_gt_even0 = is_midpoint_gt_even;
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+// the number of decimal digits in res1 is q
+if (x0 < q) { // 1 <= x0 <= q-1 => round res to q - x0 digits
+// 2 <= q <= 16, 1 <= x0 <= 15
+round64_2_18 (q, x0, res1, &res1, &incr_exp,
+	      &is_midpoint_lt_even, &is_midpoint_gt_even,
+	      &is_inexact_lt_midpoint, &is_inexact_gt_midpoint);
+if (incr_exp) {
+// res1 = 10^(q-x0), 1 <= q - x0 <= q - 1, 1 <= q - x0 <= 15
+res1 = ten2k64[q - x0];
+}
+unbexp = unbexp + x0; // expmin16
+} else if (x0 == q) {
+// the second rounding is for 0.d(0)d(1)...d(q-1) * 10^emin
+// determine relationship with 1/2 ulp
+// q <= 16
+if (res1 < midpoint64[q - 1]) { // < 1/2 ulp
+lt_half_ulp = 1;
+is_inexact_lt_midpoint = 1;
+} else if (res1 == midpoint64[q - 1]) { // = 1/2 ulp
+eq_half_ulp = 1;
+is_midpoint_gt_even = 1;
+} else { // > 1/2 ulp
+// gt_half_ulp = 1;
+is_inexact_gt_midpoint = 1;
+}
+if (lt_half_ulp || eq_half_ulp) {
+// res = +0.0 * 10^expmin16
+res1 = 0x0000000000000000ull;
+} else { // if (gt_half_ulp)
+// res = +1 * 10^expmin16
+res1 = 0x0000000000000001ull;
+}
+unbexp = expmin16;
+} else { // if (x0 > q)
+// the second rounding is for 0.0...d(0)d(1)...d(q-1) * 10^emin
+res1 = 0x0000000000000000ull;
+unbexp = expmin16;
+is_inexact_lt_midpoint = 1;
+}
+// avoid a double rounding error
+if ((is_inexact_gt_midpoint0 || is_midpoint_lt_even0) &&
+is_midpoint_lt_even) { // double rounding error upward
+// res = res - 1
+res1--; // res1 becomes odd
+is_midpoint_lt_even = 0;
+is_inexact_lt_midpoint = 1;
+} else if ((is_inexact_lt_midpoint0 || is_midpoint_gt_even0) &&
+is_midpoint_gt_even) { // double rounding error downward
+// res = res + 1
+res1++; // res1 becomes odd
+is_midpoint_gt_even = 0;
+is_inexact_gt_midpoint = 1;
+} else if (!is_midpoint_lt_even && !is_midpoint_gt_even &&
+	 !is_inexact_lt_midpoint && !is_inexact_gt_midpoint) {
+// if this rounding was exact the result may still be
+// inexact because of the previous roundings
+if (is_inexact_gt_midpoint0 || is_midpoint_lt_even0) {
+is_inexact_gt_midpoint = 1;
+}
+if (is_inexact_lt_midpoint0 || is_midpoint_gt_even0) {
+is_inexact_lt_midpoint = 1;
+}
+} else if (is_midpoint_gt_even &&
+	 (is_inexact_gt_midpoint0 || is_midpoint_lt_even0)) {
+// pulled up to a midpoint
+is_inexact_lt_midpoint = 1;
+is_inexact_gt_midpoint = 0;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else if (is_midpoint_lt_even &&
+	 (is_inexact_lt_midpoint0 || is_midpoint_gt_even0)) {
+// pulled down to a midpoint
+is_inexact_lt_midpoint = 0;
+is_inexact_gt_midpoint = 1;
+is_midpoint_lt_even = 0;
+is_midpoint_gt_even = 0;
+} else {
+;
+}
+}
+// else if unbexp >= emin then q < P (because q + unbexp < P16 + expmin16)
+// and the result is tiny and exact
+// check for inexact result
+if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even ||
+is_inexact_lt_midpoint0 || is_inexact_gt_midpoint0 ||
+is_midpoint_lt_even0 || is_midpoint_gt_even0) {
+// set the inexact flag and the underflow flag
+*pfpsf |= (INEXACT_EXCEPTION | UNDERFLOW_EXCEPTION);
+}
+} else if (is_inexact_lt_midpoint || is_inexact_gt_midpoint ||
+is_midpoint_lt_even || is_midpoint_gt_even) {
+*pfpsf |= INEXACT_EXCEPTION;
+}
+// this is the result rounded correctly to nearest, with bounded exponent
+if (rnd_mode == ROUNDING_TIES_AWAY && is_midpoint_gt_even) { // correction
+// res = res + 1
+res1++; // res1 is now odd
+} // else the result is already correct
+// assemble the result
+if (res1 < 0x0020000000000000ull) { // res < 2^53
+res1 = sign | ((UINT64) (unbexp + 398) << 53) | res1;
+} else { // res1 >= 2^53
+res1 = sign | MASK_STEERING_BITS |
+((UINT64) (unbexp + 398) << 51) | (res1 & MASK_BINARY_SIG2);
+}
+*pfpsf |= save_fpsf;
+BID_RETURN (res1);
+}

Mercurial > hg > CbC > CbC_gcc

comparison libgcc/config/libbid/bid128_fma.c @ 0:a06113de4d67