// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program 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 Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License

// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program 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 Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License

 * version 2.1 of the License, or (at your option) any later version.
 * 
 * This library 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
 * Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public

 * version 2.1 of the License, or (at your option) any later version.
 * 
 * This library 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
 * Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public

 * version 2.1 of the License, or (at your option) any later version.
 * 
 * This library 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
 * Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public

   * default rounding mode: if the two nearest representable values are equally near, the one with
   * the least significant bit zero is chosen. (In such cases, both of the nearest representable
   * values are even integers; this method returns the one that is a multiple of a greater power of
   * two.)
   *
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}

// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program 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 Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License

// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program 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 Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License

// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program 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 Affero General Public License for more details.
//
// You should have received a copy of the GNU Affero General Public License

     * 10^floor(log10(x)).
     */

    if (approxCmp > 0) {
      /*
       * The code is written so that even completely incorrect approximations will still yield the
       * correct answer eventually, but in practice this branch should almost never be entered, and
       * even then the loop should not run more than once.
       */
      do {
        approxLog10--;