103  * determines how any discarded trailing digits affect the returned
 104  * result.
 105  *
 106  * <p>For all arithmetic operators , the operation is carried out as
 107  * though an exact intermediate result were first calculated and then
 108  * rounded to the number of digits specified by the precision setting
 109  * (if necessary), using the selected rounding mode.  If the exact
 110  * result is not returned, some digit positions of the exact result
 111  * are discarded.  When rounding increases the magnitude of the
 112  * returned result, it is possible for a new digit position to be
 113  * created by a carry propagating to a leading {@literal "9"} digit.
 114  * For example, rounding the value 999.9 to three digits rounding up
 115  * would be numerically equal to one thousand, represented as
 116  * 100&times;10<sup>1</sup>.  In such cases, the new {@literal "1"} is
 117  * the leading digit position of the returned result.
 118  *
 119  * <p>Besides a logical exact result, each arithmetic operation has a
 120  * preferred scale for representing a result.  The preferred
 121  * scale for each operation is listed in the table below.
 122  *
 123  * <table border>
 124  * <caption><b>Preferred Scales for Results of Arithmetic Operations
 125  * </b></caption>

 126  * <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>


 127  * <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>
 128  * <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>
 129  * <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>
 130  * <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>
 131  * <tr><td>Square root</td><td>radicand.scale()/2</td>

 132  * </table>
 133  *
 134  * These scales are the ones used by the methods which return exact
 135  * arithmetic results; except that an exact divide may have to use a
 136  * larger scale since the exact result may have more digits.  For
 137  * example, {@code 1/32} is {@code 0.03125}.
 138  *
 139  * <p>Before rounding, the scale of the logical exact intermediate
 140  * result is the preferred scale for that operation.  If the exact
 141  * numerical result cannot be represented in {@code precision}
 142  * digits, rounding selects the set of digits to return and the scale
 143  * of the result is reduced from the scale of the intermediate result
 144  * to the least scale which can represent the {@code precision}
 145  * digits actually returned.  If the exact result can be represented
 146  * with at most {@code precision} digits, the representation
 147  * of the result with the scale closest to the preferred scale is
 148  * returned.  In particular, an exactly representable quotient may be
 149  * represented in fewer than {@code precision} digits by removing
 150  * trailing zeros and decreasing the scale.  For example, rounding to
 151  * three digits using the {@linkplain RoundingMode#FLOOR floor}

 103  * determines how any discarded trailing digits affect the returned
 104  * result.
 105  *
 106  * <p>For all arithmetic operators , the operation is carried out as
 107  * though an exact intermediate result were first calculated and then
 108  * rounded to the number of digits specified by the precision setting
 109  * (if necessary), using the selected rounding mode.  If the exact
 110  * result is not returned, some digit positions of the exact result
 111  * are discarded.  When rounding increases the magnitude of the
 112  * returned result, it is possible for a new digit position to be
 113  * created by a carry propagating to a leading {@literal "9"} digit.
 114  * For example, rounding the value 999.9 to three digits rounding up
 115  * would be numerically equal to one thousand, represented as
 116  * 100&times;10<sup>1</sup>.  In such cases, the new {@literal "1"} is
 117  * the leading digit position of the returned result.
 118  *
 119  * <p>Besides a logical exact result, each arithmetic operation has a
 120  * preferred scale for representing a result.  The preferred
 121  * scale for each operation is listed in the table below.
 122  *
 123  * <table class="plain">
 124  * <caption><b>Preferred Scales for Results of Arithmetic Operations
 125  * </b></caption>
 126  * <thead>
 127  * <tr><th>Operation</th><th>Preferred Scale of Result</th></tr>
 128  * </thead>
 129  * <tbody>
 130  * <tr><td>Add</td><td>max(addend.scale(), augend.scale())</td>
 131  * <tr><td>Subtract</td><td>max(minuend.scale(), subtrahend.scale())</td>
 132  * <tr><td>Multiply</td><td>multiplier.scale() + multiplicand.scale()</td>
 133  * <tr><td>Divide</td><td>dividend.scale() - divisor.scale()</td>
 134  * <tr><td>Square root</td><td>radicand.scale()/2</td>
 135  * </tbody>
 136  * </table>
 137  *
 138  * These scales are the ones used by the methods which return exact
 139  * arithmetic results; except that an exact divide may have to use a
 140  * larger scale since the exact result may have more digits.  For
 141  * example, {@code 1/32} is {@code 0.03125}.
 142  *
 143  * <p>Before rounding, the scale of the logical exact intermediate
 144  * result is the preferred scale for that operation.  If the exact
 145  * numerical result cannot be represented in {@code precision}
 146  * digits, rounding selects the set of digits to return and the scale
 147  * of the result is reduced from the scale of the intermediate result
 148  * to the least scale which can represent the {@code precision}
 149  * digits actually returned.  If the exact result can be represented
 150  * with at most {@code precision} digits, the representation
 151  * of the result with the scale closest to the preferred scale is
 152  * returned.  In particular, an exactly representable quotient may be
 153  * represented in fewer than {@code precision} digits by removing
 154  * trailing zeros and decreasing the scale.  For example, rounding to
 155  * three digits using the {@linkplain RoundingMode#FLOOR floor}